Extensions 1→N→G→Q→1 with N=Dic₂₀ and Q=C₄

Direct product G=N×Q with N=Dic₂₀ and Q=C₄

		d	ρ	Label	ID
C₄×Dic₂₀		320		C4xDic20	320,325

Semidirect products G=N:Q with N=Dic₂₀ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₂₀⋊₁C₄ = D₁₀.D₈	φ: C₄/C₁ → C₄ ⊆ Out Dic₂₀	80	8-	Dic20:1C4	320,241
Dic₂₀⋊₂C₄ = D₈⋊F₅	φ: C₄/C₁ → C₄ ⊆ Out Dic₂₀	80	8-	Dic20:2C4	320,1071
Dic₂₀⋊₃C₄ = Dic₂₀⋊C₄	φ: C₄/C₁ → C₄ ⊆ Out Dic₂₀	80	8-	Dic20:3C4	320,1077
Dic₂₀⋊₄C₄ = D₅.Q₃₂	φ: C₄/C₁ → C₄ ⊆ Out Dic₂₀	80	8-	Dic20:4C4	320,246
Dic₂₀⋊₅C₄ = D₈⋊₅F₅	φ: C₄/C₁ → C₄ ⊆ Out Dic₂₀	80	8-	Dic20:5C4	320,1070
Dic₂₀⋊₆C₄ = Q₁₆×F₅	φ: C₄/C₁ → C₄ ⊆ Out Dic₂₀	80	8-	Dic20:6C4	320,1076
Dic₂₀⋊₇C₄ = C₄₀.₇₈D₄	φ: C₄/C₂ → C₂ ⊆ Out Dic₂₀	320		Dic20:7C4	320,61
Dic₂₀⋊₈C₄ = D₄₀⋊₈C₄	φ: C₄/C₂ → C₂ ⊆ Out Dic₂₀	80	4	Dic20:8C4	320,76
Dic₂₀⋊₉C₄ = Dic₂₀⋊₉C₄	φ: C₄/C₂ → C₂ ⊆ Out Dic₂₀	320		Dic20:9C4	320,343
Dic₂₀⋊₁₀C₄ = D₄₀⋊₁₀C₄	φ: C₄/C₂ → C₂ ⊆ Out Dic₂₀	80	4	Dic20:10C4	320,344
Dic₂₀⋊₁₁C₄ = C₁₀.Q₃₂	φ: C₄/C₂ → C₂ ⊆ Out Dic₂₀	320		Dic20:11C4	320,50
Dic₂₀⋊₁₂C₄ = Dic₅⋊₅Q₁₆	φ: C₄/C₂ → C₂ ⊆ Out Dic₂₀	320		Dic20:12C4	320,500
Dic₂₀⋊₁₃C₄ = D₄₀⋊₁₃C₄	φ: C₄/C₂ → C₂ ⊆ Out Dic₂₀	80	4	Dic20:13C4	320,522
Dic₂₀⋊₁₄C₄ = D₄₀⋊₁₄C₄	φ: C₄/C₂ → C₂ ⊆ Out Dic₂₀	80	4	Dic20:14C4	320,46
Dic₂₀⋊₁₅C₄ = Dic₂₀⋊₁₅C₄	φ: C₄/C₂ → C₂ ⊆ Out Dic₂₀	320		Dic20:15C4	320,480
Dic₂₀⋊₁₆C₄ = D₄₀⋊₁₆C₄	φ: C₄/C₂ → C₂ ⊆ Out Dic₂₀	80	4	Dic20:16C4	320,521
Dic₂₀⋊₁₇C₄ = D₄₀⋊₁₇C₄	φ: trivial image	80	2	Dic20:17C4	320,327

Non-split extensions G=N.Q with N=Dic₂₀ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₂₀.₁C₄ = Dic₂₀.C₄	φ: C₄/C₁ → C₄ ⊆ Out Dic₂₀	160	8-	Dic20.1C4	320,248
Dic₂₀.₂C₄ = D₈.F₅	φ: C₄/C₁ → C₄ ⊆ Out Dic₂₀	160	8-	Dic20.2C4	320,243
Dic₂₀.₃C₄ = D₄₀.₃C₄	φ: C₄/C₂ → C₂ ⊆ Out Dic₂₀	160	2	Dic20.3C4	320,68
Dic₂₀.₄C₄ = C₂₀.₄D₈	φ: C₄/C₂ → C₂ ⊆ Out Dic₂₀	160	4-	Dic20.4C4	320,75
Dic₂₀.₅C₄ = D₄₀.₅C₄	φ: C₄/C₂ → C₂ ⊆ Out Dic₂₀	160	4	Dic20.5C4	320,55
Dic₂₀.₆C₄ = C₄₀.₈D₄	φ: C₄/C₂ → C₂ ⊆ Out Dic₂₀	160	4-	Dic20.6C4	320,54

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁