Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
284 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 102 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. C5×#4853 | C2 | semidirect |
| 4. C3×C5×#365 | C2 | semidirect |
| 5. C5×#4512 | C2 | semidirect |
| 6. C5×#4496 | C2 | semidirect |
| 20. C5×Dic24 | C4 | semidirect |
| 21. C5×#800 | C4 | semidirect |
| 22. #69309 | C5 | direct (N × H) |
| 26. C5×#365 | D3 | semidirect |
| 50. #4853 | C2×C5 | semidirect |
| 51. C3×#365 | C2×C5 | semidirect |
| 52. #4512 | C2×C5 | semidirect |
| 53. #4496 | C2×C5 | semidirect |
| 94. Dic24 | C4×C5 | semidirect |
| 95. #800 | C4×C5 | semidirect |
| 117. #365 | C5×D3 | semidirect |
| 217. C3×C5 | #2180 | semidirect |
| 246. C5 | #69309 | direct (N × H) |
| 255. C3 | C5×#2180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4909 | 2 |
| C5×#4894 | 2 |
| C5×#4853 | 2 |
| C3×C5×#365 | 2 |
| C5×#4512 | 2 |
| C5×#4496 | 2 |
| C5×#4488 | 2 |
| C5×#2180 | 3 |
| #69309 | 5 |