Extensions 1→N→G→Q→1 with N=C₃×C₄⋊F₅ and Q=C₂

Direct product G=N×Q with N=C₃×C₄⋊F₅ and Q=C₂

		d	ρ	Label	ID
C₆×C₄⋊F₅		120		C6xC4:F5	480,1051

Semidirect products G=N:Q with N=C₃×C₄⋊F₅ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₃×C₄⋊F₅)⋊₁C₂ = D₆₀⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out C₃×C₄⋊F₅	120	8+	(C3xC4:F5):1C2	480,227
(C₃×C₄⋊F₅)⋊₂C₂ = D₆₀⋊₃C₄	φ: C₂/C₁ → C₂ ⊆ Out C₃×C₄⋊F₅	60	8+	(C3xC4:F5):2C2	480,997
(C₃×C₄⋊F₅)⋊₃C₂ = C₄⋊F₅⋊₃S₃	φ: C₂/C₁ → C₂ ⊆ Out C₃×C₄⋊F₅	120	8	(C3xC4:F5):3C2	480,983
(C₃×C₄⋊F₅)⋊₄C₂ = S₃×C₄⋊F₅	φ: C₂/C₁ → C₂ ⊆ Out C₃×C₄⋊F₅	60	8	(C3xC4:F5):4C2	480,996
(C₃×C₄⋊F₅)⋊₅C₂ = C₃×D₂₀⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out C₃×C₄⋊F₅	120	8	(C3xC4:F5):5C2	480,287
(C₃×C₄⋊F₅)⋊₆C₂ = C₃×D₄×F₅	φ: C₂/C₁ → C₂ ⊆ Out C₃×C₄⋊F₅	60	8	(C3xC4:F5):6C2	480,1054
(C₃×C₄⋊F₅)⋊₇C₂ = C₃×D₁₀.C₂³	φ: trivial image	120	4	(C3xC4:F5):7C2	480,1052

Non-split extensions G=N.Q with N=C₃×C₄⋊F₅ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₃×C₄⋊F₅).₁C₂ = Dic₆⋊F₅	φ: C₂/C₁ → C₂ ⊆ Out C₃×C₄⋊F₅	120	8-	(C3xC4:F5).1C2	480,229
(C₃×C₄⋊F₅).₂C₂ = Dic₆⋊₅F₅	φ: C₂/C₁ → C₂ ⊆ Out C₃×C₄⋊F₅	120	8-	(C3xC4:F5).2C2	480,984
(C₃×C₄⋊F₅).₃C₂ = Dic₅.Dic₆	φ: C₂/C₁ → C₂ ⊆ Out C₃×C₄⋊F₅	120	8	(C3xC4:F5).3C2	480,235
(C₃×C₄⋊F₅).₄C₂ = Dic₅.₄Dic₆	φ: C₂/C₁ → C₂ ⊆ Out C₃×C₄⋊F₅	120	8	(C3xC4:F5).4C2	480,236
(C₃×C₄⋊F₅).₅C₂ = C₃×Q₈⋊F₅	φ: C₂/C₁ → C₂ ⊆ Out C₃×C₄⋊F₅	120	8	(C3xC4:F5).5C2	480,289
(C₃×C₄⋊F₅).₆C₂ = C₃×Q₈×F₅	φ: C₂/C₁ → C₂ ⊆ Out C₃×C₄⋊F₅	120	8	(C3xC4:F5).6C2	480,1056
(C₃×C₄⋊F₅).₇C₂ = C₃×C₄₀⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out C₃×C₄⋊F₅	120	4	(C3xC4:F5).7C2	480,273
(C₃×C₄⋊F₅).₈C₂ = C₃×D₅.D₈	φ: C₂/C₁ → C₂ ⊆ Out C₃×C₄⋊F₅	120	4	(C3xC4:F5).8C2	480,274

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