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Note: Search results may be incomplete due to uncomputed quantities: Subgroup label (103813812 objects)

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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 (45 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
43200.bn.1.a1.a1 $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ ✓ ✓ $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $C_1$ $1$ ✓
86400.by.2.c1.a1 $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ ✓ ✓ ✓ $A_6.C_2\times S_5$ $2^{7} \cdot 3^{3} \cdot 5^{2}$ $C_2$ $2$ ✓
86400.bz.2.c1.a1 $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ ✓ ✓ ✓ $\PGL(2,9):S_5$ $2^{7} \cdot 3^{3} \cdot 5^{2}$ $C_2$ $2$ ✓
86400.cb.2.c1.a1 $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ ✓ ✓ ✓ $S_6:S_5$ $2^{7} \cdot 3^{3} \cdot 5^{2}$ $C_2$ $2$ ✓
172800.h.4.g1 $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ ✓ ✓ $S_5\times S_6:C_2$ $2^{8} \cdot 3^{3} \cdot 5^{2}$ $C_2^2$ $2^{2}$ ✓
1036800.f.24.a1.a1 $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^2.D_4$ $2^{9} \cdot 3^{4} \cdot 5^{2}$ $2^{3} \cdot 3$ $-$
2073600.d.48.C $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $\PGL(2,9)\wr C_2:C_2$ $2^{10} \cdot 3^{4} \cdot 5^{2}$ $2^{4} \cdot 3$ $-$
2073600.e.48.C $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6:S_6.D_4$ $2^{10} \cdot 3^{4} \cdot 5^{2}$ $2^{4} \cdot 3$ $-$
2073600.z.48.B $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $C_2\times A_6^2.D_4$ $2^{10} \cdot 3^{4} \cdot 5^{2}$ $2^{4} \cdot 3$ $-$
2073600.ba.48.B $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^2.D_8$ $2^{10} \cdot 3^{4} \cdot 5^{2}$ $2^{4} \cdot 3$ $-$
2073600.bb.48.B $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $(C_2\times A_6^2).D_4$ $2^{10} \cdot 3^{4} \cdot 5^{2}$ $2^{4} \cdot 3$ $-$
2073600.bc.48.B $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^2.\SD_{16}$ $2^{10} \cdot 3^{4} \cdot 5^{2}$ $2^{4} \cdot 3$ $-$
4147200.a.96._.C $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $S_6^2.D_4$ $2^{11} \cdot 3^{4} \cdot 5^{2}$ $2^{5} \cdot 3$ $-$
4147200.z.96.D $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^2.C_2^2\wr C_2$ $2^{11} \cdot 3^{4} \cdot 5^{2}$ $2^{5} \cdot 3$ $-$
4147200.ba.96.D $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^2.(C_2^2\times D_4)$ $2^{11} \cdot 3^{4} \cdot 5^{2}$ $2^{5} \cdot 3$ $-$
4147200.bb.96.D $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^2.C_2^3:C_4$ $2^{11} \cdot 3^{4} \cdot 5^{2}$ $2^{5} \cdot 3$ $-$
4147200.bc.96.E $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^2.C_2^3:C_4$ $2^{11} \cdot 3^{4} \cdot 5^{2}$ $2^{5} \cdot 3$ $-$
8294400.g.192.E $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^2.D_4:D_4$ $2^{12} \cdot 3^{4} \cdot 5^{2}$ $2^{6} \cdot 3$ $-$
8294400.i.192.E $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^2.C_4^2:C_4$ $2^{12} \cdot 3^{4} \cdot 5^{2}$ $2^{6} \cdot 3$ $-$
8294400.n.192.I $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $C_2\times S_6^2.D_4$ $2^{12} \cdot 3^{4} \cdot 5^{2}$ $2^{6} \cdot 3$ $-$
8294400.o.192.I $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $(C_2\times S_6^2).D_4$ $2^{12} \cdot 3^{4} \cdot 5^{2}$ $2^{6} \cdot 3$ $-$
16588800.b.384.H $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^2.C_2\wr D_4$ $2^{13} \cdot 3^{4} \cdot 5^{2}$ $2^{7} \cdot 3$ $-$
125452800.a.2904._.C $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $M_{11}\wr C_2$ $2^{9} \cdot 3^{4} \cdot 5^{2} \cdot 11^{2}$ $2^{3} \cdot 3 \cdot 11^{2}$ $-$
217728000.c.5040._.X $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $S_5\times A_{10}$ $2^{10} \cdot 3^{5} \cdot 5^{3} \cdot 7$ $2^{4} \cdot 3^{2} \cdot 5 \cdot 7$ $-$
250905600.a.5808._.A $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $C_2\times M_{11}\wr C_2$ $2^{10} \cdot 3^{4} \cdot 5^{2} \cdot 11^{2}$ $2^{4} \cdot 3 \cdot 11^{2}$ $-$
250905600.a.5808._.G $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $C_2\times M_{11}\wr C_2$ $2^{10} \cdot 3^{4} \cdot 5^{2} \cdot 11^{2}$ $2^{4} \cdot 3 \cdot 11^{2}$ $-$
250905600.b.5808._.A $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $C_2.M_{11}\wr C_2$ $2^{10} \cdot 3^{4} \cdot 5^{2} \cdot 11^{2}$ $2^{4} \cdot 3 \cdot 11^{2}$ $-$
250905600.b.5808._.G $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $C_2.M_{11}\wr C_2$ $2^{10} \cdot 3^{4} \cdot 5^{2} \cdot 11^{2}$ $2^{4} \cdot 3 \cdot 11^{2}$ $-$
279936000.b.6480._.S $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^3.S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $2^{4} \cdot 3^{4} \cdot 5$ $-$
279936000.b.6480._.W $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^3.S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $2^{4} \cdot 3^{4} \cdot 5$ $-$
279936000.d.6480._.O $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^3.S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $2^{4} \cdot 3^{4} \cdot 5$ $-$
279936000.d.6480._.P $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^3.S_3$ $2^{10} \cdot 3^{7} \cdot 5^{3}$ $2^{4} \cdot 3^{4} \cdot 5$ $-$
559872000.d.12960._.A $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^3.A_4$ $2^{11} \cdot 3^{7} \cdot 5^{3}$ $2^{5} \cdot 3^{4} \cdot 5$ $-$
559872000.e.12960._.J $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^3.D_6$ $2^{11} \cdot 3^{7} \cdot 5^{3}$ $2^{5} \cdot 3^{4} \cdot 5$ $-$
559872000.e.12960._.O $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^3.D_6$ $2^{11} \cdot 3^{7} \cdot 5^{3}$ $2^{5} \cdot 3^{4} \cdot 5$ $-$
559872000.f.12960._.I $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^3.D_6$ $2^{11} \cdot 3^{7} \cdot 5^{3}$ $2^{5} \cdot 3^{4} \cdot 5$ $-$
559872000.j.12960._.M $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^3.D_6$ $2^{11} \cdot 3^{7} \cdot 5^{3}$ $2^{5} \cdot 3^{4} \cdot 5$ $-$
559872000.k.12960._.R $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^3.D_6$ $2^{11} \cdot 3^{7} \cdot 5^{3}$ $2^{5} \cdot 3^{4} \cdot 5$ $-$
559872000.k.12960._.T $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^3.D_6$ $2^{11} \cdot 3^{7} \cdot 5^{3}$ $2^{5} \cdot 3^{4} \cdot 5$ $-$
1119744000.d.25920._.P $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^3.S_4$ $2^{12} \cdot 3^{7} \cdot 5^{3}$ $2^{6} \cdot 3^{4} \cdot 5$ $-$
1119744000.d.25920._.T $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^3.S_4$ $2^{12} \cdot 3^{7} \cdot 5^{3}$ $2^{6} \cdot 3^{4} \cdot 5$ $-$
1119744000.h.25920._.I $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^3.S_4$ $2^{12} \cdot 3^{7} \cdot 5^{3}$ $2^{6} \cdot 3^{4} \cdot 5$ $-$
1119744000.h.25920._.Q $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^3.S_4$ $2^{12} \cdot 3^{7} \cdot 5^{3}$ $2^{6} \cdot 3^{4} \cdot 5$ $-$
1119744000.j.25920._.N $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^3.S_4$ $2^{12} \cdot 3^{7} \cdot 5^{3}$ $2^{6} \cdot 3^{4} \cdot 5$ $-$
1119744000.w.25920._.G $A_6.S_5$ $2^{6} \cdot 3^{3} \cdot 5^{2}$ $A_6^3.S_4$ $2^{12} \cdot 3^{7} \cdot 5^{3}$ $2^{6} \cdot 3^{4} \cdot 5$ $-$
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