Extensions 1→N→G→Q→1 with N=C₃₀ and Q=D₄

Direct product G=N×Q with N=C₃₀ and Q=D₄

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

Semidirect products G=N:Q with N=C₃₀ and Q=D₄

extension	φ:Q→Aut N	d	Label	ID
C₃₀⋊₁D₄ = C₂×C₁₅⋊D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₃₀	120	C30:1D4	240,145
C₃₀⋊₂D₄ = C₂×C₃⋊D₂₀	φ: D₄/C₂ → C₂² ⊆ Aut C₃₀	120	C30:2D4	240,146
C₃₀⋊₃D₄ = C₂×C₅⋊D₁₂	φ: D₄/C₂ → C₂² ⊆ Aut C₃₀	120	C30:3D4	240,147
C₃₀⋊₄D₄ = C₂×D₆₀	φ: D₄/C₄ → C₂ ⊆ Aut C₃₀	120	C30:4D4	240,177
C₃₀⋊₅D₄ = C₆×D₂₀	φ: D₄/C₄ → C₂ ⊆ Aut C₃₀	120	C30:5D4	240,157
C₃₀⋊₆D₄ = C₁₀×D₁₂	φ: D₄/C₄ → C₂ ⊆ Aut C₃₀	120	C30:6D4	240,167
C₃₀⋊₇D₄ = C₂×C₁₅⋊₇D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	120	C30:7D4	240,184
C₃₀⋊₈D₄ = C₆×C₅⋊D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	120	C30:8D4	240,164
C₃₀⋊₉D₄ = C₁₀×C₃⋊D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	120	C30:9D4	240,174

Non-split extensions G=N.Q with N=C₃₀ and Q=D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃₀.₁D₄ = C₁₅⋊D₈	φ: D₄/C₂ → C₂² ⊆ Aut C₃₀	120	4	C30.1D4	240,13
C₃₀.₂D₄ = C₃⋊D₄₀	φ: D₄/C₂ → C₂² ⊆ Aut C₃₀	120	4+	C30.2D4	240,14
C₃₀.₃D₄ = C₅⋊D₂₄	φ: D₄/C₂ → C₂² ⊆ Aut C₃₀	120	4+	C30.3D4	240,15
C₃₀.₄D₄ = C₃₀.D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₃₀	120	4	C30.4D4	240,16
C₃₀.₅D₄ = C₂₀.D₆	φ: D₄/C₂ → C₂² ⊆ Aut C₃₀	120	4	C30.5D4	240,17
C₃₀.₆D₄ = C₆.D₂₀	φ: D₄/C₂ → C₂² ⊆ Aut C₃₀	120	4-	C30.6D4	240,18
C₃₀.₇D₄ = C₁₅⋊SD₁₆	φ: D₄/C₂ → C₂² ⊆ Aut C₃₀	120	4+	C30.7D4	240,19
C₃₀.₈D₄ = D₁₂.D₅	φ: D₄/C₂ → C₂² ⊆ Aut C₃₀	120	4-	C30.8D4	240,20
C₃₀.₉D₄ = Dic₆⋊D₅	φ: D₄/C₂ → C₂² ⊆ Aut C₃₀	120	4+	C30.9D4	240,21
C₃₀.₁₀D₄ = C₁₅⋊Q₁₆	φ: D₄/C₂ → C₂² ⊆ Aut C₃₀	240	4	C30.10D4	240,22
C₃₀.₁₁D₄ = C₃⋊Dic₂₀	φ: D₄/C₂ → C₂² ⊆ Aut C₃₀	240	4-	C30.11D4	240,23
C₃₀.₁₂D₄ = C₅⋊Dic₁₂	φ: D₄/C₂ → C₂² ⊆ Aut C₃₀	240	4-	C30.12D4	240,24
C₃₀.₁₃D₄ = D₁₀⋊Dic₃	φ: D₄/C₂ → C₂² ⊆ Aut C₃₀	120		C30.13D4	240,26
C₃₀.₁₄D₄ = D₆⋊Dic₅	φ: D₄/C₂ → C₂² ⊆ Aut C₃₀	120		C30.14D4	240,27
C₃₀.₁₅D₄ = D₃₀⋊₄C₄	φ: D₄/C₂ → C₂² ⊆ Aut C₃₀	120		C30.15D4	240,28
C₃₀.₁₆D₄ = C₃₀.Q₈	φ: D₄/C₂ → C₂² ⊆ Aut C₃₀	240		C30.16D4	240,29
C₃₀.₁₇D₄ = Dic₁₅⋊₅C₄	φ: D₄/C₂ → C₂² ⊆ Aut C₃₀	240		C30.17D4	240,30
C₃₀.₁₈D₄ = C₆.Dic₁₀	φ: D₄/C₂ → C₂² ⊆ Aut C₃₀	240		C30.18D4	240,31
C₃₀.₁₉D₄ = C₂₄⋊D₅	φ: D₄/C₄ → C₂ ⊆ Aut C₃₀	120	2	C30.19D4	240,67
C₃₀.₂₀D₄ = D₁₂₀	φ: D₄/C₄ → C₂ ⊆ Aut C₃₀	120	2+	C30.20D4	240,68
C₃₀.₂₁D₄ = Dic₆₀	φ: D₄/C₄ → C₂ ⊆ Aut C₃₀	240	2-	C30.21D4	240,69
C₃₀.₂₂D₄ = C₆₀⋊₅C₄	φ: D₄/C₄ → C₂ ⊆ Aut C₃₀	240		C30.22D4	240,74
C₃₀.₂₃D₄ = C₃×C₄₀⋊C₂	φ: D₄/C₄ → C₂ ⊆ Aut C₃₀	120	2	C30.23D4	240,35
C₃₀.₂₄D₄ = C₃×D₄₀	φ: D₄/C₄ → C₂ ⊆ Aut C₃₀	120	2	C30.24D4	240,36
C₃₀.₂₅D₄ = C₃×Dic₂₀	φ: D₄/C₄ → C₂ ⊆ Aut C₃₀	240	2	C30.25D4	240,37
C₃₀.₂₆D₄ = C₃×C₄⋊Dic₅	φ: D₄/C₄ → C₂ ⊆ Aut C₃₀	240		C30.26D4	240,42
C₃₀.₂₇D₄ = C₃×D₁₀⋊C₄	φ: D₄/C₄ → C₂ ⊆ Aut C₃₀	120		C30.27D4	240,43
C₃₀.₂₈D₄ = C₅×C₂₄⋊C₂	φ: D₄/C₄ → C₂ ⊆ Aut C₃₀	120	2	C30.28D4	240,51
C₃₀.₂₉D₄ = C₅×D₂₄	φ: D₄/C₄ → C₂ ⊆ Aut C₃₀	120	2	C30.29D4	240,52
C₃₀.₃₀D₄ = C₅×Dic₁₂	φ: D₄/C₄ → C₂ ⊆ Aut C₃₀	240	2	C30.30D4	240,53
C₃₀.₃₁D₄ = C₅×C₄⋊Dic₃	φ: D₄/C₄ → C₂ ⊆ Aut C₃₀	240		C30.31D4	240,58
C₃₀.₃₂D₄ = C₃₀.₄Q₈	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	240		C30.32D4	240,73
C₃₀.₃₃D₄ = D₃₀⋊₃C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	120		C30.33D4	240,75
C₃₀.₃₄D₄ = D₄⋊D₁₅	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	120	4+	C30.34D4	240,76
C₃₀.₃₅D₄ = D₄.D₁₅	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	120	4-	C30.35D4	240,77
C₃₀.₃₆D₄ = Q₈⋊₂D₁₅	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	120	4+	C30.36D4	240,78
C₃₀.₃₇D₄ = C₁₅⋊₇Q₁₆	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	240	4-	C30.37D4	240,79
C₃₀.₃₈D₄ = C₃₀.₃₈D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	120		C30.38D4	240,80
C₃₀.₃₉D₄ = C₃×C₁₀.D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	240		C30.39D4	240,41
C₃₀.₄₀D₄ = C₃×D₄⋊D₅	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	120	4	C30.40D4	240,44
C₃₀.₄₁D₄ = C₃×D₄.D₅	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	120	4	C30.41D4	240,45
C₃₀.₄₂D₄ = C₃×Q₈⋊D₅	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	120	4	C30.42D4	240,46
C₃₀.₄₃D₄ = C₃×C₅⋊Q₁₆	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	240	4	C30.43D4	240,47
C₃₀.₄₄D₄ = C₃×C₂³.D₅	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	120		C30.44D4	240,48
C₃₀.₄₅D₄ = C₅×Dic₃⋊C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	240		C30.45D4	240,57
C₃₀.₄₆D₄ = C₅×D₆⋊C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	120		C30.46D4	240,59
C₃₀.₄₇D₄ = C₅×D₄⋊S₃	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	120	4	C30.47D4	240,60
C₃₀.₄₈D₄ = C₅×D₄.S₃	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	120	4	C30.48D4	240,61
C₃₀.₄₉D₄ = C₅×Q₈⋊₂S₃	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	120	4	C30.49D4	240,62
C₃₀.₅₀D₄ = C₅×C₃⋊Q₁₆	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	240	4	C30.50D4	240,63
C₃₀.₅₁D₄ = C₅×C₆.D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₃₀	120		C30.51D4	240,64
C₃₀.₅₂D₄ = C₁₅×C₂²⋊C₄	central extension (φ=1)	120		C30.52D4	240,82
C₃₀.₅₃D₄ = C₁₅×C₄⋊C₄	central extension (φ=1)	240		C30.53D4	240,83
C₃₀.₅₄D₄ = C₁₅×D₈	central extension (φ=1)	120	2	C30.54D4	240,86
C₃₀.₅₅D₄ = C₁₅×SD₁₆	central extension (φ=1)	120	2	C30.55D4	240,87
C₃₀.₅₆D₄ = C₁₅×Q₁₆	central extension (φ=1)	240	2	C30.56D4	240,88

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Extensions 1→N→G→Q→1 with N=C30 and Q=D4

Extensions 1→N→G→Q→1 with N=C₃₀ and Q=D₄