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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 168 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
1600000000.hv.1.a1.a1 $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_1$ $1$ ✓
1600000000.hv.2._.A $C_5^4.D_5^4.C_2^5:C_4$ $2^{11} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2$ $2$ ✓
1600000000.hv.2._.B $C_5^4.D_5^4.C_2^5:C_4$ $2^{11} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2$ $2$ ✓
1600000000.hv.2._.C $C_5^8.C_2^4.C_2^5.C_2^2$ $2^{11} \cdot 5^{8}$ ✓ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2$ $2$ ✓
1600000000.hv.2._.D $C_5^8.C_4^3.C_4^2.C_2$ $2^{11} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2$ $2$ ✓
1600000000.hv.2._.E $C_5^8.C_2^4.C_2^3.C_2^3.C_2$ $2^{11} \cdot 5^{8}$ ✓ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2$ $2$ ✓
1600000000.hv.2._.F $C_5^8.C_4^3.C_4^2.C_2$ $2^{11} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2$ $2$ ✓
1600000000.hv.2._.G $C_5^8.C_2^4.C_2^4.C_2^3$ $2^{11} \cdot 5^{8}$ ✓ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2$ $2$ ✓
1600000000.hv.4._.A $C_5^8.C_2^3.C_2^5.C_2^2$ $2^{10} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_4$ $2^{2}$ ✓
1600000000.hv.4._.B $C_5^8.C_2^3.C_2^5.C_2^2$ $2^{10} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
1600000000.hv.4._.C $C_5^4.D_5^4.C_2^3:C_8$ $2^{10} \cdot 5^{8}$ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
1600000000.hv.4._.D $C_5^4.D_5^4.C_2^4:C_4$ $2^{10} \cdot 5^{8}$ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
1600000000.hv.4._.E $C_5^4.D_5^4.C_2^3:C_8$ $2^{10} \cdot 5^{8}$ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
1600000000.hv.4._.F $C_5^4.D_5^4.C_2^4:C_4$ $2^{10} \cdot 5^{8}$ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
1600000000.hv.4._.G $C_5^8.C_2.C_2^5.C_2^4$ $2^{10} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
1600000000.hv.4._.H $C_5^8.C_2^3.C_2^5.C_2^2$ $2^{10} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2^2$ $2^{2}$ ✓
1600000000.hv.4._.I $C_5^8.C_2.C_2^5.C_2^4$ $2^{10} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_4$ $2^{2}$ ✓
1600000000.hv.4._.J $C_5^8.C_2^3.C_2^5.C_2^2$ $2^{10} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_4$ $2^{2}$ ✓
1600000000.hv.4._.K $C_5^8.C_2^3.C_2^4.C_2^3$ $2^{10} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_4$ $2^{2}$ ✓
1600000000.hv.8._.A $C_5^8.C_2^5.C_2^4$ $2^{9} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2\times C_4$ $2^{3}$ ✓
1600000000.hv.8._.B $C_5^8.C_2^3.C_2^4.C_2^2$ $2^{9} \cdot 5^{8}$ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $D_4$ $2^{3}$
1600000000.hv.8._.C $C_5^8.C_4^3.C_2^3$ $2^{9} \cdot 5^{8}$ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $D_4$ $2^{3}$
1600000000.hv.8._.D $C_5^8.C_4^3.C_2^3$ $2^{9} \cdot 5^{8}$ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $D_4$ $2^{3}$
1600000000.hv.8._.E $C_5^8.C_2^3.C_2^4.C_2^2$ $2^{9} \cdot 5^{8}$ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $D_4$ $2^{3}$
1600000000.hv.8._.F $C_5^8.C_2.C_2^4.C_2^4$ $2^{9} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2^3$ $2^{3}$ ✓
1600000000.hv.8._.G $C_5^8.C_4^3.C_2^3$ $2^{9} \cdot 5^{8}$ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $D_4$ $2^{3}$
1600000000.hv.8._.H $C_5^8.C_2^2.C_2^4.C_2^3$ $2^{9} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2\times C_4$ $2^{3}$ ✓
1600000000.hv.8._.I $C_5^8.C_4^3.C_2^3$ $2^{9} \cdot 5^{8}$ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $D_4$ $2^{3}$
1600000000.hv.8._.J $C_5^8.C_2^4.C_2^5$ $2^{9} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2\times C_4$ $2^{3}$ ✓
1600000000.hv.8._.K $C_5^8.C_2.C_2^5.C_2^3$ $2^{9} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $D_4$ $2^{3}$
1600000000.hv.8._.L $C_5^8.C_2^5.C_2^4$ $2^{9} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $D_4$ $2^{3}$
1600000000.hv.8._.M $C_5^8.C_2.C_2^5.C_2^3$ $2^{9} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $D_4$ $2^{3}$
1600000000.hv.8._.N $C_5^8.C_2^3.C_2^5.C_2$ $2^{9} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $D_4$ $2^{3}$
1600000000.hv.8._.O $C_5^8.C_2^3.C_2^4.C_2^2$ $2^{9} \cdot 5^{8}$ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $D_4$ $2^{3}$
1600000000.hv.8._.P $C_5^8.C_2^2.C_2^4.C_2^3$ $2^{9} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2\times C_4$ $2^{3}$ ✓
1600000000.hv.8._.Q $C_5^8.C_2.C_2^4.C_2^4$ $2^{9} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2\times C_4$ $2^{3}$ ✓
1600000000.hv.8._.R $C_5^8.C_2^3.C_2^4.C_2^2$ $2^{9} \cdot 5^{8}$ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $D_4$ $2^{3}$
1600000000.hv.8._.S $C_5^8.C_2^3.C_2^5.C_2$ $2^{9} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2\times C_4$ $2^{3}$ ✓
1600000000.hv.16._.A $C_5^8.C_2^5.C_2^3$ $2^{8} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2^2:C_4$ $2^{4}$
1600000000.hv.16._.B $C_5^8.C_2^4.C_2^4$ $2^{8} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $Q_{16}$ $2^{4}$
1600000000.hv.16._.C $C_5^8.C_2^4.C_2^4$ $2^{8} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $Q_{16}$ $2^{4}$
1600000000.hv.16._.D $C_5^8.C_2^4.C_2^4$ $2^{8} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $\SD_{16}$ $2^{4}$
1600000000.hv.16._.E $C_5^8.C_2^4.C_2^4$ $2^{8} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $\SD_{16}$ $2^{4}$
1600000000.hv.16._.F $C_5^8.C_2.C_2^3.C_2^4$ $2^{8} \cdot 5^{8}$ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2\times D_4$ $2^{4}$
1600000000.hv.16._.G $C_5^8.C_4^3.C_2^2$ $2^{8} \cdot 5^{8}$ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2^2:C_4$ $2^{4}$
1600000000.hv.16._.H $C_5^8.C_2^3.C_2^4.C_2$ $2^{8} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2^2:C_4$ $2^{4}$
1600000000.hv.16._.I $C_5^8.C_2.C_2^3.C_2^4$ $2^{8} \cdot 5^{8}$ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2\times D_4$ $2^{4}$
1600000000.hv.16._.J $C_5^8.C_2^5.C_2^3$ $2^{8} \cdot 5^{8}$ ✓ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2\times D_4$ $2^{4}$
1600000000.hv.16._.K $C_5^8.C_4^3.C_2^2$ $2^{8} \cdot 5^{8}$ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2^2:C_4$ $2^{4}$
1600000000.hv.16._.L $C_5^8.C_2^3.C_2^5$ $2^{8} \cdot 5^{8}$ ✓ $C_5^4.D_5^4.(C_2^5.D_4)$ $2^{12} \cdot 5^{8}$ $C_2^2:C_4$ $2^{4}$
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