Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
204 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 53 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. D5×D36 | C2 | semidirect |
| 2. #10623665 | C2 | semidirect |
| 3. D360 | C2 | semidirect |
| 4. C5×#3664 | C2 | semidirect |
| 5. C9×#676 | C2 | semidirect |
| 6. #10623544 | C2 | semidirect |
| 7. #10623543 | C2 | semidirect |
| 11. D180 | C22 | semidirect |
| 13. C5×Dic18 | C22 | semidirect |
| 18. C5×C8×C9 | C22 | semidirect |
| 19. C9×#168 | C22 | semidirect |
| 43. #3664 | D5 | semidirect |
| 67. #676 | D9 | semidirect |
| 76. Dic18 | C2×D5 | semidirect |
| 78. C8×C9 | C2×D5 | semidirect |
| 94. C5×C9 | AGL(1,ℤ/8) | semidirect |
| 104. C5×C8 | C2×D9 | semidirect |
| 105. #168 | C2×D9 | semidirect |
| 165. C9 | #4060 | semidirect |
| 176. C8 | D5×D9 | semidirect |
| 182. C5 | #63470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×D36 | 2 |
| #10623665 | 2 |
| D360 | 2 |
| C5×#3664 | 2 |
| C9×#676 | 2 |
| #10623544 | 2 |
| #10623543 | 2 |
| #91249 | 3 |
| #63470 | 5 |