Extensions 1→N→G→Q→1 with N=C₃×C₅⋊D₄ and Q=C₄

Direct product G=N×Q with N=C₃×C₅⋊D₄ and Q=C₄

		d	ρ	Label	ID
C₁₂×C₅⋊D₄		240		C12xC5:D4	480,721

Semidirect products G=N:Q with N=C₃×C₅⋊D₄ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
(C₃×C₅⋊D₄)⋊₁C₄ = D₄×C₃⋊F₅	φ: C₄/C₁ → C₄ ⊆ Out C₃×C₅⋊D₄	60	8	(C3xC5:D4):1C4	480,1067
(C₃×C₅⋊D₄)⋊₂C₄ = C₃×D₄×F₅	φ: C₄/C₁ → C₄ ⊆ Out C₃×C₅⋊D₄	60	8	(C3xC5:D4):2C4	480,1054
(C₃×C₅⋊D₄)⋊₃C₄ = Dic₃×C₅⋊D₄	φ: C₄/C₂ → C₂ ⊆ Out C₃×C₅⋊D₄	240		(C3xC5:D4):3C4	480,629
(C₃×C₅⋊D₄)⋊₄C₄ = Dic₁₅⋊₁₆D₄	φ: C₄/C₂ → C₂ ⊆ Out C₃×C₅⋊D₄	240		(C3xC5:D4):4C4	480,635
(C₃×C₅⋊D₄)⋊₅C₄ = C₃×Dic₅⋊₄D₄	φ: C₄/C₂ → C₂ ⊆ Out C₃×C₅⋊D₄	240		(C3xC5:D4):5C4	480,674

Non-split extensions G=N.Q with N=C₃×C₅⋊D₄ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
(C₃×C₅⋊D₄).₁C₄ = Dic₁₀.Dic₃	φ: C₄/C₁ → C₄ ⊆ Out C₃×C₅⋊D₄	240	8	(C3xC5:D4).1C4	480,1066
(C₃×C₅⋊D₄).₂C₄ = C₃×D₄.F₅	φ: C₄/C₁ → C₄ ⊆ Out C₃×C₅⋊D₄	240	8	(C3xC5:D4).2C4	480,1053
(C₃×C₅⋊D₄).₃C₄ = D₂₀.₃Dic₃	φ: C₄/C₂ → C₂ ⊆ Out C₃×C₅⋊D₄	240	4	(C3xC5:D4).3C4	480,359
(C₃×C₅⋊D₄).₄C₄ = D₂₀.₂Dic₃	φ: C₄/C₂ → C₂ ⊆ Out C₃×C₅⋊D₄	240	4	(C3xC5:D4).4C4	480,360
(C₃×C₅⋊D₄).₅C₄ = C₃×D₂₀.₂C₄	φ: C₄/C₂ → C₂ ⊆ Out C₃×C₅⋊D₄	240	4	(C3xC5:D4).5C4	480,700
(C₃×C₅⋊D₄).₆C₄ = C₃×D₂₀.₃C₄	φ: trivial image	240	2	(C3xC5:D4).6C4	480,694

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁