# Extensions 1→N→G→Q→1 with N=C2×C4 and Q=C5×D5

Direct product G=N×Q with N=C2×C4 and Q=C5×D5
dρLabelID
D5×C2×C2080D5xC2xC20400,182

Semidirect products G=N:Q with N=C2×C4 and Q=C5×D5
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1(C5×D5) = C5×D10⋊C4φ: C5×D5/C52C2 ⊆ Aut C2×C480(C2xC4):1(C5xD5)400,86
(C2×C4)⋊2(C5×D5) = C10×D20φ: C5×D5/C52C2 ⊆ Aut C2×C480(C2xC4):2(C5xD5)400,183
(C2×C4)⋊3(C5×D5) = C5×C4○D20φ: C5×D5/C52C2 ⊆ Aut C2×C4402(C2xC4):3(C5xD5)400,184

Non-split extensions G=N.Q with N=C2×C4 and Q=C5×D5
extensionφ:Q→Aut NdρLabelID
(C2×C4).1(C5×D5) = C5×C10.D4φ: C5×D5/C52C2 ⊆ Aut C2×C480(C2xC4).1(C5xD5)400,84
(C2×C4).2(C5×D5) = C5×C4.Dic5φ: C5×D5/C52C2 ⊆ Aut C2×C4402(C2xC4).2(C5xD5)400,82
(C2×C4).3(C5×D5) = C5×C4⋊Dic5φ: C5×D5/C52C2 ⊆ Aut C2×C480(C2xC4).3(C5xD5)400,85
(C2×C4).4(C5×D5) = C10×Dic10φ: C5×D5/C52C2 ⊆ Aut C2×C480(C2xC4).4(C5xD5)400,181
(C2×C4).5(C5×D5) = C10×C52C8central extension (φ=1)80(C2xC4).5(C5xD5)400,81
(C2×C4).6(C5×D5) = Dic5×C20central extension (φ=1)80(C2xC4).6(C5xD5)400,83

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