Extensions 1→N→G→Q→1 with N=C₃₀ and Q=C₂³

Direct product G=N×Q with N=C₃₀ and Q=C₂³

		d	ρ	Label	ID
C₂³×C₃₀		240		C2^3xC30	240,208

Semidirect products G=N:Q with N=C₃₀ and Q=C₂³

extension	φ:Q→Aut N	d	Label	ID
C₃₀⋊C₂³ = C₂²×S₃×D₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	60	C30:C2^3	240,202
C₃₀⋊₂C₂³ = C₂³×D₁₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120	C30:2C2^3	240,207
C₃₀⋊₃C₂³ = D₅×C₂²×C₆	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120	C30:3C2^3	240,205
C₃₀⋊₄C₂³ = S₃×C₂²×C₁₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120	C30:4C2^3	240,206

Non-split extensions G=N.Q with N=C₃₀ and Q=C₂³

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃₀.₁C₂³ = D₅×Dic₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	120	4-	C30.1C2^3	240,125
C₃₀.₂C₂³ = D₂₀⋊₅S₃	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	120	4-	C30.2C2^3	240,126
C₃₀.₃C₂³ = D₂₀⋊S₃	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	120	4	C30.3C2^3	240,127
C₃₀.₄C₂³ = S₃×Dic₁₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	120	4-	C30.4C2^3	240,128
C₃₀.₅C₂³ = D₁₂⋊D₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	120	4	C30.5C2^3	240,129
C₃₀.₆C₂³ = D₆₀⋊C₂	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	120	4+	C30.6C2^3	240,130
C₃₀.₇C₂³ = D₁₅⋊Q₈	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	120	4	C30.7C2^3	240,131
C₃₀.₈C₂³ = D₆.D₁₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	120	4	C30.8C2^3	240,132
C₃₀.₉C₂³ = D₁₂⋊₅D₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	120	4-	C30.9C2^3	240,133
C₃₀.₁₀C₂³ = C₁₂.₂₈D₁₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	120	4+	C30.10C2^3	240,134
C₃₀.₁₁C₂³ = C₄×S₃×D₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	60	4	C30.11C2^3	240,135
C₃₀.₁₂C₂³ = D₅×D₁₂	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	60	4+	C30.12C2^3	240,136
C₃₀.₁₃C₂³ = S₃×D₂₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	60	4+	C30.13C2^3	240,137
C₃₀.₁₄C₂³ = C₂₀⋊D₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	60	4	C30.14C2^3	240,138
C₃₀.₁₅C₂³ = C₂×D₅×Dic₃	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	120		C30.15C2^3	240,139
C₃₀.₁₆C₂³ = Dic₅.D₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	120	4	C30.16C2^3	240,140
C₃₀.₁₇C₂³ = C₃₀.C₂³	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	120	4-	C30.17C2^3	240,141
C₃₀.₁₈C₂³ = C₂×S₃×Dic₅	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	120		C30.18C2^3	240,142
C₃₀.₁₉C₂³ = Dic₃.D₁₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	120	4	C30.19C2^3	240,143
C₃₀.₂₀C₂³ = C₂×D₃₀.C₂	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	120		C30.20C2^3	240,144
C₃₀.₂₁C₂³ = C₂×C₁₅⋊D₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	120		C30.21C2^3	240,145
C₃₀.₂₂C₂³ = C₂×C₃⋊D₂₀	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	120		C30.22C2^3	240,146
C₃₀.₂₃C₂³ = C₂×C₅⋊D₁₂	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	120		C30.23C2^3	240,147
C₃₀.₂₄C₂³ = C₂×C₁₅⋊Q₈	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	240		C30.24C2^3	240,148
C₃₀.₂₅C₂³ = D₅×C₃⋊D₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	60	4	C30.25C2^3	240,149
C₃₀.₂₆C₂³ = S₃×C₅⋊D₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	60	4	C30.26C2^3	240,150
C₃₀.₂₇C₂³ = D₁₀⋊D₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₃₀	60	4+	C30.27C2^3	240,151
C₃₀.₂₈C₂³ = C₂×Dic₃₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	240		C30.28C2^3	240,175
C₃₀.₂₉C₂³ = C₂×C₄×D₁₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120		C30.29C2^3	240,176
C₃₀.₃₀C₂³ = C₂×D₆₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120		C30.30C2^3	240,177
C₃₀.₃₁C₂³ = D₆₀⋊₁₁C₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120	2	C30.31C2^3	240,178
C₃₀.₃₂C₂³ = D₄×D₁₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	60	4+	C30.32C2^3	240,179
C₃₀.₃₃C₂³ = D₄⋊₂D₁₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120	4-	C30.33C2^3	240,180
C₃₀.₃₄C₂³ = Q₈×D₁₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120	4-	C30.34C2^3	240,181
C₃₀.₃₅C₂³ = Q₈⋊₃D₁₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120	4+	C30.35C2^3	240,182
C₃₀.₃₆C₂³ = C₂²×Dic₁₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	240		C30.36C2^3	240,183
C₃₀.₃₇C₂³ = C₂×C₁₅⋊₇D₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120		C30.37C2^3	240,184
C₃₀.₃₈C₂³ = C₆×Dic₁₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	240		C30.38C2^3	240,155
C₃₀.₃₉C₂³ = D₅×C₂×C₁₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120		C30.39C2^3	240,156
C₃₀.₄₀C₂³ = C₆×D₂₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120		C30.40C2^3	240,157
C₃₀.₄₁C₂³ = C₃×C₄○D₂₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120	2	C30.41C2^3	240,158
C₃₀.₄₂C₂³ = C₃×D₄×D₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	60	4	C30.42C2^3	240,159
C₃₀.₄₃C₂³ = C₃×D₄⋊₂D₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120	4	C30.43C2^3	240,160
C₃₀.₄₄C₂³ = C₃×Q₈×D₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120	4	C30.44C2^3	240,161
C₃₀.₄₅C₂³ = C₃×Q₈⋊₂D₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120	4	C30.45C2^3	240,162
C₃₀.₄₆C₂³ = C₂×C₆×Dic₅	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	240		C30.46C2^3	240,163
C₃₀.₄₇C₂³ = C₆×C₅⋊D₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120		C30.47C2^3	240,164
C₃₀.₄₈C₂³ = C₁₀×Dic₆	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	240		C30.48C2^3	240,165
C₃₀.₄₉C₂³ = S₃×C₂×C₂₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120		C30.49C2^3	240,166
C₃₀.₅₀C₂³ = C₁₀×D₁₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120		C30.50C2^3	240,167
C₃₀.₅₁C₂³ = C₅×C₄○D₁₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120	2	C30.51C2^3	240,168
C₃₀.₅₂C₂³ = C₅×S₃×D₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	60	4	C30.52C2^3	240,169
C₃₀.₅₃C₂³ = C₅×D₄⋊₂S₃	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120	4	C30.53C2^3	240,170
C₃₀.₅₄C₂³ = C₅×S₃×Q₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120	4	C30.54C2^3	240,171
C₃₀.₅₅C₂³ = C₅×Q₈⋊₃S₃	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120	4	C30.55C2^3	240,172
C₃₀.₅₆C₂³ = Dic₃×C₂×C₁₀	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	240		C30.56C2^3	240,173
C₃₀.₅₇C₂³ = C₁₀×C₃⋊D₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₃₀	120		C30.57C2^3	240,174
C₃₀.₅₈C₂³ = D₄×C₃₀	central extension (φ=1)	120		C30.58C2^3	240,186
C₃₀.₅₉C₂³ = Q₈×C₃₀	central extension (φ=1)	240		C30.59C2^3	240,187
C₃₀.₆₀C₂³ = C₁₅×C₄○D₄	central extension (φ=1)	120	2	C30.60C2^3	240,188

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Extensions 1→N→G→Q→1 with N=C30 and Q=C23

Extensions 1→N→G→Q→1 with N=C₃₀ and Q=C₂³