# Extensions 1→N→G→Q→1 with N=C5×C4○D4 and Q=C6

Direct product G=N×Q with N=C5×C4○D4 and Q=C6
dρLabelID
C4○D4×C30240C4oD4xC30480,1183

Semidirect products G=N:Q with N=C5×C4○D4 and Q=C6
extensionφ:Q→Out NdρLabelID
(C5×C4○D4)⋊1C6 = D5×C4.A4φ: C6/C1C6 ⊆ Out C5×C4○D4804(C5xC4oD4):1C6480,1042
(C5×C4○D4)⋊2C6 = D20.A4φ: C6/C1C6 ⊆ Out C5×C4○D4804-(C5xC4oD4):2C6480,1043
(C5×C4○D4)⋊3C6 = C5×D4.A4φ: C6/C1C6 ⊆ Out C5×C4○D4804(C5xC4oD4):3C6480,1132
(C5×C4○D4)⋊4C6 = C10×C4.A4φ: C6/C2C3 ⊆ Out C5×C4○D4160(C5xC4oD4):4C6480,1130
(C5×C4○D4)⋊5C6 = C3×D4⋊D10φ: C6/C3C2 ⊆ Out C5×C4○D41204(C5xC4oD4):5C6480,742
(C5×C4○D4)⋊6C6 = C3×D4.8D10φ: C6/C3C2 ⊆ Out C5×C4○D42404(C5xC4oD4):6C6480,743
(C5×C4○D4)⋊7C6 = C3×D5×C4○D4φ: C6/C3C2 ⊆ Out C5×C4○D41204(C5xC4oD4):7C6480,1145
(C5×C4○D4)⋊8C6 = C3×D48D10φ: C6/C3C2 ⊆ Out C5×C4○D41204(C5xC4oD4):8C6480,1146
(C5×C4○D4)⋊9C6 = C3×D4.10D10φ: C6/C3C2 ⊆ Out C5×C4○D42404(C5xC4oD4):9C6480,1147
(C5×C4○D4)⋊10C6 = C15×C4○D8φ: C6/C3C2 ⊆ Out C5×C4○D42402(C5xC4oD4):10C6480,940
(C5×C4○D4)⋊11C6 = C15×C8⋊C22φ: C6/C3C2 ⊆ Out C5×C4○D41204(C5xC4oD4):11C6480,941
(C5×C4○D4)⋊12C6 = C15×2+ 1+4φ: C6/C3C2 ⊆ Out C5×C4○D41204(C5xC4oD4):12C6480,1184
(C5×C4○D4)⋊13C6 = C15×2- 1+4φ: C6/C3C2 ⊆ Out C5×C4○D42404(C5xC4oD4):13C6480,1185

Non-split extensions G=N.Q with N=C5×C4○D4 and Q=C6
extensionφ:Q→Out NdρLabelID
(C5×C4○D4).1C6 = SL2(𝔽3).Dic5φ: C6/C1C6 ⊆ Out C5×C4○D41604(C5xC4oD4).1C6480,267
(C5×C4○D4).2C6 = Dic10.A4φ: C6/C1C6 ⊆ Out C5×C4○D41204+(C5xC4oD4).2C6480,1041
(C5×C4○D4).3C6 = C5×Q8.A4φ: C6/C1C6 ⊆ Out C5×C4○D41204(C5xC4oD4).3C6480,1131
(C5×C4○D4).4C6 = C5×C8.A4φ: C6/C2C3 ⊆ Out C5×C4○D41602(C5xC4oD4).4C6480,660
(C5×C4○D4).5C6 = C3×D42Dic5φ: C6/C3C2 ⊆ Out C5×C4○D41204(C5xC4oD4).5C6480,115
(C5×C4○D4).6C6 = C3×D4.Dic5φ: C6/C3C2 ⊆ Out C5×C4○D42404(C5xC4oD4).6C6480,741
(C5×C4○D4).7C6 = C3×D4.9D10φ: C6/C3C2 ⊆ Out C5×C4○D42404(C5xC4oD4).7C6480,744
(C5×C4○D4).8C6 = C15×C4≀C2φ: C6/C3C2 ⊆ Out C5×C4○D41202(C5xC4oD4).8C6480,207
(C5×C4○D4).9C6 = C15×C8.C22φ: C6/C3C2 ⊆ Out C5×C4○D42404(C5xC4oD4).9C6480,942
(C5×C4○D4).10C6 = C15×C8○D4φ: trivial image2402(C5xC4oD4).10C6480,936

׿
×
𝔽