Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 110 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. C3×C5×#500 | C2 | semidirect |
| 4. C5×#4547 | C2 | semidirect |
| 5. C5×#4457 | C2 | semidirect |
| 18. #71373 | C5 | direct (N × H) |
| 19. C5×#500 | D3 | semidirect |
| 38. C3×#500 | C2×C5 | semidirect |
| 41. #4547 | C2×C5 | semidirect |
| 42. #4457 | C2×C5 | semidirect |
| 67. C3×C5×C8 | SD16 | semidirect |
| 95. #500 | C5×D3 | semidirect |
| 138. C5×C8 | #215 | semidirect |
| 166. C3×C8 | C5×SD16 | semidirect |
| 193. C3×C5 | #1693 | semidirect |
| 222. C8 | C5×#215 | semidirect |
| 227. C5 | #71373 | direct (N × H) |
| 238. C3 | C5×#1693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#500 | 2 |
| C5×#5083 | 2 |
| C5×#4688 | 2 |
| C5×#4547 | 2 |
| C5×#4457 | 2 |
| C5×#1693 | 3 |
| #71373 | 5 |