Extensions 1→N→G→Q→1 with N=C₃₀ and Q=M₄(2)

Direct product G=N×Q with N=C₃₀ and Q=M₄(2)

		d	ρ	Label	ID
M₄(2)×C₃₀		240		M4(2)xC30	480,935

Semidirect products G=N:Q with N=C₃₀ and Q=M₄(2)

extension	φ:Q→Aut N	d	Label	ID
C₃₀⋊₁M₄(2) = C₂×D₆.F₅	φ: M₄(2)/C₂ → C₂×C₄ ⊆ Aut C₃₀	240	C30:1M4(2)	480,1008
C₃₀⋊₂M₄(2) = C₂×Dic₃.F₅	φ: M₄(2)/C₂ → C₂×C₄ ⊆ Aut C₃₀	240	C30:2M4(2)	480,1009
C₃₀⋊₃M₄(2) = C₂×C₁₂.F₅	φ: M₄(2)/C₄ → C₄ ⊆ Aut C₃₀	240	C30:3M4(2)	480,1061
C₃₀⋊₄M₄(2) = C₆×C₄.F₅	φ: M₄(2)/C₄ → C₄ ⊆ Aut C₃₀	240	C30:4M4(2)	480,1048
C₃₀⋊₅M₄(2) = C₂×C₂₀.₃₂D₆	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₃₀	240	C30:5M4(2)	480,369
C₃₀⋊₆M₄(2) = C₂×D₆.Dic₅	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₃₀	240	C30:6M4(2)	480,370
C₃₀⋊₇M₄(2) = C₂×D₃₀.₅C₄	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₃₀	240	C30:7M4(2)	480,371
C₃₀⋊₈M₄(2) = C₂×C₁₅⋊₈M₄(2)	φ: M₄(2)/C₂² → C₄ ⊆ Aut C₃₀	240	C30:8M4(2)	480,1071
C₃₀⋊₉M₄(2) = C₆×C₂².F₅	φ: M₄(2)/C₂² → C₄ ⊆ Aut C₃₀	240	C30:9M4(2)	480,1058
C₃₀⋊₁₀M₄(2) = C₂×C₄₀⋊S₃	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₃₀	240	C30:10M4(2)	480,865
C₃₀⋊₁₁M₄(2) = C₆×C₈⋊D₅	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₃₀	240	C30:11M4(2)	480,693
C₃₀⋊₁₂M₄(2) = C₁₀×C₈⋊S₃	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₃₀	240	C30:12M4(2)	480,779
C₃₀⋊₁₃M₄(2) = C₂×C₆₀.₇C₄	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₃₀	240	C30:13M4(2)	480,886
C₃₀⋊₁₄M₄(2) = C₆×C₄.Dic₅	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₃₀	240	C30:14M4(2)	480,714
C₃₀⋊₁₅M₄(2) = C₁₀×C₄.Dic₃	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₃₀	240	C30:15M4(2)	480,800

Non-split extensions G=N.Q with N=C₃₀ and Q=M₄(2)

extension	φ:Q→Aut N	d	Label	ID
C₃₀.₁M₄(2) = C₃₀.M₄(2)	φ: M₄(2)/C₂ → C₂×C₄ ⊆ Aut C₃₀	480	C30.1M4(2)	480,245
C₃₀.₂M₄(2) = Dic₅.₂₂D₁₂	φ: M₄(2)/C₂ → C₂×C₄ ⊆ Aut C₃₀	240	C30.2M4(2)	480,246
C₃₀.₃M₄(2) = D₃₀⋊C₈	φ: M₄(2)/C₂ → C₂×C₄ ⊆ Aut C₃₀	240	C30.3M4(2)	480,247
C₃₀.₄M₄(2) = C₃₀.₄M₄(2)	φ: M₄(2)/C₂ → C₂×C₄ ⊆ Aut C₃₀	480	C30.4M4(2)	480,252
C₃₀.₅M₄(2) = Dic₁₅⋊C₈	φ: M₄(2)/C₂ → C₂×C₄ ⊆ Aut C₃₀	480	C30.5M4(2)	480,253
C₃₀.₆M₄(2) = C₆₀⋊C₈	φ: M₄(2)/C₄ → C₄ ⊆ Aut C₃₀	480	C30.6M4(2)	480,306
C₃₀.₇M₄(2) = C₃₀.₇M₄(2)	φ: M₄(2)/C₄ → C₄ ⊆ Aut C₃₀	240	C30.7M4(2)	480,308
C₃₀.₈M₄(2) = C₃×C₂₀⋊C₈	φ: M₄(2)/C₄ → C₄ ⊆ Aut C₃₀	480	C30.8M4(2)	480,281
C₃₀.₉M₄(2) = C₃×C₁₀.C₄²	φ: M₄(2)/C₄ → C₄ ⊆ Aut C₃₀	480	C30.9M4(2)	480,282
C₃₀.₁₀M₄(2) = C₃×D₁₀⋊C₈	φ: M₄(2)/C₄ → C₄ ⊆ Aut C₃₀	240	C30.10M4(2)	480,283
C₃₀.₁₁M₄(2) = C₃₀.₂₁C₄²	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₃₀	480	C30.11M4(2)	480,28
C₃₀.₁₂M₄(2) = C₃₀.₂₂C₄²	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₃₀	480	C30.12M4(2)	480,29
C₃₀.₁₃M₄(2) = C₃₀.₂₃C₄²	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₃₀	480	C30.13M4(2)	480,30
C₃₀.₁₄M₄(2) = C₆₀.₉₃D₄	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₃₀	240	C30.14M4(2)	480,31
C₃₀.₁₅M₄(2) = C₆₀.₉₄D₄	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₃₀	240	C30.15M4(2)	480,32
C₃₀.₁₆M₄(2) = D₃₀⋊₄C₈	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₃₀	240	C30.16M4(2)	480,33
C₃₀.₁₇M₄(2) = C₆₀.₁₃Q₈	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₃₀	480	C30.17M4(2)	480,58
C₃₀.₁₈M₄(2) = C₆₀.₁₄Q₈	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₃₀	480	C30.18M4(2)	480,59
C₃₀.₁₉M₄(2) = C₆₀.₁₅Q₈	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₃₀	480	C30.19M4(2)	480,60
C₃₀.₂₀M₄(2) = C₃₀.₁₁C₄²	φ: M₄(2)/C₂² → C₄ ⊆ Aut C₃₀	480	C30.20M4(2)	480,307
C₃₀.₂₁M₄(2) = Dic₅.₁₃D₁₂	φ: M₄(2)/C₂² → C₄ ⊆ Aut C₃₀	480	C30.21M4(2)	480,309
C₃₀.₂₂M₄(2) = C₃₀.₂₂M₄(2)	φ: M₄(2)/C₂² → C₄ ⊆ Aut C₃₀	240	C30.22M4(2)	480,317
C₃₀.₂₃M₄(2) = C₃×Dic₅⋊C₈	φ: M₄(2)/C₂² → C₄ ⊆ Aut C₃₀	480	C30.23M4(2)	480,284
C₃₀.₂₄M₄(2) = C₃×C₂³.₂F₅	φ: M₄(2)/C₂² → C₄ ⊆ Aut C₃₀	240	C30.24M4(2)	480,292
C₃₀.₂₅M₄(2) = C₆₀.₂₆Q₈	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₃₀	480	C30.25M4(2)	480,174
C₃₀.₂₆M₄(2) = C₁₂₀⋊₁₃C₄	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₃₀	480	C30.26M4(2)	480,175
C₃₀.₂₇M₄(2) = D₃₀⋊₃C₈	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₃₀	240	C30.27M4(2)	480,180
C₃₀.₂₈M₄(2) = C₃×C₂₀.₈Q₈	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₃₀	480	C30.28M4(2)	480,92
C₃₀.₂₉M₄(2) = C₃×C₄₀⋊₈C₄	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₃₀	480	C30.29M4(2)	480,93
C₃₀.₃₀M₄(2) = C₃×D₁₀⋊₁C₈	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₃₀	240	C30.30M4(2)	480,98
C₃₀.₃₁M₄(2) = C₅×Dic₃⋊C₈	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₃₀	480	C30.31M4(2)	480,133
C₃₀.₃₂M₄(2) = C₅×C₂₄⋊C₄	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₃₀	480	C30.32M4(2)	480,134
C₃₀.₃₃M₄(2) = C₅×D₆⋊C₈	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₃₀	240	C30.33M4(2)	480,139
C₃₀.₃₄M₄(2) = C₄².D₁₅	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₃₀	480	C30.34M4(2)	480,163
C₃₀.₃₅M₄(2) = C₆₀⋊₅C₈	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₃₀	480	C30.35M4(2)	480,164
C₃₀.₃₆M₄(2) = C₆₀.₂₁₂D₄	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₃₀	240	C30.36M4(2)	480,190
C₃₀.₃₇M₄(2) = C₃×C₄².D₅	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₃₀	480	C30.37M4(2)	480,81
C₃₀.₃₈M₄(2) = C₃×C₂₀⋊₃C₈	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₃₀	480	C30.38M4(2)	480,82
C₃₀.₃₉M₄(2) = C₃×C₂₀.₅₅D₄	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₃₀	240	C30.39M4(2)	480,108
C₃₀.₄₀M₄(2) = C₅×C₄².S₃	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₃₀	480	C30.40M4(2)	480,122
C₃₀.₄₁M₄(2) = C₅×C₁₂⋊C₈	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₃₀	480	C30.41M4(2)	480,123
C₃₀.₄₂M₄(2) = C₅×C₁₂.₅₅D₄	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₃₀	240	C30.42M4(2)	480,149
C₃₀.₄₃M₄(2) = C₁₅×C₈⋊C₄	central extension (φ=1)	480	C30.43M4(2)	480,200
C₃₀.₄₄M₄(2) = C₁₅×C₂²⋊C₈	central extension (φ=1)	240	C30.44M4(2)	480,201
C₃₀.₄₅M₄(2) = C₁₅×C₄⋊C₈	central extension (φ=1)	480	C30.45M4(2)	480,208

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Extensions 1→N→G→Q→1 with N=C30 and Q=M4(2)

Extensions 1→N→G→Q→1 with N=C₃₀ and Q=M₄(2)