Extensions 1→N→G→Q→1 with N=C₂₀ and Q=C₂²

Direct product G=N×Q with N=C₂₀ and Q=C₂²

		d	ρ	Label	ID
C₂²×C₂₀		80		C2^2xC20	80,45

Semidirect products G=N:Q with N=C₂₀ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀⋊C₂² = D₄×D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₂₀	20	4+	C20:C2^2	80,39
C₂₀⋊₂C₂² = C₂×D₂₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₂₀	40		C20:2C2^2	80,37
C₂₀⋊₃C₂² = C₂×C₄×D₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₂₀	40		C20:3C2^2	80,36
C₂₀⋊₄C₂² = D₄×C₁₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₂₀	40		C20:4C2^2	80,46

Non-split extensions G=N.Q with N=C₂₀ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀.₁C₂² = D₄⋊D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₂₀	40	4+	C20.1C2^2	80,15
C₂₀.₂C₂² = D₄.D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₂₀	40	4-	C20.2C2^2	80,16
C₂₀.₃C₂² = Q₈⋊D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₂₀	40	4+	C20.3C2^2	80,17
C₂₀.₄C₂² = C₅⋊Q₁₆	φ: C₂²/C₁ → C₂² ⊆ Aut C₂₀	80	4-	C20.4C2^2	80,18
C₂₀.₅C₂² = D₄⋊₂D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₂₀	40	4-	C20.5C2^2	80,40
C₂₀.₆C₂² = Q₈×D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₂₀	40	4-	C20.6C2^2	80,41
C₂₀.₇C₂² = Q₈⋊₂D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₂₀	40	4+	C20.7C2^2	80,42
C₂₀.₈C₂² = C₄₀⋊C₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₂₀	40	2	C20.8C2^2	80,6
C₂₀.₉C₂² = D₄₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₂₀	40	2+	C20.9C2^2	80,7
C₂₀.₁₀C₂² = Dic₂₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₂₀	80	2-	C20.10C2^2	80,8
C₂₀.₁₁C₂² = C₂×Dic₁₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₂₀	80		C20.11C2^2	80,35
C₂₀.₁₂C₂² = C₈×D₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₂₀	40	2	C20.12C2^2	80,4
C₂₀.₁₃C₂² = C₈⋊D₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₂₀	40	2	C20.13C2^2	80,5
C₂₀.₁₄C₂² = C₂×C₅⋊₂C₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₂₀	80		C20.14C2^2	80,9
C₂₀.₁₅C₂² = C₄.Dic₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₂₀	40	2	C20.15C2^2	80,10
C₂₀.₁₆C₂² = C₄○D₂₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₂₀	40	2	C20.16C2^2	80,38
C₂₀.₁₇C₂² = C₅×D₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₂₀	40	2	C20.17C2^2	80,25
C₂₀.₁₈C₂² = C₅×SD₁₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₂₀	40	2	C20.18C2^2	80,26
C₂₀.₁₉C₂² = C₅×Q₁₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₂₀	80	2	C20.19C2^2	80,27
C₂₀.₂₀C₂² = Q₈×C₁₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₂₀	80		C20.20C2^2	80,47
C₂₀.₂₁C₂² = C₅×C₄○D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂₀	40	2	C20.21C2^2	80,48
C₂₀.₂₂C₂² = C₅×M₄(2)	central extension (φ=1)	40	2	C20.22C2^2	80,24

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Extensions 1→N→G→Q→1 with N=C20 and Q=C22

Extensions 1→N→G→Q→1 with N=C₂₀ and Q=C₂²