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

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

Semidirect products G=N:Q with N=C22×C6 and Q=C2×C10
extensionφ:Q→Aut NdρLabelID
(C22×C6)⋊1(C2×C10) = C15×C22≀C2φ: C2×C10/C5 → C22 ⊆ Aut C22×C6120(C2^2xC6):1(C2xC10)480,925
(C22×C6)⋊2(C2×C10) = C15×2+ 1+4φ: C2×C10/C5 → C22 ⊆ Aut C22×C61204(C2^2xC6):2(C2xC10)480,1184
(C22×C6)⋊3(C2×C10) = C5×C23⋊2D6φ: C2×C10/C5 → C22 ⊆ Aut C22×C6120(C2^2xC6):3(C2xC10)480,816
(C22×C6)⋊4(C2×C10) = S3×D4×C10φ: C2×C10/C5 → C22 ⊆ Aut C22×C6120(C2^2xC6):4(C2xC10)480,1154
(C22×C6)⋊5(C2×C10) = C5×D4⋊6D6φ: C2×C10/C5 → C22 ⊆ Aut C22×C61204(C2^2xC6):5(C2xC10)480,1156
(C22×C6)⋊6(C2×C10) = D4×C2×C30φ: C2×C10/C10 → C2 ⊆ Aut C22×C6240(C2^2xC6):6(C2xC10)480,1181
(C22×C6)⋊7(C2×C10) = C2×C10×C3⋊D4φ: C2×C10/C10 → C2 ⊆ Aut C22×C6240(C2^2xC6):7(C2xC10)480,1164
(C22×C6)⋊8(C2×C10) = S3×C23×C10φ: C2×C10/C10 → C2 ⊆ Aut C22×C6240(C2^2xC6):8(C2xC10)480,1211

Non-split extensions G=N.Q with N=C22×C6 and Q=C2×C10
extensionφ:Q→Aut NdρLabelID
(C22×C6).1(C2×C10) = C15×C23⋊C4φ: C2×C10/C5 → C22 ⊆ Aut C22×C61204(C2^2xC6).1(C2xC10)480,202
(C22×C6).2(C2×C10) = C15×C4.4D4φ: C2×C10/C5 → C22 ⊆ Aut C22×C6240(C2^2xC6).2(C2xC10)480,929
(C22×C6).3(C2×C10) = C15×C42⋊2C2φ: C2×C10/C5 → C22 ⊆ Aut C22×C6240(C2^2xC6).3(C2xC10)480,931
(C22×C6).4(C2×C10) = C15×C4⋊1D4φ: C2×C10/C5 → C22 ⊆ Aut C22×C6240(C2^2xC6).4(C2xC10)480,932
(C22×C6).5(C2×C10) = C5×C23.6D6φ: C2×C10/C5 → C22 ⊆ Aut C22×C61204(C2^2xC6).5(C2xC10)480,125
(C22×C6).6(C2×C10) = C5×C23.7D6φ: C2×C10/C5 → C22 ⊆ Aut C22×C61204(C2^2xC6).6(C2xC10)480,153
(C22×C6).7(C2×C10) = C5×C23.16D6φ: C2×C10/C5 → C22 ⊆ Aut C22×C6240(C2^2xC6).7(C2xC10)480,756
(C22×C6).8(C2×C10) = C5×Dic3.D4φ: C2×C10/C5 → C22 ⊆ Aut C22×C6240(C2^2xC6).8(C2xC10)480,757
(C22×C6).9(C2×C10) = C5×C23.8D6φ: C2×C10/C5 → C22 ⊆ Aut C22×C6240(C2^2xC6).9(C2xC10)480,758
(C22×C6).10(C2×C10) = C5×S3×C22⋊C4φ: C2×C10/C5 → C22 ⊆ Aut C22×C6120(C2^2xC6).10(C2xC10)480,759
(C22×C6).11(C2×C10) = C5×Dic3⋊4D4φ: C2×C10/C5 → C22 ⊆ Aut C22×C6240(C2^2xC6).11(C2xC10)480,760
(C22×C6).12(C2×C10) = C5×D6⋊D4φ: C2×C10/C5 → C22 ⊆ Aut C22×C6120(C2^2xC6).12(C2xC10)480,761
(C22×C6).13(C2×C10) = C5×C23.9D6φ: C2×C10/C5 → C22 ⊆ Aut C22×C6240(C2^2xC6).13(C2xC10)480,762
(C22×C6).14(C2×C10) = C5×Dic3⋊D4φ: C2×C10/C5 → C22 ⊆ Aut C22×C6240(C2^2xC6).14(C2xC10)480,763
(C22×C6).15(C2×C10) = C5×C23.11D6φ: C2×C10/C5 → C22 ⊆ Aut C22×C6240(C2^2xC6).15(C2xC10)480,764
(C22×C6).16(C2×C10) = C5×C23.21D6φ: C2×C10/C5 → C22 ⊆ Aut C22×C6240(C2^2xC6).16(C2xC10)480,765
(C22×C6).17(C2×C10) = C5×D4×Dic3φ: C2×C10/C5 → C22 ⊆ Aut C22×C6240(C2^2xC6).17(C2xC10)480,813
(C22×C6).18(C2×C10) = C5×C23.23D6φ: C2×C10/C5 → C22 ⊆ Aut C22×C6240(C2^2xC6).18(C2xC10)480,814
(C22×C6).19(C2×C10) = C5×C23.12D6φ: C2×C10/C5 → C22 ⊆ Aut C22×C6240(C2^2xC6).19(C2xC10)480,815
(C22×C6).20(C2×C10) = C5×D6⋊3D4φ: C2×C10/C5 → C22 ⊆ Aut C22×C6240(C2^2xC6).20(C2xC10)480,817
(C22×C6).21(C2×C10) = C5×C23.14D6φ: C2×C10/C5 → C22 ⊆ Aut C22×C6240(C2^2xC6).21(C2xC10)480,818
(C22×C6).22(C2×C10) = C5×C12⋊3D4φ: C2×C10/C5 → C22 ⊆ Aut C22×C6240(C2^2xC6).22(C2xC10)480,819
(C22×C6).23(C2×C10) = C10×D4⋊2S3φ: C2×C10/C5 → C22 ⊆ Aut C22×C6240(C2^2xC6).23(C2xC10)480,1155
(C22×C6).24(C2×C10) = C22⋊C4×C30φ: C2×C10/C10 → C2 ⊆ Aut C22×C6240(C2^2xC6).24(C2xC10)480,920
(C22×C6).25(C2×C10) = C15×C42⋊C2φ: C2×C10/C10 → C2 ⊆ Aut C22×C6240(C2^2xC6).25(C2xC10)480,922
(C22×C6).26(C2×C10) = D4×C60φ: C2×C10/C10 → C2 ⊆ Aut C22×C6240(C2^2xC6).26(C2xC10)480,923
(C22×C6).27(C2×C10) = C15×C4⋊D4φ: C2×C10/C10 → C2 ⊆ Aut C22×C6240(C2^2xC6).27(C2xC10)480,926
(C22×C6).28(C2×C10) = C15×C22⋊Q8φ: C2×C10/C10 → C2 ⊆ Aut C22×C6240(C2^2xC6).28(C2xC10)480,927
(C22×C6).29(C2×C10) = C15×C22.D4φ: C2×C10/C10 → C2 ⊆ Aut C22×C6240(C2^2xC6).29(C2xC10)480,928
(C22×C6).30(C2×C10) = C4○D4×C30φ: C2×C10/C10 → C2 ⊆ Aut C22×C6240(C2^2xC6).30(C2xC10)480,1183
(C22×C6).31(C2×C10) = C5×C6.C42φ: C2×C10/C10 → C2 ⊆ Aut C22×C6480(C2^2xC6).31(C2xC10)480,150
(C22×C6).32(C2×C10) = Dic3×C2×C20φ: C2×C10/C10 → C2 ⊆ Aut C22×C6480(C2^2xC6).32(C2xC10)480,801
(C22×C6).33(C2×C10) = C10×Dic3⋊C4φ: C2×C10/C10 → C2 ⊆ Aut C22×C6480(C2^2xC6).33(C2xC10)480,802
(C22×C6).34(C2×C10) = C5×C12.48D4φ: C2×C10/C10 → C2 ⊆ Aut C22×C6240(C2^2xC6).34(C2xC10)480,803
(C22×C6).35(C2×C10) = C10×C4⋊Dic3φ: C2×C10/C10 → C2 ⊆ Aut C22×C6480(C2^2xC6).35(C2xC10)480,804
(C22×C6).36(C2×C10) = C5×C23.26D6φ: C2×C10/C10 → C2 ⊆ Aut C22×C6240(C2^2xC6).36(C2xC10)480,805
(C22×C6).37(C2×C10) = C10×D6⋊C4φ: C2×C10/C10 → C2 ⊆ Aut C22×C6240(C2^2xC6).37(C2xC10)480,806
(C22×C6).38(C2×C10) = C20×C3⋊D4φ: C2×C10/C10 → C2 ⊆ Aut C22×C6240(C2^2xC6).38(C2xC10)480,807
(C22×C6).39(C2×C10) = C5×C23.28D6φ: C2×C10/C10 → C2 ⊆ Aut C22×C6240(C2^2xC6).39(C2xC10)480,808
(C22×C6).40(C2×C10) = C5×C12⋊7D4φ: C2×C10/C10 → C2 ⊆ Aut C22×C6240(C2^2xC6).40(C2xC10)480,809
(C22×C6).41(C2×C10) = C10×C6.D4φ: C2×C10/C10 → C2 ⊆ Aut C22×C6240(C2^2xC6).41(C2xC10)480,831
(C22×C6).42(C2×C10) = C5×C24⋊4S3φ: C2×C10/C10 → C2 ⊆ Aut C22×C6120(C2^2xC6).42(C2xC10)480,832
(C22×C6).43(C2×C10) = C2×C10×Dic6φ: C2×C10/C10 → C2 ⊆ Aut C22×C6480(C2^2xC6).43(C2xC10)480,1150
(C22×C6).44(C2×C10) = S3×C22×C20φ: C2×C10/C10 → C2 ⊆ Aut C22×C6240(C2^2xC6).44(C2xC10)480,1151
(C22×C6).45(C2×C10) = C2×C10×D12φ: C2×C10/C10 → C2 ⊆ Aut C22×C6240(C2^2xC6).45(C2xC10)480,1152
(C22×C6).46(C2×C10) = C10×C4○D12φ: C2×C10/C10 → C2 ⊆ Aut C22×C6240(C2^2xC6).46(C2xC10)480,1153
(C22×C6).47(C2×C10) = Dic3×C22×C10φ: C2×C10/C10 → C2 ⊆ Aut C22×C6480(C2^2xC6).47(C2xC10)480,1163
(C22×C6).48(C2×C10) = C15×C2.C42central extension (φ=1)480(C2^2xC6).48(C2xC10)480,198
(C22×C6).49(C2×C10) = C4⋊C4×C30central extension (φ=1)480(C2^2xC6).49(C2xC10)480,921
(C22×C6).50(C2×C10) = Q8×C2×C30central extension (φ=1)480(C2^2xC6).50(C2xC10)480,1182

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