Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
888 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 234 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×#5766 | C2 | semidirect |
| 2. C3×C5×#494 | C2 | semidirect |
| 3. C5×#5192 | C2 | semidirect |
| 4. C5×#5095 | C2 | semidirect |
| 5. C5×#4700 | C2 | semidirect |
| 20. #81808 | C5 | direct (N × H) |
| 22. C5×#494 | D3 | semidirect |
| 44. #5766 | C2×C5 | semidirect |
| 45. C3×#494 | C2×C5 | semidirect |
| 46. #5192 | C2×C5 | semidirect |
| 47. #5095 | C2×C5 | semidirect |
| 48. #4700 | C2×C5 | semidirect |
| 109. #494 | C5×D3 | semidirect |
| 205. C3×C5 | #3293 | semidirect |
| 232. C5 | #81808 | direct (N × H) |
| 239. C3 | C5×#3293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5766 | 2 |
| C3×C5×#494 | 2 |
| C5×#5192 | 2 |
| C5×#5095 | 2 |
| C5×#4700 | 2 |
| C5×#3293 | 3 |
| #81808 | 5 |