Extensions 1→N→G→Q→1 with N=Dic₅ and Q=C₂²

Direct product G=N×Q with N=Dic₅ and Q=C₂²

		d	ρ	Label	ID
C₂²×Dic₅		80		C2^2xDic5	80,43

Semidirect products G=N:Q with N=Dic₅ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₅⋊₁C₂² = D₄×D₅	φ: C₂²/C₂ → C₂ ⊆ Out Dic₅	20	4+	Dic5:1C2^2	80,39
Dic₅⋊₂C₂² = C₂×C₅⋊D₄	φ: C₂²/C₂ → C₂ ⊆ Out Dic₅	40		Dic5:2C2^2	80,44
Dic₅⋊₃C₂² = C₂×C₄×D₅	φ: trivial image	40		Dic5:3C2^2	80,36

Non-split extensions G=N.Q with N=Dic₅ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₅.₁C₂² = C₂×Dic₁₀	φ: C₂²/C₂ → C₂ ⊆ Out Dic₅	80		Dic5.1C2^2	80,35
Dic₅.₂C₂² = C₄○D₂₀	φ: C₂²/C₂ → C₂ ⊆ Out Dic₅	40	2	Dic5.2C2^2	80,38
Dic₅.₃C₂² = Q₈×D₅	φ: C₂²/C₂ → C₂ ⊆ Out Dic₅	40	4-	Dic5.3C2^2	80,41
Dic₅.₄C₂² = D₅⋊C₈	φ: C₂²/C₂ → C₂ ⊆ Out Dic₅	40	4	Dic5.4C2^2	80,28
Dic₅.₅C₂² = C₄.F₅	φ: C₂²/C₂ → C₂ ⊆ Out Dic₅	40	4	Dic5.5C2^2	80,29
Dic₅.₆C₂² = C₂×C₅⋊C₈	φ: C₂²/C₂ → C₂ ⊆ Out Dic₅	80		Dic5.6C2^2	80,32
Dic₅.₇C₂² = C₂².F₅	φ: C₂²/C₂ → C₂ ⊆ Out Dic₅	40	4-	Dic5.7C2^2	80,33
Dic₅.₈C₂² = D₄⋊₂D₅	φ: trivial image	40	4-	Dic5.8C2^2	80,40
Dic₅.₉C₂² = Q₈⋊₂D₅	φ: trivial image	40	4+	Dic5.9C2^2	80,42

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁