Extensions 1→N→G→Q→1 with N=C₅ and Q=D₁₀⋊C₄

Direct product G=N×Q with N=C₅ and Q=D₁₀⋊C₄

		d	ρ	Label	ID
C₅×D₁₀⋊C₄		80		C5xD10:C4	400,86

Semidirect products G=N:Q with N=C₅ and Q=D₁₀⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊(D₁₀⋊C₄) = D₅.D₂₀	φ: D₁₀⋊C₄/D₁₀ → C₄ ⊆ Aut C₅	40	8+	C5:(D10:C4)	400,118
C₅⋊₂(D₁₀⋊C₄) = C₁₀.D₂₀	φ: D₁₀⋊C₄/C₂×Dic₅ → C₂ ⊆ Aut C₅	40		C5:2(D10:C4)	400,73
C₅⋊₃(D₁₀⋊C₄) = C₁₀.₁₁D₂₀	φ: D₁₀⋊C₄/C₂×C₂₀ → C₂ ⊆ Aut C₅	200		C5:3(D10:C4)	400,102
C₅⋊₄(D₁₀⋊C₄) = D₁₀⋊Dic₅	φ: D₁₀⋊C₄/C₂²×D₅ → C₂ ⊆ Aut C₅	80		C5:4(D10:C4)	400,72

Non-split extensions G=N.Q with N=C₅ and Q=D₁₀⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.(D₁₀⋊C₄) = D₅₀⋊C₄	φ: D₁₀⋊C₄/C₂×C₂₀ → C₂ ⊆ Aut C₅	200		C5.(D10:C4)	400,14

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