Extensions 1→N→G→Q→1 with N=Dic₃ and Q=D₁₀

Direct product G=N×Q with N=Dic₃ and Q=D₁₀

		d	ρ	Label	ID
C₂×D₅×Dic₃		120		C2xD5xDic3	240,139

Semidirect products G=N:Q with N=Dic₃ and Q=D₁₀

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₃⋊₁D₁₀ = D₅×C₃⋊D₄	φ: D₁₀/D₅ → C₂ ⊆ Out Dic₃	60	4	Dic3:1D10	240,149
Dic₃⋊₂D₁₀ = D₁₀⋊D₆	φ: D₁₀/D₅ → C₂ ⊆ Out Dic₃	60	4+	Dic3:2D10	240,151
Dic₃⋊₃D₁₀ = S₃×D₂₀	φ: D₁₀/C₁₀ → C₂ ⊆ Out Dic₃	60	4+	Dic3:3D10	240,137
Dic₃⋊₄D₁₀ = C₂×C₃⋊D₂₀	φ: D₁₀/C₁₀ → C₂ ⊆ Out Dic₃	120		Dic3:4D10	240,146
Dic₃⋊₅D₁₀ = C₄×S₃×D₅	φ: trivial image	60	4	Dic3:5D10	240,135
Dic₃⋊₆D₁₀ = C₂×D₃₀.C₂	φ: trivial image	120		Dic3:6D10	240,144

Non-split extensions G=N.Q with N=Dic₃ and Q=D₁₀

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₃.₁D₁₀ = D₅×Dic₆	φ: D₁₀/D₅ → C₂ ⊆ Out Dic₃	120	4-	Dic3.1D10	240,125
Dic₃.₂D₁₀ = D₂₀⋊S₃	φ: D₁₀/D₅ → C₂ ⊆ Out Dic₃	120	4	Dic3.2D10	240,127
Dic₃.₃D₁₀ = D₁₅⋊Q₈	φ: D₁₀/D₅ → C₂ ⊆ Out Dic₃	120	4	Dic3.3D10	240,131
Dic₃.₄D₁₀ = C₁₂.₂₈D₁₀	φ: D₁₀/D₅ → C₂ ⊆ Out Dic₃	120	4+	Dic3.4D10	240,134
Dic₃.₅D₁₀ = C₃₀.C₂³	φ: D₁₀/D₅ → C₂ ⊆ Out Dic₃	120	4-	Dic3.5D10	240,141
Dic₃.₆D₁₀ = Dic₃.D₁₀	φ: D₁₀/D₅ → C₂ ⊆ Out Dic₃	120	4	Dic3.6D10	240,143
Dic₃.₇D₁₀ = S₃×Dic₁₀	φ: D₁₀/C₁₀ → C₂ ⊆ Out Dic₃	120	4-	Dic3.7D10	240,128
Dic₃.₈D₁₀ = D₆.D₁₀	φ: D₁₀/C₁₀ → C₂ ⊆ Out Dic₃	120	4	Dic3.8D10	240,132
Dic₃.₉D₁₀ = C₂×C₁₅⋊Q₈	φ: D₁₀/C₁₀ → C₂ ⊆ Out Dic₃	240		Dic3.9D10	240,148
Dic₃.₁₀D₁₀ = D₂₀⋊₅S₃	φ: trivial image	120	4-	Dic3.10D10	240,126
Dic₃.₁₁D₁₀ = D₆₀⋊C₂	φ: trivial image	120	4+	Dic3.11D10	240,130
Dic₃.₁₂D₁₀ = Dic₅.D₆	φ: trivial image	120	4	Dic3.12D10	240,140

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁