Extensions 1→N→G→Q→1 with N=C₂₀ and Q=D₆

Direct product G=N×Q with N=C₂₀ and Q=D₆

		d	ρ	Label	ID
S₃×C₂×C₂₀		120		S3xC2xC20	240,166

Semidirect products G=N:Q with N=C₂₀ and Q=D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀⋊₁D₆ = D₅×D₁₂	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	60	4+	C20:1D6	240,136
C₂₀⋊₂D₆ = C₂₀⋊D₆	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	60	4	C20:2D6	240,138
C₂₀⋊₃D₆ = D₄×D₁₅	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	60	4+	C20:3D6	240,179
C₂₀⋊₄D₆ = S₃×D₂₀	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	60	4+	C20:4D6	240,137
C₂₀⋊₅D₆ = C₄×S₃×D₅	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	60	4	C20:5D6	240,135
C₂₀⋊₆D₆ = C₅×S₃×D₄	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	60	4	C20:6D6	240,169
C₂₀⋊₇D₆ = C₂×D₆₀	φ: D₆/C₆ → C₂ ⊆ Aut C₂₀	120		C20:7D6	240,177
C₂₀⋊₈D₆ = C₂×C₄×D₁₅	φ: D₆/C₆ → C₂ ⊆ Aut C₂₀	120		C20:8D6	240,176
C₂₀⋊₉D₆ = C₁₀×D₁₂	φ: D₆/C₆ → C₂ ⊆ Aut C₂₀	120		C20:9D6	240,167

Non-split extensions G=N.Q with N=C₂₀ and Q=D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀.₁D₆ = C₁₅⋊D₈	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	120	4	C20.1D6	240,13
C₂₀.₂D₆ = C₅⋊D₂₄	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	120	4+	C20.2D6	240,15
C₂₀.₃D₆ = C₃₀.D₄	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	120	4	C20.3D6	240,16
C₂₀.₄D₆ = C₂₀.D₆	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	120	4	C20.4D6	240,17
C₂₀.₅D₆ = D₁₂.D₅	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	120	4-	C20.5D6	240,20
C₂₀.₆D₆ = Dic₆⋊D₅	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	120	4+	C20.6D6	240,21
C₂₀.₇D₆ = C₁₅⋊Q₁₆	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	240	4	C20.7D6	240,22
C₂₀.₈D₆ = C₅⋊Dic₁₂	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	240	4-	C20.8D6	240,24
C₂₀.₉D₆ = D₄⋊D₁₅	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	120	4+	C20.9D6	240,76
C₂₀.₁₀D₆ = D₄.D₁₅	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	120	4-	C20.10D6	240,77
C₂₀.₁₁D₆ = Q₈⋊₂D₁₅	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	120	4+	C20.11D6	240,78
C₂₀.₁₂D₆ = C₁₅⋊₇Q₁₆	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	240	4-	C20.12D6	240,79
C₂₀.₁₃D₆ = D₅×Dic₆	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	120	4-	C20.13D6	240,125
C₂₀.₁₄D₆ = D₂₀⋊S₃	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	120	4	C20.14D6	240,127
C₂₀.₁₅D₆ = D₁₂⋊D₅	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	120	4	C20.15D6	240,129
C₂₀.₁₆D₆ = D₁₅⋊Q₈	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	120	4	C20.16D6	240,131
C₂₀.₁₇D₆ = D₁₂⋊₅D₅	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	120	4-	C20.17D6	240,133
C₂₀.₁₈D₆ = C₁₂.₂₈D₁₀	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	120	4+	C20.18D6	240,134
C₂₀.₁₉D₆ = D₄⋊₂D₁₅	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	120	4-	C20.19D6	240,180
C₂₀.₂₀D₆ = Q₈×D₁₅	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	120	4-	C20.20D6	240,181
C₂₀.₂₁D₆ = Q₈⋊₃D₁₅	φ: D₆/C₃ → C₂² ⊆ Aut C₂₀	120	4+	C20.21D6	240,182
C₂₀.₂₂D₆ = C₃⋊D₄₀	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	120	4+	C20.22D6	240,14
C₂₀.₂₃D₆ = C₆.D₂₀	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	120	4-	C20.23D6	240,18
C₂₀.₂₄D₆ = C₁₅⋊SD₁₆	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	120	4+	C20.24D6	240,19
C₂₀.₂₅D₆ = C₃⋊Dic₂₀	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	240	4-	C20.25D6	240,23
C₂₀.₂₆D₆ = D₂₀⋊₅S₃	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	120	4-	C20.26D6	240,126
C₂₀.₂₇D₆ = S₃×Dic₁₀	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	120	4-	C20.27D6	240,128
C₂₀.₂₈D₆ = D₆₀⋊C₂	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	120	4+	C20.28D6	240,130
C₂₀.₂₉D₆ = D₅×C₃⋊C₈	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	120	4	C20.29D6	240,7
C₂₀.₃₀D₆ = S₃×C₅⋊₂C₈	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	120	4	C20.30D6	240,8
C₂₀.₃₁D₆ = D₁₅⋊₂C₈	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	120	4	C20.31D6	240,9
C₂₀.₃₂D₆ = C₂₀.₃₂D₆	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	120	4	C20.32D6	240,10
C₂₀.₃₃D₆ = D₆.Dic₅	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	120	4	C20.33D6	240,11
C₂₀.₃₄D₆ = D₃₀.₅C₄	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	120	4	C20.34D6	240,12
C₂₀.₃₅D₆ = D₆.D₁₀	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	120	4	C20.35D6	240,132
C₂₀.₃₆D₆ = C₅×D₄⋊S₃	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	120	4	C20.36D6	240,60
C₂₀.₃₇D₆ = C₅×D₄.S₃	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	120	4	C20.37D6	240,61
C₂₀.₃₈D₆ = C₅×Q₈⋊₂S₃	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	120	4	C20.38D6	240,62
C₂₀.₃₉D₆ = C₅×C₃⋊Q₁₆	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	240	4	C20.39D6	240,63
C₂₀.₄₀D₆ = C₅×D₄⋊₂S₃	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	120	4	C20.40D6	240,170
C₂₀.₄₁D₆ = C₅×S₃×Q₈	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	120	4	C20.41D6	240,171
C₂₀.₄₂D₆ = C₅×Q₈⋊₃S₃	φ: D₆/S₃ → C₂ ⊆ Aut C₂₀	120	4	C20.42D6	240,172
C₂₀.₄₃D₆ = C₂₄⋊D₅	φ: D₆/C₆ → C₂ ⊆ Aut C₂₀	120	2	C20.43D6	240,67
C₂₀.₄₄D₆ = D₁₂₀	φ: D₆/C₆ → C₂ ⊆ Aut C₂₀	120	2+	C20.44D6	240,68
C₂₀.₄₅D₆ = Dic₆₀	φ: D₆/C₆ → C₂ ⊆ Aut C₂₀	240	2-	C20.45D6	240,69
C₂₀.₄₆D₆ = C₂×Dic₃₀	φ: D₆/C₆ → C₂ ⊆ Aut C₂₀	240		C20.46D6	240,175
C₂₀.₄₇D₆ = C₈×D₁₅	φ: D₆/C₆ → C₂ ⊆ Aut C₂₀	120	2	C20.47D6	240,65
C₂₀.₄₈D₆ = C₄₀⋊S₃	φ: D₆/C₆ → C₂ ⊆ Aut C₂₀	120	2	C20.48D6	240,66
C₂₀.₄₉D₆ = C₂×C₁₅⋊₃C₈	φ: D₆/C₆ → C₂ ⊆ Aut C₂₀	240		C20.49D6	240,70
C₂₀.₅₀D₆ = C₆₀.₇C₄	φ: D₆/C₆ → C₂ ⊆ Aut C₂₀	120	2	C20.50D6	240,71
C₂₀.₅₁D₆ = D₆₀⋊₁₁C₂	φ: D₆/C₆ → C₂ ⊆ Aut C₂₀	120	2	C20.51D6	240,178
C₂₀.₅₂D₆ = C₅×C₂₄⋊C₂	φ: D₆/C₆ → C₂ ⊆ Aut C₂₀	120	2	C20.52D6	240,51
C₂₀.₅₃D₆ = C₅×D₂₄	φ: D₆/C₆ → C₂ ⊆ Aut C₂₀	120	2	C20.53D6	240,52
C₂₀.₅₄D₆ = C₅×Dic₁₂	φ: D₆/C₆ → C₂ ⊆ Aut C₂₀	240	2	C20.54D6	240,53
C₂₀.₅₅D₆ = C₁₀×Dic₆	φ: D₆/C₆ → C₂ ⊆ Aut C₂₀	240		C20.55D6	240,165
C₂₀.₅₆D₆ = S₃×C₄₀	central extension (φ=1)	120	2	C20.56D6	240,49
C₂₀.₅₇D₆ = C₅×C₈⋊S₃	central extension (φ=1)	120	2	C20.57D6	240,50
C₂₀.₅₈D₆ = C₁₀×C₃⋊C₈	central extension (φ=1)	240		C20.58D6	240,54
C₂₀.₅₉D₆ = C₅×C₄.Dic₃	central extension (φ=1)	120	2	C20.59D6	240,55
C₂₀.₆₀D₆ = C₅×C₄○D₁₂	central extension (φ=1)	120	2	C20.60D6	240,168

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Extensions 1→N→G→Q→1 with N=C20 and Q=D6

Extensions 1→N→G→Q→1 with N=C₂₀ and Q=D₆