Extensions 1→N→G→Q→1 with N=C₄○D₄ and Q=C₅×S₃

Direct product G=N×Q with N=C₄○D₄ and Q=C₅×S₃

		d	ρ	Label	ID
C₅×S₃×C₄○D₄		120	4	C5xS3xC4oD4	480,1160

Semidirect products G=N:Q with N=C₄○D₄ and Q=C₅×S₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₄○D₄⋊₁(C₅×S₃) = C₅×C₄.₆S₄	φ: C₅×S₃/C₅ → S₃ ⊆ Out C₄○D₄	80	2	C4oD4:1(C5xS3)	480,1020
C₄○D₄⋊₂(C₅×S₃) = C₅×C₄.₃S₄	φ: C₅×S₃/C₅ → S₃ ⊆ Out C₄○D₄	80	4	C4oD4:2(C5xS3)	480,1021
C₄○D₄⋊₃(C₅×S₃) = C₅×D₄⋊D₆	φ: C₅×S₃/C₁₅ → C₂ ⊆ Out C₄○D₄	120	4	C4oD4:3(C5xS3)	480,828
C₄○D₄⋊₄(C₅×S₃) = C₅×Q₈.₁₃D₆	φ: C₅×S₃/C₁₅ → C₂ ⊆ Out C₄○D₄	240	4	C4oD4:4(C5xS3)	480,829
C₄○D₄⋊₅(C₅×S₃) = C₅×D₄○D₁₂	φ: C₅×S₃/C₁₅ → C₂ ⊆ Out C₄○D₄	120	4	C4oD4:5(C5xS3)	480,1161
C₄○D₄⋊₆(C₅×S₃) = C₅×Q₈○D₁₂	φ: C₅×S₃/C₁₅ → C₂ ⊆ Out C₄○D₄	240	4	C4oD4:6(C5xS3)	480,1162

Non-split extensions G=N.Q with N=C₄○D₄ and Q=C₅×S₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₄○D₄.₁(C₅×S₃) = C₅×U₂(𝔽₃)	φ: C₅×S₃/C₅ → S₃ ⊆ Out C₄○D₄	120	2	C4oD4.1(C5xS3)	480,257
C₄○D₄.₂(C₅×S₃) = C₅×C₄.S₄	φ: C₅×S₃/C₅ → S₃ ⊆ Out C₄○D₄	160	4	C4oD4.2(C5xS3)	480,1019
C₄○D₄.₃(C₅×S₃) = C₅×Q₈⋊₃Dic₃	φ: C₅×S₃/C₁₅ → C₂ ⊆ Out C₄○D₄	120	4	C4oD4.3(C5xS3)	480,156
C₄○D₄.₄(C₅×S₃) = C₅×Q₈.₁₄D₆	φ: C₅×S₃/C₁₅ → C₂ ⊆ Out C₄○D₄	240	4	C4oD4.4(C5xS3)	480,830
C₄○D₄.₅(C₅×S₃) = C₅×D₄.Dic₃	φ: trivial image	240	4	C4oD4.5(C5xS3)	480,827

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁