Extensions 1→N→G→Q→1 with N=C₅⋊C₈ and Q=D₄

Direct product G=N×Q with N=C₅⋊C₈ and Q=D₄

		d	ρ	Label	ID
D₄×C₅⋊C₈		160		D4xC5:C8	320,1110

Semidirect products G=N:Q with N=C₅⋊C₈ and Q=D₄

extension	φ:Q→Out N	d	ρ	Label	ID
C₅⋊C₈⋊₁D₄ = Dic₅⋊M₄(2)	φ: D₄/C₄ → C₂ ⊆ Out C₅⋊C₈	160		C5:C8:1D4	320,1033
C₅⋊C₈⋊₂D₄ = C₂₀⋊M₄(2)	φ: D₄/C₄ → C₂ ⊆ Out C₅⋊C₈	160		C5:C8:2D4	320,1043
C₅⋊C₈⋊₃D₄ = C₂₀⋊₂M₄(2)	φ: D₄/C₄ → C₂ ⊆ Out C₅⋊C₈	160		C5:C8:3D4	320,1112
C₅⋊C₈⋊₄D₄ = C₅⋊C₈⋊D₄	φ: D₄/C₂² → C₂ ⊆ Out C₅⋊C₈	160		C5:C8:4D4	320,1031
C₅⋊C₈⋊₅D₄ = D₁₀⋊M₄(2)	φ: D₄/C₂² → C₂ ⊆ Out C₅⋊C₈	160		C5:C8:5D4	320,1032
C₅⋊C₈⋊₆D₄ = D₁₀⋊₂M₄(2)	φ: D₄/C₂² → C₂ ⊆ Out C₅⋊C₈	160		C5:C8:6D4	320,1042
C₅⋊C₈⋊₇D₄ = C₅⋊C₈⋊₇D₄	φ: D₄/C₂² → C₂ ⊆ Out C₅⋊C₈	160		C5:C8:7D4	320,1111
C₅⋊C₈⋊₈D₄ = C₅⋊C₈⋊₈D₄	φ: trivial image	160		C5:C8:8D4	320,1030
C₅⋊C₈⋊₉D₄ = D₂₀⋊₂C₈	φ: trivial image	160		C5:C8:9D4	320,1040

Non-split extensions G=N.Q with N=C₅⋊C₈ and Q=D₄

extension	φ:Q→Out N	d	ρ	Label	ID
C₅⋊C₈.₁D₄ = D₈⋊F₅	φ: D₄/C₂² → C₂ ⊆ Out C₅⋊C₈	80	8-	C5:C8.1D4	320,1071
C₅⋊C₈.₂D₄ = SD₁₆⋊₂F₅	φ: D₄/C₂² → C₂ ⊆ Out C₅⋊C₈	80	8	C5:C8.2D4	320,1075
C₅⋊C₈.₃D₄ = Q₁₆⋊F₅	φ: D₄/C₂² → C₂ ⊆ Out C₅⋊C₈	80	8+	C5:C8.3D4	320,1079
C₅⋊C₈.₄D₄ = D₈⋊₅F₅	φ: trivial image	80	8-	C5:C8.4D4	320,1070
C₅⋊C₈.₅D₄ = SD₁₆⋊₃F₅	φ: trivial image	80	8	C5:C8.5D4	320,1074
C₅⋊C₈.₆D₄ = Q₁₆⋊₅F₅	φ: trivial image	80	8+	C5:C8.6D4	320,1078

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁