Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
240 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 86 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. C5×#944 | C2 | semidirect |
| 5. C5×#835 | C2 | semidirect |
| 6. C5×#816 | C2 | semidirect |
| 7. C5×Dic3⋊C8 | C2 | semidirect |
| 22. #5162 | C5 | direct (N × H) |
| 47. #944 | C2×C5 | semidirect |
| 50. #835 | C2×C5 | semidirect |
| 51. #816 | C2×C5 | semidirect |
| 52. Dic3⋊C8 | C2×C5 | semidirect |
| 77. C5×Dic3 | SD16 | semidirect |
| 158. C3×C5 | #461 | semidirect |
| 169. Dic3 | C5×SD16 | semidirect |
| 194. C5 | #5162 | direct (N × H) |
| 206. C3 | C5×#461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×SD16 | 2 |
| C5×#944 | 2 |
| C5×D4×Dic3 | 2 |
| C2×C5×#214 | 2 |
| C5×#835 | 2 |
| C5×#816 | 2 |
| C5×Dic3⋊C8 | 2 |
| C5×#461 | 3 |
| #5162 | 5 |