# Extensions 1→N→G→Q→1 with N=C2×C4 and Q=C3×Dic5

Direct product G=N×Q with N=C2×C4 and Q=C3×Dic5
dρLabelID
Dic5×C2×C12480Dic5xC2xC12480,715

Semidirect products G=N:Q with N=C2×C4 and Q=C3×Dic5
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊(C3×Dic5) = C3×C23⋊Dic5φ: C3×Dic5/C15C4 ⊆ Aut C2×C41204(C2xC4):(C3xDic5)480,112
(C2×C4)⋊2(C3×Dic5) = C3×C10.10C42φ: C3×Dic5/C30C2 ⊆ Aut C2×C4480(C2xC4):2(C3xDic5)480,109
(C2×C4)⋊3(C3×Dic5) = C6×C4⋊Dic5φ: C3×Dic5/C30C2 ⊆ Aut C2×C4480(C2xC4):3(C3xDic5)480,718
(C2×C4)⋊4(C3×Dic5) = C3×C23.21D10φ: C3×Dic5/C30C2 ⊆ Aut C2×C4240(C2xC4):4(C3xDic5)480,719

Non-split extensions G=N.Q with N=C2×C4 and Q=C3×Dic5
extensionφ:Q→Aut NdρLabelID
(C2×C4).(C3×Dic5) = C3×C20.10D4φ: C3×Dic5/C15C4 ⊆ Aut C2×C42404(C2xC4).(C3xDic5)480,114
(C2×C4).2(C3×Dic5) = C3×C42.D5φ: C3×Dic5/C30C2 ⊆ Aut C2×C4480(C2xC4).2(C3xDic5)480,81
(C2×C4).3(C3×Dic5) = C3×C203C8φ: C3×Dic5/C30C2 ⊆ Aut C2×C4480(C2xC4).3(C3xDic5)480,82
(C2×C4).4(C3×Dic5) = C3×C20.55D4φ: C3×Dic5/C30C2 ⊆ Aut C2×C4240(C2xC4).4(C3xDic5)480,108
(C2×C4).5(C3×Dic5) = C3×C20.4C8φ: C3×Dic5/C30C2 ⊆ Aut C2×C42402(C2xC4).5(C3xDic5)480,90
(C2×C4).6(C3×Dic5) = C6×C4.Dic5φ: C3×Dic5/C30C2 ⊆ Aut C2×C4240(C2xC4).6(C3xDic5)480,714
(C2×C4).7(C3×Dic5) = C12×C52C8central extension (φ=1)480(C2xC4).7(C3xDic5)480,80
(C2×C4).8(C3×Dic5) = C6×C52C16central extension (φ=1)480(C2xC4).8(C3xDic5)480,89
(C2×C4).9(C3×Dic5) = C2×C6×C52C8central extension (φ=1)480(C2xC4).9(C3xDic5)480,713

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