Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
430 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 100 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×#638 | C2 | semidirect |
| 2. C2×C3×C5×#67 | C2 | semidirect |
| 3. C2×C5×#626 | C2 | semidirect |
| 4. C2×C5×D3×Dic3 | C2 | semidirect |
| 5. C3×C5×#217 | C2 | semidirect |
| 6. C5×#3724 | C2 | semidirect |
| 7. C5×#3722 | C2 | semidirect |
| 21. #63971 | C5 | direct (N × H) |
| 27. C2×C5×#67 | D3 | semidirect |
| 32. C5×#217 | D3 | semidirect |
| 46. C2×C3×C5×D3 | D4 | semidirect |
| 47. C5×C3⋊Dic3 | D4 | semidirect |
| 52. C2×#638 | C2×C5 | semidirect |
| 53. C2×C3×#67 | C2×C5 | semidirect |
| 54. C2×#626 | C2×C5 | semidirect |
| 55. C2×D3×Dic3 | C2×C5 | semidirect |
| 56. C3×#217 | C2×C5 | semidirect |
| 57. #3724 | C2×C5 | semidirect |
| 58. #3722 | C2×C5 | semidirect |
| 137. C2×C5×D3 | #67 | semidirect |
| 152. C2×#67 | C5×D3 | semidirect |
| 157. #217 | C5×D3 | semidirect |
| 162. C32×C5 | #121 | semidirect |
| 183. C2×C3×D3 | C5×D4 | semidirect |
| 184. C3⋊Dic3 | C5×D4 | semidirect |
| 260. C3×C5 | #884 | semidirect |
| 261. C3×C5 | #939 | semidirect |
| 288. C2×D3 | C5×#67 | semidirect |
| 304. C32 | C5×#121 | semidirect |
| 333. C5 | #63971 | direct (N × H) |
| 349. C3 | C5×#884 | semidirect |
| 350. C3 | C5×#939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#638 | 2 |
| C2×C3×C5×#67 | 2 |
| C2×C5×#626 | 2 |
| C2×C5×D3×Dic3 | 2 |
| C3×C5×#217 | 2 |
| C5×#3724 | 2 |
| C5×#3722 | 2 |
| C5×#939 | 3 |
| C5×#884 | 3 |
| #63971 | 5 |