Extensions 1→N→G→Q→1 with N=C₂₀ and Q=F₅

Direct product G=N×Q with N=C₂₀ and Q=F₅

		d	ρ	Label	ID
C₂₀×F₅		80	4	C20xF5	400,137

Semidirect products G=N:Q with N=C₂₀ and Q=F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀⋊₁F₅ = C₂₀⋊F₅	φ: F₅/C₅ → C₄ ⊆ Aut C₂₀	100		C20:1F5	400,152
C₂₀⋊₂F₅ = C₂₀⋊₂F₅	φ: F₅/C₅ → C₄ ⊆ Aut C₂₀	40	4	C20:2F5	400,159
C₂₀⋊₃F₅ = C₄×C₅⋊F₅	φ: F₅/C₅ → C₄ ⊆ Aut C₂₀	100		C20:3F5	400,151
C₂₀⋊₄F₅ = C₄×C₅²⋊C₄	φ: F₅/C₅ → C₄ ⊆ Aut C₂₀	40	4	C20:4F5	400,158
C₂₀⋊₅F₅ = C₂₀⋊₅F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂₀	80	4	C20:5F5	400,145
C₂₀⋊₆F₅ = C₄×D₅.D₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂₀	80	4	C20:6F5	400,144
C₂₀⋊₇F₅ = C₅×C₄⋊F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂₀	80	4	C20:7F5	400,138

Non-split extensions G=N.Q with N=C₂₀ and Q=F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀.₁F₅ = C₁₀₀.C₄	φ: F₅/C₅ → C₄ ⊆ Aut C₂₀	200	4	C20.1F5	400,29
C₂₀.₂F₅ = C₁₀₀⋊C₄	φ: F₅/C₅ → C₄ ⊆ Aut C₂₀	100	4	C20.2F5	400,31
C₂₀.₃F₅ = C₅²⋊₇M₄(2)	φ: F₅/C₅ → C₄ ⊆ Aut C₂₀	200		C20.3F5	400,150
C₂₀.₄F₅ = C₅²⋊₈M₄(2)	φ: F₅/C₅ → C₄ ⊆ Aut C₂₀	40	4	C20.4F5	400,157
C₂₀.₅F₅ = C₂₅⋊C₁₆	φ: F₅/C₅ → C₄ ⊆ Aut C₂₀	400	4	C20.5F5	400,3
C₂₀.₆F₅ = D₂₅⋊C₈	φ: F₅/C₅ → C₄ ⊆ Aut C₂₀	200	4	C20.6F5	400,28
C₂₀.₇F₅ = C₄×C₂₅⋊C₄	φ: F₅/C₅ → C₄ ⊆ Aut C₂₀	100	4	C20.7F5	400,30
C₂₀.₈F₅ = C₅²⋊₄C₁₆	φ: F₅/C₅ → C₄ ⊆ Aut C₂₀	400		C20.8F5	400,58
C₂₀.₉F₅ = C₅²⋊₅C₁₆	φ: F₅/C₅ → C₄ ⊆ Aut C₂₀	80	4	C20.9F5	400,59
C₂₀.₁₀F₅ = C₂₀.F₅	φ: F₅/C₅ → C₄ ⊆ Aut C₂₀	200		C20.10F5	400,149
C₂₀.₁₁F₅ = C₂₀.₁₁F₅	φ: F₅/C₅ → C₄ ⊆ Aut C₂₀	40	4	C20.11F5	400,156
C₂₀.₁₂F₅ = C₂₀.₁₂F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂₀	80	4	C20.12F5	400,143
C₂₀.₁₃F₅ = C₅²⋊₃C₁₆	φ: F₅/D₅ → C₂ ⊆ Aut C₂₀	80	4	C20.13F5	400,57
C₂₀.₁₄F₅ = C₂₀.₁₄F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂₀	80	4	C20.14F5	400,142
C₂₀.₁₅F₅ = C₅×C₄.F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂₀	80	4	C20.15F5	400,136
C₂₀.₁₆F₅ = C₅×C₅⋊C₁₆	central extension (φ=1)	80	4	C20.16F5	400,56
C₂₀.₁₇F₅ = C₅×D₅⋊C₈	central extension (φ=1)	80	4	C20.17F5	400,135

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