Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
278 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 278 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×Q8×C3⋊D3 | C2 | semidirect |
| 3. C3×C5×#216 | C2 | semidirect |
| 4. C3×C5×#215 | C2 | semidirect |
| 5. C5×#3719 | C2 | semidirect |
| 6. C5×#3716 | C2 | semidirect |
| 7. C5×#3712 | C2 | semidirect |
| 21. #63951 | C5 | direct (N × H) |
| 30. C5×#216 | D3 | semidirect |
| 31. C5×#215 | D3 | semidirect |
| 45. Q8×C3⋊D3 | C2×C5 | semidirect |
| 47. C3×#216 | C2×C5 | semidirect |
| 48. C3×#215 | C2×C5 | semidirect |
| 49. #3719 | C2×C5 | semidirect |
| 50. #3716 | C2×C5 | semidirect |
| 51. #3712 | C2×C5 | semidirect |
| 129. #216 | C5×D3 | semidirect |
| 130. #215 | C5×D3 | semidirect |
| 136. C32×C5 | #137 | semidirect |
| 209. C3×C5 | #915 | semidirect |
| 210. C3×C5 | #918 | semidirect |
| 233. C32 | C5×#137 | semidirect |
| 253. C5 | #63951 | direct (N × H) |
| 262. C3 | C5×#915 | semidirect |
| 263. C3 | C5×#918 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×C3⋊D3 | 2 |
| C5×#3796 | 2 |
| C3×C5×#216 | 2 |
| C3×C5×#215 | 2 |
| C5×#3719 | 2 |
| C5×#3716 | 2 |
| C5×#3712 | 2 |
| C5×#918 | 3 |
| C5×#915 | 3 |
| #63951 | 5 |