Extensions 1→N→G→Q→1 with N=C₈₀ and Q=C₄

Direct product G=N×Q with N=C₈₀ and Q=C₄

		d	ρ	Label	ID
C₄×C₈₀		320		C4xC80	320,150

Semidirect products G=N:Q with N=C₈₀ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈₀⋊₁C₄ = C₄₀.Q₈	φ: C₄/C₁ → C₄ ⊆ Aut C₈₀	80	4	C80:1C4	320,71
C₈₀⋊₂C₄ = C₈₀⋊₂C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₈₀	80	4	C80:2C4	320,187
C₈₀⋊₃C₄ = C₈₀⋊₃C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₈₀	80	4	C80:3C4	320,188
C₈₀⋊₄C₄ = C₈₀⋊₄C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₈₀	80	4	C80:4C4	320,185
C₈₀⋊₅C₄ = C₈₀⋊₅C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₈₀	80	4	C80:5C4	320,186
C₈₀⋊₆C₄ = C₈₀⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₈₀	80	4	C80:6C4	320,70
C₈₀⋊₇C₄ = C₁₆×F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₈₀	80	4	C80:7C4	320,181
C₈₀⋊₈C₄ = C₁₆⋊₇F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₈₀	80	4	C80:8C4	320,182
C₈₀⋊₉C₄ = C₁₆⋊F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₈₀	80	4	C80:9C4	320,183
C₈₀⋊₁₀C₄ = C₁₆⋊₄F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₈₀	80	4	C80:10C4	320,184
C₈₀⋊₁₁C₄ = C₅×C₈.Q₈	φ: C₄/C₁ → C₄ ⊆ Aut C₈₀	80	4	C80:11C4	320,170
C₈₀⋊₁₂C₄ = C₅×C₁₆⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₈₀	80	4	C80:12C4	320,152
C₈₀⋊₁₃C₄ = C₈₀⋊₁₃C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₈₀	320		C80:13C4	320,62
C₈₀⋊₁₄C₄ = C₈₀⋊₁₄C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₈₀	320		C80:14C4	320,63
C₈₀⋊₁₅C₄ = C₅×C₁₆⋊₃C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₈₀	320		C80:15C4	320,171
C₈₀⋊₁₆C₄ = C₁₆×Dic₅	φ: C₄/C₂ → C₂ ⊆ Aut C₈₀	320		C80:16C4	320,58
C₈₀⋊₁₇C₄ = C₈₀⋊₁₇C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₈₀	320		C80:17C4	320,60
C₈₀⋊₁₈C₄ = C₅×C₁₆⋊₄C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₈₀	320		C80:18C4	320,172
C₈₀⋊₁₉C₄ = C₅×C₁₆⋊₅C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₈₀	320		C80:19C4	320,151

Non-split extensions G=N.Q with N=C₈₀ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈₀.₁C₄ = C₁₆.F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₈₀	160	4	C80.1C4	320,189
C₈₀.₂C₄ = C₈₀.₂C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₈₀	160	4	C80.2C4	320,190
C₈₀.₃C₄ = C₅⋊C₆₄	φ: C₄/C₁ → C₄ ⊆ Aut C₈₀	320	4	C80.3C4	320,3
C₈₀.₄C₄ = D₅⋊C₃₂	φ: C₄/C₁ → C₄ ⊆ Aut C₈₀	160	4	C80.4C4	320,179
C₈₀.₅C₄ = C₈₀.C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₈₀	160	4	C80.5C4	320,180
C₈₀.₆C₄ = C₈₀.₆C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₈₀	160	2	C80.6C4	320,64
C₈₀.₇C₄ = C₅⋊₂C₆₄	φ: C₄/C₂ → C₂ ⊆ Aut C₈₀	320	2	C80.7C4	320,1
C₈₀.₈C₄ = C₂×C₅⋊₂C₃₂	φ: C₄/C₂ → C₂ ⊆ Aut C₈₀	320		C80.8C4	320,56
C₈₀.₉C₄ = C₈₀.₉C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₈₀	160	2	C80.9C4	320,57
C₈₀.₁₀C₄ = C₅×C₈.₄Q₈	φ: C₄/C₂ → C₂ ⊆ Aut C₈₀	160	2	C80.10C4	320,173
C₈₀.₁₁C₄ = C₅×M₆(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₈₀	160	2	C80.11C4	320,175

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