Extensions 1→N→G→Q→1 with N=C₂² and Q=C₆×D₅

Direct product G=N×Q with N=C₂² and Q=C₆×D₅

		d	ρ	Label	ID
D₅×C₂²×C₆		120		D5xC2^2xC6	240,205

Semidirect products G=N:Q with N=C₂² and Q=C₆×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂²⋊(C₆×D₅) = C₂×D₅×A₄	φ: C₆×D₅/D₁₀ → C₃ ⊆ Aut C₂²	30	6+	C2^2:(C6xD5)	240,198
C₂²⋊₂(C₆×D₅) = C₃×D₄×D₅	φ: C₆×D₅/C₃×D₅ → C₂ ⊆ Aut C₂²	60	4	C2^2:2(C6xD5)	240,159
C₂²⋊₃(C₆×D₅) = C₆×C₅⋊D₄	φ: C₆×D₅/C₃₀ → C₂ ⊆ Aut C₂²	120		C2^2:3(C6xD5)	240,164

Non-split extensions G=N.Q with N=C₂² and Q=C₆×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂².₁(C₆×D₅) = C₃×D₄⋊₂D₅	φ: C₆×D₅/C₃×D₅ → C₂ ⊆ Aut C₂²	120	4	C2^2.1(C6xD5)	240,160
C₂².₂(C₆×D₅) = C₃×C₄○D₂₀	φ: C₆×D₅/C₃₀ → C₂ ⊆ Aut C₂²	120	2	C2^2.2(C6xD5)	240,158
C₂².₃(C₆×D₅) = C₁₂×Dic₅	central extension (φ=1)	240		C2^2.3(C6xD5)	240,40
C₂².₄(C₆×D₅) = C₃×C₁₀.D₄	central extension (φ=1)	240		C2^2.4(C6xD5)	240,41
C₂².₅(C₆×D₅) = C₃×C₄⋊Dic₅	central extension (φ=1)	240		C2^2.5(C6xD5)	240,42
C₂².₆(C₆×D₅) = C₃×D₁₀⋊C₄	central extension (φ=1)	120		C2^2.6(C6xD5)	240,43
C₂².₇(C₆×D₅) = C₃×C₂³.D₅	central extension (φ=1)	120		C2^2.7(C6xD5)	240,48
C₂².₈(C₆×D₅) = C₆×Dic₁₀	central extension (φ=1)	240		C2^2.8(C6xD5)	240,155
C₂².₉(C₆×D₅) = D₅×C₂×C₁₂	central extension (φ=1)	120		C2^2.9(C6xD5)	240,156
C₂².₁₀(C₆×D₅) = C₆×D₂₀	central extension (φ=1)	120		C2^2.10(C6xD5)	240,157
C₂².₁₁(C₆×D₅) = C₂×C₆×Dic₅	central extension (φ=1)	240		C2^2.11(C6xD5)	240,163

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁