Extensions 1→N→G→Q→1 with N=C₆ and Q=C₄×D₅

Direct product G=N×Q with N=C₆ and Q=C₄×D₅

		d	ρ	Label	ID
D₅×C₂×C₁₂		120		D5xC2xC12	240,156

Semidirect products G=N:Q with N=C₆ and Q=C₄×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊₁(C₄×D₅) = C₂×D₃₀.C₂	φ: C₄×D₅/Dic₅ → C₂ ⊆ Aut C₆	120		C6:1(C4xD5)	240,144
C₆⋊₂(C₄×D₅) = C₂×C₄×D₁₅	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₆	120		C6:2(C4xD5)	240,176
C₆⋊₃(C₄×D₅) = C₂×D₅×Dic₃	φ: C₄×D₅/D₁₀ → C₂ ⊆ Aut C₆	120		C6:3(C4xD5)	240,139

Non-split extensions G=N.Q with N=C₆ and Q=C₄×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁(C₄×D₅) = D₁₅⋊₂C₈	φ: C₄×D₅/Dic₅ → C₂ ⊆ Aut C₆	120	4	C6.1(C4xD5)	240,9
C₆.₂(C₄×D₅) = D₃₀.₅C₄	φ: C₄×D₅/Dic₅ → C₂ ⊆ Aut C₆	120	4	C6.2(C4xD5)	240,12
C₆.₃(C₄×D₅) = D₃₀⋊₄C₄	φ: C₄×D₅/Dic₅ → C₂ ⊆ Aut C₆	120		C6.3(C4xD5)	240,28
C₆.₄(C₄×D₅) = Dic₁₅⋊₅C₄	φ: C₄×D₅/Dic₅ → C₂ ⊆ Aut C₆	240		C6.4(C4xD5)	240,30
C₆.₅(C₄×D₅) = C₈×D₁₅	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₆	120	2	C6.5(C4xD5)	240,65
C₆.₆(C₄×D₅) = C₄₀⋊S₃	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₆	120	2	C6.6(C4xD5)	240,66
C₆.₇(C₄×D₅) = C₄×Dic₁₅	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₆	240		C6.7(C4xD5)	240,72
C₆.₈(C₄×D₅) = C₃₀.₄Q₈	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₆	240		C6.8(C4xD5)	240,73
C₆.₉(C₄×D₅) = D₃₀⋊₃C₄	φ: C₄×D₅/C₂₀ → C₂ ⊆ Aut C₆	120		C6.9(C4xD5)	240,75
C₆.₁₀(C₄×D₅) = D₅×C₃⋊C₈	φ: C₄×D₅/D₁₀ → C₂ ⊆ Aut C₆	120	4	C6.10(C4xD5)	240,7
C₆.₁₁(C₄×D₅) = C₂₀.₃₂D₆	φ: C₄×D₅/D₁₀ → C₂ ⊆ Aut C₆	120	4	C6.11(C4xD5)	240,10
C₆.₁₂(C₄×D₅) = Dic₃×Dic₅	φ: C₄×D₅/D₁₀ → C₂ ⊆ Aut C₆	240		C6.12(C4xD5)	240,25
C₆.₁₃(C₄×D₅) = D₁₀⋊Dic₃	φ: C₄×D₅/D₁₀ → C₂ ⊆ Aut C₆	120		C6.13(C4xD5)	240,26
C₆.₁₄(C₄×D₅) = C₃₀.Q₈	φ: C₄×D₅/D₁₀ → C₂ ⊆ Aut C₆	240		C6.14(C4xD5)	240,29
C₆.₁₅(C₄×D₅) = D₅×C₂₄	central extension (φ=1)	120	2	C6.15(C4xD5)	240,33
C₆.₁₆(C₄×D₅) = C₃×C₈⋊D₅	central extension (φ=1)	120	2	C6.16(C4xD5)	240,34
C₆.₁₇(C₄×D₅) = C₁₂×Dic₅	central extension (φ=1)	240		C6.17(C4xD5)	240,40
C₆.₁₈(C₄×D₅) = C₃×C₁₀.D₄	central extension (φ=1)	240		C6.18(C4xD5)	240,41
C₆.₁₉(C₄×D₅) = C₃×D₁₀⋊C₄	central extension (φ=1)	120		C6.19(C4xD5)	240,43

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