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Extensions 1→N→G→Q→1 with N=C4 and Q=C2×C3⋊F5

Direct product G=N×Q with N=C4 and Q=C2×C3⋊F5
dρLabelID
C2×C4×C3⋊F5120C2xC4xC3:F5480,1063

Semidirect products G=N:Q with N=C4 and Q=C2×C3⋊F5
extensionφ:Q→Aut NdρLabelID
C4⋊1(C2×C3⋊F5) = D4×C3⋊F5φ: C2×C3⋊F5/C3⋊F5 → C2 ⊆ Aut C4608C4:1(C2xC3:F5)480,1067
C4⋊2(C2×C3⋊F5) = C2×C60⋊C4φ: C2×C3⋊F5/C6×D5 → C2 ⊆ Aut C4120C4:2(C2xC3:F5)480,1064

Non-split extensions G=N.Q with N=C4 and Q=C2×C3⋊F5
extensionφ:Q→Aut NdρLabelID
C4.1(C2×C3⋊F5) = D20⋊Dic3φ: C2×C3⋊F5/C3⋊F5 → C2 ⊆ Aut C41208C4.1(C2xC3:F5)480,312
C4.2(C2×C3⋊F5) = Dic10⋊Dic3φ: C2×C3⋊F5/C3⋊F5 → C2 ⊆ Aut C41208C4.2(C2xC3:F5)480,313
C4.3(C2×C3⋊F5) = Dic10⋊2Dic3φ: C2×C3⋊F5/C3⋊F5 → C2 ⊆ Aut C41208C4.3(C2xC3:F5)480,314
C4.4(C2×C3⋊F5) = D20⋊2Dic3φ: C2×C3⋊F5/C3⋊F5 → C2 ⊆ Aut C41208C4.4(C2xC3:F5)480,315
C4.5(C2×C3⋊F5) = Dic10.Dic3φ: C2×C3⋊F5/C3⋊F5 → C2 ⊆ Aut C42408C4.5(C2xC3:F5)480,1066
C4.6(C2×C3⋊F5) = D20.Dic3φ: C2×C3⋊F5/C3⋊F5 → C2 ⊆ Aut C42408C4.6(C2xC3:F5)480,1068
C4.7(C2×C3⋊F5) = Q8×C3⋊F5φ: C2×C3⋊F5/C3⋊F5 → C2 ⊆ Aut C41208C4.7(C2xC3:F5)480,1069
C4.8(C2×C3⋊F5) = C120⋊C4φ: C2×C3⋊F5/C6×D5 → C2 ⊆ Aut C41204C4.8(C2xC3:F5)480,298
C4.9(C2×C3⋊F5) = D5.D24φ: C2×C3⋊F5/C6×D5 → C2 ⊆ Aut C41204C4.9(C2xC3:F5)480,299
C4.10(C2×C3⋊F5) = C40.Dic3φ: C2×C3⋊F5/C6×D5 → C2 ⊆ Aut C42404C4.10(C2xC3:F5)480,300
C4.11(C2×C3⋊F5) = C24.1F5φ: C2×C3⋊F5/C6×D5 → C2 ⊆ Aut C42404C4.11(C2xC3:F5)480,301
C4.12(C2×C3⋊F5) = C2×C12.F5φ: C2×C3⋊F5/C6×D5 → C2 ⊆ Aut C4240C4.12(C2xC3:F5)480,1061
C4.13(C2×C3⋊F5) = C24.F5central extension (φ=1)2404C4.13(C2xC3:F5)480,294
C4.14(C2×C3⋊F5) = C120.C4central extension (φ=1)2404C4.14(C2xC3:F5)480,295
C4.15(C2×C3⋊F5) = C8×C3⋊F5central extension (φ=1)1204C4.15(C2xC3:F5)480,296
C4.16(C2×C3⋊F5) = C24⋊F5central extension (φ=1)1204C4.16(C2xC3:F5)480,297
C4.17(C2×C3⋊F5) = C2×C15⋊C16central extension (φ=1)480C4.17(C2xC3:F5)480,302
C4.18(C2×C3⋊F5) = C60.C8central extension (φ=1)2404C4.18(C2xC3:F5)480,303
C4.19(C2×C3⋊F5) = C2×C60.C4central extension (φ=1)240C4.19(C2xC3:F5)480,1060
C4.20(C2×C3⋊F5) = C60.59(C2×C4)central extension (φ=1)1204C4.20(C2xC3:F5)480,1062
C4.21(C2×C3⋊F5) = (C2×C12)⋊6F5central extension (φ=1)1204C4.21(C2xC3:F5)480,1065

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