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Extensions 1→N→G→Q→1 with N=C22 and Q=C2×C3⋊F5

Direct product G=N×Q with N=C22 and Q=C2×C3⋊F5
dρLabelID
C23×C3⋊F5120C2^3xC3:F5480,1206

Semidirect products G=N:Q with N=C22 and Q=C2×C3⋊F5
extensionφ:Q→Aut NdρLabelID
C22⋊(C2×C3⋊F5) = C2×A4⋊F5φ: C2×C3⋊F5/D10 → S3 ⊆ Aut C223012+C2^2:(C2xC3:F5)480,1191
C22⋊2(C2×C3⋊F5) = D4×C3⋊F5φ: C2×C3⋊F5/C3⋊F5 → C2 ⊆ Aut C22608C2^2:2(C2xC3:F5)480,1067
C22⋊3(C2×C3⋊F5) = C2×D10.D6φ: C2×C3⋊F5/C6×D5 → C2 ⊆ Aut C22120C2^2:3(C2xC3:F5)480,1072

Non-split extensions G=N.Q with N=C22 and Q=C2×C3⋊F5
extensionφ:Q→Aut NdρLabelID
C22.1(C2×C3⋊F5) = Dic10.Dic3φ: C2×C3⋊F5/C3⋊F5 → C2 ⊆ Aut C222408C2^2.1(C2xC3:F5)480,1066
C22.2(C2×C3⋊F5) = (C2×C60)⋊C4φ: C2×C3⋊F5/C6×D5 → C2 ⊆ Aut C221204C2^2.2(C2xC3:F5)480,304
C22.3(C2×C3⋊F5) = (C2×C60).C4φ: C2×C3⋊F5/C6×D5 → C2 ⊆ Aut C222404C2^2.3(C2xC3:F5)480,310
C22.4(C2×C3⋊F5) = C3⋊(C23⋊F5)φ: C2×C3⋊F5/C6×D5 → C2 ⊆ Aut C221204C2^2.4(C2xC3:F5)480,316
C22.5(C2×C3⋊F5) = C5⋊(C12.D4)φ: C2×C3⋊F5/C6×D5 → C2 ⊆ Aut C221204C2^2.5(C2xC3:F5)480,318
C22.6(C2×C3⋊F5) = C60.59(C2×C4)φ: C2×C3⋊F5/C6×D5 → C2 ⊆ Aut C221204C2^2.6(C2xC3:F5)480,1062
C22.7(C2×C3⋊F5) = (C2×C12)⋊6F5φ: C2×C3⋊F5/C6×D5 → C2 ⊆ Aut C221204C2^2.7(C2xC3:F5)480,1065
C22.8(C2×C3⋊F5) = C2×C15⋊8M4(2)φ: C2×C3⋊F5/C6×D5 → C2 ⊆ Aut C22240C2^2.8(C2xC3:F5)480,1071
C22.9(C2×C3⋊F5) = C4×C15⋊C8central extension (φ=1)480C2^2.9(C2xC3:F5)480,305
C22.10(C2×C3⋊F5) = C60⋊C8central extension (φ=1)480C2^2.10(C2xC3:F5)480,306
C22.11(C2×C3⋊F5) = C30.11C42central extension (φ=1)480C2^2.11(C2xC3:F5)480,307
C22.12(C2×C3⋊F5) = C30.7M4(2)central extension (φ=1)240C2^2.12(C2xC3:F5)480,308
C22.13(C2×C3⋊F5) = Dic5.13D12central extension (φ=1)480C2^2.13(C2xC3:F5)480,309
C22.14(C2×C3⋊F5) = D10.10D12central extension (φ=1)120C2^2.14(C2xC3:F5)480,311
C22.15(C2×C3⋊F5) = C30.22M4(2)central extension (φ=1)240C2^2.15(C2xC3:F5)480,317
C22.16(C2×C3⋊F5) = C2×C60.C4central extension (φ=1)240C2^2.16(C2xC3:F5)480,1060
C22.17(C2×C3⋊F5) = C2×C12.F5central extension (φ=1)240C2^2.17(C2xC3:F5)480,1061
C22.18(C2×C3⋊F5) = C2×C4×C3⋊F5central extension (φ=1)120C2^2.18(C2xC3:F5)480,1063
C22.19(C2×C3⋊F5) = C2×C60⋊C4central extension (φ=1)120C2^2.19(C2xC3:F5)480,1064
C22.20(C2×C3⋊F5) = C22×C15⋊C8central extension (φ=1)480C2^2.20(C2xC3:F5)480,1070

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