Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
288 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 76 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. C5×#3830 | C2 | semidirect |
| 2. C5×#3796 | C2 | semidirect |
| 3. C3×C5×#214 | C2 | semidirect |
| 4. C3×C5×#213 | C2 | semidirect |
| 5. C5×#3719 | C2 | semidirect |
| 6. C5×#3716 | C2 | semidirect |
| 7. C5×#3710 | C2 | semidirect |
| 21. #63936 | C5 | direct (N × H) |
| 31. C5×#214 | D3 | semidirect |
| 32. C5×#213 | D3 | semidirect |
| 45. #3830 | C2×C5 | semidirect |
| 46. #3796 | C2×C5 | semidirect |
| 47. C3×#214 | C2×C5 | semidirect |
| 48. C3×#213 | C2×C5 | semidirect |
| 49. #3719 | C2×C5 | semidirect |
| 50. #3716 | C2×C5 | semidirect |
| 51. #3710 | C2×C5 | semidirect |
| 131. #214 | C5×D3 | semidirect |
| 132. #213 | C5×D3 | semidirect |
| 137. C32×C5 | #135 | semidirect |
| 214. C3×C5 | #912 | semidirect |
| 215. C3×C5 | #916 | semidirect |
| 239. C32 | C5×#135 | semidirect |
| 262. C5 | #63936 | direct (N × H) |
| 271. C3 | C5×#912 | semidirect |
| 272. C3 | C5×#916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3830 | 2 |
| C5×#3796 | 2 |
| C3×C5×#214 | 2 |
| C3×C5×#213 | 2 |
| C5×#3719 | 2 |
| C5×#3716 | 2 |
| C5×#3710 | 2 |
| C5×#916 | 3 |
| C5×#912 | 3 |
| #63936 | 5 |