Extensions 1→N→G→Q→1 with N=C₁₄ and Q=C₃×D₅

Direct product G=N×Q with N=C₁₄ and Q=C₃×D₅

		d	ρ	Label	ID
D₅×C₄₂		210	2	D5xC42	420,35

Semidirect products G=N:Q with N=C₁₄ and Q=C₃×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₄⋊(C₃×D₅) = C₂×C₅⋊F₇	φ: C₃×D₅/C₅ → C₆ ⊆ Aut C₁₄	70	6+	C14:(C3xD5)	420,19
C₁₄⋊₂(C₃×D₅) = C₂×D₅×C₇⋊C₃	φ: C₃×D₅/D₅ → C₃ ⊆ Aut C₁₄	70	6	C14:2(C3xD5)	420,18
C₁₄⋊₃(C₃×D₅) = C₆×D₃₅	φ: C₃×D₅/C₁₅ → C₂ ⊆ Aut C₁₄	210	2	C14:3(C3xD5)	420,36

Non-split extensions G=N.Q with N=C₁₄ and Q=C₃×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₄.(C₃×D₅) = C₃₅⋊₃C₁₂	φ: C₃×D₅/C₅ → C₆ ⊆ Aut C₁₄	140	6-	C14.(C3xD5)	420,3
C₁₄.₂(C₃×D₅) = Dic₅×C₇⋊C₃	φ: C₃×D₅/D₅ → C₃ ⊆ Aut C₁₄	140	6	C14.2(C3xD5)	420,2
C₁₄.₃(C₃×D₅) = C₃×Dic₃₅	φ: C₃×D₅/C₁₅ → C₂ ⊆ Aut C₁₄	420	2	C14.3(C3xD5)	420,7
C₁₄.₄(C₃×D₅) = Dic₅×C₂₁	central extension (φ=1)	420	2	C14.4(C3xD5)	420,6

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