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Extensions 1→N→G→Q→1 with N=C10 and Q=C42⋊C2

Direct product G=N×Q with N=C10 and Q=C42⋊C2
dρLabelID
C10×C42⋊C2160C10xC4^2:C2320,1516

Semidirect products G=N:Q with N=C10 and Q=C42⋊C2
extensionφ:Q→Aut NdρLabelID
C10⋊(C42⋊C2) = C2×D10.C23φ: C42⋊C2/C2×C4 → C4 ⊆ Aut C1080C10:(C4^2:C2)320,1592
C10⋊2(C42⋊C2) = C2×C42⋊D5φ: C42⋊C2/C42 → C2 ⊆ Aut C10160C10:2(C4^2:C2)320,1144
C10⋊3(C42⋊C2) = C2×C23.11D10φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C10160C10:3(C4^2:C2)320,1152
C10⋊4(C42⋊C2) = C2×C4⋊C4⋊7D5φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C10160C10:4(C4^2:C2)320,1174
C10⋊5(C42⋊C2) = C2×C23.21D10φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C10160C10:5(C4^2:C2)320,1458

Non-split extensions G=N.Q with N=C10 and Q=C42⋊C2
extensionφ:Q→Aut NdρLabelID
C10.1(C42⋊C2) = C42.6F5φ: C42⋊C2/C2×C4 → C4 ⊆ Aut C10160C10.1(C4^2:C2)320,1016
C10.2(C42⋊C2) = C42.12F5φ: C42⋊C2/C2×C4 → C4 ⊆ Aut C10160C10.2(C4^2:C2)320,1018
C10.3(C42⋊C2) = C42.15F5φ: C42⋊C2/C2×C4 → C4 ⊆ Aut C10160C10.3(C4^2:C2)320,1021
C10.4(C42⋊C2) = C42.7F5φ: C42⋊C2/C2×C4 → C4 ⊆ Aut C10160C10.4(C4^2:C2)320,1022
C10.5(C42⋊C2) = C42⋊4F5φ: C42⋊C2/C2×C4 → C4 ⊆ Aut C1080C10.5(C4^2:C2)320,1024
C10.6(C42⋊C2) = C4×C4⋊F5φ: C42⋊C2/C2×C4 → C4 ⊆ Aut C1080C10.6(C4^2:C2)320,1025
C10.7(C42⋊C2) = C42⋊9F5φ: C42⋊C2/C2×C4 → C4 ⊆ Aut C1080C10.7(C4^2:C2)320,1027
C10.8(C42⋊C2) = C42⋊5F5φ: C42⋊C2/C2×C4 → C4 ⊆ Aut C1080C10.8(C4^2:C2)320,1028
C10.9(C42⋊C2) = C23.(C2×F5)φ: C42⋊C2/C2×C4 → C4 ⊆ Aut C10160C10.9(C4^2:C2)320,1035
C10.10(C42⋊C2) = C10.(C4×D4)φ: C42⋊C2/C2×C4 → C4 ⊆ Aut C1080C10.10(C4^2:C2)320,1038
C10.11(C42⋊C2) = C4⋊C4.7F5φ: C42⋊C2/C2×C4 → C4 ⊆ Aut C10160C10.11(C4^2:C2)320,1044
C10.12(C42⋊C2) = C4⋊C4⋊5F5φ: C42⋊C2/C2×C4 → C4 ⊆ Aut C1080C10.12(C4^2:C2)320,1049
C10.13(C42⋊C2) = Dic5.12M4(2)φ: C42⋊C2/C2×C4 → C4 ⊆ Aut C10160C10.13(C4^2:C2)320,1086
C10.14(C42⋊C2) = C20.34M4(2)φ: C42⋊C2/C2×C4 → C4 ⊆ Aut C10160C10.14(C4^2:C2)320,1092
C10.15(C42⋊C2) = Dic5.13M4(2)φ: C42⋊C2/C2×C4 → C4 ⊆ Aut C10160C10.15(C4^2:C2)320,1095
C10.16(C42⋊C2) = C20.30M4(2)φ: C42⋊C2/C2×C4 → C4 ⊆ Aut C10160C10.16(C4^2:C2)320,1097
C10.17(C42⋊C2) = C4×C22⋊F5φ: C42⋊C2/C2×C4 → C4 ⊆ Aut C1080C10.17(C4^2:C2)320,1101
C10.18(C42⋊C2) = (C22×C4)⋊7F5φ: C42⋊C2/C2×C4 → C4 ⊆ Aut C1080C10.18(C4^2:C2)320,1102
C10.19(C42⋊C2) = D10⋊6(C4⋊C4)φ: C42⋊C2/C2×C4 → C4 ⊆ Aut C1080C10.19(C4^2:C2)320,1103
C10.20(C42⋊C2) = C5⋊2(C42⋊8C4)φ: C42⋊C2/C42 → C2 ⊆ Aut C10320C10.20(C4^2:C2)320,277
C10.21(C42⋊C2) = C5⋊2(C42⋊5C4)φ: C42⋊C2/C42 → C2 ⊆ Aut C10320C10.21(C4^2:C2)320,278
C10.22(C42⋊C2) = C10.51(C4×D4)φ: C42⋊C2/C42 → C2 ⊆ Aut C10320C10.22(C4^2:C2)320,279
C10.23(C42⋊C2) = C22.58(D4×D5)φ: C42⋊C2/C42 → C2 ⊆ Aut C10160C10.23(C4^2:C2)320,291
C10.24(C42⋊C2) = D10⋊2(C4⋊C4)φ: C42⋊C2/C42 → C2 ⊆ Aut C10160C10.24(C4^2:C2)320,294
C10.25(C42⋊C2) = C10.54(C4×D4)φ: C42⋊C2/C42 → C2 ⊆ Aut C10160C10.25(C4^2:C2)320,296
C10.26(C42⋊C2) = C42.282D10φ: C42⋊C2/C42 → C2 ⊆ Aut C10160C10.26(C4^2:C2)320,312
C10.27(C42⋊C2) = C42.243D10φ: C42⋊C2/C42 → C2 ⊆ Aut C10160C10.27(C4^2:C2)320,317
C10.28(C42⋊C2) = C42.182D10φ: C42⋊C2/C42 → C2 ⊆ Aut C10160C10.28(C4^2:C2)320,332
C10.29(C42⋊C2) = C42.185D10φ: C42⋊C2/C42 → C2 ⊆ Aut C10160C10.29(C4^2:C2)320,336
C10.30(C42⋊C2) = C4×C10.D4φ: C42⋊C2/C42 → C2 ⊆ Aut C10320C10.30(C4^2:C2)320,558
C10.31(C42⋊C2) = C42⋊4Dic5φ: C42⋊C2/C42 → C2 ⊆ Aut C10320C10.31(C4^2:C2)320,559
C10.32(C42⋊C2) = C10.92(C4×D4)φ: C42⋊C2/C42 → C2 ⊆ Aut C10320C10.32(C4^2:C2)320,560
C10.33(C42⋊C2) = C4×D10⋊C4φ: C42⋊C2/C42 → C2 ⊆ Aut C10160C10.33(C4^2:C2)320,565
C10.34(C42⋊C2) = (C2×C42)⋊D5φ: C42⋊C2/C42 → C2 ⊆ Aut C10160C10.34(C4^2:C2)320,567
C10.35(C42⋊C2) = Dic5.15C42φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C10320C10.35(C4^2:C2)320,275
C10.36(C42⋊C2) = Dic5⋊2C42φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C10320C10.36(C4^2:C2)320,276
C10.37(C42⋊C2) = C2.(C4×D20)φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C10320C10.37(C4^2:C2)320,280
C10.38(C42⋊C2) = C4⋊Dic5⋊15C4φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C10320C10.38(C4^2:C2)320,281
C10.39(C42⋊C2) = Dic5.14M4(2)φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C10160C10.39(C4^2:C2)320,345
C10.40(C42⋊C2) = Dic5.9M4(2)φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C10160C10.40(C4^2:C2)320,346
C10.41(C42⋊C2) = C40⋊8C4⋊C2φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C10160C10.41(C4^2:C2)320,347
C10.42(C42⋊C2) = C22⋊C4×Dic5φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C10160C10.42(C4^2:C2)320,568
C10.43(C42⋊C2) = C24.44D10φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C10160C10.43(C4^2:C2)320,569
C10.44(C42⋊C2) = C23.42D20φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C10160C10.44(C4^2:C2)320,570
C10.45(C42⋊C2) = C24.3D10φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C10160C10.45(C4^2:C2)320,571
C10.46(C42⋊C2) = C24.4D10φ: C42⋊C2/C22⋊C4 → C2 ⊆ Aut C10160C10.46(C4^2:C2)320,572
C10.47(C42⋊C2) = C10.52(C4×D4)φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C10320C10.47(C4^2:C2)320,282
C10.48(C42⋊C2) = D10⋊2C42φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C10160C10.48(C4^2:C2)320,293
C10.49(C42⋊C2) = C10.55(C4×D4)φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C10160C10.49(C4^2:C2)320,297
C10.50(C42⋊C2) = C42.200D10φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C10160C10.50(C4^2:C2)320,460
C10.51(C42⋊C2) = C42.202D10φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C10160C10.51(C4^2:C2)320,462
C10.52(C42⋊C2) = C42.31D10φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C10160C10.52(C4^2:C2)320,467
C10.53(C42⋊C2) = C4⋊C4×Dic5φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C10320C10.53(C4^2:C2)320,602
C10.54(C42⋊C2) = C20.48(C4⋊C4)φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C10320C10.54(C4^2:C2)320,604
C10.55(C42⋊C2) = C10.97(C4×D4)φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C10320C10.55(C4^2:C2)320,605
C10.56(C42⋊C2) = D10⋊4(C4⋊C4)φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C10160C10.56(C4^2:C2)320,614
C10.57(C42⋊C2) = C10.90(C4×D4)φ: C42⋊C2/C4⋊C4 → C2 ⊆ Aut C10160C10.57(C4^2:C2)320,617
C10.58(C42⋊C2) = C42.6Dic5φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C10160C10.58(C4^2:C2)320,552
C10.59(C42⋊C2) = C42.7Dic5φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C10160C10.59(C4^2:C2)320,553
C10.60(C42⋊C2) = C4×C4⋊Dic5φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C10320C10.60(C4^2:C2)320,561
C10.61(C42⋊C2) = C42⋊9Dic5φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C10320C10.61(C4^2:C2)320,563
C10.62(C42⋊C2) = C42⋊5Dic5φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C10320C10.62(C4^2:C2)320,564
C10.63(C42⋊C2) = C24.8D10φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C10160C10.63(C4^2:C2)320,578
C10.64(C42⋊C2) = C4⋊C4⋊5Dic5φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C10320C10.64(C4^2:C2)320,608
C10.65(C42⋊C2) = C42.187D10φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C10160C10.65(C4^2:C2)320,627
C10.66(C42⋊C2) = C4×C23.D5φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C10160C10.66(C4^2:C2)320,836
C10.67(C42⋊C2) = C24.63D10φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C10160C10.67(C4^2:C2)320,838
C10.68(C42⋊C2) = C24.64D10φ: C42⋊C2/C22×C4 → C2 ⊆ Aut C10160C10.68(C4^2:C2)320,839
C10.69(C42⋊C2) = C5×C42⋊4C4central extension (φ=1)320C10.69(C4^2:C2)320,877
C10.70(C42⋊C2) = C22⋊C4×C20central extension (φ=1)160C10.70(C4^2:C2)320,878
C10.71(C42⋊C2) = C4⋊C4×C20central extension (φ=1)320C10.71(C4^2:C2)320,879
C10.72(C42⋊C2) = C5×C23.7Q8central extension (φ=1)160C10.72(C4^2:C2)320,881
C10.73(C42⋊C2) = C5×C23.34D4central extension (φ=1)160C10.73(C4^2:C2)320,882
C10.74(C42⋊C2) = C5×C42⋊8C4central extension (φ=1)320C10.74(C4^2:C2)320,883
C10.75(C42⋊C2) = C5×C42⋊5C4central extension (φ=1)320C10.75(C4^2:C2)320,884
C10.76(C42⋊C2) = C5×C23.63C23central extension (φ=1)320C10.76(C4^2:C2)320,888
C10.77(C42⋊C2) = C5×C24.C22central extension (φ=1)160C10.77(C4^2:C2)320,889
C10.78(C42⋊C2) = C5×C42.12C4central extension (φ=1)160C10.78(C4^2:C2)320,932
C10.79(C42⋊C2) = C5×C42.6C4central extension (φ=1)160C10.79(C4^2:C2)320,933
C10.80(C42⋊C2) = C5×C42.7C22central extension (φ=1)160C10.80(C4^2:C2)320,934

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