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Extensions 1→N→G→Q→1 with N=C4×D5 and Q=C2×C4

Direct product G=N×Q with N=C4×D5 and Q=C2×C4
dρLabelID
D5×C2×C42160D5xC2xC4^2320,1143

Semidirect products G=N:Q with N=C4×D5 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
(C4×D5)⋊1(C2×C4) = C10.82+ 1+4φ: C2×C4/C2 → C22 ⊆ Out C4×D5160(C4xD5):1(C2xC4)320,1176
(C4×D5)⋊2(C2×C4) = C42.91D10φ: C2×C4/C2 → C22 ⊆ Out C4×D5160(C4xD5):2(C2xC4)320,1195
(C4×D5)⋊3(C2×C4) = C42⋊11D10φ: C2×C4/C2 → C22 ⊆ Out C4×D580(C4xD5):3(C2xC4)320,1217
(C4×D5)⋊4(C2×C4) = C42.108D10φ: C2×C4/C2 → C22 ⊆ Out C4×D5160(C4xD5):4(C2xC4)320,1218
(C4×D5)⋊5(C2×C4) = C42.126D10φ: C2×C4/C2 → C22 ⊆ Out C4×D5160(C4xD5):5(C2xC4)320,1246
(C4×D5)⋊6(C2×C4) = C2×D4×F5φ: C2×C4/C2 → C22 ⊆ Out C4×D540(C4xD5):6(C2xC4)320,1595
(C4×D5)⋊7(C2×C4) = D10.C24φ: C2×C4/C2 → C22 ⊆ Out C4×D5408+(C4xD5):7(C2xC4)320,1596
(C4×D5)⋊8(C2×C4) = D5.2+ 1+4φ: C2×C4/C2 → C22 ⊆ Out C4×D5408(C4xD5):8(C2xC4)320,1604
(C4×D5)⋊9(C2×C4) = C4○D4×F5φ: C2×C4/C2 → C22 ⊆ Out C4×D5408(C4xD5):9(C2xC4)320,1603
(C4×D5)⋊10(C2×C4) = C4×D4⋊2D5φ: C2×C4/C4 → C2 ⊆ Out C4×D5160(C4xD5):10(C2xC4)320,1208
(C4×D5)⋊11(C2×C4) = C4×D4×D5φ: C2×C4/C4 → C2 ⊆ Out C4×D580(C4xD5):11(C2xC4)320,1216
(C4×D5)⋊12(C2×C4) = C4×Q8⋊2D5φ: C2×C4/C4 → C2 ⊆ Out C4×D5160(C4xD5):12(C2xC4)320,1245
(C4×D5)⋊13(C2×C4) = C4×C4○D20φ: C2×C4/C4 → C2 ⊆ Out C4×D5160(C4xD5):13(C2xC4)320,1146
(C4×D5)⋊14(C2×C4) = C42.188D10φ: C2×C4/C4 → C2 ⊆ Out C4×D5160(C4xD5):14(C2xC4)320,1194
(C4×D5)⋊15(C2×C4) = C2×D5×C4⋊C4φ: C2×C4/C22 → C2 ⊆ Out C4×D5160(C4xD5):15(C2xC4)320,1173
(C4×D5)⋊16(C2×C4) = C2×C4⋊C4⋊7D5φ: C2×C4/C22 → C2 ⊆ Out C4×D5160(C4xD5):16(C2xC4)320,1174
(C4×D5)⋊17(C2×C4) = C2×C42⋊D5φ: C2×C4/C22 → C2 ⊆ Out C4×D5160(C4xD5):17(C2xC4)320,1144
(C4×D5)⋊18(C2×C4) = D5×C42⋊C2φ: C2×C4/C22 → C2 ⊆ Out C4×D580(C4xD5):18(C2xC4)320,1192
(C4×D5)⋊19(C2×C4) = C22×C4⋊F5φ: C2×C4/C22 → C2 ⊆ Out C4×D580(C4xD5):19(C2xC4)320,1591
(C4×D5)⋊20(C2×C4) = C2×D10.C23φ: C2×C4/C22 → C2 ⊆ Out C4×D580(C4xD5):20(C2xC4)320,1592
(C4×D5)⋊21(C2×C4) = C22×C4×F5φ: C2×C4/C22 → C2 ⊆ Out C4×D580(C4xD5):21(C2xC4)320,1590

Non-split extensions G=N.Q with N=C4×D5 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
(C4×D5).1(C2×C4) = (D4×D5)⋊C4φ: C2×C4/C2 → C22 ⊆ Out C4×D580(C4xD5).1(C2xC4)320,397
(C4×D5).2(C2×C4) = D4⋊(C4×D5)φ: C2×C4/C2 → C22 ⊆ Out C4×D5160(C4xD5).2(C2xC4)320,398
(C4×D5).3(C2×C4) = (Q8×D5)⋊C4φ: C2×C4/C2 → C22 ⊆ Out C4×D5160(C4xD5).3(C2xC4)320,429
(C4×D5).4(C2×C4) = Q8⋊(C4×D5)φ: C2×C4/C2 → C22 ⊆ Out C4×D5160(C4xD5).4(C2xC4)320,430
(C4×D5).5(C2×C4) = C42⋊D10φ: C2×C4/C2 → C22 ⊆ Out C4×D5804(C4xD5).5(C2xC4)320,448
(C4×D5).6(C2×C4) = C8⋊(C4×D5)φ: C2×C4/C2 → C22 ⊆ Out C4×D5160(C4xD5).6(C2xC4)320,488
(C4×D5).7(C2×C4) = C40⋊20(C2×C4)φ: C2×C4/C2 → C22 ⊆ Out C4×D5160(C4xD5).7(C2xC4)320,508
(C4×D5).8(C2×C4) = M4(2).25D10φ: C2×C4/C2 → C22 ⊆ Out C4×D5804(C4xD5).8(C2xC4)320,520
(C4×D5).9(C2×C4) = C42.125D10φ: C2×C4/C2 → C22 ⊆ Out C4×D5160(C4xD5).9(C2xC4)320,1244
(C4×D5).10(C2×C4) = C40.47C23φ: C2×C4/C2 → C22 ⊆ Out C4×D5804(C4xD5).10(C2xC4)320,1417
(C4×D5).11(C2×C4) = C20.72C24φ: C2×C4/C2 → C22 ⊆ Out C4×D5804(C4xD5).11(C2xC4)320,1422
(C4×D5).12(C2×C4) = D10.18D8φ: C2×C4/C2 → C22 ⊆ Out C4×D580(C4xD5).12(C2xC4)320,212
(C4×D5).13(C2×C4) = C20.C42φ: C2×C4/C2 → C22 ⊆ Out C4×D580(C4xD5).13(C2xC4)320,213
(C4×D5).14(C2×C4) = M4(2)⋊3F5φ: C2×C4/C2 → C22 ⊆ Out C4×D5408(C4xD5).14(C2xC4)320,238
(C4×D5).15(C2×C4) = M4(2).F5φ: C2×C4/C2 → C22 ⊆ Out C4×D5808(C4xD5).15(C2xC4)320,239
(C4×D5).16(C2×C4) = D10.C42φ: C2×C4/C2 → C22 ⊆ Out C4×D5160(C4xD5).16(C2xC4)320,1039
(C4×D5).17(C2×C4) = C4⋊C4×F5φ: C2×C4/C2 → C22 ⊆ Out C4×D580(C4xD5).17(C2xC4)320,1048
(C4×D5).18(C2×C4) = M4(2)⋊5F5φ: C2×C4/C2 → C22 ⊆ Out C4×D5808(C4xD5).18(C2xC4)320,1066
(C4×D5).19(C2×C4) = C2×D20⋊C4φ: C2×C4/C2 → C22 ⊆ Out C4×D580(C4xD5).19(C2xC4)320,1104
(C4×D5).20(C2×C4) = (D4×C10)⋊C4φ: C2×C4/C2 → C22 ⊆ Out C4×D5408+(C4xD5).20(C2xC4)320,1105
(C4×D5).21(C2×C4) = C2×D4⋊F5φ: C2×C4/C2 → C22 ⊆ Out C4×D580(C4xD5).21(C2xC4)320,1106
(C4×D5).22(C2×C4) = (C2×D4)⋊6F5φ: C2×C4/C2 → C22 ⊆ Out C4×D5808-(C4xD5).22(C2xC4)320,1107
(C4×D5).23(C2×C4) = C2×Q8⋊F5φ: C2×C4/C2 → C22 ⊆ Out C4×D580(C4xD5).23(C2xC4)320,1119
(C4×D5).24(C2×C4) = (C2×Q8)⋊4F5φ: C2×C4/C2 → C22 ⊆ Out C4×D5808-(C4xD5).24(C2xC4)320,1120
(C4×D5).25(C2×C4) = C2×Q8⋊2F5φ: C2×C4/C2 → C22 ⊆ Out C4×D580(C4xD5).25(C2xC4)320,1121
(C4×D5).26(C2×C4) = (C2×Q8)⋊6F5φ: C2×C4/C2 → C22 ⊆ Out C4×D5808+(C4xD5).26(C2xC4)320,1122
(C4×D5).27(C2×C4) = D5⋊C4≀C2φ: C2×C4/C2 → C22 ⊆ Out C4×D5408(C4xD5).27(C2xC4)320,1130
(C4×D5).28(C2×C4) = C4○D4⋊F5φ: C2×C4/C2 → C22 ⊆ Out C4×D5408(C4xD5).28(C2xC4)320,1131
(C4×D5).29(C2×C4) = C4○D20⋊C4φ: C2×C4/C2 → C22 ⊆ Out C4×D5808(C4xD5).29(C2xC4)320,1132
(C4×D5).30(C2×C4) = D4⋊F5⋊C2φ: C2×C4/C2 → C22 ⊆ Out C4×D5808(C4xD5).30(C2xC4)320,1133
(C4×D5).31(C2×C4) = C2×D4.F5φ: C2×C4/C2 → C22 ⊆ Out C4×D5160(C4xD5).31(C2xC4)320,1593
(C4×D5).32(C2×C4) = Dic5.C24φ: C2×C4/C2 → C22 ⊆ Out C4×D5808-(C4xD5).32(C2xC4)320,1594
(C4×D5).33(C2×C4) = C2×Q8.F5φ: C2×C4/C2 → C22 ⊆ Out C4×D5160(C4xD5).33(C2xC4)320,1597
(C4×D5).34(C2×C4) = Dic5.20C24φ: C2×C4/C2 → C22 ⊆ Out C4×D5808+(C4xD5).34(C2xC4)320,1598
(C4×D5).35(C2×C4) = C2×Q8×F5φ: C2×C4/C2 → C22 ⊆ Out C4×D580(C4xD5).35(C2xC4)320,1599
(C4×D5).36(C2×C4) = D5.2- 1+4φ: C2×C4/C2 → C22 ⊆ Out C4×D5808-(C4xD5).36(C2xC4)320,1600
(C4×D5).37(C2×C4) = M4(2)⋊1F5φ: C2×C4/C2 → C22 ⊆ Out C4×D5408(C4xD5).37(C2xC4)320,1065
(C4×D5).38(C2×C4) = M4(2).1F5φ: C2×C4/C2 → C22 ⊆ Out C4×D5808(C4xD5).38(C2xC4)320,1067
(C4×D5).39(C2×C4) = Dic5.22C24φ: C2×C4/C2 → C22 ⊆ Out C4×D5808(C4xD5).39(C2xC4)320,1602
(C4×D5).40(C2×C4) = C16⋊F5φ: C2×C4/C2 → C22 ⊆ Out C4×D5804(C4xD5).40(C2xC4)320,183
(C4×D5).41(C2×C4) = C16⋊4F5φ: C2×C4/C2 → C22 ⊆ Out C4×D5804(C4xD5).41(C2xC4)320,184
(C4×D5).42(C2×C4) = C42⋊3F5φ: C2×C4/C2 → C22 ⊆ Out C4×D5804(C4xD5).42(C2xC4)320,201
(C4×D5).43(C2×C4) = C20.24C42φ: C2×C4/C2 → C22 ⊆ Out C4×D5804(C4xD5).43(C2xC4)320,233
(C4×D5).44(C2×C4) = C20.25C42φ: C2×C4/C2 → C22 ⊆ Out C4×D5804(C4xD5).44(C2xC4)320,235
(C4×D5).45(C2×C4) = Dic10.C8φ: C2×C4/C2 → C22 ⊆ Out C4×D51608(C4xD5).45(C2xC4)320,1063
(C4×D5).46(C2×C4) = M4(2)×F5φ: C2×C4/C2 → C22 ⊆ Out C4×D5408(C4xD5).46(C2xC4)320,1064
(C4×D5).47(C2×C4) = Dic5.21C24φ: C2×C4/C2 → C22 ⊆ Out C4×D5808(C4xD5).47(C2xC4)320,1601
(C4×D5).48(C2×C4) = D5×D4⋊C4φ: C2×C4/C4 → C2 ⊆ Out C4×D580(C4xD5).48(C2xC4)320,396
(C4×D5).49(C2×C4) = D4⋊2D5⋊C4φ: C2×C4/C4 → C2 ⊆ Out C4×D5160(C4xD5).49(C2xC4)320,399
(C4×D5).50(C2×C4) = D5×Q8⋊C4φ: C2×C4/C4 → C2 ⊆ Out C4×D5160(C4xD5).50(C2xC4)320,428
(C4×D5).51(C2×C4) = Q8⋊2D5⋊C4φ: C2×C4/C4 → C2 ⊆ Out C4×D5160(C4xD5).51(C2xC4)320,431
(C4×D5).52(C2×C4) = D5×C4≀C2φ: C2×C4/C4 → C2 ⊆ Out C4×D5404(C4xD5).52(C2xC4)320,447
(C4×D5).53(C2×C4) = C4×Q8×D5φ: C2×C4/C4 → C2 ⊆ Out C4×D5160(C4xD5).53(C2xC4)320,1243
(C4×D5).54(C2×C4) = D5×C8○D4φ: C2×C4/C4 → C2 ⊆ Out C4×D5804(C4xD5).54(C2xC4)320,1421
(C4×D5).55(C2×C4) = C4×C8⋊D5φ: C2×C4/C4 → C2 ⊆ Out C4×D5160(C4xD5).55(C2xC4)320,314
(C4×D5).56(C2×C4) = D10.6C42φ: C2×C4/C4 → C2 ⊆ Out C4×D5160(C4xD5).56(C2xC4)320,334
(C4×D5).57(C2×C4) = D20.6C8φ: C2×C4/C4 → C2 ⊆ Out C4×D51602(C4xD5).57(C2xC4)320,528
(C4×D5).58(C2×C4) = D20.5C8φ: C2×C4/C4 → C2 ⊆ Out C4×D51604(C4xD5).58(C2xC4)320,534
(C4×D5).59(C2×C4) = C2×D20.3C4φ: C2×C4/C4 → C2 ⊆ Out C4×D5160(C4xD5).59(C2xC4)320,1410
(C4×D5).60(C2×C4) = C2×D20.2C4φ: C2×C4/C4 → C2 ⊆ Out C4×D5160(C4xD5).60(C2xC4)320,1416
(C4×D5).61(C2×C4) = C42⋊6F5φ: C2×C4/C4 → C2 ⊆ Out C4×D5404(C4xD5).61(C2xC4)320,200
(C4×D5).62(C2×C4) = D10.10D8φ: C2×C4/C4 → C2 ⊆ Out C4×D580(C4xD5).62(C2xC4)320,231
(C4×D5).63(C2×C4) = C20.10C42φ: C2×C4/C4 → C2 ⊆ Out C4×D5160(C4xD5).63(C2xC4)320,234
(C4×D5).64(C2×C4) = C4×C4.F5φ: C2×C4/C4 → C2 ⊆ Out C4×D5160(C4xD5).64(C2xC4)320,1015
(C4×D5).65(C2×C4) = C4×C4⋊F5φ: C2×C4/C4 → C2 ⊆ Out C4×D580(C4xD5).65(C2xC4)320,1025
(C4×D5).66(C2×C4) = C20.12C42φ: C2×C4/C4 → C2 ⊆ Out C4×D5804(C4xD5).66(C2xC4)320,1056
(C4×D5).67(C2×C4) = C16×F5φ: C2×C4/C4 → C2 ⊆ Out C4×D5804(C4xD5).67(C2xC4)320,181
(C4×D5).68(C2×C4) = C16⋊7F5φ: C2×C4/C4 → C2 ⊆ Out C4×D5804(C4xD5).68(C2xC4)320,182
(C4×D5).69(C2×C4) = C4×D5⋊C8φ: C2×C4/C4 → C2 ⊆ Out C4×D5160(C4xD5).69(C2xC4)320,1013
(C4×D5).70(C2×C4) = C42.5F5φ: C2×C4/C4 → C2 ⊆ Out C4×D5160(C4xD5).70(C2xC4)320,1014
(C4×D5).71(C2×C4) = C42×F5φ: C2×C4/C4 → C2 ⊆ Out C4×D580(C4xD5).71(C2xC4)320,1023
(C4×D5).72(C2×C4) = C42⋊4F5φ: C2×C4/C4 → C2 ⊆ Out C4×D580(C4xD5).72(C2xC4)320,1024
(C4×D5).73(C2×C4) = D5×C4.Q8φ: C2×C4/C22 → C2 ⊆ Out C4×D5160(C4xD5).73(C2xC4)320,486
(C4×D5).74(C2×C4) = (C8×D5)⋊C4φ: C2×C4/C22 → C2 ⊆ Out C4×D5160(C4xD5).74(C2xC4)320,487
(C4×D5).75(C2×C4) = D5×C2.D8φ: C2×C4/C22 → C2 ⊆ Out C4×D5160(C4xD5).75(C2xC4)320,506
(C4×D5).76(C2×C4) = C8.27(C4×D5)φ: C2×C4/C22 → C2 ⊆ Out C4×D5160(C4xD5).76(C2xC4)320,507
(C4×D5).77(C2×C4) = D5×C8.C4φ: C2×C4/C22 → C2 ⊆ Out C4×D5804(C4xD5).77(C2xC4)320,519
(C4×D5).78(C2×C4) = C2×D5×M4(2)φ: C2×C4/C22 → C2 ⊆ Out C4×D580(C4xD5).78(C2xC4)320,1415
(C4×D5).79(C2×C4) = D10.5C42φ: C2×C4/C22 → C2 ⊆ Out C4×D5160(C4xD5).79(C2xC4)320,316
(C4×D5).80(C2×C4) = D10.7C42φ: C2×C4/C22 → C2 ⊆ Out C4×D5160(C4xD5).80(C2xC4)320,335
(C4×D5).81(C2×C4) = C2×C80⋊C2φ: C2×C4/C22 → C2 ⊆ Out C4×D5160(C4xD5).81(C2xC4)320,527
(C4×D5).82(C2×C4) = D5×M5(2)φ: C2×C4/C22 → C2 ⊆ Out C4×D5804(C4xD5).82(C2xC4)320,533
(C4×D5).83(C2×C4) = C22×C8⋊D5φ: C2×C4/C22 → C2 ⊆ Out C4×D5160(C4xD5).83(C2xC4)320,1409
(C4×D5).84(C2×C4) = C2×C40⋊C4φ: C2×C4/C22 → C2 ⊆ Out C4×D580(C4xD5).84(C2xC4)320,1057
(C4×D5).85(C2×C4) = C2×D5.D8φ: C2×C4/C22 → C2 ⊆ Out C4×D580(C4xD5).85(C2xC4)320,1058
(C4×D5).86(C2×C4) = (C2×C8)⋊6F5φ: C2×C4/C22 → C2 ⊆ Out C4×D5804(C4xD5).86(C2xC4)320,1059
(C4×D5).87(C2×C4) = C2×C40.C4φ: C2×C4/C22 → C2 ⊆ Out C4×D5160(C4xD5).87(C2xC4)320,1060
(C4×D5).88(C2×C4) = C2×D10.Q8φ: C2×C4/C22 → C2 ⊆ Out C4×D5160(C4xD5).88(C2xC4)320,1061
(C4×D5).89(C2×C4) = (C8×D5).C4φ: C2×C4/C22 → C2 ⊆ Out C4×D5804(C4xD5).89(C2xC4)320,1062
(C4×D5).90(C2×C4) = C22×C4.F5φ: C2×C4/C22 → C2 ⊆ Out C4×D5160(C4xD5).90(C2xC4)320,1588
(C4×D5).91(C2×C4) = C2×D5⋊C16φ: C2×C4/C22 → C2 ⊆ Out C4×D5160(C4xD5).91(C2xC4)320,1051
(C4×D5).92(C2×C4) = C2×C8.F5φ: C2×C4/C22 → C2 ⊆ Out C4×D5160(C4xD5).92(C2xC4)320,1052
(C4×D5).93(C2×C4) = D5⋊M5(2)φ: C2×C4/C22 → C2 ⊆ Out C4×D5804(C4xD5).93(C2xC4)320,1053
(C4×D5).94(C2×C4) = C2×C8×F5φ: C2×C4/C22 → C2 ⊆ Out C4×D580(C4xD5).94(C2xC4)320,1054
(C4×D5).95(C2×C4) = C2×C8⋊F5φ: C2×C4/C22 → C2 ⊆ Out C4×D580(C4xD5).95(C2xC4)320,1055
(C4×D5).96(C2×C4) = C22×D5⋊C8φ: C2×C4/C22 → C2 ⊆ Out C4×D5160(C4xD5).96(C2xC4)320,1587
(C4×D5).97(C2×C4) = C2×D5⋊M4(2)φ: C2×C4/C22 → C2 ⊆ Out C4×D580(C4xD5).97(C2xC4)320,1589
(C4×D5).98(C2×C4) = D5×C4×C8φ: trivial image160(C4xD5).98(C2xC4)320,311
(C4×D5).99(C2×C4) = D5×C8⋊C4φ: trivial image160(C4xD5).99(C2xC4)320,331
(C4×D5).100(C2×C4) = D5×C2×C16φ: trivial image160(C4xD5).100(C2xC4)320,526
(C4×D5).101(C2×C4) = D5×C22×C8φ: trivial image160(C4xD5).101(C2xC4)320,1408

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