On Some Combinatorial Structures Constructed from the Groups <svg style="vertical-align:-3.186pt;width:62.674999px;" id="M1" height="19.512501" version="1.1" viewBox="0 0 62.674999 19.512501" width="62.674999"  xmlns="http://www.w3.org/2000/svg">
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<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td align="left">  Maximal subgroup</td><td align="center">Structure</td><td align="center">Order</td><td align="center">Index</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td align="left"><span style="width: 21.362499px;"><svg height="15.25" id="M646" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 21.362499 15.25" width="21.362499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,14.975,15.187)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg></span></td><td align="center"><span style="width: 94.837502px;"><svg height="16.4125" id="M647" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 94.837502 16.4125" width="94.837502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.017,-0,0,-.017,27.575,12.138)"><path d="M223 355q0 -25 -15.5 -41.5t-39.5 -16.5t-40 16.5t-16 41.5t16 41t40 16t39.5 -16t15.5 -41zM223 46q0 -26 -16 -42t-40 -16t-39.5 16t-15.5 42q0 24 16 40.5t39 16.5q24 0 40 -16.5t16 -40.5z" id="x2236"></path></g><g transform="matrix(.017,-0,0,-.017,37.961,12.138)"><path d="M713 296l-5 -25q-47 -7 -59 -20t-23 -72l-15 -79q-9 -48 -3 -74q-15 -3 -55 -13t-63 -15t-59.5 -10t-70.5 -5q-149 0 -243 80t-94 220q0 169 127.5 276.5t336.5 107.5q91 0 206 -36l-10 -165l-29 -1q1 85 -47.5 126t-146.5 41q-153 0 -243.5 -97t-90.5 -242
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</svg></span></td><td align="center">12000</td><td align="center">31</td></tr><tr><td align="left"><span style="width: 21.362499px;"><svg height="15.25" id="M648" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 21.362499 15.25" width="21.362499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,10.8,16.212)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g><g transform="matrix(.012,-0,0,-.012,16.511,16.212)"><path d="M153 550l-26 -186q79 31 111 31q90 0 141.5 -51t51.5 -119q0 -93 -89 -166q-85 -69 -173 -71q-32 0 -61.5 11.5t-41.5 23.5q-18 17 -17 34q2 16 22 33q14 9 26 -1q61 -50 124 -50q60 0 93 43.5t33 104.5q0 69 -41.5 110t-121.5 41q-53 0 -102 -20l38 305h286l6 -8
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<g transform="matrix(.017,-0,0,-.017,27.575,12.138)"><path d="M223 355q0 -25 -15.5 -41.5t-39.5 -16.5t-40 16.5t-16 41.5t16 41t40 16t39.5 -16t15.5 -41zM223 46q0 -26 -16 -42t-40 -16t-39.5 16t-15.5 42q0 24 16 40.5t39 16.5q24 0 40 -16.5t16 -40.5z" id="x2236"></path></g><g transform="matrix(.017,-0,0,-.017,37.961,12.138)"><path d="M713 296l-5 -25q-47 -7 -59 -20t-23 -72l-15 -79q-9 -48 -3 -74q-15 -3 -55 -13t-63 -15t-59.5 -10t-70.5 -5q-149 0 -243 80t-94 220q0 169 127.5 276.5t336.5 107.5q91 0 206 -36l-10 -165l-29 -1q1 85 -47.5 126t-146.5 41q-153 0 -243.5 -97t-90.5 -242
q0 -122 68.5 -198.5t188.5 -76.5q121 0 139 75l20 86q13 58 -1.5 70.5t-99.5 20.5l5 26h267z" id="x1D43A"></path></g><g transform="matrix(.017,-0,0,-.017,50.268,12.138)"><path d="M559 163q-23 -66 -68 -163h-474l6 26q62 4 79.5 19.5t28.5 75.5l78 409q7 35 8.5 49t-8 25t-24 13t-51.5 5l5 28h266l-6 -28q-65 -5 -79.5 -18t-25.5 -74l-76 -406q-10 -57 14 -75q12 -13 96 -13q93 0 126 29q41 40 76 109z" id="x1D43F"></path></g><g transform="matrix(.017,-0,0,-.017,59.975,12.138)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.017,-0,0,-.017,65.856,12.138)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g><g transform="matrix(.017,-0,0,-.017,74.016,12.138)"><path d="M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z" id="x2C"></path></g><g transform="matrix(.017,-0,0,-.017,80.73,12.138)"><path d="M153 550l-26 -186q79 31 111 31q90 0 141.5 -51t51.5 -119q0 -93 -89 -166q-85 -69 -173 -71q-32 0 -61.5 11.5t-41.5 23.5q-18 17 -17 34q2 16 22 33q14 9 26 -1q61 -50 124 -50q60 0 93 43.5t33 104.5q0 69 -41.5 110t-121.5 41q-53 0 -102 -20l38 305h286l6 -8
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</svg></span></td><td align="center">12000</td><td align="center">31</td></tr><tr><td align="left"><span style="width: 21.362499px;"><svg height="15.4" id="M650" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 21.362499 15.4" width="21.362499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></span></td><td align="center">120</td><td align="center">3100</td></tr><tr><td align="left"><span style="width: 21.362499px;"><svg height="15.25" id="M652" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 21.362499 15.25" width="21.362499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></span></td><td align="center"><span style="width: 96.212502px;"><svg height="16.4125" id="M653" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 96.212502 16.4125" width="96.212502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.138)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.017,-0,0,-.017,5.944,12.138)"><path d="M698 636l-541 -596q60 -5 176 -5q91 0 138.5 5t69.5 24q44 36 85 124l29 -15q-38 -125 -64 -173h-559l-9 16l545 598h-182q-81 0 -109 -8t-48 -31q-26 -29 -55 -103l-29 3q23 86 42 200h22q11 -16 21 -20.5t34 -4.5h428z" id="x1D44D"></path></g>
<g transform="matrix(.012,-0,0,-.012,18.2,16.212)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g>
<g transform="matrix(.017,-0,0,-.017,28.312,12.138)"><path d="M528 54l-36 -38l-198 201l-198 -201l-36 38l197 200l-197 201l36 38l198 -202l198 202l36 -38l-197 -201z" id="xD7"></path></g><g transform="matrix(.017,-0,0,-.017,42.064,12.138)"><path d="M698 636l-541 -596q60 -5 176 -5q91 0 138.5 5t69.5 24q44 36 85 124l29 -15q-38 -125 -64 -173h-559l-9 16l545 598h-182q-81 0 -109 -8t-48 -31q-26 -29 -55 -103l-29 3q23 86 42 200h22q11 -16 21 -20.5t34 -4.5h428z" id="x1D44D"></path></g>
<g transform="matrix(.012,-0,0,-.012,54.325,16.212)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g>
<g transform="matrix(.017,-0,0,-.017,60.662,12.138)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g><g transform="matrix(.017,-0,0,-.017,71.253,12.138)"><path d="M223 355q0 -25 -15.5 -41.5t-39.5 -16.5t-40 16.5t-16 41.5t16 41t40 16t39.5 -16t15.5 -41zM223 46q0 -26 -16 -42t-40 -16t-39.5 16t-15.5 42q0 24 16 40.5t39 16.5q24 0 40 -16.5t16 -40.5z" id="x2236"></path></g><g transform="matrix(.017,-0,0,-.017,81.656,12.138)"><path d="M457 488l-30 -3q-17 148 -131 148q-53 0 -84.5 -34.5t-31.5 -82.5q0 -42 25.5 -72t74.5 -62l33 -22q63 -42 95 -85t32 -102q0 -84 -67 -137t-163 -53q-58 0 -113 22t-70 43l-4 152l27 4q4 -32 15 -62.5t31 -59.5t53.5 -47t76.5 -18q56 0 92 35t36 96q0 39 -25 70t-78 68
l-31 22q-32 23 -53.5 41.5t-45 57t-23.5 77.5q0 82 58 132.5t156 50.5q46 0 101 -17l18.5 -6t17 -6t8.5 -3q-4 -55 0 -147z" id="x1D446"></path></g>
<g transform="matrix(.012,-0,0,-.012,89.825,16.212)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" id="x33"></path></g>
</svg></span></td><td align="center">96</td><td align="center">3875</td></tr><tr><td align="left"><span style="width: 21.362499px;"><svg height="15.4" id="M654" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 21.362499 15.4" width="21.362499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M865 650q-1 -4 -4 -14t-4 -14q-62 -5 -77 -19.5t-29 -82.5l-74 -394q-12 -61 -0.5 -77t75.5 -21l-6 -28h-273l8 28q64 5 82 21t29 76l36 198h-380l-37 -197q-11 -64 0.5 -78.5t79.5 -19.5l-6 -28h-268l6 28q60 6 75.5 21.5t26.5 76.5l75 394q13 66 2 81.5t-77 20.5l8 28
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<g transform="matrix(.012,-0,0,-.012,14.975,15.187)"><path d="M153 550l-26 -186q79 31 111 31q90 0 141.5 -51t51.5 -119q0 -93 -89 -166q-85 -69 -173 -71q-32 0 -61.5 11.5t-41.5 23.5q-18 17 -17 34q2 16 22 33q14 9 26 -1q61 -50 124 -50q60 0 93 43.5t33 104.5q0 69 -41.5 110t-121.5 41q-53 0 -102 -20l38 305h286l6 -8
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</svg></span></td><td align="center"><span style="width: 22.737499px;"><svg height="15.4375" id="M655" style="vertical-align:-3.41937pt" version="1.1" viewbox="0 0 22.737499 15.4375" width="22.737499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M599 650l-18 -160l-30 -2q-2 70 -11 94q-5 16 -26 24t-75 8h-94q-27 0 -33.5 -6.5t-12.5 -32.5l-43 -226h108q52 0 72.5 5t31 18t28.5 52h28l-40 -200h-28q-1 42 -6 56.5t-24.5 21t-70.5 6.5h-108l-32 -177q-13 -65 1 -80.5t88 -22.5l-8 -28h-279l6 28q61 5 77.5 20.5
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<g transform="matrix(.012,-0,0,-.012,10.637,15.187)"><path d="M244 635q90 0 143 -72t53 -177q0 -133 -65 -229.5t-171 -139.5q-79 -32 -140 -32l-5 30q109 18 185 91t101 186l-68 -36q-29 -16 -60 -16q-79 0 -129 51.5t-50 130.5q0 80 57 146.5t149 66.5zM228 602q-52 0 -78 -45.5t-26 -98.5q0 -69 36.5 -115.5t97.5 -46.5
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q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" id="x33"></path></g>
</svg></span></td><td align="center">93</td><td align="center">4000</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Maximal subgroups of the group <svg height="15.0875" id="M645" style="vertical-align:-2.3205pt" version="1.1" viewbox="0 0 44.625 15.0875" width="44.625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.138)"><path d="M559 163q-23 -66 -68 -163h-474l6 26q62 4 79.5 19.5t28.5 75.5l78 409q7 35 8.5 49t-8 25t-24 13t-51.5 5l5 28h266l-6 -28q-65 -5 -79.5 -18t-25.5 -74l-76 -406q-10 -57 14 -75q12 -13 96 -13q93 0 126 29q41 40 76 109z" id="x1D43F"></path></g><g transform="matrix(.017,-0,0,-.017,9.769,12.138)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.017,-0,0,-.017,15.65,12.138)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
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</svg>.

International Journal of Combinatorics

tab1

Table 1

Table 1: On Some Combinatorial Structures Constructed from the Groups <svg style="vertical-align:-3.186pt;width:62.674999px;" id="M1" height="19.512501" version="1.1" viewBox="0 0 62.674999 19.512501" width="62.674999"  xmlns="http://www.w3.org/2000/svg">
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			<text transform="matrix(1,0,0,-1,-71.95,59.61)">
				<tspan style="font-size: 17.93px; " x="0" y="0">𝐿</tspan>
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				<tspan style="font-size: 17.93px; " x="18.668253" y="0">3</tspan>
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				<tspan style="font-size: 17.93px; " x="44.061382" y="0">)</tspan>
			</text>

		</g>
	</g>
</svg>, <svg style="vertical-align:-3.186pt;width:62.612499px;"  height="19.512501" version="1.1" viewBox="0 0 62.612499 19.512501" width="62.612499"  xmlns="http://www.w3.org/2000/svg">
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				<tspan style="font-size: 17.93px; " x="0" y="0">𝑈</tspan>
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				<tspan style="font-size: 17.93px; " x="18.614454" y="0">5</tspan>
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</svg>, and <svg style="vertical-align:-3.186pt;width:61.375px;"  height="19.424999" version="1.1" viewBox="0 0 61.375 19.424999" width="61.375"  xmlns="http://www.w3.org/2000/svg">
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			<text transform="matrix(1,0,0,-1,-71.95,59.68)">
				<tspan style="font-size: 17.93px; " x="0" y="0">𝑆</tspan>
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				<tspan style="font-size: 17.93px; " x="26.594639" y="0">,</tspan>
				<tspan style="font-size: 17.93px; " x="34.054768" y="0">2</tspan>
				<tspan style="font-size: 17.93px; " x="43.021267" y="0">)</tspan>
			</text>

		</g>
	</g>
</svg> 

Table 1 | On Some Combinatorial Structures Constructed from the Groups 
	
		
			
				𝐿
				(
				3
				,
				5
				)
			

		
	
, 
	
		
			
				𝑈
				(
				5
				,
				2
				)
			

		
	
, and 
	
		
			
				𝑆
				(
				6
				,
				2
				)
			

		
	
 

International Journal of Combinatorics

On Some Combinatorial Structures Constructed from the Groups 𝐿 ( 3 , 5 ) , 𝑈 ( 5 , 2 ) , and 𝑆 ( 6 , 2 )

Table 1

On Some Combinatorial Structures Constructed from the Groups , , and