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Extensions 1→N→G→Q→1 with N=C10 and Q=C8○D4

Direct product G=N×Q with N=C10 and Q=C8○D4
dρLabelID
C10×C8○D4160C10xC8oD4320,1569

Semidirect products G=N:Q with N=C10 and Q=C8○D4
extensionφ:Q→Aut NdρLabelID
C10⋊1(C8○D4) = C2×D4.F5φ: C8○D4/D4 → C4 ⊆ Aut C10160C10:1(C8oD4)320,1593
C10⋊2(C8○D4) = C2×Q8.F5φ: C8○D4/Q8 → C4 ⊆ Aut C10160C10:2(C8oD4)320,1597
C10⋊3(C8○D4) = C2×D20.3C4φ: C8○D4/C2×C8 → C2 ⊆ Aut C10160C10:3(C8oD4)320,1410
C10⋊4(C8○D4) = C2×D20.2C4φ: C8○D4/M4(2) → C2 ⊆ Aut C10160C10:4(C8oD4)320,1416
C10⋊5(C8○D4) = C2×D4.Dic5φ: C8○D4/C4○D4 → C2 ⊆ Aut C10160C10:5(C8oD4)320,1490

Non-split extensions G=N.Q with N=C10 and Q=C8○D4
extensionφ:Q→Aut NdρLabelID
C10.1(C8○D4) = Dic5.C42φ: C8○D4/D4 → C4 ⊆ Aut C10160C10.1(C8oD4)320,1029
C10.2(C8○D4) = C5⋊C8⋊8D4φ: C8○D4/D4 → C4 ⊆ Aut C10160C10.2(C8oD4)320,1030
C10.3(C8○D4) = C5⋊C8⋊D4φ: C8○D4/D4 → C4 ⊆ Aut C10160C10.3(C8oD4)320,1031
C10.4(C8○D4) = D10⋊M4(2)φ: C8○D4/D4 → C4 ⊆ Aut C10160C10.4(C8oD4)320,1032
C10.5(C8○D4) = Dic5⋊M4(2)φ: C8○D4/D4 → C4 ⊆ Aut C10160C10.5(C8oD4)320,1033
C10.6(C8○D4) = C20⋊C8⋊C2φ: C8○D4/D4 → C4 ⊆ Aut C10160C10.6(C8oD4)320,1034
C10.7(C8○D4) = C23.(C2×F5)φ: C8○D4/D4 → C4 ⊆ Aut C10160C10.7(C8oD4)320,1035
C10.8(C8○D4) = D10.C42φ: C8○D4/D4 → C4 ⊆ Aut C10160C10.8(C8oD4)320,1039
C10.9(C8○D4) = Dic10⋊C8φ: C8○D4/D4 → C4 ⊆ Aut C10320C10.9(C8oD4)320,1041
C10.10(C8○D4) = C4⋊C4.7F5φ: C8○D4/D4 → C4 ⊆ Aut C10160C10.10(C8oD4)320,1044
C10.11(C8○D4) = Dic5.M4(2)φ: C8○D4/D4 → C4 ⊆ Aut C10320C10.11(C8oD4)320,1045
C10.12(C8○D4) = C4⋊C4.9F5φ: C8○D4/D4 → C4 ⊆ Aut C10160C10.12(C8oD4)320,1046
C10.13(C8○D4) = C20.M4(2)φ: C8○D4/D4 → C4 ⊆ Aut C10320C10.13(C8oD4)320,1047
C10.14(C8○D4) = D4×C5⋊C8φ: C8○D4/D4 → C4 ⊆ Aut C10160C10.14(C8oD4)320,1110
C10.15(C8○D4) = C5⋊C8⋊7D4φ: C8○D4/D4 → C4 ⊆ Aut C10160C10.15(C8oD4)320,1111
C10.16(C8○D4) = C20⋊2M4(2)φ: C8○D4/D4 → C4 ⊆ Aut C10160C10.16(C8oD4)320,1112
C10.17(C8○D4) = (C2×D4).7F5φ: C8○D4/D4 → C4 ⊆ Aut C10160C10.17(C8oD4)320,1113
C10.18(C8○D4) = (C2×D4).8F5φ: C8○D4/D4 → C4 ⊆ Aut C10160C10.18(C8oD4)320,1114
C10.19(C8○D4) = D20⋊2C8φ: C8○D4/Q8 → C4 ⊆ Aut C10160C10.19(C8oD4)320,1040
C10.20(C8○D4) = D10⋊2M4(2)φ: C8○D4/Q8 → C4 ⊆ Aut C10160C10.20(C8oD4)320,1042
C10.21(C8○D4) = C20⋊M4(2)φ: C8○D4/Q8 → C4 ⊆ Aut C10160C10.21(C8oD4)320,1043
C10.22(C8○D4) = Q8×C5⋊C8φ: C8○D4/Q8 → C4 ⊆ Aut C10320C10.22(C8oD4)320,1124
C10.23(C8○D4) = (C2×Q8).5F5φ: C8○D4/Q8 → C4 ⊆ Aut C10160C10.23(C8oD4)320,1125
C10.24(C8○D4) = C20.6M4(2)φ: C8○D4/Q8 → C4 ⊆ Aut C10320C10.24(C8oD4)320,1126
C10.25(C8○D4) = C8×Dic10φ: C8○D4/C2×C8 → C2 ⊆ Aut C10320C10.25(C8oD4)320,305
C10.26(C8○D4) = C40⋊11Q8φ: C8○D4/C2×C8 → C2 ⊆ Aut C10320C10.26(C8oD4)320,306
C10.27(C8○D4) = C8×D20φ: C8○D4/C2×C8 → C2 ⊆ Aut C10160C10.27(C8oD4)320,313
C10.28(C8○D4) = C8⋊6D20φ: C8○D4/C2×C8 → C2 ⊆ Aut C10160C10.28(C8oD4)320,315
C10.29(C8○D4) = D10.5C42φ: C8○D4/C2×C8 → C2 ⊆ Aut C10160C10.29(C8oD4)320,316
C10.30(C8○D4) = C42.243D10φ: C8○D4/C2×C8 → C2 ⊆ Aut C10160C10.30(C8oD4)320,317
C10.31(C8○D4) = C40⋊8C4⋊C2φ: C8○D4/C2×C8 → C2 ⊆ Aut C10160C10.31(C8oD4)320,347
C10.32(C8○D4) = C22⋊C8⋊D5φ: C8○D4/C2×C8 → C2 ⊆ Aut C10160C10.32(C8oD4)320,354
C10.33(C8○D4) = D10⋊4M4(2)φ: C8○D4/C2×C8 → C2 ⊆ Aut C10160C10.33(C8oD4)320,355
C10.34(C8○D4) = Dic5⋊2M4(2)φ: C8○D4/C2×C8 → C2 ⊆ Aut C10160C10.34(C8oD4)320,356
C10.35(C8○D4) = Dic5.5M4(2)φ: C8○D4/C2×C8 → C2 ⊆ Aut C10320C10.35(C8oD4)320,455
C10.36(C8○D4) = D10⋊5M4(2)φ: C8○D4/C2×C8 → C2 ⊆ Aut C10160C10.36(C8oD4)320,463
C10.37(C8○D4) = C42.30D10φ: C8○D4/C2×C8 → C2 ⊆ Aut C10160C10.37(C8oD4)320,466
C10.38(C8○D4) = C42.31D10φ: C8○D4/C2×C8 → C2 ⊆ Aut C10160C10.38(C8oD4)320,467
C10.39(C8○D4) = C20.42C42φ: C8○D4/C2×C8 → C2 ⊆ Aut C10160C10.39(C8oD4)320,728
C10.40(C8○D4) = C20.65(C4⋊C4)φ: C8○D4/C2×C8 → C2 ⊆ Aut C10160C10.40(C8oD4)320,729
C10.41(C8○D4) = C8×C5⋊D4φ: C8○D4/C2×C8 → C2 ⊆ Aut C10160C10.41(C8oD4)320,736
C10.42(C8○D4) = (C22×C8)⋊D5φ: C8○D4/C2×C8 → C2 ⊆ Aut C10160C10.42(C8oD4)320,737
C10.43(C8○D4) = C40⋊32D4φ: C8○D4/C2×C8 → C2 ⊆ Aut C10160C10.43(C8oD4)320,738
C10.44(C8○D4) = C40⋊Q8φ: C8○D4/M4(2) → C2 ⊆ Aut C10320C10.44(C8oD4)320,328
C10.45(C8○D4) = C8⋊9D20φ: C8○D4/M4(2) → C2 ⊆ Aut C10160C10.45(C8oD4)320,333
C10.46(C8○D4) = D10.7C42φ: C8○D4/M4(2) → C2 ⊆ Aut C10160C10.46(C8oD4)320,335
C10.47(C8○D4) = C42.185D10φ: C8○D4/M4(2) → C2 ⊆ Aut C10160C10.47(C8oD4)320,336
C10.48(C8○D4) = C5⋊5(C8×D4)φ: C8○D4/M4(2) → C2 ⊆ Aut C10160C10.48(C8oD4)320,352
C10.49(C8○D4) = C5⋊2C8⋊26D4φ: C8○D4/M4(2) → C2 ⊆ Aut C10160C10.49(C8oD4)320,357
C10.50(C8○D4) = Dic10⋊5C8φ: C8○D4/M4(2) → C2 ⊆ Aut C10320C10.50(C8oD4)320,457
C10.51(C8○D4) = C42.198D10φ: C8○D4/M4(2) → C2 ⊆ Aut C10320C10.51(C8oD4)320,458
C10.52(C8○D4) = D20⋊5C8φ: C8○D4/M4(2) → C2 ⊆ Aut C10160C10.52(C8oD4)320,461
C10.53(C8○D4) = C20⋊6M4(2)φ: C8○D4/M4(2) → C2 ⊆ Aut C10160C10.53(C8oD4)320,465
C10.54(C8○D4) = C20.51(C4⋊C4)φ: C8○D4/M4(2) → C2 ⊆ Aut C10160C10.54(C8oD4)320,746
C10.55(C8○D4) = C20.37C42φ: C8○D4/M4(2) → C2 ⊆ Aut C10160C10.55(C8oD4)320,749
C10.56(C8○D4) = C40⋊D4φ: C8○D4/M4(2) → C2 ⊆ Aut C10160C10.56(C8oD4)320,754
C10.57(C8○D4) = C40⋊18D4φ: C8○D4/M4(2) → C2 ⊆ Aut C10160C10.57(C8oD4)320,755
C10.58(C8○D4) = C4.89(C2×D20)φ: C8○D4/M4(2) → C2 ⊆ Aut C10160C10.58(C8oD4)320,756
C10.59(C8○D4) = C20.35C42φ: C8○D4/C4○D4 → C2 ⊆ Aut C10160C10.59(C8oD4)320,624
C10.60(C8○D4) = C42.43D10φ: C8○D4/C4○D4 → C2 ⊆ Aut C10160C10.60(C8oD4)320,626
C10.61(C8○D4) = C42.187D10φ: C8○D4/C4○D4 → C2 ⊆ Aut C10160C10.61(C8oD4)320,627
C10.62(C8○D4) = D4×C5⋊2C8φ: C8○D4/C4○D4 → C2 ⊆ Aut C10160C10.62(C8oD4)320,637
C10.63(C8○D4) = C42.47D10φ: C8○D4/C4○D4 → C2 ⊆ Aut C10160C10.63(C8oD4)320,638
C10.64(C8○D4) = C20⋊7M4(2)φ: C8○D4/C4○D4 → C2 ⊆ Aut C10160C10.64(C8oD4)320,639
C10.65(C8○D4) = Q8×C5⋊2C8φ: C8○D4/C4○D4 → C2 ⊆ Aut C10320C10.65(C8oD4)320,650
C10.66(C8○D4) = C42.210D10φ: C8○D4/C4○D4 → C2 ⊆ Aut C10320C10.66(C8oD4)320,651
C10.67(C8○D4) = (D4×C10).24C4φ: C8○D4/C4○D4 → C2 ⊆ Aut C10160C10.67(C8oD4)320,861
C10.68(C8○D4) = C5×C8○2M4(2)central extension (φ=1)160C10.68(C8oD4)320,906
C10.69(C8○D4) = C5×(C22×C8)⋊C2central extension (φ=1)160C10.69(C8oD4)320,909
C10.70(C8○D4) = C5×C42.6C22central extension (φ=1)160C10.70(C8oD4)320,925
C10.71(C8○D4) = C5×C42.7C22central extension (φ=1)160C10.71(C8oD4)320,934
C10.72(C8○D4) = D4×C40central extension (φ=1)160C10.72(C8oD4)320,935
C10.73(C8○D4) = C5×C8⋊9D4central extension (φ=1)160C10.73(C8oD4)320,936
C10.74(C8○D4) = C5×C8⋊6D4central extension (φ=1)160C10.74(C8oD4)320,937
C10.75(C8○D4) = Q8×C40central extension (φ=1)320C10.75(C8oD4)320,946
C10.76(C8○D4) = C5×C8⋊4Q8central extension (φ=1)320C10.76(C8oD4)320,947

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