Extensions 1→N→G→Q→1 with N=C₅ and Q=D₄×C₁₀

Direct product G=N×Q with N=C₅ and Q=D₄×C₁₀

		d	ρ	Label	ID
D₄×C₅×C₁₀		200		D4xC5xC10	400,202

Semidirect products G=N:Q with N=C₅ and Q=D₄×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁(D₄×C₁₀) = C₁₀×D₂₀	φ: D₄×C₁₀/C₂×C₂₀ → C₂ ⊆ Aut C₅	80		C5:1(D4xC10)	400,183
C₅⋊₂(D₄×C₁₀) = C₅×D₄×D₅	φ: D₄×C₁₀/C₅×D₄ → C₂ ⊆ Aut C₅	40	4	C5:2(D4xC10)	400,185
C₅⋊₃(D₄×C₁₀) = C₁₀×C₅⋊D₄	φ: D₄×C₁₀/C₂²×C₁₀ → C₂ ⊆ Aut C₅	40		C5:3(D4xC10)	400,190

Non-split extensions G=N.Q with N=C₅ and Q=D₄×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.(D₄×C₁₀) = D₄×C₅₀	central extension (φ=1)	200		C5.(D4xC10)	400,46

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Extensions 1→N→G→Q→1 with N=C5 and Q=D4×C10