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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 96 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
46080.b.1.a1 $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_1$ $1$ ✓
46080.b.2.A $\GL(2,\mathbb{Z}/4)\times \SL(2,5):C_2$ $2^{9} \cdot 3^{2} \cdot 5$ ✓ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2$ $2$ ✓
46080.b.2.B $C_2^2\times A_4\times \GL(2,5)$ $2^{9} \cdot 3^{2} \cdot 5$ ✓ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2$ $2$ ✓
46080.b.2.C $(C_2^2\times A_4):\GL(2,5)$ $2^{9} \cdot 3^{2} \cdot 5$ ✓ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2$ $2$ ✓
46080.b.2.D $C_2\times S_4\times \GL(2,5)$ $2^{9} \cdot 3^{2} \cdot 5$ ✓ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2$ $2$ ✓
46080.b.2.E $(C_2\times S_4):\GL(2,5)$ $2^{9} \cdot 3^{2} \cdot 5$ ✓ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2$ $2$ ✓
46080.b.2.F $A_4:C_4\times \GL(2,5)$ $2^{9} \cdot 3^{2} \cdot 5$ ✓ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2$ $2$ ✓
46080.b.2.G $C_2.(S_4\times \GL(2,5))$ $2^{9} \cdot 3^{2} \cdot 5$ ✓ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2$ $2$ ✓
46080.b.4.A $\GL(2,\mathbb{Z}/4)\times \SL(2,5)$ $2^{8} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_4$ $2^{2}$ ✓
46080.b.4.B $A_4\times \SL(2,5):C_2^3$ $2^{8} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2^2$ $2^{2}$ ✓
46080.b.4.C $\SL(2,5):\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_4$ $2^{2}$ ✓
46080.b.4.D $S_4\times \SL(2,5):C_2^2$ $2^{8} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2^2$ $2^{2}$ ✓
46080.b.4.E $\SL(2,5):\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_4$ $2^{2}$ ✓
46080.b.4.F $C_2^4.(D_6\times A_5)$ $2^{8} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2^2$ $2^{2}$ ✓
46080.b.4.G $C_2\times A_4\times \GL(2,5)$ $2^{8} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2^2$ $2^{2}$ ✓
46080.b.4.H $C_2\times A_4\times \GL(2,5)$ $2^{8} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2^2$ $2^{2}$ ✓
46080.b.4.I $C_2\times A_4:\GL(2,5)$ $2^{8} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2^2$ $2^{2}$ ✓
46080.b.4.J $C_2\times A_4:\GL(2,5)$ $2^{8} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2^2$ $2^{2}$ ✓
46080.b.4.K $\SL(2,5):\GL(2,\mathbb{Z}/4)$ $2^{8} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_4$ $2^{2}$ ✓
46080.b.6.A $C_2^4\times \GL(2,5)$ $2^{9} \cdot 3 \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $S_3$ $2 \cdot 3$
46080.b.8.A $C_2^5.\GL(2,4)$ $2^{7} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2\times C_4$ $2^{3}$ ✓
46080.b.8.B $C_2\times S_4\times \SL(2,5)$ $2^{7} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2\times C_4$ $2^{3}$ ✓
46080.b.8.C $A_4\times \SL(2,5):C_2^2$ $2^{7} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2^3$ $2^{3}$ ✓
46080.b.8.D $A_4\times \SL(2,5):C_2^2$ $2^{7} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2\times C_4$ $2^{3}$ ✓
46080.b.8.E $C_2\times \SL(2,5):S_4$ $2^{7} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2\times C_4$ $2^{3}$ ✓
46080.b.8.F $A_4:C_4\times \SL(2,5)$ $2^{7} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2\times C_4$ $2^{3}$ ✓
46080.b.8.G $A_4:C_4\times \SL(2,5)$ $2^{7} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2\times C_4$ $2^{3}$ ✓
46080.b.12.A $\SL(2,5):C_2^5$ $2^{8} \cdot 3 \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $D_6$ $2^{2} \cdot 3$
46080.b.12.B $C_2^3\times \GL(2,5)$ $2^{8} \cdot 3 \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $D_6$ $2^{2} \cdot 3$
46080.b.12.C $C_2^3\times \GL(2,5)$ $2^{8} \cdot 3 \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $D_6$ $2^{2} \cdot 3$
46080.b.16.A $C_2^4.\GL(2,4)$ $2^{6} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2^2\times C_4$ $2^{4}$ ✓
46080.b.16.B $A_4\times \SL(2,5):C_2$ $2^{6} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2\times D_4$ $2^{4}$
46080.b.16.C $A_4\times \SL(2,5):C_2$ $2^{6} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $D_4:C_2$ $2^{4}$
46080.b.24.A $C_2^4\times \SL(2,5)$ $2^{7} \cdot 3 \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_4\times S_3$ $2^{3} \cdot 3$
46080.b.24.B $C_2^2\times \GL(2,5)$ $2^{7} \cdot 3 \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $S_4$ $2^{3} \cdot 3$
46080.b.24.C $\SL(2,5):C_2^4$ $2^{7} \cdot 3 \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2\times D_6$ $2^{3} \cdot 3$
46080.b.24.D $\SL(2,5):C_2^4$ $2^{7} \cdot 3 \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_4\times S_3$ $2^{3} \cdot 3$
46080.b.32.A $A_4\times \SL(2,5)$ $2^{5} \cdot 3^{2} \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_4\times D_4$ $2^{5}$
46080.b.48.A $\SL(2,5):C_2^3$ $2^{6} \cdot 3 \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2\times S_4$ $2^{4} \cdot 3$
46080.b.48.B $C_2^3\times \SL(2,5)$ $2^{6} \cdot 3 \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_4\times D_6$ $2^{4} \cdot 3$
46080.b.48.C $C_2\times \GL(2,5)$ $2^{6} \cdot 3 \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2\times S_4$ $2^{4} \cdot 3$
46080.b.48.D $C_2\times \GL(2,5)$ $2^{6} \cdot 3 \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2\times S_4$ $2^{4} \cdot 3$
46080.b.48.E $\SL(2,5):C_2^3$ $2^{6} \cdot 3 \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_6:D_4$ $2^{4} \cdot 3$
46080.b.48.F $\SL(2,5):C_2^3$ $2^{6} \cdot 3 \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $D_{12}:C_2$ $2^{4} \cdot 3$
46080.b.96.A $C_2^2\times \SL(2,5)$ $2^{5} \cdot 3 \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_4\times S_4$ $2^{5} \cdot 3$
46080.b.96.B $\SL(2,5):C_2^2$ $2^{5} \cdot 3 \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2^2\times S_4$ $2^{5} \cdot 3$
46080.b.96.C $\SL(2,5):C_2^2$ $2^{5} \cdot 3 \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_4\times S_4$ $2^{5} \cdot 3$
46080.b.96.D $C_2^2\times \SL(2,5)$ $2^{5} \cdot 3 \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_{12}:D_4$ $2^{5} \cdot 3$
46080.b.120.A $C_4\times \GL(2,\mathbb{Z}/4)$ $2^{7} \cdot 3$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $S_5$ $2^{3} \cdot 3 \cdot 5$
46080.b.192.A $C_2\times \SL(2,5)$ $2^{4} \cdot 3 \cdot 5$ ✓ ✓ $\GL(2,5)\times \GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3^{2} \cdot 5$ $C_2^4.D_6$ $2^{6} \cdot 3$
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