# Extensions 1→N→G→Q→1 with N=C10 and Q=C2×C4⋊C4

Direct product G=N×Q with N=C10 and Q=C2×C4⋊C4
dρLabelID
C4⋊C4×C2×C10320C4:C4xC2xC10320,1515

Semidirect products G=N:Q with N=C10 and Q=C2×C4⋊C4
extensionφ:Q→Aut NdρLabelID
C10⋊(C2×C4⋊C4) = C22×C4⋊F5φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C1080C10:(C2xC4:C4)320,1591
C102(C2×C4⋊C4) = C2×D5×C4⋊C4φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10160C10:2(C2xC4:C4)320,1173
C103(C2×C4⋊C4) = C22×C10.D4φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10320C10:3(C2xC4:C4)320,1455
C104(C2×C4⋊C4) = C22×C4⋊Dic5φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10320C10:4(C2xC4:C4)320,1457

Non-split extensions G=N.Q with N=C10 and Q=C2×C4⋊C4
extensionφ:Q→Aut NdρLabelID
C10.1(C2×C4⋊C4) = C42.11F5φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C10160C10.1(C2xC4:C4)320,1017
C10.2(C2×C4⋊C4) = C203M4(2)φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C10160C10.2(C2xC4:C4)320,1019
C10.3(C2×C4⋊C4) = C42.14F5φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C10160C10.3(C2xC4:C4)320,1020
C10.4(C2×C4⋊C4) = C4×C4⋊F5φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C1080C10.4(C2xC4:C4)320,1025
C10.5(C2×C4⋊C4) = C428F5φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C1080C10.5(C2xC4:C4)320,1026
C10.6(C2×C4⋊C4) = C429F5φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C1080C10.6(C2xC4:C4)320,1027
C10.7(C2×C4⋊C4) = C20⋊C8⋊C2φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C10160C10.7(C2xC4:C4)320,1034
C10.8(C2×C4⋊C4) = D10⋊(C4⋊C4)φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C1040C10.8(C2xC4:C4)320,1037
C10.9(C2×C4⋊C4) = C4⋊C4.9F5φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C10160C10.9(C2xC4:C4)320,1046
C10.10(C2×C4⋊C4) = C20⋊(C4⋊C4)φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C1080C10.10(C2xC4:C4)320,1050
C10.11(C2×C4⋊C4) = C2×C40⋊C4φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C1080C10.11(C2xC4:C4)320,1057
C10.12(C2×C4⋊C4) = C2×D5.D8φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C1080C10.12(C2xC4:C4)320,1058
C10.13(C2×C4⋊C4) = (C2×C8)⋊6F5φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C10804C10.13(C2xC4:C4)320,1059
C10.14(C2×C4⋊C4) = C2×C40.C4φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C10160C10.14(C2xC4:C4)320,1060
C10.15(C2×C4⋊C4) = C2×D10.Q8φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C10160C10.15(C2xC4:C4)320,1061
C10.16(C2×C4⋊C4) = (C8×D5).C4φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C10804C10.16(C2xC4:C4)320,1062
C10.17(C2×C4⋊C4) = M4(2)⋊1F5φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C10408C10.17(C2xC4:C4)320,1065
C10.18(C2×C4⋊C4) = M4(2).1F5φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C10808C10.18(C2xC4:C4)320,1067
C10.19(C2×C4⋊C4) = C2×C20⋊C8φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C10320C10.19(C2xC4:C4)320,1085
C10.20(C2×C4⋊C4) = C2×Dic5⋊C8φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C10320C10.20(C2xC4:C4)320,1090
C10.21(C2×C4⋊C4) = C208M4(2)φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C10160C10.21(C2xC4:C4)320,1096
C10.22(C2×C4⋊C4) = C2×D10.3Q8φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C1080C10.22(C2xC4:C4)320,1100
C10.23(C2×C4⋊C4) = D106(C4⋊C4)φ: C2×C4⋊C4/C2×C4C4 ⊆ Aut C1080C10.23(C2xC4:C4)320,1103
C10.24(C2×C4⋊C4) = C10.49(C4×D4)φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10320C10.24(C2xC4:C4)320,274
C10.25(C2×C4⋊C4) = Dic52C42φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10320C10.25(C2xC4:C4)320,276
C10.26(C2×C4⋊C4) = C52(C428C4)φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10320C10.26(C2xC4:C4)320,277
C10.27(C2×C4⋊C4) = D5×C2.C42φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10160C10.27(C2xC4:C4)320,290
C10.28(C2×C4⋊C4) = D102(C4⋊C4)φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10160C10.28(C2xC4:C4)320,294
C10.29(C2×C4⋊C4) = D103(C4⋊C4)φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10160C10.29(C2xC4:C4)320,295
C10.30(C2×C4⋊C4) = D5×C4⋊C8φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10160C10.30(C2xC4:C4)320,459
C10.31(C2×C4⋊C4) = C205M4(2)φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10160C10.31(C2xC4:C4)320,464
C10.32(C2×C4⋊C4) = C42.30D10φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10160C10.32(C2xC4:C4)320,466
C10.33(C2×C4⋊C4) = D5×C4.Q8φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10160C10.33(C2xC4:C4)320,486
C10.34(C2×C4⋊C4) = (C8×D5)⋊C4φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10160C10.34(C2xC4:C4)320,487
C10.35(C2×C4⋊C4) = C8⋊(C4×D5)φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10160C10.35(C2xC4:C4)320,488
C10.36(C2×C4⋊C4) = D5×C2.D8φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10160C10.36(C2xC4:C4)320,506
C10.37(C2×C4⋊C4) = C8.27(C4×D5)φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10160C10.37(C2xC4:C4)320,507
C10.38(C2×C4⋊C4) = C4020(C2×C4)φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10160C10.38(C2xC4:C4)320,508
C10.39(C2×C4⋊C4) = D5×C8.C4φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10804C10.39(C2xC4:C4)320,519
C10.40(C2×C4⋊C4) = M4(2).25D10φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10804C10.40(C2xC4:C4)320,520
C10.41(C2×C4⋊C4) = C10.96(C4×D4)φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10320C10.41(C2xC4:C4)320,599
C10.42(C2×C4⋊C4) = C4⋊C4×Dic5φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10320C10.42(C2xC4:C4)320,602
C10.43(C2×C4⋊C4) = D104(C4⋊C4)φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10160C10.43(C2xC4:C4)320,614
C10.44(C2×C4⋊C4) = D105(C4⋊C4)φ: C2×C4⋊C4/C4⋊C4C2 ⊆ Aut C10160C10.44(C2xC4:C4)320,616
C10.45(C2×C4⋊C4) = C2×C203C8φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10320C10.45(C2xC4:C4)320,550
C10.46(C2×C4⋊C4) = C2013M4(2)φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10160C10.46(C2xC4:C4)320,551
C10.47(C2×C4⋊C4) = C207(C4⋊C4)φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10320C10.47(C2xC4:C4)320,555
C10.48(C2×C4⋊C4) = C4×C10.D4φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10320C10.48(C2xC4:C4)320,558
C10.49(C2×C4⋊C4) = C4×C4⋊Dic5φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10320C10.49(C2xC4:C4)320,561
C10.50(C2×C4⋊C4) = C428Dic5φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10320C10.50(C2xC4:C4)320,562
C10.51(C2×C4⋊C4) = C429Dic5φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10320C10.51(C2xC4:C4)320,563
C10.52(C2×C4⋊C4) = C24.44D10φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10160C10.52(C2xC4:C4)320,569
C10.53(C2×C4⋊C4) = C24.46D10φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10160C10.53(C2xC4:C4)320,573
C10.54(C2×C4⋊C4) = C24.47D10φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10160C10.54(C2xC4:C4)320,577
C10.55(C2×C4⋊C4) = C2×C10.D8φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10320C10.55(C2xC4:C4)320,589
C10.56(C2×C4⋊C4) = C2×C20.Q8φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10320C10.56(C2xC4:C4)320,590
C10.57(C2×C4⋊C4) = C20.47(C4⋊C4)φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10160C10.57(C2xC4:C4)320,591
C10.58(C2×C4⋊C4) = C204(C4⋊C4)φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10320C10.58(C2xC4:C4)320,600
C10.59(C2×C4⋊C4) = C205(C4⋊C4)φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10320C10.59(C2xC4:C4)320,603
C10.60(C2×C4⋊C4) = C20.48(C4⋊C4)φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10320C10.60(C2xC4:C4)320,604
C10.61(C2×C4⋊C4) = C206(C4⋊C4)φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10320C10.61(C2xC4:C4)320,612
C10.62(C2×C4⋊C4) = C20.64(C4⋊C4)φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10160C10.62(C2xC4:C4)320,622
C10.63(C2×C4⋊C4) = C20.76(C4⋊C4)φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10160C10.63(C2xC4:C4)320,625
C10.64(C2×C4⋊C4) = C42.43D10φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10160C10.64(C2xC4:C4)320,626
C10.65(C2×C4⋊C4) = C2×C20.8Q8φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10320C10.65(C2xC4:C4)320,726
C10.66(C2×C4⋊C4) = C20.65(C4⋊C4)φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10160C10.66(C2xC4:C4)320,729
C10.67(C2×C4⋊C4) = C2×C406C4φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10320C10.67(C2xC4:C4)320,731
C10.68(C2×C4⋊C4) = C2×C405C4φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10320C10.68(C2xC4:C4)320,732
C10.69(C2×C4⋊C4) = C23.22D20φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10160C10.69(C2xC4:C4)320,733
C10.70(C2×C4⋊C4) = C2×C40.6C4φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10160C10.70(C2xC4:C4)320,734
C10.71(C2×C4⋊C4) = Dic55M4(2)φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10160C10.71(C2xC4:C4)320,745
C10.72(C2×C4⋊C4) = C20.51(C4⋊C4)φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10160C10.72(C2xC4:C4)320,746
C10.73(C2×C4⋊C4) = C23.47D20φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10160C10.73(C2xC4:C4)320,748
C10.74(C2×C4⋊C4) = C2×C20.53D4φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10160C10.74(C2xC4:C4)320,750
C10.75(C2×C4⋊C4) = C23.Dic10φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10804C10.75(C2xC4:C4)320,751
C10.76(C2×C4⋊C4) = M4(2).Dic5φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10804C10.76(C2xC4:C4)320,752
C10.77(C2×C4⋊C4) = C2×C10.10C42φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10320C10.77(C2xC4:C4)320,835
C10.78(C2×C4⋊C4) = C24.62D10φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10160C10.78(C2xC4:C4)320,837
C10.79(C2×C4⋊C4) = C24.64D10φ: C2×C4⋊C4/C22×C4C2 ⊆ Aut C10160C10.79(C2xC4:C4)320,839
C10.80(C2×C4⋊C4) = C10×C2.C42central extension (φ=1)320C10.80(C2xC4:C4)320,876
C10.81(C2×C4⋊C4) = C4⋊C4×C20central extension (φ=1)320C10.81(C2xC4:C4)320,879
C10.82(C2×C4⋊C4) = C5×C23.7Q8central extension (φ=1)160C10.82(C2xC4:C4)320,881
C10.83(C2×C4⋊C4) = C5×C428C4central extension (φ=1)320C10.83(C2xC4:C4)320,883
C10.84(C2×C4⋊C4) = C5×C429C4central extension (φ=1)320C10.84(C2xC4:C4)320,885
C10.85(C2×C4⋊C4) = C5×C23.8Q8central extension (φ=1)160C10.85(C2xC4:C4)320,886
C10.86(C2×C4⋊C4) = C5×C23.65C23central extension (φ=1)320C10.86(C2xC4:C4)320,890
C10.87(C2×C4⋊C4) = C10×C4⋊C8central extension (φ=1)320C10.87(C2xC4:C4)320,923
C10.88(C2×C4⋊C4) = C5×C4⋊M4(2)central extension (φ=1)160C10.88(C2xC4:C4)320,924
C10.89(C2×C4⋊C4) = C5×C42.6C22central extension (φ=1)160C10.89(C2xC4:C4)320,925
C10.90(C2×C4⋊C4) = C10×C4.Q8central extension (φ=1)320C10.90(C2xC4:C4)320,926
C10.91(C2×C4⋊C4) = C10×C2.D8central extension (φ=1)320C10.91(C2xC4:C4)320,927
C10.92(C2×C4⋊C4) = C5×C23.25D4central extension (φ=1)160C10.92(C2xC4:C4)320,928
C10.93(C2×C4⋊C4) = C5×M4(2)⋊C4central extension (φ=1)160C10.93(C2xC4:C4)320,929
C10.94(C2×C4⋊C4) = C10×C8.C4central extension (φ=1)160C10.94(C2xC4:C4)320,930
C10.95(C2×C4⋊C4) = C5×M4(2).C4central extension (φ=1)804C10.95(C2xC4:C4)320,931

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