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Extensions 1→N→G→Q→1 with N=C5×Q8 and Q=C2×C4

Direct product G=N×Q with N=C5×Q8 and Q=C2×C4
dρLabelID
Q8×C2×C20320Q8xC2xC20320,1518

Semidirect products G=N:Q with N=C5×Q8 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
(C5×Q8)⋊1(C2×C4) = SD16×F5φ: C2×C4/C1 → C2×C4 ⊆ Out C5×Q8408(C5xQ8):1(C2xC4)320,1072
(C5×Q8)⋊2(C2×C4) = SD16⋊F5φ: C2×C4/C1 → C2×C4 ⊆ Out C5×Q8408(C5xQ8):2(C2xC4)320,1073
(C5×Q8)⋊3(C2×C4) = C2×Q8⋊F5φ: C2×C4/C2 → C4 ⊆ Out C5×Q880(C5xQ8):3(C2xC4)320,1119
(C5×Q8)⋊4(C2×C4) = C2×Q8⋊2F5φ: C2×C4/C2 → C4 ⊆ Out C5×Q880(C5xQ8):4(C2xC4)320,1121
(C5×Q8)⋊5(C2×C4) = D5⋊C4≀C2φ: C2×C4/C2 → C4 ⊆ Out C5×Q8408(C5xQ8):5(C2xC4)320,1130
(C5×Q8)⋊6(C2×C4) = C4○D4⋊F5φ: C2×C4/C2 → C4 ⊆ Out C5×Q8408(C5xQ8):6(C2xC4)320,1131
(C5×Q8)⋊7(C2×C4) = C2×Q8×F5φ: C2×C4/C2 → C4 ⊆ Out C5×Q880(C5xQ8):7(C2xC4)320,1599
(C5×Q8)⋊8(C2×C4) = C4○D4×F5φ: C2×C4/C2 → C4 ⊆ Out C5×Q8408(C5xQ8):8(C2xC4)320,1603
(C5×Q8)⋊9(C2×C4) = D5.2+ 1+4φ: C2×C4/C2 → C4 ⊆ Out C5×Q8408(C5xQ8):9(C2xC4)320,1604
(C5×Q8)⋊10(C2×C4) = Dic5⋊7SD16φ: C2×C4/C2 → C22 ⊆ Out C5×Q8160(C5xQ8):10(C2xC4)320,415
(C5×Q8)⋊11(C2×C4) = D5×Q8⋊C4φ: C2×C4/C2 → C22 ⊆ Out C5×Q8160(C5xQ8):11(C2xC4)320,428
(C5×Q8)⋊12(C2×C4) = Q8⋊(C4×D5)φ: C2×C4/C2 → C22 ⊆ Out C5×Q8160(C5xQ8):12(C2xC4)320,430
(C5×Q8)⋊13(C2×C4) = Q8⋊D5⋊6C4φ: C2×C4/C2 → C22 ⊆ Out C5×Q8160(C5xQ8):13(C2xC4)320,444
(C5×Q8)⋊14(C2×C4) = D5×C4≀C2φ: C2×C4/C2 → C22 ⊆ Out C5×Q8404(C5xQ8):14(C2xC4)320,447
(C5×Q8)⋊15(C2×C4) = SD16×Dic5φ: C2×C4/C2 → C22 ⊆ Out C5×Q8160(C5xQ8):15(C2xC4)320,788
(C5×Q8)⋊16(C2×C4) = SD16⋊Dic5φ: C2×C4/C2 → C22 ⊆ Out C5×Q8160(C5xQ8):16(C2xC4)320,791
(C5×Q8)⋊17(C2×C4) = C4×Q8⋊D5φ: C2×C4/C4 → C2 ⊆ Out C5×Q8160(C5xQ8):17(C2xC4)320,652
(C5×Q8)⋊18(C2×C4) = C42.56D10φ: C2×C4/C4 → C2 ⊆ Out C5×Q8160(C5xQ8):18(C2xC4)320,653
(C5×Q8)⋊19(C2×C4) = C4×Q8×D5φ: C2×C4/C4 → C2 ⊆ Out C5×Q8160(C5xQ8):19(C2xC4)320,1243
(C5×Q8)⋊20(C2×C4) = C4×Q8⋊2D5φ: C2×C4/C4 → C2 ⊆ Out C5×Q8160(C5xQ8):20(C2xC4)320,1245
(C5×Q8)⋊21(C2×C4) = C42.126D10φ: C2×C4/C4 → C2 ⊆ Out C5×Q8160(C5xQ8):21(C2xC4)320,1246
(C5×Q8)⋊22(C2×C4) = SD16×C20φ: C2×C4/C4 → C2 ⊆ Out C5×Q8160(C5xQ8):22(C2xC4)320,939
(C5×Q8)⋊23(C2×C4) = C5×SD16⋊C4φ: C2×C4/C4 → C2 ⊆ Out C5×Q8160(C5xQ8):23(C2xC4)320,941
(C5×Q8)⋊24(C2×C4) = C2×Q8⋊Dic5φ: C2×C4/C22 → C2 ⊆ Out C5×Q8320(C5xQ8):24(C2xC4)320,851
(C5×Q8)⋊25(C2×C4) = C4○D4⋊Dic5φ: C2×C4/C22 → C2 ⊆ Out C5×Q8160(C5xQ8):25(C2xC4)320,859
(C5×Q8)⋊26(C2×C4) = C2×D4⋊2Dic5φ: C2×C4/C22 → C2 ⊆ Out C5×Q880(C5xQ8):26(C2xC4)320,862
(C5×Q8)⋊27(C2×C4) = C2×Q8×Dic5φ: C2×C4/C22 → C2 ⊆ Out C5×Q8320(C5xQ8):27(C2xC4)320,1483
(C5×Q8)⋊28(C2×C4) = C4○D4×Dic5φ: C2×C4/C22 → C2 ⊆ Out C5×Q8160(C5xQ8):28(C2xC4)320,1498
(C5×Q8)⋊29(C2×C4) = C10.1062- 1+4φ: C2×C4/C22 → C2 ⊆ Out C5×Q8160(C5xQ8):29(C2xC4)320,1499
(C5×Q8)⋊30(C2×C4) = C10×Q8⋊C4φ: C2×C4/C22 → C2 ⊆ Out C5×Q8320(C5xQ8):30(C2xC4)320,916
(C5×Q8)⋊31(C2×C4) = C5×C23.36D4φ: C2×C4/C22 → C2 ⊆ Out C5×Q8160(C5xQ8):31(C2xC4)320,918
(C5×Q8)⋊32(C2×C4) = C10×C4≀C2φ: C2×C4/C22 → C2 ⊆ Out C5×Q880(C5xQ8):32(C2xC4)320,921
(C5×Q8)⋊33(C2×C4) = C4○D4×C20φ: trivial image160(C5xQ8):33(C2xC4)320,1519
(C5×Q8)⋊34(C2×C4) = C5×C23.33C23φ: trivial image160(C5xQ8):34(C2xC4)320,1522

Non-split extensions G=N.Q with N=C5×Q8 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
(C5×Q8).1(C2×C4) = SD16⋊3F5φ: C2×C4/C1 → C2×C4 ⊆ Out C5×Q8808(C5xQ8).1(C2xC4)320,1074
(C5×Q8).2(C2×C4) = SD16⋊2F5φ: C2×C4/C1 → C2×C4 ⊆ Out C5×Q8808(C5xQ8).2(C2xC4)320,1075
(C5×Q8).3(C2×C4) = Q16×F5φ: C2×C4/C1 → C2×C4 ⊆ Out C5×Q8808-(C5xQ8).3(C2xC4)320,1076
(C5×Q8).4(C2×C4) = Dic20⋊C4φ: C2×C4/C1 → C2×C4 ⊆ Out C5×Q8808-(C5xQ8).4(C2xC4)320,1077
(C5×Q8).5(C2×C4) = Q16⋊5F5φ: C2×C4/C1 → C2×C4 ⊆ Out C5×Q8808+(C5xQ8).5(C2xC4)320,1078
(C5×Q8).6(C2×C4) = Q16⋊F5φ: C2×C4/C1 → C2×C4 ⊆ Out C5×Q8808+(C5xQ8).6(C2xC4)320,1079
(C5×Q8).7(C2×C4) = (C2×Q8)⋊4F5φ: C2×C4/C2 → C4 ⊆ Out C5×Q8808-(C5xQ8).7(C2xC4)320,1120
(C5×Q8).8(C2×C4) = (C2×Q8)⋊6F5φ: C2×C4/C2 → C4 ⊆ Out C5×Q8808+(C5xQ8).8(C2xC4)320,1122
(C5×Q8).9(C2×C4) = C4○D20⋊C4φ: C2×C4/C2 → C4 ⊆ Out C5×Q8808(C5xQ8).9(C2xC4)320,1132
(C5×Q8).10(C2×C4) = D4⋊F5⋊C2φ: C2×C4/C2 → C4 ⊆ Out C5×Q8808(C5xQ8).10(C2xC4)320,1133
(C5×Q8).11(C2×C4) = C2×Q8.F5φ: C2×C4/C2 → C4 ⊆ Out C5×Q8160(C5xQ8).11(C2xC4)320,1597
(C5×Q8).12(C2×C4) = Dic5.20C24φ: C2×C4/C2 → C4 ⊆ Out C5×Q8808+(C5xQ8).12(C2xC4)320,1598
(C5×Q8).13(C2×C4) = D5.2- 1+4φ: C2×C4/C2 → C4 ⊆ Out C5×Q8808-(C5xQ8).13(C2xC4)320,1600
(C5×Q8).14(C2×C4) = Dic5.21C24φ: C2×C4/C2 → C4 ⊆ Out C5×Q8808(C5xQ8).14(C2xC4)320,1601
(C5×Q8).15(C2×C4) = Dic5.22C24φ: C2×C4/C2 → C4 ⊆ Out C5×Q8808(C5xQ8).15(C2xC4)320,1602
(C5×Q8).16(C2×C4) = C5⋊Q16⋊5C4φ: C2×C4/C2 → C22 ⊆ Out C5×Q8320(C5xQ8).16(C2xC4)320,416
(C5×Q8).17(C2×C4) = Dic5⋊4Q16φ: C2×C4/C2 → C22 ⊆ Out C5×Q8320(C5xQ8).17(C2xC4)320,417
(C5×Q8).18(C2×C4) = (Q8×D5)⋊C4φ: C2×C4/C2 → C22 ⊆ Out C5×Q8160(C5xQ8).18(C2xC4)320,429
(C5×Q8).19(C2×C4) = Q8⋊2D5⋊C4φ: C2×C4/C2 → C22 ⊆ Out C5×Q8160(C5xQ8).19(C2xC4)320,431
(C5×Q8).20(C2×C4) = C42⋊D10φ: C2×C4/C2 → C22 ⊆ Out C5×Q8804(C5xQ8).20(C2xC4)320,448
(C5×Q8).21(C2×C4) = M4(2).22D10φ: C2×C4/C2 → C22 ⊆ Out C5×Q8804(C5xQ8).21(C2xC4)320,450
(C5×Q8).22(C2×C4) = C42.196D10φ: C2×C4/C2 → C22 ⊆ Out C5×Q8804(C5xQ8).22(C2xC4)320,451
(C5×Q8).23(C2×C4) = Q16×Dic5φ: C2×C4/C2 → C22 ⊆ Out C5×Q8320(C5xQ8).23(C2xC4)320,810
(C5×Q8).24(C2×C4) = Q16⋊Dic5φ: C2×C4/C2 → C22 ⊆ Out C5×Q8320(C5xQ8).24(C2xC4)320,811
(C5×Q8).25(C2×C4) = D8⋊5Dic5φ: C2×C4/C2 → C22 ⊆ Out C5×Q8804(C5xQ8).25(C2xC4)320,823
(C5×Q8).26(C2×C4) = D8⋊4Dic5φ: C2×C4/C2 → C22 ⊆ Out C5×Q8804(C5xQ8).26(C2xC4)320,824
(C5×Q8).27(C2×C4) = C4×C5⋊Q16φ: C2×C4/C4 → C2 ⊆ Out C5×Q8320(C5xQ8).27(C2xC4)320,656
(C5×Q8).28(C2×C4) = C42.59D10φ: C2×C4/C4 → C2 ⊆ Out C5×Q8320(C5xQ8).28(C2xC4)320,657
(C5×Q8).29(C2×C4) = C40.93D4φ: C2×C4/C4 → C2 ⊆ Out C5×Q8804(C5xQ8).29(C2xC4)320,771
(C5×Q8).30(C2×C4) = C40.50D4φ: C2×C4/C4 → C2 ⊆ Out C5×Q8804(C5xQ8).30(C2xC4)320,772
(C5×Q8).31(C2×C4) = C42.125D10φ: C2×C4/C4 → C2 ⊆ Out C5×Q8160(C5xQ8).31(C2xC4)320,1244
(C5×Q8).32(C2×C4) = D5×C8○D4φ: C2×C4/C4 → C2 ⊆ Out C5×Q8804(C5xQ8).32(C2xC4)320,1421
(C5×Q8).33(C2×C4) = C20.72C24φ: C2×C4/C4 → C2 ⊆ Out C5×Q8804(C5xQ8).33(C2xC4)320,1422
(C5×Q8).34(C2×C4) = Q16×C20φ: C2×C4/C4 → C2 ⊆ Out C5×Q8320(C5xQ8).34(C2xC4)320,940
(C5×Q8).35(C2×C4) = C5×Q16⋊C4φ: C2×C4/C4 → C2 ⊆ Out C5×Q8320(C5xQ8).35(C2xC4)320,942
(C5×Q8).36(C2×C4) = C5×C8○D8φ: C2×C4/C4 → C2 ⊆ Out C5×Q8802(C5xQ8).36(C2xC4)320,944
(C5×Q8).37(C2×C4) = C5×C8.26D4φ: C2×C4/C4 → C2 ⊆ Out C5×Q8804(C5xQ8).37(C2xC4)320,945
(C5×Q8).38(C2×C4) = (Q8×C10)⋊16C4φ: C2×C4/C22 → C2 ⊆ Out C5×Q8160(C5xQ8).38(C2xC4)320,852
(C5×Q8).39(C2×C4) = C20.(C2×D4)φ: C2×C4/C22 → C2 ⊆ Out C5×Q8160(C5xQ8).39(C2xC4)320,860
(C5×Q8).40(C2×C4) = (D4×C10)⋊21C4φ: C2×C4/C22 → C2 ⊆ Out C5×Q8804(C5xQ8).40(C2xC4)320,863
(C5×Q8).41(C2×C4) = C10.422- 1+4φ: C2×C4/C22 → C2 ⊆ Out C5×Q8160(C5xQ8).41(C2xC4)320,1484
(C5×Q8).42(C2×C4) = C2×D4.Dic5φ: C2×C4/C22 → C2 ⊆ Out C5×Q8160(C5xQ8).42(C2xC4)320,1490
(C5×Q8).43(C2×C4) = C20.76C24φ: C2×C4/C22 → C2 ⊆ Out C5×Q8804(C5xQ8).43(C2xC4)320,1491
(C5×Q8).44(C2×C4) = C5×C23.24D4φ: C2×C4/C22 → C2 ⊆ Out C5×Q8160(C5xQ8).44(C2xC4)320,917
(C5×Q8).45(C2×C4) = C5×C23.38D4φ: C2×C4/C22 → C2 ⊆ Out C5×Q8160(C5xQ8).45(C2xC4)320,920
(C5×Q8).46(C2×C4) = C5×C42⋊C22φ: C2×C4/C22 → C2 ⊆ Out C5×Q8804(C5xQ8).46(C2xC4)320,922
(C5×Q8).47(C2×C4) = C5×C23.32C23φ: trivial image160(C5xQ8).47(C2xC4)320,1521
(C5×Q8).48(C2×C4) = C10×C8○D4φ: trivial image160(C5xQ8).48(C2xC4)320,1569
(C5×Q8).49(C2×C4) = C5×Q8○M4(2)φ: trivial image804(C5xQ8).49(C2xC4)320,1570

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