Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 532 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 |
|---|---|---|
| 1. C22×C5×D24 | C2 | semidirect |
| 2. C3×C5×#466 | C2 | semidirect |
| 3. C2×C5×#826 | C2 | semidirect |
| 4. C5×#4549 | C2 | semidirect |
| 5. C5×#4491 | C2 | semidirect |
| 8. C2×C3×C5×D8 | C22 | semidirect |
| 14. C3×C5×#107 | C22 | semidirect |
| 17. C2×C5×C3⋊C16 | C22 | semidirect |
| 18. #71075 | C5 | direct (N × H) |
| 21. C5×#466 | D3 | semidirect |
| 40. C5×D24 | D4 | semidirect |
| 42. C22×D24 | C2×C5 | semidirect |
| 43. C3×#466 | C2×C5 | semidirect |
| 44. C2×#826 | C2×C5 | semidirect |
| 45. #4549 | C2×C5 | semidirect |
| 46. #4491 | C2×C5 | semidirect |
| 51. C2×C5×D8 | C2×D3 | semidirect |
| 56. C5×#107 | C2×D3 | semidirect |
| 79. C2×C3×D8 | C22×C5 | semidirect |
| 85. C3×#107 | C22×C5 | semidirect |
| 88. C2×C3⋊C16 | C22×C5 | semidirect |
| 109. #466 | C5×D3 | semidirect |
| 117. C22×C3×C5 | D16 | semidirect |
| 143. D24 | C5×D4 | semidirect |
| 168. C2×D8 | C2×C5×D3 | semidirect |
| 173. #107 | C2×C5×D3 | semidirect |
| 209. C22×C5 | #826 | semidirect |
| 233. C3×C5 | #2184 | semidirect |
| 239. C22×C3 | C5×D16 | semidirect |
| 280. C5 | #71075 | direct (N × H) |
| 290. C22 | C5×#826 | semidirect |
| 296. C3 | C5×#2184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D24 | 2 |
| C3×C5×#466 | 2 |
| C2×C5×#826 | 2 |
| C5×#4549 | 2 |
| C5×#4491 | 2 |
| C5×#2184 | 3 |
| #71075 | 5 |