Extensions 1→N→G→Q→1 with N=D₄×C₅² and Q=C₂

Direct product G=N×Q with N=D₄×C₅² and Q=C₂

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

Semidirect products G=N:Q with N=D₄×C₅² and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄×C₅²)⋊₁C₂ = C₅×D₄⋊D₅	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₅²	40	4	(D4xC5^2):1C2	400,87
(D₄×C₅²)⋊₂C₂ = C₅²⋊₇D₈	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₅²	200		(D4xC5^2):2C2	400,103
(D₄×C₅²)⋊₃C₂ = C₅×D₄×D₅	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₅²	40	4	(D4xC5^2):3C2	400,185
(D₄×C₅²)⋊₄C₂ = C₅×D₄⋊₂D₅	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₅²	40	4	(D4xC5^2):4C2	400,186
(D₄×C₅²)⋊₅C₂ = D₄×C₅⋊D₅	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₅²	100		(D4xC5^2):5C2	400,195
(D₄×C₅²)⋊₆C₂ = C₂₀.D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₅²	200		(D4xC5^2):6C2	400,196
(D₄×C₅²)⋊₇C₂ = D₈×C₅²	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₅²	200		(D4xC5^2):7C2	400,113
(D₄×C₅²)⋊₈C₂ = C₄○D₄×C₅²	φ: trivial image	200		(D4xC5^2):8C2	400,204

Non-split extensions G=N.Q with N=D₄×C₅² and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄×C₅²).₁C₂ = C₅×D₄.D₅	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₅²	40	4	(D4xC5^2).1C2	400,88
(D₄×C₅²).₂C₂ = C₅²⋊₈SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₅²	200		(D4xC5^2).2C2	400,104
(D₄×C₅²).₃C₂ = SD₁₆×C₅²	φ: C₂/C₁ → C₂ ⊆ Out D₄×C₅²	200		(D4xC5^2).3C2	400,114

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