Extensions 1→N→G→Q→1 with N=C₆ and Q=C₅×D₄

Direct product G=N×Q with N=C₆ and Q=C₅×D₄

		d	ρ	Label	ID
D₄×C₃₀		120		D4xC30	240,186

Semidirect products G=N:Q with N=C₆ and Q=C₅×D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊₁(C₅×D₄) = C₁₀×D₁₂	φ: C₅×D₄/C₂₀ → C₂ ⊆ Aut C₆	120		C6:1(C5xD4)	240,167
C₆⋊₂(C₅×D₄) = C₁₀×C₃⋊D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₆	120		C6:2(C5xD4)	240,174

Non-split extensions G=N.Q with N=C₆ and Q=C₅×D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁(C₅×D₄) = C₅×C₂₄⋊C₂	φ: C₅×D₄/C₂₀ → C₂ ⊆ Aut C₆	120	2	C6.1(C5xD4)	240,51
C₆.₂(C₅×D₄) = C₅×D₂₄	φ: C₅×D₄/C₂₀ → C₂ ⊆ Aut C₆	120	2	C6.2(C5xD4)	240,52
C₆.₃(C₅×D₄) = C₅×Dic₁₂	φ: C₅×D₄/C₂₀ → C₂ ⊆ Aut C₆	240	2	C6.3(C5xD4)	240,53
C₆.₄(C₅×D₄) = C₅×C₄⋊Dic₃	φ: C₅×D₄/C₂₀ → C₂ ⊆ Aut C₆	240		C6.4(C5xD4)	240,58
C₆.₅(C₅×D₄) = C₅×Dic₃⋊C₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₆	240		C6.5(C5xD4)	240,57
C₆.₆(C₅×D₄) = C₅×D₆⋊C₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₆	120		C6.6(C5xD4)	240,59
C₆.₇(C₅×D₄) = C₅×D₄⋊S₃	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₆	120	4	C6.7(C5xD4)	240,60
C₆.₈(C₅×D₄) = C₅×D₄.S₃	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₆	120	4	C6.8(C5xD4)	240,61
C₆.₉(C₅×D₄) = C₅×Q₈⋊₂S₃	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₆	120	4	C6.9(C5xD4)	240,62
C₆.₁₀(C₅×D₄) = C₅×C₃⋊Q₁₆	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₆	240	4	C6.10(C5xD4)	240,63
C₆.₁₁(C₅×D₄) = C₅×C₆.D₄	φ: C₅×D₄/C₂×C₁₀ → C₂ ⊆ Aut C₆	120		C6.11(C5xD4)	240,64
C₆.₁₂(C₅×D₄) = C₁₅×C₂²⋊C₄	central extension (φ=1)	120		C6.12(C5xD4)	240,82
C₆.₁₃(C₅×D₄) = C₁₅×C₄⋊C₄	central extension (φ=1)	240		C6.13(C5xD4)	240,83
C₆.₁₄(C₅×D₄) = C₁₅×D₈	central extension (φ=1)	120	2	C6.14(C5xD4)	240,86
C₆.₁₅(C₅×D₄) = C₁₅×SD₁₆	central extension (φ=1)	120	2	C6.15(C5xD4)	240,87
C₆.₁₆(C₅×D₄) = C₁₅×Q₁₆	central extension (φ=1)	240	2	C6.16(C5xD4)	240,88

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