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

Direct product G=N×Q with N=C4 and Q=D10⋊C4
dρLabelID
C4×D10⋊C4160C4xD10:C4320,565

Semidirect products G=N:Q with N=C4 and Q=D10⋊C4
extensionφ:Q→Aut NdρLabelID
C41(D10⋊C4) = (C2×D20)⋊22C4φ: D10⋊C4/C2×Dic5C2 ⊆ Aut C4160C4:1(D10:C4)320,615
C42(D10⋊C4) = (C2×C4)⋊6D20φ: D10⋊C4/C2×C20C2 ⊆ Aut C4160C4:2(D10:C4)320,566
C43(D10⋊C4) = D104(C4⋊C4)φ: D10⋊C4/C22×D5C2 ⊆ Aut C4160C4:3(D10:C4)320,614

Non-split extensions G=N.Q with N=C4 and Q=D10⋊C4
extensionφ:Q→Aut NdρLabelID
C4.1(D10⋊C4) = D4014C4φ: D10⋊C4/C2×Dic5C2 ⊆ Aut C4804C4.1(D10:C4)320,46
C4.2(D10⋊C4) = C40.5D4φ: D10⋊C4/C2×Dic5C2 ⊆ Aut C4160C4.2(D10:C4)320,49
C4.3(D10⋊C4) = C10.Q32φ: D10⋊C4/C2×Dic5C2 ⊆ Aut C4320C4.3(D10:C4)320,50
C4.4(D10⋊C4) = D40.6C4φ: D10⋊C4/C2×Dic5C2 ⊆ Aut C4804+C4.4(D10:C4)320,53
C4.5(D10⋊C4) = C40.8D4φ: D10⋊C4/C2×Dic5C2 ⊆ Aut C41604-C4.5(D10:C4)320,54
C4.6(D10⋊C4) = D40.5C4φ: D10⋊C4/C2×Dic5C2 ⊆ Aut C41604C4.6(D10:C4)320,55
C4.7(D10⋊C4) = C2×D206C4φ: D10⋊C4/C2×Dic5C2 ⊆ Aut C4160C4.7(D10:C4)320,592
C4.8(D10⋊C4) = C2×C10.Q16φ: D10⋊C4/C2×Dic5C2 ⊆ Aut C4320C4.8(D10:C4)320,596
C4.9(D10⋊C4) = (C2×Dic5)⋊6Q8φ: D10⋊C4/C2×Dic5C2 ⊆ Aut C4320C4.9(D10:C4)320,601
C4.10(D10⋊C4) = C424D10φ: D10⋊C4/C2×Dic5C2 ⊆ Aut C4804C4.10(D10:C4)320,632
C4.11(D10⋊C4) = C23.46D20φ: D10⋊C4/C2×Dic5C2 ⊆ Aut C4160C4.11(D10:C4)320,747
C4.12(D10⋊C4) = C4.89(C2×D20)φ: D10⋊C4/C2×Dic5C2 ⊆ Aut C4160C4.12(D10:C4)320,756
C4.13(D10⋊C4) = C23.48D20φ: D10⋊C4/C2×Dic5C2 ⊆ Aut C480C4.13(D10:C4)320,758
C4.14(D10⋊C4) = C2×D207C4φ: D10⋊C4/C2×Dic5C2 ⊆ Aut C480C4.14(D10:C4)320,765
C4.15(D10⋊C4) = C40.78D4φ: D10⋊C4/C2×C20C2 ⊆ Aut C4320C4.15(D10:C4)320,61
C4.16(D10⋊C4) = D407C4φ: D10⋊C4/C2×C20C2 ⊆ Aut C4160C4.16(D10:C4)320,67
C4.17(D10⋊C4) = D40.3C4φ: D10⋊C4/C2×C20C2 ⊆ Aut C41602C4.17(D10:C4)320,68
C4.18(D10⋊C4) = D40.4C4φ: D10⋊C4/C2×C20C2 ⊆ Aut C4804+C4.18(D10:C4)320,74
C4.19(D10⋊C4) = C20.4D8φ: D10⋊C4/C2×C20C2 ⊆ Aut C41604-C4.19(D10:C4)320,75
C4.20(D10⋊C4) = D408C4φ: D10⋊C4/C2×C20C2 ⊆ Aut C4804C4.20(D10:C4)320,76
C4.21(D10⋊C4) = C2×D204C4φ: D10⋊C4/C2×C20C2 ⊆ Aut C480C4.21(D10:C4)320,554
C4.22(D10⋊C4) = (C2×C20)⋊10Q8φ: D10⋊C4/C2×C20C2 ⊆ Aut C4320C4.22(D10:C4)320,556
C4.23(D10⋊C4) = C4⋊C436D10φ: D10⋊C4/C2×C20C2 ⊆ Aut C480C4.23(D10:C4)320,628
C4.24(D10⋊C4) = C4.(C2×D20)φ: D10⋊C4/C2×C20C2 ⊆ Aut C4160C4.24(D10:C4)320,631
C4.25(D10⋊C4) = C2×C20.44D4φ: D10⋊C4/C2×C20C2 ⊆ Aut C4320C4.25(D10:C4)320,730
C4.26(D10⋊C4) = (C22×C8)⋊D5φ: D10⋊C4/C2×C20C2 ⊆ Aut C4160C4.26(D10:C4)320,737
C4.27(D10⋊C4) = C2×D205C4φ: D10⋊C4/C2×C20C2 ⊆ Aut C4160C4.27(D10:C4)320,739
C4.28(D10⋊C4) = C2×C20.46D4φ: D10⋊C4/C2×C20C2 ⊆ Aut C480C4.28(D10:C4)320,757
C4.29(D10⋊C4) = C2×C4.12D20φ: D10⋊C4/C2×C20C2 ⊆ Aut C4160C4.29(D10:C4)320,763
C4.30(D10⋊C4) = C23.20D20φ: D10⋊C4/C2×C20C2 ⊆ Aut C4804C4.30(D10:C4)320,766
C4.31(D10⋊C4) = C20.31C42φ: D10⋊C4/C22×D5C2 ⊆ Aut C4320C4.31(D10:C4)320,87
C4.32(D10⋊C4) = (C2×C20).Q8φ: D10⋊C4/C22×D5C2 ⊆ Aut C4160C4.32(D10:C4)320,88
C4.33(D10⋊C4) = C421Dic5φ: D10⋊C4/C22×D5C2 ⊆ Aut C4804C4.33(D10:C4)320,89
C4.34(D10⋊C4) = M4(2)⋊Dic5φ: D10⋊C4/C22×D5C2 ⊆ Aut C4160C4.34(D10:C4)320,112
C4.35(D10⋊C4) = (C2×C40)⋊C4φ: D10⋊C4/C22×D5C2 ⊆ Aut C4804C4.35(D10:C4)320,114
C4.36(D10⋊C4) = C20.51C42φ: D10⋊C4/C22×D5C2 ⊆ Aut C4804C4.36(D10:C4)320,118
C4.37(D10⋊C4) = C4○D209C4φ: D10⋊C4/C22×D5C2 ⊆ Aut C4160C4.37(D10:C4)320,593
C4.38(D10⋊C4) = D108M4(2)φ: D10⋊C4/C22×D5C2 ⊆ Aut C480C4.38(D10:C4)320,753
C4.39(D10⋊C4) = C23.49D20φ: D10⋊C4/C22×D5C2 ⊆ Aut C4160C4.39(D10:C4)320,760
C4.40(D10⋊C4) = D101C16central extension (φ=1)160C4.40(D10:C4)320,65
C4.41(D10⋊C4) = D20.3C8central extension (φ=1)1602C4.41(D10:C4)320,66
C4.42(D10⋊C4) = C8.25D20central extension (φ=1)804C4.42(D10:C4)320,72
C4.43(D10⋊C4) = D20.4C8central extension (φ=1)1604C4.43(D10:C4)320,73
C4.44(D10⋊C4) = C426Dic5central extension (φ=1)80C4.44(D10:C4)320,81
C4.45(D10⋊C4) = (C2×C20)⋊8C8central extension (φ=1)320C4.45(D10:C4)320,82
C4.46(D10⋊C4) = C20.32C42central extension (φ=1)80C4.46(D10:C4)320,90
C4.47(D10⋊C4) = C20.60(C4⋊C4)central extension (φ=1)804C4.47(D10:C4)320,91
C4.48(D10⋊C4) = (C2×C40)⋊15C4central extension (φ=1)320C4.48(D10:C4)320,108
C4.49(D10⋊C4) = C20.40C42central extension (φ=1)160C4.49(D10:C4)320,110
C4.50(D10⋊C4) = C20.34C42central extension (φ=1)160C4.50(D10:C4)320,116
C4.51(D10⋊C4) = M4(2)⋊4Dic5central extension (φ=1)804C4.51(D10:C4)320,117
C4.52(D10⋊C4) = C4○D2010C4central extension (φ=1)160C4.52(D10:C4)320,629
C4.53(D10⋊C4) = (C2×D20)⋊25C4central extension (φ=1)804C4.53(D10:C4)320,633
C4.54(D10⋊C4) = C2×D101C8central extension (φ=1)160C4.54(D10:C4)320,735
C4.55(D10⋊C4) = C23.23D20central extension (φ=1)160C4.55(D10:C4)320,740
C4.56(D10⋊C4) = M4(2).31D10central extension (φ=1)804C4.56(D10:C4)320,759

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