Extensions 1→N→G→Q→1 with N=C₄₀ and Q=C₈

Direct product G=N×Q with N=C₄₀ and Q=C₈

		d	ρ	Label	ID
C₈×C₄₀		320		C8xC40	320,126

Semidirect products G=N:Q with N=C₄₀ and Q=C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄₀⋊₁C₈ = C₄₀⋊₁C₈	φ: C₈/C₂ → C₄ ⊆ Aut C₄₀	320		C40:1C8	320,220
C₄₀⋊₂C₈ = C₄₀⋊₂C₈	φ: C₈/C₂ → C₄ ⊆ Aut C₄₀	320		C40:2C8	320,219
C₄₀⋊₃C₈ = C₈×C₅⋊C₈	φ: C₈/C₂ → C₄ ⊆ Aut C₄₀	320		C40:3C8	320,216
C₄₀⋊₄C₈ = C₄₀⋊C₈	φ: C₈/C₂ → C₄ ⊆ Aut C₄₀	320		C40:4C8	320,217
C₄₀⋊₅C₈ = C₄₀⋊₅C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₄₀	320		C40:5C8	320,16
C₄₀⋊₆C₈ = C₄₀⋊₆C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₄₀	320		C40:6C8	320,15
C₄₀⋊₇C₈ = C₈×C₅⋊₂C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₄₀	320		C40:7C8	320,11
C₄₀⋊₈C₈ = C₄₀⋊₈C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₄₀	320		C40:8C8	320,13
C₄₀⋊₉C₈ = C₅×C₈⋊₁C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₄₀	320		C40:9C8	320,140
C₄₀⋊₁₀C₈ = C₅×C₈⋊₂C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₄₀	320		C40:10C8	320,139
C₄₀⋊₁₁C₈ = C₅×C₈⋊C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₄₀	320		C40:11C8	320,127

Non-split extensions G=N.Q with N=C₄₀ and Q=C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄₀.₁C₈ = C₄₀.₁C₈	φ: C₈/C₂ → C₄ ⊆ Aut C₄₀	80	4	C40.1C8	320,227
C₄₀.₂C₈ = C₅⋊C₆₄	φ: C₈/C₂ → C₄ ⊆ Aut C₄₀	320	4	C40.2C8	320,3
C₄₀.₃C₈ = C₂×C₅⋊C₃₂	φ: C₈/C₂ → C₄ ⊆ Aut C₄₀	320		C40.3C8	320,214
C₄₀.₄C₈ = C₅⋊M₆(2)	φ: C₈/C₂ → C₄ ⊆ Aut C₄₀	160	4	C40.4C8	320,215
C₄₀.₅C₈ = Dic₅⋊C₁₆	φ: C₈/C₂ → C₄ ⊆ Aut C₄₀	320		C40.5C8	320,223
C₄₀.₆C₈ = C₄₀.C₈	φ: C₈/C₂ → C₄ ⊆ Aut C₄₀	320		C40.6C8	320,224
C₄₀.₇C₈ = C₄₀.₇C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₄₀	80	2	C40.7C8	320,21
C₄₀.₈C₈ = C₅⋊₂C₆₄	φ: C₈/C₄ → C₂ ⊆ Aut C₄₀	320	2	C40.8C8	320,1
C₄₀.₉C₈ = C₄×C₅⋊₂C₁₆	φ: C₈/C₄ → C₂ ⊆ Aut C₄₀	320		C40.9C8	320,18
C₄₀.₁₀C₈ = C₄₀.₁₀C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₄₀	320		C40.10C8	320,19
C₄₀.₁₁C₈ = C₂×C₅⋊₂C₃₂	φ: C₈/C₄ → C₂ ⊆ Aut C₄₀	320		C40.11C8	320,56
C₄₀.₁₂C₈ = C₈₀.₉C₄	φ: C₈/C₄ → C₂ ⊆ Aut C₄₀	160	2	C40.12C8	320,57
C₄₀.₁₃C₈ = C₅×C₈.C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₄₀	80	2	C40.13C8	320,169
C₄₀.₁₄C₈ = C₅×C₁₆⋊₅C₄	φ: C₈/C₄ → C₂ ⊆ Aut C₄₀	320		C40.14C8	320,151
C₄₀.₁₅C₈ = C₅×M₆(2)	φ: C₈/C₄ → C₂ ⊆ Aut C₄₀	160	2	C40.15C8	320,175

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