Extensions 1→N→G→Q→1 with N=C₂×C₁₀ and Q=C₂²

Direct product G=N×Q with N=C₂×C₁₀ and Q=C₂²

		d	ρ	Label	ID
C₂³×C₁₀		80		C2^3xC10	80,52

Semidirect products G=N:Q with N=C₂×C₁₀ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₁₀)⋊C₂² = D₄×D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₂×C₁₀	20	4+	(C2xC10):C2^2	80,39
(C₂×C₁₀)⋊₂C₂² = D₄×C₁₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₁₀	40		(C2xC10):2C2^2	80,46
(C₂×C₁₀)⋊₃C₂² = C₂×C₅⋊D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₁₀	40		(C2xC10):3C2^2	80,44
(C₂×C₁₀)⋊₄C₂² = C₂³×D₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₁₀	40		(C2xC10):4C2^2	80,51

Non-split extensions G=N.Q with N=C₂×C₁₀ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₁₀).C₂² = D₄⋊₂D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₂×C₁₀	40	4-	(C2xC10).C2^2	80,40
(C₂×C₁₀).₂C₂² = C₅×C₄○D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₁₀	40	2	(C2xC10).2C2^2	80,48
(C₂×C₁₀).₃C₂² = C₄×Dic₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₁₀	80		(C2xC10).3C2^2	80,11
(C₂×C₁₀).₄C₂² = C₁₀.D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₁₀	80		(C2xC10).4C2^2	80,12
(C₂×C₁₀).₅C₂² = C₄⋊Dic₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₁₀	80		(C2xC10).5C2^2	80,13
(C₂×C₁₀).₆C₂² = D₁₀⋊C₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₁₀	40		(C2xC10).6C2^2	80,14
(C₂×C₁₀).₇C₂² = C₂³.D₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₁₀	40		(C2xC10).7C2^2	80,19
(C₂×C₁₀).₈C₂² = C₂×Dic₁₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₁₀	80		(C2xC10).8C2^2	80,35
(C₂×C₁₀).₉C₂² = C₂×C₄×D₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₁₀	40		(C2xC10).9C2^2	80,36
(C₂×C₁₀).₁₀C₂² = C₂×D₂₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₁₀	40		(C2xC10).10C2^2	80,37
(C₂×C₁₀).₁₁C₂² = C₄○D₂₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₁₀	40	2	(C2xC10).11C2^2	80,38
(C₂×C₁₀).₁₂C₂² = C₂²×Dic₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₂×C₁₀	80		(C2xC10).12C2^2	80,43
(C₂×C₁₀).₁₃C₂² = C₅×C₂²⋊C₄	central extension (φ=1)	40		(C2xC10).13C2^2	80,21
(C₂×C₁₀).₁₄C₂² = C₅×C₄⋊C₄	central extension (φ=1)	80		(C2xC10).14C2^2	80,22
(C₂×C₁₀).₁₅C₂² = Q₈×C₁₀	central extension (φ=1)	80		(C2xC10).15C2^2	80,47

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