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Extensions 1→N→G→Q→1 with N=C2×C6 and Q=C2×Dic5

Direct product G=N×Q with N=C2×C6 and Q=C2×Dic5
dρLabelID
Dic5×C22×C6480Dic5xC2^2xC6480,1148

Semidirect products G=N:Q with N=C2×C6 and Q=C2×Dic5
extensionφ:Q→Aut NdρLabelID
(C2×C6)⋊1(C2×Dic5) = S3×C23.D5φ: C2×Dic5/C10 → C22 ⊆ Aut C2×C6120(C2xC6):1(C2xDic5)480,630
(C2×C6)⋊2(C2×Dic5) = Dic15⋊17D4φ: C2×Dic5/C10 → C22 ⊆ Aut C2×C6240(C2xC6):2(C2xDic5)480,636
(C2×C6)⋊3(C2×Dic5) = D4×Dic15φ: C2×Dic5/C10 → C22 ⊆ Aut C2×C6240(C2xC6):3(C2xDic5)480,899
(C2×C6)⋊4(C2×Dic5) = C3×D4×Dic5φ: C2×Dic5/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6):4(C2xDic5)480,727
(C2×C6)⋊5(C2×Dic5) = Dic5×C3⋊D4φ: C2×Dic5/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6):5(C2xDic5)480,627
(C2×C6)⋊6(C2×Dic5) = C22×S3×Dic5φ: C2×Dic5/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6):6(C2xDic5)480,1115
(C2×C6)⋊7(C2×Dic5) = C6×C23.D5φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6):7(C2xDic5)480,745
(C2×C6)⋊8(C2×Dic5) = C2×C30.38D4φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6):8(C2xDic5)480,917
(C2×C6)⋊9(C2×Dic5) = C23×Dic15φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6):9(C2xDic5)480,1178

Non-split extensions G=N.Q with N=C2×C6 and Q=C2×Dic5
extensionφ:Q→Aut NdρLabelID
(C2×C6).1(C2×Dic5) = C20.5D12φ: C2×Dic5/C10 → C22 ⊆ Aut C2×C61204(C2xC6).1(C2xDic5)480,35
(C2×C6).2(C2×Dic5) = C60.54D4φ: C2×Dic5/C10 → C22 ⊆ Aut C2×C62404(C2xC6).2(C2xDic5)480,38
(C2×C6).3(C2×Dic5) = C15⋊8(C23⋊C4)φ: C2×Dic5/C10 → C22 ⊆ Aut C2×C61204(C2xC6).3(C2xDic5)480,72
(C2×C6).4(C2×Dic5) = S3×C4.Dic5φ: C2×Dic5/C10 → C22 ⊆ Aut C2×C61204(C2xC6).4(C2xDic5)480,363
(C2×C6).5(C2×Dic5) = D12.Dic5φ: C2×Dic5/C10 → C22 ⊆ Aut C2×C62404(C2xC6).5(C2xDic5)480,364
(C2×C6).6(C2×Dic5) = C23.26(S3×D5)φ: C2×Dic5/C10 → C22 ⊆ Aut C2×C6240(C2xC6).6(C2xDic5)480,605
(C2×C6).7(C2×Dic5) = D4.Dic15φ: C2×Dic5/C10 → C22 ⊆ Aut C2×C62404(C2xC6).7(C2xDic5)480,913
(C2×C6).8(C2×Dic5) = C3×D4.Dic5φ: C2×Dic5/Dic5 → C2 ⊆ Aut C2×C62404(C2xC6).8(C2xDic5)480,741
(C2×C6).9(C2×Dic5) = Dic3×C5⋊2C8φ: C2×Dic5/Dic5 → C2 ⊆ Aut C2×C6480(C2xC6).9(C2xDic5)480,26
(C2×C6).10(C2×Dic5) = C30.22C42φ: C2×Dic5/Dic5 → C2 ⊆ Aut C2×C6480(C2xC6).10(C2xDic5)480,29
(C2×C6).11(C2×Dic5) = C60.94D4φ: C2×Dic5/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6).11(C2xDic5)480,32
(C2×C6).12(C2×Dic5) = C60.15Q8φ: C2×Dic5/Dic5 → C2 ⊆ Aut C2×C6480(C2xC6).12(C2xDic5)480,60
(C2×C6).13(C2×Dic5) = C30.24C42φ: C2×Dic5/Dic5 → C2 ⊆ Aut C2×C6480(C2xC6).13(C2xDic5)480,70
(C2×C6).14(C2×Dic5) = C2×S3×C5⋊2C8φ: C2×Dic5/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6).14(C2xDic5)480,361
(C2×C6).15(C2×Dic5) = D12.2Dic5φ: C2×Dic5/Dic5 → C2 ⊆ Aut C2×C62404(C2xC6).15(C2xDic5)480,362
(C2×C6).16(C2×Dic5) = C2×D6.Dic5φ: C2×Dic5/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6).16(C2xDic5)480,370
(C2×C6).17(C2×Dic5) = C2×Dic3×Dic5φ: C2×Dic5/Dic5 → C2 ⊆ Aut C2×C6480(C2xC6).17(C2xDic5)480,603
(C2×C6).18(C2×Dic5) = C2×D6⋊Dic5φ: C2×Dic5/Dic5 → C2 ⊆ Aut C2×C6240(C2xC6).18(C2xDic5)480,614
(C2×C6).19(C2×Dic5) = C2×C6.Dic10φ: C2×Dic5/Dic5 → C2 ⊆ Aut C2×C6480(C2xC6).19(C2xDic5)480,621
(C2×C6).20(C2×Dic5) = C3×C20.D4φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C2×C61204(C2xC6).20(C2xDic5)480,111
(C2×C6).21(C2×Dic5) = C3×C23⋊Dic5φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C2×C61204(C2xC6).21(C2xDic5)480,112
(C2×C6).22(C2×Dic5) = C3×C20.10D4φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C2×C62404(C2xC6).22(C2xDic5)480,114
(C2×C6).23(C2×Dic5) = C6×C4.Dic5φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).23(C2xDic5)480,714
(C2×C6).24(C2×Dic5) = C3×C23.21D10φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).24(C2xDic5)480,719
(C2×C6).25(C2×Dic5) = C4×C15⋊3C8φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).25(C2xDic5)480,162
(C2×C6).26(C2×Dic5) = C42.D15φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).26(C2xDic5)480,163
(C2×C6).27(C2×Dic5) = C60⋊5C8φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).27(C2xDic5)480,164
(C2×C6).28(C2×Dic5) = C60.212D4φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).28(C2xDic5)480,190
(C2×C6).29(C2×Dic5) = C30.29C42φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).29(C2xDic5)480,191
(C2×C6).30(C2×Dic5) = C60.8D4φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C2×C61204(C2xC6).30(C2xDic5)480,193
(C2×C6).31(C2×Dic5) = C23.7D30φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C2×C61204(C2xC6).31(C2xDic5)480,194
(C2×C6).32(C2×Dic5) = C60.10D4φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C2×C62404(C2xC6).32(C2xDic5)480,196
(C2×C6).33(C2×Dic5) = C22×C15⋊3C8φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).33(C2xDic5)480,885
(C2×C6).34(C2×Dic5) = C2×C60.7C4φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).34(C2xDic5)480,886
(C2×C6).35(C2×Dic5) = C2×C4×Dic15φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).35(C2xDic5)480,887
(C2×C6).36(C2×Dic5) = C2×C60⋊5C4φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C2×C6480(C2xC6).36(C2xDic5)480,890
(C2×C6).37(C2×Dic5) = C23.26D30φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C2×C6240(C2xC6).37(C2xDic5)480,891
(C2×C6).38(C2×Dic5) = C12×C5⋊2C8central extension (φ=1)480(C2xC6).38(C2xDic5)480,80
(C2×C6).39(C2×Dic5) = C3×C42.D5central extension (φ=1)480(C2xC6).39(C2xDic5)480,81
(C2×C6).40(C2×Dic5) = C3×C20⋊3C8central extension (φ=1)480(C2xC6).40(C2xDic5)480,82
(C2×C6).41(C2×Dic5) = C3×C20.55D4central extension (φ=1)240(C2xC6).41(C2xDic5)480,108
(C2×C6).42(C2×Dic5) = C3×C10.10C42central extension (φ=1)480(C2xC6).42(C2xDic5)480,109
(C2×C6).43(C2×Dic5) = C2×C6×C5⋊2C8central extension (φ=1)480(C2xC6).43(C2xDic5)480,713
(C2×C6).44(C2×Dic5) = Dic5×C2×C12central extension (φ=1)480(C2xC6).44(C2xDic5)480,715
(C2×C6).45(C2×Dic5) = C6×C4⋊Dic5central extension (φ=1)480(C2xC6).45(C2xDic5)480,718

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