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Extensions 1→N→G→Q→1 with N=C12 and Q=C4×D5

Direct product G=N×Q with N=C12 and Q=C4×D5
dρLabelID
D5×C4×C12240D5xC4xC12480,664

Semidirect products G=N:Q with N=C12 and Q=C4×D5
extensionφ:Q→Aut NdρLabelID
C12⋊1(C4×D5) = Dic3×D20φ: C4×D5/C10 → C22 ⊆ Aut C12240C12:1(C4xD5)480,501
C12⋊2(C4×D5) = D60⋊14C4φ: C4×D5/C10 → C22 ⊆ Aut C12240C12:2(C4xD5)480,504
C12⋊3(C4×D5) = D20⋊8Dic3φ: C4×D5/C10 → C22 ⊆ Aut C12240C12:3(C4xD5)480,510
C12⋊4(C4×D5) = D30.2Q8φ: C4×D5/C10 → C22 ⊆ Aut C12240C12:4(C4xD5)480,513
C12⋊5(C4×D5) = C4⋊C4×D15φ: C4×D5/C10 → C22 ⊆ Aut C12240C12:5(C4xD5)480,856
C12⋊6(C4×D5) = D60⋊11C4φ: C4×D5/C10 → C22 ⊆ Aut C12240C12:6(C4xD5)480,858
C12⋊7(C4×D5) = D60⋊17C4φ: C4×D5/Dic5 → C2 ⊆ Aut C12240C12:7(C4xD5)480,494
C12⋊8(C4×D5) = C4×D30.C2φ: C4×D5/Dic5 → C2 ⊆ Aut C12240C12:8(C4xD5)480,477
C12⋊9(C4×D5) = C3×D20⋊8C4φ: C4×D5/Dic5 → C2 ⊆ Aut C12240C12:9(C4xD5)480,686
C12⋊10(C4×D5) = C4×D60φ: C4×D5/C20 → C2 ⊆ Aut C12240C12:10(C4xD5)480,838
C12⋊11(C4×D5) = C42×D15φ: C4×D5/C20 → C2 ⊆ Aut C12240C12:11(C4xD5)480,836
C12⋊12(C4×D5) = C12×D20φ: C4×D5/C20 → C2 ⊆ Aut C12240C12:12(C4xD5)480,666
C12⋊13(C4×D5) = D5×C4⋊Dic3φ: C4×D5/D10 → C2 ⊆ Aut C12240C12:13(C4xD5)480,488
C12⋊14(C4×D5) = C4×D5×Dic3φ: C4×D5/D10 → C2 ⊆ Aut C12240C12:14(C4xD5)480,467
C12⋊15(C4×D5) = C3×D5×C4⋊C4φ: C4×D5/D10 → C2 ⊆ Aut C12240C12:15(C4xD5)480,684

Non-split extensions G=N.Q with N=C12 and Q=C4×D5
extensionφ:Q→Aut NdρLabelID
C12.1(C4×D5) = C30.D8φ: C4×D5/C10 → C22 ⊆ Aut C12240C12.1(C4xD5)480,40
C12.2(C4×D5) = C6.D40φ: C4×D5/C10 → C22 ⊆ Aut C12240C12.2(C4xD5)480,41
C12.3(C4×D5) = D60⋊12C4φ: C4×D5/C10 → C22 ⊆ Aut C12240C12.3(C4xD5)480,44
C12.4(C4×D5) = C30.Q16φ: C4×D5/C10 → C22 ⊆ Aut C12480C12.4(C4xD5)480,46
C12.5(C4×D5) = C6.Dic20φ: C4×D5/C10 → C22 ⊆ Aut C12480C12.5(C4xD5)480,47
C12.6(C4×D5) = Dic30⋊12C4φ: C4×D5/C10 → C22 ⊆ Aut C12480C12.6(C4xD5)480,50
C12.7(C4×D5) = C60.96D4φ: C4×D5/C10 → C22 ⊆ Aut C121204C12.7(C4xD5)480,52
C12.8(C4×D5) = C60.97D4φ: C4×D5/C10 → C22 ⊆ Aut C121204C12.8(C4xD5)480,53
C12.9(C4×D5) = D60⋊13C4φ: C4×D5/C10 → C22 ⊆ Aut C121204C12.9(C4xD5)480,56
C12.10(C4×D5) = C30.SD16φ: C4×D5/C10 → C22 ⊆ Aut C12480C12.10(C4xD5)480,62
C12.11(C4×D5) = C30.20D8φ: C4×D5/C10 → C22 ⊆ Aut C12480C12.11(C4xD5)480,65
C12.12(C4×D5) = C60.D4φ: C4×D5/C10 → C22 ⊆ Aut C122404C12.12(C4xD5)480,68
C12.13(C4×D5) = C60.1Q8φ: C4×D5/C10 → C22 ⊆ Aut C12480C12.13(C4xD5)480,167
C12.14(C4×D5) = C60.2Q8φ: C4×D5/C10 → C22 ⊆ Aut C12480C12.14(C4xD5)480,168
C12.15(C4×D5) = D60⋊9C4φ: C4×D5/C10 → C22 ⊆ Aut C12240C12.15(C4xD5)480,169
C12.16(C4×D5) = Dic30⋊9C4φ: C4×D5/C10 → C22 ⊆ Aut C12480C12.16(C4xD5)480,170
C12.17(C4×D5) = C60.210D4φ: C4×D5/C10 → C22 ⊆ Aut C122404C12.17(C4xD5)480,182
C12.18(C4×D5) = D60⋊10C4φ: C4×D5/C10 → C22 ⊆ Aut C121204C12.18(C4xD5)480,185
C12.19(C4×D5) = D20.3Dic3φ: C4×D5/C10 → C22 ⊆ Aut C122404C12.19(C4xD5)480,359
C12.20(C4×D5) = D20.2Dic3φ: C4×D5/C10 → C22 ⊆ Aut C122404C12.20(C4xD5)480,360
C12.21(C4×D5) = D60.4C4φ: C4×D5/C10 → C22 ⊆ Aut C122404C12.21(C4xD5)480,367
C12.22(C4×D5) = D15⋊4M4(2)φ: C4×D5/C10 → C22 ⊆ Aut C121204C12.22(C4xD5)480,368
C12.23(C4×D5) = Dic3×Dic10φ: C4×D5/C10 → C22 ⊆ Aut C12480C12.23(C4xD5)480,406
C12.24(C4×D5) = Dic15⋊6Q8φ: C4×D5/C10 → C22 ⊆ Aut C12480C12.24(C4xD5)480,407
C12.25(C4×D5) = Dic30⋊14C4φ: C4×D5/C10 → C22 ⊆ Aut C12480C12.25(C4xD5)480,416
C12.26(C4×D5) = (C4×D15)⋊8C4φ: C4×D5/C10 → C22 ⊆ Aut C12240C12.26(C4xD5)480,423
C12.27(C4×D5) = Dic15⋊10Q8φ: C4×D5/C10 → C22 ⊆ Aut C12480C12.27(C4xD5)480,852
C12.28(C4×D5) = C4⋊C4⋊7D15φ: C4×D5/C10 → C22 ⊆ Aut C12240C12.28(C4xD5)480,857
C12.29(C4×D5) = M4(2)×D15φ: C4×D5/C10 → C22 ⊆ Aut C121204C12.29(C4xD5)480,871
C12.30(C4×D5) = D60.3C4φ: C4×D5/C10 → C22 ⊆ Aut C122404C12.30(C4xD5)480,872
C12.31(C4×D5) = D60⋊15C4φ: C4×D5/Dic5 → C2 ⊆ Aut C12240C12.31(C4xD5)480,45
C12.32(C4×D5) = Dic30⋊15C4φ: C4×D5/Dic5 → C2 ⊆ Aut C12480C12.32(C4xD5)480,51
C12.33(C4×D5) = D60⋊16C4φ: C4×D5/Dic5 → C2 ⊆ Aut C121204C12.33(C4xD5)480,57
C12.34(C4×D5) = D60.5C4φ: C4×D5/Dic5 → C2 ⊆ Aut C122404C12.34(C4xD5)480,366
C12.35(C4×D5) = Dic30⋊17C4φ: C4×D5/Dic5 → C2 ⊆ Aut C12480C12.35(C4xD5)480,409
C12.36(C4×D5) = D15⋊2C16φ: C4×D5/Dic5 → C2 ⊆ Aut C122404C12.36(C4xD5)480,9
C12.37(C4×D5) = D30.5C8φ: C4×D5/Dic5 → C2 ⊆ Aut C122404C12.37(C4xD5)480,12
C12.38(C4×D5) = Dic5×C3⋊C8φ: C4×D5/Dic5 → C2 ⊆ Aut C12480C12.38(C4xD5)480,25
C12.39(C4×D5) = C30.21C42φ: C4×D5/Dic5 → C2 ⊆ Aut C12480C12.39(C4xD5)480,28
C12.40(C4×D5) = C30.22C42φ: C4×D5/Dic5 → C2 ⊆ Aut C12480C12.40(C4xD5)480,29
C12.41(C4×D5) = C2×D15⋊2C8φ: C4×D5/Dic5 → C2 ⊆ Aut C12240C12.41(C4xD5)480,365
C12.42(C4×D5) = C2×D30.5C4φ: C4×D5/Dic5 → C2 ⊆ Aut C12240C12.42(C4xD5)480,371
C12.43(C4×D5) = (C4×D15)⋊10C4φ: C4×D5/Dic5 → C2 ⊆ Aut C12240C12.43(C4xD5)480,462
C12.44(C4×D5) = C3×D20⋊6C4φ: C4×D5/Dic5 → C2 ⊆ Aut C12240C12.44(C4xD5)480,87
C12.45(C4×D5) = C3×C10.Q16φ: C4×D5/Dic5 → C2 ⊆ Aut C12480C12.45(C4xD5)480,88
C12.46(C4×D5) = C3×D20⋊7C4φ: C4×D5/Dic5 → C2 ⊆ Aut C121204C12.46(C4xD5)480,103
C12.47(C4×D5) = C3×Dic5⋊3Q8φ: C4×D5/Dic5 → C2 ⊆ Aut C12480C12.47(C4xD5)480,680
C12.48(C4×D5) = C3×D20.2C4φ: C4×D5/Dic5 → C2 ⊆ Aut C122404C12.48(C4xD5)480,700
C12.49(C4×D5) = D60⋊7C4φ: C4×D5/C20 → C2 ⊆ Aut C121202C12.49(C4xD5)480,165
C12.50(C4×D5) = Dic30⋊8C4φ: C4×D5/C20 → C2 ⊆ Aut C12480C12.50(C4xD5)480,176
C12.51(C4×D5) = D60⋊8C4φ: C4×D5/C20 → C2 ⊆ Aut C12240C12.51(C4xD5)480,181
C12.52(C4×D5) = C4×Dic30φ: C4×D5/C20 → C2 ⊆ Aut C12480C12.52(C4xD5)480,833
C12.53(C4×D5) = D60.6C4φ: C4×D5/C20 → C2 ⊆ Aut C122402C12.53(C4xD5)480,866
C12.54(C4×D5) = C16×D15φ: C4×D5/C20 → C2 ⊆ Aut C122402C12.54(C4xD5)480,157
C12.55(C4×D5) = C80⋊S3φ: C4×D5/C20 → C2 ⊆ Aut C122402C12.55(C4xD5)480,158
C12.56(C4×D5) = C4×C15⋊3C8φ: C4×D5/C20 → C2 ⊆ Aut C12480C12.56(C4xD5)480,162
C12.57(C4×D5) = C42.D15φ: C4×D5/C20 → C2 ⊆ Aut C12480C12.57(C4xD5)480,163
C12.58(C4×D5) = C8×Dic15φ: C4×D5/C20 → C2 ⊆ Aut C12480C12.58(C4xD5)480,173
C12.59(C4×D5) = C120⋊13C4φ: C4×D5/C20 → C2 ⊆ Aut C12480C12.59(C4xD5)480,175
C12.60(C4×D5) = C42⋊2D15φ: C4×D5/C20 → C2 ⊆ Aut C12240C12.60(C4xD5)480,837
C12.61(C4×D5) = C2×C8×D15φ: C4×D5/C20 → C2 ⊆ Aut C12240C12.61(C4xD5)480,864
C12.62(C4×D5) = C2×C40⋊S3φ: C4×D5/C20 → C2 ⊆ Aut C12240C12.62(C4xD5)480,865
C12.63(C4×D5) = C3×D20⋊4C4φ: C4×D5/C20 → C2 ⊆ Aut C121202C12.63(C4xD5)480,83
C12.64(C4×D5) = C3×C20.44D4φ: C4×D5/C20 → C2 ⊆ Aut C12480C12.64(C4xD5)480,94
C12.65(C4×D5) = C3×D20⋊5C4φ: C4×D5/C20 → C2 ⊆ Aut C12240C12.65(C4xD5)480,99
C12.66(C4×D5) = C12×Dic10φ: C4×D5/C20 → C2 ⊆ Aut C12480C12.66(C4xD5)480,661
C12.67(C4×D5) = C3×D20.3C4φ: C4×D5/C20 → C2 ⊆ Aut C122402C12.67(C4xD5)480,694
C12.68(C4×D5) = C60.7Q8φ: C4×D5/D10 → C2 ⊆ Aut C12480C12.68(C4xD5)480,61
C12.69(C4×D5) = C60.8Q8φ: C4×D5/D10 → C2 ⊆ Aut C12480C12.69(C4xD5)480,64
C12.70(C4×D5) = C60.105D4φ: C4×D5/D10 → C2 ⊆ Aut C122404C12.70(C4xD5)480,67
C12.71(C4×D5) = D5×C4.Dic3φ: C4×D5/D10 → C2 ⊆ Aut C121204C12.71(C4xD5)480,358
C12.72(C4×D5) = (C4×D5)⋊Dic3φ: C4×D5/D10 → C2 ⊆ Aut C12240C12.72(C4xD5)480,434
C12.73(C4×D5) = D5×C3⋊C16φ: C4×D5/D10 → C2 ⊆ Aut C122404C12.73(C4xD5)480,7
C12.74(C4×D5) = C40.51D6φ: C4×D5/D10 → C2 ⊆ Aut C122404C12.74(C4xD5)480,10
C12.75(C4×D5) = Dic3×C5⋊2C8φ: C4×D5/D10 → C2 ⊆ Aut C12480C12.75(C4xD5)480,26
C12.76(C4×D5) = Dic15⋊4C8φ: C4×D5/D10 → C2 ⊆ Aut C12480C12.76(C4xD5)480,27
C12.77(C4×D5) = C30.23C42φ: C4×D5/D10 → C2 ⊆ Aut C12480C12.77(C4xD5)480,30
C12.78(C4×D5) = C2×D5×C3⋊C8φ: C4×D5/D10 → C2 ⊆ Aut C12240C12.78(C4xD5)480,357
C12.79(C4×D5) = C2×C20.32D6φ: C4×D5/D10 → C2 ⊆ Aut C12240C12.79(C4xD5)480,369
C12.80(C4×D5) = (D5×C12)⋊C4φ: C4×D5/D10 → C2 ⊆ Aut C12240C12.80(C4xD5)480,433
C12.81(C4×D5) = C3×C10.D8φ: C4×D5/D10 → C2 ⊆ Aut C12480C12.81(C4xD5)480,85
C12.82(C4×D5) = C3×C20.Q8φ: C4×D5/D10 → C2 ⊆ Aut C12480C12.82(C4xD5)480,86
C12.83(C4×D5) = C3×C20.53D4φ: C4×D5/D10 → C2 ⊆ Aut C122404C12.83(C4xD5)480,100
C12.84(C4×D5) = C3×C4⋊C4⋊7D5φ: C4×D5/D10 → C2 ⊆ Aut C12240C12.84(C4xD5)480,685
C12.85(C4×D5) = C3×D5×M4(2)φ: C4×D5/D10 → C2 ⊆ Aut C121204C12.85(C4xD5)480,699
C12.86(C4×D5) = D5×C48central extension (φ=1)2402C12.86(C4xD5)480,75
C12.87(C4×D5) = C3×C80⋊C2central extension (φ=1)2402C12.87(C4xD5)480,76
C12.88(C4×D5) = C12×C5⋊2C8central extension (φ=1)480C12.88(C4xD5)480,80
C12.89(C4×D5) = C3×C42.D5central extension (φ=1)480C12.89(C4xD5)480,81
C12.90(C4×D5) = Dic5×C24central extension (φ=1)480C12.90(C4xD5)480,91
C12.91(C4×D5) = C3×C40⋊8C4central extension (φ=1)480C12.91(C4xD5)480,93
C12.92(C4×D5) = C3×C42⋊D5central extension (φ=1)240C12.92(C4xD5)480,665
C12.93(C4×D5) = D5×C2×C24central extension (φ=1)240C12.93(C4xD5)480,692
C12.94(C4×D5) = C6×C8⋊D5central extension (φ=1)240C12.94(C4xD5)480,693

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