Extensions 1→N→G→Q→1 with N=D₄×D₅ and Q=C₄

Direct product G=N×Q with N=D₄×D₅ and Q=C₄

		d	ρ	Label	ID
C₄×D₄×D₅		80		C4xD4xD5	320,1216

Semidirect products G=N:Q with N=D₄×D₅ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄×D₅)⋊₁C₄ = D₅×D₄⋊C₄	φ: C₄/C₂ → C₂ ⊆ Out D₄×D₅	80		(D4xD5):1C4	320,396
(D₄×D₅)⋊₂C₄ = (D₄×D₅)⋊C₄	φ: C₄/C₂ → C₂ ⊆ Out D₄×D₅	80		(D4xD5):2C4	320,397
(D₄×D₅)⋊₃C₄ = D₅×C₄≀C₂	φ: C₄/C₂ → C₂ ⊆ Out D₄×D₅	40	4	(D4xD5):3C4	320,447
(D₄×D₅)⋊₄C₄ = C₄²⋊D₁₀	φ: C₄/C₂ → C₂ ⊆ Out D₄×D₅	80	4	(D4xD5):4C4	320,448
(D₄×D₅)⋊₅C₄ = C₄²⋊₁₁D₁₀	φ: C₄/C₂ → C₂ ⊆ Out D₄×D₅	80		(D4xD5):5C4	320,1217
(D₄×D₅)⋊₆C₄ = C₂×D₂₀⋊C₄	φ: C₄/C₂ → C₂ ⊆ Out D₄×D₅	80		(D4xD5):6C4	320,1104
(D₄×D₅)⋊₇C₄ = (D₄×C₁₀)⋊C₄	φ: C₄/C₂ → C₂ ⊆ Out D₄×D₅	40	8+	(D4xD5):7C4	320,1105
(D₄×D₅)⋊₈C₄ = D₅⋊C₄≀C₂	φ: C₄/C₂ → C₂ ⊆ Out D₄×D₅	40	8	(D4xD5):8C4	320,1130
(D₄×D₅)⋊₉C₄ = D₄⋊F₅⋊C₂	φ: C₄/C₂ → C₂ ⊆ Out D₄×D₅	80	8	(D4xD5):9C4	320,1133
(D₄×D₅)⋊₁₀C₄ = C₂×D₄×F₅	φ: C₄/C₂ → C₂ ⊆ Out D₄×D₅	40		(D4xD5):10C4	320,1595
(D₄×D₅)⋊₁₁C₄ = D₁₀.C₂⁴	φ: C₄/C₂ → C₂ ⊆ Out D₄×D₅	40	8+	(D4xD5):11C4	320,1596

Non-split extensions G=N.Q with N=D₄×D₅ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄×D₅).₁C₄ = C₂₀.₇₂C₂⁴	φ: C₄/C₂ → C₂ ⊆ Out D₄×D₅	80	4	(D4xD5).1C4	320,1422
(D₄×D₅).₂C₄ = Dic₅.₂₁C₂⁴	φ: C₄/C₂ → C₂ ⊆ Out D₄×D₅	80	8	(D4xD5).2C4	320,1601
(D₄×D₅).₃C₄ = Dic₅.₂₂C₂⁴	φ: C₄/C₂ → C₂ ⊆ Out D₄×D₅	80	8	(D4xD5).3C4	320,1602
(D₄×D₅).₄C₄ = D₅×C₈○D₄	φ: trivial image	80	4	(D4xD5).4C4	320,1421

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