Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
272 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 98 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×#4878 | C2 | semidirect |
| 5. C5×#4505 | C2 | semidirect |
| 6. C5×Dic3⋊C16 | C2 | semidirect |
| 7. C5×#4489 | C2 | semidirect |
| 20. #69181 | C5 | direct (N × H) |
| 44. #4878 | C2×C5 | semidirect |
| 47. #4505 | C2×C5 | semidirect |
| 48. Dic3⋊C16 | C2×C5 | semidirect |
| 49. #4489 | C2×C5 | semidirect |
| 201. C3×C5 | #2228 | semidirect |
| 234. C5 | #69181 | direct (N × H) |
| 246. C3 | C5×#2228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Dic3×D8 | 2 |
| C5×#4878 | 2 |
| C3×C5×#357 | 2 |
| C5×#4562 | 2 |
| C5×#4505 | 2 |
| C5×Dic3⋊C16 | 2 |
| C5×#4489 | 2 |
| C5×#2228 | 3 |
| #69181 | 5 |