Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
224 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 70 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×#4912 | C2 | semidirect |
| 2. C5×D3×D16 | C2 | semidirect |
| 3. C3×C5×D32 | C2 | semidirect |
| 4. C5×#4520 | C2 | semidirect |
| 5. C5×#4519 | C2 | semidirect |
| 6. C5×#4449 | C2 | semidirect |
| 7. C5×#4447 | C2 | semidirect |
| 12. C3×C5×D16 | C22 | semidirect |
| 15. C5×Dic24 | C22 | semidirect |
| 18. C3×C5×C32 | C22 | semidirect |
| 19. C5×C3⋊C32 | C22 | semidirect |
| 20. #69377 | C5 | direct (N × H) |
| 26. C5×D32 | D3 | semidirect |
| 39. #4912 | C2×C5 | semidirect |
| 40. D3×D16 | C2×C5 | semidirect |
| 41. C3×D32 | C2×C5 | semidirect |
| 42. #4520 | C2×C5 | semidirect |
| 43. #4519 | C2×C5 | semidirect |
| 44. #4449 | C2×C5 | semidirect |
| 45. #4447 | C2×C5 | semidirect |
| 53. C5×D16 | C2×D3 | semidirect |
| 56. C5×C32 | C2×D3 | semidirect |
| 72. C3×D16 | C22×C5 | semidirect |
| 75. Dic24 | C22×C5 | semidirect |
| 78. C3×C32 | C22×C5 | semidirect |
| 79. C3⋊C32 | C22×C5 | semidirect |
| 96. D32 | C5×D3 | semidirect |
| 135. D16 | C2×C5×D3 | semidirect |
| 138. C32 | C2×C5×D3 | semidirect |
| 174. C3×C5 | #2263 | semidirect |
| 204. C5 | #69377 | direct (N × H) |
| 213. C3 | C5×#2263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4912 | 2 |
| C5×D3×D16 | 2 |
| C3×C5×D32 | 2 |
| C5×#4520 | 2 |
| C5×#4519 | 2 |
| C5×#4449 | 2 |
| C5×#4447 | 2 |
| C5×#2263 | 3 |
| #69377 | 5 |