Extensions 1→N→G→Q→1 with N=C₅⋊₂C₈ and Q=Dic₃

Direct product G=N×Q with N=C₅⋊₂C₈ and Q=Dic₃

		d	ρ	Label	ID
Dic₃×C₅⋊₂C₈		480		Dic3xC5:2C8	480,26

Semidirect products G=N:Q with N=C₅⋊₂C₈ and Q=Dic₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₅⋊₂C₈⋊₁Dic₃ = C₆₀.₇Q₈	φ: Dic₃/C₆ → C₂ ⊆ Out C₅⋊₂C₈	480		C5:2C8:1Dic3	480,61
C₅⋊₂C₈⋊₂Dic₃ = C₆₀.₈Q₈	φ: Dic₃/C₆ → C₂ ⊆ Out C₅⋊₂C₈	480		C5:2C8:2Dic3	480,64
C₅⋊₂C₈⋊₃Dic₃ = C₃₀.₂₂C₄²	φ: Dic₃/C₆ → C₂ ⊆ Out C₅⋊₂C₈	480		C5:2C8:3Dic3	480,29
C₅⋊₂C₈⋊₄Dic₃ = C₃₀.₂₃C₄²	φ: Dic₃/C₆ → C₂ ⊆ Out C₅⋊₂C₈	480		C5:2C8:4Dic3	480,30
C₅⋊₂C₈⋊₅Dic₃ = C₁₂₀⋊C₄	φ: Dic₃/C₆ → C₂ ⊆ Out C₅⋊₂C₈	120	4	C5:2C8:5Dic3	480,298
C₅⋊₂C₈⋊₆Dic₃ = D₅.D₂₄	φ: Dic₃/C₆ → C₂ ⊆ Out C₅⋊₂C₈	120	4	C5:2C8:6Dic3	480,299
C₅⋊₂C₈⋊₇Dic₃ = C₈×C₃⋊F₅	φ: Dic₃/C₆ → C₂ ⊆ Out C₅⋊₂C₈	120	4	C5:2C8:7Dic3	480,296
C₅⋊₂C₈⋊₈Dic₃ = C₂₄⋊F₅	φ: Dic₃/C₆ → C₂ ⊆ Out C₅⋊₂C₈	120	4	C5:2C8:8Dic3	480,297
C₅⋊₂C₈⋊₉Dic₃ = Dic₁₅⋊₄C₈	φ: trivial image	480		C5:2C8:9Dic3	480,27

Non-split extensions G=N.Q with N=C₅⋊₂C₈ and Q=Dic₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₅⋊₂C₈.₁Dic₃ = C₆₀.₁₀₅D₄	φ: Dic₃/C₆ → C₂ ⊆ Out C₅⋊₂C₈	240	4	C5:2C8.1Dic3	480,67
C₅⋊₂C₈.₂Dic₃ = C₄₀.₅₁D₆	φ: Dic₃/C₆ → C₂ ⊆ Out C₅⋊₂C₈	240	4	C5:2C8.2Dic3	480,10
C₅⋊₂C₈.₃Dic₃ = C₄₀.Dic₃	φ: Dic₃/C₆ → C₂ ⊆ Out C₅⋊₂C₈	240	4	C5:2C8.3Dic3	480,300
C₅⋊₂C₈.₄Dic₃ = C₂₄.₁F₅	φ: Dic₃/C₆ → C₂ ⊆ Out C₅⋊₂C₈	240	4	C5:2C8.4Dic3	480,301
C₅⋊₂C₈.₅Dic₃ = C₂×C₁₅⋊C₁₆	φ: Dic₃/C₆ → C₂ ⊆ Out C₅⋊₂C₈	480		C5:2C8.5Dic3	480,302
C₅⋊₂C₈.₆Dic₃ = C₆₀.C₈	φ: Dic₃/C₆ → C₂ ⊆ Out C₅⋊₂C₈	240	4	C5:2C8.6Dic3	480,303
C₅⋊₂C₈.₇Dic₃ = D₅×C₃⋊C₁₆	φ: trivial image	240	4	C5:2C8.7Dic3	480,7

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁