Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
260 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 82 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×#121 | C2 | semidirect |
| 2. C2×C5×#213 | C2 | semidirect |
| 3. C5×#930 | C2 | semidirect |
| 4. C2×C5×#208 | C2 | semidirect |
| 5. C5×#832 | C2 | semidirect |
| 6. C5×#809 | C2 | semidirect |
| 7. C5×#808 | C2 | semidirect |
| 22. #5039 | C5 | direct (N × H) |
| 26. C5×#121 | D3 | semidirect |
| 46. C5×C3⋊C8 | D4 | semidirect |
| 47. C3×#121 | C2×C5 | semidirect |
| 48. C2×#213 | C2×C5 | semidirect |
| 49. #930 | C2×C5 | semidirect |
| 50. C2×#208 | C2×C5 | semidirect |
| 51. #832 | C2×C5 | semidirect |
| 52. #809 | C2×C5 | semidirect |
| 53. #808 | C2×C5 | semidirect |
| 116. #121 | C5×D3 | semidirect |
| 142. C3⋊C8 | C5×D4 | semidirect |
| 171. C3×C5 | #469 | semidirect |
| 216. C5 | #5039 | direct (N × H) |
| 232. C3 | C5×#469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#121 | 2 |
| C2×C5×#213 | 2 |
| C5×#930 | 2 |
| C2×C5×#208 | 2 |
| C5×#832 | 2 |
| C5×#809 | 2 |
| C5×#808 | 2 |
| C5×#469 | 3 |
| #5039 | 5 |