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Extensions 1→N→G→Q→1 with N=C2×C4×C20 and Q=C2

Direct product G=N×Q with N=C2×C4×C20 and Q=C2
dρLabelID
C22×C4×C20320C2^2xC4xC20320,1513

Semidirect products G=N:Q with N=C2×C4×C20 and Q=C2
extensionφ:Q→Aut NdρLabelID
(C2×C4×C20)⋊1C2 = (C2×C42)⋊D5φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):1C2320,567
(C2×C4×C20)⋊2C2 = C22⋊C4×C20φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):2C2320,878
(C2×C4×C20)⋊3C2 = C5×C24.C22φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):3C2320,889
(C2×C4×C20)⋊4C2 = C2×C42⋊2D5φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):4C2320,1150
(C2×C4×C20)⋊5C2 = C10×C42⋊C2φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):5C2320,1516
(C2×C4×C20)⋊6C2 = C10×C42⋊2C2φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):6C2320,1530
(C2×C4×C20)⋊7C2 = (C2×C4)⋊6D20φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):7C2320,566
(C2×C4×C20)⋊8C2 = C2×C20⋊4D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):8C2320,1147
(C2×C4×C20)⋊9C2 = C2×C4.D20φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):9C2320,1148
(C2×C4×C20)⋊10C2 = C2×D20⋊4C4φ: C2/C1 → C2 ⊆ Aut C2×C4×C2080(C2xC4xC20):10C2320,554
(C2×C4×C20)⋊11C2 = C2×C4×D20φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):11C2320,1145
(C2×C4×C20)⋊12C2 = C4×C4○D20φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):12C2320,1146
(C2×C4×C20)⋊13C2 = C42.276D10φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):13C2320,1149
(C2×C4×C20)⋊14C2 = C42.277D10φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):14C2320,1151
(C2×C4×C20)⋊15C2 = C4×D10⋊C4φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):15C2320,565
(C2×C4×C20)⋊16C2 = D5×C2×C42φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):16C2320,1143
(C2×C4×C20)⋊17C2 = C2×C42⋊D5φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):17C2320,1144
(C2×C4×C20)⋊18C2 = C5×C24.3C22φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):18C2320,891
(C2×C4×C20)⋊19C2 = C10×C4≀C2φ: C2/C1 → C2 ⊆ Aut C2×C4×C2080(C2xC4xC20):19C2320,921
(C2×C4×C20)⋊20C2 = D4×C2×C20φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):20C2320,1517
(C2×C4×C20)⋊21C2 = C4○D4×C20φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):21C2320,1519
(C2×C4×C20)⋊22C2 = C10×C4.4D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):22C2320,1528
(C2×C4×C20)⋊23C2 = C5×C23.36C23φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):23C2320,1531
(C2×C4×C20)⋊24C2 = C10×C4⋊1D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):24C2320,1532
(C2×C4×C20)⋊25C2 = C5×C22.26C24φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20):25C2320,1534

Non-split extensions G=N.Q with N=C2×C4×C20 and Q=C2
extensionφ:Q→Aut NdρLabelID
(C2×C4×C20).1C2 = C5×C22.7C42φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).1C2320,141
(C2×C4×C20).2C2 = C10.92(C4×D4)φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).2C2320,560
(C2×C4×C20).3C2 = C42⋊5Dic5φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).3C2320,564
(C2×C4×C20).4C2 = C5×C42⋊4C4φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).4C2320,877
(C2×C4×C20).5C2 = C4⋊C4×C20φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).5C2320,879
(C2×C4×C20).6C2 = C5×C42⋊5C4φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).6C2320,884
(C2×C4×C20).7C2 = C5×C23.63C23φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).7C2320,888
(C2×C4×C20).8C2 = C10×C8⋊C4φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).8C2320,904
(C2×C4×C20).9C2 = C20⋊7(C4⋊C4)φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).9C2320,555
(C2×C4×C20).10C2 = (C2×C20)⋊10Q8φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).10C2320,556
(C2×C4×C20).11C2 = C42⋊8Dic5φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).11C2320,562
(C2×C4×C20).12C2 = C42⋊9Dic5φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).12C2320,563
(C2×C4×C20).13C2 = C2×C20⋊2Q8φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).13C2320,1140
(C2×C4×C20).14C2 = C2×C20.6Q8φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).14C2320,1141
(C2×C4×C20).15C2 = C42⋊6Dic5φ: C2/C1 → C2 ⊆ Aut C2×C4×C2080(C2xC4xC20).15C2320,81
(C2×C4×C20).16C2 = C4×C4.Dic5φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20).16C2320,549
(C2×C4×C20).17C2 = C2×C20⋊3C8φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).17C2320,550
(C2×C4×C20).18C2 = C20⋊13M4(2)φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20).18C2320,551
(C2×C4×C20).19C2 = C42.6Dic5φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20).19C2320,552
(C2×C4×C20).20C2 = C42.7Dic5φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20).20C2320,553
(C2×C4×C20).21C2 = C4×C4⋊Dic5φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).21C2320,561
(C2×C4×C20).22C2 = C2×C4×Dic10φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).22C2320,1139
(C2×C4×C20).23C2 = C42.274D10φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20).23C2320,1142
(C2×C4×C20).24C2 = (C2×C20)⋊8C8φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).24C2320,82
(C2×C4×C20).25C2 = C2×C4×C5⋊2C8φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).25C2320,547
(C2×C4×C20).26C2 = C2×C42.D5φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).26C2320,548
(C2×C4×C20).27C2 = C42×Dic5φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).27C2320,557
(C2×C4×C20).28C2 = C4×C10.D4φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).28C2320,558
(C2×C4×C20).29C2 = C42⋊4Dic5φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).29C2320,559
(C2×C4×C20).30C2 = C5×C42⋊6C4φ: C2/C1 → C2 ⊆ Aut C2×C4×C2080(C2xC4xC20).30C2320,144
(C2×C4×C20).31C2 = C5×C42⋊8C4φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).31C2320,883
(C2×C4×C20).32C2 = C5×C42⋊9C4φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).32C2320,885
(C2×C4×C20).33C2 = C5×C23.65C23φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).33C2320,890
(C2×C4×C20).34C2 = C5×C23.67C23φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).34C2320,892
(C2×C4×C20).35C2 = M4(2)×C20φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20).35C2320,905
(C2×C4×C20).36C2 = C10×C4⋊C8φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).36C2320,923
(C2×C4×C20).37C2 = C5×C4⋊M4(2)φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20).37C2320,924
(C2×C4×C20).38C2 = C5×C42.12C4φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20).38C2320,932
(C2×C4×C20).39C2 = C5×C42.6C4φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20).39C2320,933
(C2×C4×C20).40C2 = Q8×C2×C20φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).40C2320,1518
(C2×C4×C20).41C2 = C10×C42.C2φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).41C2320,1529
(C2×C4×C20).42C2 = C10×C4⋊Q8φ: C2/C1 → C2 ⊆ Aut C2×C4×C20320(C2xC4xC20).42C2320,1533
(C2×C4×C20).43C2 = C5×C23.37C23φ: C2/C1 → C2 ⊆ Aut C2×C4×C20160(C2xC4xC20).43C2320,1535

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