Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
384 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 190 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×#125 | C2 | semidirect |
| 4. C5×#890 | C2 | semidirect |
| 5. C5×#887 | C2 | semidirect |
| 7. C5×#869 | C2 | semidirect |
| 22. #5698 | C5 | direct (N × H) |
| 26. C5×#125 | D3 | semidirect |
| 39. C3×#125 | C2×C5 | semidirect |
| 42. #890 | C2×C5 | semidirect |
| 43. #887 | C2×C5 | semidirect |
| 45. #869 | C2×C5 | semidirect |
| 94. #125 | C5×D3 | semidirect |
| 132. C3×C5 | #541 | semidirect |
| 157. C5 | #5698 | direct (N × H) |
| 167. C3 | C5×#541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#125 | 2 |
| C5×#898 | 2 |
| C5×#897 | 2 |
| C5×#890 | 2 |
| C5×#887 | 2 |
| C5×#872 | 2 |
| C5×#869 | 2 |
| C5×#541 | 3 |
| #5698 | 5 |