Extensions 1→N→G→Q→1 with N=C4 and Q=C2×Dic10

Direct product G=N×Q with N=C4 and Q=C2×Dic10
dρLabelID
C2×C4×Dic10320C2xC4xDic10320,1139

Semidirect products G=N:Q with N=C4 and Q=C2×Dic10
extensionφ:Q→Aut NdρLabelID
C41(C2×Dic10) = D4×Dic10φ: C2×Dic10/Dic10C2 ⊆ Aut C4160C4:1(C2xDic10)320,1209
C42(C2×Dic10) = C2×C20⋊Q8φ: C2×Dic10/C2×Dic5C2 ⊆ Aut C4320C4:2(C2xDic10)320,1169
C43(C2×Dic10) = C2×C202Q8φ: C2×Dic10/C2×C20C2 ⊆ Aut C4320C4:3(C2xDic10)320,1140

Non-split extensions G=N.Q with N=C4 and Q=C2×Dic10
extensionφ:Q→Aut NdρLabelID
C4.1(C2×Dic10) = Dic5.14D8φ: C2×Dic10/Dic10C2 ⊆ Aut C4160C4.1(C2xDic10)320,386
C4.2(C2×Dic10) = D4⋊Dic10φ: C2×Dic10/Dic10C2 ⊆ Aut C4160C4.2(C2xDic10)320,388
C4.3(C2×Dic10) = D4.Dic10φ: C2×Dic10/Dic10C2 ⊆ Aut C4160C4.3(C2xDic10)320,390
C4.4(C2×Dic10) = D4.2Dic10φ: C2×Dic10/Dic10C2 ⊆ Aut C4160C4.4(C2xDic10)320,393
C4.5(C2×Dic10) = Q8⋊Dic10φ: C2×Dic10/Dic10C2 ⊆ Aut C4320C4.5(C2xDic10)320,418
C4.6(C2×Dic10) = Dic5.9Q16φ: C2×Dic10/Dic10C2 ⊆ Aut C4320C4.6(C2xDic10)320,421
C4.7(C2×Dic10) = Q8.Dic10φ: C2×Dic10/Dic10C2 ⊆ Aut C4320C4.7(C2xDic10)320,423
C4.8(C2×Dic10) = Q8.2Dic10φ: C2×Dic10/Dic10C2 ⊆ Aut C4320C4.8(C2xDic10)320,426
C4.9(C2×Dic10) = C20.50D8φ: C2×Dic10/Dic10C2 ⊆ Aut C4160C4.9(C2xDic10)320,634
C4.10(C2×Dic10) = C20.38SD16φ: C2×Dic10/Dic10C2 ⊆ Aut C4160C4.10(C2xDic10)320,635
C4.11(C2×Dic10) = D4.3Dic10φ: C2×Dic10/Dic10C2 ⊆ Aut C4160C4.11(C2xDic10)320,636
C4.12(C2×Dic10) = C20.48SD16φ: C2×Dic10/Dic10C2 ⊆ Aut C4320C4.12(C2xDic10)320,647
C4.13(C2×Dic10) = C20.23Q16φ: C2×Dic10/Dic10C2 ⊆ Aut C4320C4.13(C2xDic10)320,648
C4.14(C2×Dic10) = Q8.3Dic10φ: C2×Dic10/Dic10C2 ⊆ Aut C4320C4.14(C2xDic10)320,649
C4.15(C2×Dic10) = D45Dic10φ: C2×Dic10/Dic10C2 ⊆ Aut C4160C4.15(C2xDic10)320,1211
C4.16(C2×Dic10) = D46Dic10φ: C2×Dic10/Dic10C2 ⊆ Aut C4160C4.16(C2xDic10)320,1215
C4.17(C2×Dic10) = Q8×Dic10φ: C2×Dic10/Dic10C2 ⊆ Aut C4320C4.17(C2xDic10)320,1238
C4.18(C2×Dic10) = Q85Dic10φ: C2×Dic10/Dic10C2 ⊆ Aut C4320C4.18(C2xDic10)320,1241
C4.19(C2×Dic10) = Q86Dic10φ: C2×Dic10/Dic10C2 ⊆ Aut C4320C4.19(C2xDic10)320,1242
C4.20(C2×Dic10) = C405Q8φ: C2×Dic10/C2×Dic5C2 ⊆ Aut C4320C4.20(C2xDic10)320,482
C4.21(C2×Dic10) = C403Q8φ: C2×Dic10/C2×Dic5C2 ⊆ Aut C4320C4.21(C2xDic10)320,483
C4.22(C2×Dic10) = C8.8Dic10φ: C2×Dic10/C2×Dic5C2 ⊆ Aut C4320C4.22(C2xDic10)320,485
C4.23(C2×Dic10) = C402Q8φ: C2×Dic10/C2×Dic5C2 ⊆ Aut C4320C4.23(C2xDic10)320,501
C4.24(C2×Dic10) = C404Q8φ: C2×Dic10/C2×Dic5C2 ⊆ Aut C4320C4.24(C2xDic10)320,503
C4.25(C2×Dic10) = C8.6Dic10φ: C2×Dic10/C2×Dic5C2 ⊆ Aut C4320C4.25(C2xDic10)320,505
C4.26(C2×Dic10) = C2×C10.D8φ: C2×Dic10/C2×Dic5C2 ⊆ Aut C4320C4.26(C2xDic10)320,589
C4.27(C2×Dic10) = C2×C20.Q8φ: C2×Dic10/C2×Dic5C2 ⊆ Aut C4320C4.27(C2xDic10)320,590
C4.28(C2×Dic10) = C20.47(C4⋊C4)φ: C2×Dic10/C2×Dic5C2 ⊆ Aut C4160C4.28(C2xDic10)320,591
C4.29(C2×Dic10) = C20.64(C4⋊C4)φ: C2×Dic10/C2×Dic5C2 ⊆ Aut C4160C4.29(C2xDic10)320,622
C4.30(C2×Dic10) = C20.76(C4⋊C4)φ: C2×Dic10/C2×Dic5C2 ⊆ Aut C4160C4.30(C2xDic10)320,625
C4.31(C2×Dic10) = C2×C4.Dic10φ: C2×Dic10/C2×Dic5C2 ⊆ Aut C4320C4.31(C2xDic10)320,1171
C4.32(C2×Dic10) = C10.12- 1+4φ: C2×Dic10/C2×Dic5C2 ⊆ Aut C4160C4.32(C2xDic10)320,1172
C4.33(C2×Dic10) = C42.88D10φ: C2×Dic10/C2×Dic5C2 ⊆ Aut C4160C4.33(C2xDic10)320,1189
C4.34(C2×Dic10) = C42.90D10φ: C2×Dic10/C2×Dic5C2 ⊆ Aut C4160C4.34(C2xDic10)320,1191
C4.35(C2×Dic10) = C409Q8φ: C2×Dic10/C2×C20C2 ⊆ Aut C4320C4.35(C2xDic10)320,307
C4.36(C2×Dic10) = C408Q8φ: C2×Dic10/C2×C20C2 ⊆ Aut C4320C4.36(C2xDic10)320,309
C4.37(C2×Dic10) = C40.13Q8φ: C2×Dic10/C2×C20C2 ⊆ Aut C4320C4.37(C2xDic10)320,310
C4.38(C2×Dic10) = C8⋊Dic10φ: C2×Dic10/C2×C20C2 ⊆ Aut C4320C4.38(C2xDic10)320,329
C4.39(C2×Dic10) = C2×C406C4φ: C2×Dic10/C2×C20C2 ⊆ Aut C4320C4.39(C2xDic10)320,731
C4.40(C2×Dic10) = C2×C405C4φ: C2×Dic10/C2×C20C2 ⊆ Aut C4320C4.40(C2xDic10)320,732
C4.41(C2×Dic10) = C23.22D20φ: C2×Dic10/C2×C20C2 ⊆ Aut C4160C4.41(C2xDic10)320,733
C4.42(C2×Dic10) = C23.47D20φ: C2×Dic10/C2×C20C2 ⊆ Aut C4160C4.42(C2xDic10)320,748
C4.43(C2×Dic10) = C2×C20.6Q8φ: C2×Dic10/C2×C20C2 ⊆ Aut C4320C4.43(C2xDic10)320,1141
C4.44(C2×Dic10) = C8×Dic10central extension (φ=1)320C4.44(C2xDic10)320,305
C4.45(C2×Dic10) = C4011Q8central extension (φ=1)320C4.45(C2xDic10)320,306
C4.46(C2×Dic10) = C40⋊Q8central extension (φ=1)320C4.46(C2xDic10)320,328
C4.47(C2×Dic10) = C2×C203C8central extension (φ=1)320C4.47(C2xDic10)320,550
C4.48(C2×Dic10) = C2013M4(2)central extension (φ=1)160C4.48(C2xDic10)320,551
C4.49(C2×Dic10) = C42.43D10central extension (φ=1)160C4.49(C2xDic10)320,626
C4.50(C2×Dic10) = C2×C20.8Q8central extension (φ=1)320C4.50(C2xDic10)320,726
C4.51(C2×Dic10) = C20.65(C4⋊C4)central extension (φ=1)160C4.51(C2xDic10)320,729
C4.52(C2×Dic10) = Dic55M4(2)central extension (φ=1)160C4.52(C2xDic10)320,745
C4.53(C2×Dic10) = C20.51(C4⋊C4)central extension (φ=1)160C4.53(C2xDic10)320,746
C4.54(C2×Dic10) = C42.274D10central extension (φ=1)160C4.54(C2xDic10)320,1142

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