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Extensions 1→N→G→Q→1 with N=C4 and Q=C3⋊D20

Direct product G=N×Q with N=C4 and Q=C3⋊D20
dρLabelID
C4×C3⋊D20240C4xC3:D20480,519

Semidirect products G=N:Q with N=C4 and Q=C3⋊D20
extensionφ:Q→Aut NdρLabelID
C4⋊1(C3⋊D20) = C12⋊D20φ: C3⋊D20/C5×Dic3 → C2 ⊆ Aut C4240C4:1(C3:D20)480,534
C4⋊2(C3⋊D20) = C12⋊7D20φ: C3⋊D20/C6×D5 → C2 ⊆ Aut C4240C4:2(C3:D20)480,526
C4⋊3(C3⋊D20) = C12⋊2D20φ: C3⋊D20/D30 → C2 ⊆ Aut C4240C4:3(C3:D20)480,541

Non-split extensions G=N.Q with N=C4 and Q=C3⋊D20
extensionφ:Q→Aut NdρLabelID
C4.1(C3⋊D20) = C3⋊D80φ: C3⋊D20/C5×Dic3 → C2 ⊆ Aut C42404+C4.1(C3:D20)480,14
C4.2(C3⋊D20) = D40.S3φ: C3⋊D20/C5×Dic3 → C2 ⊆ Aut C42404-C4.2(C3:D20)480,18
C4.3(C3⋊D20) = C24.D10φ: C3⋊D20/C5×Dic3 → C2 ⊆ Aut C42404+C4.3(C3:D20)480,19
C4.4(C3⋊D20) = C3⋊Dic40φ: C3⋊D20/C5×Dic3 → C2 ⊆ Aut C44804-C4.4(C3:D20)480,23
C4.5(C3⋊D20) = C2×C3⋊D40φ: C3⋊D20/C5×Dic3 → C2 ⊆ Aut C4240C4.5(C3:D20)480,376
C4.6(C3⋊D20) = C2×C6.D20φ: C3⋊D20/C5×Dic3 → C2 ⊆ Aut C4240C4.6(C3:D20)480,386
C4.7(C3⋊D20) = C2×C15⋊SD16φ: C3⋊D20/C5×Dic3 → C2 ⊆ Aut C4240C4.7(C3:D20)480,390
C4.8(C3⋊D20) = C2×C3⋊Dic20φ: C3⋊D20/C5×Dic3 → C2 ⊆ Aut C4480C4.8(C3:D20)480,395
C4.9(C3⋊D20) = C60.44D4φ: C3⋊D20/C5×Dic3 → C2 ⊆ Aut C4240C4.9(C3:D20)480,440
C4.10(C3⋊D20) = C60.47D4φ: C3⋊D20/C5×Dic3 → C2 ⊆ Aut C4240C4.10(C3:D20)480,450
C4.11(C3⋊D20) = C60.48D4φ: C3⋊D20/C5×Dic3 → C2 ⊆ Aut C4480C4.11(C3:D20)480,465
C4.12(C3⋊D20) = C60.29D4φ: C3⋊D20/C6×D5 → C2 ⊆ Aut C41204+C4.12(C3:D20)480,36
C4.13(C3⋊D20) = C60.31D4φ: C3⋊D20/C6×D5 → C2 ⊆ Aut C42404-C4.13(C3:D20)480,39
C4.14(C3⋊D20) = D60⋊15C4φ: C3⋊D20/C6×D5 → C2 ⊆ Aut C4240C4.14(C3:D20)480,45
C4.15(C3⋊D20) = Dic30⋊15C4φ: C3⋊D20/C6×D5 → C2 ⊆ Aut C4480C4.15(C3:D20)480,51
C4.16(C3⋊D20) = D20⋊19D6φ: C3⋊D20/C6×D5 → C2 ⊆ Aut C41204+C4.16(C3:D20)480,377
C4.17(C3⋊D20) = C60.63D4φ: C3⋊D20/C6×D5 → C2 ⊆ Aut C42404-C4.17(C3:D20)480,389
C4.18(C3⋊D20) = C60.68D4φ: C3⋊D20/C6×D5 → C2 ⊆ Aut C4240C4.18(C3:D20)480,436
C4.19(C3⋊D20) = C60.28D4φ: C3⋊D20/D30 → C2 ⊆ Aut C41204C4.19(C3:D20)480,34
C4.20(C3⋊D20) = C12.6D20φ: C3⋊D20/D30 → C2 ⊆ Aut C42404C4.20(C3:D20)480,37
C4.21(C3⋊D20) = C30.D8φ: C3⋊D20/D30 → C2 ⊆ Aut C4240C4.21(C3:D20)480,40
C4.22(C3⋊D20) = C30.Q16φ: C3⋊D20/D30 → C2 ⊆ Aut C4480C4.22(C3:D20)480,46
C4.23(C3⋊D20) = D60⋊30C22φ: C3⋊D20/D30 → C2 ⊆ Aut C41204C4.23(C3:D20)480,388
C4.24(C3⋊D20) = C12.D20φ: C3⋊D20/D30 → C2 ⊆ Aut C42404C4.24(C3:D20)480,391
C4.25(C3⋊D20) = D30⋊10Q8φ: C3⋊D20/D30 → C2 ⊆ Aut C4240C4.25(C3:D20)480,466
C4.26(C3⋊D20) = C60.93D4central extension (φ=1)240C4.26(C3:D20)480,31
C4.27(C3⋊D20) = D30⋊4C8central extension (φ=1)240C4.27(C3:D20)480,33
C4.28(C3⋊D20) = C60.97D4central extension (φ=1)1204C4.28(C3:D20)480,53
C4.29(C3⋊D20) = D60⋊13C4central extension (φ=1)1204C4.29(C3:D20)480,56
C4.30(C3⋊D20) = C60.15Q8central extension (φ=1)480C4.30(C3:D20)480,60
C4.31(C3⋊D20) = C12.59D20central extension (φ=1)2404C4.31(C3:D20)480,69
C4.32(C3⋊D20) = D20.31D6central extension (φ=1)2404C4.32(C3:D20)480,387

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