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Extensions 1→N→G→Q→1 with N=C4×C5⋊D4 and Q=C2

Direct product G=N×Q with N=C4×C5⋊D4 and Q=C2
dρLabelID
C2×C4×C5⋊D4160C2xC4xC5:D4320,1460

Semidirect products G=N:Q with N=C4×C5⋊D4 and Q=C2
extensionφ:Q→Out NdρLabelID
(C4×C5⋊D4)⋊1C2 = C24.27D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):1C2320,1162
(C4×C5⋊D4)⋊2C2 = C24.31D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):2C2320,1167
(C4×C5⋊D4)⋊3C2 = C42.102D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):3C2320,1210
(C4×C5⋊D4)⋊4C2 = C42.228D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):4C2320,1220
(C4×C5⋊D4)⋊5C2 = C42.229D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):5C2320,1229
(C4×C5⋊D4)⋊6C2 = C10.612+ 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):6C2320,1329
(C4×C5⋊D4)⋊7C2 = C10.632+ 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):7C2320,1332
(C4×C5⋊D4)⋊8C2 = C10.842- 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):8C2320,1334
(C4×C5⋊D4)⋊9C2 = C10.662+ 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):9C2320,1335
(C4×C5⋊D4)⋊10C2 = C10.2- 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):10C2320,1179
(C4×C5⋊D4)⋊11C2 = C10.112+ 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):11C2320,1186
(C4×C5⋊D4)⋊12C2 = C42.95D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):12C2320,1202
(C4×C5⋊D4)⋊13C2 = C42.97D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):13C2320,1204
(C4×C5⋊D4)⋊14C2 = Dic10⋊19D4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):14C2320,1270
(C4×C5⋊D4)⋊15C2 = Dic10⋊20D4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):15C2320,1271
(C4×C5⋊D4)⋊16C2 = D20⋊19D4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):16C2320,1281
(C4×C5⋊D4)⋊17C2 = C10.732- 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):17C2320,1283
(C4×C5⋊D4)⋊18C2 = D20⋊20D4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):18C2320,1284
(C4×C5⋊D4)⋊19C2 = C10.432+ 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):19C2320,1286
(C4×C5⋊D4)⋊20C2 = C10.452+ 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):20C2320,1288
(C4×C5⋊D4)⋊21C2 = C10.1152+ 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):21C2320,1290
(C4×C5⋊D4)⋊22C2 = D20⋊21D4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):22C2320,1302
(C4×C5⋊D4)⋊23C2 = D20⋊22D4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):23C2320,1303
(C4×C5⋊D4)⋊24C2 = Dic10⋊22D4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):24C2320,1305
(C4×C5⋊D4)⋊25C2 = D4×C5⋊D4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):25C2320,1473
(C4×C5⋊D4)⋊26C2 = C24.42D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):26C2320,1478
(C4×C5⋊D4)⋊27C2 = C10.452- 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):27C2320,1489
(C4×C5⋊D4)⋊28C2 = C10.1042- 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):28C2320,1496
(C4×C5⋊D4)⋊29C2 = C10.1452+ 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):29C2320,1501
(C4×C5⋊D4)⋊30C2 = C10.1072- 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):30C2320,1503
(C4×C5⋊D4)⋊31C2 = C10.1482+ 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):31C2320,1506
(C4×C5⋊D4)⋊32C2 = C42.277D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):32C2320,1151
(C4×C5⋊D4)⋊33C2 = C24.24D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):33C2320,1158
(C4×C5⋊D4)⋊34C2 = C24.30D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):34C2320,1166
(C4×C5⋊D4)⋊35C2 = C10.82+ 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):35C2320,1176
(C4×C5⋊D4)⋊36C2 = C10.62- 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):36C2320,1187
(C4×C5⋊D4)⋊37C2 = C4×D4⋊2D5φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):37C2320,1208
(C4×C5⋊D4)⋊38C2 = C42.104D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):38C2320,1212
(C4×C5⋊D4)⋊39C2 = C4×D4×D5φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):39C2320,1216
(C4×C5⋊D4)⋊40C2 = C42⋊11D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):40C2320,1217
(C4×C5⋊D4)⋊41C2 = C42.108D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):41C2320,1218
(C4×C5⋊D4)⋊42C2 = C42⋊12D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):42C2320,1219
(C4×C5⋊D4)⋊43C2 = C42⋊16D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):43C2320,1228
(C4×C5⋊D4)⋊44C2 = C42.113D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):44C2320,1230
(C4×C5⋊D4)⋊45C2 = C42.114D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):45C2320,1231
(C4×C5⋊D4)⋊46C2 = C42⋊17D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):46C2320,1232
(C4×C5⋊D4)⋊47C2 = C42.118D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):47C2320,1236
(C4×C5⋊D4)⋊48C2 = C10.622+ 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):48C2320,1331
(C4×C5⋊D4)⋊49C2 = C10.642+ 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):49C2320,1333
(C4×C5⋊D4)⋊50C2 = C10.672+ 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):50C2320,1336
(C4×C5⋊D4)⋊51C2 = C24.72D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):51C2320,1463
(C4×C5⋊D4)⋊52C2 = C42.93D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):52C2320,1200
(C4×C5⋊D4)⋊53C2 = C10.342+ 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):53C2320,1273
(C4×C5⋊D4)⋊54C2 = C10.402+ 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):54C2320,1282
(C4×C5⋊D4)⋊55C2 = C10.422+ 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):55C2320,1285
(C4×C5⋊D4)⋊56C2 = C10.442+ 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):56C2320,1287
(C4×C5⋊D4)⋊57C2 = C10.532+ 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):57C2320,1309
(C4×C5⋊D4)⋊58C2 = C10.202- 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):58C2320,1310
(C4×C5⋊D4)⋊59C2 = C10.222- 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):59C2320,1312
(C4×C5⋊D4)⋊60C2 = (C2×C20)⋊15D4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D480(C4xC5:D4):60C2320,1500
(C4×C5⋊D4)⋊61C2 = (C2×C20)⋊17D4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4):61C2320,1504
(C4×C5⋊D4)⋊62C2 = C4×C4○D20φ: trivial image160(C4xC5:D4):62C2320,1146

Non-split extensions G=N.Q with N=C4×C5⋊D4 and Q=C2
extensionφ:Q→Out NdρLabelID
(C4×C5⋊D4).1C2 = D10⋊4M4(2)φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4).1C2320,355
(C4×C5⋊D4).2C2 = Dic5⋊2M4(2)φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4).2C2320,356
(C4×C5⋊D4).3C2 = C10.102+ 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4).3C2320,1183
(C4×C5⋊D4).4C2 = C10.52- 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4).4C2320,1185
(C4×C5⋊D4).5C2 = C42.94D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4).5C2320,1201
(C4×C5⋊D4).6C2 = C42.98D10φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4).6C2320,1205
(C4×C5⋊D4).7C2 = Dic10⋊21D4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4).7C2320,1304
(C4×C5⋊D4).8C2 = C10.1182+ 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4).8C2320,1307
(C4×C5⋊D4).9C2 = C10.212- 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4).9C2320,1311
(C4×C5⋊D4).10C2 = C10.232- 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4).10C2320,1313
(C4×C5⋊D4).11C2 = C10.772- 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4).11C2320,1314
(C4×C5⋊D4).12C2 = Q8×C5⋊D4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4).12C2320,1487
(C4×C5⋊D4).13C2 = C5⋊5(C8×D4)φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4).13C2320,352
(C4×C5⋊D4).14C2 = C5⋊2C8⋊26D4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4).14C2320,357
(C4×C5⋊D4).15C2 = C40⋊32D4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4).15C2320,738
(C4×C5⋊D4).16C2 = C40⋊D4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4).16C2320,754
(C4×C5⋊D4).17C2 = C40⋊18D4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4).17C2320,755
(C4×C5⋊D4).18C2 = C10.522+ 1+4φ: C2/C1 → C2 ⊆ Out C4×C5⋊D4160(C4xC5:D4).18C2320,1308
(C4×C5⋊D4).19C2 = C8×C5⋊D4φ: trivial image160(C4xC5:D4).19C2320,736

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