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Extensions 1→N→G→Q→1 with N=C3×Dic5 and Q=C2×C4

Direct product G=N×Q with N=C3×Dic5 and Q=C2×C4
dρLabelID
Dic5×C2×C12480Dic5xC2xC12480,715

Semidirect products G=N:Q with N=C3×Dic5 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
(C3×Dic5)⋊1(C2×C4) = S3×C10.D4φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5240(C3xDic5):1(C2xC4)480,475
(C3×Dic5)⋊2(C2×C4) = D30.Q8φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5240(C3xDic5):2(C2xC4)480,480
(C3×Dic5)⋊3(C2×C4) = Dic15⋊14D4φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5240(C3xDic5):3(C2xC4)480,482
(C3×Dic5)⋊4(C2×C4) = C15⋊22(C4×D4)φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5240(C3xDic5):4(C2xC4)480,522
(C3×Dic5)⋊5(C2×C4) = Dic3×C5⋊D4φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5240(C3xDic5):5(C2xC4)480,629
(C3×Dic5)⋊6(C2×C4) = Dic15⋊16D4φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5240(C3xDic5):6(C2xC4)480,635
(C3×Dic5)⋊7(C2×C4) = C4×S3×F5φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5608(C3xDic5):7(C2xC4)480,994
(C3×Dic5)⋊8(C2×C4) = F5×D12φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5608+(C3xDic5):8(C2xC4)480,995
(C3×Dic5)⋊9(C2×C4) = S3×C4⋊F5φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5608(C3xDic5):9(C2xC4)480,996
(C3×Dic5)⋊10(C2×C4) = D60⋊3C4φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5608+(C3xDic5):10(C2xC4)480,997
(C3×Dic5)⋊11(C2×C4) = D4×C3⋊F5φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5608(C3xDic5):11(C2xC4)480,1067
(C3×Dic5)⋊12(C2×C4) = C3×D4×F5φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5608(C3xDic5):12(C2xC4)480,1054
(C3×Dic5)⋊13(C2×C4) = C4×S3×Dic5φ: C2×C4/C4 → C2 ⊆ Out C3×Dic5240(C3xDic5):13(C2xC4)480,473
(C3×Dic5)⋊14(C2×C4) = C4×D30.C2φ: C2×C4/C4 → C2 ⊆ Out C3×Dic5240(C3xDic5):14(C2xC4)480,477
(C3×Dic5)⋊15(C2×C4) = Dic5⋊4D12φ: C2×C4/C4 → C2 ⊆ Out C3×Dic5240(C3xDic5):15(C2xC4)480,481
(C3×Dic5)⋊16(C2×C4) = C4×C5⋊D12φ: C2×C4/C4 → C2 ⊆ Out C3×Dic5240(C3xDic5):16(C2xC4)480,521
(C3×Dic5)⋊17(C2×C4) = C3×Dic5⋊4D4φ: C2×C4/C4 → C2 ⊆ Out C3×Dic5240(C3xDic5):17(C2xC4)480,674
(C3×Dic5)⋊18(C2×C4) = C12×C5⋊D4φ: C2×C4/C4 → C2 ⊆ Out C3×Dic5240(C3xDic5):18(C2xC4)480,721
(C3×Dic5)⋊19(C2×C4) = C4×D5×Dic3φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5240(C3xDic5):19(C2xC4)480,467
(C3×Dic5)⋊20(C2×C4) = D5×C4⋊Dic3φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5240(C3xDic5):20(C2xC4)480,488
(C3×Dic5)⋊21(C2×C4) = C2×Dic3×Dic5φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5480(C3xDic5):21(C2xC4)480,603
(C3×Dic5)⋊22(C2×C4) = C2×C30.Q8φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5480(C3xDic5):22(C2xC4)480,617
(C3×Dic5)⋊23(C2×C4) = C3×D5×C4⋊C4φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5240(C3xDic5):23(C2xC4)480,684
(C3×Dic5)⋊24(C2×C4) = C6×C10.D4φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5480(C3xDic5):24(C2xC4)480,716
(C3×Dic5)⋊25(C2×C4) = C2×C4×C3⋊F5φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5120(C3xDic5):25(C2xC4)480,1063
(C3×Dic5)⋊26(C2×C4) = C2×C60⋊C4φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5120(C3xDic5):26(C2xC4)480,1064
(C3×Dic5)⋊27(C2×C4) = F5×C2×C12φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5120(C3xDic5):27(C2xC4)480,1050
(C3×Dic5)⋊28(C2×C4) = C6×C4⋊F5φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5120(C3xDic5):28(C2xC4)480,1051
(C3×Dic5)⋊29(C2×C4) = D5×C4×C12φ: trivial image240(C3xDic5):29(C2xC4)480,664

Non-split extensions G=N.Q with N=C3×Dic5 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
(C3×Dic5).1(C2×C4) = S3×C8⋊D5φ: C2×C4/C2 → C22 ⊆ Out C3×Dic51204(C3xDic5).1(C2xC4)480,321
(C3×Dic5).2(C2×C4) = C40⋊D6φ: C2×C4/C2 → C22 ⊆ Out C3×Dic51204(C3xDic5).2(C2xC4)480,322
(C3×Dic5).3(C2×C4) = C40.55D6φ: C2×C4/C2 → C22 ⊆ Out C3×Dic52404(C3xDic5).3(C2xC4)480,343
(C3×Dic5).4(C2×C4) = C40.35D6φ: C2×C4/C2 → C22 ⊆ Out C3×Dic52404(C3xDic5).4(C2xC4)480,344
(C3×Dic5).5(C2×C4) = D20.3Dic3φ: C2×C4/C2 → C22 ⊆ Out C3×Dic52404(C3xDic5).5(C2xC4)480,359
(C3×Dic5).6(C2×C4) = D20.2Dic3φ: C2×C4/C2 → C22 ⊆ Out C3×Dic52404(C3xDic5).6(C2xC4)480,360
(C3×Dic5).7(C2×C4) = Dic3⋊5Dic10φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5480(C3xDic5).7(C2xC4)480,400
(C3×Dic5).8(C2×C4) = Dic15⋊5Q8φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5480(C3xDic5).8(C2xC4)480,401
(C3×Dic5).9(C2×C4) = Dic3×Dic10φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5480(C3xDic5).9(C2xC4)480,406
(C3×Dic5).10(C2×C4) = Dic15⋊6Q8φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5480(C3xDic5).10(C2xC4)480,407
(C3×Dic5).11(C2×C4) = (S3×Dic5)⋊C4φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5240(C3xDic5).11(C2xC4)480,476
(C3×Dic5).12(C2×C4) = D30.23(C2×C4)φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5240(C3xDic5).12(C2xC4)480,479
(C3×Dic5).13(C2×C4) = F5×C3⋊C8φ: C2×C4/C2 → C22 ⊆ Out C3×Dic51208(C3xDic5).13(C2xC4)480,223
(C3×Dic5).14(C2×C4) = C30.C42φ: C2×C4/C2 → C22 ⊆ Out C3×Dic51208(C3xDic5).14(C2xC4)480,224
(C3×Dic5).15(C2×C4) = C30.3C42φ: C2×C4/C2 → C22 ⊆ Out C3×Dic51208(C3xDic5).15(C2xC4)480,225
(C3×Dic5).16(C2×C4) = C30.4C42φ: C2×C4/C2 → C22 ⊆ Out C3×Dic51208(C3xDic5).16(C2xC4)480,226
(C3×Dic5).17(C2×C4) = Dic3×C5⋊C8φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5480(C3xDic5).17(C2xC4)480,244
(C3×Dic5).18(C2×C4) = C30.M4(2)φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5480(C3xDic5).18(C2xC4)480,245
(C3×Dic5).19(C2×C4) = F5×Dic6φ: C2×C4/C2 → C22 ⊆ Out C3×Dic51208-(C3xDic5).19(C2xC4)480,982
(C3×Dic5).20(C2×C4) = C4⋊F5⋊3S3φ: C2×C4/C2 → C22 ⊆ Out C3×Dic51208(C3xDic5).20(C2xC4)480,983
(C3×Dic5).21(C2×C4) = Dic6⋊5F5φ: C2×C4/C2 → C22 ⊆ Out C3×Dic51208-(C3xDic5).21(C2xC4)480,984
(C3×Dic5).22(C2×C4) = (C4×S3)⋊F5φ: C2×C4/C2 → C22 ⊆ Out C3×Dic51208(C3xDic5).22(C2xC4)480,985
(C3×Dic5).23(C2×C4) = C2×S3×C5⋊C8φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5240(C3xDic5).23(C2xC4)480,1002
(C3×Dic5).24(C2×C4) = C5⋊C8.D6φ: C2×C4/C2 → C22 ⊆ Out C3×Dic52408(C3xDic5).24(C2xC4)480,1003
(C3×Dic5).25(C2×C4) = S3×C22.F5φ: C2×C4/C2 → C22 ⊆ Out C3×Dic51208-(C3xDic5).25(C2xC4)480,1004
(C3×Dic5).26(C2×C4) = D15⋊C8⋊C2φ: C2×C4/C2 → C22 ⊆ Out C3×Dic52408(C3xDic5).26(C2xC4)480,1005
(C3×Dic5).27(C2×C4) = C2×D15⋊C8φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5240(C3xDic5).27(C2xC4)480,1006
(C3×Dic5).28(C2×C4) = D15⋊2M4(2)φ: C2×C4/C2 → C22 ⊆ Out C3×Dic51208+(C3xDic5).28(C2xC4)480,1007
(C3×Dic5).29(C2×C4) = C2×D6.F5φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5240(C3xDic5).29(C2xC4)480,1008
(C3×Dic5).30(C2×C4) = C2×Dic3.F5φ: C2×C4/C2 → C22 ⊆ Out C3×Dic5240(C3xDic5).30(C2xC4)480,1009
(C3×Dic5).31(C2×C4) = Dic10.Dic3φ: C2×C4/C2 → C22 ⊆ Out C3×Dic52408(C3xDic5).31(C2xC4)480,1066
(C3×Dic5).32(C2×C4) = Q8×C3⋊F5φ: C2×C4/C2 → C22 ⊆ Out C3×Dic51208(C3xDic5).32(C2xC4)480,1069
(C3×Dic5).33(C2×C4) = C3×D4.F5φ: C2×C4/C2 → C22 ⊆ Out C3×Dic52408(C3xDic5).33(C2xC4)480,1053
(C3×Dic5).34(C2×C4) = C3×Q8×F5φ: C2×C4/C2 → C22 ⊆ Out C3×Dic51208(C3xDic5).34(C2xC4)480,1056
(C3×Dic5).35(C2×C4) = S3×C8×D5φ: C2×C4/C4 → C2 ⊆ Out C3×Dic51204(C3xDic5).35(C2xC4)480,319
(C3×Dic5).36(C2×C4) = D5×C8⋊S3φ: C2×C4/C4 → C2 ⊆ Out C3×Dic51204(C3xDic5).36(C2xC4)480,320
(C3×Dic5).37(C2×C4) = C40.54D6φ: C2×C4/C4 → C2 ⊆ Out C3×Dic52404(C3xDic5).37(C2xC4)480,341
(C3×Dic5).38(C2×C4) = C40.34D6φ: C2×C4/C4 → C2 ⊆ Out C3×Dic52404(C3xDic5).38(C2xC4)480,342
(C3×Dic5).39(C2×C4) = Dic5⋊5Dic6φ: C2×C4/C4 → C2 ⊆ Out C3×Dic5480(C3xDic5).39(C2xC4)480,399
(C3×Dic5).40(C2×C4) = D6.(C4×D5)φ: C2×C4/C4 → C2 ⊆ Out C3×Dic5240(C3xDic5).40(C2xC4)480,474
(C3×Dic5).41(C2×C4) = D30.C2⋊C4φ: C2×C4/C4 → C2 ⊆ Out C3×Dic5240(C3xDic5).41(C2xC4)480,478
(C3×Dic5).42(C2×C4) = C4×C15⋊Q8φ: C2×C4/C4 → C2 ⊆ Out C3×Dic5480(C3xDic5).42(C2xC4)480,543
(C3×Dic5).43(C2×C4) = C12×Dic10φ: C2×C4/C4 → C2 ⊆ Out C3×Dic5480(C3xDic5).43(C2xC4)480,661
(C3×Dic5).44(C2×C4) = C3×Dic5⋊3Q8φ: C2×C4/C4 → C2 ⊆ Out C3×Dic5480(C3xDic5).44(C2xC4)480,680
(C3×Dic5).45(C2×C4) = C3×D20.3C4φ: C2×C4/C4 → C2 ⊆ Out C3×Dic52402(C3xDic5).45(C2xC4)480,694
(C3×Dic5).46(C2×C4) = C3×D20.2C4φ: C2×C4/C4 → C2 ⊆ Out C3×Dic52404(C3xDic5).46(C2xC4)480,700
(C3×Dic5).47(C2×C4) = C8×C3⋊F5φ: C2×C4/C4 → C2 ⊆ Out C3×Dic51204(C3xDic5).47(C2xC4)480,296
(C3×Dic5).48(C2×C4) = C24⋊F5φ: C2×C4/C4 → C2 ⊆ Out C3×Dic51204(C3xDic5).48(C2xC4)480,297
(C3×Dic5).49(C2×C4) = C4×C15⋊C8φ: C2×C4/C4 → C2 ⊆ Out C3×Dic5480(C3xDic5).49(C2xC4)480,305
(C3×Dic5).50(C2×C4) = C30.11C42φ: C2×C4/C4 → C2 ⊆ Out C3×Dic5480(C3xDic5).50(C2xC4)480,307
(C3×Dic5).51(C2×C4) = F5×C24φ: C2×C4/C4 → C2 ⊆ Out C3×Dic51204(C3xDic5).51(C2xC4)480,271
(C3×Dic5).52(C2×C4) = C3×C8⋊F5φ: C2×C4/C4 → C2 ⊆ Out C3×Dic51204(C3xDic5).52(C2xC4)480,272
(C3×Dic5).53(C2×C4) = C12×C5⋊C8φ: C2×C4/C4 → C2 ⊆ Out C3×Dic5480(C3xDic5).53(C2xC4)480,280
(C3×Dic5).54(C2×C4) = C3×C10.C42φ: C2×C4/C4 → C2 ⊆ Out C3×Dic5480(C3xDic5).54(C2xC4)480,282
(C3×Dic5).55(C2×C4) = C2×D5×C3⋊C8φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5240(C3xDic5).55(C2xC4)480,357
(C3×Dic5).56(C2×C4) = D5×C4.Dic3φ: C2×C4/C22 → C2 ⊆ Out C3×Dic51204(C3xDic5).56(C2xC4)480,358
(C3×Dic5).57(C2×C4) = C2×C20.32D6φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5240(C3xDic5).57(C2xC4)480,369
(C3×Dic5).58(C2×C4) = (D5×C12)⋊C4φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5240(C3xDic5).58(C2xC4)480,433
(C3×Dic5).59(C2×C4) = (C4×D5)⋊Dic3φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5240(C3xDic5).59(C2xC4)480,434
(C3×Dic5).60(C2×C4) = (C6×Dic5)⋊7C4φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5240(C3xDic5).60(C2xC4)480,604
(C3×Dic5).61(C2×C4) = C3×C42⋊D5φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5240(C3xDic5).61(C2xC4)480,665
(C3×Dic5).62(C2×C4) = C3×C23.11D10φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5240(C3xDic5).62(C2xC4)480,670
(C3×Dic5).63(C2×C4) = C6×C8⋊D5φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5240(C3xDic5).63(C2xC4)480,693
(C3×Dic5).64(C2×C4) = C2×C60.C4φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5240(C3xDic5).64(C2xC4)480,1060
(C3×Dic5).65(C2×C4) = C2×C12.F5φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5240(C3xDic5).65(C2xC4)480,1061
(C3×Dic5).66(C2×C4) = C60.59(C2×C4)φ: C2×C4/C22 → C2 ⊆ Out C3×Dic51204(C3xDic5).66(C2xC4)480,1062
(C3×Dic5).67(C2×C4) = (C2×C12)⋊6F5φ: C2×C4/C22 → C2 ⊆ Out C3×Dic51204(C3xDic5).67(C2xC4)480,1065
(C3×Dic5).68(C2×C4) = C22×C15⋊C8φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5480(C3xDic5).68(C2xC4)480,1070
(C3×Dic5).69(C2×C4) = C2×C15⋊8M4(2)φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5240(C3xDic5).69(C2xC4)480,1071
(C3×Dic5).70(C2×C4) = C6×D5⋊C8φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5240(C3xDic5).70(C2xC4)480,1047
(C3×Dic5).71(C2×C4) = C6×C4.F5φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5240(C3xDic5).71(C2xC4)480,1048
(C3×Dic5).72(C2×C4) = C3×D5⋊M4(2)φ: C2×C4/C22 → C2 ⊆ Out C3×Dic51204(C3xDic5).72(C2xC4)480,1049
(C3×Dic5).73(C2×C4) = C3×D10.C23φ: C2×C4/C22 → C2 ⊆ Out C3×Dic51204(C3xDic5).73(C2xC4)480,1052
(C3×Dic5).74(C2×C4) = C2×C6×C5⋊C8φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5480(C3xDic5).74(C2xC4)480,1057
(C3×Dic5).75(C2×C4) = C6×C22.F5φ: C2×C4/C22 → C2 ⊆ Out C3×Dic5240(C3xDic5).75(C2xC4)480,1058
(C3×Dic5).76(C2×C4) = C3×C4⋊C4⋊7D5φ: trivial image240(C3xDic5).76(C2xC4)480,685
(C3×Dic5).77(C2×C4) = D5×C2×C24φ: trivial image240(C3xDic5).77(C2xC4)480,692
(C3×Dic5).78(C2×C4) = C3×D5×M4(2)φ: trivial image1204(C3xDic5).78(C2xC4)480,699

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