Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
200 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 74 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×#888 | C2 | semidirect |
| 3. C3×C5×#103 | C2 | semidirect |
| 4. C5×#835 | C2 | semidirect |
| 6. C5×#815 | C2 | semidirect |
| 20. #4794 | C5 | direct (N × H) |
| 24. C5×#103 | D3 | semidirect |
| 43. #888 | C2×C5 | semidirect |
| 44. C3×#103 | C2×C5 | semidirect |
| 45. #835 | C2×C5 | semidirect |
| 47. #815 | C2×C5 | semidirect |
| 100. #103 | C5×D3 | semidirect |
| 144. C3×C5 | #489 | semidirect |
| 178. C5 | #4794 | direct (N × H) |
| 190. C3 | C5×#489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#947 | 2 |
| C5×#888 | 2 |
| C3×C5×#103 | 2 |
| C5×#835 | 2 |
| C5×#821 | 2 |
| C5×#815 | 2 |
| C5×#809 | 2 |
| C5×#489 | 3 |
| #4794 | 5 |