Extensions 1→N→G→Q→1 with N=D₈ and Q=C₃×D₅

Direct product G=N×Q with N=D₈ and Q=C₃×D₅

		d	ρ	Label	ID
C₃×D₅×D₈		120	4	C3xD5xD8	480,703

Semidirect products G=N:Q with N=D₈ and Q=C₃×D₅

extension	φ:Q→Out N	d	ρ	Label	ID
D₈⋊₁(C₃×D₅) = C₃×C₅⋊D₁₆	φ: C₃×D₅/C₁₅ → C₂ ⊆ Out D₈	240	4	D8:1(C3xD5)	480,104
D₈⋊₂(C₃×D₅) = C₃×D₈⋊D₅	φ: C₃×D₅/C₁₅ → C₂ ⊆ Out D₈	120	4	D8:2(C3xD5)	480,704
D₈⋊₃(C₃×D₅) = C₃×D₈⋊₃D₅	φ: trivial image	240	4	D8:3(C3xD5)	480,705

Non-split extensions G=N.Q with N=D₈ and Q=C₃×D₅

extension	φ:Q→Out N	d	ρ	Label	ID
D₈.(C₃×D₅) = C₃×D₈.D₅	φ: C₃×D₅/C₁₅ → C₂ ⊆ Out D₈	240	4	D8.(C3xD5)	480,105

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=D8 and Q=C3×D5