Extensions 1→N→G→Q→1 with N=C₅×M₄(2) and Q=C₄

Direct product G=N×Q with N=C₅×M₄(2) and Q=C₄

		d	ρ	Label	ID
M₄(2)×C₂₀		160		M4(2)xC20	320,905

Semidirect products G=N:Q with N=C₅×M₄(2) and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
(C₅×M₄(2))⋊₁C₄ = M₄(2)⋊₁F₅	φ: C₄/C₁ → C₄ ⊆ Out C₅×M₄(2)	40	8	(C5xM4(2)):1C4	320,1065
(C₅×M₄(2))⋊₂C₄ = M₄(2)⋊F₅	φ: C₄/C₁ → C₄ ⊆ Out C₅×M₄(2)	40	8	(C5xM4(2)):2C4	320,237
(C₅×M₄(2))⋊₃C₄ = M₄(2)⋊₃F₅	φ: C₄/C₁ → C₄ ⊆ Out C₅×M₄(2)	40	8	(C5xM4(2)):3C4	320,238
(C₅×M₄(2))⋊₄C₄ = M₄(2)⋊₄F₅	φ: C₄/C₁ → C₄ ⊆ Out C₅×M₄(2)	80	8	(C5xM4(2)):4C4	320,240
(C₅×M₄(2))⋊₅C₄ = M₄(2)×F₅	φ: C₄/C₁ → C₄ ⊆ Out C₅×M₄(2)	40	8	(C5xM4(2)):5C4	320,1064
(C₅×M₄(2))⋊₆C₄ = M₄(2)⋊₅F₅	φ: C₄/C₁ → C₄ ⊆ Out C₅×M₄(2)	80	8	(C5xM4(2)):6C4	320,1066
(C₅×M₄(2))⋊₇C₄ = C₂³.₄₇D₂₀	φ: C₄/C₂ → C₂ ⊆ Out C₅×M₄(2)	160		(C5xM4(2)):7C4	320,748
(C₅×M₄(2))⋊₈C₄ = M₄(2)×Dic₅	φ: C₄/C₂ → C₂ ⊆ Out C₅×M₄(2)	160		(C5xM4(2)):8C4	320,744
(C₅×M₄(2))⋊₉C₄ = C₂₀.₃₇C₄²	φ: C₄/C₂ → C₂ ⊆ Out C₅×M₄(2)	160		(C5xM4(2)):9C4	320,749
(C₅×M₄(2))⋊₁₀C₄ = C₅×M₄(2)⋊C₄	φ: C₄/C₂ → C₂ ⊆ Out C₅×M₄(2)	160		(C5xM4(2)):10C4	320,929
(C₅×M₄(2))⋊₁₁C₄ = M₄(2)⋊Dic₅	φ: C₄/C₂ → C₂ ⊆ Out C₅×M₄(2)	160		(C5xM4(2)):11C4	320,112
(C₅×M₄(2))⋊₁₂C₄ = C₂₀.₃₃C₄²	φ: C₄/C₂ → C₂ ⊆ Out C₅×M₄(2)	80		(C5xM4(2)):12C4	320,113
(C₅×M₄(2))⋊₁₃C₄ = M₄(2)⋊₄Dic₅	φ: C₄/C₂ → C₂ ⊆ Out C₅×M₄(2)	80	4	(C5xM4(2)):13C4	320,117
(C₅×M₄(2))⋊₁₄C₄ = C₅×C₄²⋊₆C₄	φ: C₄/C₂ → C₂ ⊆ Out C₅×M₄(2)	80		(C5xM4(2)):14C4	320,144
(C₅×M₄(2))⋊₁₅C₄ = C₅×C₂².C₄²	φ: C₄/C₂ → C₂ ⊆ Out C₅×M₄(2)	160		(C5xM4(2)):15C4	320,148
(C₅×M₄(2))⋊₁₆C₄ = C₅×M₄(2)⋊₄C₄	φ: C₄/C₂ → C₂ ⊆ Out C₅×M₄(2)	80	4	(C5xM4(2)):16C4	320,149
(C₅×M₄(2))⋊₁₇C₄ = C₅×C₈○₂M₄(2)	φ: trivial image	160		(C5xM4(2)):17C4	320,906

Non-split extensions G=N.Q with N=C₅×M₄(2) and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
(C₅×M₄(2)).₁C₄ = M₄(2).₁F₅	φ: C₄/C₁ → C₄ ⊆ Out C₅×M₄(2)	80	8	(C5xM4(2)).1C4	320,1067
(C₅×M₄(2)).₂C₄ = D₂₀.C₈	φ: C₄/C₁ → C₄ ⊆ Out C₅×M₄(2)	160	8	(C5xM4(2)).2C4	320,236
(C₅×M₄(2)).₃C₄ = M₄(2).F₅	φ: C₄/C₁ → C₄ ⊆ Out C₅×M₄(2)	80	8	(C5xM4(2)).3C4	320,239
(C₅×M₄(2)).₄C₄ = Dic₁₀.C₈	φ: C₄/C₁ → C₄ ⊆ Out C₅×M₄(2)	160	8	(C5xM4(2)).4C4	320,1063
(C₅×M₄(2)).₅C₄ = M₄(2).Dic₅	φ: C₄/C₂ → C₂ ⊆ Out C₅×M₄(2)	80	4	(C5xM4(2)).5C4	320,752
(C₅×M₄(2)).₆C₄ = C₄₀.₇₀C₂³	φ: C₄/C₂ → C₂ ⊆ Out C₅×M₄(2)	160	4	(C5xM4(2)).6C4	320,767
(C₅×M₄(2)).₇C₄ = C₅×M₄(2).C₄	φ: C₄/C₂ → C₂ ⊆ Out C₅×M₄(2)	80	4	(C5xM4(2)).7C4	320,931
(C₅×M₄(2)).₈C₄ = C₂₀.₃₄C₄²	φ: C₄/C₂ → C₂ ⊆ Out C₅×M₄(2)	160		(C5xM4(2)).8C4	320,116
(C₅×M₄(2)).₉C₄ = C₄₀.₉₂D₄	φ: C₄/C₂ → C₂ ⊆ Out C₅×M₄(2)	160	4	(C5xM4(2)).9C4	320,119
(C₅×M₄(2)).₁₀C₄ = C₅×C₄.C₄²	φ: C₄/C₂ → C₂ ⊆ Out C₅×M₄(2)	160		(C5xM4(2)).10C4	320,146
(C₅×M₄(2)).₁₁C₄ = C₅×D₄.C₈	φ: C₄/C₂ → C₂ ⊆ Out C₅×M₄(2)	160	2	(C5xM4(2)).11C4	320,155
(C₅×M₄(2)).₁₂C₄ = C₅×D₄○C₁₆	φ: trivial image	160	2	(C5xM4(2)).12C4	320,1005

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