Extensions 1→N→G→Q→1 with N=D₄⋊₂D₅ and Q=C₄

Direct product G=N×Q with N=D₄⋊₂D₅ and Q=C₄

		d	ρ	Label	ID
C₄×D₄⋊₂D₅		160		C4xD4:2D5	320,1208

Semidirect products G=N:Q with N=D₄⋊₂D₅ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊₂D₅⋊₁C₄ = D₄⋊(C₄×D₅)	φ: C₄/C₂ → C₂ ⊆ Out D₄⋊₂D₅	160		D4:2D5:1C4	320,398
D₄⋊₂D₅⋊₂C₄ = D₄⋊₂D₅⋊C₄	φ: C₄/C₂ → C₂ ⊆ Out D₄⋊₂D₅	160		D4:2D5:2C4	320,399
D₄⋊₂D₅⋊₃C₄ = D₅×C₄≀C₂	φ: C₄/C₂ → C₂ ⊆ Out D₄⋊₂D₅	40	4	D4:2D5:3C4	320,447
D₄⋊₂D₅⋊₄C₄ = C₄²⋊D₁₀	φ: C₄/C₂ → C₂ ⊆ Out D₄⋊₂D₅	80	4	D4:2D5:4C4	320,448
D₄⋊₂D₅⋊₅C₄ = C₄².₁₀₈D₁₀	φ: C₄/C₂ → C₂ ⊆ Out D₄⋊₂D₅	160		D4:2D5:5C4	320,1218
D₄⋊₂D₅⋊₆C₄ = C₂×D₄⋊F₅	φ: C₄/C₂ → C₂ ⊆ Out D₄⋊₂D₅	80		D4:2D5:6C4	320,1106
D₄⋊₂D₅⋊₇C₄ = (C₂×D₄)⋊₆F₅	φ: C₄/C₂ → C₂ ⊆ Out D₄⋊₂D₅	80	8-	D4:2D5:7C4	320,1107
D₄⋊₂D₅⋊₈C₄ = C₄○D₄⋊F₅	φ: C₄/C₂ → C₂ ⊆ Out D₄⋊₂D₅	40	8	D4:2D5:8C4	320,1131
D₄⋊₂D₅⋊₉C₄ = C₄○D₂₀⋊C₄	φ: C₄/C₂ → C₂ ⊆ Out D₄⋊₂D₅	80	8	D4:2D5:9C4	320,1132
D₄⋊₂D₅⋊₁₀C₄ = C₄○D₄×F₅	φ: C₄/C₂ → C₂ ⊆ Out D₄⋊₂D₅	40	8	D4:2D5:10C4	320,1603
D₄⋊₂D₅⋊₁₁C₄ = D₅.2₊¹⁺⁴	φ: C₄/C₂ → C₂ ⊆ Out D₄⋊₂D₅	40	8	D4:2D5:11C4	320,1604

Non-split extensions G=N.Q with N=D₄⋊₂D₅ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊₂D₅.₁C₄ = C₂₀.₇₂C₂⁴	φ: C₄/C₂ → C₂ ⊆ Out D₄⋊₂D₅	80	4	D4:2D5.1C4	320,1422
D₄⋊₂D₅.₂C₄ = C₂×D₄.F₅	φ: C₄/C₂ → C₂ ⊆ Out D₄⋊₂D₅	160		D4:2D5.2C4	320,1593
D₄⋊₂D₅.₃C₄ = Dic₅.C₂⁴	φ: C₄/C₂ → C₂ ⊆ Out D₄⋊₂D₅	80	8-	D4:2D5.3C4	320,1594
D₄⋊₂D₅.₄C₄ = D₅×C₈○D₄	φ: trivial image	80	4	D4:2D5.4C4	320,1421

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁