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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 132 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
7200.dx.1.a1.a1 $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $C_1$ $1$ ✓
7200.dx.2.a1.a1 $C_5\times S_6$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
7200.dx.2.b1.a1 $C_5\times \PGL(2,9)$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
7200.dx.2.c1.a1 $A_6.C_{10}$ $2^{4} \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ ✓ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $C_2$ $2$ ✓
7200.dx.4.a1.a1 $C_5\times A_6$ $2^{3} \cdot 3^{2} \cdot 5^{2}$ ✓ ✓ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $C_2^2$ $2^{2}$ ✓
7200.dx.5.a1.a1 $S_6:C_2$ $2^{5} \cdot 3^{2} \cdot 5$ ✓ ✓ ✓ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $C_5$ $5$ ✓
7200.dx.10.a1.a1 $S_6$ $2^{4} \cdot 3^{2} \cdot 5$ ✓ ✓ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $C_{10}$ $2 \cdot 5$ ✓
7200.dx.10.b1.a1 $\PGL(2,9)$ $2^{4} \cdot 3^{2} \cdot 5$ ✓ ✓ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $C_{10}$ $2 \cdot 5$ ✓
7200.dx.10.c1.a1 $A_6.C_2$ $2^{4} \cdot 3^{2} \cdot 5$ ✓ ✓ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $C_{10}$ $2 \cdot 5$ ✓
7200.dx.10.d1.a1 $F_9:C_{10}$ $2^{4} \cdot 3^{2} \cdot 5$ ✓ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2 \cdot 5$ $-$
7200.dx.12.a1.a1 $C_5\times S_5$ $2^{3} \cdot 3 \cdot 5^{2}$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{2} \cdot 3$ $-$
7200.dx.20.a1.a1 $A_6$ $2^{3} \cdot 3^{2} \cdot 5$ ✓ ✓ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $C_2\times C_{10}$ $2^{2} \cdot 5$ ✓ ✓
7200.dx.20.b1.a1 $S_3^2:C_{10}$ $2^{3} \cdot 3^{2} \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{2} \cdot 5$ $-$
7200.dx.20.c1.a1 $C_5\times \PSU(3,2)$ $2^{3} \cdot 3^{2} \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{2} \cdot 5$ $-$
7200.dx.20.d1.a1 $C_5\times F_9$ $2^{3} \cdot 3^{2} \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{2} \cdot 5$ $-$
7200.dx.24.a1.a1 $C_5\times A_5$ $2^{2} \cdot 3 \cdot 5^{2}$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{3} \cdot 3$ $-$
7200.dx.30.a1.a1 $C_{10}\times S_4$ $2^{4} \cdot 3 \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2 \cdot 3 \cdot 5$ $-$
7200.dx.36.a1.a1 $C_{10}\times F_5$ $2^{3} \cdot 5^{2}$ ✓ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{2} \cdot 3^{2}$ $-$
7200.dx.40.a1.a1 $C_5\times S_3^2$ $2^{2} \cdot 3^{2} \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{3} \cdot 5$ $-$
7200.dx.40.b1.a1 $C_3^2:C_{20}$ $2^{2} \cdot 3^{2} \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{3} \cdot 5$ $-$
7200.dx.40.c1.a1 $C_3^2:C_{20}$ $2^{2} \cdot 3^{2} \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{3} \cdot 5$ $-$
7200.dx.45.a1.a1 $D_8:C_{10}$ $2^{5} \cdot 5$ ✓ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $3^{2} \cdot 5$ $-$
7200.dx.50.a1.a1 $F_9:C_2$ $2^{4} \cdot 3^{2}$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2 \cdot 5^{2}$ $-$
7200.dx.60.a1.a1 $C_{10}\times A_4$ $2^{3} \cdot 3 \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{2} \cdot 3 \cdot 5$ $-$
7200.dx.60.b1.a1 $C_5\times S_4$ $2^{3} \cdot 3 \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{2} \cdot 3 \cdot 5$ $-$
7200.dx.60.c1.a1 $S_5$ $2^{3} \cdot 3 \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{2} \cdot 3 \cdot 5$ $-$
7200.dx.60.d1.a1 $C_5\times S_4$ $2^{3} \cdot 3 \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{2} \cdot 3 \cdot 5$ $-$
7200.dx.72.a1.a1 $C_5\times D_{10}$ $2^{2} \cdot 5^{2}$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{3} \cdot 3^{2}$ $-$
7200.dx.72.b1.a1 $C_5\times F_5$ $2^{2} \cdot 5^{2}$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{3} \cdot 3^{2}$ $-$
7200.dx.72.c1.a1 $C_5\times F_5$ $2^{2} \cdot 5^{2}$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{3} \cdot 3^{2}$ $-$
7200.dx.80.a1.a1 $S_3\times C_{15}$ $2 \cdot 3^{2} \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{4} \cdot 5$ $-$
7200.dx.80.b1.a1 $C_{15}:S_3$ $2 \cdot 3^{2} \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{4} \cdot 5$ $-$
7200.dx.90.a1.a1 $D_4:C_{10}$ $2^{4} \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2 \cdot 3^{2} \cdot 5$ $-$
7200.dx.90.b1.a1 $C_5\times \OD_{16}$ $2^{4} \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2 \cdot 3^{2} \cdot 5$ $-$
7200.dx.90.c1.a1 $C_5\times D_8$ $2^{4} \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2 \cdot 3^{2} \cdot 5$ $-$
7200.dx.90.d1.a1 $C_5\times \SD_{16}$ $2^{4} \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2 \cdot 3^{2} \cdot 5$ $-$
7200.dx.90.e1.a1 $D_4\times C_{10}$ $2^{4} \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2 \cdot 3^{2} \cdot 5$ $-$
7200.dx.90.f1.a1 $C_5\times D_8$ $2^{4} \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2 \cdot 3^{2} \cdot 5$ $-$
7200.dx.90.g1.a1 $C_5\times \SD_{16}$ $2^{4} \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2 \cdot 3^{2} \cdot 5$ $-$
7200.dx.100.a1.a1 $\SOPlus(4,2)$ $2^{3} \cdot 3^{2}$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{2} \cdot 5^{2}$ $-$
7200.dx.100.b1.a1 $\PSU(3,2)$ $2^{3} \cdot 3^{2}$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{2} \cdot 5^{2}$ $-$
7200.dx.100.c1.a1 $F_9$ $2^{3} \cdot 3^{2}$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{2} \cdot 5^{2}$ $-$
7200.dx.120.a1.a1 $S_3\times C_{10}$ $2^{2} \cdot 3 \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{3} \cdot 3 \cdot 5$ $-$
7200.dx.120.b1.a1 $C_5\times A_4$ $2^{2} \cdot 3 \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{3} \cdot 3 \cdot 5$ $-$
7200.dx.120.c1.a1 $A_5$ $2^{2} \cdot 3 \cdot 5$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{3} \cdot 3 \cdot 5$ $-$
7200.dx.144.a1.a1 $C_5\times C_{10}$ $2 \cdot 5^{2}$ ✓ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{4} \cdot 3^{2}$ $-$
7200.dx.144.b1.a1 $C_5\times D_5$ $2 \cdot 5^{2}$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{4} \cdot 3^{2}$ $-$
7200.dx.144.c1.a1 $C_5\times D_5$ $2 \cdot 5^{2}$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{4} \cdot 3^{2}$ $-$
7200.dx.150.a1.a1 $C_2\times S_4$ $2^{4} \cdot 3$ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2 \cdot 3 \cdot 5^{2}$ $-$
7200.dx.160.a1.a1 $C_3\times C_{15}$ $3^{2} \cdot 5$ ✓ $S_6:C_{10}$ $2^{5} \cdot 3^{2} \cdot 5^{2}$ $2^{5} \cdot 5$ $-$
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