Extensions 1→N→G→Q→1 with N=C₅ and Q=C₅×C₄○D₄

Direct product G=N×Q with N=C₅ and Q=C₅×C₄○D₄

		d	ρ	Label	ID
C₄○D₄×C₅²		200		C4oD4xC5^2	400,204

Semidirect products G=N:Q with N=C₅ and Q=C₅×C₄○D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁(C₅×C₄○D₄) = C₅×C₄○D₂₀	φ: C₅×C₄○D₄/C₂×C₂₀ → C₂ ⊆ Aut C₅	40	2	C5:1(C5xC4oD4)	400,184
C₅⋊₂(C₅×C₄○D₄) = C₅×D₄⋊₂D₅	φ: C₅×C₄○D₄/C₅×D₄ → C₂ ⊆ Aut C₅	40	4	C5:2(C5xC4oD4)	400,186
C₅⋊₃(C₅×C₄○D₄) = C₅×Q₈⋊₂D₅	φ: C₅×C₄○D₄/C₅×Q₈ → C₂ ⊆ Aut C₅	80	4	C5:3(C5xC4oD4)	400,188

Non-split extensions G=N.Q with N=C₅ and Q=C₅×C₄○D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.(C₅×C₄○D₄) = C₄○D₄×C₂₅	central extension (φ=1)	200	2	C5.(C5xC4oD4)	400,48

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Extensions 1→N→G→Q→1 with N=C5 and Q=C5×C4○D4