Extensions 1→N→G→Q→1 with N=C₅ and Q=C₂²×C₄

Direct product G=N×Q with N=C₅ and Q=C₂²×C₄

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

Semidirect products G=N:Q with N=C₅ and Q=C₂²×C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊(C₂²×C₄) = C₂²×F₅	φ: C₂²×C₄/C₂² → C₄ ⊆ Aut C₅	20		C5:(C2^2xC4)	80,50
C₅⋊₂(C₂²×C₄) = C₂×C₄×D₅	φ: C₂²×C₄/C₂×C₄ → C₂ ⊆ Aut C₅	40		C5:2(C2^2xC4)	80,36
C₅⋊₃(C₂²×C₄) = C₂²×Dic₅	φ: C₂²×C₄/C₂³ → C₂ ⊆ Aut C₅	80		C5:3(C2^2xC4)	80,43

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁