Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
496 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 214 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×C5×2−1+4 | C2 | semidirect |
| 2. C3×#4150 | C2 | semidirect |
| 3. C3×#4097 | C2 | semidirect |
| 4. C3×#4096 | C2 | semidirect |
| 5. C3×#4094 | C2 | semidirect |
| 6. C2×C3×#689 | C2 | semidirect |
| 7. C3×#4088 | C2 | semidirect |
| 8. #66172 | C3 | direct (N × H) |
| 26. C5×2−1+4 | C2×C3 | semidirect |
| 27. #4150 | C2×C3 | semidirect |
| 28. #4097 | C2×C3 | semidirect |
| 29. #4096 | C2×C3 | semidirect |
| 30. #4094 | C2×C3 | semidirect |
| 31. C2×#689 | C2×C3 | semidirect |
| 32. #4088 | C2×C3 | semidirect |
| 51. C3×2−1+4 | D5 | semidirect |
| 115. 2−1+4 | C3×D5 | semidirect |
| 165. C3×C5 | #578 | semidirect |
| 198. C5 | C3×#578 | semidirect |
| 206. C3 | #66172 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×2−1+4 | 2 |
| C3×#4150 | 2 |
| C3×#4097 | 2 |
| C3×#4096 | 2 |
| C3×#4094 | 2 |
| C2×C3×#689 | 2 |
| C3×#4088 | 2 |
| #66172 | 3 |
| C3×#578 | 5 |