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

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

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

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

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊(C₅×C₁₀) = D₈×C₅²	φ: C₅×C₁₀/C₅² → C₂ ⊆ Out D₄	200		D4:(C5xC10)	400,113
D₄⋊₂(C₅×C₁₀) = C₄○D₄×C₅²	φ: trivial image	200		D4:2(C5xC10)	400,204

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

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.(C₅×C₁₀) = SD₁₆×C₅²	φ: C₅×C₁₀/C₅² → C₂ ⊆ Out D₄	200		D4.(C5xC10)	400,114

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