Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
326 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×D60 | C2 | semidirect |
| 2. C2×C3×C5×D12 | C2 | semidirect |
| 3. C2×C3⋊(C3⋊#168) | C2 | semidirect |
| 4. #10623798 | C2 | direct (N × H) |
| 11. C3×D60 | C22 | semidirect |
| 13. C3×C5×D12 | C22 | semidirect |
| 14. C3⋊(C3⋊#168) | C22 | semidirect |
| 17. C2×D60 | D3 | semidirect |
| 18. C2×C5×D12 | D3 | semidirect |
| 34. C2×C3×D12 | D5 | semidirect |
| 47. D60 | C2×D3 | semidirect |
| 49. C5×D12 | C2×D3 | semidirect |
| 57. C2×C32×C5 | D8 | semidirect |
| 71. C3×D12 | C2×D5 | semidirect |
| 93. C2×D12 | D15 | semidirect |
| 99. C32×C5 | C2×D8 | semidirect |
| 119. C2×C3×C5 | #213 | semidirect |
| 120. C2×C3×C5 | #213 | semidirect |
| 140. D12 | C2×D15 | semidirect |
| 151. C2×C32 | #686 | semidirect |
| 160. C3×C5 | C2×#213 | semidirect |
| 161. C3×C5 | C2×#213 | semidirect |
| 180. C2×C5 | #3713 | semidirect |
| 183. C32 | C2×#686 | semidirect |
| 196. C2×C3 | #6652 | semidirect |
| 197. C2×C3 | #6715 | semidirect |
| 202. C5 | C2×#3713 | semidirect |
| 211. C3 | C2×#6652 | semidirect |
| 212. C3 | C2×#6715 | semidirect |
| 215. C2 | #10623798 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D60 | 2 |
| C2×C3×C5×D12 | 2 |
| C2×C3⋊(C3⋊#168) | 2 |
| #10623798 | 2 |
| C2×#6715 | 3 |
| C2×#6652 | 3 |
| C2×#3713 | 5 |