# Extensions 1→N→G→Q→1 with N=C52 and Q=C23

Direct product G=N×Q with N=C52 and Q=C23
dρLabelID
C23×C52416C2^3xC52416,227

Semidirect products G=N:Q with N=C52 and Q=C23
extensionφ:Q→Aut NdρLabelID
C52⋊C23 = C2×D4×D13φ: C23/C2C22 ⊆ Aut C52104C52:C2^3416,216
C522C23 = C22×D52φ: C23/C22C2 ⊆ Aut C52208C52:2C2^3416,214
C523C23 = C22×C4×D13φ: C23/C22C2 ⊆ Aut C52208C52:3C2^3416,213
C524C23 = D4×C2×C26φ: C23/C22C2 ⊆ Aut C52208C52:4C2^3416,228

Non-split extensions G=N.Q with N=C52 and Q=C23
extensionφ:Q→Aut NdρLabelID
C52.1C23 = D8×D13φ: C23/C2C22 ⊆ Aut C521044+C52.1C2^3416,131
C52.2C23 = D8⋊D13φ: C23/C2C22 ⊆ Aut C521044C52.2C2^3416,132
C52.3C23 = D83D13φ: C23/C2C22 ⊆ Aut C522084-C52.3C2^3416,133
C52.4C23 = SD16×D13φ: C23/C2C22 ⊆ Aut C521044C52.4C2^3416,134
C52.5C23 = Q8⋊D26φ: C23/C2C22 ⊆ Aut C521044+C52.5C2^3416,135
C52.6C23 = D4.D26φ: C23/C2C22 ⊆ Aut C522084-C52.6C2^3416,136
C52.7C23 = D26.6D4φ: C23/C2C22 ⊆ Aut C522084C52.7C2^3416,137
C52.8C23 = Q16×D13φ: C23/C2C22 ⊆ Aut C522084-C52.8C2^3416,138
C52.9C23 = Q16⋊D13φ: C23/C2C22 ⊆ Aut C522084C52.9C2^3416,139
C52.10C23 = D104⋊C2φ: C23/C2C22 ⊆ Aut C522084+C52.10C2^3416,140
C52.11C23 = C2×D4⋊D13φ: C23/C2C22 ⊆ Aut C52208C52.11C2^3416,152
C52.12C23 = D526C22φ: C23/C2C22 ⊆ Aut C521044C52.12C2^3416,153
C52.13C23 = C2×D4.D13φ: C23/C2C22 ⊆ Aut C52208C52.13C2^3416,154
C52.14C23 = C2×Q8⋊D13φ: C23/C2C22 ⊆ Aut C52208C52.14C2^3416,162
C52.15C23 = Q8.D26φ: C23/C2C22 ⊆ Aut C522084C52.15C2^3416,163
C52.16C23 = C2×C13⋊Q16φ: C23/C2C22 ⊆ Aut C52416C52.16C2^3416,164
C52.17C23 = D4⋊D26φ: C23/C2C22 ⊆ Aut C521044+C52.17C2^3416,170
C52.18C23 = C52.C23φ: C23/C2C22 ⊆ Aut C522084C52.18C2^3416,171
C52.19C23 = D4.9D26φ: C23/C2C22 ⊆ Aut C522084-C52.19C2^3416,172
C52.20C23 = C2×D42D13φ: C23/C2C22 ⊆ Aut C52208C52.20C2^3416,217
C52.21C23 = D46D26φ: C23/C2C22 ⊆ Aut C521044C52.21C2^3416,218
C52.22C23 = C2×Q8×D13φ: C23/C2C22 ⊆ Aut C52208C52.22C2^3416,219
C52.23C23 = C2×D52⋊C2φ: C23/C2C22 ⊆ Aut C52208C52.23C2^3416,220
C52.24C23 = Q8.10D26φ: C23/C2C22 ⊆ Aut C522084C52.24C2^3416,221
C52.25C23 = C4○D4×D13φ: C23/C2C22 ⊆ Aut C521044C52.25C2^3416,222
C52.26C23 = D48D26φ: C23/C2C22 ⊆ Aut C521044+C52.26C2^3416,223
C52.27C23 = D4.10D26φ: C23/C2C22 ⊆ Aut C522084-C52.27C2^3416,224
C52.28C23 = C2×C104⋊C2φ: C23/C22C2 ⊆ Aut C52208C52.28C2^3416,123
C52.29C23 = C2×D104φ: C23/C22C2 ⊆ Aut C52208C52.29C2^3416,124
C52.30C23 = D1047C2φ: C23/C22C2 ⊆ Aut C522082C52.30C2^3416,125
C52.31C23 = C2×Dic52φ: C23/C22C2 ⊆ Aut C52416C52.31C2^3416,126
C52.32C23 = C8⋊D26φ: C23/C22C2 ⊆ Aut C521044+C52.32C2^3416,129
C52.33C23 = C8.D26φ: C23/C22C2 ⊆ Aut C522084-C52.33C2^3416,130
C52.34C23 = C22×Dic26φ: C23/C22C2 ⊆ Aut C52416C52.34C2^3416,212
C52.35C23 = C2×C8×D13φ: C23/C22C2 ⊆ Aut C52208C52.35C2^3416,120
C52.36C23 = C2×C8⋊D13φ: C23/C22C2 ⊆ Aut C52208C52.36C2^3416,121
C52.37C23 = D52.3C4φ: C23/C22C2 ⊆ Aut C522082C52.37C2^3416,122
C52.38C23 = M4(2)×D13φ: C23/C22C2 ⊆ Aut C521044C52.38C2^3416,127
C52.39C23 = D52.2C4φ: C23/C22C2 ⊆ Aut C522084C52.39C2^3416,128
C52.40C23 = C22×C132C8φ: C23/C22C2 ⊆ Aut C52416C52.40C2^3416,141
C52.41C23 = C2×C52.4C4φ: C23/C22C2 ⊆ Aut C52208C52.41C2^3416,142
C52.42C23 = D4.Dic13φ: C23/C22C2 ⊆ Aut C522084C52.42C2^3416,169
C52.43C23 = C2×D525C2φ: C23/C22C2 ⊆ Aut C52208C52.43C2^3416,215
C52.44C23 = D8×C26φ: C23/C22C2 ⊆ Aut C52208C52.44C2^3416,193
C52.45C23 = SD16×C26φ: C23/C22C2 ⊆ Aut C52208C52.45C2^3416,194
C52.46C23 = Q16×C26φ: C23/C22C2 ⊆ Aut C52416C52.46C2^3416,195
C52.47C23 = C13×C4○D8φ: C23/C22C2 ⊆ Aut C522082C52.47C2^3416,196
C52.48C23 = C13×C8⋊C22φ: C23/C22C2 ⊆ Aut C521044C52.48C2^3416,197
C52.49C23 = C13×C8.C22φ: C23/C22C2 ⊆ Aut C522084C52.49C2^3416,198
C52.50C23 = Q8×C2×C26φ: C23/C22C2 ⊆ Aut C52416C52.50C2^3416,229
C52.51C23 = C13×2+ 1+4φ: C23/C22C2 ⊆ Aut C521044C52.51C2^3416,231
C52.52C23 = C13×2- 1+4φ: C23/C22C2 ⊆ Aut C522084C52.52C2^3416,232
C52.53C23 = M4(2)×C26central extension (φ=1)208C52.53C2^3416,191
C52.54C23 = C13×C8○D4central extension (φ=1)2082C52.54C2^3416,192
C52.55C23 = C4○D4×C26central extension (φ=1)208C52.55C2^3416,230

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