Extensions 1→N→G→Q→1 with N=C₅ and Q=C₅²⋊C₄

Direct product G=N×Q with N=C₅ and Q=C₅²⋊C₄

		d	ρ	Label	ID
C₅×C₅²⋊C₄		20	4	C5xC5^2:C4	500,44

Semidirect products G=N:Q with N=C₅ and Q=C₅²⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊(C₅²⋊C₄) = C₅³⋊₉C₄	φ: C₅²⋊C₄/C₅² → C₄ ⊆ Aut C₅	50		C5:(C5^2:C4)	500,49
C₅⋊₂(C₅²⋊C₄) = C₅³⋊₆C₄	φ: C₅²⋊C₄/C₅⋊D₅ → C₂ ⊆ Aut C₅	20	4	C5:2(C5^2:C4)	500,46

Non-split extensions G=N.Q with N=C₅ and Q=C₅²⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.(C₅²⋊C₄) = C₂₅⋊₂F₅	φ: C₅²⋊C₄/C₅² → C₄ ⊆ Aut C₅	50	4+	C5.(C5^2:C4)	500,24
C₅.₂(C₅²⋊C₄) = He₅⋊₄C₄	central stem extension (φ=1)	25	5	C5.2(C5^2:C4)	500,25

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Extensions 1→N→G→Q→1 with N=C5 and Q=C52⋊C4