Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
532 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 532 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 |
|---|---|---|
| 1. C2×C5×D3×D8 | C2 | semidirect |
| 2. C2×C5×#826 | C2 | semidirect |
| 3. C2×C5×D48 | C2 | semidirect |
| 4. C5×#4883 | C2 | semidirect |
| 5. C3×C5×#357 | C2 | semidirect |
| 6. C5×(C2×D3)⋊C16 | C2 | semidirect |
| 7. C5×#4491 | C2 | semidirect |
| 15. C2×C5×D24 | C22 | semidirect |
| 18. C2×C3×C5×C16 | C22 | semidirect |
| 19. C3×C5×#107 | C22 | semidirect |
| 21. C2×C5×C3⋊C16 | C22 | semidirect |
| 24. #69191 | C5 | direct (N × H) |
| 30. C5×#357 | D3 | semidirect |
| 42. C3×C5×D8 | D4 | semidirect |
| 51. C5×D24 | D4 | semidirect |
| 56. C2×D3×D8 | C2×C5 | semidirect |
| 57. C2×#826 | C2×C5 | semidirect |
| 58. C2×D48 | C2×C5 | semidirect |
| 59. #4883 | C2×C5 | semidirect |
| 60. C3×#357 | C2×C5 | semidirect |
| 61. (C2×D3)⋊C16 | C2×C5 | semidirect |
| 62. #4491 | C2×C5 | semidirect |
| 75. C2×C5×C16 | C2×D3 | semidirect |
| 76. C5×#107 | C2×D3 | semidirect |
| 108. C2×D24 | C22×C5 | semidirect |
| 111. C2×C3×C16 | C22×C5 | semidirect |
| 112. C3×#107 | C22×C5 | semidirect |
| 114. C2×C3⋊C16 | C22×C5 | semidirect |
| 132. C5×D8 | D12 | semidirect |
| 146. #357 | C5×D3 | semidirect |
| 161. C2×C5×D3 | D16 | semidirect |
| 176. C3×D8 | C5×D4 | semidirect |
| 185. D24 | C5×D4 | semidirect |
| 225. C2×C16 | C2×C5×D3 | semidirect |
| 226. #107 | C2×C5×D3 | semidirect |
| 291. D8 | C5×D12 | semidirect |
| 300. C3×C5 | #2184 | semidirect |
| 314. C2×D3 | C5×D16 | semidirect |
| 356. C5 | #69191 | direct (N × H) |
| 375. C3 | C5×#2184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D3×D8 | 2 |
| C2×C5×#826 | 2 |
| C2×C5×D48 | 2 |
| C5×#4883 | 2 |
| C3×C5×#357 | 2 |
| C5×(C2×D3)⋊C16 | 2 |
| C5×#4491 | 2 |
| C5×#2184 | 3 |
| #69191 | 5 |