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Extensions 1→N→G→Q→1 with N=C2×C6 and Q=C5×D4

Direct product G=N×Q with N=C2×C6 and Q=C5×D4
dρLabelID
D4×C2×C30240D4xC2xC30480,1181

Semidirect products G=N:Q with N=C2×C6 and Q=C5×D4
extensionφ:Q→Aut NdρLabelID
(C2×C6)⋊1(C5×D4) = C5×D6⋊D4φ: C5×D4/C10 → C22 ⊆ Aut C2×C6120(C2xC6):1(C5xD4)480,761
(C2×C6)⋊2(C5×D4) = C5×C23⋊2D6φ: C5×D4/C10 → C22 ⊆ Aut C2×C6120(C2xC6):2(C5xD4)480,816
(C2×C6)⋊3(C5×D4) = C5×C23.14D6φ: C5×D4/C10 → C22 ⊆ Aut C2×C6240(C2xC6):3(C5xD4)480,818
(C2×C6)⋊4(C5×D4) = C15×C4⋊D4φ: C5×D4/C20 → C2 ⊆ Aut C2×C6240(C2xC6):4(C5xD4)480,926
(C2×C6)⋊5(C5×D4) = C5×C12⋊7D4φ: C5×D4/C20 → C2 ⊆ Aut C2×C6240(C2xC6):5(C5xD4)480,809
(C2×C6)⋊6(C5×D4) = C2×C10×D12φ: C5×D4/C20 → C2 ⊆ Aut C2×C6240(C2xC6):6(C5xD4)480,1152
(C2×C6)⋊7(C5×D4) = C15×C22≀C2φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C6120(C2xC6):7(C5xD4)480,925
(C2×C6)⋊8(C5×D4) = C5×C24⋊4S3φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C6120(C2xC6):8(C5xD4)480,832
(C2×C6)⋊9(C5×D4) = C2×C10×C3⋊D4φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6):9(C5xD4)480,1164

Non-split extensions G=N.Q with N=C2×C6 and Q=C5×D4
extensionφ:Q→Aut NdρLabelID
(C2×C6).1(C5×D4) = C5×D12⋊C4φ: C5×D4/C10 → C22 ⊆ Aut C2×C61204(C2xC6).1(C5xD4)480,144
(C2×C6).2(C5×D4) = C5×C23.7D6φ: C5×D4/C10 → C22 ⊆ Aut C2×C61204(C2xC6).2(C5xD4)480,153
(C2×C6).3(C5×D4) = C5×Q8⋊3Dic3φ: C5×D4/C10 → C22 ⊆ Aut C2×C61204(C2xC6).3(C5xD4)480,156
(C2×C6).4(C5×D4) = C5×C23.21D6φ: C5×D4/C10 → C22 ⊆ Aut C2×C6240(C2xC6).4(C5xD4)480,765
(C2×C6).5(C5×D4) = C5×C8⋊D6φ: C5×D4/C10 → C22 ⊆ Aut C2×C61204(C2xC6).5(C5xD4)480,787
(C2×C6).6(C5×D4) = C5×C8.D6φ: C5×D4/C10 → C22 ⊆ Aut C2×C62404(C2xC6).6(C5xD4)480,788
(C2×C6).7(C5×D4) = C5×C23.23D6φ: C5×D4/C10 → C22 ⊆ Aut C2×C6240(C2xC6).7(C5xD4)480,814
(C2×C6).8(C5×D4) = C5×D4⋊D6φ: C5×D4/C10 → C22 ⊆ Aut C2×C61204(C2xC6).8(C5xD4)480,828
(C2×C6).9(C5×D4) = C5×Q8.13D6φ: C5×D4/C10 → C22 ⊆ Aut C2×C62404(C2xC6).9(C5xD4)480,829
(C2×C6).10(C5×D4) = C5×Q8.14D6φ: C5×D4/C10 → C22 ⊆ Aut C2×C62404(C2xC6).10(C5xD4)480,830
(C2×C6).11(C5×D4) = C15×C4○D8φ: C5×D4/C20 → C2 ⊆ Aut C2×C62402(C2xC6).11(C5xD4)480,940
(C2×C6).12(C5×D4) = C5×C2.Dic12φ: C5×D4/C20 → C2 ⊆ Aut C2×C6480(C2xC6).12(C5xD4)480,135
(C2×C6).13(C5×D4) = C5×C8⋊Dic3φ: C5×D4/C20 → C2 ⊆ Aut C2×C6480(C2xC6).13(C5xD4)480,136
(C2×C6).14(C5×D4) = C5×C24⋊1C4φ: C5×D4/C20 → C2 ⊆ Aut C2×C6480(C2xC6).14(C5xD4)480,137
(C2×C6).15(C5×D4) = C5×C2.D24φ: C5×D4/C20 → C2 ⊆ Aut C2×C6240(C2xC6).15(C5xD4)480,140
(C2×C6).16(C5×D4) = C10×C24⋊C2φ: C5×D4/C20 → C2 ⊆ Aut C2×C6240(C2xC6).16(C5xD4)480,781
(C2×C6).17(C5×D4) = C10×D24φ: C5×D4/C20 → C2 ⊆ Aut C2×C6240(C2xC6).17(C5xD4)480,782
(C2×C6).18(C5×D4) = C5×C4○D24φ: C5×D4/C20 → C2 ⊆ Aut C2×C62402(C2xC6).18(C5xD4)480,783
(C2×C6).19(C5×D4) = C10×Dic12φ: C5×D4/C20 → C2 ⊆ Aut C2×C6480(C2xC6).19(C5xD4)480,784
(C2×C6).20(C5×D4) = C10×C4⋊Dic3φ: C5×D4/C20 → C2 ⊆ Aut C2×C6480(C2xC6).20(C5xD4)480,804
(C2×C6).21(C5×D4) = C15×C23⋊C4φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C61204(C2xC6).21(C5xD4)480,202
(C2×C6).22(C5×D4) = C15×C4≀C2φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C61202(C2xC6).22(C5xD4)480,207
(C2×C6).23(C5×D4) = C15×C22.D4φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).23(C5xD4)480,928
(C2×C6).24(C5×D4) = C15×C8⋊C22φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C61204(C2xC6).24(C5xD4)480,941
(C2×C6).25(C5×D4) = C15×C8.C22φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C62404(C2xC6).25(C5xD4)480,942
(C2×C6).26(C5×D4) = C5×C42⋊4S3φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C61202(C2xC6).26(C5xD4)480,124
(C2×C6).27(C5×D4) = C5×C23.6D6φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C61204(C2xC6).27(C5xD4)480,125
(C2×C6).28(C5×D4) = C5×C6.Q16φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).28(C5xD4)480,126
(C2×C6).29(C5×D4) = C5×C12.Q8φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).29(C5xD4)480,127
(C2×C6).30(C5×D4) = C5×C6.D8φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).30(C5xD4)480,128
(C2×C6).31(C5×D4) = C5×C6.SD16φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).31(C5xD4)480,129
(C2×C6).32(C5×D4) = C5×C6.C42φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).32(C5xD4)480,150
(C2×C6).33(C5×D4) = C5×D4⋊Dic3φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).33(C5xD4)480,151
(C2×C6).34(C5×D4) = C5×Q8⋊2Dic3φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).34(C5xD4)480,154
(C2×C6).35(C5×D4) = C10×Dic3⋊C4φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).35(C5xD4)480,802
(C2×C6).36(C5×D4) = C10×D6⋊C4φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).36(C5xD4)480,806
(C2×C6).37(C5×D4) = C5×C23.28D6φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).37(C5xD4)480,808
(C2×C6).38(C5×D4) = C10×D4⋊S3φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).38(C5xD4)480,810
(C2×C6).39(C5×D4) = C5×D12⋊6C22φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C61204(C2xC6).39(C5xD4)480,811
(C2×C6).40(C5×D4) = C10×D4.S3φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).40(C5xD4)480,812
(C2×C6).41(C5×D4) = C10×Q8⋊2S3φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).41(C5xD4)480,820
(C2×C6).42(C5×D4) = C5×Q8.11D6φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C62404(C2xC6).42(C5xD4)480,821
(C2×C6).43(C5×D4) = C10×C3⋊Q16φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).43(C5xD4)480,822
(C2×C6).44(C5×D4) = C10×C6.D4φ: C5×D4/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).44(C5xD4)480,831
(C2×C6).45(C5×D4) = C15×C2.C42central extension (φ=1)480(C2xC6).45(C5xD4)480,198
(C2×C6).46(C5×D4) = C15×D4⋊C4central extension (φ=1)240(C2xC6).46(C5xD4)480,205
(C2×C6).47(C5×D4) = C15×Q8⋊C4central extension (φ=1)480(C2xC6).47(C5xD4)480,206
(C2×C6).48(C5×D4) = C15×C4.Q8central extension (φ=1)480(C2xC6).48(C5xD4)480,209
(C2×C6).49(C5×D4) = C15×C2.D8central extension (φ=1)480(C2xC6).49(C5xD4)480,210
(C2×C6).50(C5×D4) = C22⋊C4×C30central extension (φ=1)240(C2xC6).50(C5xD4)480,920
(C2×C6).51(C5×D4) = C4⋊C4×C30central extension (φ=1)480(C2xC6).51(C5xD4)480,921
(C2×C6).52(C5×D4) = D8×C30central extension (φ=1)240(C2xC6).52(C5xD4)480,937
(C2×C6).53(C5×D4) = SD16×C30central extension (φ=1)240(C2xC6).53(C5xD4)480,938
(C2×C6).54(C5×D4) = Q16×C30central extension (φ=1)480(C2xC6).54(C5xD4)480,939

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