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Extensions 1→N→G→Q→1 with N=C2×C10 and Q=C2×Q8

Direct product G=N×Q with N=C2×C10 and Q=C2×Q8
dρLabelID
Q8×C22×C10320Q8xC2^2xC10320,1630

Semidirect products G=N:Q with N=C2×C10 and Q=C2×Q8
extensionφ:Q→Aut NdρLabelID
(C2×C10)⋊1(C2×Q8) = D4×Dic10φ: C2×Q8/C4 → C22 ⊆ Aut C2×C10160(C2xC10):1(C2xQ8)320,1209
(C2×C10)⋊2(C2×Q8) = D5×C22⋊Q8φ: C2×Q8/C4 → C22 ⊆ Aut C2×C1080(C2xC10):2(C2xQ8)320,1298
(C2×C10)⋊3(C2×Q8) = Dic10⋊21D4φ: C2×Q8/C4 → C22 ⊆ Aut C2×C10160(C2xC10):3(C2xQ8)320,1304
(C2×C10)⋊4(C2×Q8) = C2×Dic5.14D4φ: C2×Q8/C22 → C22 ⊆ Aut C2×C10160(C2xC10):4(C2xQ8)320,1153
(C2×C10)⋊5(C2×Q8) = C10×C22⋊Q8φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10):5(C2xQ8)320,1525
(C2×C10)⋊6(C2×Q8) = C2×C20.48D4φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10):6(C2xQ8)320,1456
(C2×C10)⋊7(C2×Q8) = C23×Dic10φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10):7(C2xQ8)320,1608
(C2×C10)⋊8(C2×Q8) = C5×D4×Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10160(C2xC10):8(C2xQ8)320,1551
(C2×C10)⋊9(C2×Q8) = Q8×C5⋊D4φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10160(C2xC10):9(C2xQ8)320,1487
(C2×C10)⋊10(C2×Q8) = C22×Q8×D5φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10160(C2xC10):10(C2xQ8)320,1615

Non-split extensions G=N.Q with N=C2×C10 and Q=C2×Q8
extensionφ:Q→Aut NdρLabelID
(C2×C10).1(C2×Q8) = D5×C8.C4φ: C2×Q8/C4 → C22 ⊆ Aut C2×C10804(C2xC10).1(C2xQ8)320,519
(C2×C10).2(C2×Q8) = M4(2).25D10φ: C2×Q8/C4 → C22 ⊆ Aut C2×C10804(C2xC10).2(C2xQ8)320,520
(C2×C10).3(C2×Q8) = D4⋊5Dic10φ: C2×Q8/C4 → C22 ⊆ Aut C2×C10160(C2xC10).3(C2xQ8)320,1211
(C2×C10).4(C2×Q8) = D4⋊6Dic10φ: C2×Q8/C4 → C22 ⊆ Aut C2×C10160(C2xC10).4(C2xQ8)320,1215
(C2×C10).5(C2×Q8) = (Q8×Dic5)⋊C2φ: C2×Q8/C4 → C22 ⊆ Aut C2×C10160(C2xC10).5(C2xQ8)320,1294
(C2×C10).6(C2×Q8) = C10.502+ 1+4φ: C2×Q8/C4 → C22 ⊆ Aut C2×C10160(C2xC10).6(C2xQ8)320,1295
(C2×C10).7(C2×Q8) = C10.512+ 1+4φ: C2×Q8/C4 → C22 ⊆ Aut C2×C1080(C2xC10).7(C2xQ8)320,1306
(C2×C10).8(C2×Q8) = C10.1182+ 1+4φ: C2×Q8/C4 → C22 ⊆ Aut C2×C10160(C2xC10).8(C2xQ8)320,1307
(C2×C10).9(C2×Q8) = C10.522+ 1+4φ: C2×Q8/C4 → C22 ⊆ Aut C2×C10160(C2xC10).9(C2xQ8)320,1308
(C2×C10).10(C2×Q8) = C2×C20.53D4φ: C2×Q8/C22 → C22 ⊆ Aut C2×C10160(C2xC10).10(C2xQ8)320,750
(C2×C10).11(C2×Q8) = C23.Dic10φ: C2×Q8/C22 → C22 ⊆ Aut C2×C10804(C2xC10).11(C2xQ8)320,751
(C2×C10).12(C2×Q8) = C42.88D10φ: C2×Q8/C22 → C22 ⊆ Aut C2×C10160(C2xC10).12(C2xQ8)320,1189
(C2×C10).13(C2×Q8) = C42.90D10φ: C2×Q8/C22 → C22 ⊆ Aut C2×C10160(C2xC10).13(C2xQ8)320,1191
(C2×C10).14(C2×Q8) = C10×C8.C4φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).14(C2xQ8)320,930
(C2×C10).15(C2×Q8) = C5×M4(2).C4φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10804(C2xC10).15(C2xQ8)320,931
(C2×C10).16(C2×Q8) = C5×C23.37C23φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).16(C2xQ8)320,1535
(C2×C10).17(C2×Q8) = C5×C23⋊2Q8φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C1080(C2xC10).17(C2xQ8)320,1545
(C2×C10).18(C2×Q8) = C5×C23.41C23φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).18(C2xQ8)320,1546
(C2×C10).19(C2×Q8) = C4⋊Dic5⋊15C4φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).19(C2xQ8)320,281
(C2×C10).20(C2×Q8) = C10.52(C4×D4)φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).20(C2xQ8)320,282
(C2×C10).21(C2×Q8) = (C2×C4).Dic10φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).21(C2xQ8)320,287
(C2×C10).22(C2×Q8) = C10.(C4⋊Q8)φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).22(C2xQ8)320,288
(C2×C10).23(C2×Q8) = C20⋊7(C4⋊C4)φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).23(C2xQ8)320,555
(C2×C10).24(C2×Q8) = (C2×C20)⋊10Q8φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).24(C2xQ8)320,556
(C2×C10).25(C2×Q8) = C4×C10.D4φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).25(C2xQ8)320,558
(C2×C10).26(C2×Q8) = C10.92(C4×D4)φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).26(C2xQ8)320,560
(C2×C10).27(C2×Q8) = C4×C4⋊Dic5φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).27(C2xQ8)320,561
(C2×C10).28(C2×Q8) = C42⋊8Dic5φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).28(C2xQ8)320,562
(C2×C10).29(C2×Q8) = C42⋊9Dic5φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).29(C2xQ8)320,563
(C2×C10).30(C2×Q8) = C24.44D10φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).30(C2xQ8)320,569
(C2×C10).31(C2×Q8) = C24.46D10φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).31(C2xQ8)320,573
(C2×C10).32(C2×Q8) = C23⋊Dic10φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).32(C2xQ8)320,574
(C2×C10).33(C2×Q8) = C24.6D10φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).33(C2xQ8)320,575
(C2×C10).34(C2×Q8) = C24.7D10φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).34(C2xQ8)320,576
(C2×C10).35(C2×Q8) = C24.47D10φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).35(C2xQ8)320,577
(C2×C10).36(C2×Q8) = C20.48(C4⋊C4)φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).36(C2xQ8)320,604
(C2×C10).37(C2×Q8) = (C2×C20).54D4φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).37(C2xQ8)320,611
(C2×C10).38(C2×Q8) = C20⋊6(C4⋊C4)φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).38(C2xQ8)320,612
(C2×C10).39(C2×Q8) = (C2×C20).55D4φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).39(C2xQ8)320,613
(C2×C10).40(C2×Q8) = C2×C40.6C4φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).40(C2xQ8)320,734
(C2×C10).41(C2×Q8) = M4(2).Dic5φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10804(C2xC10).41(C2xQ8)320,752
(C2×C10).42(C2×Q8) = C2×C10.10C42φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).42(C2xQ8)320,835
(C2×C10).43(C2×Q8) = C24.62D10φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).43(C2xQ8)320,837
(C2×C10).44(C2×Q8) = C24.64D10φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).44(C2xQ8)320,839
(C2×C10).45(C2×Q8) = C2×C4×Dic10φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).45(C2xQ8)320,1139
(C2×C10).46(C2×Q8) = C2×C20⋊2Q8φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).46(C2xQ8)320,1140
(C2×C10).47(C2×Q8) = C2×C20.6Q8φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).47(C2xQ8)320,1141
(C2×C10).48(C2×Q8) = C42.274D10φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).48(C2xQ8)320,1142
(C2×C10).49(C2×Q8) = C23⋊2Dic10φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C1080(C2xC10).49(C2xQ8)320,1155
(C2×C10).50(C2×Q8) = C2×C20⋊Q8φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).50(C2xQ8)320,1169
(C2×C10).51(C2×Q8) = C2×C4.Dic10φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).51(C2xQ8)320,1171
(C2×C10).52(C2×Q8) = C10.12- 1+4φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10160(C2xC10).52(C2xQ8)320,1172
(C2×C10).53(C2×Q8) = C22×C10.D4φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).53(C2xQ8)320,1455
(C2×C10).54(C2×Q8) = C22×C4⋊Dic5φ: C2×Q8/C2×C4 → C2 ⊆ Aut C2×C10320(C2xC10).54(C2xQ8)320,1457
(C2×C10).55(C2×Q8) = C5×D4⋊3Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10160(C2xC10).55(C2xQ8)320,1556
(C2×C10).56(C2×Q8) = (C2×C20)⋊Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).56(C2xQ8)320,273
(C2×C10).57(C2×Q8) = C10.49(C4×D4)φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).57(C2xQ8)320,274
(C2×C10).58(C2×Q8) = Dic5⋊2C42φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).58(C2xQ8)320,276
(C2×C10).59(C2×Q8) = C5⋊2(C42⋊8C4)φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).59(C2xQ8)320,277
(C2×C10).60(C2×Q8) = C10.51(C4×D4)φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).60(C2xQ8)320,279
(C2×C10).61(C2×Q8) = C2.(C4×D20)φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).61(C2xQ8)320,280
(C2×C10).62(C2×Q8) = (C2×Dic5)⋊Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).62(C2xQ8)320,283
(C2×C10).63(C2×Q8) = C2.(C20⋊Q8)φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).63(C2xQ8)320,284
(C2×C10).64(C2×Q8) = (C2×Dic5).Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).64(C2xQ8)320,285
(C2×C10).65(C2×Q8) = (C2×C20).28D4φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).65(C2xQ8)320,286
(C2×C10).66(C2×Q8) = D5×C2.C42φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10160(C2xC10).66(C2xQ8)320,290
(C2×C10).67(C2×Q8) = D10⋊2(C4⋊C4)φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10160(C2xC10).67(C2xQ8)320,294
(C2×C10).68(C2×Q8) = D10⋊3(C4⋊C4)φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10160(C2xC10).68(C2xQ8)320,295
(C2×C10).69(C2×Q8) = (C2×C4).20D20φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10160(C2xC10).69(C2xQ8)320,300
(C2×C10).70(C2×Q8) = (C22×D5).Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10160(C2xC10).70(C2xQ8)320,303
(C2×C10).71(C2×Q8) = (C2×C20).33D4φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10160(C2xC10).71(C2xQ8)320,304
(C2×C10).72(C2×Q8) = C10.96(C4×D4)φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).72(C2xQ8)320,599
(C2×C10).73(C2×Q8) = C20⋊4(C4⋊C4)φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).73(C2xQ8)320,600
(C2×C10).74(C2×Q8) = (C2×Dic5)⋊6Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).74(C2xQ8)320,601
(C2×C10).75(C2×Q8) = C4⋊C4×Dic5φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).75(C2xQ8)320,602
(C2×C10).76(C2×Q8) = C20⋊5(C4⋊C4)φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).76(C2xQ8)320,603
(C2×C10).77(C2×Q8) = C10.97(C4×D4)φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).77(C2xQ8)320,605
(C2×C10).78(C2×Q8) = (C2×C4)⋊Dic10φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).78(C2xQ8)320,606
(C2×C10).79(C2×Q8) = (C2×C20).287D4φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).79(C2xQ8)320,607
(C2×C10).80(C2×Q8) = C4⋊C4⋊5Dic5φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).80(C2xQ8)320,608
(C2×C10).81(C2×Q8) = (C2×C20).288D4φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).81(C2xQ8)320,609
(C2×C10).82(C2×Q8) = (C2×C20).53D4φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).82(C2xQ8)320,610
(C2×C10).83(C2×Q8) = D10⋊4(C4⋊C4)φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10160(C2xC10).83(C2xQ8)320,614
(C2×C10).84(C2×Q8) = D10⋊5(C4⋊C4)φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10160(C2xC10).84(C2xQ8)320,616
(C2×C10).85(C2×Q8) = (C2×C20).289D4φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10160(C2xC10).85(C2xQ8)320,619
(C2×C10).86(C2×Q8) = (C2×C20).56D4φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10160(C2xC10).86(C2xQ8)320,621
(C2×C10).87(C2×Q8) = C10.C22≀C2φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).87(C2xQ8)320,856
(C2×C10).88(C2×Q8) = (Q8×C10)⋊17C4φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).88(C2xQ8)320,857
(C2×C10).89(C2×Q8) = (C22×D5)⋊Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10160(C2xC10).89(C2xQ8)320,858
(C2×C10).90(C2×Q8) = C2×Dic5⋊3Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).90(C2xQ8)320,1168
(C2×C10).91(C2×Q8) = C2×Dic5.Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).91(C2xQ8)320,1170
(C2×C10).92(C2×Q8) = C2×D5×C4⋊C4φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10160(C2xC10).92(C2xQ8)320,1173
(C2×C10).93(C2×Q8) = C2×D10⋊Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10160(C2xC10).93(C2xQ8)320,1180
(C2×C10).94(C2×Q8) = C2×D10⋊2Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10160(C2xC10).94(C2xQ8)320,1181
(C2×C10).95(C2×Q8) = C10.102+ 1+4φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10160(C2xC10).95(C2xQ8)320,1183
(C2×C10).96(C2×Q8) = C2×Dic5⋊Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).96(C2xQ8)320,1482
(C2×C10).97(C2×Q8) = C2×Q8×Dic5φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10320(C2xC10).97(C2xQ8)320,1483
(C2×C10).98(C2×Q8) = C2×D10⋊3Q8φ: C2×Q8/Q8 → C2 ⊆ Aut C2×C10160(C2xC10).98(C2xQ8)320,1485
(C2×C10).99(C2×Q8) = C10×C2.C42central extension (φ=1)320(C2xC10).99(C2xQ8)320,876
(C2×C10).100(C2×Q8) = C4⋊C4×C20central extension (φ=1)320(C2xC10).100(C2xQ8)320,879
(C2×C10).101(C2×Q8) = C5×C23.7Q8central extension (φ=1)160(C2xC10).101(C2xQ8)320,881
(C2×C10).102(C2×Q8) = C5×C42⋊8C4central extension (φ=1)320(C2xC10).102(C2xQ8)320,883
(C2×C10).103(C2×Q8) = C5×C42⋊9C4central extension (φ=1)320(C2xC10).103(C2xQ8)320,885
(C2×C10).104(C2×Q8) = C5×C23.8Q8central extension (φ=1)160(C2xC10).104(C2xQ8)320,886
(C2×C10).105(C2×Q8) = C5×C23.63C23central extension (φ=1)320(C2xC10).105(C2xQ8)320,888
(C2×C10).106(C2×Q8) = C5×C23.65C23central extension (φ=1)320(C2xC10).106(C2xQ8)320,890
(C2×C10).107(C2×Q8) = C5×C23.67C23central extension (φ=1)320(C2xC10).107(C2xQ8)320,892
(C2×C10).108(C2×Q8) = C5×C23⋊Q8central extension (φ=1)160(C2xC10).108(C2xQ8)320,894
(C2×C10).109(C2×Q8) = C5×C23.78C23central extension (φ=1)320(C2xC10).109(C2xQ8)320,896
(C2×C10).110(C2×Q8) = C5×C23.Q8central extension (φ=1)160(C2xC10).110(C2xQ8)320,897
(C2×C10).111(C2×Q8) = C5×C23.81C23central extension (φ=1)320(C2xC10).111(C2xQ8)320,899
(C2×C10).112(C2×Q8) = C5×C23.4Q8central extension (φ=1)160(C2xC10).112(C2xQ8)320,900
(C2×C10).113(C2×Q8) = C5×C23.83C23central extension (φ=1)320(C2xC10).113(C2xQ8)320,901
(C2×C10).114(C2×Q8) = C4⋊C4×C2×C10central extension (φ=1)320(C2xC10).114(C2xQ8)320,1515
(C2×C10).115(C2×Q8) = Q8×C2×C20central extension (φ=1)320(C2xC10).115(C2xQ8)320,1518
(C2×C10).116(C2×Q8) = C10×C42.C2central extension (φ=1)320(C2xC10).116(C2xQ8)320,1529
(C2×C10).117(C2×Q8) = C10×C4⋊Q8central extension (φ=1)320(C2xC10).117(C2xQ8)320,1533

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