Extensions 1→N→G→Q→1 with N=C₃×D₅ and Q=C₄⋊C₄

Direct product G=N×Q with N=C₃×D₅ and Q=C₄⋊C₄

		d	ρ	Label	ID
C₃×D₅×C₄⋊C₄		240		C3xD5xC4:C4	480,684

Semidirect products G=N:Q with N=C₃×D₅ and Q=C₄⋊C₄

extension	φ:Q→Out N	d	ρ	Label	ID
(C₃×D₅)⋊(C₄⋊C₄) = C₂×Dic₃⋊F₅	φ: C₄⋊C₄/C₂² → C₂² ⊆ Out C₃×D₅	120		(C3xD5):(C4:C4)	480,1001
(C₃×D₅)⋊₂(C₄⋊C₄) = D₅×Dic₃⋊C₄	φ: C₄⋊C₄/C₂×C₄ → C₂ ⊆ Out C₃×D₅	240		(C3xD5):2(C4:C4)	480,468
(C₃×D₅)⋊₃(C₄⋊C₄) = D₅×C₄⋊Dic₃	φ: C₄⋊C₄/C₂×C₄ → C₂ ⊆ Out C₃×D₅	240		(C3xD5):3(C4:C4)	480,488
(C₃×D₅)⋊₄(C₄⋊C₄) = C₂×C₆₀⋊C₄	φ: C₄⋊C₄/C₂×C₄ → C₂ ⊆ Out C₃×D₅	120		(C3xD5):4(C4:C4)	480,1064
(C₃×D₅)⋊₅(C₄⋊C₄) = C₆×C₄⋊F₅	φ: C₄⋊C₄/C₂×C₄ → C₂ ⊆ Out C₃×D₅	120		(C3xD5):5(C4:C4)	480,1051

Non-split extensions G=N.Q with N=C₃×D₅ and Q=C₄⋊C₄

extension	φ:Q→Out N	d	ρ	Label	ID
(C₃×D₅).(C₄⋊C₄) = D₁₀.₂₀D₁₂	φ: C₄⋊C₄/C₂² → C₂² ⊆ Out C₃×D₅	120		(C3xD5).(C4:C4)	480,243
(C₃×D₅).₂(C₄⋊C₄) = D₁₀.₁₀D₁₂	φ: C₄⋊C₄/C₂×C₄ → C₂ ⊆ Out C₃×D₅	120		(C3xD5).2(C4:C4)	480,311
(C₃×D₅).₃(C₄⋊C₄) = C₃×D₁₀.₃Q₈	φ: C₄⋊C₄/C₂×C₄ → C₂ ⊆ Out C₃×D₅	120		(C3xD5).3(C4:C4)	480,286

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁