Extensions 1→N→G→Q→1 with N=C₁₀ and Q=C₄

Direct product G=N×Q with N=C₁₀ and Q=C₄

		d	ρ	Label	ID
C₂×C₂₀		40		C2xC20	40,9

Semidirect products G=N:Q with N=C₁₀ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀⋊C₄ = C₂×F₅	φ: C₄/C₁ → C₄ ⊆ Aut C₁₀	10	4+	C10:C4	40,12
C₁₀⋊₂C₄ = C₂×Dic₅	φ: C₄/C₂ → C₂ ⊆ Aut C₁₀	40		C10:2C4	40,7

Non-split extensions G=N.Q with N=C₁₀ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀.C₄ = C₅⋊C₈	φ: C₄/C₁ → C₄ ⊆ Aut C₁₀	40	4-	C10.C4	40,3
C₁₀.₂C₄ = C₅⋊₂C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₁₀	40	2	C10.2C4	40,1

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C10 and Q=C4