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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 102 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
2400000000.gf.1.a1.a1 $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_1$ $1$ ✓
2400000000.gf.2._.A $C_5^7.(C_2^3\times F_5).\GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3 \cdot 5^{8}$ ✓ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2$ $2$ ✓
2400000000.gf.2._.B $C_5^4.D_5^4.(C_2^3.S_4)$ $2^{10} \cdot 3 \cdot 5^{8}$ ✓ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2$ $2$ ✓
2400000000.gf.2._.C $C_5^4.D_5^4.\SL(2,3):D_4$ $2^{10} \cdot 3 \cdot 5^{8}$ ✓ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2$ $2$ ✓
2400000000.gf.2._.D $C_5^7.(C_2^3\times F_5).\GL(2,\mathbb{Z}/4)$ $2^{10} \cdot 3 \cdot 5^{8}$ ✓ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2$ $2$ ✓
2400000000.gf.2._.E $C_5^4.D_5^4.\SL(2,3).Q_8$ $2^{10} \cdot 3 \cdot 5^{8}$ ✓ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2$ $2$ ✓
2400000000.gf.2._.F $C_5^4.(D_5^4.\GL(2,3)).C_2^2$ $2^{10} \cdot 3 \cdot 5^{8}$ ✓ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2$ $2$ ✓
2400000000.gf.2._.G $C_5^8.C_4.C_4^2.C_3.C_4^2$ $2^{10} \cdot 3 \cdot 5^{8}$ ✓ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2$ $2$ ✓
2400000000.gf.4._.A $C_5^8.C_4.C_4^2.C_{12}.C_2$ $2^{9} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
2400000000.gf.4._.B $C_5^4.D_5^4.(C_2^2\times \SL(2,3))$ $2^{9} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
2400000000.gf.4._.C $C_5^4.D_5^4.\SL(2,3):C_4$ $2^{9} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
2400000000.gf.4._.D $C_5^8.C_4.C_4^2.C_6.C_2^2$ $2^{9} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
2400000000.gf.4._.E $C_5^4.D_5^4.\SL(2,3):C_4$ $2^{9} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
2400000000.gf.4._.F $C_5^4.(C_2\times D_5^4.\GL(2,3))$ $2^{9} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
2400000000.gf.4._.G $C_5^6.F_5^2:C_2^3.A_4$ $2^{9} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_4$ $2^{2}$ ✓
2400000000.gf.4._.H $C_5^4.D_5^4.\SL(2,3).C_2^2$ $2^{9} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_4$ $2^{2}$ ✓
2400000000.gf.4._.I $C_5^6.F_5^2:C_2^3.A_4$ $2^{9} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_4$ $2^{2}$ ✓
2400000000.gf.4._.J $C_5^4.D_5^4.\SL(2,3):C_2^2$ $2^{9} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
2400000000.gf.4._.K $C_5^4.D_5^4.\SL(2,3).C_2^2$ $2^{9} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_4$ $2^{2}$ ✓
2400000000.gf.6._.A $C_5^8.C_2.C_2^5.C_2^4$ $2^{10} \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $S_3$ $2 \cdot 3$
2400000000.gf.8._.A $C_5^4.D_5^4.\SL(2,3):C_2$ $2^{8} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2\times C_4$ $2^{3}$ ✓
2400000000.gf.8._.B $C_5^8.C_4.C_4^2.C_6.C_2$ $2^{8} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $D_4$ $2^{3}$
2400000000.gf.8._.C $C_5^4.(D_5^4.\GL(2,3))$ $2^{8} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $D_4$ $2^{3}$
2400000000.gf.8._.D $C_5^8.C_4.C_4^2.C_{12}$ $2^{8} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2\times C_4$ $2^{3}$ ✓
2400000000.gf.8._.E $C_5^8.C_4.C_4^2.C_{12}$ $2^{8} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2\times C_4$ $2^{3}$ ✓
2400000000.gf.8._.F $C_5^4.(C_2\times D_5^4.\SL(2,3))$ $2^{8} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2^3$ $2^{3}$ ✓
2400000000.gf.8._.G $C_5^4.D_5^4.(C_2\times \SL(2,3))$ $2^{8} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2\times C_4$ $2^{3}$ ✓
2400000000.gf.8._.H $C_5^4.D_5^4.(C_2\times \SL(2,3))$ $2^{8} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2\times C_4$ $2^{3}$ ✓
2400000000.gf.8._.I $C_5^4.D_5^4.\SL(2,3):C_2$ $2^{8} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2\times C_4$ $2^{3}$ ✓
2400000000.gf.12._.A $C_5^8.C_2^4.D_4.C_2^2$ $2^{9} \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_3:C_4$ $2^{2} \cdot 3$
2400000000.gf.12._.B $C_5^8.C_2.C_2^5.C_2^3$ $2^{9} \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $D_6$ $2^{2} \cdot 3$
2400000000.gf.12._.C $C_5^8.C_2.C_2^6.C_2^2$ $2^{9} \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $D_6$ $2^{2} \cdot 3$
2400000000.gf.12._.D $C_5^8.C_4\wr C_2.C_4^2$ $2^{9} \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_3:C_4$ $2^{2} \cdot 3$
2400000000.gf.12._.E $C_5^8.C_2^4.D_4.C_2^2$ $2^{9} \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_3:C_4$ $2^{2} \cdot 3$
2400000000.gf.12._.F $C_5^8.C_2^4.D_4.C_2^2$ $2^{9} \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_3:C_4$ $2^{2} \cdot 3$
2400000000.gf.12._.G $C_5^8.C_2.C_2^5.C_2^3$ $2^{9} \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $D_6$ $2^{2} \cdot 3$
2400000000.gf.16._.A $C_5^4.D_5^4.\SL(2,3)$ $2^{7} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2^2\times C_4$ $2^{4}$ ✓
2400000000.gf.16._.B $C_5^8.C_4.C_4^2.C_6$ $2^{7} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2\times D_4$ $2^{4}$
2400000000.gf.16._.C $C_5^4.D_5^4.\SL(2,3)$ $2^{7} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $D_4:C_2$ $2^{4}$
2400000000.gf.24._.A $C_5^7.(C_2^3\times F_5).C_2^3$ $2^{8} \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_6:C_4$ $2^{3} \cdot 3$
2400000000.gf.24._.B $C_5^8.C_2^3.C_4^2.C_2$ $2^{8} \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_6:C_4$ $2^{3} \cdot 3$
2400000000.gf.24._.C $C_5^8.C_4.C_4^3$ $2^{8} \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_6:C_4$ $2^{3} \cdot 3$
2400000000.gf.24._.D $C_5^4.(C_2\times D_5^4.Q_8)$ $2^{8} \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2\times D_6$ $2^{3} \cdot 3$
2400000000.gf.24._.E $C_5^8.C_4.C_2.C_2^5$ $2^{8} \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $S_4$ $2^{3} \cdot 3$
2400000000.gf.24._.F $C_5^4.D_5^4.(C_2\times Q_8)$ $2^{8} \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_6:C_4$ $2^{3} \cdot 3$
2400000000.gf.24._.G $C_5^4.D_5^4.(C_2\times Q_8)$ $2^{8} \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_6:C_4$ $2^{3} \cdot 3$
2400000000.gf.24._.H $C_5^8.(C_4\times \OD_{16}).C_4$ $2^{8} \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_6:C_4$ $2^{3} \cdot 3$
2400000000.gf.32._.A $C_5^8.C_4.C_4^2.C_3$ $2^{6} \cdot 3 \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_4\times D_4$ $2^{5}$
2400000000.gf.48._.A $C_5^8.C_4.C_2^5$ $2^{7} \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2\times S_4$ $2^{4} \cdot 3$
2400000000.gf.48._.B $C_5^7.D_{10}.C_2^5$ $2^{7} \cdot 5^{8}$ ✓ ✓ $C_5^4.(D_5^4.\GL(2,3)).D_4$ $2^{11} \cdot 3 \cdot 5^{8}$ $C_2\times S_4$ $2^{4} \cdot 3$
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