Extensions 1→N→G→Q→1 with N=C₅×C₁₀ and Q=C₂²

Direct product G=N×Q with N=C₅×C₁₀ and Q=C₂²

		d	ρ	Label	ID
C₂×C₁₀²		200		C2xC10^2	200,52

Semidirect products G=N:Q with N=C₅×C₁₀ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₅×C₁₀)⋊C₂² = C₂×D₅²	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₁₀	20	4+	(C5xC10):C2^2	200,49
(C₅×C₁₀)⋊₂C₂² = D₅×C₂×C₁₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₁₀	40		(C5xC10):2C2^2	200,50
(C₅×C₁₀)⋊₃C₂² = C₂²×C₅⋊D₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₁₀	100		(C5xC10):3C2^2	200,51

Non-split extensions G=N.Q with N=C₅×C₁₀ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₅×C₁₀).₁C₂² = D₅×Dic₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₁₀	40	4-	(C5xC10).1C2^2	200,22
(C₅×C₁₀).₂C₂² = Dic₅⋊₂D₅	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₁₀	20	4+	(C5xC10).2C2^2	200,23
(C₅×C₁₀).₃C₂² = C₅²⋊₂D₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₁₀	40	4-	(C5xC10).3C2^2	200,24
(C₅×C₁₀).₄C₂² = C₅⋊D₂₀	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₁₀	20	4+	(C5xC10).4C2^2	200,25
(C₅×C₁₀).₅C₂² = C₅²⋊₂Q₈	φ: C₂²/C₁ → C₂² ⊆ Aut C₅×C₁₀	40	4-	(C5xC10).5C2^2	200,26
(C₅×C₁₀).₆C₂² = C₅×Dic₁₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₁₀	40	2	(C5xC10).6C2^2	200,27
(C₅×C₁₀).₇C₂² = D₅×C₂₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₁₀	40	2	(C5xC10).7C2^2	200,28
(C₅×C₁₀).₈C₂² = C₅×D₂₀	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₁₀	40	2	(C5xC10).8C2^2	200,29
(C₅×C₁₀).₉C₂² = C₁₀×Dic₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₁₀	40		(C5xC10).9C2^2	200,30
(C₅×C₁₀).₁₀C₂² = C₅×C₅⋊D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₁₀	20	2	(C5xC10).10C2^2	200,31
(C₅×C₁₀).₁₁C₂² = C₅²⋊₄Q₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₁₀	200		(C5xC10).11C2^2	200,32
(C₅×C₁₀).₁₂C₂² = C₄×C₅⋊D₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₁₀	100		(C5xC10).12C2^2	200,33
(C₅×C₁₀).₁₃C₂² = C₂₀⋊D₅	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₁₀	100		(C5xC10).13C2^2	200,34
(C₅×C₁₀).₁₄C₂² = C₂×C₅²⋊₆C₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₁₀	200		(C5xC10).14C2^2	200,35
(C₅×C₁₀).₁₅C₂² = C₅²⋊₇D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₅×C₁₀	100		(C5xC10).15C2^2	200,36
(C₅×C₁₀).₁₆C₂² = D₄×C₅²	central extension (φ=1)	100		(C5xC10).16C2^2	200,38
(C₅×C₁₀).₁₇C₂² = Q₈×C₅²	central extension (φ=1)	200		(C5xC10).17C2^2	200,39

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁