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Extensions 1→N→G→Q→1 with N=C22 and Q=C2×C4×D5

Direct product G=N×Q with N=C22 and Q=C2×C4×D5
dρLabelID
D5×C23×C4160D5xC2^3xC4320,1609

Semidirect products G=N:Q with N=C22 and Q=C2×C4×D5
extensionφ:Q→Aut NdρLabelID
C22⋊1(C2×C4×D5) = C4×D4×D5φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C2280C2^2:1(C2xC4xD5)320,1216
C22⋊2(C2×C4×D5) = C2×Dic5⋊4D4φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C22160C2^2:2(C2xC4xD5)320,1157
C22⋊3(C2×C4×D5) = C2×C4×C5⋊D4φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C22160C2^2:3(C2xC4xD5)320,1460
C22⋊4(C2×C4×D5) = C2×D5×C22⋊C4φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C2280C2^2:4(C2xC4xD5)320,1156

Non-split extensions G=N.Q with N=C22 and Q=C2×C4×D5
extensionφ:Q→Aut NdρLabelID
C22.1(C2×C4×D5) = C4×D4⋊2D5φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C22160C2^2.1(C2xC4xD5)320,1208
C22.2(C2×C4×D5) = C42⋊11D10φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C2280C2^2.2(C2xC4xD5)320,1217
C22.3(C2×C4×D5) = C42.108D10φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C22160C2^2.3(C2xC4xD5)320,1218
C22.4(C2×C4×D5) = D5×C8○D4φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C22804C2^2.4(C2xC4xD5)320,1421
C22.5(C2×C4×D5) = C20.72C24φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C22804C2^2.5(C2xC4xD5)320,1422
C22.6(C2×C4×D5) = C42.188D10φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C22160C2^2.6(C2xC4xD5)320,1194
C22.7(C2×C4×D5) = C42.91D10φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C22160C2^2.7(C2xC4xD5)320,1195
C22.8(C2×C4×D5) = C2×D20.2C4φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C22160C2^2.8(C2xC4xD5)320,1416
C22.9(C2×C4×D5) = C4×C4○D20φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C22160C2^2.9(C2xC4xD5)320,1146
C22.10(C2×C4×D5) = C10.82+ 1+4φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C22160C2^2.10(C2xC4xD5)320,1176
C22.11(C2×C4×D5) = C2×D20.3C4φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C22160C2^2.11(C2xC4xD5)320,1410
C22.12(C2×C4×D5) = C23⋊C4⋊5D5φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C22808-C2^2.12(C2xC4xD5)320,367
C22.13(C2×C4×D5) = D5×C23⋊C4φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C22408+C2^2.13(C2xC4xD5)320,370
C22.14(C2×C4×D5) = D5×C4.D4φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C22408+C2^2.14(C2xC4xD5)320,371
C22.15(C2×C4×D5) = M4(2).19D10φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C22808-C2^2.15(C2xC4xD5)320,372
C22.16(C2×C4×D5) = D5×C4.10D4φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C22808-C2^2.16(C2xC4xD5)320,377
C22.17(C2×C4×D5) = M4(2).21D10φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C22808+C2^2.17(C2xC4xD5)320,378
C22.18(C2×C4×D5) = C2×C23.1D10φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C2280C2^2.18(C2xC4xD5)320,581
C22.19(C2×C4×D5) = (C2×D20)⋊25C4φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C22804C2^2.19(C2xC4xD5)320,633
C22.20(C2×C4×D5) = C2×C20.46D4φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C2280C2^2.20(C2xC4xD5)320,757
C22.21(C2×C4×D5) = M4(2).31D10φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C22804C2^2.21(C2xC4xD5)320,759
C22.22(C2×C4×D5) = C2×C4.12D20φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C22160C2^2.22(C2xC4xD5)320,763
C22.23(C2×C4×D5) = C2×C23.11D10φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C22160C2^2.23(C2xC4xD5)320,1152
C22.24(C2×C4×D5) = C24.24D10φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C2280C2^2.24(C2xC4xD5)320,1158
C22.25(C2×C4×D5) = C42.87D10φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C22160C2^2.25(C2xC4xD5)320,1188
C22.26(C2×C4×D5) = D5×C42⋊C2φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C2280C2^2.26(C2xC4xD5)320,1192
C22.27(C2×C4×D5) = C42⋊7D10φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C2280C2^2.27(C2xC4xD5)320,1193
C22.28(C2×C4×D5) = C40.47C23φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C22804C2^2.28(C2xC4xD5)320,1417
C22.29(C2×C4×D5) = Dic5.15C42central extension (φ=1)320C2^2.29(C2xC4xD5)320,275
C22.30(C2×C4×D5) = Dic5⋊2C42central extension (φ=1)320C2^2.30(C2xC4xD5)320,276
C22.31(C2×C4×D5) = D5×C2.C42central extension (φ=1)160C2^2.31(C2xC4xD5)320,290
C22.32(C2×C4×D5) = D10⋊2C42central extension (φ=1)160C2^2.32(C2xC4xD5)320,293
C22.33(C2×C4×D5) = C8×Dic10central extension (φ=1)320C2^2.33(C2xC4xD5)320,305
C22.34(C2×C4×D5) = D5×C4×C8central extension (φ=1)160C2^2.34(C2xC4xD5)320,311
C22.35(C2×C4×D5) = C42.282D10central extension (φ=1)160C2^2.35(C2xC4xD5)320,312
C22.36(C2×C4×D5) = C8×D20central extension (φ=1)160C2^2.36(C2xC4xD5)320,313
C22.37(C2×C4×D5) = C4×C8⋊D5central extension (φ=1)160C2^2.37(C2xC4xD5)320,314
C22.38(C2×C4×D5) = D10.5C42central extension (φ=1)160C2^2.38(C2xC4xD5)320,316
C22.39(C2×C4×D5) = D5×C8⋊C4central extension (φ=1)160C2^2.39(C2xC4xD5)320,331
C22.40(C2×C4×D5) = D10.6C42central extension (φ=1)160C2^2.40(C2xC4xD5)320,334
C22.41(C2×C4×D5) = D10.7C42central extension (φ=1)160C2^2.41(C2xC4xD5)320,335
C22.42(C2×C4×D5) = Dic5.14M4(2)central extension (φ=1)160C2^2.42(C2xC4xD5)320,345
C22.43(C2×C4×D5) = D5×C22⋊C8central extension (φ=1)80C2^2.43(C2xC4xD5)320,351
C22.44(C2×C4×D5) = C5⋊5(C8×D4)central extension (φ=1)160C2^2.44(C2xC4xD5)320,352
C22.45(C2×C4×D5) = Dic10⋊5C8central extension (φ=1)320C2^2.45(C2xC4xD5)320,457
C22.46(C2×C4×D5) = D5×C4⋊C8central extension (φ=1)160C2^2.46(C2xC4xD5)320,459
C22.47(C2×C4×D5) = C42.200D10central extension (φ=1)160C2^2.47(C2xC4xD5)320,460
C22.48(C2×C4×D5) = D20⋊5C8central extension (φ=1)160C2^2.48(C2xC4xD5)320,461
C22.49(C2×C4×D5) = C42×Dic5central extension (φ=1)320C2^2.49(C2xC4xD5)320,557
C22.50(C2×C4×D5) = C4×C10.D4central extension (φ=1)320C2^2.50(C2xC4xD5)320,558
C22.51(C2×C4×D5) = C42⋊4Dic5central extension (φ=1)320C2^2.51(C2xC4xD5)320,559
C22.52(C2×C4×D5) = C4×C4⋊Dic5central extension (φ=1)320C2^2.52(C2xC4xD5)320,561
C22.53(C2×C4×D5) = C4×D10⋊C4central extension (φ=1)160C2^2.53(C2xC4xD5)320,565
C22.54(C2×C4×D5) = C22⋊C4×Dic5central extension (φ=1)160C2^2.54(C2xC4xD5)320,568
C22.55(C2×C4×D5) = C4⋊C4×Dic5central extension (φ=1)320C2^2.55(C2xC4xD5)320,602
C22.56(C2×C4×D5) = C2×C8×Dic5central extension (φ=1)320C2^2.56(C2xC4xD5)320,725
C22.57(C2×C4×D5) = C2×C20.8Q8central extension (φ=1)320C2^2.57(C2xC4xD5)320,726
C22.58(C2×C4×D5) = C2×C40⋊8C4central extension (φ=1)320C2^2.58(C2xC4xD5)320,727
C22.59(C2×C4×D5) = C20.42C42central extension (φ=1)160C2^2.59(C2xC4xD5)320,728
C22.60(C2×C4×D5) = C2×D10⋊1C8central extension (φ=1)160C2^2.60(C2xC4xD5)320,735
C22.61(C2×C4×D5) = C8×C5⋊D4central extension (φ=1)160C2^2.61(C2xC4xD5)320,736
C22.62(C2×C4×D5) = M4(2)×Dic5central extension (φ=1)160C2^2.62(C2xC4xD5)320,744
C22.63(C2×C4×D5) = C20.37C42central extension (φ=1)160C2^2.63(C2xC4xD5)320,749
C22.64(C2×C4×D5) = C2×C10.10C42central extension (φ=1)320C2^2.64(C2xC4xD5)320,835
C22.65(C2×C4×D5) = C4×C23.D5central extension (φ=1)160C2^2.65(C2xC4xD5)320,836
C22.66(C2×C4×D5) = C2×C4×Dic10central extension (φ=1)320C2^2.66(C2xC4xD5)320,1139
C22.67(C2×C4×D5) = D5×C2×C42central extension (φ=1)160C2^2.67(C2xC4xD5)320,1143
C22.68(C2×C4×D5) = C2×C42⋊D5central extension (φ=1)160C2^2.68(C2xC4xD5)320,1144
C22.69(C2×C4×D5) = C2×C4×D20central extension (φ=1)160C2^2.69(C2xC4xD5)320,1145
C22.70(C2×C4×D5) = C2×Dic5⋊3Q8central extension (φ=1)320C2^2.70(C2xC4xD5)320,1168
C22.71(C2×C4×D5) = C2×D5×C4⋊C4central extension (φ=1)160C2^2.71(C2xC4xD5)320,1173
C22.72(C2×C4×D5) = C2×C4⋊C4⋊7D5central extension (φ=1)160C2^2.72(C2xC4xD5)320,1174
C22.73(C2×C4×D5) = C2×D20⋊8C4central extension (φ=1)160C2^2.73(C2xC4xD5)320,1175
C22.74(C2×C4×D5) = D5×C22×C8central extension (φ=1)160C2^2.74(C2xC4xD5)320,1408
C22.75(C2×C4×D5) = C22×C8⋊D5central extension (φ=1)160C2^2.75(C2xC4xD5)320,1409
C22.76(C2×C4×D5) = C2×D5×M4(2)central extension (φ=1)80C2^2.76(C2xC4xD5)320,1415
C22.77(C2×C4×D5) = C22×C4×Dic5central extension (φ=1)320C2^2.77(C2xC4xD5)320,1454
C22.78(C2×C4×D5) = C22×C10.D4central extension (φ=1)320C2^2.78(C2xC4xD5)320,1455
C22.79(C2×C4×D5) = C22×D10⋊C4central extension (φ=1)160C2^2.79(C2xC4xD5)320,1459
C22.80(C2×C4×D5) = (C2×C20)⋊Q8central stem extension (φ=1)320C2^2.80(C2xC4xD5)320,273
C22.81(C2×C4×D5) = C10.49(C4×D4)central stem extension (φ=1)320C2^2.81(C2xC4xD5)320,274
C22.82(C2×C4×D5) = C5⋊2(C42⋊8C4)central stem extension (φ=1)320C2^2.82(C2xC4xD5)320,277
C22.83(C2×C4×D5) = C5⋊2(C42⋊5C4)central stem extension (φ=1)320C2^2.83(C2xC4xD5)320,278
C22.84(C2×C4×D5) = C10.51(C4×D4)central stem extension (φ=1)320C2^2.84(C2xC4xD5)320,279
C22.85(C2×C4×D5) = C2.(C4×D20)central stem extension (φ=1)320C2^2.85(C2xC4xD5)320,280
C22.86(C2×C4×D5) = C4⋊Dic5⋊15C4central stem extension (φ=1)320C2^2.86(C2xC4xD5)320,281
C22.87(C2×C4×D5) = C10.52(C4×D4)central stem extension (φ=1)320C2^2.87(C2xC4xD5)320,282
C22.88(C2×C4×D5) = C22.58(D4×D5)central stem extension (φ=1)160C2^2.88(C2xC4xD5)320,291
C22.89(C2×C4×D5) = (C2×C4)⋊9D20central stem extension (φ=1)160C2^2.89(C2xC4xD5)320,292
C22.90(C2×C4×D5) = D10⋊2(C4⋊C4)central stem extension (φ=1)160C2^2.90(C2xC4xD5)320,294
C22.91(C2×C4×D5) = D10⋊3(C4⋊C4)central stem extension (φ=1)160C2^2.91(C2xC4xD5)320,295
C22.92(C2×C4×D5) = C10.54(C4×D4)central stem extension (φ=1)160C2^2.92(C2xC4xD5)320,296
C22.93(C2×C4×D5) = C10.55(C4×D4)central stem extension (φ=1)160C2^2.93(C2xC4xD5)320,297
C22.94(C2×C4×D5) = C40⋊11Q8central stem extension (φ=1)320C2^2.94(C2xC4xD5)320,306
C22.95(C2×C4×D5) = C8⋊6D20central stem extension (φ=1)160C2^2.95(C2xC4xD5)320,315
C22.96(C2×C4×D5) = C42.243D10central stem extension (φ=1)160C2^2.96(C2xC4xD5)320,317
C22.97(C2×C4×D5) = C40⋊Q8central stem extension (φ=1)320C2^2.97(C2xC4xD5)320,328
C22.98(C2×C4×D5) = C42.182D10central stem extension (φ=1)160C2^2.98(C2xC4xD5)320,332
C22.99(C2×C4×D5) = C8⋊9D20central stem extension (φ=1)160C2^2.99(C2xC4xD5)320,333
C22.100(C2×C4×D5) = C42.185D10central stem extension (φ=1)160C2^2.100(C2xC4xD5)320,336
C22.101(C2×C4×D5) = Dic5.9M4(2)central stem extension (φ=1)160C2^2.101(C2xC4xD5)320,346
C22.102(C2×C4×D5) = C40⋊8C4⋊C2central stem extension (φ=1)160C2^2.102(C2xC4xD5)320,347
C22.103(C2×C4×D5) = D10⋊7M4(2)central stem extension (φ=1)80C2^2.103(C2xC4xD5)320,353
C22.104(C2×C4×D5) = C22⋊C8⋊D5central stem extension (φ=1)160C2^2.104(C2xC4xD5)320,354
C22.105(C2×C4×D5) = D10⋊4M4(2)central stem extension (φ=1)160C2^2.105(C2xC4xD5)320,355
C22.106(C2×C4×D5) = Dic5⋊2M4(2)central stem extension (φ=1)160C2^2.106(C2xC4xD5)320,356
C22.107(C2×C4×D5) = C5⋊2C8⋊26D4central stem extension (φ=1)160C2^2.107(C2xC4xD5)320,357
C22.108(C2×C4×D5) = Dic5.5M4(2)central stem extension (φ=1)320C2^2.108(C2xC4xD5)320,455
C22.109(C2×C4×D5) = C42.198D10central stem extension (φ=1)320C2^2.109(C2xC4xD5)320,458
C22.110(C2×C4×D5) = C42.202D10central stem extension (φ=1)160C2^2.110(C2xC4xD5)320,462
C22.111(C2×C4×D5) = D10⋊5M4(2)central stem extension (φ=1)160C2^2.111(C2xC4xD5)320,463
C22.112(C2×C4×D5) = C20⋊5M4(2)central stem extension (φ=1)160C2^2.112(C2xC4xD5)320,464
C22.113(C2×C4×D5) = C20⋊6M4(2)central stem extension (φ=1)160C2^2.113(C2xC4xD5)320,465
C22.114(C2×C4×D5) = C42.30D10central stem extension (φ=1)160C2^2.114(C2xC4xD5)320,466
C22.115(C2×C4×D5) = C42.31D10central stem extension (φ=1)160C2^2.115(C2xC4xD5)320,467
C22.116(C2×C4×D5) = C20⋊7(C4⋊C4)central stem extension (φ=1)320C2^2.116(C2xC4xD5)320,555
C22.117(C2×C4×D5) = (C2×C20)⋊10Q8central stem extension (φ=1)320C2^2.117(C2xC4xD5)320,556
C22.118(C2×C4×D5) = C10.92(C4×D4)central stem extension (φ=1)320C2^2.118(C2xC4xD5)320,560
C22.119(C2×C4×D5) = (C2×C4)⋊6D20central stem extension (φ=1)160C2^2.119(C2xC4xD5)320,566
C22.120(C2×C4×D5) = (C2×C42)⋊D5central stem extension (φ=1)160C2^2.120(C2xC4xD5)320,567
C22.121(C2×C4×D5) = C24.44D10central stem extension (φ=1)160C2^2.121(C2xC4xD5)320,569
C22.122(C2×C4×D5) = C23.42D20central stem extension (φ=1)160C2^2.122(C2xC4xD5)320,570
C22.123(C2×C4×D5) = C24.3D10central stem extension (φ=1)160C2^2.123(C2xC4xD5)320,571
C22.124(C2×C4×D5) = C24.4D10central stem extension (φ=1)160C2^2.124(C2xC4xD5)320,572
C22.125(C2×C4×D5) = C24.46D10central stem extension (φ=1)160C2^2.125(C2xC4xD5)320,573
C22.126(C2×C4×D5) = C24.48D10central stem extension (φ=1)80C2^2.126(C2xC4xD5)320,582
C22.127(C2×C4×D5) = C24.12D10central stem extension (φ=1)160C2^2.127(C2xC4xD5)320,583
C22.128(C2×C4×D5) = C24.13D10central stem extension (φ=1)160C2^2.128(C2xC4xD5)320,584
C22.129(C2×C4×D5) = C23.45D20central stem extension (φ=1)160C2^2.129(C2xC4xD5)320,585
C22.130(C2×C4×D5) = C10.96(C4×D4)central stem extension (φ=1)320C2^2.130(C2xC4xD5)320,599
C22.131(C2×C4×D5) = C20⋊4(C4⋊C4)central stem extension (φ=1)320C2^2.131(C2xC4xD5)320,600
C22.132(C2×C4×D5) = (C2×Dic5)⋊6Q8central stem extension (φ=1)320C2^2.132(C2xC4xD5)320,601
C22.133(C2×C4×D5) = C20⋊5(C4⋊C4)central stem extension (φ=1)320C2^2.133(C2xC4xD5)320,603
C22.134(C2×C4×D5) = C20.48(C4⋊C4)central stem extension (φ=1)320C2^2.134(C2xC4xD5)320,604
C22.135(C2×C4×D5) = C10.97(C4×D4)central stem extension (φ=1)320C2^2.135(C2xC4xD5)320,605
C22.136(C2×C4×D5) = D10⋊4(C4⋊C4)central stem extension (φ=1)160C2^2.136(C2xC4xD5)320,614
C22.137(C2×C4×D5) = (C2×D20)⋊22C4central stem extension (φ=1)160C2^2.137(C2xC4xD5)320,615
C22.138(C2×C4×D5) = D10⋊5(C4⋊C4)central stem extension (φ=1)160C2^2.138(C2xC4xD5)320,616
C22.139(C2×C4×D5) = C10.90(C4×D4)central stem extension (φ=1)160C2^2.139(C2xC4xD5)320,617
C22.140(C2×C4×D5) = C20.65(C4⋊C4)central stem extension (φ=1)160C2^2.140(C2xC4xD5)320,729
C22.141(C2×C4×D5) = (C22×C8)⋊D5central stem extension (φ=1)160C2^2.141(C2xC4xD5)320,737
C22.142(C2×C4×D5) = C40⋊32D4central stem extension (φ=1)160C2^2.142(C2xC4xD5)320,738
C22.143(C2×C4×D5) = Dic5⋊5M4(2)central stem extension (φ=1)160C2^2.143(C2xC4xD5)320,745
C22.144(C2×C4×D5) = C20.51(C4⋊C4)central stem extension (φ=1)160C2^2.144(C2xC4xD5)320,746
C22.145(C2×C4×D5) = D10⋊8M4(2)central stem extension (φ=1)80C2^2.145(C2xC4xD5)320,753
C22.146(C2×C4×D5) = C40⋊D4central stem extension (φ=1)160C2^2.146(C2xC4xD5)320,754
C22.147(C2×C4×D5) = C40⋊18D4central stem extension (φ=1)160C2^2.147(C2xC4xD5)320,755
C22.148(C2×C4×D5) = C4.89(C2×D20)central stem extension (φ=1)160C2^2.148(C2xC4xD5)320,756
C22.149(C2×C4×D5) = C24.62D10central stem extension (φ=1)160C2^2.149(C2xC4xD5)320,837
C22.150(C2×C4×D5) = C24.65D10central stem extension (φ=1)160C2^2.150(C2xC4xD5)320,840

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