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

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

Semidirect products G=N:Q with N=C2×C6 and Q=C22×C10
extensionφ:Q→Aut NdρLabelID
(C2×C6)⋊(C22×C10) = S3×D4×C10φ: C22×C10/C10C22 ⊆ Aut C2×C6120(C2xC6):(C2^2xC10)480,1154
(C2×C6)⋊2(C22×C10) = D4×C2×C30φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6):2(C2^2xC10)480,1181
(C2×C6)⋊3(C22×C10) = C2×C10×C3⋊D4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6):3(C2^2xC10)480,1164
(C2×C6)⋊4(C22×C10) = S3×C23×C10φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6):4(C2^2xC10)480,1211

Non-split extensions G=N.Q with N=C2×C6 and Q=C22×C10
extensionφ:Q→Aut NdρLabelID
(C2×C6).1(C22×C10) = C10×D42S3φ: C22×C10/C10C22 ⊆ Aut C2×C6240(C2xC6).1(C2^2xC10)480,1155
(C2×C6).2(C22×C10) = C5×D46D6φ: C22×C10/C10C22 ⊆ Aut C2×C61204(C2xC6).2(C2^2xC10)480,1156
(C2×C6).3(C22×C10) = C5×S3×C4○D4φ: C22×C10/C10C22 ⊆ Aut C2×C61204(C2xC6).3(C2^2xC10)480,1160
(C2×C6).4(C22×C10) = C5×D4○D12φ: C22×C10/C10C22 ⊆ Aut C2×C61204(C2xC6).4(C2^2xC10)480,1161
(C2×C6).5(C22×C10) = C5×Q8○D12φ: C22×C10/C10C22 ⊆ Aut C2×C62404(C2xC6).5(C2^2xC10)480,1162
(C2×C6).6(C22×C10) = C4○D4×C30φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).6(C2^2xC10)480,1183
(C2×C6).7(C22×C10) = C15×2+ 1+4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C61204(C2xC6).7(C2^2xC10)480,1184
(C2×C6).8(C22×C10) = C15×2- 1+4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C62404(C2xC6).8(C2^2xC10)480,1185
(C2×C6).9(C22×C10) = C20×Dic6φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6480(C2xC6).9(C2^2xC10)480,747
(C2×C6).10(C22×C10) = C5×C122Q8φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6480(C2xC6).10(C2^2xC10)480,748
(C2×C6).11(C22×C10) = C5×C12.6Q8φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6480(C2xC6).11(C2^2xC10)480,749
(C2×C6).12(C22×C10) = S3×C4×C20φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).12(C2^2xC10)480,750
(C2×C6).13(C22×C10) = C5×C422S3φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).13(C2^2xC10)480,751
(C2×C6).14(C22×C10) = C20×D12φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).14(C2^2xC10)480,752
(C2×C6).15(C22×C10) = C5×C4⋊D12φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).15(C2^2xC10)480,753
(C2×C6).16(C22×C10) = C5×C427S3φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).16(C2^2xC10)480,754
(C2×C6).17(C22×C10) = C5×C423S3φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).17(C2^2xC10)480,755
(C2×C6).18(C22×C10) = C5×C23.16D6φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).18(C2^2xC10)480,756
(C2×C6).19(C22×C10) = C5×Dic3.D4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).19(C2^2xC10)480,757
(C2×C6).20(C22×C10) = C5×C23.8D6φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).20(C2^2xC10)480,758
(C2×C6).21(C22×C10) = C5×S3×C22⋊C4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6120(C2xC6).21(C2^2xC10)480,759
(C2×C6).22(C22×C10) = C5×Dic34D4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).22(C2^2xC10)480,760
(C2×C6).23(C22×C10) = C5×D6⋊D4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6120(C2xC6).23(C2^2xC10)480,761
(C2×C6).24(C22×C10) = C5×C23.9D6φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).24(C2^2xC10)480,762
(C2×C6).25(C22×C10) = C5×Dic3⋊D4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).25(C2^2xC10)480,763
(C2×C6).26(C22×C10) = C5×C23.11D6φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).26(C2^2xC10)480,764
(C2×C6).27(C22×C10) = C5×C23.21D6φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).27(C2^2xC10)480,765
(C2×C6).28(C22×C10) = C5×Dic6⋊C4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6480(C2xC6).28(C2^2xC10)480,766
(C2×C6).29(C22×C10) = C5×C12⋊Q8φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6480(C2xC6).29(C2^2xC10)480,767
(C2×C6).30(C22×C10) = C5×Dic3.Q8φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6480(C2xC6).30(C2^2xC10)480,768
(C2×C6).31(C22×C10) = C5×C4.Dic6φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6480(C2xC6).31(C2^2xC10)480,769
(C2×C6).32(C22×C10) = C5×S3×C4⋊C4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).32(C2^2xC10)480,770
(C2×C6).33(C22×C10) = C5×C4⋊C47S3φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).33(C2^2xC10)480,771
(C2×C6).34(C22×C10) = C5×Dic35D4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).34(C2^2xC10)480,772
(C2×C6).35(C22×C10) = C5×D6.D4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).35(C2^2xC10)480,773
(C2×C6).36(C22×C10) = C5×C12⋊D4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).36(C2^2xC10)480,774
(C2×C6).37(C22×C10) = C5×D6⋊Q8φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).37(C2^2xC10)480,775
(C2×C6).38(C22×C10) = C5×C4.D12φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).38(C2^2xC10)480,776
(C2×C6).39(C22×C10) = C5×C4⋊C4⋊S3φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).39(C2^2xC10)480,777
(C2×C6).40(C22×C10) = Dic3×C2×C20φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6480(C2xC6).40(C2^2xC10)480,801
(C2×C6).41(C22×C10) = C10×Dic3⋊C4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6480(C2xC6).41(C2^2xC10)480,802
(C2×C6).42(C22×C10) = C5×C12.48D4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).42(C2^2xC10)480,803
(C2×C6).43(C22×C10) = C10×C4⋊Dic3φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6480(C2xC6).43(C2^2xC10)480,804
(C2×C6).44(C22×C10) = C5×C23.26D6φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).44(C2^2xC10)480,805
(C2×C6).45(C22×C10) = C10×D6⋊C4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).45(C2^2xC10)480,806
(C2×C6).46(C22×C10) = C20×C3⋊D4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).46(C2^2xC10)480,807
(C2×C6).47(C22×C10) = C5×C23.28D6φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).47(C2^2xC10)480,808
(C2×C6).48(C22×C10) = C5×C127D4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).48(C2^2xC10)480,809
(C2×C6).49(C22×C10) = C5×D4×Dic3φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).49(C2^2xC10)480,813
(C2×C6).50(C22×C10) = C5×C23.23D6φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).50(C2^2xC10)480,814
(C2×C6).51(C22×C10) = C5×C23.12D6φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).51(C2^2xC10)480,815
(C2×C6).52(C22×C10) = C5×C232D6φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6120(C2xC6).52(C2^2xC10)480,816
(C2×C6).53(C22×C10) = C5×D63D4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).53(C2^2xC10)480,817
(C2×C6).54(C22×C10) = C5×C23.14D6φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).54(C2^2xC10)480,818
(C2×C6).55(C22×C10) = C5×C123D4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).55(C2^2xC10)480,819
(C2×C6).56(C22×C10) = C5×Dic3⋊Q8φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6480(C2xC6).56(C2^2xC10)480,823
(C2×C6).57(C22×C10) = C5×Q8×Dic3φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6480(C2xC6).57(C2^2xC10)480,824
(C2×C6).58(C22×C10) = C5×D63Q8φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).58(C2^2xC10)480,825
(C2×C6).59(C22×C10) = C5×C12.23D4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).59(C2^2xC10)480,826
(C2×C6).60(C22×C10) = C10×C6.D4φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).60(C2^2xC10)480,831
(C2×C6).61(C22×C10) = C5×C244S3φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6120(C2xC6).61(C2^2xC10)480,832
(C2×C6).62(C22×C10) = C2×C10×Dic6φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6480(C2xC6).62(C2^2xC10)480,1150
(C2×C6).63(C22×C10) = S3×C22×C20φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).63(C2^2xC10)480,1151
(C2×C6).64(C22×C10) = C2×C10×D12φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).64(C2^2xC10)480,1152
(C2×C6).65(C22×C10) = C10×C4○D12φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).65(C2^2xC10)480,1153
(C2×C6).66(C22×C10) = S3×Q8×C10φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).66(C2^2xC10)480,1157
(C2×C6).67(C22×C10) = C10×Q83S3φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6240(C2xC6).67(C2^2xC10)480,1158
(C2×C6).68(C22×C10) = C5×Q8.15D6φ: C22×C10/C2×C10C2 ⊆ Aut C2×C62404(C2xC6).68(C2^2xC10)480,1159
(C2×C6).69(C22×C10) = Dic3×C22×C10φ: C22×C10/C2×C10C2 ⊆ Aut C2×C6480(C2xC6).69(C2^2xC10)480,1163
(C2×C6).70(C22×C10) = C22⋊C4×C30central extension (φ=1)240(C2xC6).70(C2^2xC10)480,920
(C2×C6).71(C22×C10) = C4⋊C4×C30central extension (φ=1)480(C2xC6).71(C2^2xC10)480,921
(C2×C6).72(C22×C10) = C15×C42⋊C2central extension (φ=1)240(C2xC6).72(C2^2xC10)480,922
(C2×C6).73(C22×C10) = D4×C60central extension (φ=1)240(C2xC6).73(C2^2xC10)480,923
(C2×C6).74(C22×C10) = Q8×C60central extension (φ=1)480(C2xC6).74(C2^2xC10)480,924
(C2×C6).75(C22×C10) = C15×C22≀C2central extension (φ=1)120(C2xC6).75(C2^2xC10)480,925
(C2×C6).76(C22×C10) = C15×C4⋊D4central extension (φ=1)240(C2xC6).76(C2^2xC10)480,926
(C2×C6).77(C22×C10) = C15×C22⋊Q8central extension (φ=1)240(C2xC6).77(C2^2xC10)480,927
(C2×C6).78(C22×C10) = C15×C22.D4central extension (φ=1)240(C2xC6).78(C2^2xC10)480,928
(C2×C6).79(C22×C10) = C15×C4.4D4central extension (φ=1)240(C2xC6).79(C2^2xC10)480,929
(C2×C6).80(C22×C10) = C15×C42.C2central extension (φ=1)480(C2xC6).80(C2^2xC10)480,930
(C2×C6).81(C22×C10) = C15×C422C2central extension (φ=1)240(C2xC6).81(C2^2xC10)480,931
(C2×C6).82(C22×C10) = C15×C41D4central extension (φ=1)240(C2xC6).82(C2^2xC10)480,932
(C2×C6).83(C22×C10) = C15×C4⋊Q8central extension (φ=1)480(C2xC6).83(C2^2xC10)480,933
(C2×C6).84(C22×C10) = Q8×C2×C30central extension (φ=1)480(C2xC6).84(C2^2xC10)480,1182

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