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

Direct product G=N×Q with N=C30 and Q=C23
dρLabelID
C23×C30240C2^3xC30240,208

Semidirect products G=N:Q with N=C30 and Q=C23
extensionφ:Q→Aut NdρLabelID
C30⋊C23 = C22×S3×D5φ: C23/C2C22 ⊆ Aut C3060C30:C2^3240,202
C302C23 = C23×D15φ: C23/C22C2 ⊆ Aut C30120C30:2C2^3240,207
C303C23 = D5×C22×C6φ: C23/C22C2 ⊆ Aut C30120C30:3C2^3240,205
C304C23 = S3×C22×C10φ: C23/C22C2 ⊆ Aut C30120C30:4C2^3240,206

Non-split extensions G=N.Q with N=C30 and Q=C23
extensionφ:Q→Aut NdρLabelID
C30.1C23 = D5×Dic6φ: C23/C2C22 ⊆ Aut C301204-C30.1C2^3240,125
C30.2C23 = D205S3φ: C23/C2C22 ⊆ Aut C301204-C30.2C2^3240,126
C30.3C23 = D20⋊S3φ: C23/C2C22 ⊆ Aut C301204C30.3C2^3240,127
C30.4C23 = S3×Dic10φ: C23/C2C22 ⊆ Aut C301204-C30.4C2^3240,128
C30.5C23 = D12⋊D5φ: C23/C2C22 ⊆ Aut C301204C30.5C2^3240,129
C30.6C23 = D60⋊C2φ: C23/C2C22 ⊆ Aut C301204+C30.6C2^3240,130
C30.7C23 = D15⋊Q8φ: C23/C2C22 ⊆ Aut C301204C30.7C2^3240,131
C30.8C23 = D6.D10φ: C23/C2C22 ⊆ Aut C301204C30.8C2^3240,132
C30.9C23 = D125D5φ: C23/C2C22 ⊆ Aut C301204-C30.9C2^3240,133
C30.10C23 = C12.28D10φ: C23/C2C22 ⊆ Aut C301204+C30.10C2^3240,134
C30.11C23 = C4×S3×D5φ: C23/C2C22 ⊆ Aut C30604C30.11C2^3240,135
C30.12C23 = D5×D12φ: C23/C2C22 ⊆ Aut C30604+C30.12C2^3240,136
C30.13C23 = S3×D20φ: C23/C2C22 ⊆ Aut C30604+C30.13C2^3240,137
C30.14C23 = C20⋊D6φ: C23/C2C22 ⊆ Aut C30604C30.14C2^3240,138
C30.15C23 = C2×D5×Dic3φ: C23/C2C22 ⊆ Aut C30120C30.15C2^3240,139
C30.16C23 = Dic5.D6φ: C23/C2C22 ⊆ Aut C301204C30.16C2^3240,140
C30.17C23 = C30.C23φ: C23/C2C22 ⊆ Aut C301204-C30.17C2^3240,141
C30.18C23 = C2×S3×Dic5φ: C23/C2C22 ⊆ Aut C30120C30.18C2^3240,142
C30.19C23 = Dic3.D10φ: C23/C2C22 ⊆ Aut C301204C30.19C2^3240,143
C30.20C23 = C2×D30.C2φ: C23/C2C22 ⊆ Aut C30120C30.20C2^3240,144
C30.21C23 = C2×C15⋊D4φ: C23/C2C22 ⊆ Aut C30120C30.21C2^3240,145
C30.22C23 = C2×C3⋊D20φ: C23/C2C22 ⊆ Aut C30120C30.22C2^3240,146
C30.23C23 = C2×C5⋊D12φ: C23/C2C22 ⊆ Aut C30120C30.23C2^3240,147
C30.24C23 = C2×C15⋊Q8φ: C23/C2C22 ⊆ Aut C30240C30.24C2^3240,148
C30.25C23 = D5×C3⋊D4φ: C23/C2C22 ⊆ Aut C30604C30.25C2^3240,149
C30.26C23 = S3×C5⋊D4φ: C23/C2C22 ⊆ Aut C30604C30.26C2^3240,150
C30.27C23 = D10⋊D6φ: C23/C2C22 ⊆ Aut C30604+C30.27C2^3240,151
C30.28C23 = C2×Dic30φ: C23/C22C2 ⊆ Aut C30240C30.28C2^3240,175
C30.29C23 = C2×C4×D15φ: C23/C22C2 ⊆ Aut C30120C30.29C2^3240,176
C30.30C23 = C2×D60φ: C23/C22C2 ⊆ Aut C30120C30.30C2^3240,177
C30.31C23 = D6011C2φ: C23/C22C2 ⊆ Aut C301202C30.31C2^3240,178
C30.32C23 = D4×D15φ: C23/C22C2 ⊆ Aut C30604+C30.32C2^3240,179
C30.33C23 = D42D15φ: C23/C22C2 ⊆ Aut C301204-C30.33C2^3240,180
C30.34C23 = Q8×D15φ: C23/C22C2 ⊆ Aut C301204-C30.34C2^3240,181
C30.35C23 = Q83D15φ: C23/C22C2 ⊆ Aut C301204+C30.35C2^3240,182
C30.36C23 = C22×Dic15φ: C23/C22C2 ⊆ Aut C30240C30.36C2^3240,183
C30.37C23 = C2×C157D4φ: C23/C22C2 ⊆ Aut C30120C30.37C2^3240,184
C30.38C23 = C6×Dic10φ: C23/C22C2 ⊆ Aut C30240C30.38C2^3240,155
C30.39C23 = D5×C2×C12φ: C23/C22C2 ⊆ Aut C30120C30.39C2^3240,156
C30.40C23 = C6×D20φ: C23/C22C2 ⊆ Aut C30120C30.40C2^3240,157
C30.41C23 = C3×C4○D20φ: C23/C22C2 ⊆ Aut C301202C30.41C2^3240,158
C30.42C23 = C3×D4×D5φ: C23/C22C2 ⊆ Aut C30604C30.42C2^3240,159
C30.43C23 = C3×D42D5φ: C23/C22C2 ⊆ Aut C301204C30.43C2^3240,160
C30.44C23 = C3×Q8×D5φ: C23/C22C2 ⊆ Aut C301204C30.44C2^3240,161
C30.45C23 = C3×Q82D5φ: C23/C22C2 ⊆ Aut C301204C30.45C2^3240,162
C30.46C23 = C2×C6×Dic5φ: C23/C22C2 ⊆ Aut C30240C30.46C2^3240,163
C30.47C23 = C6×C5⋊D4φ: C23/C22C2 ⊆ Aut C30120C30.47C2^3240,164
C30.48C23 = C10×Dic6φ: C23/C22C2 ⊆ Aut C30240C30.48C2^3240,165
C30.49C23 = S3×C2×C20φ: C23/C22C2 ⊆ Aut C30120C30.49C2^3240,166
C30.50C23 = C10×D12φ: C23/C22C2 ⊆ Aut C30120C30.50C2^3240,167
C30.51C23 = C5×C4○D12φ: C23/C22C2 ⊆ Aut C301202C30.51C2^3240,168
C30.52C23 = C5×S3×D4φ: C23/C22C2 ⊆ Aut C30604C30.52C2^3240,169
C30.53C23 = C5×D42S3φ: C23/C22C2 ⊆ Aut C301204C30.53C2^3240,170
C30.54C23 = C5×S3×Q8φ: C23/C22C2 ⊆ Aut C301204C30.54C2^3240,171
C30.55C23 = C5×Q83S3φ: C23/C22C2 ⊆ Aut C301204C30.55C2^3240,172
C30.56C23 = Dic3×C2×C10φ: C23/C22C2 ⊆ Aut C30240C30.56C2^3240,173
C30.57C23 = C10×C3⋊D4φ: C23/C22C2 ⊆ Aut C30120C30.57C2^3240,174
C30.58C23 = D4×C30central extension (φ=1)120C30.58C2^3240,186
C30.59C23 = Q8×C30central extension (φ=1)240C30.59C2^3240,187
C30.60C23 = C15×C4○D4central extension (φ=1)1202C30.60C2^3240,188

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