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Extensions 1→N→G→Q→1 with N=C2×C6 and Q=C2×C20

Direct product G=N×Q with N=C2×C6 and Q=C2×C20
dρLabelID
C23×C60480C2^3xC60480,1180

Semidirect products G=N:Q with N=C2×C6 and Q=C2×C20
extensionφ:Q→Aut NdρLabelID
(C2×C6)⋊1(C2×C20) = C5×S3×C22⋊C4φ: C2×C20/C10 → C22 ⊆ Aut C2×C6120(C2xC6):1(C2xC20)480,759
(C2×C6)⋊2(C2×C20) = C5×Dic3⋊4D4φ: C2×C20/C10 → C22 ⊆ Aut C2×C6240(C2xC6):2(C2xC20)480,760
(C2×C6)⋊3(C2×C20) = C5×D4×Dic3φ: C2×C20/C10 → C22 ⊆ Aut C2×C6240(C2xC6):3(C2xC20)480,813
(C2×C6)⋊4(C2×C20) = D4×C60φ: C2×C20/C20 → C2 ⊆ Aut C2×C6240(C2xC6):4(C2xC20)480,923
(C2×C6)⋊5(C2×C20) = C20×C3⋊D4φ: C2×C20/C20 → C2 ⊆ Aut C2×C6240(C2xC6):5(C2xC20)480,807
(C2×C6)⋊6(C2×C20) = S3×C22×C20φ: C2×C20/C20 → C2 ⊆ Aut C2×C6240(C2xC6):6(C2xC20)480,1151
(C2×C6)⋊7(C2×C20) = C22⋊C4×C30φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6):7(C2xC20)480,920
(C2×C6)⋊8(C2×C20) = C10×C6.D4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6):8(C2xC20)480,831
(C2×C6)⋊9(C2×C20) = Dic3×C22×C10φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6):9(C2xC20)480,1163

Non-split extensions G=N.Q with N=C2×C6 and Q=C2×C20
extensionφ:Q→Aut NdρLabelID
(C2×C6).1(C2×C20) = C5×C23.6D6φ: C2×C20/C10 → C22 ⊆ Aut C2×C61204(C2xC6).1(C2xC20)480,125
(C2×C6).2(C2×C20) = C5×C12.46D4φ: C2×C20/C10 → C22 ⊆ Aut C2×C61204(C2xC6).2(C2xC20)480,142
(C2×C6).3(C2×C20) = C5×C12.47D4φ: C2×C20/C10 → C22 ⊆ Aut C2×C62404(C2xC6).3(C2xC20)480,143
(C2×C6).4(C2×C20) = C5×C23.16D6φ: C2×C20/C10 → C22 ⊆ Aut C2×C6240(C2xC6).4(C2xC20)480,756
(C2×C6).5(C2×C20) = C5×S3×M4(2)φ: C2×C20/C10 → C22 ⊆ Aut C2×C61204(C2xC6).5(C2xC20)480,785
(C2×C6).6(C2×C20) = C5×D12.C4φ: C2×C20/C10 → C22 ⊆ Aut C2×C62404(C2xC6).6(C2xC20)480,786
(C2×C6).7(C2×C20) = C5×D4.Dic3φ: C2×C20/C10 → C22 ⊆ Aut C2×C62404(C2xC6).7(C2xC20)480,827
(C2×C6).8(C2×C20) = C15×C8○D4φ: C2×C20/C20 → C2 ⊆ Aut C2×C62402(C2xC6).8(C2xC20)480,936
(C2×C6).9(C2×C20) = Dic3×C40φ: C2×C20/C20 → C2 ⊆ Aut C2×C6480(C2xC6).9(C2xC20)480,132
(C2×C6).10(C2×C20) = C5×Dic3⋊C8φ: C2×C20/C20 → C2 ⊆ Aut C2×C6480(C2xC6).10(C2xC20)480,133
(C2×C6).11(C2×C20) = C5×C24⋊C4φ: C2×C20/C20 → C2 ⊆ Aut C2×C6480(C2xC6).11(C2xC20)480,134
(C2×C6).12(C2×C20) = C5×D6⋊C8φ: C2×C20/C20 → C2 ⊆ Aut C2×C6240(C2xC6).12(C2xC20)480,139
(C2×C6).13(C2×C20) = C5×C6.C42φ: C2×C20/C20 → C2 ⊆ Aut C2×C6480(C2xC6).13(C2xC20)480,150
(C2×C6).14(C2×C20) = S3×C2×C40φ: C2×C20/C20 → C2 ⊆ Aut C2×C6240(C2xC6).14(C2xC20)480,778
(C2×C6).15(C2×C20) = C10×C8⋊S3φ: C2×C20/C20 → C2 ⊆ Aut C2×C6240(C2xC6).15(C2xC20)480,779
(C2×C6).16(C2×C20) = C5×C8○D12φ: C2×C20/C20 → C2 ⊆ Aut C2×C62402(C2xC6).16(C2xC20)480,780
(C2×C6).17(C2×C20) = C10×Dic3⋊C4φ: C2×C20/C20 → C2 ⊆ Aut C2×C6480(C2xC6).17(C2xC20)480,802
(C2×C6).18(C2×C20) = C10×D6⋊C4φ: C2×C20/C20 → C2 ⊆ Aut C2×C6240(C2xC6).18(C2xC20)480,806
(C2×C6).19(C2×C20) = C15×C23⋊C4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C61204(C2xC6).19(C2xC20)480,202
(C2×C6).20(C2×C20) = C15×C4.D4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C61204(C2xC6).20(C2xC20)480,203
(C2×C6).21(C2×C20) = C15×C4.10D4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C62404(C2xC6).21(C2xC20)480,204
(C2×C6).22(C2×C20) = C15×C42⋊C2φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).22(C2xC20)480,922
(C2×C6).23(C2×C20) = M4(2)×C30φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).23(C2xC20)480,935
(C2×C6).24(C2×C20) = C20×C3⋊C8φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).24(C2xC20)480,121
(C2×C6).25(C2×C20) = C5×C42.S3φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).25(C2xC20)480,122
(C2×C6).26(C2×C20) = C5×C12⋊C8φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).26(C2xC20)480,123
(C2×C6).27(C2×C20) = C5×C12.55D4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).27(C2xC20)480,149
(C2×C6).28(C2×C20) = C5×C12.D4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C61204(C2xC6).28(C2xC20)480,152
(C2×C6).29(C2×C20) = C5×C23.7D6φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C61204(C2xC6).29(C2xC20)480,153
(C2×C6).30(C2×C20) = C5×C12.10D4φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C62404(C2xC6).30(C2xC20)480,155
(C2×C6).31(C2×C20) = C2×C10×C3⋊C8φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).31(C2xC20)480,799
(C2×C6).32(C2×C20) = C10×C4.Dic3φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).32(C2xC20)480,800
(C2×C6).33(C2×C20) = Dic3×C2×C20φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).33(C2xC20)480,801
(C2×C6).34(C2×C20) = C10×C4⋊Dic3φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).34(C2xC20)480,804
(C2×C6).35(C2×C20) = C5×C23.26D6φ: C2×C20/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).35(C2xC20)480,805
(C2×C6).36(C2×C20) = C15×C2.C42central extension (φ=1)480(C2xC6).36(C2xC20)480,198
(C2×C6).37(C2×C20) = C15×C8⋊C4central extension (φ=1)480(C2xC6).37(C2xC20)480,200
(C2×C6).38(C2×C20) = C15×C22⋊C8central extension (φ=1)240(C2xC6).38(C2xC20)480,201
(C2×C6).39(C2×C20) = C15×C4⋊C8central extension (φ=1)480(C2xC6).39(C2xC20)480,208
(C2×C6).40(C2×C20) = C4⋊C4×C30central extension (φ=1)480(C2xC6).40(C2xC20)480,921

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