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

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

Semidirect products G=N:Q with N=C2×C4 and Q=C3⋊F5
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊(C3⋊F5) = (C2×C60)⋊C4φ: C3⋊F5/C15 → C4 ⊆ Aut C2×C41204(C2xC4):(C3:F5)480,304
(C2×C4)⋊2(C3⋊F5) = D10.10D12φ: C3⋊F5/C3×D5 → C2 ⊆ Aut C2×C4120(C2xC4):2(C3:F5)480,311
(C2×C4)⋊3(C3⋊F5) = C2×C60⋊C4φ: C3⋊F5/C3×D5 → C2 ⊆ Aut C2×C4120(C2xC4):3(C3:F5)480,1064
(C2×C4)⋊4(C3⋊F5) = (C2×C12)⋊6F5φ: C3⋊F5/C3×D5 → C2 ⊆ Aut C2×C41204(C2xC4):4(C3:F5)480,1065

Non-split extensions G=N.Q with N=C2×C4 and Q=C3⋊F5
extensionφ:Q→Aut NdρLabelID
(C2×C4).(C3⋊F5) = (C2×C60).C4φ: C3⋊F5/C15 → C4 ⊆ Aut C2×C42404(C2xC4).(C3:F5)480,310
(C2×C4).2(C3⋊F5) = C30.11C42φ: C3⋊F5/C3×D5 → C2 ⊆ Aut C2×C4480(C2xC4).2(C3:F5)480,307
(C2×C4).3(C3⋊F5) = C30.7M4(2)φ: C3⋊F5/C3×D5 → C2 ⊆ Aut C2×C4240(C2xC4).3(C3:F5)480,308
(C2×C4).4(C3⋊F5) = Dic5.13D12φ: C3⋊F5/C3×D5 → C2 ⊆ Aut C2×C4480(C2xC4).4(C3:F5)480,309
(C2×C4).5(C3⋊F5) = C60.C8φ: C3⋊F5/C3×D5 → C2 ⊆ Aut C2×C42404(C2xC4).5(C3:F5)480,303
(C2×C4).6(C3⋊F5) = C60⋊C8φ: C3⋊F5/C3×D5 → C2 ⊆ Aut C2×C4480(C2xC4).6(C3:F5)480,306
(C2×C4).7(C3⋊F5) = C2×C12.F5φ: C3⋊F5/C3×D5 → C2 ⊆ Aut C2×C4240(C2xC4).7(C3:F5)480,1061
(C2×C4).8(C3⋊F5) = C60.59(C2×C4)φ: C3⋊F5/C3×D5 → C2 ⊆ Aut C2×C41204(C2xC4).8(C3:F5)480,1062
(C2×C4).9(C3⋊F5) = C2×C15⋊C16central extension (φ=1)480(C2xC4).9(C3:F5)480,302
(C2×C4).10(C3⋊F5) = C4×C15⋊C8central extension (φ=1)480(C2xC4).10(C3:F5)480,305
(C2×C4).11(C3⋊F5) = C2×C60.C4central extension (φ=1)240(C2xC4).11(C3:F5)480,1060

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