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Extensions 1→N→G→Q→1 with N=C2×C10 and Q=M4(2)

Direct product G=N×Q with N=C2×C10 and Q=M4(2)
dρLabelID
M4(2)×C2×C10160M4(2)xC2xC10320,1568

Semidirect products G=N:Q with N=C2×C10 and Q=M4(2)
extensionφ:Q→Aut NdρLabelID
(C2×C10)⋊1M4(2) = C5⋊C8⋊D4φ: M4(2)/C2 → C2×C4 ⊆ Aut C2×C10160(C2xC10):1M4(2)320,1031
(C2×C10)⋊2M4(2) = C5⋊C8⋊7D4φ: M4(2)/C2 → C2×C4 ⊆ Aut C2×C10160(C2xC10):2M4(2)320,1111
(C2×C10)⋊3M4(2) = D10⋊10M4(2)φ: M4(2)/C4 → C4 ⊆ Aut C2×C1080(C2xC10):3M4(2)320,1094
(C2×C10)⋊4M4(2) = C22×C4.F5φ: M4(2)/C4 → C4 ⊆ Aut C2×C10160(C2xC10):4M4(2)320,1588
(C2×C10)⋊5M4(2) = D10⋊7M4(2)φ: M4(2)/C4 → C22 ⊆ Aut C2×C1080(C2xC10):5M4(2)320,353
(C2×C10)⋊6M4(2) = C5⋊2C8⋊26D4φ: M4(2)/C4 → C22 ⊆ Aut C2×C10160(C2xC10):6M4(2)320,357
(C2×C10)⋊7M4(2) = C42.47D10φ: M4(2)/C4 → C22 ⊆ Aut C2×C10160(C2xC10):7M4(2)320,638
(C2×C10)⋊8M4(2) = C24.4F5φ: M4(2)/C22 → C4 ⊆ Aut C2×C1080(C2xC10):8M4(2)320,1136
(C2×C10)⋊9M4(2) = C22×C22.F5φ: M4(2)/C22 → C4 ⊆ Aut C2×C10160(C2xC10):9M4(2)320,1606
(C2×C10)⋊10M4(2) = C5×C8⋊9D4φ: M4(2)/C8 → C2 ⊆ Aut C2×C10160(C2xC10):10M4(2)320,936
(C2×C10)⋊11M4(2) = C40⋊32D4φ: M4(2)/C8 → C2 ⊆ Aut C2×C10160(C2xC10):11M4(2)320,738
(C2×C10)⋊12M4(2) = C22×C8⋊D5φ: M4(2)/C8 → C2 ⊆ Aut C2×C10160(C2xC10):12M4(2)320,1409
(C2×C10)⋊13M4(2) = C5×C24.4C4φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C1080(C2xC10):13M4(2)320,908
(C2×C10)⋊14M4(2) = C24.4Dic5φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C1080(C2xC10):14M4(2)320,834
(C2×C10)⋊15M4(2) = C22×C4.Dic5φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10):15M4(2)320,1453

Non-split extensions G=N.Q with N=C2×C10 and Q=M4(2)
extensionφ:Q→Aut NdρLabelID
(C2×C10).1M4(2) = D20.C8φ: M4(2)/C2 → C2×C4 ⊆ Aut C2×C101608(C2xC10).1M4(2)320,236
(C2×C10).2M4(2) = D4.(C5⋊C8)φ: M4(2)/C2 → C2×C4 ⊆ Aut C2×C101608(C2xC10).2M4(2)320,270
(C2×C10).3M4(2) = C40.1C8φ: M4(2)/C4 → C4 ⊆ Aut C2×C10804(C2xC10).3M4(2)320,227
(C2×C10).4M4(2) = C20.23C42φ: M4(2)/C4 → C4 ⊆ Aut C2×C10804(C2xC10).4M4(2)320,228
(C2×C10).5M4(2) = (C22×C4).F5φ: M4(2)/C4 → C4 ⊆ Aut C2×C10160(C2xC10).5M4(2)320,252
(C2×C10).6M4(2) = C5⋊(C23⋊C8)φ: M4(2)/C4 → C4 ⊆ Aut C2×C1080(C2xC10).6M4(2)320,253
(C2×C10).7M4(2) = C2×C20⋊C8φ: M4(2)/C4 → C4 ⊆ Aut C2×C10320(C2xC10).7M4(2)320,1085
(C2×C10).8M4(2) = C2×D10⋊C8φ: M4(2)/C4 → C4 ⊆ Aut C2×C10160(C2xC10).8M4(2)320,1089
(C2×C10).9M4(2) = C20.30M4(2)φ: M4(2)/C4 → C4 ⊆ Aut C2×C10160(C2xC10).9M4(2)320,1097
(C2×C10).10M4(2) = C5⋊3(C23⋊C8)φ: M4(2)/C4 → C22 ⊆ Aut C2×C1080(C2xC10).10M4(2)320,26
(C2×C10).11M4(2) = (C2×Dic5)⋊C8φ: M4(2)/C4 → C22 ⊆ Aut C2×C10160(C2xC10).11M4(2)320,27
(C2×C10).12M4(2) = C40.9Q8φ: M4(2)/C4 → C22 ⊆ Aut C2×C10804(C2xC10).12M4(2)320,69
(C2×C10).13M4(2) = C80⋊C4φ: M4(2)/C4 → C22 ⊆ Aut C2×C10804(C2xC10).13M4(2)320,70
(C2×C10).14M4(2) = D20.4C8φ: M4(2)/C4 → C22 ⊆ Aut C2×C101604(C2xC10).14M4(2)320,73
(C2×C10).15M4(2) = C40.92D4φ: M4(2)/C4 → C22 ⊆ Aut C2×C101604(C2xC10).15M4(2)320,119
(C2×C10).16M4(2) = Dic5.9M4(2)φ: M4(2)/C4 → C22 ⊆ Aut C2×C10160(C2xC10).16M4(2)320,346
(C2×C10).17M4(2) = C42.3F5φ: M4(2)/C22 → C4 ⊆ Aut C2×C10804(C2xC10).17M4(2)320,198
(C2×C10).18M4(2) = C42.9F5φ: M4(2)/C22 → C4 ⊆ Aut C2×C10804(C2xC10).18M4(2)320,199
(C2×C10).19M4(2) = (C2×C20)⋊1C8φ: M4(2)/C22 → C4 ⊆ Aut C2×C10160(C2xC10).19M4(2)320,251
(C2×C10).20M4(2) = C10.(C4⋊C8)φ: M4(2)/C22 → C4 ⊆ Aut C2×C10320(C2xC10).20M4(2)320,256
(C2×C10).21M4(2) = C24.F5φ: M4(2)/C22 → C4 ⊆ Aut C2×C1080(C2xC10).21M4(2)320,271
(C2×C10).22M4(2) = C2×C10.C42φ: M4(2)/C22 → C4 ⊆ Aut C2×C10320(C2xC10).22M4(2)320,1087
(C2×C10).23M4(2) = C2×Dic5⋊C8φ: M4(2)/C22 → C4 ⊆ Aut C2×C10320(C2xC10).23M4(2)320,1090
(C2×C10).24M4(2) = Dic5.13M4(2)φ: M4(2)/C22 → C4 ⊆ Aut C2×C10160(C2xC10).24M4(2)320,1095
(C2×C10).25M4(2) = C2×C23.2F5φ: M4(2)/C22 → C4 ⊆ Aut C2×C10160(C2xC10).25M4(2)320,1135
(C2×C10).26M4(2) = C5×D4.C8φ: M4(2)/C8 → C2 ⊆ Aut C2×C101602(C2xC10).26M4(2)320,155
(C2×C10).27M4(2) = D20.3C8φ: M4(2)/C8 → C2 ⊆ Aut C2×C101602(C2xC10).27M4(2)320,66
(C2×C10).28M4(2) = (C2×C40)⋊15C4φ: M4(2)/C8 → C2 ⊆ Aut C2×C10320(C2xC10).28M4(2)320,108
(C2×C10).29M4(2) = C2×C20.8Q8φ: M4(2)/C8 → C2 ⊆ Aut C2×C10320(C2xC10).29M4(2)320,726
(C2×C10).30M4(2) = C2×C40⋊8C4φ: M4(2)/C8 → C2 ⊆ Aut C2×C10320(C2xC10).30M4(2)320,727
(C2×C10).31M4(2) = C2×D10⋊1C8φ: M4(2)/C8 → C2 ⊆ Aut C2×C10160(C2xC10).31M4(2)320,735
(C2×C10).32M4(2) = C5×C23⋊C8φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C1080(C2xC10).32M4(2)320,128
(C2×C10).33M4(2) = C5×C22.M4(2)φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).33M4(2)320,129
(C2×C10).34M4(2) = C5×C16⋊C4φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C10804(C2xC10).34M4(2)320,152
(C2×C10).35M4(2) = C5×C8.C8φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C10802(C2xC10).35M4(2)320,169
(C2×C10).36M4(2) = C5×C42.6C4φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).36M4(2)320,933
(C2×C10).37M4(2) = C40.7C8φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C10802(C2xC10).37M4(2)320,21
(C2×C10).38M4(2) = C20.45C42φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C10804(C2xC10).38M4(2)320,24
(C2×C10).39M4(2) = (C2×C20)⋊8C8φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).39M4(2)320,82
(C2×C10).40M4(2) = C24.Dic5φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C1080(C2xC10).40M4(2)320,83
(C2×C10).41M4(2) = (C2×C20)⋊C8φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).41M4(2)320,86
(C2×C10).42M4(2) = C2×C42.D5φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).42M4(2)320,548
(C2×C10).43M4(2) = C2×C20⋊3C8φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).43M4(2)320,550
(C2×C10).44M4(2) = C42.7Dic5φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).44M4(2)320,553
(C2×C10).45M4(2) = C2×C20.55D4φ: M4(2)/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).45M4(2)320,833
(C2×C10).46M4(2) = C5×C22.7C42central extension (φ=1)320(C2xC10).46M4(2)320,141
(C2×C10).47M4(2) = C10×C8⋊C4central extension (φ=1)320(C2xC10).47M4(2)320,904
(C2×C10).48M4(2) = C10×C22⋊C8central extension (φ=1)160(C2xC10).48M4(2)320,907
(C2×C10).49M4(2) = C10×C4⋊C8central extension (φ=1)320(C2xC10).49M4(2)320,923

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