Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
492 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 216 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×C5×D4×C9 | C2 | semidirect |
| 2. C2×C5×#611 | C2 | semidirect |
| 3. C22×C5×Dic9 | C2 | semidirect |
| 4. C5×#3699 | C2 | direct (N × H) |
| 5. C2×C4×C5×D9 | C2 | semidirect |
| 6. C2×C5×Dic18 | C2 | semidirect |
| 10. C5×D4×C9 | C22 | semidirect |
| 12. C5×#611 | C22 | semidirect |
| 15. C2×C5×Dic9 | C22 | semidirect |
| 16. C4×C5×D9 | C22 | semidirect |
| 17. C5×Dic18 | C22 | semidirect |
| 18. C2×#3699 | C5 | direct (N × H) |
| 34. C2×D4×C9 | C2×C5 | semidirect |
| 35. C2×#611 | C2×C5 | semidirect |
| 36. C22×Dic9 | C2×C5 | semidirect |
| 37. #3699 | C2×C5 | direct (N × H) |
| 38. C2×C4×D9 | C2×C5 | semidirect |
| 39. C2×Dic18 | C2×C5 | semidirect |
| 52. C2×C5×C9 | #41 | semidirect |
| 58. C2×C5×D4 | D9 | semidirect |
| 63. D4×C9 | C22×C5 | semidirect |
| 65. #611 | C22×C5 | semidirect |
| 68. C2×Dic9 | C22×C5 | semidirect |
| 69. C4×D9 | C22×C5 | semidirect |
| 70. Dic18 | C22×C5 | semidirect |
| 85. C5×C9 | C2×#41 | semidirect |
| 90. C5×D4 | C2×D9 | semidirect |
| 128. C2×C9 | C5×#41 | semidirect |
| 134. C2×D4 | C5×D9 | semidirect |
| 148. C2×C5 | #3699 | direct (N × H) |
| 150. C9 | C2×C5×#41 | semidirect |
| 155. D4 | C2×C5×D9 | semidirect |
| 165. C5 | C2×#3699 | direct (N × H) |
| 177. C2 | C5×#3699 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×C9 | 2 |
| C2×C5×#611 | 2 |
| C22×C5×Dic9 | 2 |
| C5×#3699 | 2 |
| C2×C4×C5×D9 | 2 |
| C2×C5×Dic18 | 2 |
| C2×C5×#237 | 3 |
| C2×#3699 | 5 |