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Extensions 1→N→G→Q→1 with N=C6 and Q=C2×C5⋊C8

Direct product G=N×Q with N=C6 and Q=C2×C5⋊C8
dρLabelID
C2×C6×C5⋊C8480C2xC6xC5:C8480,1057

Semidirect products G=N:Q with N=C6 and Q=C2×C5⋊C8
extensionφ:Q→Aut NdρLabelID
C6⋊1(C2×C5⋊C8) = C2×S3×C5⋊C8φ: C2×C5⋊C8/C5⋊C8 → C2 ⊆ Aut C6240C6:1(C2xC5:C8)480,1002
C6⋊2(C2×C5⋊C8) = C22×C15⋊C8φ: C2×C5⋊C8/C2×Dic5 → C2 ⊆ Aut C6480C6:2(C2xC5:C8)480,1070

Non-split extensions G=N.Q with N=C6 and Q=C2×C5⋊C8
extensionφ:Q→Aut NdρLabelID
C6.1(C2×C5⋊C8) = S3×C5⋊C16φ: C2×C5⋊C8/C5⋊C8 → C2 ⊆ Aut C62408C6.1(C2xC5:C8)480,239
C6.2(C2×C5⋊C8) = C15⋊M5(2)φ: C2×C5⋊C8/C5⋊C8 → C2 ⊆ Aut C62408C6.2(C2xC5:C8)480,241
C6.3(C2×C5⋊C8) = Dic3×C5⋊C8φ: C2×C5⋊C8/C5⋊C8 → C2 ⊆ Aut C6480C6.3(C2xC5:C8)480,244
C6.4(C2×C5⋊C8) = Dic5.22D12φ: C2×C5⋊C8/C5⋊C8 → C2 ⊆ Aut C6240C6.4(C2xC5:C8)480,246
C6.5(C2×C5⋊C8) = C30.4M4(2)φ: C2×C5⋊C8/C5⋊C8 → C2 ⊆ Aut C6480C6.5(C2xC5:C8)480,252
C6.6(C2×C5⋊C8) = C2×C15⋊C16φ: C2×C5⋊C8/C2×Dic5 → C2 ⊆ Aut C6480C6.6(C2xC5:C8)480,302
C6.7(C2×C5⋊C8) = C60.C8φ: C2×C5⋊C8/C2×Dic5 → C2 ⊆ Aut C62404C6.7(C2xC5:C8)480,303
C6.8(C2×C5⋊C8) = C4×C15⋊C8φ: C2×C5⋊C8/C2×Dic5 → C2 ⊆ Aut C6480C6.8(C2xC5:C8)480,305
C6.9(C2×C5⋊C8) = C60⋊C8φ: C2×C5⋊C8/C2×Dic5 → C2 ⊆ Aut C6480C6.9(C2xC5:C8)480,306
C6.10(C2×C5⋊C8) = C30.22M4(2)φ: C2×C5⋊C8/C2×Dic5 → C2 ⊆ Aut C6240C6.10(C2xC5:C8)480,317
C6.11(C2×C5⋊C8) = C6×C5⋊C16central extension (φ=1)480C6.11(C2xC5:C8)480,277
C6.12(C2×C5⋊C8) = C3×C20.C8central extension (φ=1)2404C6.12(C2xC5:C8)480,278
C6.13(C2×C5⋊C8) = C12×C5⋊C8central extension (φ=1)480C6.13(C2xC5:C8)480,280
C6.14(C2×C5⋊C8) = C3×C20⋊C8central extension (φ=1)480C6.14(C2xC5:C8)480,281
C6.15(C2×C5⋊C8) = C3×C23.2F5central extension (φ=1)240C6.15(C2xC5:C8)480,292

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