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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 934 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
10749542400000000.da.1.a1.a1 $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_1$ $1$ ✓
10749542400000000.da.2._.A $A_5^4.A_5^4.C_2^2\wr C_2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
10749542400000000.da.2._.B $A_5^8.(C_2^3.C_4)$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
10749542400000000.da.2._.C $A_5^8.C_2^3.C_2^2$ $2^{21} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ ✓ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2$ $2$ ✓
10749542400000000.da.4._.A $A_5^4.A_5^4.C_2^3.C_2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
10749542400000000.da.4._.B $A_5^2.A_5^2.A_5^2.A_5^2.C_2^2:C_4$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_4$ $2^{2}$ ✓
10749542400000000.da.4._.C $A_5^4.A_5^4.C_2^4$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_4$ $2^{2}$ ✓
10749542400000000.da.4._.D $A_5^2.A_5^2.A_5^4.C_4.C_2^2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{2}$ $-$
10749542400000000.da.4._.E $A_5^2.A_5^2.A_5^4.C_2^2:C_4$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{2}$ $-$
10749542400000000.da.4._.F $A_5^4.A_5^4.\OD_{16}$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{2}$ $-$
10749542400000000.da.4._.G $A_5^4.A_5^4.C_2^3.C_2$ $2^{20} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{2}$ $-$
10749542400000000.da.8._.A $A_5^2.A_5^2.A_5^2.A_5^2.C_2^3$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2\times C_4$ $2^{3}$ ✓
10749542400000000.da.8._.B $A_5^2.A_5^2.A_5^2.A_5^2.C_2^3$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
10749542400000000.da.8._.C $A_5^2.A_5^2.A_5^2.A_5^2.C_2^2.C_2$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $D_4$ $2^{3}$
10749542400000000.da.8._.D $A_5.A_5.A_5.A_5.A_5^2.A_5^2.C_4.C_2$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.da.8._.E $A_5^2.A_5^2.A_5^2.A_5^2.C_2^3$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.da.8._.F $A_5^2.A_5^2.A_5^4.D_4$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.da.8._.G $A_5^2.A_5^2.A_5^4.D_4$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.da.8._.H $A_5^4.A_5^4.C_2^3$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.da.8._.I $A_5^4.A_5^4.C_2^3$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.da.8._.J $A_5^4.A_5^4.C_2^3$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.da.8._.K $A_5^4.A_5^4.D_4$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.da.8._.L $A_5^4.A_5^4.C_8$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.da.8._.M $A_5^4.A_5^4.C_2^2.C_2$ $2^{19} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3}$ $-$
10749542400000000.da.16._.A $A_5.A_5.A_5.A_5.A_5.A_5.A_5.S_5.C_2$ $2^{18} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2^2:C_4$ $2^{4}$
10749542400000000.da.16._.B $A_5^2.A_5^2.A_5^2.A_5^2.C_2^2$ $2^{18} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{4}$ $-$
10749542400000000.da.16._.C $A_5^2.A_5^2.A_5^2.A_5^2.C_2^2$ $2^{18} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{4}$ $-$
10749542400000000.da.16._.D $A_5^2.A_5^2.A_5^2.A_5^2.C_2^2$ $2^{18} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{4}$ $-$
10749542400000000.da.16._.E $A_5^2.A_5^2.A_5^2.A_5^2.C_2^2$ $2^{18} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{4}$ $-$
10749542400000000.da.16._.F $A_5^2.A_5^2.A_5^2.A_5^2.C_4$ $2^{18} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{4}$ $-$
10749542400000000.da.16._.G $A_5.A_5.A_5.A_5.A_5^2.A_5^2.C_4$ $2^{18} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{4}$ $-$
10749542400000000.da.16._.H $A_5^2.A_5^2.A_5^2.A_5^2.C_2^2$ $2^{18} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{4}$ $-$
10749542400000000.da.16._.I $A_5^2.A_5^2.A_5^2.A_5^2.C_2^2$ $2^{18} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{4}$ $-$
10749542400000000.da.16._.J $A_5^2.A_5^2.A_5^2.A_5^2.C_2^2$ $2^{18} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{4}$ $-$
10749542400000000.da.16._.K $A_5^2.A_5^2.A_5^2.A_5^2.C_2^2$ $2^{18} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{4}$ $-$
10749542400000000.da.16._.L $A_5^4.A_5^4.C_2^2$ $2^{18} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{4}$ $-$
10749542400000000.da.16._.M $A_5^4.A_5^4.C_2^2$ $2^{18} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{4}$ $-$
10749542400000000.da.16._.N $A_5^4.A_5^4.C_2^2$ $2^{18} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{4}$ $-$
10749542400000000.da.16._.O $A_5^4.A_5^4.C_2^2$ $2^{18} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{4}$ $-$
10749542400000000.da.16._.P $A_5^4.A_5^4.C_4$ $2^{18} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{4}$ $-$
10749542400000000.da.32._.A $A_5.A_5.A_5.A_5.A_5.A_5.A_5.S_5$ $2^{17} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2^3:C_4$ $2^{5}$
10749542400000000.da.32._.B $A_5.A_5.A_5.A_5.A_5.A_5.A_5.S_5$ $2^{17} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{5}$ $-$
10749542400000000.da.32._.C $A_5^2.A_5^2.A_5^2.A_5^2.C_2$ $2^{17} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{5}$ $-$
10749542400000000.da.32._.D $A_5^2.A_5^2.A_5^2.A_5^2.C_2$ $2^{17} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{5}$ $-$
10749542400000000.da.32._.E $A_5^2.A_5^2.A_5^2.A_5^2.C_2$ $2^{17} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{5}$ $-$
10749542400000000.da.32._.F $A_5^2.A_5^2.A_5^2.A_5^2.C_2$ $2^{17} \cdot 3^{8} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{5}$ $-$
10749542400000000.da.40.a1.a1 $A_4.A_5.A_5.A_5.A_5^2.A_5^2.C_4.C_2$ $2^{19} \cdot 3^{8} \cdot 5^{7}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{3} \cdot 5$ $-$
10749542400000000.da.48.a1.a1 $D_5.A_5.A_5.A_5.A_5^2.A_5^2.C_4.C_2$ $2^{18} \cdot 3^{7} \cdot 5^{8}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{4} \cdot 3$ $-$
10749542400000000.da.64.a1.a1 $A_5.A_5.A_5.A_5.A_5.A_5.A_5.A_5$ $2^{16} \cdot 3^{8} \cdot 5^{8}$ ✓ ✓ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $C_2\wr C_4$ $2^{6}$ ✓
10749542400000000.da.80._.A $A_4.A_5.A_5.A_5.A_5^2.A_5^2.C_4$ $2^{18} \cdot 3^{8} \cdot 5^{7}$ $A_5^8.C_2\wr C_4$ $2^{22} \cdot 3^{8} \cdot 5^{8}$ $2^{4} \cdot 5$ $-$
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