Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
248 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 2. C2×C5×#214 | C2 | semidirect |
| 3. C5×#924 | C2 | semidirect |
| 4. C22×C5×C3⋊C8 | C2 | semidirect |
| 5. C5×#832 | C2 | semidirect |
| 6. C5×#810 | C2 | semidirect |
| 7. C5×#808 | C2 | semidirect |
| 22. #5041 | C5 | direct (N × H) |
| 45. C5×C3⋊C8 | D4 | semidirect |
| 47. C2×#214 | C2×C5 | semidirect |
| 48. #924 | C2×C5 | semidirect |
| 49. C22×C3⋊C8 | C2×C5 | semidirect |
| 50. #832 | C2×C5 | semidirect |
| 51. #810 | C2×C5 | semidirect |
| 52. #808 | C2×C5 | semidirect |
| 72. C22×C3×C5 | SD16 | semidirect |
| 136. C3⋊C8 | C5×D4 | semidirect |
| 142. C22×C5 | #214 | semidirect |
| 163. C3×C5 | #465 | semidirect |
| 169. C22×C3 | C5×SD16 | semidirect |
| 203. C5 | #5041 | direct (N × H) |
| 209. C22 | C5×#214 | semidirect |
| 217. C3 | C5×#465 | 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×#214 | 2 |
| C5×#924 | 2 |
| C22×C5×C3⋊C8 | 2 |
| C5×#832 | 2 |
| C5×#810 | 2 |
| C5×#808 | 2 |
| C5×#465 | 3 |
| #5041 | 5 |