# Extensions 1→N→G→Q→1 with N=C2×C10 and Q=C22×C6

Direct product G=N×Q with N=C2×C10 and Q=C22×C6
dρLabelID
C24×C30480C2^4xC30480,1213

Semidirect products G=N:Q with N=C2×C10 and Q=C22×C6
extensionφ:Q→Aut NdρLabelID
(C2×C10)⋊(C22×C6) = C22×D5×A4φ: C22×C6/C22C6 ⊆ Aut C2×C1060(C2xC10):(C2^2xC6)480,1202
(C2×C10)⋊2(C22×C6) = C6×D4×D5φ: C22×C6/C6C22 ⊆ Aut C2×C10120(C2xC10):2(C2^2xC6)480,1139
(C2×C10)⋊3(C22×C6) = A4×C22×C10φ: C22×C6/C23C3 ⊆ Aut C2×C10120(C2xC10):3(C2^2xC6)480,1208
(C2×C10)⋊4(C22×C6) = D4×C2×C30φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10):4(C2^2xC6)480,1181
(C2×C10)⋊5(C22×C6) = C2×C6×C5⋊D4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10):5(C2^2xC6)480,1149
(C2×C10)⋊6(C22×C6) = D5×C23×C6φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10):6(C2^2xC6)480,1210

Non-split extensions G=N.Q with N=C2×C10 and Q=C22×C6
extensionφ:Q→Aut NdρLabelID
(C2×C10).1(C22×C6) = C6×D42D5φ: C22×C6/C6C22 ⊆ Aut C2×C10240(C2xC10).1(C2^2xC6)480,1140
(C2×C10).2(C22×C6) = C3×D46D10φ: C22×C6/C6C22 ⊆ Aut C2×C101204(C2xC10).2(C2^2xC6)480,1141
(C2×C10).3(C22×C6) = C3×D5×C4○D4φ: C22×C6/C6C22 ⊆ Aut C2×C101204(C2xC10).3(C2^2xC6)480,1145
(C2×C10).4(C22×C6) = C3×D48D10φ: C22×C6/C6C22 ⊆ Aut C2×C101204(C2xC10).4(C2^2xC6)480,1146
(C2×C10).5(C22×C6) = C3×D4.10D10φ: C22×C6/C6C22 ⊆ Aut C2×C102404(C2xC10).5(C2^2xC6)480,1147
(C2×C10).6(C22×C6) = C4○D4×C30φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).6(C2^2xC6)480,1183
(C2×C10).7(C22×C6) = C15×2+ 1+4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C101204(C2xC10).7(C2^2xC6)480,1184
(C2×C10).8(C22×C6) = C15×2- 1+4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C102404(C2xC10).8(C2^2xC6)480,1185
(C2×C10).9(C22×C6) = C12×Dic10φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10480(C2xC10).9(C2^2xC6)480,661
(C2×C10).10(C22×C6) = C3×C202Q8φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10480(C2xC10).10(C2^2xC6)480,662
(C2×C10).11(C22×C6) = C3×C20.6Q8φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10480(C2xC10).11(C2^2xC6)480,663
(C2×C10).12(C22×C6) = D5×C4×C12φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).12(C2^2xC6)480,664
(C2×C10).13(C22×C6) = C3×C42⋊D5φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).13(C2^2xC6)480,665
(C2×C10).14(C22×C6) = C12×D20φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).14(C2^2xC6)480,666
(C2×C10).15(C22×C6) = C3×C204D4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).15(C2^2xC6)480,667
(C2×C10).16(C22×C6) = C3×C4.D20φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).16(C2^2xC6)480,668
(C2×C10).17(C22×C6) = C3×C422D5φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).17(C2^2xC6)480,669
(C2×C10).18(C22×C6) = C3×C23.11D10φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).18(C2^2xC6)480,670
(C2×C10).19(C22×C6) = C3×Dic5.14D4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).19(C2^2xC6)480,671
(C2×C10).20(C22×C6) = C3×C23.D10φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).20(C2^2xC6)480,672
(C2×C10).21(C22×C6) = C3×D5×C22⋊C4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10120(C2xC10).21(C2^2xC6)480,673
(C2×C10).22(C22×C6) = C3×Dic54D4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).22(C2^2xC6)480,674
(C2×C10).23(C22×C6) = C3×C22⋊D20φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10120(C2xC10).23(C2^2xC6)480,675
(C2×C10).24(C22×C6) = C3×D10.12D4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).24(C2^2xC6)480,676
(C2×C10).25(C22×C6) = C3×D10⋊D4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).25(C2^2xC6)480,677
(C2×C10).26(C22×C6) = C3×Dic5.5D4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).26(C2^2xC6)480,678
(C2×C10).27(C22×C6) = C3×C22.D20φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).27(C2^2xC6)480,679
(C2×C10).28(C22×C6) = C3×Dic53Q8φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10480(C2xC10).28(C2^2xC6)480,680
(C2×C10).29(C22×C6) = C3×C20⋊Q8φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10480(C2xC10).29(C2^2xC6)480,681
(C2×C10).30(C22×C6) = C3×Dic5.Q8φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10480(C2xC10).30(C2^2xC6)480,682
(C2×C10).31(C22×C6) = C3×C4.Dic10φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10480(C2xC10).31(C2^2xC6)480,683
(C2×C10).32(C22×C6) = C3×D5×C4⋊C4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).32(C2^2xC6)480,684
(C2×C10).33(C22×C6) = C3×C4⋊C47D5φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).33(C2^2xC6)480,685
(C2×C10).34(C22×C6) = C3×D208C4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).34(C2^2xC6)480,686
(C2×C10).35(C22×C6) = C3×D10.13D4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).35(C2^2xC6)480,687
(C2×C10).36(C22×C6) = C3×C4⋊D20φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).36(C2^2xC6)480,688
(C2×C10).37(C22×C6) = C3×D10⋊Q8φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).37(C2^2xC6)480,689
(C2×C10).38(C22×C6) = C3×D102Q8φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).38(C2^2xC6)480,690
(C2×C10).39(C22×C6) = C3×C4⋊C4⋊D5φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).39(C2^2xC6)480,691
(C2×C10).40(C22×C6) = Dic5×C2×C12φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10480(C2xC10).40(C2^2xC6)480,715
(C2×C10).41(C22×C6) = C6×C10.D4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10480(C2xC10).41(C2^2xC6)480,716
(C2×C10).42(C22×C6) = C3×C20.48D4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).42(C2^2xC6)480,717
(C2×C10).43(C22×C6) = C6×C4⋊Dic5φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10480(C2xC10).43(C2^2xC6)480,718
(C2×C10).44(C22×C6) = C3×C23.21D10φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).44(C2^2xC6)480,719
(C2×C10).45(C22×C6) = C6×D10⋊C4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).45(C2^2xC6)480,720
(C2×C10).46(C22×C6) = C12×C5⋊D4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).46(C2^2xC6)480,721
(C2×C10).47(C22×C6) = C3×C23.23D10φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).47(C2^2xC6)480,722
(C2×C10).48(C22×C6) = C3×C207D4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).48(C2^2xC6)480,723
(C2×C10).49(C22×C6) = C3×D4×Dic5φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).49(C2^2xC6)480,727
(C2×C10).50(C22×C6) = C3×C23.18D10φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).50(C2^2xC6)480,728
(C2×C10).51(C22×C6) = C3×C20.17D4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).51(C2^2xC6)480,729
(C2×C10).52(C22×C6) = C3×C23⋊D10φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10120(C2xC10).52(C2^2xC6)480,730
(C2×C10).53(C22×C6) = C3×C202D4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).53(C2^2xC6)480,731
(C2×C10).54(C22×C6) = C3×Dic5⋊D4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).54(C2^2xC6)480,732
(C2×C10).55(C22×C6) = C3×C20⋊D4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).55(C2^2xC6)480,733
(C2×C10).56(C22×C6) = C3×Dic5⋊Q8φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10480(C2xC10).56(C2^2xC6)480,737
(C2×C10).57(C22×C6) = C3×Q8×Dic5φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10480(C2xC10).57(C2^2xC6)480,738
(C2×C10).58(C22×C6) = C3×D103Q8φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).58(C2^2xC6)480,739
(C2×C10).59(C22×C6) = C3×C20.23D4φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).59(C2^2xC6)480,740
(C2×C10).60(C22×C6) = C6×C23.D5φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).60(C2^2xC6)480,745
(C2×C10).61(C22×C6) = C3×C242D5φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10120(C2xC10).61(C2^2xC6)480,746
(C2×C10).62(C22×C6) = C2×C6×Dic10φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10480(C2xC10).62(C2^2xC6)480,1135
(C2×C10).63(C22×C6) = D5×C22×C12φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).63(C2^2xC6)480,1136
(C2×C10).64(C22×C6) = C2×C6×D20φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).64(C2^2xC6)480,1137
(C2×C10).65(C22×C6) = C6×C4○D20φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).65(C2^2xC6)480,1138
(C2×C10).66(C22×C6) = C6×Q8×D5φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).66(C2^2xC6)480,1142
(C2×C10).67(C22×C6) = C6×Q82D5φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10240(C2xC10).67(C2^2xC6)480,1143
(C2×C10).68(C22×C6) = C3×Q8.10D10φ: C22×C6/C2×C6C2 ⊆ Aut C2×C102404(C2xC10).68(C2^2xC6)480,1144
(C2×C10).69(C22×C6) = Dic5×C22×C6φ: C22×C6/C2×C6C2 ⊆ Aut C2×C10480(C2xC10).69(C2^2xC6)480,1148
(C2×C10).70(C22×C6) = C22⋊C4×C30central extension (φ=1)240(C2xC10).70(C2^2xC6)480,920
(C2×C10).71(C22×C6) = C4⋊C4×C30central extension (φ=1)480(C2xC10).71(C2^2xC6)480,921
(C2×C10).72(C22×C6) = C15×C42⋊C2central extension (φ=1)240(C2xC10).72(C2^2xC6)480,922
(C2×C10).73(C22×C6) = D4×C60central extension (φ=1)240(C2xC10).73(C2^2xC6)480,923
(C2×C10).74(C22×C6) = Q8×C60central extension (φ=1)480(C2xC10).74(C2^2xC6)480,924
(C2×C10).75(C22×C6) = C15×C22≀C2central extension (φ=1)120(C2xC10).75(C2^2xC6)480,925
(C2×C10).76(C22×C6) = C15×C4⋊D4central extension (φ=1)240(C2xC10).76(C2^2xC6)480,926
(C2×C10).77(C22×C6) = C15×C22⋊Q8central extension (φ=1)240(C2xC10).77(C2^2xC6)480,927
(C2×C10).78(C22×C6) = C15×C22.D4central extension (φ=1)240(C2xC10).78(C2^2xC6)480,928
(C2×C10).79(C22×C6) = C15×C4.4D4central extension (φ=1)240(C2xC10).79(C2^2xC6)480,929
(C2×C10).80(C22×C6) = C15×C42.C2central extension (φ=1)480(C2xC10).80(C2^2xC6)480,930
(C2×C10).81(C22×C6) = C15×C422C2central extension (φ=1)240(C2xC10).81(C2^2xC6)480,931
(C2×C10).82(C22×C6) = C15×C41D4central extension (φ=1)240(C2xC10).82(C2^2xC6)480,932
(C2×C10).83(C22×C6) = C15×C4⋊Q8central extension (φ=1)480(C2xC10).83(C2^2xC6)480,933
(C2×C10).84(C22×C6) = Q8×C2×C30central extension (φ=1)480(C2xC10).84(C2^2xC6)480,1182

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