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Extensions 1→N→G→Q→1 with N=C40 and Q=C2×C6

Direct product G=N×Q with N=C40 and Q=C2×C6
dρLabelID
C22×C120480C2^2xC120480,934

Semidirect products G=N:Q with N=C40 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
C40⋊1(C2×C6) = C3×C8⋊D10φ: C2×C6/C3 → C22 ⊆ Aut C401204C40:1(C2xC6)480,701
C40⋊2(C2×C6) = C3×D5×D8φ: C2×C6/C3 → C22 ⊆ Aut C401204C40:2(C2xC6)480,703
C40⋊3(C2×C6) = C3×D40⋊C2φ: C2×C6/C3 → C22 ⊆ Aut C401204C40:3(C2xC6)480,707
C40⋊4(C2×C6) = C3×D8⋊D5φ: C2×C6/C3 → C22 ⊆ Aut C401204C40:4(C2xC6)480,704
C40⋊5(C2×C6) = C3×D5×SD16φ: C2×C6/C3 → C22 ⊆ Aut C401204C40:5(C2xC6)480,706
C40⋊6(C2×C6) = C3×D5×M4(2)φ: C2×C6/C3 → C22 ⊆ Aut C401204C40:6(C2xC6)480,699
C40⋊7(C2×C6) = C15×C8⋊C22φ: C2×C6/C3 → C22 ⊆ Aut C401204C40:7(C2xC6)480,941
C40⋊8(C2×C6) = C6×D40φ: C2×C6/C6 → C2 ⊆ Aut C40240C40:8(C2xC6)480,696
C40⋊9(C2×C6) = C6×C40⋊C2φ: C2×C6/C6 → C2 ⊆ Aut C40240C40:9(C2xC6)480,695
C40⋊10(C2×C6) = D5×C2×C24φ: C2×C6/C6 → C2 ⊆ Aut C40240C40:10(C2xC6)480,692
C40⋊11(C2×C6) = C6×C8⋊D5φ: C2×C6/C6 → C2 ⊆ Aut C40240C40:11(C2xC6)480,693
C40⋊12(C2×C6) = D8×C30φ: C2×C6/C6 → C2 ⊆ Aut C40240C40:12(C2xC6)480,937
C40⋊13(C2×C6) = SD16×C30φ: C2×C6/C6 → C2 ⊆ Aut C40240C40:13(C2xC6)480,938
C40⋊14(C2×C6) = M4(2)×C30φ: C2×C6/C6 → C2 ⊆ Aut C40240C40:14(C2xC6)480,935

Non-split extensions G=N.Q with N=C40 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
C40.1(C2×C6) = C3×C8.D10φ: C2×C6/C3 → C22 ⊆ Aut C402404C40.1(C2xC6)480,702
C40.2(C2×C6) = C3×C5⋊D16φ: C2×C6/C3 → C22 ⊆ Aut C402404C40.2(C2xC6)480,104
C40.3(C2×C6) = C3×D8.D5φ: C2×C6/C3 → C22 ⊆ Aut C402404C40.3(C2xC6)480,105
C40.4(C2×C6) = C3×C5⋊SD32φ: C2×C6/C3 → C22 ⊆ Aut C402404C40.4(C2xC6)480,106
C40.5(C2×C6) = C3×C5⋊Q32φ: C2×C6/C3 → C22 ⊆ Aut C404804C40.5(C2xC6)480,107
C40.6(C2×C6) = C3×D8⋊3D5φ: C2×C6/C3 → C22 ⊆ Aut C402404C40.6(C2xC6)480,705
C40.7(C2×C6) = C3×D5×Q16φ: C2×C6/C3 → C22 ⊆ Aut C402404C40.7(C2xC6)480,710
C40.8(C2×C6) = C3×Q8.D10φ: C2×C6/C3 → C22 ⊆ Aut C402404C40.8(C2xC6)480,712
C40.9(C2×C6) = C3×SD16⋊D5φ: C2×C6/C3 → C22 ⊆ Aut C402404C40.9(C2xC6)480,708
C40.10(C2×C6) = C3×Q16⋊D5φ: C2×C6/C3 → C22 ⊆ Aut C402404C40.10(C2xC6)480,711
C40.11(C2×C6) = C3×SD16⋊3D5φ: C2×C6/C3 → C22 ⊆ Aut C402404C40.11(C2xC6)480,709
C40.12(C2×C6) = C3×D20.2C4φ: C2×C6/C3 → C22 ⊆ Aut C402404C40.12(C2xC6)480,700
C40.13(C2×C6) = C15×C8.C22φ: C2×C6/C3 → C22 ⊆ Aut C402404C40.13(C2xC6)480,942
C40.14(C2×C6) = C3×D80φ: C2×C6/C6 → C2 ⊆ Aut C402402C40.14(C2xC6)480,77
C40.15(C2×C6) = C3×C16⋊D5φ: C2×C6/C6 → C2 ⊆ Aut C402402C40.15(C2xC6)480,78
C40.16(C2×C6) = C3×Dic40φ: C2×C6/C6 → C2 ⊆ Aut C404802C40.16(C2xC6)480,79
C40.17(C2×C6) = C3×D40⋊7C2φ: C2×C6/C6 → C2 ⊆ Aut C402402C40.17(C2xC6)480,697
C40.18(C2×C6) = C6×Dic20φ: C2×C6/C6 → C2 ⊆ Aut C40480C40.18(C2xC6)480,698
C40.19(C2×C6) = D5×C48φ: C2×C6/C6 → C2 ⊆ Aut C402402C40.19(C2xC6)480,75
C40.20(C2×C6) = C3×C80⋊C2φ: C2×C6/C6 → C2 ⊆ Aut C402402C40.20(C2xC6)480,76
C40.21(C2×C6) = C6×C5⋊2C16φ: C2×C6/C6 → C2 ⊆ Aut C40480C40.21(C2xC6)480,89
C40.22(C2×C6) = C3×C20.4C8φ: C2×C6/C6 → C2 ⊆ Aut C402402C40.22(C2xC6)480,90
C40.23(C2×C6) = C3×D20.3C4φ: C2×C6/C6 → C2 ⊆ Aut C402402C40.23(C2xC6)480,694
C40.24(C2×C6) = C15×D16φ: C2×C6/C6 → C2 ⊆ Aut C402402C40.24(C2xC6)480,214
C40.25(C2×C6) = C15×SD32φ: C2×C6/C6 → C2 ⊆ Aut C402402C40.25(C2xC6)480,215
C40.26(C2×C6) = C15×Q32φ: C2×C6/C6 → C2 ⊆ Aut C404802C40.26(C2xC6)480,216
C40.27(C2×C6) = Q16×C30φ: C2×C6/C6 → C2 ⊆ Aut C40480C40.27(C2xC6)480,939
C40.28(C2×C6) = C15×C4○D8φ: C2×C6/C6 → C2 ⊆ Aut C402402C40.28(C2xC6)480,940
C40.29(C2×C6) = C15×C8○D4φ: C2×C6/C6 → C2 ⊆ Aut C402402C40.29(C2xC6)480,936
C40.30(C2×C6) = C15×M5(2)central extension (φ=1)2402C40.30(C2xC6)480,213

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