Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
376 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 1. C5×#4848 | C2 | semidirect |
| 3. C5×C8×Dic6 | C2 | semidirect |
| 4. C3×C5×#335 | C2 | semidirect |
| 5. C5×#4485 | C2 | semidirect |
| 18. #68586 | C5 | direct (N × H) |
| 22. C5×#335 | D3 | semidirect |
| 39. #4848 | C2×C5 | semidirect |
| 41. C8×Dic6 | C2×C5 | semidirect |
| 42. C3×#335 | C2×C5 | semidirect |
| 43. #4485 | C2×C5 | semidirect |
| 68. C5×Dic6 | D8 | semidirect |
| 71. C3×C5×C8 | SD16 | semidirect |
| 102. #335 | C5×D3 | semidirect |
| 146. C5×C8 | #204 | semidirect |
| 174. Dic6 | C5×D8 | semidirect |
| 177. C3×C8 | C5×SD16 | semidirect |
| 205. C3×C5 | #1668 | semidirect |
| 237. C8 | C5×#204 | semidirect |
| 242. C5 | #68586 | direct (N × H) |
| 254. C3 | C5×#1668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4848 | 2 |
| C5×#4695 | 2 |
| C5×C8×Dic6 | 2 |
| C3×C5×#335 | 2 |
| C5×#4485 | 2 |
| C5×#1668 | 3 |
| #68586 | 5 |