Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
460 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 102 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×#912 | C2 | semidirect |
| 2. C2×C5×#826 | C2 | semidirect |
| 3. C2×C5×#800 | C2 | semidirect |
| 4. C5×#4883 | C2 | semidirect |
| 5. C3×C5×#357 | C2 | semidirect |
| 6. C5×(C2×D3)⋊C16 | C2 | semidirect |
| 7. C5×#4492 | C2 | semidirect |
| 24. #69192 | C5 | direct (N × H) |
| 30. C5×#357 | D3 | semidirect |
| 42. C3×C5×D8 | D4 | semidirect |
| 49. C5×Dic12 | D4 | semidirect |
| 56. C2×#912 | C2×C5 | semidirect |
| 57. C2×#826 | C2×C5 | semidirect |
| 58. C2×#800 | C2×C5 | semidirect |
| 59. #4883 | C2×C5 | semidirect |
| 60. C3×#357 | C2×C5 | semidirect |
| 61. (C2×D3)⋊C16 | C2×C5 | semidirect |
| 62. #4492 | C2×C5 | semidirect |
| 130. C5×D8 | D12 | semidirect |
| 144. #357 | C5×D3 | semidirect |
| 171. C3×D8 | C5×D4 | semidirect |
| 178. Dic12 | C5×D4 | semidirect |
| 278. D8 | C5×D12 | semidirect |
| 287. C3×C5 | #2186 | semidirect |
| 336. C5 | #69192 | direct (N × H) |
| 352. C3 | C5×#2186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#912 | 2 |
| C2×C5×#826 | 2 |
| C2×C5×#800 | 2 |
| C5×#4883 | 2 |
| C3×C5×#357 | 2 |
| C5×(C2×D3)⋊C16 | 2 |
| C5×#4492 | 2 |
| C5×#2186 | 3 |
| #69192 | 5 |