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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 (29 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
21499084800000000.gn.1.a1.a1 $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_1$ $1$ ✓
21499084800000000.gn.2._.A $A_5^4.A_5^4.C_2^2.C_2^4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
21499084800000000.gn.2._.B $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
21499084800000000.gn.2._.C $A_5^8.C_2\wr C_2^2$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
21499084800000000.gn.2._.D $A_5^8.(D_4.D_4)$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
21499084800000000.gn.2._.E $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
21499084800000000.gn.2._.F $A_5^8.C_2\wr C_2^2$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
21499084800000000.gn.2._.G $A_5^8.(C_4.D_4).C_2$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
21499084800000000.gn.4._.A $A_5^8.C_2^3.C_2^2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
21499084800000000.gn.4._.B $A_5^4.A_5^4.C_2.D_4.C_2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
21499084800000000.gn.4._.C $A_5^4.A_5^4.C_2^2\wr C_2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
21499084800000000.gn.4._.D $A_5^4.A_5^4.(C_4.D_4)$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
21499084800000000.gn.4._.E $A_5^8.(C_2^3.C_4)$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
21499084800000000.gn.4._.F $A_5^8.C_2^3.C_2^2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
21499084800000000.gn.4._.G $A_5^8.D_4.C_2^2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
21499084800000000.gn.8._.A $A_5^4.A_5^4.C_2^3.C_2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_2^3$ $2^{3}$ ✓
21499084800000000.gn.8._.B $A_5^2.A_5^2.A_5^2.A_5^2.C_2^2:C_4$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
21499084800000000.gn.8._.C $A_5^4.A_5^4.C_2.C_2^3$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
21499084800000000.gn.8._.D $A_5^2.A_5^2.A_5^2.A_5^2.C_4^2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
21499084800000000.gn.8._.E $A_5^4.A_5^4.C_2^4$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
21499084800000000.gn.8._.F $A_5^2.A_5^2.A_5^2.A_5^2.C_2^2:C_4$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
21499084800000000.gn.8._.G $A_5^4.A_5^4.C_2^4$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
21499084800000000.gn.16._.A $A_5^2.A_5^2.A_5^2.A_5^2.C_2^3$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_2\times D_4$ $2^{4}$
21499084800000000.gn.16._.B $A_5^2.A_5^2.A_5^2.A_5^2.C_2^3$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_2\times D_4$ $2^{4}$
21499084800000000.gn.16._.C $A_5^2.A_5^2.A_5^2.A_5^2.C_2^2.C_2$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_2\times D_4$ $2^{4}$
21499084800000000.gn.32._.A $A_5.A_5.A_5.A_5.A_5.A_5.A_5.S_5.C_2$ $2^{18} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_2^2\wr C_2$ $2^{5}$
21499084800000000.gn.64._.A $A_5.A_5.A_5.A_5.A_5.A_5.A_5.S_5$ $2^{17} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_2\wr C_2^2$ $2^{6}$
21499084800000000.gn.128.a1.a1 $A_5.A_5.A_5.A_5.A_5.A_5.A_5.A_5$ $2^{16} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $C_4^2:D_4$ $2^{7}$ ✓
21499084800000000.gn.21499084800000000.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$
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