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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 948 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
171992678400000000.cu.1.a1.a1 $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_1$ $1$ ✓
171992678400000000.cu.2._.A $A_5^4.A_5^4.C_2^5.C_2^4$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.B $A_5^8.D_4^2.C_2^2.C_2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.C $A_5^8.D_4^2.C_2^2.C_2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.D $A_5^8.C_2^2.C_2^6.C_2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.E $A_5^8.C_2.C_2^5.C_2^3$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.F $A_5^8.D_4^2.C_2^2.C_2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.G $A_5^8.C_2^2.D_4^2.C_2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.H $A_5^8.C_4.C_2^4.C_2^3$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.I $A_5^8.C_2.C_2^4.C_2^4$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.J $A_5^8.D_4^2.C_2^2.C_2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.K $A_5^8.C_2^2.D_4^2.C_2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.L $A_5^8.Q_8^2.C_2.C_2^2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.M $A_5^8.C_4.C_2^4.C_2^3$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.N $A_5^8.D_4^2.C_2^2.C_2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.O $A_5^8.D_4^2.C_2^2.C_2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.P $A_5^8.C_2^2:\OD_{16}.C_2^3$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.Q $A_5^8.C_4.C_2^4.C_2^3$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.R $A_5^8.D_4^2.C_2^2.C_2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.S $A_5^8.D_4^2.C_2^2.C_2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.T $A_5^8.C_2^2:\OD_{16}.C_2^3$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.U $A_5^8.C_2^3.C_2^5.C_2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.V $A_5^8.D_4^2.C_2^2.C_2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.W $A_5^8.C_2^2.D_4^2.C_2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.X $A_5^8.C_2\wr C_4.C_2^3$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.Y $A_5^8.C_2.C_2^4.C_2^4$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.Z $A_5^8.D_4^2.C_2^2.C_2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.BA $A_5^8.C_2^2.D_4^2.C_2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.BB $A_5^8.C_4.C_2^4.C_2^3$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.BC $A_5^8.D_4^2.C_2^2.C_2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.BD $A_5^8.D_4^2.C_2^2.C_2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.2._.BE $A_5^8.C_2^2.C_2^6.C_2$ $2^{25} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
171992678400000000.cu.4._.A $A_5^8.C_2^2.C_2^5.C_2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.cu.4._.B $A_5^4.A_5^4.C_2^5.C_2^3$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.cu.4._.C $A_5^4.A_5^4.C_2^4.C_2^4$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.cu.4._.D $A_5^4.A_5^4.C_2^4.C_2^4$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.cu.4._.E $A_5^4.A_5^4.C_2^4.C_2^4$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.cu.4._.F $A_5^4.A_5^4.C_2^5.C_2^3$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.cu.4._.G $A_5^4.A_5^4.C_2^3.C_2^5$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.cu.4._.H $A_5^4.A_5^4.C_2^4.C_2^4$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.cu.4._.I $A_5^4.A_5^4.C_2^4.C_2^4$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.cu.4._.J $A_5^4.A_5^4.C_2^5.C_2^3$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.cu.4._.K $A_5^4.A_5^4.C_2^4.C_2^4$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.cu.4._.L $A_5^4.A_5^4.C_2^4.C_2^4$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.cu.4._.M $A_5^4.A_5^4.C_2^3.C_2^5$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.cu.4._.N $A_5^4.A_5^4.C_2^5.C_2^3$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.cu.4._.O $A_5^4.A_5^4.C_2^4.C_2^4$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.cu.4._.P $A_5^4.A_5^4.C_2^4.C_2^4$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.cu.4._.Q $A_5^8.C_2^2.C_2^5.C_2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
171992678400000000.cu.4._.R $A_5^8.C_4.C_2^4.C_2^2$ $2^{24} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.C_4.C_2^4.C_2^4$ $2^{26} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
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