Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
524 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 90 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×#5683 | C2 | semidirect |
| 2. C3×C5×#496 | C2 | semidirect |
| 3. C5×#5074 | C2 | semidirect |
| 4. C5×#4540 | C2 | semidirect |
| 5. C5×#4464 | C2 | semidirect |
| 9. C3×C5×#127 | C22 | semidirect |
| 18. C3×C5×#97 | C22 | semidirect |
| 19. C5×#803 | C22 | semidirect |
| 20. #71326 | C5 | direct (N × H) |
| 23. C5×#496 | D3 | semidirect |
| 48. #5683 | C2×C5 | semidirect |
| 49. C3×#496 | C2×C5 | semidirect |
| 50. #5074 | C2×C5 | semidirect |
| 51. #4540 | C2×C5 | semidirect |
| 52. #4464 | C2×C5 | semidirect |
| 57. C5×#127 | C2×D3 | semidirect |
| 65. C5×#97 | C2×D3 | semidirect |
| 90. C3×#127 | C22×C5 | semidirect |
| 99. C3×#97 | C22×C5 | semidirect |
| 100. #803 | C22×C5 | semidirect |
| 125. #496 | C5×D3 | semidirect |
| 188. #127 | C2×C5×D3 | semidirect |
| 196. #97 | C2×C5×D3 | semidirect |
| 258. C3×C5 | #1655 | semidirect |
| 303. C5 | #71326 | direct (N × H) |
| 317. C3 | C5×#1655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5683 | 2 |
| C3×C5×#496 | 2 |
| C5×#5074 | 2 |
| C5×#4540 | 2 |
| C5×#4464 | 2 |
| C5×#1655 | 3 |
| #71326 | 5 |