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Extensions 1→N→G→Q→1 with N=C2×C10 and Q=D12

Direct product G=N×Q with N=C2×C10 and Q=D12
dρLabelID
C2×C10×D12240C2xC10xD12480,1152

Semidirect products G=N:Q with N=C2×C10 and Q=D12
extensionφ:Q→Aut NdρLabelID
(C2×C10)⋊D12 = Dic5⋊S4φ: D12/C2 → D6 ⊆ Aut C2×C10606(C2xC10):D12480,978
(C2×C10)⋊2D12 = C5×C4⋊S4φ: D12/C4 → S3 ⊆ Aut C2×C10606(C2xC10):2D12480,1015
(C2×C10)⋊3D12 = C20⋊S4φ: D12/C4 → S3 ⊆ Aut C2×C10606+(C2xC10):3D12480,1026
(C2×C10)⋊4D12 = (C2×C10)⋊4D12φ: D12/C6 → C22 ⊆ Aut C2×C10240(C2xC10):4D12480,642
(C2×C10)⋊5D12 = D30⋊19D4φ: D12/C6 → C22 ⊆ Aut C2×C10120(C2xC10):5D12480,649
(C2×C10)⋊6D12 = D30⋊16D4φ: D12/C6 → C22 ⊆ Aut C2×C10120(C2xC10):6D12480,847
(C2×C10)⋊7D12 = C5×C12⋊7D4φ: D12/C12 → C2 ⊆ Aut C2×C10240(C2xC10):7D12480,809
(C2×C10)⋊8D12 = C60⋊29D4φ: D12/C12 → C2 ⊆ Aut C2×C10240(C2xC10):8D12480,895
(C2×C10)⋊9D12 = C22×D60φ: D12/C12 → C2 ⊆ Aut C2×C10240(C2xC10):9D12480,1167
(C2×C10)⋊10D12 = C5×D6⋊D4φ: D12/D6 → C2 ⊆ Aut C2×C10120(C2xC10):10D12480,761
(C2×C10)⋊11D12 = (C2×C10)⋊11D12φ: D12/D6 → C2 ⊆ Aut C2×C10120(C2xC10):11D12480,646
(C2×C10)⋊12D12 = C22×C5⋊D12φ: D12/D6 → C2 ⊆ Aut C2×C10240(C2xC10):12D12480,1120

Non-split extensions G=N.Q with N=C2×C10 and Q=D12
extensionφ:Q→Aut NdρLabelID
(C2×C10).1D12 = C60.98D4φ: D12/C6 → C22 ⊆ Aut C2×C101204(C2xC10).1D12480,54
(C2×C10).2D12 = C15⋊8(C23⋊C4)φ: D12/C6 → C22 ⊆ Aut C2×C101204(C2xC10).2D12480,72
(C2×C10).3D12 = C23.6D30φ: D12/C6 → C22 ⊆ Aut C2×C101204(C2xC10).3D12480,166
(C2×C10).4D12 = D60⋊10C4φ: D12/C6 → C22 ⊆ Aut C2×C101204(C2xC10).4D12480,185
(C2×C10).5D12 = C20.60D12φ: D12/C6 → C22 ⊆ Aut C2×C102404(C2xC10).5D12480,379
(C2×C10).6D12 = C60.38D4φ: D12/C6 → C22 ⊆ Aut C2×C101204+(C2xC10).6D12480,381
(C2×C10).7D12 = D12.33D10φ: D12/C6 → C22 ⊆ Aut C2×C102404-(C2xC10).7D12480,398
(C2×C10).8D12 = (C2×C10).D12φ: D12/C6 → C22 ⊆ Aut C2×C10240(C2xC10).8D12480,619
(C2×C10).9D12 = C22.D60φ: D12/C6 → C22 ⊆ Aut C2×C10240(C2xC10).9D12480,851
(C2×C10).10D12 = C8⋊D30φ: D12/C6 → C22 ⊆ Aut C2×C101204+(C2xC10).10D12480,873
(C2×C10).11D12 = C8.D30φ: D12/C6 → C22 ⊆ Aut C2×C102404-(C2xC10).11D12480,874
(C2×C10).12D12 = C5×C4○D24φ: D12/C12 → C2 ⊆ Aut C2×C102402(C2xC10).12D12480,783
(C2×C10).13D12 = Dic30⋊8C4φ: D12/C12 → C2 ⊆ Aut C2×C10480(C2xC10).13D12480,176
(C2×C10).14D12 = C120⋊10C4φ: D12/C12 → C2 ⊆ Aut C2×C10480(C2xC10).14D12480,177
(C2×C10).15D12 = C120⋊9C4φ: D12/C12 → C2 ⊆ Aut C2×C10480(C2xC10).15D12480,178
(C2×C10).16D12 = D60⋊8C4φ: D12/C12 → C2 ⊆ Aut C2×C10240(C2xC10).16D12480,181
(C2×C10).17D12 = C30.29C42φ: D12/C12 → C2 ⊆ Aut C2×C10480(C2xC10).17D12480,191
(C2×C10).18D12 = C2×C24⋊D5φ: D12/C12 → C2 ⊆ Aut C2×C10240(C2xC10).18D12480,867
(C2×C10).19D12 = C2×D120φ: D12/C12 → C2 ⊆ Aut C2×C10240(C2xC10).19D12480,868
(C2×C10).20D12 = C40.69D6φ: D12/C12 → C2 ⊆ Aut C2×C102402(C2xC10).20D12480,869
(C2×C10).21D12 = C2×Dic60φ: D12/C12 → C2 ⊆ Aut C2×C10480(C2xC10).21D12480,870
(C2×C10).22D12 = C2×C60⋊5C4φ: D12/C12 → C2 ⊆ Aut C2×C10480(C2xC10).22D12480,890
(C2×C10).23D12 = C2×D30⋊3C4φ: D12/C12 → C2 ⊆ Aut C2×C10240(C2xC10).23D12480,892
(C2×C10).24D12 = C5×C23.6D6φ: D12/D6 → C2 ⊆ Aut C2×C101204(C2xC10).24D12480,125
(C2×C10).25D12 = C5×D12⋊C4φ: D12/D6 → C2 ⊆ Aut C2×C101204(C2xC10).25D12480,144
(C2×C10).26D12 = C5×C23.21D6φ: D12/D6 → C2 ⊆ Aut C2×C10240(C2xC10).26D12480,765
(C2×C10).27D12 = C5×C8⋊D6φ: D12/D6 → C2 ⊆ Aut C2×C101204(C2xC10).27D12480,787
(C2×C10).28D12 = C5×C8.D6φ: D12/D6 → C2 ⊆ Aut C2×C102404(C2xC10).28D12480,788
(C2×C10).29D12 = C10.D24φ: D12/D6 → C2 ⊆ Aut C2×C10240(C2xC10).29D12480,43
(C2×C10).30D12 = D60⋊15C4φ: D12/D6 → C2 ⊆ Aut C2×C10240(C2xC10).30D12480,45
(C2×C10).31D12 = C10.Dic12φ: D12/D6 → C2 ⊆ Aut C2×C10480(C2xC10).31D12480,49
(C2×C10).32D12 = Dic30⋊15C4φ: D12/D6 → C2 ⊆ Aut C2×C10480(C2xC10).32D12480,51
(C2×C10).33D12 = D60⋊13C4φ: D12/D6 → C2 ⊆ Aut C2×C101204(C2xC10).33D12480,56
(C2×C10).34D12 = C60.7Q8φ: D12/D6 → C2 ⊆ Aut C2×C10480(C2xC10).34D12480,61
(C2×C10).35D12 = C60.8Q8φ: D12/D6 → C2 ⊆ Aut C2×C10480(C2xC10).35D12480,64
(C2×C10).36D12 = C30.24C42φ: D12/D6 → C2 ⊆ Aut C2×C10480(C2xC10).36D12480,70
(C2×C10).37D12 = C15⋊9(C23⋊C4)φ: D12/D6 → C2 ⊆ Aut C2×C101204(C2xC10).37D12480,73
(C2×C10).38D12 = C2×C5⋊D24φ: D12/D6 → C2 ⊆ Aut C2×C10240(C2xC10).38D12480,378
(C2×C10).39D12 = D60⋊36C22φ: D12/D6 → C2 ⊆ Aut C2×C101204(C2xC10).39D12480,380
(C2×C10).40D12 = C2×D12.D5φ: D12/D6 → C2 ⊆ Aut C2×C10240(C2xC10).40D12480,392
(C2×C10).41D12 = C2×Dic6⋊D5φ: D12/D6 → C2 ⊆ Aut C2×C10240(C2xC10).41D12480,393
(C2×C10).42D12 = C2×C5⋊Dic12φ: D12/D6 → C2 ⊆ Aut C2×C10480(C2xC10).42D12480,396
(C2×C10).43D12 = C20.D12φ: D12/D6 → C2 ⊆ Aut C2×C102404(C2xC10).43D12480,397
(C2×C10).44D12 = C2×D6⋊Dic5φ: D12/D6 → C2 ⊆ Aut C2×C10240(C2xC10).44D12480,614
(C2×C10).45D12 = C2×D30⋊4C4φ: D12/D6 → C2 ⊆ Aut C2×C10240(C2xC10).45D12480,616
(C2×C10).46D12 = C2×C30.Q8φ: D12/D6 → C2 ⊆ Aut C2×C10480(C2xC10).46D12480,617
(C2×C10).47D12 = C10.(C2×D12)φ: D12/D6 → C2 ⊆ Aut C2×C10240(C2xC10).47D12480,618
(C2×C10).48D12 = C5×C2.Dic12central extension (φ=1)480(C2xC10).48D12480,135
(C2×C10).49D12 = C5×C8⋊Dic3central extension (φ=1)480(C2xC10).49D12480,136
(C2×C10).50D12 = C5×C24⋊1C4central extension (φ=1)480(C2xC10).50D12480,137
(C2×C10).51D12 = C5×C2.D24central extension (φ=1)240(C2xC10).51D12480,140
(C2×C10).52D12 = C5×C6.C42central extension (φ=1)480(C2xC10).52D12480,150
(C2×C10).53D12 = C10×C24⋊C2central extension (φ=1)240(C2xC10).53D12480,781
(C2×C10).54D12 = C10×D24central extension (φ=1)240(C2xC10).54D12480,782
(C2×C10).55D12 = C10×Dic12central extension (φ=1)480(C2xC10).55D12480,784
(C2×C10).56D12 = C10×C4⋊Dic3central extension (φ=1)480(C2xC10).56D12480,804
(C2×C10).57D12 = C10×D6⋊C4central extension (φ=1)240(C2xC10).57D12480,806

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