Extensions 1→N→G→Q→1 with N=C₄ and Q=D₅²

Direct product G=N×Q with N=C₄ and Q=D₅²

		d	ρ	Label	ID
C₄×D₅²		40	4	C4xD5^2	400,169

Semidirect products G=N:Q with N=C₄ and Q=D₅²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁D₅² = D₅×D₂₀	φ: D₅²/C₅×D₅ → C₂ ⊆ Aut C₄	40	4+	C4:1D5^2	400,170
C₄⋊₂D₅² = C₂₀⋊D₁₀	φ: D₅²/C₅⋊D₅ → C₂ ⊆ Aut C₄	40	4	C4:2D5^2	400,171

Non-split extensions G=N.Q with N=C₄ and Q=D₅²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁D₅² = C₅⋊D₄₀	φ: D₅²/C₅×D₅ → C₂ ⊆ Aut C₄	40	4+	C4.1D5^2	400,65
C₄.₂D₅² = C₅²⋊₃SD₁₆	φ: D₅²/C₅×D₅ → C₂ ⊆ Aut C₄	80	4-	C4.2D5^2	400,67
C₄.₃D₅² = C₅²⋊₄SD₁₆	φ: D₅²/C₅×D₅ → C₂ ⊆ Aut C₄	40	4+	C4.3D5^2	400,68
C₄.₄D₅² = C₅²⋊₃Q₁₆	φ: D₅²/C₅×D₅ → C₂ ⊆ Aut C₄	80	4-	C4.4D5^2	400,70
C₄.₅D₅² = D₅×Dic₁₀	φ: D₅²/C₅×D₅ → C₂ ⊆ Aut C₄	80	4-	C4.5D5^2	400,163
C₄.₆D₅² = D₂₀⋊₅D₅	φ: D₅²/C₅×D₅ → C₂ ⊆ Aut C₄	80	4-	C4.6D5^2	400,164
C₄.₇D₅² = Dic₁₀⋊₅D₅	φ: D₅²/C₅×D₅ → C₂ ⊆ Aut C₄	40	4+	C4.7D5^2	400,168
C₄.₈D₅² = C₅²⋊₂D₈	φ: D₅²/C₅⋊D₅ → C₂ ⊆ Aut C₄	80	4	C4.8D5^2	400,64
C₄.₉D₅² = D₂₀.D₅	φ: D₅²/C₅⋊D₅ → C₂ ⊆ Aut C₄	80	4	C4.9D5^2	400,66
C₄.₁₀D₅² = C₅²⋊₂Q₁₆	φ: D₅²/C₅⋊D₅ → C₂ ⊆ Aut C₄	80	4	C4.10D5^2	400,69
C₄.₁₁D₅² = D₂₀⋊D₅	φ: D₅²/C₅⋊D₅ → C₂ ⊆ Aut C₄	40	4	C4.11D5^2	400,165
C₄.₁₂D₅² = Dic₁₀⋊D₅	φ: D₅²/C₅⋊D₅ → C₂ ⊆ Aut C₄	40	4	C4.12D5^2	400,166
C₄.₁₃D₅² = D₅×C₅⋊₂C₈	central extension (φ=1)	80	4	C4.13D5^2	400,60
C₄.₁₄D₅² = C₂₀.₂₉D₁₀	central extension (φ=1)	40	4	C4.14D5^2	400,61
C₄.₁₅D₅² = C₂₀.₃₀D₁₀	central extension (φ=1)	80	4	C4.15D5^2	400,62
C₄.₁₆D₅² = C₂₀.₃₁D₁₀	central extension (φ=1)	40	4	C4.16D5^2	400,63
C₄.₁₇D₅² = D₁₀.₉D₁₀	central extension (φ=1)	40	4	C4.17D5^2	400,167

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