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

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

		d	ρ	Label	ID
D₅×C₄²		80		D5xC4^2	160,92

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

extension	φ:Q→Out N	d	ρ	Label	ID
(C₄×D₅)⋊₁C₄ = D₅×C₄⋊C₄	φ: C₄/C₂ → C₂ ⊆ Out C₄×D₅	80		(C4xD5):1C4	160,112
(C₄×D₅)⋊₂C₄ = C₄⋊C₄⋊₇D₅	φ: C₄/C₂ → C₂ ⊆ Out C₄×D₅	80		(C4xD5):2C4	160,113
(C₄×D₅)⋊₃C₄ = C₄²⋊D₅	φ: C₄/C₂ → C₂ ⊆ Out C₄×D₅	80		(C4xD5):3C4	160,93
(C₄×D₅)⋊₄C₄ = C₂×C₄⋊F₅	φ: C₄/C₂ → C₂ ⊆ Out C₄×D₅	40		(C4xD5):4C4	160,204
(C₄×D₅)⋊₅C₄ = C₂×C₄×F₅	φ: C₄/C₂ → C₂ ⊆ Out C₄×D₅	40		(C4xD5):5C4	160,203
(C₄×D₅)⋊₆C₄ = D₁₀.C₂³	φ: C₄/C₂ → C₂ ⊆ Out C₄×D₅	40	4	(C4xD5):6C4	160,205

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

extension	φ:Q→Out N	d	ρ	Label	ID
(C₄×D₅).₁C₄ = D₅×M₄(2)	φ: C₄/C₂ → C₂ ⊆ Out C₄×D₅	40	4	(C4xD5).1C4	160,127
(C₄×D₅).₂C₄ = C₈₀⋊C₂	φ: C₄/C₂ → C₂ ⊆ Out C₄×D₅	80	2	(C4xD5).2C4	160,5
(C₄×D₅).₃C₄ = C₂×C₈⋊D₅	φ: C₄/C₂ → C₂ ⊆ Out C₄×D₅	80		(C4xD5).3C4	160,121
(C₄×D₅).₄C₄ = C₂×C₄.F₅	φ: C₄/C₂ → C₂ ⊆ Out C₄×D₅	80		(C4xD5).4C4	160,201
(C₄×D₅).₅C₄ = D₅⋊C₁₆	φ: C₄/C₂ → C₂ ⊆ Out C₄×D₅	80	4	(C4xD5).5C4	160,64
(C₄×D₅).₆C₄ = C₈.F₅	φ: C₄/C₂ → C₂ ⊆ Out C₄×D₅	80	4	(C4xD5).6C4	160,65
(C₄×D₅).₇C₄ = C₂×D₅⋊C₈	φ: C₄/C₂ → C₂ ⊆ Out C₄×D₅	80		(C4xD5).7C4	160,200
(C₄×D₅).₈C₄ = D₅⋊M₄(2)	φ: C₄/C₂ → C₂ ⊆ Out C₄×D₅	40	4	(C4xD5).8C4	160,202
(C₄×D₅).₉C₄ = D₅×C₁₆	φ: trivial image	80	2	(C4xD5).9C4	160,4
(C₄×D₅).₁₀C₄ = D₅×C₂×C₈	φ: trivial image	80		(C4xD5).10C4	160,120

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