Extensions 1→N→G→Q→1 with N=C₃₀ and Q=D₆

Direct product G=N×Q with N=C₃₀ and Q=D₆

		d	ρ	Label	ID
S₃×C₂×C₃₀		120		S3xC2xC30	360,158

Semidirect products G=N:Q with N=C₃₀ and Q=D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃₀⋊₁D₆ = C₂×D₅×C₃⋊S₃	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	90		C30:1D6	360,152
C₃₀⋊₂D₆ = C₂×D₁₅⋊S₃	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	60	4	C30:2D6	360,155
C₃₀⋊₃D₆ = C₂×S₃×D₁₅	φ: D₆/S₃ → C₂ ⊆ Aut C₃₀	60	4+	C30:3D6	360,154
C₃₀⋊₄D₆ = S₃×C₆×D₅	φ: D₆/S₃ → C₂ ⊆ Aut C₃₀	60	4	C30:4D6	360,151
C₃₀⋊₅D₆ = S₃²×C₁₀	φ: D₆/S₃ → C₂ ⊆ Aut C₃₀	60	4	C30:5D6	360,153
C₃₀⋊₆D₆ = C₂²×C₃⋊D₁₅	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	180		C30:6D6	360,161
C₃₀⋊₇D₆ = C₂×C₆×D₁₅	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	120		C30:7D6	360,159
C₃₀⋊₈D₆ = C₃⋊S₃×C₂×C₁₀	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	180		C30:8D6	360,160

Non-split extensions G=N.Q with N=C₃₀ and Q=D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃₀.₁D₆ = C₄₅⋊Q₈	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	360	4-	C30.1D6	360,7
C₃₀.₂D₆ = D₉×Dic₅	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	180	4-	C30.2D6	360,8
C₃₀.₃D₆ = D₉₀.C₂	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	180	4+	C30.3D6	360,9
C₃₀.₄D₆ = C₅⋊D₃₆	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	180	4+	C30.4D6	360,10
C₃₀.₅D₆ = D₅×Dic₉	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	180	4-	C30.5D6	360,11
C₃₀.₆D₆ = C₄₅⋊D₄	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	180	4-	C30.6D6	360,12
C₃₀.₇D₆ = C₉⋊D₂₀	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	180	4+	C30.7D6	360,13
C₃₀.₈D₆ = C₂×D₅×D₉	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	90	4+	C30.8D6	360,45
C₃₀.₉D₆ = D₅×C₃⋊Dic₃	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	180		C30.9D6	360,65
C₃₀.₁₀D₆ = C₃⋊S₃×Dic₅	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	180		C30.10D6	360,66
C₃₀.₁₁D₆ = C₃₀.D₆	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	180		C30.11D6	360,67
C₃₀.₁₂D₆ = C₃₀.₁₂D₆	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	180		C30.12D6	360,68
C₃₀.₁₃D₆ = C₃²⋊₇D₂₀	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	180		C30.13D6	360,69
C₃₀.₁₄D₆ = C₁₅⋊D₁₂	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	180		C30.14D6	360,70
C₃₀.₁₅D₆ = C₁₅⋊Dic₆	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	360		C30.15D6	360,71
C₃₀.₁₆D₆ = Dic₃×D₁₅	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	120	4-	C30.16D6	360,77
C₃₀.₁₇D₆ = D₃₀.S₃	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	120	4	C30.17D6	360,84
C₃₀.₁₈D₆ = Dic₁₅⋊S₃	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	60	4	C30.18D6	360,85
C₃₀.₁₉D₆ = D₃₀⋊S₃	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	60	4	C30.19D6	360,86
C₃₀.₂₀D₆ = C₃²⋊₃D₂₀	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	120	4	C30.20D6	360,87
C₃₀.₂₁D₆ = C₃²⋊₃Dic₁₀	φ: D₆/C₃ → C₂² ⊆ Aut C₃₀	120	4	C30.21D6	360,88
C₃₀.₂₂D₆ = S₃×Dic₁₅	φ: D₆/S₃ → C₂ ⊆ Aut C₃₀	120	4-	C30.22D6	360,78
C₃₀.₂₃D₆ = C₆.D₃₀	φ: D₆/S₃ → C₂ ⊆ Aut C₃₀	60	4+	C30.23D6	360,79
C₃₀.₂₄D₆ = D₆⋊D₁₅	φ: D₆/S₃ → C₂ ⊆ Aut C₃₀	120	4-	C30.24D6	360,80
C₃₀.₂₅D₆ = C₃⋊D₆₀	φ: D₆/S₃ → C₂ ⊆ Aut C₃₀	60	4+	C30.25D6	360,81
C₃₀.₂₆D₆ = D₆⋊₂D₁₅	φ: D₆/S₃ → C₂ ⊆ Aut C₃₀	60	4+	C30.26D6	360,82
C₃₀.₂₇D₆ = C₃⋊Dic₃₀	φ: D₆/S₃ → C₂ ⊆ Aut C₃₀	120	4-	C30.27D6	360,83
C₃₀.₂₈D₆ = C₃×D₅×Dic₃	φ: D₆/S₃ → C₂ ⊆ Aut C₃₀	60	4	C30.28D6	360,58
C₃₀.₂₉D₆ = C₃×S₃×Dic₅	φ: D₆/S₃ → C₂ ⊆ Aut C₃₀	120	4	C30.29D6	360,59
C₃₀.₃₀D₆ = C₃×D₃₀.C₂	φ: D₆/S₃ → C₂ ⊆ Aut C₃₀	120	4	C30.30D6	360,60
C₃₀.₃₁D₆ = C₃×C₁₅⋊D₄	φ: D₆/S₃ → C₂ ⊆ Aut C₃₀	60	4	C30.31D6	360,61
C₃₀.₃₂D₆ = C₃×C₃⋊D₂₀	φ: D₆/S₃ → C₂ ⊆ Aut C₃₀	60	4	C30.32D6	360,62
C₃₀.₃₃D₆ = C₃×C₅⋊D₁₂	φ: D₆/S₃ → C₂ ⊆ Aut C₃₀	120	4	C30.33D6	360,63
C₃₀.₃₄D₆ = C₃×C₁₅⋊Q₈	φ: D₆/S₃ → C₂ ⊆ Aut C₃₀	120	4	C30.34D6	360,64
C₃₀.₃₅D₆ = C₅×S₃×Dic₃	φ: D₆/S₃ → C₂ ⊆ Aut C₃₀	120	4	C30.35D6	360,72
C₃₀.₃₆D₆ = C₅×C₆.D₆	φ: D₆/S₃ → C₂ ⊆ Aut C₃₀	60	4	C30.36D6	360,73
C₃₀.₃₇D₆ = C₅×D₆⋊S₃	φ: D₆/S₃ → C₂ ⊆ Aut C₃₀	120	4	C30.37D6	360,74
C₃₀.₃₈D₆ = C₅×C₃⋊D₁₂	φ: D₆/S₃ → C₂ ⊆ Aut C₃₀	60	4	C30.38D6	360,75
C₃₀.₃₉D₆ = C₅×C₃²⋊₂Q₈	φ: D₆/S₃ → C₂ ⊆ Aut C₃₀	120	4	C30.39D6	360,76
C₃₀.₄₀D₆ = Dic₉₀	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	360	2-	C30.40D6	360,25
C₃₀.₄₁D₆ = C₄×D₄₅	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	180	2	C30.41D6	360,26
C₃₀.₄₂D₆ = D₁₈₀	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	180	2+	C30.42D6	360,27
C₃₀.₄₃D₆ = C₂×Dic₄₅	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	360		C30.43D6	360,28
C₃₀.₄₄D₆ = C₄₅⋊₇D₄	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	180	2	C30.44D6	360,29
C₃₀.₄₅D₆ = C₂²×D₄₅	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	180		C30.45D6	360,49
C₃₀.₄₆D₆ = C₁₂.D₁₅	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	360		C30.46D6	360,110
C₃₀.₄₇D₆ = C₄×C₃⋊D₁₅	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	180		C30.47D6	360,111
C₃₀.₄₈D₆ = C₆₀⋊S₃	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	180		C30.48D6	360,112
C₃₀.₄₉D₆ = C₂×C₃⋊Dic₁₅	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	360		C30.49D6	360,113
C₃₀.₅₀D₆ = C₆²⋊D₅	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	180		C30.50D6	360,114
C₃₀.₅₁D₆ = C₃×Dic₃₀	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	120	2	C30.51D6	360,100
C₃₀.₅₂D₆ = C₁₂×D₁₅	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	120	2	C30.52D6	360,101
C₃₀.₅₃D₆ = C₃×D₆₀	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	120	2	C30.53D6	360,102
C₃₀.₅₄D₆ = C₆×Dic₁₅	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	120		C30.54D6	360,103
C₃₀.₅₅D₆ = C₃×C₁₅⋊₇D₄	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	60	2	C30.55D6	360,104
C₃₀.₅₆D₆ = C₅×Dic₁₈	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	360	2	C30.56D6	360,20
C₃₀.₅₇D₆ = D₉×C₂₀	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	180	2	C30.57D6	360,21
C₃₀.₅₈D₆ = C₅×D₃₆	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	180	2	C30.58D6	360,22
C₃₀.₅₉D₆ = C₁₀×Dic₉	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	360		C30.59D6	360,23
C₃₀.₆₀D₆ = C₅×C₉⋊D₄	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	180	2	C30.60D6	360,24
C₃₀.₆₁D₆ = D₉×C₂×C₁₀	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	180		C30.61D6	360,48
C₃₀.₆₂D₆ = C₅×C₃²⋊₄Q₈	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	360		C30.62D6	360,105
C₃₀.₆₃D₆ = C₃⋊S₃×C₂₀	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	180		C30.63D6	360,106
C₃₀.₆₄D₆ = C₅×C₁₂⋊S₃	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	180		C30.64D6	360,107
C₃₀.₆₅D₆ = C₁₀×C₃⋊Dic₃	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	360		C30.65D6	360,108
C₃₀.₆₆D₆ = C₅×C₃²⋊₇D₄	φ: D₆/C₆ → C₂ ⊆ Aut C₃₀	180		C30.66D6	360,109
C₃₀.₆₇D₆ = C₁₅×Dic₆	central extension (φ=1)	120	2	C30.67D6	360,95
C₃₀.₆₈D₆ = S₃×C₆₀	central extension (φ=1)	120	2	C30.68D6	360,96
C₃₀.₆₉D₆ = C₁₅×D₁₂	central extension (φ=1)	120	2	C30.69D6	360,97
C₃₀.₇₀D₆ = Dic₃×C₃₀	central extension (φ=1)	120		C30.70D6	360,98
C₃₀.₇₁D₆ = C₁₅×C₃⋊D₄	central extension (φ=1)	60	2	C30.71D6	360,99

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Extensions 1→N→G→Q→1 with N=C30 and Q=D6

Extensions 1→N→G→Q→1 with N=C₃₀ and Q=D₆