Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
516 conjugacy classes of subgroups; only the 374 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 374 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×#948 | C2 | semidirect |
| 3. C2×C5×#208 | C2 | semidirect |
| 11. C5×#208 | C22 | semidirect |
| 12. C2×C5×C3⋊C8 | C22 | semidirect |
| 13. #5819 | C5 | direct (N × H) |
| 26. #948 | C2×C5 | semidirect |
| 27. C2×#208 | C2×C5 | semidirect |
| 49. #208 | C22×C5 | semidirect |
| 50. C2×C3⋊C8 | C22×C5 | semidirect |
| 87. C3×C5 | #568 | semidirect |
| 108. C5 | #5819 | direct (N × H) |
| 115. C3 | C5×#568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×#41 | 2 |
| C5×#948 | 2 |
| C2×C5×#208 | 2 |
| C5×#568 | 3 |
| #5819 | 5 |