Extensions 1→N→G→Q→1 with N=C₈ and Q=C₂×C₁₀

Direct product G=N×Q with N=C₈ and Q=C₂×C₁₀

		d	ρ	Label	ID
C₂²×C₄₀		160		C2^2xC40	160,190

Semidirect products G=N:Q with N=C₈ and Q=C₂×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈⋊(C₂×C₁₀) = C₅×C₈⋊C₂²	φ: C₂×C₁₀/C₅ → C₂² ⊆ Aut C₈	40	4	C8:(C2xC10)	160,197
C₈⋊₂(C₂×C₁₀) = C₁₀×D₈	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₈	80		C8:2(C2xC10)	160,193
C₈⋊₃(C₂×C₁₀) = C₁₀×SD₁₆	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₈	80		C8:3(C2xC10)	160,194
C₈⋊₄(C₂×C₁₀) = C₁₀×M₄(2)	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₈	80		C8:4(C2xC10)	160,191

Non-split extensions G=N.Q with N=C₈ and Q=C₂×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈.(C₂×C₁₀) = C₅×C₈.C₂²	φ: C₂×C₁₀/C₅ → C₂² ⊆ Aut C₈	80	4	C8.(C2xC10)	160,198
C₈.₂(C₂×C₁₀) = C₅×D₁₆	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₈	80	2	C8.2(C2xC10)	160,61
C₈.₃(C₂×C₁₀) = C₅×SD₃₂	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₈	80	2	C8.3(C2xC10)	160,62
C₈.₄(C₂×C₁₀) = C₅×Q₃₂	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₈	160	2	C8.4(C2xC10)	160,63
C₈.₅(C₂×C₁₀) = C₁₀×Q₁₆	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₈	160		C8.5(C2xC10)	160,195
C₈.₆(C₂×C₁₀) = C₅×C₄○D₈	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₈	80	2	C8.6(C2xC10)	160,196
C₈.₇(C₂×C₁₀) = C₅×C₈○D₄	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₈	80	2	C8.7(C2xC10)	160,192
C₈.₈(C₂×C₁₀) = C₅×M₅(2)	central extension (φ=1)	80	2	C8.8(C2xC10)	160,60

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁