# Extensions 1→N→G→Q→1 with N=C2×C10 and Q=C2×Dic3

Direct product G=N×Q with N=C2×C10 and Q=C2×Dic3
dρLabelID
Dic3×C22×C10480Dic3xC2^2xC10480,1163

Semidirect products G=N:Q with N=C2×C10 and Q=C2×Dic3
extensionφ:Q→Aut NdρLabelID
(C2×C10)⋊1(C2×Dic3) = C2×A4⋊F5φ: C2×Dic3/C2Dic3 ⊆ Aut C2×C103012+(C2xC10):1(C2xDic3)480,1191
(C2×C10)⋊2(C2×Dic3) = D5×A4⋊C4φ: C2×Dic3/C2D6 ⊆ Aut C2×C10606(C2xC10):2(C2xDic3)480,979
(C2×C10)⋊3(C2×Dic3) = D4×C3⋊F5φ: C2×Dic3/C3C2×C4 ⊆ Aut C2×C10608(C2xC10):3(C2xDic3)480,1067
(C2×C10)⋊4(C2×Dic3) = C10×A4⋊C4φ: C2×Dic3/C22S3 ⊆ Aut C2×C10120(C2xC10):4(C2xDic3)480,1022
(C2×C10)⋊5(C2×Dic3) = C2×A4⋊Dic5φ: C2×Dic3/C22S3 ⊆ Aut C2×C10120(C2xC10):5(C2xDic3)480,1033
(C2×C10)⋊6(C2×Dic3) = C2×D10.D6φ: C2×Dic3/C6C4 ⊆ Aut C2×C10120(C2xC10):6(C2xDic3)480,1072
(C2×C10)⋊7(C2×Dic3) = C23×C3⋊F5φ: C2×Dic3/C6C4 ⊆ Aut C2×C10120(C2xC10):7(C2xDic3)480,1206
(C2×C10)⋊8(C2×Dic3) = D5×C6.D4φ: C2×Dic3/C6C22 ⊆ Aut C2×C10120(C2xC10):8(C2xDic3)480,623
(C2×C10)⋊9(C2×Dic3) = Dic1516D4φ: C2×Dic3/C6C22 ⊆ Aut C2×C10240(C2xC10):9(C2xDic3)480,635
(C2×C10)⋊10(C2×Dic3) = D4×Dic15φ: C2×Dic3/C6C22 ⊆ Aut C2×C10240(C2xC10):10(C2xDic3)480,899
(C2×C10)⋊11(C2×Dic3) = C5×D4×Dic3φ: C2×Dic3/Dic3C2 ⊆ Aut C2×C10240(C2xC10):11(C2xDic3)480,813
(C2×C10)⋊12(C2×Dic3) = Dic3×C5⋊D4φ: C2×Dic3/Dic3C2 ⊆ Aut C2×C10240(C2xC10):12(C2xDic3)480,629
(C2×C10)⋊13(C2×Dic3) = C22×D5×Dic3φ: C2×Dic3/Dic3C2 ⊆ Aut C2×C10240(C2xC10):13(C2xDic3)480,1112
(C2×C10)⋊14(C2×Dic3) = C10×C6.D4φ: C2×Dic3/C2×C6C2 ⊆ Aut C2×C10240(C2xC10):14(C2xDic3)480,831
(C2×C10)⋊15(C2×Dic3) = C2×C30.38D4φ: C2×Dic3/C2×C6C2 ⊆ Aut C2×C10240(C2xC10):15(C2xDic3)480,917
(C2×C10)⋊16(C2×Dic3) = C23×Dic15φ: C2×Dic3/C2×C6C2 ⊆ Aut C2×C10480(C2xC10):16(C2xDic3)480,1178

Non-split extensions G=N.Q with N=C2×C10 and Q=C2×Dic3
extensionφ:Q→Aut NdρLabelID
(C2×C10).(C2×Dic3) = Dic10.Dic3φ: C2×Dic3/C3C2×C4 ⊆ Aut C2×C102408(C2xC10).(C2xDic3)480,1066
(C2×C10).2(C2×Dic3) = (C2×C60)⋊C4φ: C2×Dic3/C6C4 ⊆ Aut C2×C101204(C2xC10).2(C2xDic3)480,304
(C2×C10).3(C2×Dic3) = C4×C15⋊C8φ: C2×Dic3/C6C4 ⊆ Aut C2×C10480(C2xC10).3(C2xDic3)480,305
(C2×C10).4(C2×Dic3) = C60⋊C8φ: C2×Dic3/C6C4 ⊆ Aut C2×C10480(C2xC10).4(C2xDic3)480,306
(C2×C10).5(C2×Dic3) = C30.11C42φ: C2×Dic3/C6C4 ⊆ Aut C2×C10480(C2xC10).5(C2xDic3)480,307
(C2×C10).6(C2×Dic3) = C30.7M4(2)φ: C2×Dic3/C6C4 ⊆ Aut C2×C10240(C2xC10).6(C2xDic3)480,308
(C2×C10).7(C2×Dic3) = Dic5.13D12φ: C2×Dic3/C6C4 ⊆ Aut C2×C10480(C2xC10).7(C2xDic3)480,309
(C2×C10).8(C2×Dic3) = (C2×C60).C4φ: C2×Dic3/C6C4 ⊆ Aut C2×C102404(C2xC10).8(C2xDic3)480,310
(C2×C10).9(C2×Dic3) = D10.10D12φ: C2×Dic3/C6C4 ⊆ Aut C2×C10120(C2xC10).9(C2xDic3)480,311
(C2×C10).10(C2×Dic3) = C3⋊(C23⋊F5)φ: C2×Dic3/C6C4 ⊆ Aut C2×C101204(C2xC10).10(C2xDic3)480,316
(C2×C10).11(C2×Dic3) = C30.22M4(2)φ: C2×Dic3/C6C4 ⊆ Aut C2×C10240(C2xC10).11(C2xDic3)480,317
(C2×C10).12(C2×Dic3) = C5⋊(C12.D4)φ: C2×Dic3/C6C4 ⊆ Aut C2×C101204(C2xC10).12(C2xDic3)480,318
(C2×C10).13(C2×Dic3) = C2×C60.C4φ: C2×Dic3/C6C4 ⊆ Aut C2×C10240(C2xC10).13(C2xDic3)480,1060
(C2×C10).14(C2×Dic3) = C2×C12.F5φ: C2×Dic3/C6C4 ⊆ Aut C2×C10240(C2xC10).14(C2xDic3)480,1061
(C2×C10).15(C2×Dic3) = C60.59(C2×C4)φ: C2×Dic3/C6C4 ⊆ Aut C2×C101204(C2xC10).15(C2xDic3)480,1062
(C2×C10).16(C2×Dic3) = C2×C4×C3⋊F5φ: C2×Dic3/C6C4 ⊆ Aut C2×C10120(C2xC10).16(C2xDic3)480,1063
(C2×C10).17(C2×Dic3) = C2×C60⋊C4φ: C2×Dic3/C6C4 ⊆ Aut C2×C10120(C2xC10).17(C2xDic3)480,1064
(C2×C10).18(C2×Dic3) = (C2×C12)⋊6F5φ: C2×Dic3/C6C4 ⊆ Aut C2×C101204(C2xC10).18(C2xDic3)480,1065
(C2×C10).19(C2×Dic3) = C22×C15⋊C8φ: C2×Dic3/C6C4 ⊆ Aut C2×C10480(C2xC10).19(C2xDic3)480,1070
(C2×C10).20(C2×Dic3) = C2×C158M4(2)φ: C2×Dic3/C6C4 ⊆ Aut C2×C10240(C2xC10).20(C2xDic3)480,1071
(C2×C10).21(C2×Dic3) = C60.28D4φ: C2×Dic3/C6C22 ⊆ Aut C2×C101204(C2xC10).21(C2xDic3)480,34
(C2×C10).22(C2×Dic3) = C12.6D20φ: C2×Dic3/C6C22 ⊆ Aut C2×C102404(C2xC10).22(C2xDic3)480,37
(C2×C10).23(C2×Dic3) = (C2×C6).D20φ: C2×Dic3/C6C22 ⊆ Aut C2×C101204(C2xC10).23(C2xDic3)480,71
(C2×C10).24(C2×Dic3) = D5×C4.Dic3φ: C2×Dic3/C6C22 ⊆ Aut C2×C101204(C2xC10).24(C2xDic3)480,358
(C2×C10).25(C2×Dic3) = D20.2Dic3φ: C2×Dic3/C6C22 ⊆ Aut C2×C102404(C2xC10).25(C2xDic3)480,360
(C2×C10).26(C2×Dic3) = (C6×Dic5)⋊7C4φ: C2×Dic3/C6C22 ⊆ Aut C2×C10240(C2xC10).26(C2xDic3)480,604
(C2×C10).27(C2×Dic3) = D4.Dic15φ: C2×Dic3/C6C22 ⊆ Aut C2×C102404(C2xC10).27(C2xDic3)480,913
(C2×C10).28(C2×Dic3) = C5×D4.Dic3φ: C2×Dic3/Dic3C2 ⊆ Aut C2×C102404(C2xC10).28(C2xDic3)480,827
(C2×C10).29(C2×Dic3) = Dic5×C3⋊C8φ: C2×Dic3/Dic3C2 ⊆ Aut C2×C10480(C2xC10).29(C2xDic3)480,25
(C2×C10).30(C2×Dic3) = C30.21C42φ: C2×Dic3/Dic3C2 ⊆ Aut C2×C10480(C2xC10).30(C2xDic3)480,28
(C2×C10).31(C2×Dic3) = C60.93D4φ: C2×Dic3/Dic3C2 ⊆ Aut C2×C10240(C2xC10).31(C2xDic3)480,31
(C2×C10).32(C2×Dic3) = C60.13Q8φ: C2×Dic3/Dic3C2 ⊆ Aut C2×C10480(C2xC10).32(C2xDic3)480,58
(C2×C10).33(C2×Dic3) = C30.24C42φ: C2×Dic3/Dic3C2 ⊆ Aut C2×C10480(C2xC10).33(C2xDic3)480,70
(C2×C10).34(C2×Dic3) = C2×D5×C3⋊C8φ: C2×Dic3/Dic3C2 ⊆ Aut C2×C10240(C2xC10).34(C2xDic3)480,357
(C2×C10).35(C2×Dic3) = D20.3Dic3φ: C2×Dic3/Dic3C2 ⊆ Aut C2×C102404(C2xC10).35(C2xDic3)480,359
(C2×C10).36(C2×Dic3) = C2×C20.32D6φ: C2×Dic3/Dic3C2 ⊆ Aut C2×C10240(C2xC10).36(C2xDic3)480,369
(C2×C10).37(C2×Dic3) = C2×Dic3×Dic5φ: C2×Dic3/Dic3C2 ⊆ Aut C2×C10480(C2xC10).37(C2xDic3)480,603
(C2×C10).38(C2×Dic3) = C2×D10⋊Dic3φ: C2×Dic3/Dic3C2 ⊆ Aut C2×C10240(C2xC10).38(C2xDic3)480,611
(C2×C10).39(C2×Dic3) = C2×C30.Q8φ: C2×Dic3/Dic3C2 ⊆ Aut C2×C10480(C2xC10).39(C2xDic3)480,617
(C2×C10).40(C2×Dic3) = C5×C12.D4φ: C2×Dic3/C2×C6C2 ⊆ Aut C2×C101204(C2xC10).40(C2xDic3)480,152
(C2×C10).41(C2×Dic3) = C5×C23.7D6φ: C2×Dic3/C2×C6C2 ⊆ Aut C2×C101204(C2xC10).41(C2xDic3)480,153
(C2×C10).42(C2×Dic3) = C5×C12.10D4φ: C2×Dic3/C2×C6C2 ⊆ Aut C2×C102404(C2xC10).42(C2xDic3)480,155
(C2×C10).43(C2×Dic3) = C10×C4.Dic3φ: C2×Dic3/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).43(C2xDic3)480,800
(C2×C10).44(C2×Dic3) = C5×C23.26D6φ: C2×Dic3/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).44(C2xDic3)480,805
(C2×C10).45(C2×Dic3) = C4×C153C8φ: C2×Dic3/C2×C6C2 ⊆ Aut C2×C10480(C2xC10).45(C2xDic3)480,162
(C2×C10).46(C2×Dic3) = C42.D15φ: C2×Dic3/C2×C6C2 ⊆ Aut C2×C10480(C2xC10).46(C2xDic3)480,163
(C2×C10).47(C2×Dic3) = C605C8φ: C2×Dic3/C2×C6C2 ⊆ Aut C2×C10480(C2xC10).47(C2xDic3)480,164
(C2×C10).48(C2×Dic3) = C60.212D4φ: C2×Dic3/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).48(C2xDic3)480,190
(C2×C10).49(C2×Dic3) = C30.29C42φ: C2×Dic3/C2×C6C2 ⊆ Aut C2×C10480(C2xC10).49(C2xDic3)480,191
(C2×C10).50(C2×Dic3) = C60.8D4φ: C2×Dic3/C2×C6C2 ⊆ Aut C2×C101204(C2xC10).50(C2xDic3)480,193
(C2×C10).51(C2×Dic3) = C23.7D30φ: C2×Dic3/C2×C6C2 ⊆ Aut C2×C101204(C2xC10).51(C2xDic3)480,194
(C2×C10).52(C2×Dic3) = C60.10D4φ: C2×Dic3/C2×C6C2 ⊆ Aut C2×C102404(C2xC10).52(C2xDic3)480,196
(C2×C10).53(C2×Dic3) = C22×C153C8φ: C2×Dic3/C2×C6C2 ⊆ Aut C2×C10480(C2xC10).53(C2xDic3)480,885
(C2×C10).54(C2×Dic3) = C2×C60.7C4φ: C2×Dic3/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).54(C2xDic3)480,886
(C2×C10).55(C2×Dic3) = C2×C4×Dic15φ: C2×Dic3/C2×C6C2 ⊆ Aut C2×C10480(C2xC10).55(C2xDic3)480,887
(C2×C10).56(C2×Dic3) = C2×C605C4φ: C2×Dic3/C2×C6C2 ⊆ Aut C2×C10480(C2xC10).56(C2xDic3)480,890
(C2×C10).57(C2×Dic3) = C23.26D30φ: C2×Dic3/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).57(C2xDic3)480,891
(C2×C10).58(C2×Dic3) = C20×C3⋊C8central extension (φ=1)480(C2xC10).58(C2xDic3)480,121
(C2×C10).59(C2×Dic3) = C5×C42.S3central extension (φ=1)480(C2xC10).59(C2xDic3)480,122
(C2×C10).60(C2×Dic3) = C5×C12⋊C8central extension (φ=1)480(C2xC10).60(C2xDic3)480,123
(C2×C10).61(C2×Dic3) = C5×C12.55D4central extension (φ=1)240(C2xC10).61(C2xDic3)480,149
(C2×C10).62(C2×Dic3) = C5×C6.C42central extension (φ=1)480(C2xC10).62(C2xDic3)480,150
(C2×C10).63(C2×Dic3) = C2×C10×C3⋊C8central extension (φ=1)480(C2xC10).63(C2xDic3)480,799
(C2×C10).64(C2×Dic3) = Dic3×C2×C20central extension (φ=1)480(C2xC10).64(C2xDic3)480,801
(C2×C10).65(C2×Dic3) = C10×C4⋊Dic3central extension (φ=1)480(C2xC10).65(C2xDic3)480,804

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