Extensions 1→N→G→Q→1 with N=D₄.Dic₅ and Q=C₂

Direct product G=N×Q with N=D₄.Dic₅ and Q=C₂

		d	ρ	Label	ID
C₂×D₄.Dic₅		160		C2xD4.Dic5	320,1490

Semidirect products G=N:Q with N=D₄.Dic₅ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.Dic₅⋊₁C₂ = M₄(2).₂₂D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₄.Dic₅	80	4	D4.Dic5:1C2	320,450
D₄.Dic₅⋊₂C₂ = C₄².₁₉₆D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₄.Dic₅	80	4	D4.Dic5:2C2	320,451
D₄.Dic₅⋊₃C₂ = D₈⋊₅Dic₅	φ: C₂/C₁ → C₂ ⊆ Out D₄.Dic₅	80	4	D4.Dic5:3C2	320,823
D₄.Dic₅⋊₄C₂ = D₈⋊₄Dic₅	φ: C₂/C₁ → C₂ ⊆ Out D₄.Dic₅	80	4	D4.Dic5:4C2	320,824
D₄.Dic₅⋊₅C₂ = M₄(2).D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₄.Dic₅	80	8+	D4.Dic5:5C2	320,826
D₄.Dic₅⋊₆C₂ = M₄(2).₁₃D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₄.Dic₅	80	8-	D4.Dic5:6C2	320,827
D₄.Dic₅⋊₇C₂ = M₄(2).₁₅D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₄.Dic₅	80	8+	D4.Dic5:7C2	320,830
D₄.Dic₅⋊₈C₂ = C₂₀.₇₂C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out D₄.Dic₅	80	4	D4.Dic5:8C2	320,1422
D₄.Dic₅⋊₉C₂ = C₂₀.₇₆C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out D₄.Dic₅	80	4	D4.Dic5:9C2	320,1491
D₄.Dic₅⋊₁₀C₂ = D₂₀.₃₂C₂³	φ: C₂/C₁ → C₂ ⊆ Out D₄.Dic₅	80	8+	D4.Dic5:10C2	320,1507
D₄.Dic₅⋊₁₁C₂ = D₂₀.₃₃C₂³	φ: C₂/C₁ → C₂ ⊆ Out D₄.Dic₅	80	8-	D4.Dic5:11C2	320,1508
D₄.Dic₅⋊₁₂C₂ = D₂₀.₃₄C₂³	φ: C₂/C₁ → C₂ ⊆ Out D₄.Dic₅	80	8+	D4.Dic5:12C2	320,1509
D₄.Dic₅⋊₁₃C₂ = D₂₀.₃₅C₂³	φ: C₂/C₁ → C₂ ⊆ Out D₄.Dic₅	160	8-	D4.Dic5:13C2	320,1510
D₄.Dic₅⋊₁₄C₂ = D₅×C₈○D₄	φ: trivial image	80	4	D4.Dic5:14C2	320,1421

Non-split extensions G=N.Q with N=D₄.Dic₅ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.Dic₅.₁C₂ = M₄(2).₁₆D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₄.Dic₅	160	8-	D4.Dic5.1C2	320,831
D₄.Dic₅.₂C₂ = D₄.(C₅⋊C₈)	φ: C₂/C₁ → C₂ ⊆ Out D₄.Dic₅	160	8	D4.Dic5.2C2	320,270
D₄.Dic₅.₃C₂ = C₅⋊C₁₆.C₂²	φ: C₂/C₁ → C₂ ⊆ Out D₄.Dic₅	160	8	D4.Dic5.3C2	320,1129

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁