Extensions 1→N→G→Q→1 with N=C₄×F₅ and Q=C₂²

Direct product G=N×Q with N=C₄×F₅ and Q=C₂²

		d	ρ	Label	ID
C₂²×C₄×F₅		80		C2^2xC4xF5	320,1590

Semidirect products G=N:Q with N=C₄×F₅ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
(C₄×F₅)⋊₁C₂² = (C₂×D₄)⋊₆F₅	φ: C₂²/C₁ → C₂² ⊆ Out C₄×F₅	80	8-	(C4xF5):1C2^2	320,1107
(C₄×F₅)⋊₂C₂² = (C₂×Q₈)⋊₆F₅	φ: C₂²/C₁ → C₂² ⊆ Out C₄×F₅	80	8+	(C4xF5):2C2^2	320,1122
(C₄×F₅)⋊₃C₂² = D₄⋊F₅⋊C₂	φ: C₂²/C₁ → C₂² ⊆ Out C₄×F₅	80	8	(C4xF5):3C2^2	320,1133
(C₄×F₅)⋊₄C₂² = D₁₀.C₂⁴	φ: C₂²/C₁ → C₂² ⊆ Out C₄×F₅	40	8+	(C4xF5):4C2^2	320,1596
(C₄×F₅)⋊₅C₂² = C₂×D₄⋊F₅	φ: C₂²/C₂ → C₂ ⊆ Out C₄×F₅	80		(C4xF5):5C2^2	320,1106
(C₄×F₅)⋊₆C₂² = C₂×Q₈⋊₂F₅	φ: C₂²/C₂ → C₂ ⊆ Out C₄×F₅	80		(C4xF5):6C2^2	320,1121
(C₄×F₅)⋊₇C₂² = D₅⋊C₄≀C₂	φ: C₂²/C₂ → C₂ ⊆ Out C₄×F₅	40	8	(C4xF5):7C2^2	320,1130
(C₄×F₅)⋊₈C₂² = C₂×D₄×F₅	φ: C₂²/C₂ → C₂ ⊆ Out C₄×F₅	40		(C4xF5):8C2^2	320,1595
(C₄×F₅)⋊₉C₂² = C₂×D₁₀.C₂³	φ: C₂²/C₂ → C₂ ⊆ Out C₄×F₅	80		(C4xF5):9C2^2	320,1592

Non-split extensions G=N.Q with N=C₄×F₅ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
(C₄×F₅).₁C₂² = D₄₀⋊C₄	φ: C₂²/C₁ → C₂² ⊆ Out C₄×F₅	40	8+	(C4xF5).1C2^2	320,1069
(C₄×F₅).₂C₂² = D₈⋊F₅	φ: C₂²/C₁ → C₂² ⊆ Out C₄×F₅	80	8-	(C4xF5).2C2^2	320,1071
(C₄×F₅).₃C₂² = SD₁₆⋊F₅	φ: C₂²/C₁ → C₂² ⊆ Out C₄×F₅	40	8	(C4xF5).3C2^2	320,1073
(C₄×F₅).₄C₂² = SD₁₆⋊₂F₅	φ: C₂²/C₁ → C₂² ⊆ Out C₄×F₅	80	8	(C4xF5).4C2^2	320,1075
(C₄×F₅).₅C₂² = Dic₂₀⋊C₄	φ: C₂²/C₁ → C₂² ⊆ Out C₄×F₅	80	8-	(C4xF5).5C2^2	320,1077
(C₄×F₅).₆C₂² = Q₁₆⋊F₅	φ: C₂²/C₁ → C₂² ⊆ Out C₄×F₅	80	8+	(C4xF5).6C2^2	320,1079
(C₄×F₅).₇C₂² = D₅.2_-¹⁺⁴	φ: C₂²/C₁ → C₂² ⊆ Out C₄×F₅	80	8-	(C4xF5).7C2^2	320,1600
(C₄×F₅).₈C₂² = D₅.2₊¹⁺⁴	φ: C₂²/C₁ → C₂² ⊆ Out C₄×F₅	40	8	(C4xF5).8C2^2	320,1604
(C₄×F₅).₉C₂² = D₈×F₅	φ: C₂²/C₂ → C₂ ⊆ Out C₄×F₅	40	8+	(C4xF5).9C2^2	320,1068
(C₄×F₅).₁₀C₂² = D₈⋊₅F₅	φ: C₂²/C₂ → C₂ ⊆ Out C₄×F₅	80	8-	(C4xF5).10C2^2	320,1070
(C₄×F₅).₁₁C₂² = SD₁₆×F₅	φ: C₂²/C₂ → C₂ ⊆ Out C₄×F₅	40	8	(C4xF5).11C2^2	320,1072
(C₄×F₅).₁₂C₂² = SD₁₆⋊₃F₅	φ: C₂²/C₂ → C₂ ⊆ Out C₄×F₅	80	8	(C4xF5).12C2^2	320,1074
(C₄×F₅).₁₃C₂² = Q₁₆×F₅	φ: C₂²/C₂ → C₂ ⊆ Out C₄×F₅	80	8-	(C4xF5).13C2^2	320,1076
(C₄×F₅).₁₄C₂² = Q₁₆⋊₅F₅	φ: C₂²/C₂ → C₂ ⊆ Out C₄×F₅	80	8+	(C4xF5).14C2^2	320,1078
(C₄×F₅).₁₅C₂² = C₂×Q₈×F₅	φ: C₂²/C₂ → C₂ ⊆ Out C₄×F₅	80		(C4xF5).15C2^2	320,1599
(C₄×F₅).₁₆C₂² = C₂×C₈⋊F₅	φ: C₂²/C₂ → C₂ ⊆ Out C₄×F₅	80		(C4xF5).16C2^2	320,1055
(C₄×F₅).₁₇C₂² = C₂₀.₁₂C₄²	φ: C₂²/C₂ → C₂ ⊆ Out C₄×F₅	80	4	(C4xF5).17C2^2	320,1056
(C₄×F₅).₁₈C₂² = M₄(2)×F₅	φ: C₂²/C₂ → C₂ ⊆ Out C₄×F₅	40	8	(C4xF5).18C2^2	320,1064
(C₄×F₅).₁₉C₂² = M₄(2)⋊₅F₅	φ: C₂²/C₂ → C₂ ⊆ Out C₄×F₅	80	8	(C4xF5).19C2^2	320,1066
(C₄×F₅).₂₀C₂² = C₂×C₈×F₅	φ: trivial image	80		(C4xF5).20C2^2	320,1054
(C₄×F₅).₂₁C₂² = C₄○D₄×F₅	φ: trivial image	40	8	(C4xF5).21C2^2	320,1603

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Extensions 1→N→G→Q→1 with N=C4×F5 and Q=C22

Extensions 1→N→G→Q→1 with N=C₄×F₅ and Q=C₂²