Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
514 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 72 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×#5923 | C2 | semidirect |
| 2. C2×C5×#986 | C2 | semidirect |
| 3. C5×#568⋊C3 | C2 | semidirect |
| 4. C5×#5407 | C2 | semidirect |
| 5. C5×#5406 | C2 | semidirect |
| 10. C5×#986 | C22 | semidirect |
| 12. C5×#984 | C22 | semidirect |
| 16. C5×#131⋊C3 | C22 | semidirect |
| 17. #85454 | C5 | direct (N × H) |
| 21. C5×#568 | D3 | semidirect |
| 40. #5923 | C2×C5 | semidirect |
| 41. C2×#986 | C2×C5 | semidirect |
| 42. #568⋊C3 | C2×C5 | semidirect |
| 43. #5407 | C2×C5 | semidirect |
| 44. #5406 | C2×C5 | semidirect |
| 68. C5×#131 | C2×D3 | semidirect |
| 93. #986 | C22×C5 | semidirect |
| 95. #984 | C22×C5 | semidirect |
| 99. #131⋊C3 | C22×C5 | semidirect |
| 154. #568 | C5×D3 | semidirect |
| 238. #131 | C2×C5×D3 | semidirect |
| 382. C5 | #85454 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5923 | 2 |
| C2×C5×#986 | 2 |
| C5×#568⋊C3 | 2 |
| C5×#5407 | 2 |
| C5×#5406 | 2 |
| C5×#3068 | 3 |
| C5×#908 | 4 |
| #85454 | 5 |