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Extensions 1→N→G→Q→1 with N=C10×C4⋊C4 and Q=C2

Direct product G=N×Q with N=C10×C4⋊C4 and Q=C2
dρLabelID
C4⋊C4×C2×C10320C4:C4xC2xC10320,1515

Semidirect products G=N:Q with N=C10×C4⋊C4 and Q=C2
extensionφ:Q→Out NdρLabelID
(C10×C4⋊C4)⋊1C2 = C2×D20⋊6C4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):1C2320,592
(C10×C4⋊C4)⋊2C2 = C4○D20⋊9C4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):2C2320,593
(C10×C4⋊C4)⋊3C2 = (C2×C10).40D8φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):3C2320,594
(C10×C4⋊C4)⋊4C2 = C4⋊C4.228D10φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):4C2320,595
(C10×C4⋊C4)⋊5C2 = D10⋊4(C4⋊C4)φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):5C2320,614
(C10×C4⋊C4)⋊6C2 = (C2×D20)⋊22C4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):6C2320,615
(C10×C4⋊C4)⋊7C2 = C2×D5×C4⋊C4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):7C2320,1173
(C10×C4⋊C4)⋊8C2 = C2×C4⋊C4⋊7D5φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):8C2320,1174
(C10×C4⋊C4)⋊9C2 = C2×D20⋊8C4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):9C2320,1175
(C10×C4⋊C4)⋊10C2 = C10.82+ 1+4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):10C2320,1176
(C10×C4⋊C4)⋊11C2 = C2×D10.13D4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):11C2320,1177
(C10×C4⋊C4)⋊12C2 = C2×C4⋊D20φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):12C2320,1178
(C10×C4⋊C4)⋊13C2 = C10.2- 1+4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):13C2320,1179
(C10×C4⋊C4)⋊14C2 = C2×D10⋊Q8φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):14C2320,1180
(C10×C4⋊C4)⋊15C2 = C2×D10⋊2Q8φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):15C2320,1181
(C10×C4⋊C4)⋊16C2 = C10.2+ 1+4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):16C2320,1182
(C10×C4⋊C4)⋊17C2 = C10.102+ 1+4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):17C2320,1183
(C10×C4⋊C4)⋊18C2 = C2×C4⋊C4⋊D5φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):18C2320,1184
(C10×C4⋊C4)⋊19C2 = C10.52- 1+4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):19C2320,1185
(C10×C4⋊C4)⋊20C2 = C10.112+ 1+4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):20C2320,1186
(C10×C4⋊C4)⋊21C2 = C10.62- 1+4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):21C2320,1187
(C10×C4⋊C4)⋊22C2 = (C2×C4)⋊3D20φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):22C2320,618
(C10×C4⋊C4)⋊23C2 = (C2×C20).56D4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):23C2320,621
(C10×C4⋊C4)⋊24C2 = D10⋊5(C4⋊C4)φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):24C2320,616
(C10×C4⋊C4)⋊25C2 = C10.90(C4×D4)φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):25C2320,617
(C10×C4⋊C4)⋊26C2 = (C2×C20).289D4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):26C2320,619
(C10×C4⋊C4)⋊27C2 = (C2×C20).290D4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):27C2320,620
(C10×C4⋊C4)⋊28C2 = C5×C23.7Q8φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):28C2320,881
(C10×C4⋊C4)⋊29C2 = C5×C23.8Q8φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):29C2320,886
(C10×C4⋊C4)⋊30C2 = C5×C24.C22φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):30C2320,889
(C10×C4⋊C4)⋊31C2 = C5×C24.3C22φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):31C2320,891
(C10×C4⋊C4)⋊32C2 = C5×C23.10D4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):32C2320,895
(C10×C4⋊C4)⋊33C2 = C5×C23.Q8φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):33C2320,897
(C10×C4⋊C4)⋊34C2 = C5×C23.11D4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):34C2320,898
(C10×C4⋊C4)⋊35C2 = C5×C23.4Q8φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):35C2320,900
(C10×C4⋊C4)⋊36C2 = C10×D4⋊C4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):36C2320,915
(C10×C4⋊C4)⋊37C2 = C5×C23.36D4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):37C2320,918
(C10×C4⋊C4)⋊38C2 = C5×C22.D8φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):38C2320,981
(C10×C4⋊C4)⋊39C2 = C5×C23.46D4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):39C2320,982
(C10×C4⋊C4)⋊40C2 = C5×C23.33C23φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):40C2320,1522
(C10×C4⋊C4)⋊41C2 = C10×C4⋊D4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):41C2320,1524
(C10×C4⋊C4)⋊42C2 = C10×C22⋊Q8φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):42C2320,1525
(C10×C4⋊C4)⋊43C2 = C10×C22.D4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):43C2320,1526
(C10×C4⋊C4)⋊44C2 = C10×C42⋊2C2φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):44C2320,1530
(C10×C4⋊C4)⋊45C2 = C5×C22.31C24φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):45C2320,1539
(C10×C4⋊C4)⋊46C2 = C5×C22.33C24φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):46C2320,1541
(C10×C4⋊C4)⋊47C2 = C5×D4⋊6D4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):47C2320,1549
(C10×C4⋊C4)⋊48C2 = C5×C22.46C24φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):48C2320,1554
(C10×C4⋊C4)⋊49C2 = C5×C22.47C24φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):49C2320,1555
(C10×C4⋊C4)⋊50C2 = C5×D4⋊3Q8φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4):50C2320,1556
(C10×C4⋊C4)⋊51C2 = C10×C42⋊C2φ: trivial image160(C10xC4:C4):51C2320,1516
(C10×C4⋊C4)⋊52C2 = D4×C2×C20φ: trivial image160(C10xC4:C4):52C2320,1517

Non-split extensions G=N.Q with N=C10×C4⋊C4 and Q=C2
extensionφ:Q→Out NdρLabelID
(C10×C4⋊C4).1C2 = C20.31C42φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).1C2320,87
(C10×C4⋊C4).2C2 = (C2×C20).Q8φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4).2C2320,88
(C10×C4⋊C4).3C2 = C2×C10.D8φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).3C2320,589
(C10×C4⋊C4).4C2 = C2×C20.Q8φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).4C2320,590
(C10×C4⋊C4).5C2 = C20.47(C4⋊C4)φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4).5C2320,591
(C10×C4⋊C4).6C2 = C2×C10.Q16φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).6C2320,596
(C10×C4⋊C4).7C2 = C4⋊C4.230D10φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4).7C2320,597
(C10×C4⋊C4).8C2 = C4⋊C4.231D10φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4).8C2320,598
(C10×C4⋊C4).9C2 = C20⋊4(C4⋊C4)φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).9C2320,600
(C10×C4⋊C4).10C2 = (C2×Dic5)⋊6Q8φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).10C2320,601
(C10×C4⋊C4).11C2 = C4⋊C4×Dic5φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).11C2320,602
(C10×C4⋊C4).12C2 = C20⋊5(C4⋊C4)φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).12C2320,603
(C10×C4⋊C4).13C2 = C20.48(C4⋊C4)φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).13C2320,604
(C10×C4⋊C4).14C2 = C4⋊C4⋊5Dic5φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).14C2320,608
(C10×C4⋊C4).15C2 = C20⋊6(C4⋊C4)φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).15C2320,612
(C10×C4⋊C4).16C2 = C2×Dic5⋊3Q8φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).16C2320,1168
(C10×C4⋊C4).17C2 = C2×C20⋊Q8φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).17C2320,1169
(C10×C4⋊C4).18C2 = C2×Dic5.Q8φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).18C2320,1170
(C10×C4⋊C4).19C2 = C2×C4.Dic10φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).19C2320,1171
(C10×C4⋊C4).20C2 = C10.12- 1+4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4).20C2320,1172
(C10×C4⋊C4).21C2 = (C2×C4)⋊Dic10φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).21C2320,606
(C10×C4⋊C4).22C2 = (C2×C20).53D4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).22C2320,610
(C10×C4⋊C4).23C2 = (C2×C20).54D4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).23C2320,611
(C10×C4⋊C4).24C2 = (C2×C20).55D4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).24C2320,613
(C10×C4⋊C4).25C2 = (C2×C20)⋊C8φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4).25C2320,86
(C10×C4⋊C4).26C2 = C10.96(C4×D4)φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).26C2320,599
(C10×C4⋊C4).27C2 = C10.97(C4×D4)φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).27C2320,605
(C10×C4⋊C4).28C2 = C5×C22.M4(2)φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4).28C2320,129
(C10×C4⋊C4).29C2 = C5×C22.4Q16φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).29C2320,145
(C10×C4⋊C4).30C2 = C5×C22.C42φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4).30C2320,148
(C10×C4⋊C4).31C2 = (C2×C20).287D4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).31C2320,607
(C10×C4⋊C4).32C2 = (C2×C20).288D4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).32C2320,609
(C10×C4⋊C4).33C2 = C5×C42⋊8C4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).33C2320,883
(C10×C4⋊C4).34C2 = C5×C42⋊9C4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).34C2320,885
(C10×C4⋊C4).35C2 = C5×C23.63C23φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).35C2320,888
(C10×C4⋊C4).36C2 = C5×C23.65C23φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).36C2320,890
(C10×C4⋊C4).37C2 = C5×C23.67C23φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).37C2320,892
(C10×C4⋊C4).38C2 = C5×C23.78C23φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).38C2320,896
(C10×C4⋊C4).39C2 = C5×C23.81C23φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).39C2320,899
(C10×C4⋊C4).40C2 = C5×C23.83C23φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).40C2320,901
(C10×C4⋊C4).41C2 = C10×Q8⋊C4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).41C2320,916
(C10×C4⋊C4).42C2 = C10×C4.Q8φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).42C2320,926
(C10×C4⋊C4).43C2 = C10×C2.D8φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).43C2320,927
(C10×C4⋊C4).44C2 = C5×M4(2)⋊C4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4).44C2320,929
(C10×C4⋊C4).45C2 = C5×C23.47D4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4).45C2320,984
(C10×C4⋊C4).46C2 = C5×C23.48D4φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4).46C2320,985
(C10×C4⋊C4).47C2 = C10×C42.C2φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).47C2320,1529
(C10×C4⋊C4).48C2 = C10×C4⋊Q8φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4320(C10xC4:C4).48C2320,1533
(C10×C4⋊C4).49C2 = C5×C23.41C23φ: C2/C1 → C2 ⊆ Out C10×C4⋊C4160(C10xC4:C4).49C2320,1546
(C10×C4⋊C4).50C2 = C4⋊C4×C20φ: trivial image320(C10xC4:C4).50C2320,879
(C10×C4⋊C4).51C2 = Q8×C2×C20φ: trivial image320(C10xC4:C4).51C2320,1518

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