Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
216 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 67 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×#131 | C2 | semidirect |
| 2. #91838 | C2 | semidirect |
| 3. C2×D120 | C2 | semidirect |
| 4. #91107 | C2 | semidirect |
| 5. #91103 | C2 | semidirect |
| 19. C5×#131 | D3 | semidirect |
| 36. C3×#131 | D5 | semidirect |
| 85. #131 | D15 | semidirect |
| 122. C3×C5 | #472 | semidirect |
| 150. C5 | #5142 | semidirect |
| 158. C3 | #65431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#131 | 2 |
| #91838 | 2 |
| C2×D120 | 2 |
| #91107 | 2 |
| #91103 | 2 |
| #65431 | 3 |
| #5142 | 5 |