Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
616 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 616 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 |
|---|---|---|
| 2. C5×#5040 | C2 | semidirect |
| 3. C5×#4947 | C2 | semidirect |
| 4. C5×#4537 | C2 | semidirect |
| 5. C5×#4525 | C2 | semidirect |
| 8. C22×C5×Dic6 | C22 | semidirect |
| 17. C5×C3⋊#95 | C22 | semidirect |
| 18. C5×#830 | C22 | semidirect |
| 20. #71846 | C5 | direct (N × H) |
| 50. #5040 | C2×C5 | semidirect |
| 51. #4947 | C2×C5 | semidirect |
| 52. #4537 | C2×C5 | semidirect |
| 53. #4525 | C2×C5 | semidirect |
| 76. C23×C3×C5 | SD16 | semidirect |
| 99. C22×Dic6 | C22×C5 | semidirect |
| 108. C3⋊#95 | C22×C5 | semidirect |
| 109. #830 | C22×C5 | semidirect |
| 189. C23×C5 | #214 | semidirect |
| 239. C23×C3 | C5×SD16 | semidirect |
| 303. C3×C5 | #1601 | semidirect |
| 338. C23 | C5×#214 | semidirect |
| 367. C5 | #71846 | direct (N × H) |
| 387. C3 | C5×#1601 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#534 | 2 |
| C5×#5040 | 2 |
| C5×#4947 | 2 |
| C5×#4537 | 2 |
| C5×#4525 | 2 |
| C5×#1601 | 3 |
| #71846 | 5 |