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Extensions 1→N→G→Q→1 with N=C2×C4 and Q=C2×C20

Direct product G=N×Q with N=C2×C4 and Q=C2×C20
dρLabelID
C22×C4×C20320C2^2xC4xC20320,1513

Semidirect products G=N:Q with N=C2×C4 and Q=C2×C20
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1(C2×C20) = C10×C23⋊C4φ: C2×C20/C10 → C4 ⊆ Aut C2×C480(C2xC4):1(C2xC20)320,910
(C2×C4)⋊2(C2×C20) = C5×C23.8Q8φ: C2×C20/C10 → C22 ⊆ Aut C2×C4160(C2xC4):2(C2xC20)320,886
(C2×C4)⋊3(C2×C20) = C5×C23.23D4φ: C2×C20/C10 → C22 ⊆ Aut C2×C4160(C2xC4):3(C2xC20)320,887
(C2×C4)⋊4(C2×C20) = C5×C22.11C24φ: C2×C20/C10 → C22 ⊆ Aut C2×C480(C2xC4):4(C2xC20)320,1520
(C2×C4)⋊5(C2×C20) = C5×C23.33C23φ: C2×C20/C10 → C22 ⊆ Aut C2×C4160(C2xC4):5(C2xC20)320,1522
(C2×C4)⋊6(C2×C20) = C22⋊C4×C20φ: C2×C20/C20 → C2 ⊆ Aut C2×C4160(C2xC4):6(C2xC20)320,878
(C2×C4)⋊7(C2×C20) = D4×C2×C20φ: C2×C20/C20 → C2 ⊆ Aut C2×C4160(C2xC4):7(C2xC20)320,1517
(C2×C4)⋊8(C2×C20) = C4○D4×C20φ: C2×C20/C20 → C2 ⊆ Aut C2×C4160(C2xC4):8(C2xC20)320,1519
(C2×C4)⋊9(C2×C20) = C10×C2.C42φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4320(C2xC4):9(C2xC20)320,876
(C2×C4)⋊10(C2×C20) = C4⋊C4×C2×C10φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4320(C2xC4):10(C2xC20)320,1515
(C2×C4)⋊11(C2×C20) = C10×C42⋊C2φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4160(C2xC4):11(C2xC20)320,1516

Non-split extensions G=N.Q with N=C2×C4 and Q=C2×C20
extensionφ:Q→Aut NdρLabelID
(C2×C4).1(C2×C20) = C5×C42⋊C4φ: C2×C20/C10 → C4 ⊆ Aut C2×C4404(C2xC4).1(C2xC20)320,158
(C2×C4).2(C2×C20) = C5×C42⋊3C4φ: C2×C20/C10 → C4 ⊆ Aut C2×C4804(C2xC4).2(C2xC20)320,159
(C2×C4).3(C2×C20) = C5×C42.C4φ: C2×C20/C10 → C4 ⊆ Aut C2×C4804(C2xC4).3(C2xC20)320,160
(C2×C4).4(C2×C20) = C5×C42.3C4φ: C2×C20/C10 → C4 ⊆ Aut C2×C4804(C2xC4).4(C2xC20)320,161
(C2×C4).5(C2×C20) = C10×C4.10D4φ: C2×C20/C10 → C4 ⊆ Aut C2×C4160(C2xC4).5(C2xC20)320,913
(C2×C4).6(C2×C20) = C5×M4(2).8C22φ: C2×C20/C10 → C4 ⊆ Aut C2×C4804(C2xC4).6(C2xC20)320,914
(C2×C4).7(C2×C20) = C5×C22.SD16φ: C2×C20/C10 → C22 ⊆ Aut C2×C480(C2xC4).7(C2xC20)320,132
(C2×C4).8(C2×C20) = C5×C23.31D4φ: C2×C20/C10 → C22 ⊆ Aut C2×C480(C2xC4).8(C2xC20)320,133
(C2×C4).9(C2×C20) = C5×C42.C22φ: C2×C20/C10 → C22 ⊆ Aut C2×C4160(C2xC4).9(C2xC20)320,134
(C2×C4).10(C2×C20) = C5×C42.2C22φ: C2×C20/C10 → C22 ⊆ Aut C2×C4320(C2xC4).10(C2xC20)320,135
(C2×C4).11(C2×C20) = C5×C4.D8φ: C2×C20/C10 → C22 ⊆ Aut C2×C4160(C2xC4).11(C2xC20)320,136
(C2×C4).12(C2×C20) = C5×C4.10D8φ: C2×C20/C10 → C22 ⊆ Aut C2×C4320(C2xC4).12(C2xC20)320,137
(C2×C4).13(C2×C20) = C5×C4.6Q16φ: C2×C20/C10 → C22 ⊆ Aut C2×C4320(C2xC4).13(C2xC20)320,138
(C2×C4).14(C2×C20) = C5×C22.C42φ: C2×C20/C10 → C22 ⊆ Aut C2×C4160(C2xC4).14(C2xC20)320,148
(C2×C4).15(C2×C20) = C5×M4(2)⋊4C4φ: C2×C20/C10 → C22 ⊆ Aut C2×C4804(C2xC4).15(C2xC20)320,149
(C2×C4).16(C2×C20) = C5×C23.65C23φ: C2×C20/C10 → C22 ⊆ Aut C2×C4320(C2xC4).16(C2xC20)320,890
(C2×C4).17(C2×C20) = C5×C23.67C23φ: C2×C20/C10 → C22 ⊆ Aut C2×C4320(C2xC4).17(C2xC20)320,892
(C2×C4).18(C2×C20) = C5×C23.C23φ: C2×C20/C10 → C22 ⊆ Aut C2×C4804(C2xC4).18(C2xC20)320,911
(C2×C4).19(C2×C20) = C10×C4.D4φ: C2×C20/C10 → C22 ⊆ Aut C2×C480(C2xC4).19(C2xC20)320,912
(C2×C4).20(C2×C20) = C5×C23.36D4φ: C2×C20/C10 → C22 ⊆ Aut C2×C4160(C2xC4).20(C2xC20)320,918
(C2×C4).21(C2×C20) = C5×C23.37D4φ: C2×C20/C10 → C22 ⊆ Aut C2×C480(C2xC4).21(C2xC20)320,919
(C2×C4).22(C2×C20) = C5×C23.38D4φ: C2×C20/C10 → C22 ⊆ Aut C2×C4160(C2xC4).22(C2xC20)320,920
(C2×C4).23(C2×C20) = C5×C42⋊C22φ: C2×C20/C10 → C22 ⊆ Aut C2×C4804(C2xC4).23(C2xC20)320,922
(C2×C4).24(C2×C20) = C5×C42.6C22φ: C2×C20/C10 → C22 ⊆ Aut C2×C4160(C2xC4).24(C2xC20)320,925
(C2×C4).25(C2×C20) = C5×M4(2)⋊C4φ: C2×C20/C10 → C22 ⊆ Aut C2×C4160(C2xC4).25(C2xC20)320,929
(C2×C4).26(C2×C20) = C5×M4(2).C4φ: C2×C20/C10 → C22 ⊆ Aut C2×C4804(C2xC4).26(C2xC20)320,931
(C2×C4).27(C2×C20) = C5×C42.7C22φ: C2×C20/C10 → C22 ⊆ Aut C2×C4160(C2xC4).27(C2xC20)320,934
(C2×C4).28(C2×C20) = C5×C8⋊9D4φ: C2×C20/C10 → C22 ⊆ Aut C2×C4160(C2xC4).28(C2xC20)320,936
(C2×C4).29(C2×C20) = C5×C8⋊6D4φ: C2×C20/C10 → C22 ⊆ Aut C2×C4160(C2xC4).29(C2xC20)320,937
(C2×C4).30(C2×C20) = C5×C8⋊4Q8φ: C2×C20/C10 → C22 ⊆ Aut C2×C4320(C2xC4).30(C2xC20)320,947
(C2×C4).31(C2×C20) = C5×C23.32C23φ: C2×C20/C10 → C22 ⊆ Aut C2×C4160(C2xC4).31(C2xC20)320,1521
(C2×C4).32(C2×C20) = C5×Q8○M4(2)φ: C2×C20/C10 → C22 ⊆ Aut C2×C4804(C2xC4).32(C2xC20)320,1570
(C2×C4).33(C2×C20) = C5×C23.63C23φ: C2×C20/C20 → C2 ⊆ Aut C2×C4320(C2xC4).33(C2xC20)320,888
(C2×C4).34(C2×C20) = C5×C24.C22φ: C2×C20/C20 → C2 ⊆ Aut C2×C4160(C2xC4).34(C2xC20)320,889
(C2×C4).35(C2×C20) = C5×C8○2M4(2)φ: C2×C20/C20 → C2 ⊆ Aut C2×C4160(C2xC4).35(C2xC20)320,906
(C2×C4).36(C2×C20) = D4×C40φ: C2×C20/C20 → C2 ⊆ Aut C2×C4160(C2xC4).36(C2xC20)320,935
(C2×C4).37(C2×C20) = Q8×C40φ: C2×C20/C20 → C2 ⊆ Aut C2×C4320(C2xC4).37(C2xC20)320,946
(C2×C4).38(C2×C20) = C5×D4⋊C8φ: C2×C20/C20 → C2 ⊆ Aut C2×C4160(C2xC4).38(C2xC20)320,130
(C2×C4).39(C2×C20) = C5×Q8⋊C8φ: C2×C20/C20 → C2 ⊆ Aut C2×C4320(C2xC4).39(C2xC20)320,131
(C2×C4).40(C2×C20) = C5×C22.4Q16φ: C2×C20/C20 → C2 ⊆ Aut C2×C4320(C2xC4).40(C2xC20)320,145
(C2×C4).41(C2×C20) = C5×C4.C42φ: C2×C20/C20 → C2 ⊆ Aut C2×C4160(C2xC4).41(C2xC20)320,146
(C2×C4).42(C2×C20) = C5×D4.C8φ: C2×C20/C20 → C2 ⊆ Aut C2×C41602(C2xC4).42(C2xC20)320,155
(C2×C4).43(C2×C20) = C4⋊C4×C20φ: C2×C20/C20 → C2 ⊆ Aut C2×C4320(C2xC4).43(C2xC20)320,879
(C2×C4).44(C2×C20) = C5×C24.3C22φ: C2×C20/C20 → C2 ⊆ Aut C2×C4160(C2xC4).44(C2xC20)320,891
(C2×C4).45(C2×C20) = M4(2)×C20φ: C2×C20/C20 → C2 ⊆ Aut C2×C4160(C2xC4).45(C2xC20)320,905
(C2×C4).46(C2×C20) = C5×(C22×C8)⋊C2φ: C2×C20/C20 → C2 ⊆ Aut C2×C4160(C2xC4).46(C2xC20)320,909
(C2×C4).47(C2×C20) = C10×D4⋊C4φ: C2×C20/C20 → C2 ⊆ Aut C2×C4160(C2xC4).47(C2xC20)320,915
(C2×C4).48(C2×C20) = C10×Q8⋊C4φ: C2×C20/C20 → C2 ⊆ Aut C2×C4320(C2xC4).48(C2xC20)320,916
(C2×C4).49(C2×C20) = C5×C23.24D4φ: C2×C20/C20 → C2 ⊆ Aut C2×C4160(C2xC4).49(C2xC20)320,917
(C2×C4).50(C2×C20) = C10×C4≀C2φ: C2×C20/C20 → C2 ⊆ Aut C2×C480(C2xC4).50(C2xC20)320,921
(C2×C4).51(C2×C20) = C5×D4○C16φ: C2×C20/C20 → C2 ⊆ Aut C2×C41602(C2xC4).51(C2xC20)320,1005
(C2×C4).52(C2×C20) = Q8×C2×C20φ: C2×C20/C20 → C2 ⊆ Aut C2×C4320(C2xC4).52(C2xC20)320,1518
(C2×C4).53(C2×C20) = C10×C8○D4φ: C2×C20/C20 → C2 ⊆ Aut C2×C4160(C2xC4).53(C2xC20)320,1569
(C2×C4).54(C2×C20) = C5×C42⋊4C4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4320(C2xC4).54(C2xC20)320,877
(C2×C4).55(C2×C20) = C5×C23.7Q8φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4160(C2xC4).55(C2xC20)320,881
(C2×C4).56(C2×C20) = C5×C23.34D4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4160(C2xC4).56(C2xC20)320,882
(C2×C4).57(C2×C20) = C5×C42⋊5C4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4320(C2xC4).57(C2xC20)320,884
(C2×C4).58(C2×C20) = C10×C8⋊C4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4320(C2xC4).58(C2xC20)320,904
(C2×C4).59(C2×C20) = C10×C22⋊C8φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4160(C2xC4).59(C2xC20)320,907
(C2×C4).60(C2×C20) = C5×C42.6C4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4160(C2xC4).60(C2xC20)320,933
(C2×C4).61(C2×C20) = C5×C8⋊2C8φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4320(C2xC4).61(C2xC20)320,139
(C2×C4).62(C2×C20) = C5×C8⋊1C8φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4320(C2xC4).62(C2xC20)320,140
(C2×C4).63(C2×C20) = C5×C4.9C42φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4804(C2xC4).63(C2xC20)320,142
(C2×C4).64(C2×C20) = C5×C4.10C42φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4804(C2xC4).64(C2xC20)320,143
(C2×C4).65(C2×C20) = C5×C42⋊6C4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C480(C2xC4).65(C2xC20)320,144
(C2×C4).66(C2×C20) = C5×C16⋊C4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4804(C2xC4).66(C2xC20)320,152
(C2×C4).67(C2×C20) = C5×C23.C8φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4804(C2xC4).67(C2xC20)320,154
(C2×C4).68(C2×C20) = C5×C8.C8φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4802(C2xC4).68(C2xC20)320,169
(C2×C4).69(C2×C20) = C5×C42⋊8C4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4320(C2xC4).69(C2xC20)320,883
(C2×C4).70(C2×C20) = C5×C42⋊9C4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4320(C2xC4).70(C2xC20)320,885
(C2×C4).71(C2×C20) = C5×C24.4C4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C480(C2xC4).71(C2xC20)320,908
(C2×C4).72(C2×C20) = C10×C4⋊C8φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4320(C2xC4).72(C2xC20)320,923
(C2×C4).73(C2×C20) = C5×C4⋊M4(2)φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4160(C2xC4).73(C2xC20)320,924
(C2×C4).74(C2×C20) = C10×C4.Q8φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4320(C2xC4).74(C2xC20)320,926
(C2×C4).75(C2×C20) = C10×C2.D8φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4320(C2xC4).75(C2xC20)320,927
(C2×C4).76(C2×C20) = C5×C23.25D4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4160(C2xC4).76(C2xC20)320,928
(C2×C4).77(C2×C20) = C10×C8.C4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4160(C2xC4).77(C2xC20)320,930
(C2×C4).78(C2×C20) = C5×C42.12C4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4160(C2xC4).78(C2xC20)320,932
(C2×C4).79(C2×C20) = M4(2)×C2×C10φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C4160(C2xC4).79(C2xC20)320,1568
(C2×C4).80(C2×C20) = C5×C8⋊C8central extension (φ=1)320(C2xC4).80(C2xC20)320,127
(C2×C4).81(C2×C20) = C5×C22.7C42central extension (φ=1)320(C2xC4).81(C2xC20)320,141
(C2×C4).82(C2×C20) = C5×C16⋊5C4central extension (φ=1)320(C2xC4).82(C2xC20)320,151
(C2×C4).83(C2×C20) = C5×C22⋊C16central extension (φ=1)160(C2xC4).83(C2xC20)320,153
(C2×C4).84(C2×C20) = C5×C4⋊C16central extension (φ=1)320(C2xC4).84(C2xC20)320,168
(C2×C4).85(C2×C20) = C10×M5(2)central extension (φ=1)160(C2xC4).85(C2xC20)320,1004

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