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Extensions 1→N→G→Q→1 with N=C20 and Q=C22×C6

Direct product G=N×Q with N=C20 and Q=C22×C6
dρLabelID
C23×C60480C2^3xC60480,1180

Semidirect products G=N:Q with N=C20 and Q=C22×C6
extensionφ:Q→Aut NdρLabelID
C20⋊(C22×C6) = C6×D4×D5φ: C22×C6/C6 → C22 ⊆ Aut C20120C20:(C2^2xC6)480,1139
C20⋊2(C22×C6) = C2×C6×D20φ: C22×C6/C2×C6 → C2 ⊆ Aut C20240C20:2(C2^2xC6)480,1137
C20⋊3(C22×C6) = D5×C22×C12φ: C22×C6/C2×C6 → C2 ⊆ Aut C20240C20:3(C2^2xC6)480,1136
C20⋊4(C22×C6) = D4×C2×C30φ: C22×C6/C2×C6 → C2 ⊆ Aut C20240C20:4(C2^2xC6)480,1181

Non-split extensions G=N.Q with N=C20 and Q=C22×C6
extensionφ:Q→Aut NdρLabelID
C20.1(C22×C6) = C3×D5×D8φ: C22×C6/C6 → C22 ⊆ Aut C201204C20.1(C2^2xC6)480,703
C20.2(C22×C6) = C3×D8⋊D5φ: C22×C6/C6 → C22 ⊆ Aut C201204C20.2(C2^2xC6)480,704
C20.3(C22×C6) = C3×D8⋊3D5φ: C22×C6/C6 → C22 ⊆ Aut C202404C20.3(C2^2xC6)480,705
C20.4(C22×C6) = C3×D5×SD16φ: C22×C6/C6 → C22 ⊆ Aut C201204C20.4(C2^2xC6)480,706
C20.5(C22×C6) = C3×D40⋊C2φ: C22×C6/C6 → C22 ⊆ Aut C201204C20.5(C2^2xC6)480,707
C20.6(C22×C6) = C3×SD16⋊D5φ: C22×C6/C6 → C22 ⊆ Aut C202404C20.6(C2^2xC6)480,708
C20.7(C22×C6) = C3×SD16⋊3D5φ: C22×C6/C6 → C22 ⊆ Aut C202404C20.7(C2^2xC6)480,709
C20.8(C22×C6) = C3×D5×Q16φ: C22×C6/C6 → C22 ⊆ Aut C202404C20.8(C2^2xC6)480,710
C20.9(C22×C6) = C3×Q16⋊D5φ: C22×C6/C6 → C22 ⊆ Aut C202404C20.9(C2^2xC6)480,711
C20.10(C22×C6) = C3×Q8.D10φ: C22×C6/C6 → C22 ⊆ Aut C202404C20.10(C2^2xC6)480,712
C20.11(C22×C6) = C6×D4⋊D5φ: C22×C6/C6 → C22 ⊆ Aut C20240C20.11(C2^2xC6)480,724
C20.12(C22×C6) = C3×D4.D10φ: C22×C6/C6 → C22 ⊆ Aut C201204C20.12(C2^2xC6)480,725
C20.13(C22×C6) = C6×D4.D5φ: C22×C6/C6 → C22 ⊆ Aut C20240C20.13(C2^2xC6)480,726
C20.14(C22×C6) = C6×Q8⋊D5φ: C22×C6/C6 → C22 ⊆ Aut C20240C20.14(C2^2xC6)480,734
C20.15(C22×C6) = C3×C20.C23φ: C22×C6/C6 → C22 ⊆ Aut C202404C20.15(C2^2xC6)480,735
C20.16(C22×C6) = C6×C5⋊Q16φ: C22×C6/C6 → C22 ⊆ Aut C20480C20.16(C2^2xC6)480,736
C20.17(C22×C6) = C3×D4⋊D10φ: C22×C6/C6 → C22 ⊆ Aut C201204C20.17(C2^2xC6)480,742
C20.18(C22×C6) = C3×D4.8D10φ: C22×C6/C6 → C22 ⊆ Aut C202404C20.18(C2^2xC6)480,743
C20.19(C22×C6) = C3×D4.9D10φ: C22×C6/C6 → C22 ⊆ Aut C202404C20.19(C2^2xC6)480,744
C20.20(C22×C6) = C6×D4⋊2D5φ: C22×C6/C6 → C22 ⊆ Aut C20240C20.20(C2^2xC6)480,1140
C20.21(C22×C6) = C3×D4⋊6D10φ: C22×C6/C6 → C22 ⊆ Aut C201204C20.21(C2^2xC6)480,1141
C20.22(C22×C6) = C6×Q8×D5φ: C22×C6/C6 → C22 ⊆ Aut C20240C20.22(C2^2xC6)480,1142
C20.23(C22×C6) = C6×Q8⋊2D5φ: C22×C6/C6 → C22 ⊆ Aut C20240C20.23(C2^2xC6)480,1143
C20.24(C22×C6) = C3×Q8.10D10φ: C22×C6/C6 → C22 ⊆ Aut C202404C20.24(C2^2xC6)480,1144
C20.25(C22×C6) = C3×D4⋊8D10φ: C22×C6/C6 → C22 ⊆ Aut C201204C20.25(C2^2xC6)480,1146
C20.26(C22×C6) = C3×D4.10D10φ: C22×C6/C6 → C22 ⊆ Aut C202404C20.26(C2^2xC6)480,1147
C20.27(C22×C6) = C6×C40⋊C2φ: C22×C6/C2×C6 → C2 ⊆ Aut C20240C20.27(C2^2xC6)480,695
C20.28(C22×C6) = C6×D40φ: C22×C6/C2×C6 → C2 ⊆ Aut C20240C20.28(C2^2xC6)480,696
C20.29(C22×C6) = C3×D40⋊7C2φ: C22×C6/C2×C6 → C2 ⊆ Aut C202402C20.29(C2^2xC6)480,697
C20.30(C22×C6) = C6×Dic20φ: C22×C6/C2×C6 → C2 ⊆ Aut C20480C20.30(C2^2xC6)480,698
C20.31(C22×C6) = C3×C8⋊D10φ: C22×C6/C2×C6 → C2 ⊆ Aut C201204C20.31(C2^2xC6)480,701
C20.32(C22×C6) = C3×C8.D10φ: C22×C6/C2×C6 → C2 ⊆ Aut C202404C20.32(C2^2xC6)480,702
C20.33(C22×C6) = C2×C6×Dic10φ: C22×C6/C2×C6 → C2 ⊆ Aut C20480C20.33(C2^2xC6)480,1135
C20.34(C22×C6) = D5×C2×C24φ: C22×C6/C2×C6 → C2 ⊆ Aut C20240C20.34(C2^2xC6)480,692
C20.35(C22×C6) = C6×C8⋊D5φ: C22×C6/C2×C6 → C2 ⊆ Aut C20240C20.35(C2^2xC6)480,693
C20.36(C22×C6) = C3×D20.3C4φ: C22×C6/C2×C6 → C2 ⊆ Aut C202402C20.36(C2^2xC6)480,694
C20.37(C22×C6) = C3×D5×M4(2)φ: C22×C6/C2×C6 → C2 ⊆ Aut C201204C20.37(C2^2xC6)480,699
C20.38(C22×C6) = C3×D20.2C4φ: C22×C6/C2×C6 → C2 ⊆ Aut C202404C20.38(C2^2xC6)480,700
C20.39(C22×C6) = C2×C6×C5⋊2C8φ: C22×C6/C2×C6 → C2 ⊆ Aut C20480C20.39(C2^2xC6)480,713
C20.40(C22×C6) = C6×C4.Dic5φ: C22×C6/C2×C6 → C2 ⊆ Aut C20240C20.40(C2^2xC6)480,714
C20.41(C22×C6) = C3×D4.Dic5φ: C22×C6/C2×C6 → C2 ⊆ Aut C202404C20.41(C2^2xC6)480,741
C20.42(C22×C6) = C6×C4○D20φ: C22×C6/C2×C6 → C2 ⊆ Aut C20240C20.42(C2^2xC6)480,1138
C20.43(C22×C6) = C3×D5×C4○D4φ: C22×C6/C2×C6 → C2 ⊆ Aut C201204C20.43(C2^2xC6)480,1145
C20.44(C22×C6) = D8×C30φ: C22×C6/C2×C6 → C2 ⊆ Aut C20240C20.44(C2^2xC6)480,937
C20.45(C22×C6) = SD16×C30φ: C22×C6/C2×C6 → C2 ⊆ Aut C20240C20.45(C2^2xC6)480,938
C20.46(C22×C6) = Q16×C30φ: C22×C6/C2×C6 → C2 ⊆ Aut C20480C20.46(C2^2xC6)480,939
C20.47(C22×C6) = C15×C4○D8φ: C22×C6/C2×C6 → C2 ⊆ Aut C202402C20.47(C2^2xC6)480,940
C20.48(C22×C6) = C15×C8⋊C22φ: C22×C6/C2×C6 → C2 ⊆ Aut C201204C20.48(C2^2xC6)480,941
C20.49(C22×C6) = C15×C8.C22φ: C22×C6/C2×C6 → C2 ⊆ Aut C202404C20.49(C2^2xC6)480,942
C20.50(C22×C6) = Q8×C2×C30φ: C22×C6/C2×C6 → C2 ⊆ Aut C20480C20.50(C2^2xC6)480,1182
C20.51(C22×C6) = C4○D4×C30φ: C22×C6/C2×C6 → C2 ⊆ Aut C20240C20.51(C2^2xC6)480,1183
C20.52(C22×C6) = C15×2+ 1+4φ: C22×C6/C2×C6 → C2 ⊆ Aut C201204C20.52(C2^2xC6)480,1184
C20.53(C22×C6) = C15×2- 1+4φ: C22×C6/C2×C6 → C2 ⊆ Aut C202404C20.53(C2^2xC6)480,1185
C20.54(C22×C6) = M4(2)×C30central extension (φ=1)240C20.54(C2^2xC6)480,935
C20.55(C22×C6) = C15×C8○D4central extension (φ=1)2402C20.55(C2^2xC6)480,936

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