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Extensions 1→N→G→Q→1 with N=C10 and Q=C4.4D4

Direct product G=N×Q with N=C10 and Q=C4.4D4
dρLabelID
C10×C4.4D4160C10xC4.4D4320,1528

Semidirect products G=N:Q with N=C10 and Q=C4.4D4
extensionφ:Q→Aut NdρLabelID
C10⋊1(C4.4D4) = C2×C4.D20φ: C4.4D4/C42 → C2 ⊆ Aut C10160C10:1(C4.4D4)320,1148
C10⋊2(C4.4D4) = C2×Dic5.5D4φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10160C10:2(C4.4D4)320,1163
C10⋊3(C4.4D4) = C2×C20.17D4φ: C4.4D4/C2×D4 → C2 ⊆ Aut C10160C10:3(C4.4D4)320,1469
C10⋊4(C4.4D4) = C2×C20.23D4φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C10160C10:4(C4.4D4)320,1486

Non-split extensions G=N.Q with N=C10 and Q=C4.4D4
extensionφ:Q→Aut NdρLabelID
C10.1(C4.4D4) = (C2×C20).28D4φ: C4.4D4/C42 → C2 ⊆ Aut C10320C10.1(C4.4D4)320,286
C10.2(C4.4D4) = (C2×Dic5)⋊3D4φ: C4.4D4/C42 → C2 ⊆ Aut C10160C10.2(C4.4D4)320,299
C10.3(C4.4D4) = (C2×C4).21D20φ: C4.4D4/C42 → C2 ⊆ Aut C10160C10.3(C4.4D4)320,301
C10.4(C4.4D4) = C20.14Q16φ: C4.4D4/C42 → C2 ⊆ Aut C10320C10.4(C4.4D4)320,308
C10.5(C4.4D4) = C4.5D40φ: C4.4D4/C42 → C2 ⊆ Aut C10160C10.5(C4.4D4)320,321
C10.6(C4.4D4) = C42.264D10φ: C4.4D4/C42 → C2 ⊆ Aut C10160C10.6(C4.4D4)320,324
C10.7(C4.4D4) = C42.14D10φ: C4.4D4/C42 → C2 ⊆ Aut C10320C10.7(C4.4D4)320,330
C10.8(C4.4D4) = C42.19D10φ: C4.4D4/C42 → C2 ⊆ Aut C10160C10.8(C4.4D4)320,340
C10.9(C4.4D4) = C42.20D10φ: C4.4D4/C42 → C2 ⊆ Aut C10160C10.9(C4.4D4)320,341
C10.10(C4.4D4) = (C2×C20)⋊10Q8φ: C4.4D4/C42 → C2 ⊆ Aut C10320C10.10(C4.4D4)320,556
C10.11(C4.4D4) = C42⋊9Dic5φ: C4.4D4/C42 → C2 ⊆ Aut C10320C10.11(C4.4D4)320,563
C10.12(C4.4D4) = (C2×C4)⋊6D20φ: C4.4D4/C42 → C2 ⊆ Aut C10160C10.12(C4.4D4)320,566
C10.13(C4.4D4) = (C2×C42)⋊D5φ: C4.4D4/C42 → C2 ⊆ Aut C10160C10.13(C4.4D4)320,567
C10.14(C4.4D4) = (C2×C20)⋊Q8φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10320C10.14(C4.4D4)320,273
C10.15(C4.4D4) = C5⋊2(C42⋊8C4)φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10320C10.15(C4.4D4)320,277
C10.16(C4.4D4) = (C2×Dic5).Q8φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10320C10.16(C4.4D4)320,285
C10.17(C4.4D4) = (C2×C4).Dic10φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10320C10.17(C4.4D4)320,287
C10.18(C4.4D4) = C10.54(C4×D4)φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10160C10.18(C4.4D4)320,296
C10.19(C4.4D4) = C10.55(C4×D4)φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10160C10.19(C4.4D4)320,297
C10.20(C4.4D4) = (C2×C4).20D20φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10160C10.20(C4.4D4)320,300
C10.21(C4.4D4) = C10.(C4⋊D4)φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10160C10.21(C4.4D4)320,302
C10.22(C4.4D4) = Dic5.5D8φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10160C10.22(C4.4D4)320,387
C10.23(C4.4D4) = C4⋊C4.D10φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10160C10.23(C4.4D4)320,391
C10.24(C4.4D4) = C20⋊Q8⋊C2φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10160C10.24(C4.4D4)320,392
C10.25(C4.4D4) = (C8×Dic5)⋊C2φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10160C10.25(C4.4D4)320,395
C10.26(C4.4D4) = Dic5.3Q16φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10320C10.26(C4.4D4)320,419
C10.27(C4.4D4) = Q8⋊C4⋊D5φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10160C10.27(C4.4D4)320,422
C10.28(C4.4D4) = C40⋊8C4.C2φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10320C10.28(C4.4D4)320,424
C10.29(C4.4D4) = Q8⋊Dic5⋊C2φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10160C10.29(C4.4D4)320,427
C10.30(C4.4D4) = C24.3D10φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10160C10.30(C4.4D4)320,571
C10.31(C4.4D4) = C23⋊Dic10φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10160C10.31(C4.4D4)320,574
C10.32(C4.4D4) = C24.8D10φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10160C10.32(C4.4D4)320,578
C10.33(C4.4D4) = C24.9D10φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10160C10.33(C4.4D4)320,579
C10.34(C4.4D4) = C24.13D10φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10160C10.34(C4.4D4)320,584
C10.35(C4.4D4) = C24.14D10φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10160C10.35(C4.4D4)320,586
C10.36(C4.4D4) = C24.16D10φ: C4.4D4/C22⋊C4 → C2 ⊆ Aut C10160C10.36(C4.4D4)320,588
C10.37(C4.4D4) = C24.4D10φ: C4.4D4/C2×D4 → C2 ⊆ Aut C10160C10.37(C4.4D4)320,572
C10.38(C4.4D4) = C23.14D20φ: C4.4D4/C2×D4 → C2 ⊆ Aut C10160C10.38(C4.4D4)320,580
C10.39(C4.4D4) = (C2×Dic5)⋊6Q8φ: C4.4D4/C2×D4 → C2 ⊆ Aut C10320C10.39(C4.4D4)320,601
C10.40(C4.4D4) = (C2×C20).288D4φ: C4.4D4/C2×D4 → C2 ⊆ Aut C10320C10.40(C4.4D4)320,609
C10.41(C4.4D4) = C42.62D10φ: C4.4D4/C2×D4 → C2 ⊆ Aut C10160C10.41(C4.4D4)320,682
C10.42(C4.4D4) = C42.213D10φ: C4.4D4/C2×D4 → C2 ⊆ Aut C10160C10.42(C4.4D4)320,683
C10.43(C4.4D4) = C20.16D8φ: C4.4D4/C2×D4 → C2 ⊆ Aut C10160C10.43(C4.4D4)320,697
C10.44(C4.4D4) = C42.72D10φ: C4.4D4/C2×D4 → C2 ⊆ Aut C10160C10.44(C4.4D4)320,698
C10.45(C4.4D4) = C20.Q16φ: C4.4D4/C2×D4 → C2 ⊆ Aut C10320C10.45(C4.4D4)320,708
C10.46(C4.4D4) = C42.77D10φ: C4.4D4/C2×D4 → C2 ⊆ Aut C10320C10.46(C4.4D4)320,709
C10.47(C4.4D4) = C24.19D10φ: C4.4D4/C2×D4 → C2 ⊆ Aut C10160C10.47(C4.4D4)320,848
C10.48(C4.4D4) = C24.20D10φ: C4.4D4/C2×D4 → C2 ⊆ Aut C10160C10.48(C4.4D4)320,849
C10.49(C4.4D4) = C20.48(C4⋊C4)φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C10320C10.49(C4.4D4)320,604
C10.50(C4.4D4) = (C2×C20).55D4φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C10320C10.50(C4.4D4)320,613
C10.51(C4.4D4) = (C2×D20)⋊22C4φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C10160C10.51(C4.4D4)320,615
C10.52(C4.4D4) = C10.90(C4×D4)φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C10160C10.52(C4.4D4)320,617
C10.53(C4.4D4) = (C2×C4)⋊3D20φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C10160C10.53(C4.4D4)320,618
C10.54(C4.4D4) = (C2×C20).290D4φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C10160C10.54(C4.4D4)320,620
C10.55(C4.4D4) = C42.70D10φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C10160C10.55(C4.4D4)320,694
C10.56(C4.4D4) = C42.216D10φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C10160C10.56(C4.4D4)320,695
C10.57(C4.4D4) = C42.71D10φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C10320C10.57(C4.4D4)320,696
C10.58(C4.4D4) = C20.D8φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C10160C10.58(C4.4D4)320,715
C10.59(C4.4D4) = C42.82D10φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C10160C10.59(C4.4D4)320,716
C10.60(C4.4D4) = C20.11Q16φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C10320C10.60(C4.4D4)320,720
C10.61(C4.4D4) = (Q8×C10)⋊17C4φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C10320C10.61(C4.4D4)320,857
C10.62(C4.4D4) = (C22×D5)⋊Q8φ: C4.4D4/C2×Q8 → C2 ⊆ Aut C10160C10.62(C4.4D4)320,858
C10.63(C4.4D4) = C5×C42⋊8C4central extension (φ=1)320C10.63(C4.4D4)320,883
C10.64(C4.4D4) = C5×C24.C22central extension (φ=1)160C10.64(C4.4D4)320,889
C10.65(C4.4D4) = C5×C24.3C22central extension (φ=1)160C10.65(C4.4D4)320,891
C10.66(C4.4D4) = C5×C23.67C23central extension (φ=1)320C10.66(C4.4D4)320,892
C10.67(C4.4D4) = C5×C23⋊Q8central extension (φ=1)160C10.67(C4.4D4)320,894
C10.68(C4.4D4) = C5×C23.10D4central extension (φ=1)160C10.68(C4.4D4)320,895
C10.69(C4.4D4) = C5×C23.11D4central extension (φ=1)160C10.69(C4.4D4)320,898
C10.70(C4.4D4) = C5×C23.83C23central extension (φ=1)320C10.70(C4.4D4)320,901
C10.71(C4.4D4) = C5×C4.4D8central extension (φ=1)160C10.71(C4.4D4)320,987
C10.72(C4.4D4) = C5×C4.SD16central extension (φ=1)320C10.72(C4.4D4)320,988
C10.73(C4.4D4) = C5×C42.78C22central extension (φ=1)160C10.73(C4.4D4)320,989
C10.74(C4.4D4) = C5×C42.28C22central extension (φ=1)160C10.74(C4.4D4)320,990
C10.75(C4.4D4) = C5×C42.29C22central extension (φ=1)160C10.75(C4.4D4)320,991
C10.76(C4.4D4) = C5×C42.30C22central extension (φ=1)320C10.76(C4.4D4)320,992

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