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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 at least 1000)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
8192.wy.1.a1.a1 $C_2^{10}.D_4$ $2^{13}$ $2$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_1$ $1$ ✓
8192.wy.2._.A $C_2^9.D_4$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.B $C_2^9.D_4$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.C $C_2^9.D_4$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.D $C_2^9.D_4$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.E $C_2^9.D_4$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.F $C_2^9.D_4$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.G $C_2^9.D_4$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.H $C_2^9.D_4$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.I $C_2^9.D_4$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.J $C_2^9.D_4$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.K $C_2^9.D_4$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.L $C_2^9.D_4$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.M $C_2^9.D_4$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.N $C_2^9.D_4$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.O $C_2^9.D_4$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.P $C_2^9.D_4$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.Q $C_2^5.C_2^5.C_2^2$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.R $C_2^5.C_2^5.C_2^2$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.S $C_2^5.C_2^5.C_2^2$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.T $C_2^6.D_4^2$ $2^{12}$ ✓ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.U $C_2.C_2^6.C_2^5$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.V $C_2.C_2^6.C_2^5$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.W $C_2^5.C_2^5.C_2^2$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.X $C_2^8.C_2^4$ $2^{12}$ ✓ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.Y $C_2^5.C_2^5.C_2^2$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.Z $C_2^5.C_2^5.C_2^2$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.BA $C_2^5.C_2^5.C_2^2$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.BB $C_2^{10}.C_4$ $2^{12}$ ✓ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.BC $C_2^5.C_2^5.C_2^2$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.BD $C_2^5.C_2^5.C_2^2$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.2._.BE $C_2.C_2^6.C_2^5$ $2^{12}$ ✓ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2$ $2$ ✓
8192.wy.4._.A $C_2^8.C_2^3$ $2^{11}$ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2^2$ $2^{2}$ ✓
8192.wy.4._.B $C_2^5.C_2^4.C_2^2$ $2^{11}$ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2^2$ $2^{2}$ ✓
8192.wy.4._.C $C_2^7.C_2^4$ $2^{11}$ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2^2$ $2^{2}$ ✓
8192.wy.4._.D $C_2^5.C_2^5.C_2$ $2^{11}$ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2^2$ $2^{2}$ ✓
8192.wy.4._.E $C_2^5.C_2^4.C_2^2$ $2^{11}$ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2^2$ $2^{2}$ ✓
8192.wy.4._.F $C_2^5.C_2^4.C_2^2$ $2^{11}$ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2^2$ $2^{2}$ ✓
8192.wy.4._.G $C_2^5.C_2^5.C_2$ $2^{11}$ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2^2$ $2^{2}$ ✓
8192.wy.4._.H $C_2^5.C_2^5.C_2$ $2^{11}$ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2^2$ $2^{2}$ ✓
8192.wy.4._.I $C_2^7.C_2^4$ $2^{11}$ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2^2$ $2^{2}$ ✓
8192.wy.4._.J $C_2^5.C_2^4.C_2^2$ $2^{11}$ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2^2$ $2^{2}$ ✓
8192.wy.4._.K $C_2^7.C_2^4$ $2^{11}$ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2^2$ $2^{2}$ ✓
8192.wy.4._.L $C_2^5.C_2^4.C_2^2$ $2^{11}$ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2^2$ $2^{2}$ ✓
8192.wy.4._.M $C_2^5.C_2^5.C_2$ $2^{11}$ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2^2$ $2^{2}$ ✓
8192.wy.4._.N $C_2.C_2^6.C_2^4$ $2^{11}$ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2^2$ $2^{2}$ ✓
8192.wy.4._.O $C_2.C_2^6.C_2^4$ $2^{11}$ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2^2$ $2^{2}$ ✓
8192.wy.4._.P $C_2^5.C_2^5.C_2$ $2^{11}$ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2^2$ $2^{2}$ ✓
8192.wy.4._.Q $C_2^5.D_4^2$ $2^{11}$ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2^2$ $2^{2}$ ✓
8192.wy.4._.R $C_2^5.C_2^4.C_2^2$ $2^{11}$ ✓ $C_2^{10}.D_4$ $2^{13}$ $C_2^2$ $2^{2}$ ✓
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