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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 70 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
42998169600000000.bv.1.a1.a1 $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_1$ $1$ ✓
42998169600000000.bv.2._.C $A_5^8.C_4^2.C_2^3$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
42998169600000000.bv.2._.D $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
42998169600000000.bv.2._.G $A_5^8.C_4^2:C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
42998169600000000.bv.2._.H $A_5^8.C_2^3.C_2^4$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
42998169600000000.bv.2._.I $A_5^4.A_5^4.D_4^2.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
42998169600000000.bv.2._.J $A_5^8.C_2^4.C_2^3$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
42998169600000000.bv.2._.N $A_5^8.C_2\wr C_4.C_2$ $2^{23} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
42998169600000000.bv.4._.A $A_5^2.A_5^2.A_5^2.A_5^2.D_4^2$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
42998169600000000.bv.4._.H $A_5^4.A_5^4.C_2^4.C_2^2$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
42998169600000000.bv.4._.N $A_5^4.A_5^4.C_2^3.C_2^3$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
42998169600000000.bv.4._.O $A_5^8.C_2.C_2^5$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
42998169600000000.bv.4._.R $A_5^8.C_2.C_2^4.C_2$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
42998169600000000.bv.4._.S $A_5^4.A_5^4.C_2^3.C_2^3$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
42998169600000000.bv.4._.T $A_5^8.C_2^3.C_2^3$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
42998169600000000.bv.4._.BB $A_5^8.C_2^3.C_2^3$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
42998169600000000.bv.4._.BC $A_5^4.A_5^4.D_4^2$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
42998169600000000.bv.4._.BD $A_5^4.A_5^4.C_2^4.C_2^2$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
42998169600000000.bv.4._.BE $A_5^4.A_5^4.C_2^3.C_2^3$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
42998169600000000.bv.8._.A $A_5^4.A_5^4.C_2.D_4.C_2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2^3$ $2^{3}$ ✓
42998169600000000.bv.8._.B $A_5^2.A_5^2.A_5^2.A_5^2.C_4:D_4$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2^3$ $2^{3}$ ✓
42998169600000000.bv.8._.C $A_5^2.A_5^2.A_5^2.A_5^2.C_2^4.C_2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2^3$ $2^{3}$ ✓
42998169600000000.bv.8._.D $A_5^2.A_5^2.A_5^2.A_5^2.C_2^2\wr C_2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2^3$ $2^{3}$ ✓
42998169600000000.bv.8._.I $A_5^4.A_5^4.(C_4.D_4)$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2^3$ $2^{3}$ ✓
42998169600000000.bv.8._.J $A_5^4.A_5^4.C_2^2\wr C_2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2^3$ $2^{3}$ ✓
42998169600000000.bv.8._.M $A_5^4.A_5^4.C_4^2.C_2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
42998169600000000.bv.8._.N $A_5^4.A_5^4.C_2.C_2^4$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2^3$ $2^{3}$ ✓
42998169600000000.bv.8._.O $A_5^4.A_5^4.(C_4.D_4)$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
42998169600000000.bv.8._.P $A_5^4.A_5^4.C_4:Q_8$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
42998169600000000.bv.8._.Q $A_5^4.A_5^4.C_2.C_2^4$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
42998169600000000.bv.8._.S $A_5^4.A_5^4.C_2^2.C_2^3$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
42998169600000000.bv.8._.T $A_5^4.A_5^4.C_2^4.C_2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
42998169600000000.bv.8._.U $A_5^4.A_5^4.C_2^2\wr C_2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
42998169600000000.bv.8._.V $A_5^4.A_5^4.C_2^4.C_2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
42998169600000000.bv.8._.X $A_5^2.A_5^2.A_5^2.A_5^2.C_2^4.C_2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
42998169600000000.bv.8._.Y $A_5^2.A_5^2.A_5^2.A_5^2.C_2^4.C_2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
42998169600000000.bv.8._.Z $A_5^4.A_5^4.C_2^3.C_2^2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
42998169600000000.bv.8._.BA $A_5^4.A_5^4.C_2^2\wr C_2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
42998169600000000.bv.16._.A $A_5^2.A_5^2.A_5^2.A_5^2.C_2^3.C_2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2\times D_4$ $2^{4}$
42998169600000000.bv.16._.B $A_5.A_5.A_5.A_5.A_5.A_5.A_5.S_5.C_2^3$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2\times D_4$ $2^{4}$
42998169600000000.bv.16._.C $A_5^2.A_5^2.A_5^2.A_5^2.C_4^2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2\times D_4$ $2^{4}$
42998169600000000.bv.16._.D $A_5^2.A_5^2.A_5^2.A_5^2.C_2^3.C_2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2\times D_4$ $2^{4}$
42998169600000000.bv.16._.E $A_5^2.A_5^2.A_5^2.A_5^2.C_2^3.C_2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2\times D_4$ $2^{4}$
42998169600000000.bv.16._.F $A_5^2.A_5^2.A_5^2.A_5^2.C_2^3.C_2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2^4$ $2^{4}$ ✓
42998169600000000.bv.16._.G $A_5^2.A_5^2.A_5^2.A_5^2.C_2^2:C_4$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2\times D_4$ $2^{4}$
42998169600000000.bv.16._.H $A_5^2.A_5^2.A_5^2.A_5^2.C_2^4$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2\times D_4$ $2^{4}$
42998169600000000.bv.16._.I $A_5^4.A_5^4.C_2.C_2^3$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2\times D_4$ $2^{4}$
42998169600000000.bv.16._.J $A_5^4.A_5^4.C_4^2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2\times D_4$ $2^{4}$
42998169600000000.bv.16._.K $A_5^4.A_5^4.C_2^3.C_2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2\times D_4$ $2^{4}$
42998169600000000.bv.16._.L $A_5^4.A_5^4.C_2^4$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4^2.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ $C_2\times D_4$ $2^{4}$
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