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Extensions 1→N→G→Q→1 with N=C2×C10 and Q=D4

Direct product G=N×Q with N=C2×C10 and Q=D4
dρLabelID
D4×C2×C1080D4xC2xC10160,229

Semidirect products G=N:Q with N=C2×C10 and Q=D4
extensionφ:Q→Aut NdρLabelID
(C2×C10)⋊1D4 = C22⋊D20φ: D4/C2 → C22 ⊆ Aut C2×C1040(C2xC10):1D4160,103
(C2×C10)⋊2D4 = C23⋊D10φ: D4/C2 → C22 ⊆ Aut C2×C1040(C2xC10):2D4160,158
(C2×C10)⋊3D4 = Dic5⋊D4φ: D4/C2 → C22 ⊆ Aut C2×C1080(C2xC10):3D4160,160
(C2×C10)⋊4D4 = C5×C4⋊D4φ: D4/C4 → C2 ⊆ Aut C2×C1080(C2xC10):4D4160,182
(C2×C10)⋊5D4 = C20⋊7D4φ: D4/C4 → C2 ⊆ Aut C2×C1080(C2xC10):5D4160,151
(C2×C10)⋊6D4 = C22×D20φ: D4/C4 → C2 ⊆ Aut C2×C1080(C2xC10):6D4160,215
(C2×C10)⋊7D4 = C5×C22≀C2φ: D4/C22 → C2 ⊆ Aut C2×C1040(C2xC10):7D4160,181
(C2×C10)⋊8D4 = C24⋊2D5φ: D4/C22 → C2 ⊆ Aut C2×C1040(C2xC10):8D4160,174
(C2×C10)⋊9D4 = C22×C5⋊D4φ: D4/C22 → C2 ⊆ Aut C2×C1080(C2xC10):9D4160,227

Non-split extensions G=N.Q with N=C2×C10 and Q=D4
extensionφ:Q→Aut NdρLabelID
(C2×C10).1D4 = D20⋊7C4φ: D4/C2 → C22 ⊆ Aut C2×C10404(C2xC10).1D4160,32
(C2×C10).2D4 = C23⋊Dic5φ: D4/C2 → C22 ⊆ Aut C2×C10404(C2xC10).2D4160,41
(C2×C10).3D4 = D4⋊2Dic5φ: D4/C2 → C22 ⊆ Aut C2×C10404(C2xC10).3D4160,44
(C2×C10).4D4 = C22.D20φ: D4/C2 → C22 ⊆ Aut C2×C1080(C2xC10).4D4160,107
(C2×C10).5D4 = C8⋊D10φ: D4/C2 → C22 ⊆ Aut C2×C10404+(C2xC10).5D4160,129
(C2×C10).6D4 = C8.D10φ: D4/C2 → C22 ⊆ Aut C2×C10804-(C2xC10).6D4160,130
(C2×C10).7D4 = C23.18D10φ: D4/C2 → C22 ⊆ Aut C2×C1080(C2xC10).7D4160,156
(C2×C10).8D4 = D4⋊D10φ: D4/C2 → C22 ⊆ Aut C2×C10404+(C2xC10).8D4160,170
(C2×C10).9D4 = D4.8D10φ: D4/C2 → C22 ⊆ Aut C2×C10804(C2xC10).9D4160,171
(C2×C10).10D4 = D4.9D10φ: D4/C2 → C22 ⊆ Aut C2×C10804-(C2xC10).10D4160,172
(C2×C10).11D4 = C5×C4○D8φ: D4/C4 → C2 ⊆ Aut C2×C10802(C2xC10).11D4160,196
(C2×C10).12D4 = C20.44D4φ: D4/C4 → C2 ⊆ Aut C2×C10160(C2xC10).12D4160,23
(C2×C10).13D4 = C40⋊6C4φ: D4/C4 → C2 ⊆ Aut C2×C10160(C2xC10).13D4160,24
(C2×C10).14D4 = C40⋊5C4φ: D4/C4 → C2 ⊆ Aut C2×C10160(C2xC10).14D4160,25
(C2×C10).15D4 = D20⋊5C4φ: D4/C4 → C2 ⊆ Aut C2×C1080(C2xC10).15D4160,28
(C2×C10).16D4 = C2×C40⋊C2φ: D4/C4 → C2 ⊆ Aut C2×C1080(C2xC10).16D4160,123
(C2×C10).17D4 = C2×D40φ: D4/C4 → C2 ⊆ Aut C2×C1080(C2xC10).17D4160,124
(C2×C10).18D4 = D40⋊7C2φ: D4/C4 → C2 ⊆ Aut C2×C10802(C2xC10).18D4160,125
(C2×C10).19D4 = C2×Dic20φ: D4/C4 → C2 ⊆ Aut C2×C10160(C2xC10).19D4160,126
(C2×C10).20D4 = C2×C4⋊Dic5φ: D4/C4 → C2 ⊆ Aut C2×C10160(C2xC10).20D4160,146
(C2×C10).21D4 = C5×C23⋊C4φ: D4/C22 → C2 ⊆ Aut C2×C10404(C2xC10).21D4160,49
(C2×C10).22D4 = C5×C4≀C2φ: D4/C22 → C2 ⊆ Aut C2×C10402(C2xC10).22D4160,54
(C2×C10).23D4 = C5×C22.D4φ: D4/C22 → C2 ⊆ Aut C2×C1080(C2xC10).23D4160,184
(C2×C10).24D4 = C5×C8⋊C22φ: D4/C22 → C2 ⊆ Aut C2×C10404(C2xC10).24D4160,197
(C2×C10).25D4 = C5×C8.C22φ: D4/C22 → C2 ⊆ Aut C2×C10804(C2xC10).25D4160,198
(C2×C10).26D4 = D20⋊4C4φ: D4/C22 → C2 ⊆ Aut C2×C10402(C2xC10).26D4160,12
(C2×C10).27D4 = C23.1D10φ: D4/C22 → C2 ⊆ Aut C2×C10404(C2xC10).27D4160,13
(C2×C10).28D4 = C10.D8φ: D4/C22 → C2 ⊆ Aut C2×C10160(C2xC10).28D4160,14
(C2×C10).29D4 = C20.Q8φ: D4/C22 → C2 ⊆ Aut C2×C10160(C2xC10).29D4160,15
(C2×C10).30D4 = D20⋊6C4φ: D4/C22 → C2 ⊆ Aut C2×C1080(C2xC10).30D4160,16
(C2×C10).31D4 = C10.Q16φ: D4/C22 → C2 ⊆ Aut C2×C10160(C2xC10).31D4160,17
(C2×C10).32D4 = C10.10C42φ: D4/C22 → C2 ⊆ Aut C2×C10160(C2xC10).32D4160,38
(C2×C10).33D4 = D4⋊Dic5φ: D4/C22 → C2 ⊆ Aut C2×C1080(C2xC10).33D4160,39
(C2×C10).34D4 = Q8⋊Dic5φ: D4/C22 → C2 ⊆ Aut C2×C10160(C2xC10).34D4160,42
(C2×C10).35D4 = C2×C10.D4φ: D4/C22 → C2 ⊆ Aut C2×C10160(C2xC10).35D4160,144
(C2×C10).36D4 = C2×D10⋊C4φ: D4/C22 → C2 ⊆ Aut C2×C1080(C2xC10).36D4160,148
(C2×C10).37D4 = C23.23D10φ: D4/C22 → C2 ⊆ Aut C2×C1080(C2xC10).37D4160,150
(C2×C10).38D4 = C2×D4⋊D5φ: D4/C22 → C2 ⊆ Aut C2×C1080(C2xC10).38D4160,152
(C2×C10).39D4 = D4.D10φ: D4/C22 → C2 ⊆ Aut C2×C10404(C2xC10).39D4160,153
(C2×C10).40D4 = C2×D4.D5φ: D4/C22 → C2 ⊆ Aut C2×C1080(C2xC10).40D4160,154
(C2×C10).41D4 = C2×Q8⋊D5φ: D4/C22 → C2 ⊆ Aut C2×C1080(C2xC10).41D4160,162
(C2×C10).42D4 = C20.C23φ: D4/C22 → C2 ⊆ Aut C2×C10804(C2xC10).42D4160,163
(C2×C10).43D4 = C2×C5⋊Q16φ: D4/C22 → C2 ⊆ Aut C2×C10160(C2xC10).43D4160,164
(C2×C10).44D4 = C2×C23.D5φ: D4/C22 → C2 ⊆ Aut C2×C1080(C2xC10).44D4160,173
(C2×C10).45D4 = C5×C2.C42central extension (φ=1)160(C2xC10).45D4160,45
(C2×C10).46D4 = C5×D4⋊C4central extension (φ=1)80(C2xC10).46D4160,52
(C2×C10).47D4 = C5×Q8⋊C4central extension (φ=1)160(C2xC10).47D4160,53
(C2×C10).48D4 = C5×C4.Q8central extension (φ=1)160(C2xC10).48D4160,56
(C2×C10).49D4 = C5×C2.D8central extension (φ=1)160(C2xC10).49D4160,57
(C2×C10).50D4 = C10×C22⋊C4central extension (φ=1)80(C2xC10).50D4160,176
(C2×C10).51D4 = C10×C4⋊C4central extension (φ=1)160(C2xC10).51D4160,177
(C2×C10).52D4 = C10×D8central extension (φ=1)80(C2xC10).52D4160,193
(C2×C10).53D4 = C10×SD16central extension (φ=1)80(C2xC10).53D4160,194
(C2×C10).54D4 = C10×Q16central extension (φ=1)160(C2xC10).54D4160,195

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