Extensions 1→N→G→Q→1 with N=Q₈ and Q=C₅×D₄

Direct product G=N×Q with N=Q₈ and Q=C₅×D₄

		d	ρ	Label	ID
C₅×D₄×Q₈		160		C5xD4xQ8	320,1551

Semidirect products G=N:Q with N=Q₈ and Q=C₅×D₄

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊₁(C₅×D₄) = C₅×C₄⋊SD₁₆	φ: C₅×D₄/C₂₀ → C₂ ⊆ Out Q₈	160		Q8:1(C5xD4)	320,961
Q₈⋊₂(C₅×D₄) = C₅×Q₈⋊D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Out Q₈	160		Q8:2(C5xD4)	320,949
Q₈⋊₃(C₅×D₄) = C₅×D₄⋊D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Out Q₈	160		Q8:3(C5xD4)	320,950
Q₈⋊₄(C₅×D₄) = C₅×D₄⋊₄D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Out Q₈	40	4	Q8:4(C5xD4)	320,954
Q₈⋊₅(C₅×D₄) = C₅×Q₈⋊₅D₄	φ: trivial image	160		Q8:5(C5xD4)	320,1550
Q₈⋊₆(C₅×D₄) = C₅×Q₈⋊₆D₄	φ: trivial image	160		Q8:6(C5xD4)	320,1552

Non-split extensions G=N.Q with N=Q₈ and Q=C₅×D₄

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈.₁(C₅×D₄) = C₅×C₄⋊₂Q₁₆	φ: C₅×D₄/C₂₀ → C₂ ⊆ Out Q₈	320		Q8.1(C5xD4)	320,963
Q₈.₂(C₅×D₄) = C₅×Q₈.D₄	φ: C₅×D₄/C₂₀ → C₂ ⊆ Out Q₈	160		Q8.2(C5xD4)	320,965
Q₈.₃(C₅×D₄) = C₅×D₄.₃D₄	φ: C₅×D₄/C₂₀ → C₂ ⊆ Out Q₈	80	4	Q8.3(C5xD4)	320,972
Q₈.₄(C₅×D₄) = C₅×D₄.₄D₄	φ: C₅×D₄/C₂₀ → C₂ ⊆ Out Q₈	80	4	Q8.4(C5xD4)	320,973
Q₈.₅(C₅×D₄) = C₅×D₄.₅D₄	φ: C₅×D₄/C₂₀ → C₂ ⊆ Out Q₈	160	4	Q8.5(C5xD4)	320,974
Q₈.₆(C₅×D₄) = C₅×C₂²⋊Q₁₆	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Out Q₈	160		Q8.6(C5xD4)	320,952
Q₈.₇(C₅×D₄) = C₅×D₄.₇D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Out Q₈	160		Q8.7(C5xD4)	320,953
Q₈.₈(C₅×D₄) = C₅×D₄.₈D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Out Q₈	80	4	Q8.8(C5xD4)	320,955
Q₈.₉(C₅×D₄) = C₅×D₄.₉D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Out Q₈	80	4	Q8.9(C5xD4)	320,956
Q₈.₁₀(C₅×D₄) = C₅×D₄.₁₀D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Out Q₈	80	4	Q8.10(C5xD4)	320,957
Q₈.₁₁(C₅×D₄) = C₅×D₄○D₈	φ: trivial image	80	4	Q8.11(C5xD4)	320,1578
Q₈.₁₂(C₅×D₄) = C₅×D₄○SD₁₆	φ: trivial image	80	4	Q8.12(C5xD4)	320,1579
Q₈.₁₃(C₅×D₄) = C₅×Q₈○D₈	φ: trivial image	160	4	Q8.13(C5xD4)	320,1580

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁