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Extensions 1→N→G→Q→1 with N=C5×C4⋊C4 and Q=C4

Direct product G=N×Q with N=C5×C4⋊C4 and Q=C4
dρLabelID
C4⋊C4×C20320C4:C4xC20320,879

Semidirect products G=N:Q with N=C5×C4⋊C4 and Q=C4
extensionφ:Q→Out NdρLabelID
(C5×C4⋊C4)⋊1C4 = D10.1D8φ: C4/C1 → C4 ⊆ Out C5×C4⋊C480(C5xC4:C4):1C4320,206
(C5×C4⋊C4)⋊2C4 = D10.1Q16φ: C4/C1 → C4 ⊆ Out C5×C4⋊C480(C5xC4:C4):2C4320,207
(C5×C4⋊C4)⋊3C4 = D10.18D8φ: C4/C1 → C4 ⊆ Out C5×C4⋊C480(C5xC4:C4):3C4320,212
(C5×C4⋊C4)⋊4C4 = C20.C42φ: C4/C1 → C4 ⊆ Out C5×C4⋊C480(C5xC4:C4):4C4320,213
(C5×C4⋊C4)⋊5C4 = C4⋊C4×F5φ: C4/C1 → C4 ⊆ Out C5×C4⋊C480(C5xC4:C4):5C4320,1048
(C5×C4⋊C4)⋊6C4 = C4⋊C4⋊5F5φ: C4/C1 → C4 ⊆ Out C5×C4⋊C480(C5xC4:C4):6C4320,1049
(C5×C4⋊C4)⋊7C4 = C20⋊(C4⋊C4)φ: C4/C1 → C4 ⊆ Out C5×C4⋊C480(C5xC4:C4):7C4320,1050
(C5×C4⋊C4)⋊8C4 = C4⋊C4⋊Dic5φ: C4/C1 → C4 ⊆ Out C5×C4⋊C480(C5xC4:C4):8C4320,95
(C5×C4⋊C4)⋊9C4 = C10.29C4≀C2φ: C4/C1 → C4 ⊆ Out C5×C4⋊C480(C5xC4:C4):9C4320,96
(C5×C4⋊C4)⋊10C4 = C5×C22.SD16φ: C4/C1 → C4 ⊆ Out C5×C4⋊C480(C5xC4:C4):10C4320,132
(C5×C4⋊C4)⋊11C4 = C5×C23.31D4φ: C4/C1 → C4 ⊆ Out C5×C4⋊C480(C5xC4:C4):11C4320,133
(C5×C4⋊C4)⋊12C4 = C20.31C42φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4320(C5xC4:C4):12C4320,87
(C5×C4⋊C4)⋊13C4 = C20.32C42φ: C4/C2 → C2 ⊆ Out C5×C4⋊C480(C5xC4:C4):13C4320,90
(C5×C4⋊C4)⋊14C4 = C4⋊C4×Dic5φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4320(C5xC4:C4):14C4320,602
(C5×C4⋊C4)⋊15C4 = C4⋊C4⋊5Dic5φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4320(C5xC4:C4):15C4320,608
(C5×C4⋊C4)⋊16C4 = C20⋊6(C4⋊C4)φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4320(C5xC4:C4):16C4320,612
(C5×C4⋊C4)⋊17C4 = C5×C42⋊6C4φ: C4/C2 → C2 ⊆ Out C5×C4⋊C480(C5xC4:C4):17C4320,144
(C5×C4⋊C4)⋊18C4 = C5×C22.4Q16φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4320(C5xC4:C4):18C4320,145
(C5×C4⋊C4)⋊19C4 = C5×C23.63C23φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4320(C5xC4:C4):19C4320,888
(C5×C4⋊C4)⋊20C4 = C5×C23.65C23φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4320(C5xC4:C4):20C4320,890

Non-split extensions G=N.Q with N=C5×C4⋊C4 and Q=C4
extensionφ:Q→Out NdρLabelID
(C5×C4⋊C4).1C4 = C10.C4≀C2φ: C4/C1 → C4 ⊆ Out C5×C4⋊C4320(C5xC4:C4).1C4320,208
(C5×C4⋊C4).2C4 = Dic5.D8φ: C4/C1 → C4 ⊆ Out C5×C4⋊C4320(C5xC4:C4).2C4320,211
(C5×C4⋊C4).3C4 = D20⋊C8φ: C4/C1 → C4 ⊆ Out C5×C4⋊C4160(C5xC4:C4).3C4320,209
(C5×C4⋊C4).4C4 = Dic10⋊1C8φ: C4/C1 → C4 ⊆ Out C5×C4⋊C4320(C5xC4:C4).4C4320,210
(C5×C4⋊C4).5C4 = D10.C42φ: C4/C1 → C4 ⊆ Out C5×C4⋊C4160(C5xC4:C4).5C4320,1039
(C5×C4⋊C4).6C4 = D20⋊2C8φ: C4/C1 → C4 ⊆ Out C5×C4⋊C4160(C5xC4:C4).6C4320,1040
(C5×C4⋊C4).7C4 = Dic10⋊C8φ: C4/C1 → C4 ⊆ Out C5×C4⋊C4320(C5xC4:C4).7C4320,1041
(C5×C4⋊C4).8C4 = D10⋊2M4(2)φ: C4/C1 → C4 ⊆ Out C5×C4⋊C4160(C5xC4:C4).8C4320,1042
(C5×C4⋊C4).9C4 = C20⋊M4(2)φ: C4/C1 → C4 ⊆ Out C5×C4⋊C4160(C5xC4:C4).9C4320,1043
(C5×C4⋊C4).10C4 = C4⋊C4.7F5φ: C4/C1 → C4 ⊆ Out C5×C4⋊C4160(C5xC4:C4).10C4320,1044
(C5×C4⋊C4).11C4 = Dic5.M4(2)φ: C4/C1 → C4 ⊆ Out C5×C4⋊C4320(C5xC4:C4).11C4320,1045
(C5×C4⋊C4).12C4 = C4⋊C4.9F5φ: C4/C1 → C4 ⊆ Out C5×C4⋊C4160(C5xC4:C4).12C4320,1046
(C5×C4⋊C4).13C4 = C20.M4(2)φ: C4/C1 → C4 ⊆ Out C5×C4⋊C4320(C5xC4:C4).13C4320,1047
(C5×C4⋊C4).14C4 = C42.8D10φ: C4/C1 → C4 ⊆ Out C5×C4⋊C4320(C5xC4:C4).14C4320,101
(C5×C4⋊C4).15C4 = C20.10D8φ: C4/C1 → C4 ⊆ Out C5×C4⋊C4320(C5xC4:C4).15C4320,105
(C5×C4⋊C4).16C4 = C5×C42.2C22φ: C4/C1 → C4 ⊆ Out C5×C4⋊C4320(C5xC4:C4).16C4320,135
(C5×C4⋊C4).17C4 = C5×C4.10D8φ: C4/C1 → C4 ⊆ Out C5×C4⋊C4320(C5xC4:C4).17C4320,137
(C5×C4⋊C4).18C4 = C20.57D8φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4160(C5xC4:C4).18C4320,92
(C5×C4⋊C4).19C4 = C20.26Q16φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4320(C5xC4:C4).19C4320,93
(C5×C4⋊C4).20C4 = C20.35C42φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4160(C5xC4:C4).20C4320,624
(C5×C4⋊C4).21C4 = C42.43D10φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4160(C5xC4:C4).21C4320,626
(C5×C4⋊C4).22C4 = C42.187D10φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4160(C5xC4:C4).22C4320,627
(C5×C4⋊C4).23C4 = D4×C5⋊2C8φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4160(C5xC4:C4).23C4320,637
(C5×C4⋊C4).24C4 = C42.47D10φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4160(C5xC4:C4).24C4320,638
(C5×C4⋊C4).25C4 = C20⋊7M4(2)φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4160(C5xC4:C4).25C4320,639
(C5×C4⋊C4).26C4 = Q8×C5⋊2C8φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4320(C5xC4:C4).26C4320,650
(C5×C4⋊C4).27C4 = C42.210D10φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4320(C5xC4:C4).27C4320,651
(C5×C4⋊C4).28C4 = C5×D4⋊C8φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4160(C5xC4:C4).28C4320,130
(C5×C4⋊C4).29C4 = C5×Q8⋊C8φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4320(C5xC4:C4).29C4320,131
(C5×C4⋊C4).30C4 = C5×C42.6C22φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4160(C5xC4:C4).30C4320,925
(C5×C4⋊C4).31C4 = C5×C42.7C22φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4160(C5xC4:C4).31C4320,934
(C5×C4⋊C4).32C4 = C5×C8⋊9D4φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4160(C5xC4:C4).32C4320,936
(C5×C4⋊C4).33C4 = C5×C8⋊6D4φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4160(C5xC4:C4).33C4320,937
(C5×C4⋊C4).34C4 = C5×C8⋊4Q8φ: C4/C2 → C2 ⊆ Out C5×C4⋊C4320(C5xC4:C4).34C4320,947
(C5×C4⋊C4).35C4 = C5×C8○2M4(2)φ: trivial image160(C5xC4:C4).35C4320,906
(C5×C4⋊C4).36C4 = D4×C40φ: trivial image160(C5xC4:C4).36C4320,935
(C5×C4⋊C4).37C4 = Q8×C40φ: trivial image320(C5xC4:C4).37C4320,946

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