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Extensions 1→N→G→Q→1 with N=C2×C20 and Q=Q8

Direct product G=N×Q with N=C2×C20 and Q=Q8
dρLabelID
Q8×C2×C20320Q8xC2xC20320,1518

Semidirect products G=N:Q with N=C2×C20 and Q=Q8
extensionφ:Q→Aut NdρLabelID
(C2×C20)⋊1Q8 = (C2×Dic5)⋊Q8φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20):1Q8320,283
(C2×C20)⋊2Q8 = C2×C20⋊Q8φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20):2Q8320,1169
(C2×C20)⋊3Q8 = C10.12- 1+4φ: Q8/C2 → C22 ⊆ Aut C2×C20160(C2xC20):3Q8320,1172
(C2×C20)⋊4Q8 = C42.88D10φ: Q8/C2 → C22 ⊆ Aut C2×C20160(C2xC20):4Q8320,1189
(C2×C20)⋊5Q8 = C42.90D10φ: Q8/C2 → C22 ⊆ Aut C2×C20160(C2xC20):5Q8320,1191
(C2×C20)⋊6Q8 = (C2×C20)⋊Q8φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20):6Q8320,273
(C2×C20)⋊7Q8 = (C2×C4)⋊Dic10φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20):7Q8320,606
(C2×C20)⋊8Q8 = C5×C23.78C23φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20):8Q8320,896
(C2×C20)⋊9Q8 = C5×C23.41C23φ: Q8/C2 → C22 ⊆ Aut C2×C20160(C2xC20):9Q8320,1546
(C2×C20)⋊10Q8 = (C2×C20)⋊10Q8φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20):10Q8320,556
(C2×C20)⋊11Q8 = C5×C23.67C23φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20):11Q8320,892
(C2×C20)⋊12Q8 = C2×C20⋊2Q8φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20):12Q8320,1140
(C2×C20)⋊13Q8 = C42.274D10φ: Q8/C4 → C2 ⊆ Aut C2×C20160(C2xC20):13Q8320,1142
(C2×C20)⋊14Q8 = C2×C4×Dic10φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20):14Q8320,1139
(C2×C20)⋊15Q8 = C10×C4⋊Q8φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20):15Q8320,1533
(C2×C20)⋊16Q8 = C5×C23.37C23φ: Q8/C4 → C2 ⊆ Aut C2×C20160(C2xC20):16Q8320,1535

Non-split extensions G=N.Q with N=C2×C20 and Q=Q8
extensionφ:Q→Aut NdρLabelID
(C2×C20).1Q8 = C2.(C20⋊Q8)φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20).1Q8320,284
(C2×C20).2Q8 = (C2×C4).Dic10φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20).2Q8320,287
(C2×C20).3Q8 = C10.(C4⋊Q8)φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20).3Q8320,288
(C2×C20).4Q8 = C20.31C42φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20).4Q8320,87
(C2×C20).5Q8 = (C2×C20).Q8φ: Q8/C2 → C22 ⊆ Aut C2×C20160(C2xC20).5Q8320,88
(C2×C20).6Q8 = C42⋊1Dic5φ: Q8/C2 → C22 ⊆ Aut C2×C20804(C2xC20).6Q8320,89
(C2×C20).7Q8 = C20.32C42φ: Q8/C2 → C22 ⊆ Aut C2×C2080(C2xC20).7Q8320,90
(C2×C20).8Q8 = C20.60(C4⋊C4)φ: Q8/C2 → C22 ⊆ Aut C2×C20804(C2xC20).8Q8320,91
(C2×C20).9Q8 = M4(2)⋊Dic5φ: Q8/C2 → C22 ⊆ Aut C2×C20160(C2xC20).9Q8320,112
(C2×C20).10Q8 = C20.33C42φ: Q8/C2 → C22 ⊆ Aut C2×C2080(C2xC20).10Q8320,113
(C2×C20).11Q8 = (C2×C40)⋊C4φ: Q8/C2 → C22 ⊆ Aut C2×C20804(C2xC20).11Q8320,114
(C2×C20).12Q8 = C23.9D20φ: Q8/C2 → C22 ⊆ Aut C2×C20804(C2xC20).12Q8320,115
(C2×C20).13Q8 = M4(2)⋊4Dic5φ: Q8/C2 → C22 ⊆ Aut C2×C20804(C2xC20).13Q8320,117
(C2×C20).14Q8 = C2×C10.D8φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20).14Q8320,589
(C2×C20).15Q8 = C2×C20.Q8φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20).15Q8320,590
(C2×C20).16Q8 = C20.47(C4⋊C4)φ: Q8/C2 → C22 ⊆ Aut C2×C20160(C2xC20).16Q8320,591
(C2×C20).17Q8 = C20⋊4(C4⋊C4)φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20).17Q8320,600
(C2×C20).18Q8 = C20⋊5(C4⋊C4)φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20).18Q8320,603
(C2×C20).19Q8 = C20.48(C4⋊C4)φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20).19Q8320,604
(C2×C20).20Q8 = C20⋊6(C4⋊C4)φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20).20Q8320,612
(C2×C20).21Q8 = C20.64(C4⋊C4)φ: Q8/C2 → C22 ⊆ Aut C2×C20160(C2xC20).21Q8320,622
(C2×C20).22Q8 = C20.76(C4⋊C4)φ: Q8/C2 → C22 ⊆ Aut C2×C20160(C2xC20).22Q8320,625
(C2×C20).23Q8 = C42.43D10φ: Q8/C2 → C22 ⊆ Aut C2×C20160(C2xC20).23Q8320,626
(C2×C20).24Q8 = Dic5⋊5M4(2)φ: Q8/C2 → C22 ⊆ Aut C2×C20160(C2xC20).24Q8320,745
(C2×C20).25Q8 = C20.51(C4⋊C4)φ: Q8/C2 → C22 ⊆ Aut C2×C20160(C2xC20).25Q8320,746
(C2×C20).26Q8 = C23.47D20φ: Q8/C2 → C22 ⊆ Aut C2×C20160(C2xC20).26Q8320,748
(C2×C20).27Q8 = C2×C20.53D4φ: Q8/C2 → C22 ⊆ Aut C2×C20160(C2xC20).27Q8320,750
(C2×C20).28Q8 = C23.Dic10φ: Q8/C2 → C22 ⊆ Aut C2×C20804(C2xC20).28Q8320,751
(C2×C20).29Q8 = M4(2).Dic5φ: Q8/C2 → C22 ⊆ Aut C2×C20804(C2xC20).29Q8320,752
(C2×C20).30Q8 = C2×C4.Dic10φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20).30Q8320,1171
(C2×C20).31Q8 = C20.53D8φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20).31Q8320,37
(C2×C20).32Q8 = C20.39SD16φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20).32Q8320,38
(C2×C20).33Q8 = C10.49(C4×D4)φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20).33Q8320,274
(C2×C20).34Q8 = C4⋊Dic5⋊15C4φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20).34Q8320,281
(C2×C20).35Q8 = C10.52(C4×D4)φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20).35Q8320,282
(C2×C20).36Q8 = C5×C4.9C42φ: Q8/C2 → C22 ⊆ Aut C2×C20804(C2xC20).36Q8320,142
(C2×C20).37Q8 = C5×C22.C42φ: Q8/C2 → C22 ⊆ Aut C2×C20160(C2xC20).37Q8320,148
(C2×C20).38Q8 = C5×M4(2)⋊4C4φ: Q8/C2 → C22 ⊆ Aut C2×C20804(C2xC20).38Q8320,149
(C2×C20).39Q8 = (C2×C20).54D4φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20).39Q8320,611
(C2×C20).40Q8 = (C2×C20).55D4φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20).40Q8320,613
(C2×C20).41Q8 = C5×C23.81C23φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20).41Q8320,899
(C2×C20).42Q8 = C5×C23.83C23φ: Q8/C2 → C22 ⊆ Aut C2×C20320(C2xC20).42Q8320,901
(C2×C20).43Q8 = C5×M4(2)⋊C4φ: Q8/C2 → C22 ⊆ Aut C2×C20160(C2xC20).43Q8320,929
(C2×C20).44Q8 = C5×M4(2).C4φ: Q8/C2 → C22 ⊆ Aut C2×C20804(C2xC20).44Q8320,931
(C2×C20).45Q8 = C40⋊6C8φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).45Q8320,15
(C2×C20).46Q8 = C40⋊5C8φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).46Q8320,16
(C2×C20).47Q8 = C5×C8⋊2C8φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).47Q8320,139
(C2×C20).48Q8 = C5×C8⋊1C8φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).48Q8320,140
(C2×C20).49Q8 = C10.92(C4×D4)φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).49Q8320,560
(C2×C20).50Q8 = C5×C23.63C23φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).50Q8320,888
(C2×C20).51Q8 = C20.39C42φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).51Q8320,109
(C2×C20).52Q8 = C20⋊7(C4⋊C4)φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).52Q8320,555
(C2×C20).53Q8 = C42⋊8Dic5φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).53Q8320,562
(C2×C20).54Q8 = C42⋊9Dic5φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).54Q8320,563
(C2×C20).55Q8 = C2×C40⋊6C4φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).55Q8320,731
(C2×C20).56Q8 = C2×C40⋊5C4φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).56Q8320,732
(C2×C20).57Q8 = C2×C20.6Q8φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).57Q8320,1141
(C2×C20).58Q8 = C42⋊6Dic5φ: Q8/C4 → C2 ⊆ Aut C2×C2080(C2xC20).58Q8320,81
(C2×C20).59Q8 = C20⋊13M4(2)φ: Q8/C4 → C2 ⊆ Aut C2×C20160(C2xC20).59Q8320,551
(C2×C20).60Q8 = C20.65(C4⋊C4)φ: Q8/C4 → C2 ⊆ Aut C2×C20160(C2xC20).60Q8320,729
(C2×C20).61Q8 = C23.22D20φ: Q8/C4 → C2 ⊆ Aut C2×C20160(C2xC20).61Q8320,733
(C2×C20).62Q8 = C2×C40.6C4φ: Q8/C4 → C2 ⊆ Aut C2×C20160(C2xC20).62Q8320,734
(C2×C20).63Q8 = (C2×C20)⋊8C8φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).63Q8320,82
(C2×C20).64Q8 = (C2×C40)⋊15C4φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).64Q8320,108
(C2×C20).65Q8 = C2×C20⋊3C8φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).65Q8320,550
(C2×C20).66Q8 = C4×C10.D4φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).66Q8320,558
(C2×C20).67Q8 = C4×C4⋊Dic5φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).67Q8320,561
(C2×C20).68Q8 = C2×C20.8Q8φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).68Q8320,726
(C2×C20).69Q8 = C5×C42⋊6C4φ: Q8/C4 → C2 ⊆ Aut C2×C2080(C2xC20).69Q8320,144
(C2×C20).70Q8 = C5×C22.4Q16φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).70Q8320,145
(C2×C20).71Q8 = C5×C42⋊8C4φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).71Q8320,883
(C2×C20).72Q8 = C5×C42⋊9C4φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).72Q8320,885
(C2×C20).73Q8 = C5×C23.65C23φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).73Q8320,890
(C2×C20).74Q8 = C5×C4⋊M4(2)φ: Q8/C4 → C2 ⊆ Aut C2×C20160(C2xC20).74Q8320,924
(C2×C20).75Q8 = C5×C42.6C22φ: Q8/C4 → C2 ⊆ Aut C2×C20160(C2xC20).75Q8320,925
(C2×C20).76Q8 = C10×C4.Q8φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).76Q8320,926
(C2×C20).77Q8 = C10×C2.D8φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).77Q8320,927
(C2×C20).78Q8 = C5×C23.25D4φ: Q8/C4 → C2 ⊆ Aut C2×C20160(C2xC20).78Q8320,928
(C2×C20).79Q8 = C10×C8.C4φ: Q8/C4 → C2 ⊆ Aut C2×C20160(C2xC20).79Q8320,930
(C2×C20).80Q8 = C10×C42.C2φ: Q8/C4 → C2 ⊆ Aut C2×C20320(C2xC20).80Q8320,1529
(C2×C20).81Q8 = C5×C22.7C42central extension (φ=1)320(C2xC20).81Q8320,141
(C2×C20).82Q8 = C4⋊C4×C20central extension (φ=1)320(C2xC20).82Q8320,879
(C2×C20).83Q8 = C10×C4⋊C8central extension (φ=1)320(C2xC20).83Q8320,923

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