Extensions 1→N→G→Q→1 with N=C₂²×D₅ and Q=Q₈

Direct product G=N×Q with N=C₂²×D₅ and Q=Q₈

		d	ρ	Label	ID
C₂²×Q₈×D₅		160		C2^2xQ8xD5	320,1615

Semidirect products G=N:Q with N=C₂²×D₅ and Q=Q₈

extension	φ:Q→Out N	d	Label	ID
(C₂²×D₅)⋊₁Q₈ = (C₂×C₄).₂₀D₂₀	φ: Q₈/C₂ → C₂² ⊆ Out C₂²×D₅	160	(C2^2xD5):1Q8	320,300
(C₂²×D₅)⋊₂Q₈ = (C₂²×D₅)⋊Q₈	φ: Q₈/C₂ → C₂² ⊆ Out C₂²×D₅	160	(C2^2xD5):2Q8	320,858
(C₂²×D₅)⋊₃Q₈ = C₁₀.₅₁2₊¹⁺⁴	φ: Q₈/C₂ → C₂² ⊆ Out C₂²×D₅	80	(C2^2xD5):3Q8	320,1306
(C₂²×D₅)⋊₄Q₈ = C₂×D₁₀⋊Q₈	φ: Q₈/C₄ → C₂ ⊆ Out C₂²×D₅	160	(C2^2xD5):4Q8	320,1180
(C₂²×D₅)⋊₅Q₈ = C₂×D₁₀⋊₂Q₈	φ: Q₈/C₄ → C₂ ⊆ Out C₂²×D₅	160	(C2^2xD5):5Q8	320,1181
(C₂²×D₅)⋊₆Q₈ = D₅×C₂²⋊Q₈	φ: Q₈/C₄ → C₂ ⊆ Out C₂²×D₅	80	(C2^2xD5):6Q8	320,1298
(C₂²×D₅)⋊₇Q₈ = C₂×D₁₀⋊₃Q₈	φ: Q₈/C₄ → C₂ ⊆ Out C₂²×D₅	160	(C2^2xD5):7Q8	320,1485

Non-split extensions G=N.Q with N=C₂²×D₅ and Q=Q₈

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂²×D₅).₁Q₈ = (C₂²×D₅).Q₈	φ: Q₈/C₂ → C₂² ⊆ Out C₂²×D₅	160		(C2^2xD5).1Q8	320,303
(C₂²×D₅).₂Q₈ = (C₂×C₂₀).₃₃D₄	φ: Q₈/C₂ → C₂² ⊆ Out C₂²×D₅	160		(C2^2xD5).2Q8	320,304
(C₂²×D₅).₃Q₈ = M₄(2).₂₅D₁₀	φ: Q₈/C₂ → C₂² ⊆ Out C₂²×D₅	80	4	(C2^2xD5).3Q8	320,520
(C₂²×D₅).₄Q₈ = (C₂×C₂₀).₂₈₉D₄	φ: Q₈/C₂ → C₂² ⊆ Out C₂²×D₅	160		(C2^2xD5).4Q8	320,619
(C₂²×D₅).₅Q₈ = (C₂×C₂₀).₅₆D₄	φ: Q₈/C₂ → C₂² ⊆ Out C₂²×D₅	160		(C2^2xD5).5Q8	320,621
(C₂²×D₅).₆Q₈ = (C₂²×F₅)⋊C₄	φ: Q₈/C₂ → C₂² ⊆ Out C₂²×D₅	40	8+	(C2^2xD5).6Q8	320,204
(C₂²×D₅).₇Q₈ = C₂₀.₂₅C₄²	φ: Q₈/C₂ → C₂² ⊆ Out C₂²×D₅	80	4	(C2^2xD5).7Q8	320,235
(C₂²×D₅).₈Q₈ = M₄(2).F₅	φ: Q₈/C₂ → C₂² ⊆ Out C₂²×D₅	80	8	(C2^2xD5).8Q8	320,239
(C₂²×D₅).₉Q₈ = C₂²⋊F₅⋊C₄	φ: Q₈/C₂ → C₂² ⊆ Out C₂²×D₅	80		(C2^2xD5).9Q8	320,255
(C₂²×D₅).₁₀Q₈ = D₁₀⋊(C₄⋊C₄)	φ: Q₈/C₂ → C₂² ⊆ Out C₂²×D₅	40		(C2^2xD5).10Q8	320,1037
(C₂²×D₅).₁₁Q₈ = M₄(2).₁F₅	φ: Q₈/C₂ → C₂² ⊆ Out C₂²×D₅	80	8	(C2^2xD5).11Q8	320,1067
(C₂²×D₅).₁₂Q₈ = D₁₀⋊₂(C₄⋊C₄)	φ: Q₈/C₄ → C₂ ⊆ Out C₂²×D₅	160		(C2^2xD5).12Q8	320,294
(C₂²×D₅).₁₃Q₈ = D₁₀⋊₃(C₄⋊C₄)	φ: Q₈/C₄ → C₂ ⊆ Out C₂²×D₅	160		(C2^2xD5).13Q8	320,295
(C₂²×D₅).₁₄Q₈ = D₅×C₈.C₄	φ: Q₈/C₄ → C₂ ⊆ Out C₂²×D₅	80	4	(C2^2xD5).14Q8	320,519
(C₂²×D₅).₁₅Q₈ = D₁₀⋊₄(C₄⋊C₄)	φ: Q₈/C₄ → C₂ ⊆ Out C₂²×D₅	160		(C2^2xD5).15Q8	320,614
(C₂²×D₅).₁₆Q₈ = D₁₀⋊₅(C₄⋊C₄)	φ: Q₈/C₄ → C₂ ⊆ Out C₂²×D₅	160		(C2^2xD5).16Q8	320,616
(C₂²×D₅).₁₇Q₈ = C₂₀.₁₀C₄²	φ: Q₈/C₄ → C₂ ⊆ Out C₂²×D₅	160		(C2^2xD5).17Q8	320,234
(C₂²×D₅).₁₈Q₈ = C₂×C₄₀.C₄	φ: Q₈/C₄ → C₂ ⊆ Out C₂²×D₅	160		(C2^2xD5).18Q8	320,1060
(C₂²×D₅).₁₉Q₈ = C₂×D₁₀.Q₈	φ: Q₈/C₄ → C₂ ⊆ Out C₂²×D₅	160		(C2^2xD5).19Q8	320,1061
(C₂²×D₅).₂₀Q₈ = (C₈×D₅).C₄	φ: Q₈/C₄ → C₂ ⊆ Out C₂²×D₅	80	4	(C2^2xD5).20Q8	320,1062
(C₂²×D₅).₂₁Q₈ = C₂×D₁₀.₃Q₈	φ: Q₈/C₄ → C₂ ⊆ Out C₂²×D₅	80		(C2^2xD5).21Q8	320,1100
(C₂²×D₅).₂₂Q₈ = D₁₀⋊₆(C₄⋊C₄)	φ: Q₈/C₄ → C₂ ⊆ Out C₂²×D₅	80		(C2^2xD5).22Q8	320,1103
(C₂²×D₅).₂₃Q₈ = C₂²×C₄⋊F₅	φ: Q₈/C₄ → C₂ ⊆ Out C₂²×D₅	80		(C2^2xD5).23Q8	320,1591
(C₂²×D₅).₂₄Q₈ = D₅×C₂.C₄²	φ: trivial image	160		(C2^2xD5).24Q8	320,290
(C₂²×D₅).₂₅Q₈ = C₂×D₅×C₄⋊C₄	φ: trivial image	160		(C2^2xD5).25Q8	320,1173

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C22×D5 and Q=Q8

Extensions 1→N→G→Q→1 with N=C₂²×D₅ and Q=Q₈