Extensions 1→N→G→Q→1 with N=C₅×C₂₀ and Q=C₄

Direct product G=N×Q with N=C₅×C₂₀ and Q=C₄

		d	ρ	Label	ID
C₂₀²		400		C20^2	400,108

Semidirect products G=N:Q with N=C₅×C₂₀ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₅×C₂₀)⋊₁C₄ = C₂₀⋊₅F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₅×C₂₀	80	4	(C5xC20):1C4	400,145
(C₅×C₂₀)⋊₂C₄ = C₅×C₄⋊F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₅×C₂₀	80	4	(C5xC20):2C4	400,138
(C₅×C₂₀)⋊₃C₄ = C₂₀⋊F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₅×C₂₀	100		(C5xC20):3C4	400,152
(C₅×C₂₀)⋊₄C₄ = C₂₀⋊₂F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₅×C₂₀	40	4	(C5xC20):4C4	400,159
(C₅×C₂₀)⋊₅C₄ = C₂₀×F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₅×C₂₀	80	4	(C5xC20):5C4	400,137
(C₅×C₂₀)⋊₆C₄ = C₄×D₅.D₅	φ: C₄/C₁ → C₄ ⊆ Aut C₅×C₂₀	80	4	(C5xC20):6C4	400,144
(C₅×C₂₀)⋊₇C₄ = C₄×C₅⋊F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₅×C₂₀	100		(C5xC20):7C4	400,151
(C₅×C₂₀)⋊₈C₄ = C₄×C₅²⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₅×C₂₀	40	4	(C5xC20):8C4	400,158
(C₅×C₂₀)⋊₉C₄ = C₂₀⋊₃Dic₅	φ: C₄/C₂ → C₂ ⊆ Aut C₅×C₂₀	400		(C5xC20):9C4	400,101
(C₅×C₂₀)⋊₁₀C₄ = C₅×C₄⋊Dic₅	φ: C₄/C₂ → C₂ ⊆ Aut C₅×C₂₀	80		(C5xC20):10C4	400,85
(C₅×C₂₀)⋊₁₁C₄ = Dic₅×C₂₀	φ: C₄/C₂ → C₂ ⊆ Aut C₅×C₂₀	80		(C5xC20):11C4	400,83
(C₅×C₂₀)⋊₁₂C₄ = C₄×C₅²⋊₆C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₅×C₂₀	400		(C5xC20):12C4	400,99
(C₅×C₂₀)⋊₁₃C₄ = C₄⋊C₄×C₅²	φ: C₄/C₂ → C₂ ⊆ Aut C₅×C₂₀	400		(C5xC20):13C4	400,110

Non-split extensions G=N.Q with N=C₅×C₂₀ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₅×C₂₀).₁C₄ = C₂₀.₁₂F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₅×C₂₀	80	4	(C5xC20).1C4	400,143
(C₅×C₂₀).₂C₄ = C₅×C₄.F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₅×C₂₀	80	4	(C5xC20).2C4	400,136
(C₅×C₂₀).₃C₄ = C₅²⋊₇M₄(2)	φ: C₄/C₁ → C₄ ⊆ Aut C₅×C₂₀	200		(C5xC20).3C4	400,150
(C₅×C₂₀).₄C₄ = C₅²⋊₈M₄(2)	φ: C₄/C₁ → C₄ ⊆ Aut C₅×C₂₀	40	4	(C5xC20).4C4	400,157
(C₅×C₂₀).₅C₄ = C₅×C₅⋊C₁₆	φ: C₄/C₁ → C₄ ⊆ Aut C₅×C₂₀	80	4	(C5xC20).5C4	400,56
(C₅×C₂₀).₆C₄ = C₅²⋊₃C₁₆	φ: C₄/C₁ → C₄ ⊆ Aut C₅×C₂₀	80	4	(C5xC20).6C4	400,57
(C₅×C₂₀).₇C₄ = C₅²⋊₄C₁₆	φ: C₄/C₁ → C₄ ⊆ Aut C₅×C₂₀	400		(C5xC20).7C4	400,58
(C₅×C₂₀).₈C₄ = C₅²⋊₅C₁₆	φ: C₄/C₁ → C₄ ⊆ Aut C₅×C₂₀	80	4	(C5xC20).8C4	400,59
(C₅×C₂₀).₉C₄ = C₅×D₅⋊C₈	φ: C₄/C₁ → C₄ ⊆ Aut C₅×C₂₀	80	4	(C5xC20).9C4	400,135
(C₅×C₂₀).₁₀C₄ = C₂₀.₁₄F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₅×C₂₀	80	4	(C5xC20).10C4	400,142
(C₅×C₂₀).₁₁C₄ = C₂₀.F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₅×C₂₀	200		(C5xC20).11C4	400,149
(C₅×C₂₀).₁₂C₄ = C₂₀.₁₁F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₅×C₂₀	40	4	(C5xC20).12C4	400,156
(C₅×C₂₀).₁₃C₄ = C₂₀.₅₉D₁₀	φ: C₄/C₂ → C₂ ⊆ Aut C₅×C₂₀	200		(C5xC20).13C4	400,98
(C₅×C₂₀).₁₄C₄ = C₅×C₄.Dic₅	φ: C₄/C₂ → C₂ ⊆ Aut C₅×C₂₀	40	2	(C5xC20).14C4	400,82
(C₅×C₂₀).₁₅C₄ = C₅×C₅⋊₂C₁₆	φ: C₄/C₂ → C₂ ⊆ Aut C₅×C₂₀	80	2	(C5xC20).15C4	400,49
(C₅×C₂₀).₁₆C₄ = C₅²⋊₇C₁₆	φ: C₄/C₂ → C₂ ⊆ Aut C₅×C₂₀	400		(C5xC20).16C4	400,50
(C₅×C₂₀).₁₇C₄ = C₁₀×C₅⋊₂C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₅×C₂₀	80		(C5xC20).17C4	400,81
(C₅×C₂₀).₁₈C₄ = C₂×C₅²⋊₇C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₅×C₂₀	400		(C5xC20).18C4	400,97
(C₅×C₂₀).₁₉C₄ = M₄(2)×C₅²	φ: C₄/C₂ → C₂ ⊆ Aut C₅×C₂₀	200		(C5xC20).19C4	400,112

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁