# Extensions 1→N→G→Q→1 with N=C2×C4 and Q=D10

Direct product G=N×Q with N=C2×C4 and Q=D10
dρLabelID
D5×C22×C480D5xC2^2xC4160,214

Semidirect products G=N:Q with N=C2×C4 and Q=D10
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1D10 = C22⋊D20φ: D10/C5C22 ⊆ Aut C2×C440(C2xC4):1D10160,103
(C2×C4)⋊2D10 = C23⋊D10φ: D10/C5C22 ⊆ Aut C2×C440(C2xC4):2D10160,158
(C2×C4)⋊3D10 = D46D10φ: D10/C5C22 ⊆ Aut C2×C4404(C2xC4):3D10160,219
(C2×C4)⋊4D10 = D48D10φ: D10/C5C22 ⊆ Aut C2×C4404+(C2xC4):4D10160,224
(C2×C4)⋊5D10 = D5×C22⋊C4φ: D10/D5C2 ⊆ Aut C2×C440(C2xC4):5D10160,101
(C2×C4)⋊6D10 = C2×D4×D5φ: D10/D5C2 ⊆ Aut C2×C440(C2xC4):6D10160,217
(C2×C4)⋊7D10 = D5×C4○D4φ: D10/D5C2 ⊆ Aut C2×C4404(C2xC4):7D10160,223
(C2×C4)⋊8D10 = C2×D10⋊C4φ: D10/C10C2 ⊆ Aut C2×C480(C2xC4):8D10160,148
(C2×C4)⋊9D10 = C22×D20φ: D10/C10C2 ⊆ Aut C2×C480(C2xC4):9D10160,215
(C2×C4)⋊10D10 = C2×C4○D20φ: D10/C10C2 ⊆ Aut C2×C480(C2xC4):10D10160,216

Non-split extensions G=N.Q with N=C2×C4 and Q=D10
extensionφ:Q→Aut NdρLabelID
(C2×C4).1D10 = C20.46D4φ: D10/C5C22 ⊆ Aut C2×C4404+(C2xC4).1D10160,30
(C2×C4).2D10 = C4.12D20φ: D10/C5C22 ⊆ Aut C2×C4804-(C2xC4).2D10160,31
(C2×C4).3D10 = C20.D4φ: D10/C5C22 ⊆ Aut C2×C4404(C2xC4).3D10160,40
(C2×C4).4D10 = C20.10D4φ: D10/C5C22 ⊆ Aut C2×C4804(C2xC4).4D10160,43
(C2×C4).5D10 = Dic5.14D4φ: D10/C5C22 ⊆ Aut C2×C480(C2xC4).5D10160,99
(C2×C4).6D10 = D10.12D4φ: D10/C5C22 ⊆ Aut C2×C480(C2xC4).6D10160,104
(C2×C4).7D10 = D10⋊D4φ: D10/C5C22 ⊆ Aut C2×C480(C2xC4).7D10160,105
(C2×C4).8D10 = Dic5.5D4φ: D10/C5C22 ⊆ Aut C2×C480(C2xC4).8D10160,106
(C2×C4).9D10 = C22.D20φ: D10/C5C22 ⊆ Aut C2×C480(C2xC4).9D10160,107
(C2×C4).10D10 = Dic5.Q8φ: D10/C5C22 ⊆ Aut C2×C4160(C2xC4).10D10160,110
(C2×C4).11D10 = D10.13D4φ: D10/C5C22 ⊆ Aut C2×C480(C2xC4).11D10160,115
(C2×C4).12D10 = C4⋊D20φ: D10/C5C22 ⊆ Aut C2×C480(C2xC4).12D10160,116
(C2×C4).13D10 = D10⋊Q8φ: D10/C5C22 ⊆ Aut C2×C480(C2xC4).13D10160,117
(C2×C4).14D10 = D102Q8φ: D10/C5C22 ⊆ Aut C2×C480(C2xC4).14D10160,118
(C2×C4).15D10 = C8⋊D10φ: D10/C5C22 ⊆ Aut C2×C4404+(C2xC4).15D10160,129
(C2×C4).16D10 = C8.D10φ: D10/C5C22 ⊆ Aut C2×C4804-(C2xC4).16D10160,130
(C2×C4).17D10 = D4.D10φ: D10/C5C22 ⊆ Aut C2×C4404(C2xC4).17D10160,153
(C2×C4).18D10 = C23.18D10φ: D10/C5C22 ⊆ Aut C2×C480(C2xC4).18D10160,156
(C2×C4).19D10 = Dic5⋊D4φ: D10/C5C22 ⊆ Aut C2×C480(C2xC4).19D10160,160
(C2×C4).20D10 = C20.C23φ: D10/C5C22 ⊆ Aut C2×C4804(C2xC4).20D10160,163
(C2×C4).21D10 = D103Q8φ: D10/C5C22 ⊆ Aut C2×C480(C2xC4).21D10160,167
(C2×C4).22D10 = D4⋊D10φ: D10/C5C22 ⊆ Aut C2×C4404+(C2xC4).22D10160,170
(C2×C4).23D10 = D4.9D10φ: D10/C5C22 ⊆ Aut C2×C4804-(C2xC4).23D10160,172
(C2×C4).24D10 = Q8.10D10φ: D10/C5C22 ⊆ Aut C2×C4804(C2xC4).24D10160,222
(C2×C4).25D10 = D4.10D10φ: D10/C5C22 ⊆ Aut C2×C4804-(C2xC4).25D10160,225
(C2×C4).26D10 = C23.11D10φ: D10/D5C2 ⊆ Aut C2×C480(C2xC4).26D10160,98
(C2×C4).27D10 = C23.D10φ: D10/D5C2 ⊆ Aut C2×C480(C2xC4).27D10160,100
(C2×C4).28D10 = Dic54D4φ: D10/D5C2 ⊆ Aut C2×C480(C2xC4).28D10160,102
(C2×C4).29D10 = Dic53Q8φ: D10/D5C2 ⊆ Aut C2×C4160(C2xC4).29D10160,108
(C2×C4).30D10 = D5×C4⋊C4φ: D10/D5C2 ⊆ Aut C2×C480(C2xC4).30D10160,112
(C2×C4).31D10 = D208C4φ: D10/D5C2 ⊆ Aut C2×C480(C2xC4).31D10160,114
(C2×C4).32D10 = C4⋊C4⋊D5φ: D10/D5C2 ⊆ Aut C2×C480(C2xC4).32D10160,119
(C2×C4).33D10 = C10.D8φ: D10/D5C2 ⊆ Aut C2×C4160(C2xC4).33D10160,14
(C2×C4).34D10 = C20.Q8φ: D10/D5C2 ⊆ Aut C2×C4160(C2xC4).34D10160,15
(C2×C4).35D10 = D206C4φ: D10/D5C2 ⊆ Aut C2×C480(C2xC4).35D10160,16
(C2×C4).36D10 = C10.Q16φ: D10/D5C2 ⊆ Aut C2×C4160(C2xC4).36D10160,17
(C2×C4).37D10 = C20.53D4φ: D10/D5C2 ⊆ Aut C2×C4804(C2xC4).37D10160,29
(C2×C4).38D10 = D207C4φ: D10/D5C2 ⊆ Aut C2×C4404(C2xC4).38D10160,32
(C2×C4).39D10 = D4⋊Dic5φ: D10/D5C2 ⊆ Aut C2×C480(C2xC4).39D10160,39
(C2×C4).40D10 = Q8⋊Dic5φ: D10/D5C2 ⊆ Aut C2×C4160(C2xC4).40D10160,42
(C2×C4).41D10 = D42Dic5φ: D10/D5C2 ⊆ Aut C2×C4404(C2xC4).41D10160,44
(C2×C4).42D10 = C20⋊Q8φ: D10/D5C2 ⊆ Aut C2×C4160(C2xC4).42D10160,109
(C2×C4).43D10 = C4.Dic10φ: D10/D5C2 ⊆ Aut C2×C4160(C2xC4).43D10160,111
(C2×C4).44D10 = C4⋊C47D5φ: D10/D5C2 ⊆ Aut C2×C480(C2xC4).44D10160,113
(C2×C4).45D10 = D5×M4(2)φ: D10/D5C2 ⊆ Aut C2×C4404(C2xC4).45D10160,127
(C2×C4).46D10 = D20.2C4φ: D10/D5C2 ⊆ Aut C2×C4804(C2xC4).46D10160,128
(C2×C4).47D10 = C2×D4⋊D5φ: D10/D5C2 ⊆ Aut C2×C480(C2xC4).47D10160,152
(C2×C4).48D10 = C2×D4.D5φ: D10/D5C2 ⊆ Aut C2×C480(C2xC4).48D10160,154
(C2×C4).49D10 = D4×Dic5φ: D10/D5C2 ⊆ Aut C2×C480(C2xC4).49D10160,155
(C2×C4).50D10 = C20.17D4φ: D10/D5C2 ⊆ Aut C2×C480(C2xC4).50D10160,157
(C2×C4).51D10 = C202D4φ: D10/D5C2 ⊆ Aut C2×C480(C2xC4).51D10160,159
(C2×C4).52D10 = C20⋊D4φ: D10/D5C2 ⊆ Aut C2×C480(C2xC4).52D10160,161
(C2×C4).53D10 = C2×Q8⋊D5φ: D10/D5C2 ⊆ Aut C2×C480(C2xC4).53D10160,162
(C2×C4).54D10 = C2×C5⋊Q16φ: D10/D5C2 ⊆ Aut C2×C4160(C2xC4).54D10160,164
(C2×C4).55D10 = Dic5⋊Q8φ: D10/D5C2 ⊆ Aut C2×C4160(C2xC4).55D10160,165
(C2×C4).56D10 = Q8×Dic5φ: D10/D5C2 ⊆ Aut C2×C4160(C2xC4).56D10160,166
(C2×C4).57D10 = C20.23D4φ: D10/D5C2 ⊆ Aut C2×C480(C2xC4).57D10160,168
(C2×C4).58D10 = D4.Dic5φ: D10/D5C2 ⊆ Aut C2×C4804(C2xC4).58D10160,169
(C2×C4).59D10 = D4.8D10φ: D10/D5C2 ⊆ Aut C2×C4804(C2xC4).59D10160,171
(C2×C4).60D10 = C2×D42D5φ: D10/D5C2 ⊆ Aut C2×C480(C2xC4).60D10160,218
(C2×C4).61D10 = C2×Q8×D5φ: D10/D5C2 ⊆ Aut C2×C480(C2xC4).61D10160,220
(C2×C4).62D10 = C2×Q82D5φ: D10/D5C2 ⊆ Aut C2×C480(C2xC4).62D10160,221
(C2×C4).63D10 = C422D5φ: D10/C10C2 ⊆ Aut C2×C480(C2xC4).63D10160,97
(C2×C4).64D10 = C2×C10.D4φ: D10/C10C2 ⊆ Aut C2×C4160(C2xC4).64D10160,144
(C2×C4).65D10 = C23.23D10φ: D10/C10C2 ⊆ Aut C2×C480(C2xC4).65D10160,150
(C2×C4).66D10 = D204C4φ: D10/C10C2 ⊆ Aut C2×C4402(C2xC4).66D10160,12
(C2×C4).67D10 = C20.44D4φ: D10/C10C2 ⊆ Aut C2×C4160(C2xC4).67D10160,23
(C2×C4).68D10 = C406C4φ: D10/C10C2 ⊆ Aut C2×C4160(C2xC4).68D10160,24
(C2×C4).69D10 = C405C4φ: D10/C10C2 ⊆ Aut C2×C4160(C2xC4).69D10160,25
(C2×C4).70D10 = C40.6C4φ: D10/C10C2 ⊆ Aut C2×C4802(C2xC4).70D10160,26
(C2×C4).71D10 = D205C4φ: D10/C10C2 ⊆ Aut C2×C480(C2xC4).71D10160,28
(C2×C4).72D10 = C4×Dic10φ: D10/C10C2 ⊆ Aut C2×C4160(C2xC4).72D10160,89
(C2×C4).73D10 = C202Q8φ: D10/C10C2 ⊆ Aut C2×C4160(C2xC4).73D10160,90
(C2×C4).74D10 = C20.6Q8φ: D10/C10C2 ⊆ Aut C2×C4160(C2xC4).74D10160,91
(C2×C4).75D10 = C4×D20φ: D10/C10C2 ⊆ Aut C2×C480(C2xC4).75D10160,94
(C2×C4).76D10 = C204D4φ: D10/C10C2 ⊆ Aut C2×C480(C2xC4).76D10160,95
(C2×C4).77D10 = C4.D20φ: D10/C10C2 ⊆ Aut C2×C480(C2xC4).77D10160,96
(C2×C4).78D10 = D20.3C4φ: D10/C10C2 ⊆ Aut C2×C4802(C2xC4).78D10160,122
(C2×C4).79D10 = C2×C40⋊C2φ: D10/C10C2 ⊆ Aut C2×C480(C2xC4).79D10160,123
(C2×C4).80D10 = C2×D40φ: D10/C10C2 ⊆ Aut C2×C480(C2xC4).80D10160,124
(C2×C4).81D10 = D407C2φ: D10/C10C2 ⊆ Aut C2×C4802(C2xC4).81D10160,125
(C2×C4).82D10 = C2×Dic20φ: D10/C10C2 ⊆ Aut C2×C4160(C2xC4).82D10160,126
(C2×C4).83D10 = C20.48D4φ: D10/C10C2 ⊆ Aut C2×C480(C2xC4).83D10160,145
(C2×C4).84D10 = C2×C4⋊Dic5φ: D10/C10C2 ⊆ Aut C2×C4160(C2xC4).84D10160,146
(C2×C4).85D10 = C207D4φ: D10/C10C2 ⊆ Aut C2×C480(C2xC4).85D10160,151
(C2×C4).86D10 = C22×Dic10φ: D10/C10C2 ⊆ Aut C2×C4160(C2xC4).86D10160,213
(C2×C4).87D10 = C4×C52C8central extension (φ=1)160(C2xC4).87D10160,9
(C2×C4).88D10 = C42.D5central extension (φ=1)160(C2xC4).88D10160,10
(C2×C4).89D10 = C203C8central extension (φ=1)160(C2xC4).89D10160,11
(C2×C4).90D10 = C8×Dic5central extension (φ=1)160(C2xC4).90D10160,20
(C2×C4).91D10 = C20.8Q8central extension (φ=1)160(C2xC4).91D10160,21
(C2×C4).92D10 = C408C4central extension (φ=1)160(C2xC4).92D10160,22
(C2×C4).93D10 = D101C8central extension (φ=1)80(C2xC4).93D10160,27
(C2×C4).94D10 = C20.55D4central extension (φ=1)80(C2xC4).94D10160,37
(C2×C4).95D10 = D5×C42central extension (φ=1)80(C2xC4).95D10160,92
(C2×C4).96D10 = C42⋊D5central extension (φ=1)80(C2xC4).96D10160,93
(C2×C4).97D10 = D5×C2×C8central extension (φ=1)80(C2xC4).97D10160,120
(C2×C4).98D10 = C2×C8⋊D5central extension (φ=1)80(C2xC4).98D10160,121
(C2×C4).99D10 = C22×C52C8central extension (φ=1)160(C2xC4).99D10160,141
(C2×C4).100D10 = C2×C4.Dic5central extension (φ=1)80(C2xC4).100D10160,142
(C2×C4).101D10 = C2×C4×Dic5central extension (φ=1)160(C2xC4).101D10160,143
(C2×C4).102D10 = C23.21D10central extension (φ=1)80(C2xC4).102D10160,147
(C2×C4).103D10 = C4×C5⋊D4central extension (φ=1)80(C2xC4).103D10160,149

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