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Extensions 1→N→G→Q→1 with N=C5×D4 and Q=C2×C4

Direct product G=N×Q with N=C5×D4 and Q=C2×C4
dρLabelID
D4×C2×C20160D4xC2xC20320,1517

Semidirect products G=N:Q with N=C5×D4 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
(C5×D4)⋊1(C2×C4) = D8×F5φ: C2×C4/C1 → C2×C4 ⊆ Out C5×D4408+(C5xD4):1(C2xC4)320,1068
(C5×D4)⋊2(C2×C4) = D40⋊C4φ: C2×C4/C1 → C2×C4 ⊆ Out C5×D4408+(C5xD4):2(C2xC4)320,1069
(C5×D4)⋊3(C2×C4) = C2×D20⋊C4φ: C2×C4/C2 → C4 ⊆ Out C5×D480(C5xD4):3(C2xC4)320,1104
(C5×D4)⋊4(C2×C4) = C2×D4⋊F5φ: C2×C4/C2 → C4 ⊆ Out C5×D480(C5xD4):4(C2xC4)320,1106
(C5×D4)⋊5(C2×C4) = D5⋊C4≀C2φ: C2×C4/C2 → C4 ⊆ Out C5×D4408(C5xD4):5(C2xC4)320,1130
(C5×D4)⋊6(C2×C4) = C4○D4⋊F5φ: C2×C4/C2 → C4 ⊆ Out C5×D4408(C5xD4):6(C2xC4)320,1131
(C5×D4)⋊7(C2×C4) = C2×D4×F5φ: C2×C4/C2 → C4 ⊆ Out C5×D440(C5xD4):7(C2xC4)320,1595
(C5×D4)⋊8(C2×C4) = D10.C24φ: C2×C4/C2 → C4 ⊆ Out C5×D4408+(C5xD4):8(C2xC4)320,1596
(C5×D4)⋊9(C2×C4) = C4○D4×F5φ: C2×C4/C2 → C4 ⊆ Out C5×D4408(C5xD4):9(C2xC4)320,1603
(C5×D4)⋊10(C2×C4) = D5.2+ 1+4φ: C2×C4/C2 → C4 ⊆ Out C5×D4408(C5xD4):10(C2xC4)320,1604
(C5×D4)⋊11(C2×C4) = Dic5⋊4D8φ: C2×C4/C2 → C22 ⊆ Out C5×D4160(C5xD4):11(C2xC4)320,383
(C5×D4)⋊12(C2×C4) = D5×D4⋊C4φ: C2×C4/C2 → C22 ⊆ Out C5×D480(C5xD4):12(C2xC4)320,396
(C5×D4)⋊13(C2×C4) = D4⋊(C4×D5)φ: C2×C4/C2 → C22 ⊆ Out C5×D4160(C5xD4):13(C2xC4)320,398
(C5×D4)⋊14(C2×C4) = D4⋊D5⋊6C4φ: C2×C4/C2 → C22 ⊆ Out C5×D4160(C5xD4):14(C2xC4)320,412
(C5×D4)⋊15(C2×C4) = D5×C4≀C2φ: C2×C4/C2 → C22 ⊆ Out C5×D4404(C5xD4):15(C2xC4)320,447
(C5×D4)⋊16(C2×C4) = D8×Dic5φ: C2×C4/C2 → C22 ⊆ Out C5×D4160(C5xD4):16(C2xC4)320,776
(C5×D4)⋊17(C2×C4) = D8⋊Dic5φ: C2×C4/C2 → C22 ⊆ Out C5×D4160(C5xD4):17(C2xC4)320,779
(C5×D4)⋊18(C2×C4) = C4×D4⋊D5φ: C2×C4/C4 → C2 ⊆ Out C5×D4160(C5xD4):18(C2xC4)320,640
(C5×D4)⋊19(C2×C4) = C42.48D10φ: C2×C4/C4 → C2 ⊆ Out C5×D4160(C5xD4):19(C2xC4)320,641
(C5×D4)⋊20(C2×C4) = C4×D4⋊2D5φ: C2×C4/C4 → C2 ⊆ Out C5×D4160(C5xD4):20(C2xC4)320,1208
(C5×D4)⋊21(C2×C4) = C4×D4×D5φ: C2×C4/C4 → C2 ⊆ Out C5×D480(C5xD4):21(C2xC4)320,1216
(C5×D4)⋊22(C2×C4) = C42⋊11D10φ: C2×C4/C4 → C2 ⊆ Out C5×D480(C5xD4):22(C2xC4)320,1217
(C5×D4)⋊23(C2×C4) = C42.108D10φ: C2×C4/C4 → C2 ⊆ Out C5×D4160(C5xD4):23(C2xC4)320,1218
(C5×D4)⋊24(C2×C4) = D8×C20φ: C2×C4/C4 → C2 ⊆ Out C5×D4160(C5xD4):24(C2xC4)320,938
(C5×D4)⋊25(C2×C4) = C5×D8⋊C4φ: C2×C4/C4 → C2 ⊆ Out C5×D4160(C5xD4):25(C2xC4)320,943
(C5×D4)⋊26(C2×C4) = C2×D4⋊Dic5φ: C2×C4/C22 → C2 ⊆ Out C5×D4160(C5xD4):26(C2xC4)320,841
(C5×D4)⋊27(C2×C4) = C4○D4⋊Dic5φ: C2×C4/C22 → C2 ⊆ Out C5×D4160(C5xD4):27(C2xC4)320,859
(C5×D4)⋊28(C2×C4) = C2×D4⋊2Dic5φ: C2×C4/C22 → C2 ⊆ Out C5×D480(C5xD4):28(C2xC4)320,862
(C5×D4)⋊29(C2×C4) = C2×D4×Dic5φ: C2×C4/C22 → C2 ⊆ Out C5×D4160(C5xD4):29(C2xC4)320,1467
(C5×D4)⋊30(C2×C4) = C24.38D10φ: C2×C4/C22 → C2 ⊆ Out C5×D480(C5xD4):30(C2xC4)320,1470
(C5×D4)⋊31(C2×C4) = C4○D4×Dic5φ: C2×C4/C22 → C2 ⊆ Out C5×D4160(C5xD4):31(C2xC4)320,1498
(C5×D4)⋊32(C2×C4) = C10.1062- 1+4φ: C2×C4/C22 → C2 ⊆ Out C5×D4160(C5xD4):32(C2xC4)320,1499
(C5×D4)⋊33(C2×C4) = C10×D4⋊C4φ: C2×C4/C22 → C2 ⊆ Out C5×D4160(C5xD4):33(C2xC4)320,915
(C5×D4)⋊34(C2×C4) = C5×C23.36D4φ: C2×C4/C22 → C2 ⊆ Out C5×D4160(C5xD4):34(C2xC4)320,918
(C5×D4)⋊35(C2×C4) = C10×C4≀C2φ: C2×C4/C22 → C2 ⊆ Out C5×D480(C5xD4):35(C2xC4)320,921
(C5×D4)⋊36(C2×C4) = C4○D4×C20φ: trivial image160(C5xD4):36(C2xC4)320,1519
(C5×D4)⋊37(C2×C4) = C5×C22.11C24φ: trivial image80(C5xD4):37(C2xC4)320,1520
(C5×D4)⋊38(C2×C4) = C5×C23.33C23φ: trivial image160(C5xD4):38(C2xC4)320,1522

Non-split extensions G=N.Q with N=C5×D4 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
(C5×D4).1(C2×C4) = D8⋊5F5φ: C2×C4/C1 → C2×C4 ⊆ Out C5×D4808-(C5xD4).1(C2xC4)320,1070
(C5×D4).2(C2×C4) = D8⋊F5φ: C2×C4/C1 → C2×C4 ⊆ Out C5×D4808-(C5xD4).2(C2xC4)320,1071
(C5×D4).3(C2×C4) = SD16×F5φ: C2×C4/C1 → C2×C4 ⊆ Out C5×D4408(C5xD4).3(C2xC4)320,1072
(C5×D4).4(C2×C4) = SD16⋊F5φ: C2×C4/C1 → C2×C4 ⊆ Out C5×D4408(C5xD4).4(C2xC4)320,1073
(C5×D4).5(C2×C4) = SD16⋊3F5φ: C2×C4/C1 → C2×C4 ⊆ Out C5×D4808(C5xD4).5(C2xC4)320,1074
(C5×D4).6(C2×C4) = SD16⋊2F5φ: C2×C4/C1 → C2×C4 ⊆ Out C5×D4808(C5xD4).6(C2xC4)320,1075
(C5×D4).7(C2×C4) = (D4×C10)⋊C4φ: C2×C4/C2 → C4 ⊆ Out C5×D4408+(C5xD4).7(C2xC4)320,1105
(C5×D4).8(C2×C4) = (C2×D4)⋊6F5φ: C2×C4/C2 → C4 ⊆ Out C5×D4808-(C5xD4).8(C2xC4)320,1107
(C5×D4).9(C2×C4) = C4○D20⋊C4φ: C2×C4/C2 → C4 ⊆ Out C5×D4808(C5xD4).9(C2xC4)320,1132
(C5×D4).10(C2×C4) = D4⋊F5⋊C2φ: C2×C4/C2 → C4 ⊆ Out C5×D4808(C5xD4).10(C2xC4)320,1133
(C5×D4).11(C2×C4) = C2×D4.F5φ: C2×C4/C2 → C4 ⊆ Out C5×D4160(C5xD4).11(C2xC4)320,1593
(C5×D4).12(C2×C4) = Dic5.C24φ: C2×C4/C2 → C4 ⊆ Out C5×D4808-(C5xD4).12(C2xC4)320,1594
(C5×D4).13(C2×C4) = Dic5.21C24φ: C2×C4/C2 → C4 ⊆ Out C5×D4808(C5xD4).13(C2xC4)320,1601
(C5×D4).14(C2×C4) = Dic5.22C24φ: C2×C4/C2 → C4 ⊆ Out C5×D4808(C5xD4).14(C2xC4)320,1602
(C5×D4).15(C2×C4) = D4.D5⋊5C4φ: C2×C4/C2 → C22 ⊆ Out C5×D4160(C5xD4).15(C2xC4)320,384
(C5×D4).16(C2×C4) = Dic5⋊6SD16φ: C2×C4/C2 → C22 ⊆ Out C5×D4160(C5xD4).16(C2xC4)320,385
(C5×D4).17(C2×C4) = (D4×D5)⋊C4φ: C2×C4/C2 → C22 ⊆ Out C5×D480(C5xD4).17(C2xC4)320,397
(C5×D4).18(C2×C4) = D4⋊2D5⋊C4φ: C2×C4/C2 → C22 ⊆ Out C5×D4160(C5xD4).18(C2xC4)320,399
(C5×D4).19(C2×C4) = C42⋊D10φ: C2×C4/C2 → C22 ⊆ Out C5×D4804(C5xD4).19(C2xC4)320,448
(C5×D4).20(C2×C4) = M4(2).22D10φ: C2×C4/C2 → C22 ⊆ Out C5×D4804(C5xD4).20(C2xC4)320,450
(C5×D4).21(C2×C4) = C42.196D10φ: C2×C4/C2 → C22 ⊆ Out C5×D4804(C5xD4).21(C2xC4)320,451
(C5×D4).22(C2×C4) = SD16×Dic5φ: C2×C4/C2 → C22 ⊆ Out C5×D4160(C5xD4).22(C2xC4)320,788
(C5×D4).23(C2×C4) = SD16⋊Dic5φ: C2×C4/C2 → C22 ⊆ Out C5×D4160(C5xD4).23(C2xC4)320,791
(C5×D4).24(C2×C4) = D8⋊5Dic5φ: C2×C4/C2 → C22 ⊆ Out C5×D4804(C5xD4).24(C2xC4)320,823
(C5×D4).25(C2×C4) = D8⋊4Dic5φ: C2×C4/C2 → C22 ⊆ Out C5×D4804(C5xD4).25(C2xC4)320,824
(C5×D4).26(C2×C4) = C4×D4.D5φ: C2×C4/C4 → C2 ⊆ Out C5×D4160(C5xD4).26(C2xC4)320,644
(C5×D4).27(C2×C4) = C42.51D10φ: C2×C4/C4 → C2 ⊆ Out C5×D4160(C5xD4).27(C2xC4)320,645
(C5×D4).28(C2×C4) = C40.93D4φ: C2×C4/C4 → C2 ⊆ Out C5×D4804(C5xD4).28(C2xC4)320,771
(C5×D4).29(C2×C4) = C40.50D4φ: C2×C4/C4 → C2 ⊆ Out C5×D4804(C5xD4).29(C2xC4)320,772
(C5×D4).30(C2×C4) = D5×C8○D4φ: C2×C4/C4 → C2 ⊆ Out C5×D4804(C5xD4).30(C2xC4)320,1421
(C5×D4).31(C2×C4) = C20.72C24φ: C2×C4/C4 → C2 ⊆ Out C5×D4804(C5xD4).31(C2xC4)320,1422
(C5×D4).32(C2×C4) = SD16×C20φ: C2×C4/C4 → C2 ⊆ Out C5×D4160(C5xD4).32(C2xC4)320,939
(C5×D4).33(C2×C4) = C5×SD16⋊C4φ: C2×C4/C4 → C2 ⊆ Out C5×D4160(C5xD4).33(C2xC4)320,941
(C5×D4).34(C2×C4) = C5×C8○D8φ: C2×C4/C4 → C2 ⊆ Out C5×D4802(C5xD4).34(C2xC4)320,944
(C5×D4).35(C2×C4) = C5×C8.26D4φ: C2×C4/C4 → C2 ⊆ Out C5×D4804(C5xD4).35(C2xC4)320,945
(C5×D4).36(C2×C4) = (D4×C10)⋊18C4φ: C2×C4/C22 → C2 ⊆ Out C5×D480(C5xD4).36(C2xC4)320,842
(C5×D4).37(C2×C4) = C20.(C2×D4)φ: C2×C4/C22 → C2 ⊆ Out C5×D4160(C5xD4).37(C2xC4)320,860
(C5×D4).38(C2×C4) = (D4×C10)⋊21C4φ: C2×C4/C22 → C2 ⊆ Out C5×D4804(C5xD4).38(C2xC4)320,863
(C5×D4).39(C2×C4) = C2×D4.Dic5φ: C2×C4/C22 → C2 ⊆ Out C5×D4160(C5xD4).39(C2xC4)320,1490
(C5×D4).40(C2×C4) = C20.76C24φ: C2×C4/C22 → C2 ⊆ Out C5×D4804(C5xD4).40(C2xC4)320,1491
(C5×D4).41(C2×C4) = C5×C23.24D4φ: C2×C4/C22 → C2 ⊆ Out C5×D4160(C5xD4).41(C2xC4)320,917
(C5×D4).42(C2×C4) = C5×C23.37D4φ: C2×C4/C22 → C2 ⊆ Out C5×D480(C5xD4).42(C2xC4)320,919
(C5×D4).43(C2×C4) = C5×C42⋊C22φ: C2×C4/C22 → C2 ⊆ Out C5×D4804(C5xD4).43(C2xC4)320,922
(C5×D4).44(C2×C4) = C10×C8○D4φ: trivial image160(C5xD4).44(C2xC4)320,1569
(C5×D4).45(C2×C4) = C5×Q8○M4(2)φ: trivial image804(C5xD4).45(C2xC4)320,1570

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