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Extensions 1→N→G→Q→1 with N=C2×C10 and Q=C3⋊D4

Direct product G=N×Q with N=C2×C10 and Q=C3⋊D4
dρLabelID
C2×C10×C3⋊D4240C2xC10xC3:D4480,1164

Semidirect products G=N:Q with N=C2×C10 and Q=C3⋊D4
extensionφ:Q→Aut NdρLabelID
(C2×C10)⋊1(C3⋊D4) = D10⋊S4φ: C3⋊D4/C2 → D6 ⊆ Aut C2×C10606(C2xC10):1(C3:D4)480,980
(C2×C10)⋊2(C3⋊D4) = A4⋊D20φ: C3⋊D4/C2 → D6 ⊆ Aut C2×C10606+(C2xC10):2(C3:D4)480,981
(C2×C10)⋊3(C3⋊D4) = C5×A4⋊D4φ: C3⋊D4/C22 → S3 ⊆ Aut C2×C10606(C2xC10):3(C3:D4)480,1023
(C2×C10)⋊4(C3⋊D4) = C24⋊2D15φ: C3⋊D4/C22 → S3 ⊆ Aut C2×C10606(C2xC10):4(C3:D4)480,1034
(C2×C10)⋊5(C3⋊D4) = (C2×C30)⋊D4φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C10120(C2xC10):5(C3:D4)480,639
(C2×C10)⋊6(C3⋊D4) = (C2×C6)⋊8D20φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C10120(C2xC10):6(C3:D4)480,640
(C2×C10)⋊7(C3⋊D4) = Dic15⋊18D4φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C10240(C2xC10):7(C3:D4)480,647
(C2×C10)⋊8(C3⋊D4) = D30⋊18D4φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C10120(C2xC10):8(C3:D4)480,648
(C2×C10)⋊9(C3⋊D4) = D30⋊17D4φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C10120(C2xC10):9(C3:D4)480,902
(C2×C10)⋊10(C3⋊D4) = Dic15⋊12D4φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C10240(C2xC10):10(C3:D4)480,904
(C2×C10)⋊11(C3⋊D4) = C5×C23.14D6φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2×C10240(C2xC10):11(C3:D4)480,818
(C2×C10)⋊12(C3⋊D4) = (C2×C6)⋊D20φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2×C10240(C2xC10):12(C3:D4)480,645
(C2×C10)⋊13(C3⋊D4) = C22×C3⋊D20φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2×C10240(C2xC10):13(C3:D4)480,1119
(C2×C10)⋊14(C3⋊D4) = C5×C23⋊2D6φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C10120(C2xC10):14(C3:D4)480,816
(C2×C10)⋊15(C3⋊D4) = C15⋊C22≀C2φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C10120(C2xC10):15(C3:D4)480,644
(C2×C10)⋊16(C3⋊D4) = C22×C15⋊D4φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C10240(C2xC10):16(C3:D4)480,1118
(C2×C10)⋊17(C3⋊D4) = C5×C24⋊4S3φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C10120(C2xC10):17(C3:D4)480,832
(C2×C10)⋊18(C3⋊D4) = C24⋊5D15φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C10120(C2xC10):18(C3:D4)480,918
(C2×C10)⋊19(C3⋊D4) = C22×C15⋊7D4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10):19(C3:D4)480,1179

Non-split extensions G=N.Q with N=C2×C10 and Q=C3⋊D4
extensionφ:Q→Aut NdρLabelID
(C2×C10).1(C3⋊D4) = C60.96D4φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C101204(C2xC10).1(C3:D4)480,52
(C2×C10).2(C3⋊D4) = C60.99D4φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C101204(C2xC10).2(C3:D4)480,55
(C2×C10).3(C3⋊D4) = D60⋊16C4φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C101204(C2xC10).3(C3:D4)480,57
(C2×C10).4(C3⋊D4) = C15⋊8(C23⋊C4)φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C101204(C2xC10).4(C3:D4)480,72
(C2×C10).5(C3⋊D4) = C15⋊9(C23⋊C4)φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C101204(C2xC10).5(C3:D4)480,73
(C2×C10).6(C3⋊D4) = C23.7D30φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C101204(C2xC10).6(C3:D4)480,194
(C2×C10).7(C3⋊D4) = Q8⋊3Dic15φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C101204(C2xC10).7(C3:D4)480,197
(C2×C10).8(C3⋊D4) = D20.34D6φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C102404(C2xC10).8(C3:D4)480,373
(C2×C10).9(C3⋊D4) = C60.36D4φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C101204(C2xC10).9(C3:D4)480,374
(C2×C10).10(C3⋊D4) = D20⋊19D6φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C101204+(C2xC10).10(C3:D4)480,377
(C2×C10).11(C3⋊D4) = D12.37D10φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C102404(C2xC10).11(C3:D4)480,385
(C2×C10).12(C3⋊D4) = D60⋊30C22φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C101204(C2xC10).12(C3:D4)480,388
(C2×C10).13(C3⋊D4) = C60.63D4φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C102404-(C2xC10).13(C3:D4)480,389
(C2×C10).14(C3⋊D4) = C12.D20φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C102404(C2xC10).14(C3:D4)480,391
(C2×C10).15(C3⋊D4) = C6.(C2×D20)φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C10240(C2xC10).15(C3:D4)480,613
(C2×C10).16(C3⋊D4) = C30.(C2×D4)φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C10240(C2xC10).16(C3:D4)480,615
(C2×C10).17(C3⋊D4) = C6.D4⋊D5φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C10240(C2xC10).17(C3:D4)480,622
(C2×C10).18(C3⋊D4) = C23.22D30φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C10240(C2xC10).18(C3:D4)480,900
(C2×C10).19(C3⋊D4) = D4⋊D30φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C101204+(C2xC10).19(C3:D4)480,914
(C2×C10).20(C3⋊D4) = D4.8D30φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C102404(C2xC10).20(C3:D4)480,915
(C2×C10).21(C3⋊D4) = D4.9D30φ: C3⋊D4/C6 → C22 ⊆ Aut C2×C102404-(C2xC10).21(C3:D4)480,916
(C2×C10).22(C3⋊D4) = C5×Q8.13D6φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2×C102404(C2xC10).22(C3:D4)480,829
(C2×C10).23(C3⋊D4) = C6.D40φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2×C10240(C2xC10).23(C3:D4)480,41
(C2×C10).24(C3⋊D4) = D60⋊12C4φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2×C10240(C2xC10).24(C3:D4)480,44
(C2×C10).25(C3⋊D4) = C6.Dic20φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2×C10480(C2xC10).25(C3:D4)480,47
(C2×C10).26(C3⋊D4) = Dic30⋊12C4φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2×C10480(C2xC10).26(C3:D4)480,50
(C2×C10).27(C3⋊D4) = C60.Q8φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2×C10480(C2xC10).27(C3:D4)480,63
(C2×C10).28(C3⋊D4) = C60.5Q8φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2×C10480(C2xC10).28(C3:D4)480,66
(C2×C10).29(C3⋊D4) = C30.24C42φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2×C10480(C2xC10).29(C3:D4)480,70
(C2×C10).30(C3⋊D4) = C2×C3⋊D40φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2×C10240(C2xC10).30(C3:D4)480,376
(C2×C10).31(C3⋊D4) = C2×C6.D20φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2×C10240(C2xC10).31(C3:D4)480,386
(C2×C10).32(C3⋊D4) = D20.31D6φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2×C102404(C2xC10).32(C3:D4)480,387
(C2×C10).33(C3⋊D4) = C2×C15⋊SD16φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2×C10240(C2xC10).33(C3:D4)480,390
(C2×C10).34(C3⋊D4) = C2×C3⋊Dic20φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2×C10480(C2xC10).34(C3:D4)480,395
(C2×C10).35(C3⋊D4) = C2×D10⋊Dic3φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2×C10240(C2xC10).35(C3:D4)480,611
(C2×C10).36(C3⋊D4) = C2×D30⋊4C4φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2×C10240(C2xC10).36(C3:D4)480,616
(C2×C10).37(C3⋊D4) = C2×C6.Dic10φ: C3⋊D4/Dic3 → C2 ⊆ Aut C2×C10480(C2xC10).37(C3:D4)480,621
(C2×C10).38(C3⋊D4) = C5×C23.7D6φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C101204(C2xC10).38(C3:D4)480,153
(C2×C10).39(C3⋊D4) = C5×Q8⋊3Dic3φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C101204(C2xC10).39(C3:D4)480,156
(C2×C10).40(C3⋊D4) = C5×C23.23D6φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C10240(C2xC10).40(C3:D4)480,814
(C2×C10).41(C3⋊D4) = C5×D4⋊D6φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C101204(C2xC10).41(C3:D4)480,828
(C2×C10).42(C3⋊D4) = C5×Q8.14D6φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C102404(C2xC10).42(C3:D4)480,830
(C2×C10).43(C3⋊D4) = C30.D8φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C10240(C2xC10).43(C3:D4)480,40
(C2×C10).44(C3⋊D4) = D12⋊Dic5φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C10240(C2xC10).44(C3:D4)480,42
(C2×C10).45(C3⋊D4) = C30.Q16φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C10480(C2xC10).45(C3:D4)480,46
(C2×C10).46(C3⋊D4) = Dic6⋊Dic5φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C10480(C2xC10).46(C3:D4)480,48
(C2×C10).47(C3⋊D4) = C60.97D4φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C101204(C2xC10).47(C3:D4)480,53
(C2×C10).48(C3⋊D4) = C30.SD16φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C10480(C2xC10).48(C3:D4)480,62
(C2×C10).49(C3⋊D4) = C30.20D8φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C10480(C2xC10).49(C3:D4)480,65
(C2×C10).50(C3⋊D4) = (C2×C6).D20φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C101204(C2xC10).50(C3:D4)480,71
(C2×C10).51(C3⋊D4) = C2×C15⋊D8φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C10240(C2xC10).51(C3:D4)480,372
(C2×C10).52(C3⋊D4) = D20⋊21D6φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C101204(C2xC10).52(C3:D4)480,375
(C2×C10).53(C3⋊D4) = C2×C30.D4φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C10240(C2xC10).53(C3:D4)480,382
(C2×C10).54(C3⋊D4) = D20.37D6φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C102404(C2xC10).54(C3:D4)480,383
(C2×C10).55(C3⋊D4) = C2×C20.D6φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C10240(C2xC10).55(C3:D4)480,384
(C2×C10).56(C3⋊D4) = C2×C15⋊Q16φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C10480(C2xC10).56(C3:D4)480,394
(C2×C10).57(C3⋊D4) = (C2×C30).D4φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C10240(C2xC10).57(C3:D4)480,612
(C2×C10).58(C3⋊D4) = C2×D6⋊Dic5φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C10240(C2xC10).58(C3:D4)480,614
(C2×C10).59(C3⋊D4) = C2×Dic15⋊5C4φ: C3⋊D4/D6 → C2 ⊆ Aut C2×C10480(C2xC10).59(C3:D4)480,620
(C2×C10).60(C3⋊D4) = C5×C42⋊4S3φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C101202(C2xC10).60(C3:D4)480,124
(C2×C10).61(C3⋊D4) = C5×C23.6D6φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C101204(C2xC10).61(C3:D4)480,125
(C2×C10).62(C3⋊D4) = C5×C23.28D6φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).62(C3:D4)480,808
(C2×C10).63(C3⋊D4) = C5×D12⋊6C22φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C101204(C2xC10).63(C3:D4)480,811
(C2×C10).64(C3⋊D4) = C5×Q8.11D6φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C102404(C2xC10).64(C3:D4)480,821
(C2×C10).65(C3⋊D4) = D60⋊7C4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C101202(C2xC10).65(C3:D4)480,165
(C2×C10).66(C3⋊D4) = C23.6D30φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C101204(C2xC10).66(C3:D4)480,166
(C2×C10).67(C3⋊D4) = C60.1Q8φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C10480(C2xC10).67(C3:D4)480,167
(C2×C10).68(C3⋊D4) = C60.2Q8φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C10480(C2xC10).68(C3:D4)480,168
(C2×C10).69(C3⋊D4) = D60⋊9C4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).69(C3:D4)480,169
(C2×C10).70(C3⋊D4) = Dic30⋊9C4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C10480(C2xC10).70(C3:D4)480,170
(C2×C10).71(C3⋊D4) = C30.29C42φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C10480(C2xC10).71(C3:D4)480,191
(C2×C10).72(C3⋊D4) = D4⋊Dic15φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).72(C3:D4)480,192
(C2×C10).73(C3⋊D4) = Q8⋊2Dic15φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C10480(C2xC10).73(C3:D4)480,195
(C2×C10).74(C3⋊D4) = C2×C30.4Q8φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C10480(C2xC10).74(C3:D4)480,888
(C2×C10).75(C3⋊D4) = C2×D30⋊3C4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).75(C3:D4)480,892
(C2×C10).76(C3⋊D4) = C23.28D30φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).76(C3:D4)480,894
(C2×C10).77(C3⋊D4) = C2×D4⋊D15φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).77(C3:D4)480,896
(C2×C10).78(C3⋊D4) = D4.D30φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C101204(C2xC10).78(C3:D4)480,897
(C2×C10).79(C3⋊D4) = C2×D4.D15φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).79(C3:D4)480,898
(C2×C10).80(C3⋊D4) = C2×Q8⋊2D15φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).80(C3:D4)480,906
(C2×C10).81(C3⋊D4) = Q8.11D30φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C102404(C2xC10).81(C3:D4)480,907
(C2×C10).82(C3⋊D4) = C2×C15⋊7Q16φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C10480(C2xC10).82(C3:D4)480,908
(C2×C10).83(C3⋊D4) = C2×C30.38D4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C2×C10240(C2xC10).83(C3:D4)480,917
(C2×C10).84(C3⋊D4) = C5×C6.Q16central extension (φ=1)480(C2xC10).84(C3:D4)480,126
(C2×C10).85(C3⋊D4) = C5×C12.Q8central extension (φ=1)480(C2xC10).85(C3:D4)480,127
(C2×C10).86(C3⋊D4) = C5×C6.D8central extension (φ=1)240(C2xC10).86(C3:D4)480,128
(C2×C10).87(C3⋊D4) = C5×C6.SD16central extension (φ=1)480(C2xC10).87(C3:D4)480,129
(C2×C10).88(C3⋊D4) = C5×C6.C42central extension (φ=1)480(C2xC10).88(C3:D4)480,150
(C2×C10).89(C3⋊D4) = C5×D4⋊Dic3central extension (φ=1)240(C2xC10).89(C3:D4)480,151
(C2×C10).90(C3⋊D4) = C5×Q8⋊2Dic3central extension (φ=1)480(C2xC10).90(C3:D4)480,154
(C2×C10).91(C3⋊D4) = C10×Dic3⋊C4central extension (φ=1)480(C2xC10).91(C3:D4)480,802
(C2×C10).92(C3⋊D4) = C10×D6⋊C4central extension (φ=1)240(C2xC10).92(C3:D4)480,806
(C2×C10).93(C3⋊D4) = C10×D4⋊S3central extension (φ=1)240(C2xC10).93(C3:D4)480,810
(C2×C10).94(C3⋊D4) = C10×D4.S3central extension (φ=1)240(C2xC10).94(C3:D4)480,812
(C2×C10).95(C3⋊D4) = C10×Q8⋊2S3central extension (φ=1)240(C2xC10).95(C3:D4)480,820
(C2×C10).96(C3⋊D4) = C10×C3⋊Q16central extension (φ=1)480(C2xC10).96(C3:D4)480,822
(C2×C10).97(C3⋊D4) = C10×C6.D4central extension (φ=1)240(C2xC10).97(C3:D4)480,831

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