Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
616 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 106 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. C3×C5×#393 | C2 | semidirect |
| 3. C5×#5227 | C2 | semidirect |
| 4. C5×#4525 | C2 | semidirect |
| 5. C5×#4451 | C2 | semidirect |
| 7. C22×C3×C5×Q8 | C22 | semidirect |
| 17. C3×C5×#95 | C22 | semidirect |
| 19. C5×#830 | C22 | semidirect |
| 20. #69699 | C5 | direct (N × H) |
| 23. C5×#393 | D3 | semidirect |
| 50. C3×#393 | C2×C5 | semidirect |
| 51. #5227 | C2×C5 | semidirect |
| 52. #4525 | C2×C5 | semidirect |
| 53. #4451 | C2×C5 | semidirect |
| 54. C22×C5×Q8 | C2×D3 | semidirect |
| 66. C5×#95 | C2×D3 | semidirect |
| 72. C23×C3×C5 | SD16 | semidirect |
| 98. C22×C3×Q8 | C22×C5 | semidirect |
| 108. C3×#95 | C22×C5 | semidirect |
| 110. #830 | C22×C5 | semidirect |
| 136. #393 | C5×D3 | semidirect |
| 189. C23×C5 | #215 | semidirect |
| 211. C22×Q8 | C2×C5×D3 | semidirect |
| 223. #95 | C2×C5×D3 | semidirect |
| 235. C23×C3 | C5×SD16 | semidirect |
| 303. C3×C5 | #1601 | semidirect |
| 338. C23 | C5×#215 | semidirect |
| 367. C5 | #69699 | 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 |
|---|---|
| C5×#5493 | 2 |
| C3×C5×#393 | 2 |
| C5×#5227 | 2 |
| C5×#4525 | 2 |
| C5×#4451 | 2 |
| C5×#1601 | 3 |
| #69699 | 5 |