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Extensions 1→N→G→Q→1 with N=C5×Q8 and Q=C2×C6

Direct product G=N×Q with N=C5×Q8 and Q=C2×C6
dρLabelID
Q8×C2×C30480Q8xC2xC30480,1182

Semidirect products G=N:Q with N=C5×Q8 and Q=C2×C6
extensionφ:Q→Out NdρLabelID
(C5×Q8)⋊(C2×C6) = C2×D5×SL2(𝔽3)φ: C2×C6/C2 → C6 ⊆ Out C5×Q880(C5xQ8):(C2xC6)480,1039
(C5×Q8)⋊2(C2×C6) = C3×D5×SD16φ: C2×C6/C3 → C22 ⊆ Out C5×Q81204(C5xQ8):2(C2xC6)480,706
(C5×Q8)⋊3(C2×C6) = C3×D40⋊C2φ: C2×C6/C3 → C22 ⊆ Out C5×Q81204(C5xQ8):3(C2xC6)480,707
(C5×Q8)⋊4(C2×C6) = C2×C10×SL2(𝔽3)φ: C2×C6/C22 → C3 ⊆ Out C5×Q8160(C5xQ8):4(C2xC6)480,1128
(C5×Q8)⋊5(C2×C6) = C6×Q8⋊D5φ: C2×C6/C6 → C2 ⊆ Out C5×Q8240(C5xQ8):5(C2xC6)480,734
(C5×Q8)⋊6(C2×C6) = C3×D4⋊D10φ: C2×C6/C6 → C2 ⊆ Out C5×Q81204(C5xQ8):6(C2xC6)480,742
(C5×Q8)⋊7(C2×C6) = C6×Q8×D5φ: C2×C6/C6 → C2 ⊆ Out C5×Q8240(C5xQ8):7(C2xC6)480,1142
(C5×Q8)⋊8(C2×C6) = C6×Q8⋊2D5φ: C2×C6/C6 → C2 ⊆ Out C5×Q8240(C5xQ8):8(C2xC6)480,1143
(C5×Q8)⋊9(C2×C6) = C3×D5×C4○D4φ: C2×C6/C6 → C2 ⊆ Out C5×Q81204(C5xQ8):9(C2xC6)480,1145
(C5×Q8)⋊10(C2×C6) = C3×D4⋊8D10φ: C2×C6/C6 → C2 ⊆ Out C5×Q81204(C5xQ8):10(C2xC6)480,1146
(C5×Q8)⋊11(C2×C6) = SD16×C30φ: C2×C6/C6 → C2 ⊆ Out C5×Q8240(C5xQ8):11(C2xC6)480,938
(C5×Q8)⋊12(C2×C6) = C15×C8⋊C22φ: C2×C6/C6 → C2 ⊆ Out C5×Q81204(C5xQ8):12(C2xC6)480,941
(C5×Q8)⋊13(C2×C6) = C4○D4×C30φ: trivial image240(C5xQ8):13(C2xC6)480,1183
(C5×Q8)⋊14(C2×C6) = C15×2+ 1+4φ: trivial image1204(C5xQ8):14(C2xC6)480,1184

Non-split extensions G=N.Q with N=C5×Q8 and Q=C2×C6
extensionφ:Q→Out NdρLabelID
(C5×Q8).1(C2×C6) = C2×Dic5.A4φ: C2×C6/C2 → C6 ⊆ Out C5×Q8160(C5xQ8).1(C2xC6)480,1038
(C5×Q8).2(C2×C6) = SL2(𝔽3).11D10φ: C2×C6/C2 → C6 ⊆ Out C5×Q8804(C5xQ8).2(C2xC6)480,1040
(C5×Q8).3(C2×C6) = Dic10.A4φ: C2×C6/C2 → C6 ⊆ Out C5×Q81204+(C5xQ8).3(C2xC6)480,1041
(C5×Q8).4(C2×C6) = D5×C4.A4φ: C2×C6/C2 → C6 ⊆ Out C5×Q8804(C5xQ8).4(C2xC6)480,1042
(C5×Q8).5(C2×C6) = D20.A4φ: C2×C6/C2 → C6 ⊆ Out C5×Q8804-(C5xQ8).5(C2xC6)480,1043
(C5×Q8).6(C2×C6) = C3×SD16⋊D5φ: C2×C6/C3 → C22 ⊆ Out C5×Q82404(C5xQ8).6(C2xC6)480,708
(C5×Q8).7(C2×C6) = C3×SD16⋊3D5φ: C2×C6/C3 → C22 ⊆ Out C5×Q82404(C5xQ8).7(C2xC6)480,709
(C5×Q8).8(C2×C6) = C3×D5×Q16φ: C2×C6/C3 → C22 ⊆ Out C5×Q82404(C5xQ8).8(C2xC6)480,710
(C5×Q8).9(C2×C6) = C3×Q16⋊D5φ: C2×C6/C3 → C22 ⊆ Out C5×Q82404(C5xQ8).9(C2xC6)480,711
(C5×Q8).10(C2×C6) = C3×Q8.D10φ: C2×C6/C3 → C22 ⊆ Out C5×Q82404(C5xQ8).10(C2xC6)480,712
(C5×Q8).11(C2×C6) = C10×C4.A4φ: C2×C6/C22 → C3 ⊆ Out C5×Q8160(C5xQ8).11(C2xC6)480,1130
(C5×Q8).12(C2×C6) = C5×Q8.A4φ: C2×C6/C22 → C3 ⊆ Out C5×Q81204(C5xQ8).12(C2xC6)480,1131
(C5×Q8).13(C2×C6) = C5×D4.A4φ: C2×C6/C22 → C3 ⊆ Out C5×Q8804(C5xQ8).13(C2xC6)480,1132
(C5×Q8).14(C2×C6) = C3×C20.C23φ: C2×C6/C6 → C2 ⊆ Out C5×Q82404(C5xQ8).14(C2xC6)480,735
(C5×Q8).15(C2×C6) = C6×C5⋊Q16φ: C2×C6/C6 → C2 ⊆ Out C5×Q8480(C5xQ8).15(C2xC6)480,736
(C5×Q8).16(C2×C6) = C3×D4.8D10φ: C2×C6/C6 → C2 ⊆ Out C5×Q82404(C5xQ8).16(C2xC6)480,743
(C5×Q8).17(C2×C6) = C3×D4.9D10φ: C2×C6/C6 → C2 ⊆ Out C5×Q82404(C5xQ8).17(C2xC6)480,744
(C5×Q8).18(C2×C6) = C3×Q8.10D10φ: C2×C6/C6 → C2 ⊆ Out C5×Q82404(C5xQ8).18(C2xC6)480,1144
(C5×Q8).19(C2×C6) = C3×D4.10D10φ: C2×C6/C6 → C2 ⊆ Out C5×Q82404(C5xQ8).19(C2xC6)480,1147
(C5×Q8).20(C2×C6) = Q16×C30φ: C2×C6/C6 → C2 ⊆ Out C5×Q8480(C5xQ8).20(C2xC6)480,939
(C5×Q8).21(C2×C6) = C15×C4○D8φ: C2×C6/C6 → C2 ⊆ Out C5×Q82402(C5xQ8).21(C2xC6)480,940
(C5×Q8).22(C2×C6) = C15×C8.C22φ: C2×C6/C6 → C2 ⊆ Out C5×Q82404(C5xQ8).22(C2xC6)480,942
(C5×Q8).23(C2×C6) = C15×2- 1+4φ: trivial image2404(C5xQ8).23(C2xC6)480,1185

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