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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 384 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
2160.dm.1.a1.a1 $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ ✓ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_1$ $1$ ✓
2160.dm.2.a1.a1 $C_5\times S_3^3$ $2^{3} \cdot 3^{3} \cdot 5$ ✓ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_2$ $2$ ✓
2160.dm.2.a1.b1 $C_5\times S_3^3$ $2^{3} \cdot 3^{3} \cdot 5$ ✓ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_2$ $2$ ✓
2160.dm.2.b1.a1 $S_3\times C_3^2:C_{20}$ $2^{3} \cdot 3^{3} \cdot 5$ ✓ ✓ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_2$ $2$ ✓
2160.dm.2.c1.a1 $C_5\times S_3^2:S_3$ $2^{3} \cdot 3^{3} \cdot 5$ ✓ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_2$ $2$ ✓
2160.dm.2.c1.b1 $C_5\times S_3^2:S_3$ $2^{3} \cdot 3^{3} \cdot 5$ ✓ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_2$ $2$ ✓
2160.dm.2.d1.a1 $S_3^2:C_{30}$ $2^{3} \cdot 3^{3} \cdot 5$ ✓ ✓ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_2$ $2$ ✓
2160.dm.2.e1.a1 $C_5\times C_3^2:D_{12}$ $2^{3} \cdot 3^{3} \cdot 5$ ✓ ✓ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_2$ $2$ ✓
2160.dm.3.a1.a1 $C_{10}\times \SOPlus(4,2)$ $2^{4} \cdot 3^{2} \cdot 5$ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $3$ $-$
2160.dm.4.a1.a1 $C_{15}:S_3^2$ $2^{2} \cdot 3^{3} \cdot 5$ ✓ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_2^2$ $2^{2}$ ✓
2160.dm.4.b1.a1 $C_{15}\times S_3^2$ $2^{2} \cdot 3^{3} \cdot 5$ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_2^2$ $2^{2}$ ✓
2160.dm.4.b1.b1 $C_{15}\times S_3^2$ $2^{2} \cdot 3^{3} \cdot 5$ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_2^2$ $2^{2}$ ✓
2160.dm.4.c1.a1 $C_{15}:S_3^2$ $2^{2} \cdot 3^{3} \cdot 5$ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_2^2$ $2^{2}$ ✓
2160.dm.4.c1.b1 $C_{15}:S_3^2$ $2^{2} \cdot 3^{3} \cdot 5$ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_2^2$ $2^{2}$ ✓
2160.dm.4.d1.a1 $C_3^2:C_{60}$ $2^{2} \cdot 3^{3} \cdot 5$ ✓ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_2^2$ $2^{2}$ ✓
2160.dm.4.e1.a1 $C_3^3:C_{20}$ $2^{2} \cdot 3^{3} \cdot 5$ ✓ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_2^2$ $2^{2}$ ✓
2160.dm.4.f1.a1 $C_{15}\times S_3^2$ $2^{2} \cdot 3^{3} \cdot 5$ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{2}$ $-$
2160.dm.4.f1.b1 $C_{15}\times S_3^2$ $2^{2} \cdot 3^{3} \cdot 5$ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{2}$ $-$
2160.dm.4.g1.a1 $C_{15}:S_3^2$ $2^{2} \cdot 3^{3} \cdot 5$ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{2}$ $-$
2160.dm.4.g1.b1 $C_{15}:S_3^2$ $2^{2} \cdot 3^{3} \cdot 5$ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{2}$ $-$
2160.dm.5.a1.a1 $S_3^3:C_2$ $2^{4} \cdot 3^{3}$ ✓ ✓ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_5$ $5$ ✓
2160.dm.6.a1.a1 $S_3^2:C_{10}$ $2^{3} \cdot 3^{2} \cdot 5$ ✓ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $S_3$ $2 \cdot 3$
2160.dm.6.b1.a1 $C_{10}\times S_3^2$ $2^{3} \cdot 3^{2} \cdot 5$ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $2 \cdot 3$ $-$
2160.dm.6.b1.b1 $C_{10}\times S_3^2$ $2^{3} \cdot 3^{2} \cdot 5$ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $2 \cdot 3$ $-$
2160.dm.6.c1.a1 $C_2\times C_3^2:C_{20}$ $2^{3} \cdot 3^{2} \cdot 5$ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $2 \cdot 3$ $-$
2160.dm.6.d1.a1 $C_{10}\times S_3^2$ $2^{3} \cdot 3^{2} \cdot 5$ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $2 \cdot 3$ $-$
2160.dm.6.d1.b1 $C_{10}\times S_3^2$ $2^{3} \cdot 3^{2} \cdot 5$ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $2 \cdot 3$ $-$
2160.dm.6.e1.a1 $S_3^2:C_{10}$ $2^{3} \cdot 3^{2} \cdot 5$ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $2 \cdot 3$ $-$
2160.dm.6.e1.b1 $S_3^2:C_{10}$ $2^{3} \cdot 3^{2} \cdot 5$ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $2 \cdot 3$ $-$
2160.dm.6.f1.a1 $S_3^2:C_{10}$ $2^{3} \cdot 3^{2} \cdot 5$ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $2 \cdot 3$ $-$
2160.dm.8.a1.a1 $C_3^2:C_{30}$ $2 \cdot 3^{3} \cdot 5$ ✓ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $D_4$ $2^{3}$
2160.dm.8.b1.a1 $C_3^2:C_{30}$ $2 \cdot 3^{3} \cdot 5$ ✓ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_2^3$ $2^{3}$ ✓
2160.dm.8.c1.a1 $C_3^3:C_{10}$ $2 \cdot 3^{3} \cdot 5$ ✓ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $D_4$ $2^{3}$
2160.dm.8.d1.a1 $C_3^2:C_{30}$ $2 \cdot 3^{3} \cdot 5$ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{3}$ $-$
2160.dm.8.d1.b1 $C_3^2:C_{30}$ $2 \cdot 3^{3} \cdot 5$ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{3}$ $-$
2160.dm.8.e1.a1 $C_3^2:C_{30}$ $2 \cdot 3^{3} \cdot 5$ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{3}$ $-$
2160.dm.8.e1.b1 $C_3^2:C_{30}$ $2 \cdot 3^{3} \cdot 5$ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{3}$ $-$
2160.dm.9.a1.a1 $C_{20}:D_6$ $2^{4} \cdot 3 \cdot 5$ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $3^{2}$ $-$
2160.dm.10.a1.a1 $S_3^3$ $2^{3} \cdot 3^{3}$ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓
2160.dm.10.a1.b1 $S_3^3$ $2^{3} \cdot 3^{3}$ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓
2160.dm.10.b1.a1 $C_3^2:C_4\times S_3$ $2^{3} \cdot 3^{3}$ ✓ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓
2160.dm.10.c1.a1 $S_3^2:S_3$ $2^{3} \cdot 3^{3}$ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓
2160.dm.10.c1.b1 $S_3^2:S_3$ $2^{3} \cdot 3^{3}$ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓
2160.dm.10.d1.a1 $S_3^2:C_6$ $2^{3} \cdot 3^{3}$ ✓ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓
2160.dm.10.e1.a1 $C_3^2:D_{12}$ $2^{3} \cdot 3^{3}$ ✓ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $C_{10}$ $2 \cdot 5$ ✓
2160.dm.12.a1.a1 $C_5\times S_3^2$ $2^{2} \cdot 3^{2} \cdot 5$ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $D_6$ $2^{2} \cdot 3$
2160.dm.12.a1.b1 $C_5\times S_3^2$ $2^{2} \cdot 3^{2} \cdot 5$ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $D_6$ $2^{2} \cdot 3$
2160.dm.12.b1.a1 $C_3^2:C_{20}$ $2^{2} \cdot 3^{2} \cdot 5$ ✓ ✓ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $D_6$ $2^{2} \cdot 3$
2160.dm.12.c1.a1 $S_3\times C_{30}$ $2^{2} \cdot 3^{2} \cdot 5$ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{2} \cdot 3$ $-$
2160.dm.12.c1.b1 $S_3\times C_{30}$ $2^{2} \cdot 3^{2} \cdot 5$ $S_3^3:C_{10}$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{2} \cdot 3$ $-$
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