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Subgroup label Subgroup order Cyclic Abelian Solvable
Normal Characteristic Perfect Maximal Central
Ambient label Ambient order Direct product Semidirect product
Quotient label Subgroup index Cyclic quotient Abelian quotient Solvable quotient
Maximal quotient Non-trivial proper Hall subgroup Sylow subgroup
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Results (1-50 of 136 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1440.2534.1.a1.a1 $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ ✓ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_1$ $1$ ✓
1440.2534.2.a1.a1 $A_4\times C_{60}$ $2^{4} \cdot 3^{2} \cdot 5$ ✓ ✓ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_2$ $2$ ✓
1440.2534.3.a1.a1 $C_{60}.D_4$ $2^{5} \cdot 3 \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $3$ $-$
1440.2534.3.b1.a1 $C_{20}.S_4$ $2^{5} \cdot 3 \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $3$ $-$
1440.2534.3.b1.b1 $C_{20}.S_4$ $2^{5} \cdot 3 \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $3$ $-$
1440.2534.3.b1.c1 $C_{20}.S_4$ $2^{5} \cdot 3 \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $3$ $-$
1440.2534.4.a1.a1 $A_4\times C_{30}$ $2^{3} \cdot 3^{2} \cdot 5$ ✓ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_4$ $2^{2}$ ✓
1440.2534.4.b1.a1 $C_{12}.D_{15}$ $2^{3} \cdot 3^{2} \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{2}$ $-$
1440.2534.5.a1.a1 $C_{12}.S_4$ $2^{5} \cdot 3^{2}$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $5$ $-$
1440.2534.6.a1.a1 $C_2^2\times C_{60}$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $S_3$ $2 \cdot 3$
1440.2534.6.b1.a1 $A_4\times C_{20}$ $2^{4} \cdot 3 \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $S_3$ $2 \cdot 3$
1440.2534.6.b1.b1 $A_4\times C_{20}$ $2^{4} \cdot 3 \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $S_3$ $2 \cdot 3$
1440.2534.6.b1.c1 $A_4\times C_{20}$ $2^{4} \cdot 3 \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $S_3$ $2 \cdot 3$
1440.2534.6.c1.a1 $C_{30}:C_8$ $2^{4} \cdot 3 \cdot 5$ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $2 \cdot 3$ $-$
1440.2534.6.d1.a1 $C_{30}:C_8$ $2^{4} \cdot 3 \cdot 5$ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $2 \cdot 3$ $-$
1440.2534.8.a1.a1 $A_4\times C_{15}$ $2^{2} \cdot 3^{2} \cdot 5$ ✓ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_8$ $2^{3}$ ✓
1440.2534.8.b1.a1 $C_3\times C_{60}$ $2^{2} \cdot 3^{2} \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{3}$ $-$
1440.2534.9.a1.a1 $C_{20}.D_4$ $2^{5} \cdot 5$ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $3^{2}$ $-$
1440.2534.10.a1.a1 $C_{12}\times A_4$ $2^{4} \cdot 3^{2}$ ✓ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $D_5$ $2 \cdot 5$
1440.2534.12.a1.a1 $C_2^2\times C_{30}$ $2^{3} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_3:C_4$ $2^{2} \cdot 3$
1440.2534.12.b1.a1 $C_{10}\times A_4$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_3:C_4$ $2^{2} \cdot 3$
1440.2534.12.b1.b1 $C_{10}\times A_4$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_3:C_4$ $2^{2} \cdot 3$
1440.2534.12.b1.c1 $C_{10}\times A_4$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_3:C_4$ $2^{2} \cdot 3$
1440.2534.12.c1.a1 $C_2\times C_{60}$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3$ $-$
1440.2534.12.d1.a1 $C_2\times C_{60}$ $2^{3} \cdot 3 \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3$ $-$
1440.2534.12.e1.a1 $C_{15}:C_8$ $2^{3} \cdot 3 \cdot 5$ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3$ $-$
1440.2534.12.f1.a1 $C_{15}:C_8$ $2^{3} \cdot 3 \cdot 5$ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3$ $-$
1440.2534.12.g1.a1 $C_{15}:C_8$ $2^{3} \cdot 3 \cdot 5$ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3$ $-$
1440.2534.12.g1.b1 $C_{15}:C_8$ $2^{3} \cdot 3 \cdot 5$ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3$ $-$
1440.2534.12.g1.c1 $C_{15}:C_8$ $2^{3} \cdot 3 \cdot 5$ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 3$ $-$
1440.2534.15.a1.a1 $C_{12}.D_4$ $2^{5} \cdot 3$ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $3 \cdot 5$ $-$
1440.2534.15.b1.a1 $A_4:C_8$ $2^{5} \cdot 3$ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $3 \cdot 5$ $-$
1440.2534.15.b1.b1 $A_4:C_8$ $2^{5} \cdot 3$ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $3 \cdot 5$ $-$
1440.2534.15.b1.c1 $A_4:C_8$ $2^{5} \cdot 3$ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $3 \cdot 5$ $-$
1440.2534.16.a1.a1 $C_3\times C_{30}$ $2 \cdot 3^{2} \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{4}$ $-$
1440.2534.18.a1.a1 $C_2^2\times C_{20}$ $2^{4} \cdot 5$ ✓ ✓ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_3:S_3$ $2 \cdot 3^{2}$
1440.2534.18.b1.a1 $C_{10}:C_8$ $2^{4} \cdot 5$ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $2 \cdot 3^{2}$ $-$
1440.2534.18.c1.a1 $C_{10}:C_8$ $2^{4} \cdot 5$ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $2 \cdot 3^{2}$ $-$
1440.2534.20.a1.a1 $C_6\times A_4$ $2^{3} \cdot 3^{2}$ ✓ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_5:C_4$ $2^{2} \cdot 5$
1440.2534.20.b1.a1 $C_3^2:C_8$ $2^{3} \cdot 3^{2}$ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{2} \cdot 5$ $-$
1440.2534.24.a1.a1 $C_{60}$ $2^{2} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $S_4$ $2^{3} \cdot 3$
1440.2534.24.b1.a1 $C_2\times C_{30}$ $2^{2} \cdot 3 \cdot 5$ ✓ ✓ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_3:C_8$ $2^{3} \cdot 3$
1440.2534.24.c1.a1 $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_3:C_8$ $2^{3} \cdot 3$
1440.2534.24.c1.b1 $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_3:C_8$ $2^{3} \cdot 3$
1440.2534.24.c1.c1 $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $C_3:C_8$ $2^{3} \cdot 3$
1440.2534.24.d1.a1 $C_2\times C_{30}$ $2^{2} \cdot 3 \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{3} \cdot 3$ $-$
1440.2534.24.e1.a1 $C_{60}$ $2^{2} \cdot 3 \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{3} \cdot 3$ $-$
1440.2534.24.f1.a1 $C_{60}$ $2^{2} \cdot 3 \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{3} \cdot 3$ $-$
1440.2534.24.f1.b1 $C_{60}$ $2^{2} \cdot 3 \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{3} \cdot 3$ $-$
1440.2534.24.f1.c1 $C_{60}$ $2^{2} \cdot 3 \cdot 5$ ✓ $C_{60}.S_4$ $2^{5} \cdot 3^{2} \cdot 5$ $2^{3} \cdot 3$ $-$
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