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

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

		d	ρ	Label	ID
C₄²×C₂₀		320		C4^2xC20	320,875

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

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₄×C₂₀)⋊₁C₄ = C₄²⋊F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	40	4+	(C4xC20):1C4	320,191
(C₄×C₂₀)⋊₂C₄ = C₄²⋊₂F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80	4	(C4xC20):2C4	320,192
(C₄×C₂₀)⋊₃C₄ = C₄²⋊₁Dic₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80	4	(C4xC20):3C4	320,89
(C₄×C₂₀)⋊₄C₄ = C₄²⋊₅F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80		(C4xC20):4C4	320,1028
(C₄×C₂₀)⋊₅C₄ = C₄²⋊₈F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80		(C4xC20):5C4	320,1026
(C₄×C₂₀)⋊₆C₄ = C₄²⋊₉F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80		(C4xC20):6C4	320,1027
(C₄×C₂₀)⋊₇C₄ = C₄²⋊₆F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	40	4	(C4xC20):7C4	320,200
(C₄×C₂₀)⋊₈C₄ = C₄²⋊₃F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80	4	(C4xC20):8C4	320,201
(C₄×C₂₀)⋊₉C₄ = C₄×C₄⋊F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80		(C4xC20):9C4	320,1025
(C₄×C₂₀)⋊₁₀C₄ = C₄²×F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80		(C4xC20):10C4	320,1023
(C₄×C₂₀)⋊₁₁C₄ = C₄²⋊₄F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80		(C4xC20):11C4	320,1024
(C₄×C₂₀)⋊₁₂C₄ = C₄²⋊Dic₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80	4	(C4xC20):12C4	320,99
(C₄×C₂₀)⋊₁₃C₄ = C₄²⋊₃Dic₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	40	4	(C4xC20):13C4	320,103
(C₄×C₂₀)⋊₁₄C₄ = C₅×C₄.₉C₄²	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80	4	(C4xC20):14C4	320,142
(C₄×C₂₀)⋊₁₅C₄ = C₅×C₄²⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	40	4	(C4xC20):15C4	320,158
(C₄×C₂₀)⋊₁₆C₄ = C₅×C₄²⋊₃C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80	4	(C4xC20):16C4	320,159
(C₄×C₂₀)⋊₁₇C₄ = C₄²⋊₅Dic₅	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	320		(C4xC20):17C4	320,564
(C₄×C₂₀)⋊₁₈C₄ = C₅×C₄²⋊₄C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	320		(C4xC20):18C4	320,877
(C₄×C₂₀)⋊₁₉C₄ = C₅×C₄²⋊₅C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	320		(C4xC20):19C4	320,884
(C₄×C₂₀)⋊₂₀C₄ = C₄²⋊₈Dic₅	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	320		(C4xC20):20C4	320,562
(C₄×C₂₀)⋊₂₁C₄ = C₄²⋊₉Dic₅	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	320		(C4xC20):21C4	320,563
(C₄×C₂₀)⋊₂₂C₄ = C₄²⋊₆Dic₅	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	80		(C4xC20):22C4	320,81
(C₄×C₂₀)⋊₂₃C₄ = C₄×C₄⋊Dic₅	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	320		(C4xC20):23C4	320,561
(C₄×C₂₀)⋊₂₄C₄ = C₄²×Dic₅	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	320		(C4xC20):24C4	320,557
(C₄×C₂₀)⋊₂₅C₄ = C₄²⋊₄Dic₅	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	320		(C4xC20):25C4	320,559
(C₄×C₂₀)⋊₂₆C₄ = C₅×C₄²⋊₆C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	80		(C4xC20):26C4	320,144
(C₄×C₂₀)⋊₂₇C₄ = C₄⋊C₄×C₂₀	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	320		(C4xC20):27C4	320,879
(C₄×C₂₀)⋊₂₈C₄ = C₅×C₄²⋊₈C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	320		(C4xC20):28C4	320,883
(C₄×C₂₀)⋊₂₉C₄ = C₅×C₄²⋊₉C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	320		(C4xC20):29C4	320,885

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

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₄×C₂₀).₁C₄ = C₄².F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80	4-	(C4xC20).1C4	320,193
(C₄×C₂₀).₂C₄ = C₄².₂F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80	4	(C4xC20).2C4	320,194
(C₄×C₂₀).₃C₄ = C₂₀.₄₅C₄²	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80	4	(C4xC20).3C4	320,24
(C₄×C₂₀).₄C₄ = C₄².₇F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	160		(C4xC20).4C4	320,1022
(C₄×C₂₀).₅C₄ = C₂₀⋊₃M₄(2)	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	160		(C4xC20).5C4	320,1019
(C₄×C₂₀).₆C₄ = C₄².₁₄F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	160		(C4xC20).6C4	320,1020
(C₄×C₂₀).₇C₄ = C₄².₁₅F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	160		(C4xC20).7C4	320,1021
(C₄×C₂₀).₈C₄ = C₂₀⋊C₁₆	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	320		(C4xC20).8C4	320,196
(C₄×C₂₀).₉C₄ = C₄².₃F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80	4	(C4xC20).9C4	320,198
(C₄×C₂₀).₁₀C₄ = C₄².₉F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80	4	(C4xC20).10C4	320,199
(C₄×C₂₀).₁₁C₄ = C₄×C₄.F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	160		(C4xC20).11C4	320,1015
(C₄×C₂₀).₁₂C₄ = C₄².₁₁F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	160		(C4xC20).12C4	320,1017
(C₄×C₂₀).₁₃C₄ = C₄².₁₂F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	160		(C4xC20).13C4	320,1018
(C₄×C₂₀).₁₄C₄ = C₄×C₅⋊C₁₆	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	320		(C4xC20).14C4	320,195
(C₄×C₂₀).₁₅C₄ = C₄².₄F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	320		(C4xC20).15C4	320,197
(C₄×C₂₀).₁₆C₄ = C₄×D₅⋊C₈	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	160		(C4xC20).16C4	320,1013
(C₄×C₂₀).₁₇C₄ = C₄².₅F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	160		(C4xC20).17C4	320,1014
(C₄×C₂₀).₁₈C₄ = C₄².₆F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	160		(C4xC20).18C4	320,1016
(C₄×C₂₀).₁₉C₄ = C₄².Dic₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80	4	(C4xC20).19C4	320,100
(C₄×C₂₀).₂₀C₄ = C₄².₃Dic₅	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80	4	(C4xC20).20C4	320,106
(C₄×C₂₀).₂₁C₄ = C₅×C₁₆⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80	4	(C4xC20).21C4	320,152
(C₄×C₂₀).₂₂C₄ = C₅×C₄².C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80	4	(C4xC20).22C4	320,160
(C₄×C₂₀).₂₃C₄ = C₅×C₄².₃C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₄×C₂₀	80	4	(C4xC20).23C4	320,161
(C₄×C₂₀).₂₄C₄ = C₅×C₁₆⋊₅C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	320		(C4xC20).24C4	320,151
(C₄×C₂₀).₂₅C₄ = C₁₀×C₈⋊C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	320		(C4xC20).25C4	320,904
(C₄×C₂₀).₂₆C₄ = C₅×C₄².₁₂C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	160		(C4xC20).26C4	320,932
(C₄×C₂₀).₂₇C₄ = C₅×C₄².₆C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	160		(C4xC20).27C4	320,933
(C₄×C₂₀).₂₈C₄ = C₂₀⋊₁₃M₄(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	160		(C4xC20).28C4	320,551
(C₄×C₂₀).₂₉C₄ = C₄².₇Dic₅	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	160		(C4xC20).29C4	320,553
(C₄×C₂₀).₃₀C₄ = C₂₀⋊₃C₁₆	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	320		(C4xC20).30C4	320,20
(C₄×C₂₀).₃₁C₄ = C₄₀.₇C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	80	2	(C4xC20).31C4	320,21
(C₄×C₂₀).₃₂C₄ = C₄×C₄.Dic₅	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	160		(C4xC20).32C4	320,549
(C₄×C₂₀).₃₃C₄ = C₂×C₂₀⋊₃C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	320		(C4xC20).33C4	320,550
(C₄×C₂₀).₃₄C₄ = C₄×C₅⋊₂C₁₆	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	320		(C4xC20).34C4	320,18
(C₄×C₂₀).₃₅C₄ = C₄₀.₁₀C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	320		(C4xC20).35C4	320,19
(C₄×C₂₀).₃₆C₄ = C₂×C₄×C₅⋊₂C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	320		(C4xC20).36C4	320,547
(C₄×C₂₀).₃₇C₄ = C₂×C₄².D₅	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	320		(C4xC20).37C4	320,548
(C₄×C₂₀).₃₈C₄ = C₄².₆Dic₅	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	160		(C4xC20).38C4	320,552
(C₄×C₂₀).₃₉C₄ = C₅×C₄⋊C₁₆	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	320		(C4xC20).39C4	320,168
(C₄×C₂₀).₄₀C₄ = C₅×C₈.C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	80	2	(C4xC20).40C4	320,169
(C₄×C₂₀).₄₁C₄ = M₄(2)×C₂₀	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	160		(C4xC20).41C4	320,905
(C₄×C₂₀).₄₂C₄ = C₁₀×C₄⋊C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	320		(C4xC20).42C4	320,923
(C₄×C₂₀).₄₃C₄ = C₅×C₄⋊M₄(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₄×C₂₀	160		(C4xC20).43C4	320,924

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

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