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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 55 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
2160.ck.1.a1.a1 $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ ✓ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $C_1$ $1$ ✓
2160.ck.2.a1.a1 $C_3\times A_6$ $2^{3} \cdot 3^{3} \cdot 5$ ✓ ✓ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $C_2$ $2$ ✓
2160.ck.3.a1.a1 $\PGL(2,9)$ $2^{4} \cdot 3^{2} \cdot 5$ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $3$ $-$
2160.ck.6.a1.a1 $A_6$ $2^{3} \cdot 3^{2} \cdot 5$ ✓ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $S_3$ $2 \cdot 3$ ✓
2160.ck.10.a1.a1 $C_3:F_9$ $2^{3} \cdot 3^{3}$ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2 \cdot 5$ $-$
2160.ck.12.a1.a1 $\GL(2,4)$ $2^{2} \cdot 3^{2} \cdot 5$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{2} \cdot 3$ $-$
2160.ck.20.a1.a1 $C_3^2:C_{12}$ $2^{2} \cdot 3^{3}$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{2} \cdot 5$ $-$
2160.ck.30.a1.a1 $C_3\times S_4$ $2^{3} \cdot 3^{2}$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2 \cdot 3 \cdot 5$ $-$
2160.ck.30.b1.a1 $F_9$ $2^{3} \cdot 3^{2}$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2 \cdot 3 \cdot 5$ $-$
2160.ck.36.a1.a1 $S_3\times D_5$ $2^{2} \cdot 3 \cdot 5$ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{2} \cdot 3^{2}$ $-$
2160.ck.36.b1.a1 $A_5$ $2^{2} \cdot 3 \cdot 5$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{2} \cdot 3^{2}$ $-$
2160.ck.40.a1.a1 $C_3^2:C_6$ $2 \cdot 3^{3}$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{3} \cdot 5$ $-$
2160.ck.45.a1.a1 $C_3:D_8$ $2^{4} \cdot 3$ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $3^{2} \cdot 5$ $-$
2160.ck.60.a1.a1 $C_3\times A_4$ $2^{2} \cdot 3^{2}$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $-$
2160.ck.60.b1.a1 $C_3^2:C_4$ $2^{2} \cdot 3^{2}$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{2} \cdot 3 \cdot 5$ $-$
2160.ck.72.a1.a1 $C_3\times D_5$ $2 \cdot 3 \cdot 5$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{3} \cdot 3^{2}$ $-$
2160.ck.72.b1.a1 $C_5\times S_3$ $2 \cdot 3 \cdot 5$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{3} \cdot 3^{2}$ $-$
2160.ck.72.c1.a1 $D_{15}$ $2 \cdot 3 \cdot 5$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{3} \cdot 3^{2}$ $-$
2160.ck.80.a1.a1 $C_3^3$ $3^{3}$ $3$ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{4} \cdot 5$ $-$
2160.ck.90.a1.a1 $D_{12}$ $2^{3} \cdot 3$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2 \cdot 3^{2} \cdot 5$ $-$
2160.ck.90.b1.a1 $C_3:C_8$ $2^{3} \cdot 3$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2 \cdot 3^{2} \cdot 5$ $-$
2160.ck.90.c1.a1 $C_3\times D_4$ $2^{3} \cdot 3$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2 \cdot 3^{2} \cdot 5$ $-$
2160.ck.90.d1.a1 $S_4$ $2^{3} \cdot 3$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2 \cdot 3^{2} \cdot 5$ $-$
2160.ck.108.a1.a1 $D_{10}$ $2^{2} \cdot 5$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{2} \cdot 3^{3}$ $-$
2160.ck.120.a1.a1 $C_3\times S_3$ $2 \cdot 3^{2}$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{3} \cdot 3 \cdot 5$ $-$
2160.ck.120.b1.a1 $C_3:S_3$ $2 \cdot 3^{2}$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{3} \cdot 3 \cdot 5$ $-$
2160.ck.135.a1.a1 $D_8$ $2^{4}$ $2$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $3^{3} \cdot 5$ $-$
2160.ck.144.a1.a1 $C_{15}$ $3 \cdot 5$ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{4} \cdot 3^{2}$ $-$
2160.ck.180.a1.a1 $D_6$ $2^{2} \cdot 3$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
2160.ck.180.b1.a1 $C_{12}$ $2^{2} \cdot 3$ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
2160.ck.180.c1.a1 $C_2\times C_6$ $2^{2} \cdot 3$ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
2160.ck.180.d1.a1 $A_4$ $2^{2} \cdot 3$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
2160.ck.180.e1.a1 $A_4$ $2^{2} \cdot 3$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{2} \cdot 3^{2} \cdot 5$ $-$
2160.ck.216.a1.a1 $D_5$ $2 \cdot 5$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{3} \cdot 3^{3}$ $-$
2160.ck.216.b1.a1 $C_{10}$ $2 \cdot 5$ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{3} \cdot 3^{3}$ $-$
2160.ck.216.c1.a1 $D_5$ $2 \cdot 5$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{3} \cdot 3^{3}$ $-$
2160.ck.240.a1.a1 $C_3^2$ $3^{2}$ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{4} \cdot 3 \cdot 5$ $-$
2160.ck.240.b1.a1 $C_3^2$ $3^{2}$ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{4} \cdot 3 \cdot 5$ $-$
2160.ck.240.c1.a1 $C_3^2$ $3^{2}$ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{4} \cdot 3 \cdot 5$ $-$
2160.ck.270.a1.a1 $D_4$ $2^{3}$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2 \cdot 3^{3} \cdot 5$ $-$
2160.ck.270.b1.a1 $C_8$ $2^{3}$ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2 \cdot 3^{3} \cdot 5$ $-$
2160.ck.270.c1.a1 $D_4$ $2^{3}$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2 \cdot 3^{3} \cdot 5$ $-$
2160.ck.360.a1.a1 $C_6$ $2 \cdot 3$ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{3} \cdot 3^{2} \cdot 5$ $-$
2160.ck.360.b1.a1 $S_3$ $2 \cdot 3$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{3} \cdot 3^{2} \cdot 5$ $-$
2160.ck.360.c1.a1 $S_3$ $2 \cdot 3$ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{3} \cdot 3^{2} \cdot 5$ $-$
2160.ck.432.a1.a1 $C_5$ $5$ $5$ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{4} \cdot 3^{3}$ $-$
2160.ck.540.a1.a1 $C_2^2$ $2^{2}$ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{2} \cdot 3^{3} \cdot 5$ $-$
2160.ck.540.b1.a1 $C_4$ $2^{2}$ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{2} \cdot 3^{3} \cdot 5$ $-$
2160.ck.540.c1.a1 $C_2^2$ $2^{2}$ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $2^{2} \cdot 3^{3} \cdot 5$ $-$
2160.ck.720.a1.a1 $C_3$ $3$ ✓ ✓ ✓ $A_6:S_3$ $2^{4} \cdot 3^{3} \cdot 5$ $\PGL(2,9)$ $2^{4} \cdot 3^{2} \cdot 5$ ✓
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