Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
248 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 3. C3×C5×#365 | C2 | semidirect |
| 4. C5×#4517 | C2 | semidirect |
| 6. C5×#4496 | C2 | semidirect |
| 7. C5×#4487 | C2 | semidirect |
| 20. #69314 | C5 | direct (N × H) |
| 24. C5×#365 | D3 | semidirect |
| 47. C3×#365 | C2×C5 | semidirect |
| 48. #4517 | C2×C5 | semidirect |
| 50. #4496 | C2×C5 | semidirect |
| 51. #4487 | C2×C5 | semidirect |
| 109. #365 | C5×D3 | semidirect |
| 205. C3×C5 | #2239 | semidirect |
| 234. C5 | #69314 | direct (N × H) |
| 243. C3 | C5×#2239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4893 | 2 |
| C5×#4867 | 2 |
| C3×C5×#365 | 2 |
| C5×#4517 | 2 |
| C5×#4514 | 2 |
| C5×#4496 | 2 |
| C5×#4487 | 2 |
| C5×#2239 | 3 |
| #69314 | 5 |