Extensions 1→N→G→Q→1 with N=C₄ and Q=C₂×C₅⋊₂C₈

Direct product G=N×Q with N=C₄ and Q=C₂×C₅⋊₂C₈

		d	ρ	Label	ID
C₂×C₄×C₅⋊₂C₈		320		C2xC4xC5:2C8	320,547

Semidirect products G=N:Q with N=C₄ and Q=C₂×C₅⋊₂C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁(C₂×C₅⋊₂C₈) = D₄×C₅⋊₂C₈	φ: C₂×C₅⋊₂C₈/C₅⋊₂C₈ → C₂ ⊆ Aut C₄	160		C4:1(C2xC5:2C8)	320,637
C₄⋊₂(C₂×C₅⋊₂C₈) = C₂×C₂₀⋊₃C₈	φ: C₂×C₅⋊₂C₈/C₂×C₂₀ → C₂ ⊆ Aut C₄	320		C4:2(C2xC5:2C8)	320,550

Non-split extensions G=N.Q with N=C₄ and Q=C₂×C₅⋊₂C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₂×C₅⋊₂C₈) = C₂₀.₅₇D₈	φ: C₂×C₅⋊₂C₈/C₅⋊₂C₈ → C₂ ⊆ Aut C₄	160		C4.1(C2xC5:2C8)	320,92
C₄.₂(C₂×C₅⋊₂C₈) = C₂₀.₂₆Q₁₆	φ: C₂×C₅⋊₂C₈/C₅⋊₂C₈ → C₂ ⊆ Aut C₄	320		C4.2(C2xC5:2C8)	320,93
C₄.₃(C₂×C₅⋊₂C₈) = C₄₀.₉₂D₄	φ: C₂×C₅⋊₂C₈/C₅⋊₂C₈ → C₂ ⊆ Aut C₄	160	4	C4.3(C2xC5:2C8)	320,119
C₄.₄(C₂×C₅⋊₂C₈) = Q₈×C₅⋊₂C₈	φ: C₂×C₅⋊₂C₈/C₅⋊₂C₈ → C₂ ⊆ Aut C₄	320		C4.4(C2xC5:2C8)	320,650
C₄.₅(C₂×C₅⋊₂C₈) = C₄₀.₇₀C₂³	φ: C₂×C₅⋊₂C₈/C₅⋊₂C₈ → C₂ ⊆ Aut C₄	160	4	C4.5(C2xC5:2C8)	320,767
C₄.₆(C₂×C₅⋊₂C₈) = C₄₀⋊₆C₈	φ: C₂×C₅⋊₂C₈/C₂×C₂₀ → C₂ ⊆ Aut C₄	320		C4.6(C2xC5:2C8)	320,15
C₄.₇(C₂×C₅⋊₂C₈) = C₄₀⋊₅C₈	φ: C₂×C₅⋊₂C₈/C₂×C₂₀ → C₂ ⊆ Aut C₄	320		C4.7(C2xC5:2C8)	320,16
C₄.₈(C₂×C₅⋊₂C₈) = C₄₀.₇C₈	φ: C₂×C₅⋊₂C₈/C₂×C₂₀ → C₂ ⊆ Aut C₄	80	2	C4.8(C2xC5:2C8)	320,21
C₄.₉(C₂×C₅⋊₂C₈) = C₂×C₂₀.₄C₈	φ: C₂×C₅⋊₂C₈/C₂×C₂₀ → C₂ ⊆ Aut C₄	160		C4.9(C2xC5:2C8)	320,724
C₄.₁₀(C₂×C₅⋊₂C₈) = C₈×C₅⋊₂C₈	central extension (φ=1)	320		C4.10(C2xC5:2C8)	320,11
C₄.₁₁(C₂×C₅⋊₂C₈) = C₄₀⋊₈C₈	central extension (φ=1)	320		C4.11(C2xC5:2C8)	320,13
C₄.₁₂(C₂×C₅⋊₂C₈) = C₄×C₅⋊₂C₁₆	central extension (φ=1)	320		C4.12(C2xC5:2C8)	320,18
C₄.₁₃(C₂×C₅⋊₂C₈) = C₄₀.₁₀C₈	central extension (φ=1)	320		C4.13(C2xC5:2C8)	320,19
C₄.₁₄(C₂×C₅⋊₂C₈) = C₂×C₅⋊₂C₃₂	central extension (φ=1)	320		C4.14(C2xC5:2C8)	320,56
C₄.₁₅(C₂×C₅⋊₂C₈) = C₈₀.₉C₄	central extension (φ=1)	160	2	C4.15(C2xC5:2C8)	320,57
C₄.₁₆(C₂×C₅⋊₂C₈) = C₄².₆Dic₅	central extension (φ=1)	160		C4.16(C2xC5:2C8)	320,552
C₄.₁₇(C₂×C₅⋊₂C₈) = C₂²×C₅⋊₂C₁₆	central extension (φ=1)	320		C4.17(C2xC5:2C8)	320,723

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁