Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
270 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 80 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. C3×C5×#237 | C2 | semidirect |
| 2. C5×#3799 | C2 | semidirect |
| 3. C5×#3753 | C2 | semidirect |
| 4. C3×C5×#214 | C2 | semidirect |
| 5. C5×#3718 | C2 | semidirect |
| 6. C5×#3717 | C2 | semidirect |
| 7. C5×D3×C3⋊C8 | C2 | semidirect |
| 21. #63935 | C5 | direct (N × H) |
| 24. C5×#237 | D3 | semidirect |
| 30. C5×#214 | D3 | semidirect |
| 45. C3×#237 | C2×C5 | semidirect |
| 46. #3799 | C2×C5 | semidirect |
| 47. #3753 | C2×C5 | semidirect |
| 48. C3×#214 | C2×C5 | semidirect |
| 49. #3718 | C2×C5 | semidirect |
| 50. #3717 | C2×C5 | semidirect |
| 51. D3×C3⋊C8 | C2×C5 | semidirect |
| 120. #237 | C5×D3 | semidirect |
| 126. #214 | C5×D3 | semidirect |
| 133. C32×C5 | #135 | semidirect |
| 208. C3×C5 | #916 | semidirect |
| 209. C3×C5 | #950 | semidirect |
| 231. C32 | C5×#135 | semidirect |
| 254. C5 | #63935 | direct (N × H) |
| 263. C3 | C5×#916 | semidirect |
| 264. C3 | C5×#950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#237 | 2 |
| C5×#3799 | 2 |
| C5×#3753 | 2 |
| C3×C5×#214 | 2 |
| C5×#3718 | 2 |
| C5×#3717 | 2 |
| C5×D3×C3⋊C8 | 2 |
| C5×#950 | 3 |
| C5×#916 | 3 |
| #63935 | 5 |