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Extensions 1→N→G→Q→1 with N=C2×C40 and Q=C4

Direct product G=N×Q with N=C2×C40 and Q=C4
dρLabelID
C2×C4×C40320C2xC4xC40320,903

Semidirect products G=N:Q with N=C2×C40 and Q=C4
extensionφ:Q→Aut NdρLabelID
(C2×C40)⋊1C4 = D10.3M4(2)φ: C4/C1 → C4 ⊆ Aut C2×C4080(C2xC40):1C4320,230
(C2×C40)⋊2C4 = D10.10D8φ: C4/C1 → C4 ⊆ Aut C2×C4080(C2xC40):2C4320,231
(C2×C40)⋊3C4 = (C2×C8)⋊F5φ: C4/C1 → C4 ⊆ Aut C2×C40804(C2xC40):3C4320,232
(C2×C40)⋊4C4 = C20.24C42φ: C4/C1 → C4 ⊆ Aut C2×C40804(C2xC40):4C4320,233
(C2×C40)⋊5C4 = C2×D5.D8φ: C4/C1 → C4 ⊆ Aut C2×C4080(C2xC40):5C4320,1058
(C2×C40)⋊6C4 = (C2×C8)⋊6F5φ: C4/C1 → C4 ⊆ Aut C2×C40804(C2xC40):6C4320,1059
(C2×C40)⋊7C4 = C2×C40⋊C4φ: C4/C1 → C4 ⊆ Aut C2×C4080(C2xC40):7C4320,1057
(C2×C40)⋊8C4 = C2×C8×F5φ: C4/C1 → C4 ⊆ Aut C2×C4080(C2xC40):8C4320,1054
(C2×C40)⋊9C4 = C2×C8⋊F5φ: C4/C1 → C4 ⊆ Aut C2×C4080(C2xC40):9C4320,1055
(C2×C40)⋊10C4 = C20.12C42φ: C4/C1 → C4 ⊆ Aut C2×C40804(C2xC40):10C4320,1056
(C2×C40)⋊11C4 = (C2×C40)⋊C4φ: C4/C1 → C4 ⊆ Aut C2×C40804(C2xC40):11C4320,114
(C2×C40)⋊12C4 = C23.9D20φ: C4/C1 → C4 ⊆ Aut C2×C40804(C2xC40):12C4320,115
(C2×C40)⋊13C4 = C5×C4.9C42φ: C4/C1 → C4 ⊆ Aut C2×C40804(C2xC40):13C4320,142
(C2×C40)⋊14C4 = C5×M4(2)⋊4C4φ: C4/C1 → C4 ⊆ Aut C2×C40804(C2xC40):14C4320,149
(C2×C40)⋊15C4 = (C2×C40)⋊15C4φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40):15C4320,108
(C2×C40)⋊16C4 = C20.39C42φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40):16C4320,109
(C2×C40)⋊17C4 = C5×C22.7C42φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40):17C4320,141
(C2×C40)⋊18C4 = C5×C22.4Q16φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40):18C4320,145
(C2×C40)⋊19C4 = C2×C40⋊5C4φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40):19C4320,732
(C2×C40)⋊20C4 = C23.22D20φ: C4/C2 → C2 ⊆ Aut C2×C40160(C2xC40):20C4320,733
(C2×C40)⋊21C4 = C2×C40⋊6C4φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40):21C4320,731
(C2×C40)⋊22C4 = C2×C8×Dic5φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40):22C4320,725
(C2×C40)⋊23C4 = C2×C40⋊8C4φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40):23C4320,727
(C2×C40)⋊24C4 = C20.42C42φ: C4/C2 → C2 ⊆ Aut C2×C40160(C2xC40):24C4320,728
(C2×C40)⋊25C4 = C10×C2.D8φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40):25C4320,927
(C2×C40)⋊26C4 = C5×C23.25D4φ: C4/C2 → C2 ⊆ Aut C2×C40160(C2xC40):26C4320,928
(C2×C40)⋊27C4 = C10×C4.Q8φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40):27C4320,926
(C2×C40)⋊28C4 = C10×C8⋊C4φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40):28C4320,904
(C2×C40)⋊29C4 = C5×C8○2M4(2)φ: C4/C2 → C2 ⊆ Aut C2×C40160(C2xC40):29C4320,906

Non-split extensions G=N.Q with N=C2×C40 and Q=C4
extensionφ:Q→Aut NdρLabelID
(C2×C40).1C4 = C20.31M4(2)φ: C4/C1 → C4 ⊆ Aut C2×C40320(C2xC40).1C4320,218
(C2×C40).2C4 = C20.26M4(2)φ: C4/C1 → C4 ⊆ Aut C2×C40320(C2xC40).2C4320,221
(C2×C40).3C4 = Dic5.13D8φ: C4/C1 → C4 ⊆ Aut C2×C40320(C2xC40).3C4320,222
(C2×C40).4C4 = D10⋊C16φ: C4/C1 → C4 ⊆ Aut C2×C40160(C2xC40).4C4320,225
(C2×C40).5C4 = C10.M5(2)φ: C4/C1 → C4 ⊆ Aut C2×C40320(C2xC40).5C4320,226
(C2×C40).6C4 = C20.23C42φ: C4/C1 → C4 ⊆ Aut C2×C40804(C2xC40).6C4320,228
(C2×C40).7C4 = C20.10M4(2)φ: C4/C1 → C4 ⊆ Aut C2×C40804(C2xC40).7C4320,229
(C2×C40).8C4 = C20.10C42φ: C4/C1 → C4 ⊆ Aut C2×C40160(C2xC40).8C4320,234
(C2×C40).9C4 = C20.25C42φ: C4/C1 → C4 ⊆ Aut C2×C40804(C2xC40).9C4320,235
(C2×C40).10C4 = C40⋊1C8φ: C4/C1 → C4 ⊆ Aut C2×C40320(C2xC40).10C4320,220
(C2×C40).11C4 = C2×D10.Q8φ: C4/C1 → C4 ⊆ Aut C2×C40160(C2xC40).11C4320,1061
(C2×C40).12C4 = C40.1C8φ: C4/C1 → C4 ⊆ Aut C2×C40804(C2xC40).12C4320,227
(C2×C40).13C4 = (C8×D5).C4φ: C4/C1 → C4 ⊆ Aut C2×C40804(C2xC40).13C4320,1062
(C2×C40).14C4 = C40⋊2C8φ: C4/C1 → C4 ⊆ Aut C2×C40320(C2xC40).14C4320,219
(C2×C40).15C4 = C2×C40.C4φ: C4/C1 → C4 ⊆ Aut C2×C40160(C2xC40).15C4320,1060
(C2×C40).16C4 = C2×C5⋊C32φ: C4/C1 → C4 ⊆ Aut C2×C40320(C2xC40).16C4320,214
(C2×C40).17C4 = C5⋊M6(2)φ: C4/C1 → C4 ⊆ Aut C2×C401604(C2xC40).17C4320,215
(C2×C40).18C4 = C8×C5⋊C8φ: C4/C1 → C4 ⊆ Aut C2×C40320(C2xC40).18C4320,216
(C2×C40).19C4 = C40⋊C8φ: C4/C1 → C4 ⊆ Aut C2×C40320(C2xC40).19C4320,217
(C2×C40).20C4 = Dic5⋊C16φ: C4/C1 → C4 ⊆ Aut C2×C40320(C2xC40).20C4320,223
(C2×C40).21C4 = C40.C8φ: C4/C1 → C4 ⊆ Aut C2×C40320(C2xC40).21C4320,224
(C2×C40).22C4 = C2×D5⋊C16φ: C4/C1 → C4 ⊆ Aut C2×C40160(C2xC40).22C4320,1051
(C2×C40).23C4 = C2×C8.F5φ: C4/C1 → C4 ⊆ Aut C2×C40160(C2xC40).23C4320,1052
(C2×C40).24C4 = D5⋊M5(2)φ: C4/C1 → C4 ⊆ Aut C2×C40804(C2xC40).24C4320,1053
(C2×C40).25C4 = C20.45C42φ: C4/C1 → C4 ⊆ Aut C2×C40804(C2xC40).25C4320,24
(C2×C40).26C4 = C40.D4φ: C4/C1 → C4 ⊆ Aut C2×C40804(C2xC40).26C4320,111
(C2×C40).27C4 = C20.51C42φ: C4/C1 → C4 ⊆ Aut C2×C40804(C2xC40).27C4320,118
(C2×C40).28C4 = C5×C4.10C42φ: C4/C1 → C4 ⊆ Aut C2×C40804(C2xC40).28C4320,143
(C2×C40).29C4 = C5×C16⋊C4φ: C4/C1 → C4 ⊆ Aut C2×C40804(C2xC40).29C4320,152
(C2×C40).30C4 = C5×C23.C8φ: C4/C1 → C4 ⊆ Aut C2×C40804(C2xC40).30C4320,154
(C2×C40).31C4 = C42.279D10φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40).31C4320,12
(C2×C40).32C4 = C40⋊6C8φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40).32C4320,15
(C2×C40).33C4 = C40⋊5C8φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40).33C4320,16
(C2×C40).34C4 = C20⋊3C16φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40).34C4320,20
(C2×C40).35C4 = C40.91D4φ: C4/C2 → C2 ⊆ Aut C2×C40160(C2xC40).35C4320,107
(C2×C40).36C4 = C20.40C42φ: C4/C2 → C2 ⊆ Aut C2×C40160(C2xC40).36C4320,110
(C2×C40).37C4 = C5×C8⋊2C8φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40).37C4320,139
(C2×C40).38C4 = C5×C8⋊1C8φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40).38C4320,140
(C2×C40).39C4 = C5×C4.C42φ: C4/C2 → C2 ⊆ Aut C2×C40160(C2xC40).39C4320,146
(C2×C40).40C4 = C5×C22⋊C16φ: C4/C2 → C2 ⊆ Aut C2×C40160(C2xC40).40C4320,153
(C2×C40).41C4 = C5×C4⋊C16φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40).41C4320,168
(C2×C40).42C4 = C40.7C8φ: C4/C2 → C2 ⊆ Aut C2×C40802(C2xC40).42C4320,21
(C2×C40).43C4 = C2×C40.6C4φ: C4/C2 → C2 ⊆ Aut C2×C40160(C2xC40).43C4320,734
(C2×C40).44C4 = C8×C5⋊2C8φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40).44C4320,11
(C2×C40).45C4 = C40⋊8C8φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40).45C4320,13
(C2×C40).46C4 = C4×C5⋊2C16φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40).46C4320,18
(C2×C40).47C4 = C40.10C8φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40).47C4320,19
(C2×C40).48C4 = C2×C5⋊2C32φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40).48C4320,56
(C2×C40).49C4 = C80.9C4φ: C4/C2 → C2 ⊆ Aut C2×C401602(C2xC40).49C4320,57
(C2×C40).50C4 = C22×C5⋊2C16φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40).50C4320,723
(C2×C40).51C4 = C2×C20.4C8φ: C4/C2 → C2 ⊆ Aut C2×C40160(C2xC40).51C4320,724
(C2×C40).52C4 = C5×C8.C8φ: C4/C2 → C2 ⊆ Aut C2×C40802(C2xC40).52C4320,169
(C2×C40).53C4 = C10×C8.C4φ: C4/C2 → C2 ⊆ Aut C2×C40160(C2xC40).53C4320,930
(C2×C40).54C4 = C5×C8⋊C8φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40).54C4320,127
(C2×C40).55C4 = C5×C16⋊5C4φ: C4/C2 → C2 ⊆ Aut C2×C40320(C2xC40).55C4320,151
(C2×C40).56C4 = C5×M6(2)φ: C4/C2 → C2 ⊆ Aut C2×C401602(C2xC40).56C4320,175
(C2×C40).57C4 = C10×M5(2)φ: C4/C2 → C2 ⊆ Aut C2×C40160(C2xC40).57C4320,1004

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