Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
300 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 134 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×#208 | C2 | semidirect |
| 3. C5×#836 | C2 | semidirect |
| 4. C5×#833 | C2 | semidirect |
| 16. #5237 | C5 | direct (N × H) |
| 35. C2×#208 | C2×C5 | semidirect |
| 36. #836 | C2×C5 | semidirect |
| 37. #833 | C2×C5 | semidirect |
| 121. C3×C5 | #413 | semidirect |
| 152. C5 | #5237 | direct (N × H) |
| 162. C3 | C5×#413 | 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 |
| C2×C5×#208 | 2 |
| C5×#836 | 2 |
| C5×#833 | 2 |
| C5×#413 | 3 |
| #5237 | 5 |