Extensions 1→N→G→Q→1 with N=Dic₅ and Q=D₆

Direct product G=N×Q with N=Dic₅ and Q=D₆

		d	ρ	Label	ID
C₂×S₃×Dic₅		120		C2xS3xDic5	240,142

Semidirect products G=N:Q with N=Dic₅ and Q=D₆

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₅⋊₁D₆ = S₃×C₅⋊D₄	φ: D₆/S₃ → C₂ ⊆ Out Dic₅	60	4	Dic5:1D6	240,150
Dic₅⋊₂D₆ = D₁₀⋊D₆	φ: D₆/S₃ → C₂ ⊆ Out Dic₅	60	4+	Dic5:2D6	240,151
Dic₅⋊₃D₆ = D₅×D₁₂	φ: D₆/C₆ → C₂ ⊆ Out Dic₅	60	4+	Dic5:3D6	240,136
Dic₅⋊₄D₆ = C₂×C₅⋊D₁₂	φ: D₆/C₆ → C₂ ⊆ Out Dic₅	120		Dic5:4D6	240,147
Dic₅⋊₅D₆ = C₄×S₃×D₅	φ: trivial image	60	4	Dic5:5D6	240,135
Dic₅⋊₆D₆ = C₂×D₃₀.C₂	φ: trivial image	120		Dic5:6D6	240,144

Non-split extensions G=N.Q with N=Dic₅ and Q=D₆

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₅.₁D₆ = S₃×Dic₁₀	φ: D₆/S₃ → C₂ ⊆ Out Dic₅	120	4-	Dic5.1D6	240,128
Dic₅.₂D₆ = D₁₂⋊D₅	φ: D₆/S₃ → C₂ ⊆ Out Dic₅	120	4	Dic5.2D6	240,129
Dic₅.₃D₆ = D₆₀⋊C₂	φ: D₆/S₃ → C₂ ⊆ Out Dic₅	120	4+	Dic5.3D6	240,130
Dic₅.₄D₆ = D₁₅⋊Q₈	φ: D₆/S₃ → C₂ ⊆ Out Dic₅	120	4	Dic5.4D6	240,131
Dic₅.₅D₆ = Dic₅.D₆	φ: D₆/S₃ → C₂ ⊆ Out Dic₅	120	4	Dic5.5D6	240,140
Dic₅.₆D₆ = C₃₀.C₂³	φ: D₆/S₃ → C₂ ⊆ Out Dic₅	120	4-	Dic5.6D6	240,141
Dic₅.₇D₆ = S₃×C₅⋊C₈	φ: D₆/S₃ → C₂ ⊆ Out Dic₅	120	8-	Dic5.7D6	240,98
Dic₅.₈D₆ = D₁₅⋊C₈	φ: D₆/S₃ → C₂ ⊆ Out Dic₅	120	8+	Dic5.8D6	240,99
Dic₅.₉D₆ = D₆.F₅	φ: D₆/S₃ → C₂ ⊆ Out Dic₅	120	8-	Dic5.9D6	240,100
Dic₅.₁₀D₆ = Dic₃.F₅	φ: D₆/S₃ → C₂ ⊆ Out Dic₅	120	8+	Dic5.10D6	240,101
Dic₅.₁₁D₆ = D₅×Dic₆	φ: D₆/C₆ → C₂ ⊆ Out Dic₅	120	4-	Dic5.11D6	240,125
Dic₅.₁₂D₆ = D₆.D₁₀	φ: D₆/C₆ → C₂ ⊆ Out Dic₅	120	4	Dic5.12D6	240,132
Dic₅.₁₃D₆ = Dic₃.D₁₀	φ: D₆/C₆ → C₂ ⊆ Out Dic₅	120	4	Dic5.13D6	240,143
Dic₅.₁₄D₆ = C₂×C₁₅⋊Q₈	φ: D₆/C₆ → C₂ ⊆ Out Dic₅	240		Dic5.14D6	240,148
Dic₅.₁₅D₆ = C₆₀.C₄	φ: D₆/C₆ → C₂ ⊆ Out Dic₅	120	4	Dic5.15D6	240,118
Dic₅.₁₆D₆ = C₁₂.F₅	φ: D₆/C₆ → C₂ ⊆ Out Dic₅	120	4	Dic5.16D6	240,119
Dic₅.₁₇D₆ = C₂×C₁₅⋊C₈	φ: D₆/C₆ → C₂ ⊆ Out Dic₅	240		Dic5.17D6	240,122
Dic₅.₁₈D₆ = C₁₅⋊₈M₄(2)	φ: D₆/C₆ → C₂ ⊆ Out Dic₅	120	4	Dic5.18D6	240,123
Dic₅.₁₉D₆ = D₁₂⋊₅D₅	φ: trivial image	120	4-	Dic5.19D6	240,133
Dic₅.₂₀D₆ = C₁₂.₂₈D₁₀	φ: trivial image	120	4+	Dic5.20D6	240,134

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Extensions 1→N→G→Q→1 with N=Dic5 and Q=D6

Extensions 1→N→G→Q→1 with N=Dic₅ and Q=D₆