Extensions 1→N→G→Q→1 with N=D₄ and Q=C₅×D₄

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

		d	ρ	Label	ID
C₅×D₄²		80		C5xD4^2	320,1547

Semidirect products G=N:Q with N=D₄ and Q=C₅×D₄

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊₁(C₅×D₄) = C₅×C₄⋊D₈	φ: C₅×D₄/C₂₀ → C₂ ⊆ Out D₄	160		D4:1(C5xD4)	320,960
D₄⋊₂(C₅×D₄) = C₅×C₂²⋊D₈	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Out D₄	80		D4:2(C5xD4)	320,948
D₄⋊₃(C₅×D₄) = C₅×D₄⋊D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Out D₄	160		D4:3(C5xD4)	320,950
D₄⋊₄(C₅×D₄) = C₅×D₄⋊₄D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Out D₄	40	4	D4:4(C5xD4)	320,954
D₄⋊₅(C₅×D₄) = C₅×D₄⋊₅D₄	φ: trivial image	80		D4:5(C5xD4)	320,1548
D₄⋊₆(C₅×D₄) = C₅×D₄⋊₆D₄	φ: trivial image	160		D4:6(C5xD4)	320,1549

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

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.₁(C₅×D₄) = C₅×D₄.D₄	φ: C₅×D₄/C₂₀ → C₂ ⊆ Out D₄	160		D4.1(C5xD4)	320,962
D₄.₂(C₅×D₄) = C₅×D₄.₂D₄	φ: C₅×D₄/C₂₀ → C₂ ⊆ Out D₄	160		D4.2(C5xD4)	320,964
D₄.₃(C₅×D₄) = C₅×D₄.₃D₄	φ: C₅×D₄/C₂₀ → C₂ ⊆ Out D₄	80	4	D4.3(C5xD4)	320,972
D₄.₄(C₅×D₄) = C₅×D₄.₄D₄	φ: C₅×D₄/C₂₀ → C₂ ⊆ Out D₄	80	4	D4.4(C5xD4)	320,973
D₄.₅(C₅×D₄) = C₅×D₄.₅D₄	φ: C₅×D₄/C₂₀ → C₂ ⊆ Out D₄	160	4	D4.5(C5xD4)	320,974
D₄.₆(C₅×D₄) = C₅×C₂²⋊SD₁₆	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Out D₄	80		D4.6(C5xD4)	320,951
D₄.₇(C₅×D₄) = C₅×D₄.₇D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Out D₄	160		D4.7(C5xD4)	320,953
D₄.₈(C₅×D₄) = C₅×D₄.₈D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Out D₄	80	4	D4.8(C5xD4)	320,955
D₄.₉(C₅×D₄) = C₅×D₄.₉D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Out D₄	80	4	D4.9(C5xD4)	320,956
D₄.₁₀(C₅×D₄) = C₅×D₄.₁₀D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Out D₄	80	4	D4.10(C5xD4)	320,957
D₄.₁₁(C₅×D₄) = C₅×D₄○D₈	φ: trivial image	80	4	D4.11(C5xD4)	320,1578
D₄.₁₂(C₅×D₄) = C₅×D₄○SD₁₆	φ: trivial image	80	4	D4.12(C5xD4)	320,1579
D₄.₁₃(C₅×D₄) = C₅×Q₈○D₈	φ: trivial image	160	4	D4.13(C5xD4)	320,1580

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁