Extensions 1→N→G→Q→1 with N=C₄ and Q=C₃×F₅

Direct product G=N×Q with N=C₄ and Q=C₃×F₅

		d	ρ	Label	ID
C₁₂×F₅		60	4	C12xF5	240,113

Semidirect products G=N:Q with N=C₄ and Q=C₃×F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(C₃×F₅) = C₃×C₄⋊F₅	φ: C₃×F₅/C₃×D₅ → C₂ ⊆ Aut C₄	60	4	C4:(C3xF5)	240,114

Non-split extensions G=N.Q with N=C₄ and Q=C₃×F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.(C₃×F₅) = C₃×C₄.F₅	φ: C₃×F₅/C₃×D₅ → C₂ ⊆ Aut C₄	120	4	C4.(C3xF5)	240,112
C₄.₂(C₃×F₅) = C₃×C₅⋊C₁₆	central extension (φ=1)	240	4	C4.2(C3xF5)	240,5
C₄.₃(C₃×F₅) = C₃×D₅⋊C₈	central extension (φ=1)	120	4	C4.3(C3xF5)	240,111

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C4 and Q=C3×F5