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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 555 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
10749542400000000.cu.1.a1.a1 $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_1$ $1$ ✓
10749542400000000.cu.2._.A $A_5^4.A_5^4.C_4:D_4$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
10749542400000000.cu.2._.B $A_5^8.D_4.C_2^2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
10749542400000000.cu.2._.C $A_5^4.A_5^4.C_4\wr C_2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
10749542400000000.cu.2._.D $A_5^8.D_8.C_2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
10749542400000000.cu.2._.E $A_5^4.A_5^4.C_4\wr C_2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
10749542400000000.cu.2._.F $A_5^8.(C_2^3.C_4)$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
10749542400000000.cu.2._.G $A_5^8.D_8.C_2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
10749542400000000.cu.4._.A $A_5^4.A_5^4.\OD_{16}$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
10749542400000000.cu.4._.B $A_5^2.A_5^2.A_5^2.A_5^2.C_4^2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
10749542400000000.cu.4._.C $A_5^4.A_5^4.C_2^3.C_2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
10749542400000000.cu.4._.D $A_5^4.A_5^4.C_2^3.C_2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
10749542400000000.cu.4._.E $A_5^4.A_5^4.D_4.C_2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
10749542400000000.cu.4._.F $A_5^4.A_5^4.D_4:C_2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
10749542400000000.cu.4._.G $A_5^4.A_5^4.\OD_{16}$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
10749542400000000.cu.4._.H $A_5^2.A_5^2.A_5^4.C_4.C_2^2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{2}$ $-$
10749542400000000.cu.4._.I $A_5^4.A_5^4.D_4.C_2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{2}$ $-$
10749542400000000.cu.4._.J $A_5^8.D_4.C_2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{2}$ $-$
10749542400000000.cu.4._.K $A_5^8.D_4:C_2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{2}$ $-$
10749542400000000.cu.4._.L $A_5^8.D_4:C_2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{2}$ $-$
10749542400000000.cu.4._.M $A_5^2.A_5^2.A_5^4.C_4.C_2^2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{2}$ $-$
10749542400000000.cu.4._.N $A_5^8.D_4.C_2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{2}$ $-$
10749542400000000.cu.4._.O $A_5^8.D_8$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{2}$ $-$
10749542400000000.cu.4._.P $A_5^8.\SD_{16}$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{2}$ $-$
10749542400000000.cu.4._.Q $A_5^4.A_5^4.D_4.C_2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{2}$ $-$
10749542400000000.cu.4._.R $A_5^8.\SD_{16}$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{2}$ $-$
10749542400000000.cu.4._.S $A_5^8.D_8$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{2}$ $-$
10749542400000000.cu.8._.A $A_5^4.A_5^4.Q_8$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
10749542400000000.cu.8._.B $A_5^2.A_5^2.A_5^2.A_5^2.C_2^3$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
10749542400000000.cu.8._.C $A_5^2.A_5^2.A_5^2.A_5^2.C_2^3$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
10749542400000000.cu.8._.D $A_5^2.A_5^2.A_5^2.A_5^2.C_2^2.C_2$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2^3$ $2^{3}$ ✓
10749542400000000.cu.8._.E $A_5^4.A_5^4.D_4$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
10749542400000000.cu.8._.F $A_5^4.A_5^4.Q_8$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
10749542400000000.cu.8._.G $A_5^4.A_5^4.D_4$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ ✓ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
10749542400000000.cu.8._.H $A_5.A_5.A_5.A_5.A_5^2.A_5^2.C_4.C_2$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.cu.8._.I $A_5^4.A_5^4.D_4$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.cu.8._.J $A_5^2.A_5^2.A_5^2.A_5^2.D_4$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.cu.8._.K $A_5^4.A_5^4.C_4.C_2$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.cu.8._.L $A_5^2.A_5^2.A_5^2.A_5^2.C_2^3$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.cu.8._.M $A_5^4.A_5^4.D_4$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.cu.8._.N $A_5^4.A_5^4.D_4$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.cu.8._.O $A_5^4.A_5^4.C_2^3$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.cu.8._.P $A_5^4.A_5^4.D_4$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.cu.8._.Q $A_5^4.A_5^4.D_4$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.cu.8._.R $A_5^4.A_5^4.C_2^3$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.cu.8._.S $A_5^2.A_5^2.A_5^2.A_5^2.D_4$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.cu.8._.T $A_5^4.A_5^4.C_2^2.C_2$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.cu.8._.U $A_5^4.A_5^4.D_4$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.cu.8._.V $A_5^4.A_5^4.D_4$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.cu.8._.W $A_5^4.A_5^4.C_4.C_2$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.D_4:D_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
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