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Extensions 1→N→G→Q→1 with N=C2×C52 and Q=C22

Direct product G=N×Q with N=C2×C52 and Q=C22
dρLabelID
C23×C52416C2^3xC52416,227

Semidirect products G=N:Q with N=C2×C52 and Q=C22
extensionφ:Q→Aut NdρLabelID
(C2×C52)⋊1C22 = C22⋊D52φ: C22/C1 → C22 ⊆ Aut C2×C52104(C2xC52):1C2^2416,103
(C2×C52)⋊2C22 = C2×D4×D13φ: C22/C1 → C22 ⊆ Aut C2×C52104(C2xC52):2C2^2416,216
(C2×C52)⋊3C22 = D4⋊6D26φ: C22/C1 → C22 ⊆ Aut C2×C521044(C2xC52):3C2^2416,218
(C2×C52)⋊4C22 = C4○D4×D13φ: C22/C1 → C22 ⊆ Aut C2×C521044(C2xC52):4C2^2416,222
(C2×C52)⋊5C22 = D4⋊8D26φ: C22/C1 → C22 ⊆ Aut C2×C521044+(C2xC52):5C2^2416,223
(C2×C52)⋊6C22 = C22⋊C4×D13φ: C22/C1 → C22 ⊆ Aut C2×C52104(C2xC52):6C2^2416,101
(C2×C52)⋊7C22 = C23⋊D26φ: C22/C1 → C22 ⊆ Aut C2×C52104(C2xC52):7C2^2416,158
(C2×C52)⋊8C22 = C13×C22≀C2φ: C22/C1 → C22 ⊆ Aut C2×C52104(C2xC52):8C2^2416,181
(C2×C52)⋊9C22 = C13×2+ 1+4φ: C22/C1 → C22 ⊆ Aut C2×C521044(C2xC52):9C2^2416,231
(C2×C52)⋊10C22 = C2×D26⋊C4φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52):10C2^2416,148
(C2×C52)⋊11C22 = C22⋊C4×C26φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52):11C2^2416,176
(C2×C52)⋊12C22 = C22×D52φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52):12C2^2416,214
(C2×C52)⋊13C22 = C2×D52⋊5C2φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52):13C2^2416,215
(C2×C52)⋊14C22 = C22×C4×D13φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52):14C2^2416,213
(C2×C52)⋊15C22 = D4×C2×C26φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52):15C2^2416,228
(C2×C52)⋊16C22 = C4○D4×C26φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52):16C2^2416,230

Non-split extensions G=N.Q with N=C2×C52 and Q=C22
extensionφ:Q→Aut NdρLabelID
(C2×C52).1C22 = C22⋊Dic26φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).1C2^2416,99
(C2×C52).2C22 = C23.D26φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).2C2^2416,100
(C2×C52).3C22 = C22.D52φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).3C2^2416,107
(C2×C52).4C22 = C52⋊Q8φ: C22/C1 → C22 ⊆ Aut C2×C52416(C2xC52).4C2^2416,109
(C2×C52).5C22 = C4⋊2D52φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).5C2^2416,116
(C2×C52).6C22 = D26⋊2Q8φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).6C2^2416,118
(C2×C52).7C22 = C4⋊C4⋊D13φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).7C2^2416,119
(C2×C52).8C22 = C26.D8φ: C22/C1 → C22 ⊆ Aut C2×C52416(C2xC52).8C2^2416,14
(C2×C52).9C22 = C52.Q8φ: C22/C1 → C22 ⊆ Aut C2×C52416(C2xC52).9C2^2416,15
(C2×C52).10C22 = D52⋊6C4φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).10C2^2416,16
(C2×C52).11C22 = C26.Q16φ: C22/C1 → C22 ⊆ Aut C2×C52416(C2xC52).11C2^2416,17
(C2×C52).12C22 = C52.53D4φ: C22/C1 → C22 ⊆ Aut C2×C522084(C2xC52).12C2^2416,29
(C2×C52).13C22 = C52.46D4φ: C22/C1 → C22 ⊆ Aut C2×C521044+(C2xC52).13C2^2416,30
(C2×C52).14C22 = C4.12D52φ: C22/C1 → C22 ⊆ Aut C2×C522084-(C2xC52).14C2^2416,31
(C2×C52).15C22 = D52⋊7C4φ: C22/C1 → C22 ⊆ Aut C2×C521044(C2xC52).15C2^2416,32
(C2×C52).16C22 = D4⋊Dic13φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).16C2^2416,39
(C2×C52).17C22 = C52.D4φ: C22/C1 → C22 ⊆ Aut C2×C521044(C2xC52).17C2^2416,40
(C2×C52).18C22 = Q8⋊Dic13φ: C22/C1 → C22 ⊆ Aut C2×C52416(C2xC52).18C2^2416,42
(C2×C52).19C22 = C52.10D4φ: C22/C1 → C22 ⊆ Aut C2×C522084(C2xC52).19C2^2416,43
(C2×C52).20C22 = C52.56D4φ: C22/C1 → C22 ⊆ Aut C2×C521044(C2xC52).20C2^2416,44
(C2×C52).21C22 = Dic13⋊3Q8φ: C22/C1 → C22 ⊆ Aut C2×C52416(C2xC52).21C2^2416,108
(C2×C52).22C22 = C4.Dic26φ: C22/C1 → C22 ⊆ Aut C2×C52416(C2xC52).22C2^2416,111
(C2×C52).23C22 = C4⋊C4×D13φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).23C2^2416,112
(C2×C52).24C22 = D52⋊8C4φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).24C2^2416,114
(C2×C52).25C22 = M4(2)×D13φ: C22/C1 → C22 ⊆ Aut C2×C521044(C2xC52).25C2^2416,127
(C2×C52).26C22 = D52.2C4φ: C22/C1 → C22 ⊆ Aut C2×C522084(C2xC52).26C2^2416,128
(C2×C52).27C22 = C8⋊D26φ: C22/C1 → C22 ⊆ Aut C2×C521044+(C2xC52).27C2^2416,129
(C2×C52).28C22 = C8.D26φ: C22/C1 → C22 ⊆ Aut C2×C522084-(C2xC52).28C2^2416,130
(C2×C52).29C22 = C2×D4⋊D13φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).29C2^2416,152
(C2×C52).30C22 = D52⋊6C22φ: C22/C1 → C22 ⊆ Aut C2×C521044(C2xC52).30C2^2416,153
(C2×C52).31C22 = C2×D4.D13φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).31C2^2416,154
(C2×C52).32C22 = D4×Dic13φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).32C2^2416,155
(C2×C52).33C22 = C52.17D4φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).33C2^2416,157
(C2×C52).34C22 = C52⋊2D4φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).34C2^2416,159
(C2×C52).35C22 = C52⋊D4φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).35C2^2416,161
(C2×C52).36C22 = C2×Q8⋊D13φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).36C2^2416,162
(C2×C52).37C22 = Q8.D26φ: C22/C1 → C22 ⊆ Aut C2×C522084(C2xC52).37C2^2416,163
(C2×C52).38C22 = C2×C13⋊Q16φ: C22/C1 → C22 ⊆ Aut C2×C52416(C2xC52).38C2^2416,164
(C2×C52).39C22 = Q8×Dic13φ: C22/C1 → C22 ⊆ Aut C2×C52416(C2xC52).39C2^2416,166
(C2×C52).40C22 = C52.23D4φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).40C2^2416,168
(C2×C52).41C22 = D4.Dic13φ: C22/C1 → C22 ⊆ Aut C2×C522084(C2xC52).41C2^2416,169
(C2×C52).42C22 = D4⋊D26φ: C22/C1 → C22 ⊆ Aut C2×C521044+(C2xC52).42C2^2416,170
(C2×C52).43C22 = C52.C23φ: C22/C1 → C22 ⊆ Aut C2×C522084(C2xC52).43C2^2416,171
(C2×C52).44C22 = D4.9D26φ: C22/C1 → C22 ⊆ Aut C2×C522084-(C2xC52).44C2^2416,172
(C2×C52).45C22 = C2×D4⋊2D13φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).45C2^2416,217
(C2×C52).46C22 = C2×Q8×D13φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).46C2^2416,219
(C2×C52).47C22 = C2×D52⋊C2φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).47C2^2416,220
(C2×C52).48C22 = Q8.10D26φ: C22/C1 → C22 ⊆ Aut C2×C522084(C2xC52).48C2^2416,221
(C2×C52).49C22 = D4.10D26φ: C22/C1 → C22 ⊆ Aut C2×C522084-(C2xC52).49C2^2416,224
(C2×C52).50C22 = C23.11D26φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).50C2^2416,98
(C2×C52).51C22 = Dic13⋊4D4φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).51C2^2416,102
(C2×C52).52C22 = D26.12D4φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).52C2^2416,104
(C2×C52).53C22 = D26⋊D4φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).53C2^2416,105
(C2×C52).54C22 = C23.6D26φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).54C2^2416,106
(C2×C52).55C22 = Dic13.Q8φ: C22/C1 → C22 ⊆ Aut C2×C52416(C2xC52).55C2^2416,110
(C2×C52).56C22 = C4⋊C4⋊7D13φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).56C2^2416,113
(C2×C52).57C22 = D26.13D4φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).57C2^2416,115
(C2×C52).58C22 = D26⋊Q8φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).58C2^2416,117
(C2×C52).59C22 = C13×C4.D4φ: C22/C1 → C22 ⊆ Aut C2×C521044(C2xC52).59C2^2416,50
(C2×C52).60C22 = C13×C4.10D4φ: C22/C1 → C22 ⊆ Aut C2×C522084(C2xC52).60C2^2416,51
(C2×C52).61C22 = C23.18D26φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).61C2^2416,156
(C2×C52).62C22 = Dic13⋊D4φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).62C2^2416,160
(C2×C52).63C22 = Dic13⋊Q8φ: C22/C1 → C22 ⊆ Aut C2×C52416(C2xC52).63C2^2416,165
(C2×C52).64C22 = D26⋊3Q8φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).64C2^2416,167
(C2×C52).65C22 = C13×C22.D4φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).65C2^2416,184
(C2×C52).66C22 = C13×C4.4D4φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).66C2^2416,185
(C2×C52).67C22 = C13×C42.C2φ: C22/C1 → C22 ⊆ Aut C2×C52416(C2xC52).67C2^2416,186
(C2×C52).68C22 = C13×C42⋊2C2φ: C22/C1 → C22 ⊆ Aut C2×C52208(C2xC52).68C2^2416,187
(C2×C52).69C22 = C13×C8⋊C22φ: C22/C1 → C22 ⊆ Aut C2×C521044(C2xC52).69C2^2416,197
(C2×C52).70C22 = C13×C8.C22φ: C22/C1 → C22 ⊆ Aut C2×C522084(C2xC52).70C2^2416,198
(C2×C52).71C22 = C13×2- 1+4φ: C22/C1 → C22 ⊆ Aut C2×C522084(C2xC52).71C2^2416,232
(C2×C52).72C22 = C52.6Q8φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).72C2^2416,91
(C2×C52).73C22 = C42⋊D13φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).73C2^2416,93
(C2×C52).74C22 = C4.D52φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).74C2^2416,96
(C2×C52).75C22 = C42⋊2D13φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).75C2^2416,97
(C2×C52).76C22 = C2×C26.D4φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).76C2^2416,144
(C2×C52).77C22 = C4×C13⋊D4φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).77C2^2416,149
(C2×C52).78C22 = C23.23D26φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).78C2^2416,150
(C2×C52).79C22 = C13×C42⋊C2φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).79C2^2416,178
(C2×C52).80C22 = C52.44D4φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).80C2^2416,23
(C2×C52).81C22 = C104⋊6C4φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).81C2^2416,24
(C2×C52).82C22 = C104⋊5C4φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).82C2^2416,25
(C2×C52).83C22 = D52⋊5C4φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).83C2^2416,28
(C2×C52).84C22 = C4×Dic26φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).84C2^2416,89
(C2×C52).85C22 = C52⋊2Q8φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).85C2^2416,90
(C2×C52).86C22 = C4×D52φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).86C2^2416,94
(C2×C52).87C22 = C4⋊D52φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).87C2^2416,95
(C2×C52).88C22 = C2×C104⋊C2φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).88C2^2416,123
(C2×C52).89C22 = C2×D104φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).89C2^2416,124
(C2×C52).90C22 = C2×Dic52φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).90C2^2416,126
(C2×C52).91C22 = C52.48D4φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).91C2^2416,145
(C2×C52).92C22 = C2×C52⋊3C4φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).92C2^2416,146
(C2×C52).93C22 = C23.21D26φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).93C2^2416,147
(C2×C52).94C22 = C52⋊7D4φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).94C2^2416,151
(C2×C52).95C22 = C22×Dic26φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).95C2^2416,212
(C2×C52).96C22 = D52⋊4C4φ: C22/C2 → C2 ⊆ Aut C2×C521042(C2xC52).96C2^2416,12
(C2×C52).97C22 = C104.6C4φ: C22/C2 → C2 ⊆ Aut C2×C522082(C2xC52).97C2^2416,26
(C2×C52).98C22 = D52.3C4φ: C22/C2 → C2 ⊆ Aut C2×C522082(C2xC52).98C2^2416,122
(C2×C52).99C22 = D104⋊7C2φ: C22/C2 → C2 ⊆ Aut C2×C522082(C2xC52).99C2^2416,125
(C2×C52).100C22 = C2×C52.4C4φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).100C2^2416,142
(C2×C52).101C22 = C4×C13⋊2C8φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).101C2^2416,9
(C2×C52).102C22 = C26.7C42φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).102C2^2416,10
(C2×C52).103C22 = C52⋊3C8φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).103C2^2416,11
(C2×C52).104C22 = C8×Dic13φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).104C2^2416,20
(C2×C52).105C22 = C52.8Q8φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).105C2^2416,21
(C2×C52).106C22 = C104⋊8C4φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).106C2^2416,22
(C2×C52).107C22 = D26⋊1C8φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).107C2^2416,27
(C2×C52).108C22 = C52.55D4φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).108C2^2416,37
(C2×C52).109C22 = C42×D13φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).109C2^2416,92
(C2×C52).110C22 = C2×C8×D13φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).110C2^2416,120
(C2×C52).111C22 = C2×C8⋊D13φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).111C2^2416,121
(C2×C52).112C22 = C22×C13⋊2C8φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).112C2^2416,141
(C2×C52).113C22 = C2×C4×Dic13φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).113C2^2416,143
(C2×C52).114C22 = C13×D4⋊C4φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).114C2^2416,52
(C2×C52).115C22 = C13×Q8⋊C4φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).115C2^2416,53
(C2×C52).116C22 = C13×C4≀C2φ: C22/C2 → C2 ⊆ Aut C2×C521042(C2xC52).116C2^2416,54
(C2×C52).117C22 = C13×C4.Q8φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).117C2^2416,56
(C2×C52).118C22 = C13×C2.D8φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).118C2^2416,57
(C2×C52).119C22 = C13×C8.C4φ: C22/C2 → C2 ⊆ Aut C2×C522082(C2xC52).119C2^2416,58
(C2×C52).120C22 = C4⋊C4×C26φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).120C2^2416,177
(C2×C52).121C22 = D4×C52φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).121C2^2416,179
(C2×C52).122C22 = Q8×C52φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).122C2^2416,180
(C2×C52).123C22 = C13×C4⋊D4φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).123C2^2416,182
(C2×C52).124C22 = C13×C22⋊Q8φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).124C2^2416,183
(C2×C52).125C22 = C13×C4⋊1D4φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).125C2^2416,188
(C2×C52).126C22 = C13×C4⋊Q8φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).126C2^2416,189
(C2×C52).127C22 = M4(2)×C26φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).127C2^2416,191
(C2×C52).128C22 = C13×C8○D4φ: C22/C2 → C2 ⊆ Aut C2×C522082(C2xC52).128C2^2416,192
(C2×C52).129C22 = D8×C26φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).129C2^2416,193
(C2×C52).130C22 = SD16×C26φ: C22/C2 → C2 ⊆ Aut C2×C52208(C2xC52).130C2^2416,194
(C2×C52).131C22 = Q16×C26φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).131C2^2416,195
(C2×C52).132C22 = C13×C4○D8φ: C22/C2 → C2 ⊆ Aut C2×C522082(C2xC52).132C2^2416,196
(C2×C52).133C22 = Q8×C2×C26φ: C22/C2 → C2 ⊆ Aut C2×C52416(C2xC52).133C2^2416,229
(C2×C52).134C22 = C13×C8⋊C4central extension (φ=1)416(C2xC52).134C2^2416,47
(C2×C52).135C22 = C13×C22⋊C8central extension (φ=1)208(C2xC52).135C2^2416,48
(C2×C52).136C22 = C13×C4⋊C8central extension (φ=1)416(C2xC52).136C2^2416,55

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