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

		d	ρ	Label	ID
D₅×C₂×C₂₀		80		D5xC2xC20	400,182

Semidirect products G=N:Q with N=C₂×C₄ and Q=C₅×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₄)⋊₁(C₅×D₅) = C₅×D₁₀⋊C₄	φ: C₅×D₅/C₅² → C₂ ⊆ Aut C₂×C₄	80		(C2xC4):1(C5xD5)	400,86
(C₂×C₄)⋊₂(C₅×D₅) = C₁₀×D₂₀	φ: C₅×D₅/C₅² → C₂ ⊆ Aut C₂×C₄	80		(C2xC4):2(C5xD5)	400,183
(C₂×C₄)⋊₃(C₅×D₅) = C₅×C₄○D₂₀	φ: C₅×D₅/C₅² → C₂ ⊆ Aut C₂×C₄	40	2	(C2xC4):3(C5xD5)	400,184

Non-split extensions G=N.Q with N=C₂×C₄ and Q=C₅×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₄).₁(C₅×D₅) = C₅×C₁₀.D₄	φ: C₅×D₅/C₅² → C₂ ⊆ Aut C₂×C₄	80		(C2xC4).1(C5xD5)	400,84
(C₂×C₄).₂(C₅×D₅) = C₅×C₄.Dic₅	φ: C₅×D₅/C₅² → C₂ ⊆ Aut C₂×C₄	40	2	(C2xC4).2(C5xD5)	400,82
(C₂×C₄).₃(C₅×D₅) = C₅×C₄⋊Dic₅	φ: C₅×D₅/C₅² → C₂ ⊆ Aut C₂×C₄	80		(C2xC4).3(C5xD5)	400,85
(C₂×C₄).₄(C₅×D₅) = C₁₀×Dic₁₀	φ: C₅×D₅/C₅² → C₂ ⊆ Aut C₂×C₄	80		(C2xC4).4(C5xD5)	400,181
(C₂×C₄).₅(C₅×D₅) = C₁₀×C₅⋊₂C₈	central extension (φ=1)	80		(C2xC4).5(C5xD5)	400,81
(C₂×C₄).₆(C₅×D₅) = Dic₅×C₂₀	central extension (φ=1)	80		(C2xC4).6(C5xD5)	400,83

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