Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
268 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 90 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×#5125 | C2 | semidirect |
| 3. C3×C5×#349 | C2 | semidirect |
| 4. C5×#4516 | C2 | semidirect |
| 5. C5×#4513 | C2 | semidirect |
| 16. #69116 | C5 | direct (N × H) |
| 21. C5×#349 | D3 | semidirect |
| 36. #5125 | C2×C5 | semidirect |
| 37. C3×#349 | C2×C5 | semidirect |
| 38. #4516 | C2×C5 | semidirect |
| 39. #4513 | C2×C5 | semidirect |
| 89. #349 | C5×D3 | semidirect |
| 175. C3×C5 | #2238 | semidirect |
| 207. C5 | #69116 | direct (N × H) |
| 218. C3 | C5×#2238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5135 | 2 |
| C5×#5125 | 2 |
| C3×C5×#349 | 2 |
| C5×#4516 | 2 |
| C5×#4513 | 2 |
| C5×#2238 | 3 |
| #69116 | 5 |