Extensions 1→N→G→Q→1 with N=C₅²⋊₆C₄ and Q=C₄

Direct product G=N×Q with N=C₅²⋊₆C₄ and Q=C₄

		d	ρ	Label	ID
C₄×C₅²⋊₆C₄		400		C4xC5^2:6C4	400,99

Semidirect products G=N:Q with N=C₅²⋊₆C₄ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
C₅²⋊₆C₄⋊₁C₄ = Dic₅×F₅	φ: C₄/C₁ → C₄ ⊆ Out C₅²⋊₆C₄	80	8-	C5^2:6C4:1C4	400,117
C₅²⋊₆C₄⋊₂C₄ = D₅.Dic₁₀	φ: C₄/C₁ → C₄ ⊆ Out C₅²⋊₆C₄	80	8-	C5^2:6C4:2C4	400,119
C₅²⋊₆C₄⋊₃C₄ = Dic₅²	φ: C₄/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	80		C5^2:6C4:3C4	400,71
C₅²⋊₆C₄⋊₄C₄ = C₁₀.Dic₁₀	φ: C₄/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	80		C5^2:6C4:4C4	400,75
C₅²⋊₆C₄⋊₅C₄ = C₁₀².₂₂C₂²	φ: C₄/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	400		C5^2:6C4:5C4	400,100
C₅²⋊₆C₄⋊₆C₄ = C₄×C₅⋊F₅	φ: C₄/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	100		C5^2:6C4:6C4	400,151
C₅²⋊₆C₄⋊₇C₄ = C₂₀⋊F₅	φ: C₄/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	100		C5^2:6C4:7C4	400,152
C₅²⋊₆C₄⋊₈C₄ = C₄×C₅²⋊C₄	φ: C₄/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	40	4	C5^2:6C4:8C4	400,158
C₅²⋊₆C₄⋊₉C₄ = C₂₀⋊₂F₅	φ: C₄/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	40	4	C5^2:6C4:9C4	400,159

Non-split extensions G=N.Q with N=C₅²⋊₆C₄ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
C₅²⋊₆C₄.₁C₄ = C₅²⋊C₁₆	φ: C₄/C₁ → C₄ ⊆ Out C₅²⋊₆C₄	80	8-	C5^2:6C4.1C4	400,116
C₅²⋊₆C₄.₂C₄ = D₅×C₅⋊C₈	φ: C₄/C₁ → C₄ ⊆ Out C₅²⋊₆C₄	80	8-	C5^2:6C4.2C4	400,120
C₅²⋊₆C₄.₃C₄ = D₁₀.F₅	φ: C₄/C₁ → C₄ ⊆ Out C₅²⋊₆C₄	80	8-	C5^2:6C4.3C4	400,122
C₅²⋊₆C₄.₄C₄ = C₂₀.₂₉D₁₀	φ: C₄/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	40	4	C5^2:6C4.4C4	400,61
C₅²⋊₆C₄.₅C₄ = C₂₀.₃₁D₁₀	φ: C₄/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	40	4	C5^2:6C4.5C4	400,63
C₅²⋊₆C₄.₆C₄ = C₄₀⋊D₅	φ: C₄/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	200		C5^2:6C4.6C4	400,93
C₅²⋊₆C₄.₇C₄ = C₂×C₅²⋊₄C₈	φ: C₄/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	400		C5^2:6C4.7C4	400,153
C₅²⋊₆C₄.₈C₄ = C₅²⋊₁₃M₄(2)	φ: C₄/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	200		C5^2:6C4.8C4	400,154
C₅²⋊₆C₄.₉C₄ = C₂×C₅²⋊₅C₈	φ: C₄/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	80		C5^2:6C4.9C4	400,160
C₅²⋊₆C₄.₁₀C₄ = C₅²⋊₁₄M₄(2)	φ: C₄/C₂ → C₂ ⊆ Out C₅²⋊₆C₄	40	4-	C5^2:6C4.10C4	400,161
C₅²⋊₆C₄.₁₁C₄ = C₈×C₅⋊D₅	φ: trivial image	200		C5^2:6C4.11C4	400,92

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