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Extensions 1→N→G→Q→1 with N=C6 and Q=D10⋊C4

Direct product G=N×Q with N=C6 and Q=D10⋊C4
dρLabelID
C6×D10⋊C4240C6xD10:C4480,720

Semidirect products G=N:Q with N=C6 and Q=D10⋊C4
extensionφ:Q→Aut NdρLabelID
C6⋊1(D10⋊C4) = C2×D30⋊4C4φ: D10⋊C4/C2×Dic5 → C2 ⊆ Aut C6240C6:1(D10:C4)480,616
C6⋊2(D10⋊C4) = C2×D30⋊3C4φ: D10⋊C4/C2×C20 → C2 ⊆ Aut C6240C6:2(D10:C4)480,892
C6⋊3(D10⋊C4) = C2×D10⋊Dic3φ: D10⋊C4/C22×D5 → C2 ⊆ Aut C6240C6:3(D10:C4)480,611

Non-split extensions G=N.Q with N=C6 and Q=D10⋊C4
extensionφ:Q→Aut NdρLabelID
C6.1(D10⋊C4) = D30⋊4C8φ: D10⋊C4/C2×Dic5 → C2 ⊆ Aut C6240C6.1(D10:C4)480,33
C6.2(D10⋊C4) = C60.29D4φ: D10⋊C4/C2×Dic5 → C2 ⊆ Aut C61204+C6.2(D10:C4)480,36
C6.3(D10⋊C4) = C60.31D4φ: D10⋊C4/C2×Dic5 → C2 ⊆ Aut C62404-C6.3(D10:C4)480,39
C6.4(D10⋊C4) = D60⋊12C4φ: D10⋊C4/C2×Dic5 → C2 ⊆ Aut C6240C6.4(D10:C4)480,44
C6.5(D10⋊C4) = D60⋊15C4φ: D10⋊C4/C2×Dic5 → C2 ⊆ Aut C6240C6.5(D10:C4)480,45
C6.6(D10⋊C4) = Dic30⋊12C4φ: D10⋊C4/C2×Dic5 → C2 ⊆ Aut C6480C6.6(D10:C4)480,50
C6.7(D10⋊C4) = Dic30⋊15C4φ: D10⋊C4/C2×Dic5 → C2 ⊆ Aut C6480C6.7(D10:C4)480,51
C6.8(D10⋊C4) = D60⋊13C4φ: D10⋊C4/C2×Dic5 → C2 ⊆ Aut C61204C6.8(D10:C4)480,56
C6.9(D10⋊C4) = D60⋊16C4φ: D10⋊C4/C2×Dic5 → C2 ⊆ Aut C61204C6.9(D10:C4)480,57
C6.10(D10⋊C4) = C30.24C42φ: D10⋊C4/C2×Dic5 → C2 ⊆ Aut C6480C6.10(D10:C4)480,70
C6.11(D10⋊C4) = C15⋊9(C23⋊C4)φ: D10⋊C4/C2×Dic5 → C2 ⊆ Aut C61204C6.11(D10:C4)480,73
C6.12(D10⋊C4) = D60⋊7C4φ: D10⋊C4/C2×C20 → C2 ⊆ Aut C61202C6.12(D10:C4)480,165
C6.13(D10⋊C4) = C23.6D30φ: D10⋊C4/C2×C20 → C2 ⊆ Aut C61204C6.13(D10:C4)480,166
C6.14(D10⋊C4) = D60⋊9C4φ: D10⋊C4/C2×C20 → C2 ⊆ Aut C6240C6.14(D10:C4)480,169
C6.15(D10⋊C4) = Dic30⋊9C4φ: D10⋊C4/C2×C20 → C2 ⊆ Aut C6480C6.15(D10:C4)480,170
C6.16(D10⋊C4) = Dic30⋊8C4φ: D10⋊C4/C2×C20 → C2 ⊆ Aut C6480C6.16(D10:C4)480,176
C6.17(D10⋊C4) = D30⋊3C8φ: D10⋊C4/C2×C20 → C2 ⊆ Aut C6240C6.17(D10:C4)480,180
C6.18(D10⋊C4) = D60⋊8C4φ: D10⋊C4/C2×C20 → C2 ⊆ Aut C6240C6.18(D10:C4)480,181
C6.19(D10⋊C4) = M4(2)⋊D15φ: D10⋊C4/C2×C20 → C2 ⊆ Aut C61204+C6.19(D10:C4)480,183
C6.20(D10⋊C4) = C4.D60φ: D10⋊C4/C2×C20 → C2 ⊆ Aut C62404-C6.20(D10:C4)480,184
C6.21(D10⋊C4) = D60⋊10C4φ: D10⋊C4/C2×C20 → C2 ⊆ Aut C61204C6.21(D10:C4)480,185
C6.22(D10⋊C4) = C30.29C42φ: D10⋊C4/C2×C20 → C2 ⊆ Aut C6480C6.22(D10:C4)480,191
C6.23(D10⋊C4) = C60.93D4φ: D10⋊C4/C22×D5 → C2 ⊆ Aut C6240C6.23(D10:C4)480,31
C6.24(D10⋊C4) = C60.28D4φ: D10⋊C4/C22×D5 → C2 ⊆ Aut C61204C6.24(D10:C4)480,34
C6.25(D10⋊C4) = C12.6D20φ: D10⋊C4/C22×D5 → C2 ⊆ Aut C62404C6.25(D10:C4)480,37
C6.26(D10⋊C4) = C30.D8φ: D10⋊C4/C22×D5 → C2 ⊆ Aut C6240C6.26(D10:C4)480,40
C6.27(D10⋊C4) = C6.D40φ: D10⋊C4/C22×D5 → C2 ⊆ Aut C6240C6.27(D10:C4)480,41
C6.28(D10⋊C4) = C30.Q16φ: D10⋊C4/C22×D5 → C2 ⊆ Aut C6480C6.28(D10:C4)480,46
C6.29(D10⋊C4) = C6.Dic20φ: D10⋊C4/C22×D5 → C2 ⊆ Aut C6480C6.29(D10:C4)480,47
C6.30(D10⋊C4) = C60.96D4φ: D10⋊C4/C22×D5 → C2 ⊆ Aut C61204C6.30(D10:C4)480,52
C6.31(D10⋊C4) = C60.97D4φ: D10⋊C4/C22×D5 → C2 ⊆ Aut C61204C6.31(D10:C4)480,53
C6.32(D10⋊C4) = (C2×C6).D20φ: D10⋊C4/C22×D5 → C2 ⊆ Aut C61204C6.32(D10:C4)480,71
C6.33(D10⋊C4) = C3×D20⋊4C4central extension (φ=1)1202C6.33(D10:C4)480,83
C6.34(D10⋊C4) = C3×C23.1D10central extension (φ=1)1204C6.34(D10:C4)480,84
C6.35(D10⋊C4) = C3×D20⋊6C4central extension (φ=1)240C6.35(D10:C4)480,87
C6.36(D10⋊C4) = C3×C10.Q16central extension (φ=1)480C6.36(D10:C4)480,88
C6.37(D10⋊C4) = C3×C20.44D4central extension (φ=1)480C6.37(D10:C4)480,94
C6.38(D10⋊C4) = C3×D10⋊1C8central extension (φ=1)240C6.38(D10:C4)480,98
C6.39(D10⋊C4) = C3×D20⋊5C4central extension (φ=1)240C6.39(D10:C4)480,99
C6.40(D10⋊C4) = C3×C20.46D4central extension (φ=1)1204C6.40(D10:C4)480,101
C6.41(D10⋊C4) = C3×C4.12D20central extension (φ=1)2404C6.41(D10:C4)480,102
C6.42(D10⋊C4) = C3×D20⋊7C4central extension (φ=1)1204C6.42(D10:C4)480,103
C6.43(D10⋊C4) = C3×C10.10C42central extension (φ=1)480C6.43(D10:C4)480,109

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