Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
340 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 1. C5×#5088 | C2 | semidirect |
| 2. C5×#5084 | C2 | semidirect |
| 4. C5×#4838 | C2 | semidirect |
| 5. C3×C5×#333 | C2 | semidirect |
| 6. C5×#4485 | C2 | semidirect |
| 7. C5×#4479 | C2 | semidirect |
| 24. #68502 | C5 | direct (N × H) |
| 30. C5×#333 | D3 | semidirect |
| 50. #5088 | C2×C5 | semidirect |
| 51. #5084 | C2×C5 | semidirect |
| 53. #4838 | C2×C5 | semidirect |
| 54. C3×#333 | C2×C5 | semidirect |
| 55. #4485 | C2×C5 | semidirect |
| 56. #4479 | C2×C5 | semidirect |
| 133. #333 | C5×D3 | semidirect |
| 263. C3×C5 | #1697 | semidirect |
| 310. C5 | #68502 | direct (N × H) |
| 325. C3 | C5×#1697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5088 | 2 |
| C5×#5084 | 2 |
| C5×#4843 | 2 |
| C5×#4838 | 2 |
| C3×C5×#333 | 2 |
| C5×#4485 | 2 |
| C5×#4479 | 2 |
| C5×#1697 | 3 |
| #68502 | 5 |