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Extensions 1→N→G→Q→1 with N=C6×D5 and Q=C2×C4

Direct product G=N×Q with N=C6×D5 and Q=C2×C4
dρLabelID
D5×C22×C12240D5xC2^2xC12480,1136

Semidirect products G=N:Q with N=C6×D5 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
(C6×D5)⋊1(C2×C4) = Dic3⋊4D20φ: C2×C4/C2 → C22 ⊆ Out C6×D5240(C6xD5):1(C2xC4)480,471
(C6×D5)⋊2(C2×C4) = Dic15⋊13D4φ: C2×C4/C2 → C22 ⊆ Out C6×D5240(C6xD5):2(C2xC4)480,472
(C6×D5)⋊3(C2×C4) = Dic3×D20φ: C2×C4/C2 → C22 ⊆ Out C6×D5240(C6xD5):3(C2xC4)480,501
(C6×D5)⋊4(C2×C4) = D20⋊8Dic3φ: C2×C4/C2 → C22 ⊆ Out C6×D5240(C6xD5):4(C2xC4)480,510
(C6×D5)⋊5(C2×C4) = C15⋊17(C4×D4)φ: C2×C4/C2 → C22 ⊆ Out C6×D5240(C6xD5):5(C2xC4)480,517
(C6×D5)⋊6(C2×C4) = Dic15⋊9D4φ: C2×C4/C2 → C22 ⊆ Out C6×D5240(C6xD5):6(C2xC4)480,518
(C6×D5)⋊7(C2×C4) = S3×D10⋊C4φ: C2×C4/C2 → C22 ⊆ Out C6×D5120(C6xD5):7(C2xC4)480,548
(C6×D5)⋊8(C2×C4) = D30.27D4φ: C2×C4/C2 → C22 ⊆ Out C6×D5120(C6xD5):8(C2xC4)480,549
(C6×D5)⋊9(C2×C4) = Dic3×C5⋊D4φ: C2×C4/C2 → C22 ⊆ Out C6×D5240(C6xD5):9(C2xC4)480,629
(C6×D5)⋊10(C2×C4) = Dic15⋊16D4φ: C2×C4/C2 → C22 ⊆ Out C6×D5240(C6xD5):10(C2xC4)480,635
(C6×D5)⋊11(C2×C4) = F5×C3⋊D4φ: C2×C4/C2 → C22 ⊆ Out C6×D5608(C6xD5):11(C2xC4)480,1010
(C6×D5)⋊12(C2×C4) = S3×C22⋊F5φ: C2×C4/C2 → C22 ⊆ Out C6×D5608+(C6xD5):12(C2xC4)480,1011
(C6×D5)⋊13(C2×C4) = C3⋊D4⋊F5φ: C2×C4/C2 → C22 ⊆ Out C6×D5608(C6xD5):13(C2xC4)480,1012
(C6×D5)⋊14(C2×C4) = C22×S3×F5φ: C2×C4/C2 → C22 ⊆ Out C6×D560(C6xD5):14(C2xC4)480,1197
(C6×D5)⋊15(C2×C4) = D4×C3⋊F5φ: C2×C4/C2 → C22 ⊆ Out C6×D5608(C6xD5):15(C2xC4)480,1067
(C6×D5)⋊16(C2×C4) = C3×D4×F5φ: C2×C4/C2 → C22 ⊆ Out C6×D5608(C6xD5):16(C2xC4)480,1054
(C6×D5)⋊17(C2×C4) = C4×C15⋊D4φ: C2×C4/C4 → C2 ⊆ Out C6×D5240(C6xD5):17(C2xC4)480,515
(C6×D5)⋊18(C2×C4) = D6⋊(C4×D5)φ: C2×C4/C4 → C2 ⊆ Out C6×D5240(C6xD5):18(C2xC4)480,516
(C6×D5)⋊19(C2×C4) = C4×C3⋊D20φ: C2×C4/C4 → C2 ⊆ Out C6×D5240(C6xD5):19(C2xC4)480,519
(C6×D5)⋊20(C2×C4) = C15⋊20(C4×D4)φ: C2×C4/C4 → C2 ⊆ Out C6×D5240(C6xD5):20(C2xC4)480,520
(C6×D5)⋊21(C2×C4) = S3×C2×C4×D5φ: C2×C4/C4 → C2 ⊆ Out C6×D5120(C6xD5):21(C2xC4)480,1086
(C6×D5)⋊22(C2×C4) = C12×D20φ: C2×C4/C4 → C2 ⊆ Out C6×D5240(C6xD5):22(C2xC4)480,666
(C6×D5)⋊23(C2×C4) = C3×Dic5⋊4D4φ: C2×C4/C4 → C2 ⊆ Out C6×D5240(C6xD5):23(C2xC4)480,674
(C6×D5)⋊24(C2×C4) = C3×D20⋊8C4φ: C2×C4/C4 → C2 ⊆ Out C6×D5240(C6xD5):24(C2xC4)480,686
(C6×D5)⋊25(C2×C4) = C12×C5⋊D4φ: C2×C4/C4 → C2 ⊆ Out C6×D5240(C6xD5):25(C2xC4)480,721
(C6×D5)⋊26(C2×C4) = C2×D10⋊Dic3φ: C2×C4/C22 → C2 ⊆ Out C6×D5240(C6xD5):26(C2xC4)480,611
(C6×D5)⋊27(C2×C4) = D5×C6.D4φ: C2×C4/C22 → C2 ⊆ Out C6×D5120(C6xD5):27(C2xC4)480,623
(C6×D5)⋊28(C2×C4) = C22×D5×Dic3φ: C2×C4/C22 → C2 ⊆ Out C6×D5240(C6xD5):28(C2xC4)480,1112
(C6×D5)⋊29(C2×C4) = C3×D5×C22⋊C4φ: C2×C4/C22 → C2 ⊆ Out C6×D5120(C6xD5):29(C2xC4)480,673
(C6×D5)⋊30(C2×C4) = C6×D10⋊C4φ: C2×C4/C22 → C2 ⊆ Out C6×D5240(C6xD5):30(C2xC4)480,720
(C6×D5)⋊31(C2×C4) = C2×D10.D6φ: C2×C4/C22 → C2 ⊆ Out C6×D5120(C6xD5):31(C2xC4)480,1072
(C6×D5)⋊32(C2×C4) = C23×C3⋊F5φ: C2×C4/C22 → C2 ⊆ Out C6×D5120(C6xD5):32(C2xC4)480,1206
(C6×D5)⋊33(C2×C4) = C6×C22⋊F5φ: C2×C4/C22 → C2 ⊆ Out C6×D5120(C6xD5):33(C2xC4)480,1059
(C6×D5)⋊34(C2×C4) = F5×C22×C6φ: C2×C4/C22 → C2 ⊆ Out C6×D5120(C6xD5):34(C2xC4)480,1205

Non-split extensions G=N.Q with N=C6×D5 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
(C6×D5).1(C2×C4) = S3×C8⋊D5φ: C2×C4/C2 → C22 ⊆ Out C6×D51204(C6xD5).1(C2xC4)480,321
(C6×D5).2(C2×C4) = C40⋊D6φ: C2×C4/C2 → C22 ⊆ Out C6×D51204(C6xD5).2(C2xC4)480,322
(C6×D5).3(C2×C4) = C40.55D6φ: C2×C4/C2 → C22 ⊆ Out C6×D52404(C6xD5).3(C2xC4)480,343
(C6×D5).4(C2×C4) = C40.35D6φ: C2×C4/C2 → C22 ⊆ Out C6×D52404(C6xD5).4(C2xC4)480,344
(C6×D5).5(C2×C4) = D20.3Dic3φ: C2×C4/C2 → C22 ⊆ Out C6×D52404(C6xD5).5(C2xC4)480,359
(C6×D5).6(C2×C4) = D20.2Dic3φ: C2×C4/C2 → C22 ⊆ Out C6×D52404(C6xD5).6(C2xC4)480,360
(C6×D5).7(C2×C4) = (D5×Dic3)⋊C4φ: C2×C4/C2 → C22 ⊆ Out C6×D5240(C6xD5).7(C2xC4)480,469
(C6×D5).8(C2×C4) = D10.19(C4×S3)φ: C2×C4/C2 → C22 ⊆ Out C6×D5240(C6xD5).8(C2xC4)480,470
(C6×D5).9(C2×C4) = F5×C3⋊C8φ: C2×C4/C2 → C22 ⊆ Out C6×D51208(C6xD5).9(C2xC4)480,223
(C6×D5).10(C2×C4) = C30.C42φ: C2×C4/C2 → C22 ⊆ Out C6×D51208(C6xD5).10(C2xC4)480,224
(C6×D5).11(C2×C4) = C30.3C42φ: C2×C4/C2 → C22 ⊆ Out C6×D51208(C6xD5).11(C2xC4)480,225
(C6×D5).12(C2×C4) = C30.4C42φ: C2×C4/C2 → C22 ⊆ Out C6×D51208(C6xD5).12(C2xC4)480,226
(C6×D5).13(C2×C4) = D10.20D12φ: C2×C4/C2 → C22 ⊆ Out C6×D5120(C6xD5).13(C2xC4)480,243
(C6×D5).14(C2×C4) = S3×D5⋊C8φ: C2×C4/C2 → C22 ⊆ Out C6×D51208(C6xD5).14(C2xC4)480,986
(C6×D5).15(C2×C4) = D12.2F5φ: C2×C4/C2 → C22 ⊆ Out C6×D52408-(C6xD5).15(C2xC4)480,987
(C6×D5).16(C2×C4) = S3×C4.F5φ: C2×C4/C2 → C22 ⊆ Out C6×D51208(C6xD5).16(C2xC4)480,988
(C6×D5).17(C2×C4) = D12.F5φ: C2×C4/C2 → C22 ⊆ Out C6×D52408-(C6xD5).17(C2xC4)480,989
(C6×D5).18(C2×C4) = D60.C4φ: C2×C4/C2 → C22 ⊆ Out C6×D52408+(C6xD5).18(C2xC4)480,990
(C6×D5).19(C2×C4) = D15⋊M4(2)φ: C2×C4/C2 → C22 ⊆ Out C6×D51208(C6xD5).19(C2xC4)480,991
(C6×D5).20(C2×C4) = Dic6.F5φ: C2×C4/C2 → C22 ⊆ Out C6×D52408+(C6xD5).20(C2xC4)480,992
(C6×D5).21(C2×C4) = C5⋊C8⋊D6φ: C2×C4/C2 → C22 ⊆ Out C6×D51208(C6xD5).21(C2xC4)480,993
(C6×D5).22(C2×C4) = C2×Dic3×F5φ: C2×C4/C2 → C22 ⊆ Out C6×D5120(C6xD5).22(C2xC4)480,998
(C6×D5).23(C2×C4) = C22⋊F5.S3φ: C2×C4/C2 → C22 ⊆ Out C6×D51208-(C6xD5).23(C2xC4)480,999
(C6×D5).24(C2×C4) = C2×D6⋊F5φ: C2×C4/C2 → C22 ⊆ Out C6×D5120(C6xD5).24(C2xC4)480,1000
(C6×D5).25(C2×C4) = C2×Dic3⋊F5φ: C2×C4/C2 → C22 ⊆ Out C6×D5120(C6xD5).25(C2xC4)480,1001
(C6×D5).26(C2×C4) = Dic10.Dic3φ: C2×C4/C2 → C22 ⊆ Out C6×D52408(C6xD5).26(C2xC4)480,1066
(C6×D5).27(C2×C4) = D20.Dic3φ: C2×C4/C2 → C22 ⊆ Out C6×D52408(C6xD5).27(C2xC4)480,1068
(C6×D5).28(C2×C4) = C3×D4.F5φ: C2×C4/C2 → C22 ⊆ Out C6×D52408(C6xD5).28(C2xC4)480,1053
(C6×D5).29(C2×C4) = C3×Q8.F5φ: C2×C4/C2 → C22 ⊆ Out C6×D52408(C6xD5).29(C2xC4)480,1055
(C6×D5).30(C2×C4) = S3×C8×D5φ: C2×C4/C4 → C2 ⊆ Out C6×D51204(C6xD5).30(C2xC4)480,319
(C6×D5).31(C2×C4) = D5×C8⋊S3φ: C2×C4/C4 → C2 ⊆ Out C6×D51204(C6xD5).31(C2xC4)480,320
(C6×D5).32(C2×C4) = C40.54D6φ: C2×C4/C4 → C2 ⊆ Out C6×D52404(C6xD5).32(C2xC4)480,341
(C6×D5).33(C2×C4) = C40.34D6φ: C2×C4/C4 → C2 ⊆ Out C6×D52404(C6xD5).33(C2xC4)480,342
(C6×D5).34(C2×C4) = C4×D5×Dic3φ: C2×C4/C4 → C2 ⊆ Out C6×D5240(C6xD5).34(C2xC4)480,467
(C6×D5).35(C2×C4) = D5×Dic3⋊C4φ: C2×C4/C4 → C2 ⊆ Out C6×D5240(C6xD5).35(C2xC4)480,468
(C6×D5).36(C2×C4) = D5×D6⋊C4φ: C2×C4/C4 → C2 ⊆ Out C6×D5120(C6xD5).36(C2xC4)480,547
(C6×D5).37(C2×C4) = C3×D20.3C4φ: C2×C4/C4 → C2 ⊆ Out C6×D52402(C6xD5).37(C2xC4)480,694
(C6×D5).38(C2×C4) = C3×D20.2C4φ: C2×C4/C4 → C2 ⊆ Out C6×D52404(C6xD5).38(C2xC4)480,700
(C6×D5).39(C2×C4) = C8×C3⋊F5φ: C2×C4/C4 → C2 ⊆ Out C6×D51204(C6xD5).39(C2xC4)480,296
(C6×D5).40(C2×C4) = C24⋊F5φ: C2×C4/C4 → C2 ⊆ Out C6×D51204(C6xD5).40(C2xC4)480,297
(C6×D5).41(C2×C4) = D10.10D12φ: C2×C4/C4 → C2 ⊆ Out C6×D5120(C6xD5).41(C2xC4)480,311
(C6×D5).42(C2×C4) = C2×C4×C3⋊F5φ: C2×C4/C4 → C2 ⊆ Out C6×D5120(C6xD5).42(C2xC4)480,1063
(C6×D5).43(C2×C4) = F5×C24φ: C2×C4/C4 → C2 ⊆ Out C6×D51204(C6xD5).43(C2xC4)480,271
(C6×D5).44(C2×C4) = C3×C8⋊F5φ: C2×C4/C4 → C2 ⊆ Out C6×D51204(C6xD5).44(C2xC4)480,272
(C6×D5).45(C2×C4) = C3×D10.3Q8φ: C2×C4/C4 → C2 ⊆ Out C6×D5120(C6xD5).45(C2xC4)480,286
(C6×D5).46(C2×C4) = F5×C2×C12φ: C2×C4/C4 → C2 ⊆ Out C6×D5120(C6xD5).46(C2xC4)480,1050
(C6×D5).47(C2×C4) = C2×D5×C3⋊C8φ: C2×C4/C22 → C2 ⊆ Out C6×D5240(C6xD5).47(C2xC4)480,357
(C6×D5).48(C2×C4) = D5×C4.Dic3φ: C2×C4/C22 → C2 ⊆ Out C6×D51204(C6xD5).48(C2xC4)480,358
(C6×D5).49(C2×C4) = C2×C20.32D6φ: C2×C4/C22 → C2 ⊆ Out C6×D5240(C6xD5).49(C2xC4)480,369
(C6×D5).50(C2×C4) = (D5×C12)⋊C4φ: C2×C4/C22 → C2 ⊆ Out C6×D5240(C6xD5).50(C2xC4)480,433
(C6×D5).51(C2×C4) = (C4×D5)⋊Dic3φ: C2×C4/C22 → C2 ⊆ Out C6×D5240(C6xD5).51(C2xC4)480,434
(C6×D5).52(C2×C4) = D5×C4⋊Dic3φ: C2×C4/C22 → C2 ⊆ Out C6×D5240(C6xD5).52(C2xC4)480,488
(C6×D5).53(C2×C4) = C3×C42⋊D5φ: C2×C4/C22 → C2 ⊆ Out C6×D5240(C6xD5).53(C2xC4)480,665
(C6×D5).54(C2×C4) = C3×C4⋊C4⋊7D5φ: C2×C4/C22 → C2 ⊆ Out C6×D5240(C6xD5).54(C2xC4)480,685
(C6×D5).55(C2×C4) = C6×C8⋊D5φ: C2×C4/C22 → C2 ⊆ Out C6×D5240(C6xD5).55(C2xC4)480,693
(C6×D5).56(C2×C4) = C2×C60.C4φ: C2×C4/C22 → C2 ⊆ Out C6×D5240(C6xD5).56(C2xC4)480,1060
(C6×D5).57(C2×C4) = C2×C12.F5φ: C2×C4/C22 → C2 ⊆ Out C6×D5240(C6xD5).57(C2xC4)480,1061
(C6×D5).58(C2×C4) = C60.59(C2×C4)φ: C2×C4/C22 → C2 ⊆ Out C6×D51204(C6xD5).58(C2xC4)480,1062
(C6×D5).59(C2×C4) = C2×C60⋊C4φ: C2×C4/C22 → C2 ⊆ Out C6×D5120(C6xD5).59(C2xC4)480,1064
(C6×D5).60(C2×C4) = (C2×C12)⋊6F5φ: C2×C4/C22 → C2 ⊆ Out C6×D51204(C6xD5).60(C2xC4)480,1065
(C6×D5).61(C2×C4) = C6×D5⋊C8φ: C2×C4/C22 → C2 ⊆ Out C6×D5240(C6xD5).61(C2xC4)480,1047
(C6×D5).62(C2×C4) = C6×C4.F5φ: C2×C4/C22 → C2 ⊆ Out C6×D5240(C6xD5).62(C2xC4)480,1048
(C6×D5).63(C2×C4) = C3×D5⋊M4(2)φ: C2×C4/C22 → C2 ⊆ Out C6×D51204(C6xD5).63(C2xC4)480,1049
(C6×D5).64(C2×C4) = C6×C4⋊F5φ: C2×C4/C22 → C2 ⊆ Out C6×D5120(C6xD5).64(C2xC4)480,1051
(C6×D5).65(C2×C4) = C3×D10.C23φ: C2×C4/C22 → C2 ⊆ Out C6×D51204(C6xD5).65(C2xC4)480,1052
(C6×D5).66(C2×C4) = D5×C4×C12φ: trivial image240(C6xD5).66(C2xC4)480,664
(C6×D5).67(C2×C4) = C3×D5×C4⋊C4φ: trivial image240(C6xD5).67(C2xC4)480,684
(C6×D5).68(C2×C4) = D5×C2×C24φ: trivial image240(C6xD5).68(C2xC4)480,692
(C6×D5).69(C2×C4) = C3×D5×M4(2)φ: trivial image1204(C6xD5).69(C2xC4)480,699

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