Extensions 1→N→G→Q→1 with N=C₆ and Q=C₂²×C₁₀

Direct product G=N×Q with N=C₆ and Q=C₂²×C₁₀

		d	ρ	Label	ID
C₂³×C₃₀		240		C2^3xC30	240,208

Semidirect products G=N:Q with N=C₆ and Q=C₂²×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊(C₂²×C₁₀) = S₃×C₂²×C₁₀	φ: C₂²×C₁₀/C₂×C₁₀ → C₂ ⊆ Aut C₆	120		C6:(C2^2xC10)	240,206

Non-split extensions G=N.Q with N=C₆ and Q=C₂²×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁(C₂²×C₁₀) = C₁₀×Dic₆	φ: C₂²×C₁₀/C₂×C₁₀ → C₂ ⊆ Aut C₆	240		C6.1(C2^2xC10)	240,165
C₆.₂(C₂²×C₁₀) = S₃×C₂×C₂₀	φ: C₂²×C₁₀/C₂×C₁₀ → C₂ ⊆ Aut C₆	120		C6.2(C2^2xC10)	240,166
C₆.₃(C₂²×C₁₀) = C₁₀×D₁₂	φ: C₂²×C₁₀/C₂×C₁₀ → C₂ ⊆ Aut C₆	120		C6.3(C2^2xC10)	240,167
C₆.₄(C₂²×C₁₀) = C₅×C₄○D₁₂	φ: C₂²×C₁₀/C₂×C₁₀ → C₂ ⊆ Aut C₆	120	2	C6.4(C2^2xC10)	240,168
C₆.₅(C₂²×C₁₀) = C₅×S₃×D₄	φ: C₂²×C₁₀/C₂×C₁₀ → C₂ ⊆ Aut C₆	60	4	C6.5(C2^2xC10)	240,169
C₆.₆(C₂²×C₁₀) = C₅×D₄⋊₂S₃	φ: C₂²×C₁₀/C₂×C₁₀ → C₂ ⊆ Aut C₆	120	4	C6.6(C2^2xC10)	240,170
C₆.₇(C₂²×C₁₀) = C₅×S₃×Q₈	φ: C₂²×C₁₀/C₂×C₁₀ → C₂ ⊆ Aut C₆	120	4	C6.7(C2^2xC10)	240,171
C₆.₈(C₂²×C₁₀) = C₅×Q₈⋊₃S₃	φ: C₂²×C₁₀/C₂×C₁₀ → C₂ ⊆ Aut C₆	120	4	C6.8(C2^2xC10)	240,172
C₆.₉(C₂²×C₁₀) = Dic₃×C₂×C₁₀	φ: C₂²×C₁₀/C₂×C₁₀ → C₂ ⊆ Aut C₆	240		C6.9(C2^2xC10)	240,173
C₆.₁₀(C₂²×C₁₀) = C₁₀×C₃⋊D₄	φ: C₂²×C₁₀/C₂×C₁₀ → C₂ ⊆ Aut C₆	120		C6.10(C2^2xC10)	240,174
C₆.₁₁(C₂²×C₁₀) = D₄×C₃₀	central extension (φ=1)	120		C6.11(C2^2xC10)	240,186
C₆.₁₂(C₂²×C₁₀) = Q₈×C₃₀	central extension (φ=1)	240		C6.12(C2^2xC10)	240,187
C₆.₁₃(C₂²×C₁₀) = C₁₅×C₄○D₄	central extension (φ=1)	120	2	C6.13(C2^2xC10)	240,188

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