Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
452 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 452 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×#5748 | C2 | semidirect |
| 2. C5×#5135 | C2 | semidirect |
| 3. C5×#4908 | C2 | semidirect |
| 4. C3×C5×#349 | C2 | semidirect |
| 5. C5×#4518 | C2 | semidirect |
| 14. C2×C5×D24 | C22 | semidirect |
| 15. C3×C5×M32 | C22 | semidirect |
| 17. C5×#817 | C22 | semidirect |
| 20. #69120 | C5 | direct (N × H) |
| 25. C5×#349 | D3 | semidirect |
| 43. C5×Dic12 | D4 | semidirect |
| 46. C5×D24 | D4 | semidirect |
| 50. #5748 | C2×C5 | semidirect |
| 51. #5135 | C2×C5 | semidirect |
| 52. #4908 | C2×C5 | semidirect |
| 53. C3×#349 | C2×C5 | semidirect |
| 54. #4518 | C2×C5 | semidirect |
| 65. C5×M32 | C2×D3 | semidirect |
| 98. C2×D24 | C22×C5 | semidirect |
| 99. C3×M32 | C22×C5 | semidirect |
| 101. #817 | C22×C5 | semidirect |
| 132. #349 | C5×D3 | semidirect |
| 163. Dic12 | C5×D4 | semidirect |
| 166. D24 | C5×D4 | semidirect |
| 202. M32 | C2×C5×D3 | semidirect |
| 269. C3×C5 | #2190 | semidirect |
| 315. C5 | #69120 | direct (N × H) |
| 329. C3 | C5×#2190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5748 | 2 |
| C5×#5135 | 2 |
| C5×#4908 | 2 |
| C3×C5×#349 | 2 |
| C5×#4518 | 2 |
| C5×#2190 | 3 |
| #69120 | 5 |