Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
124 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 58 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×C11×#41 | C2 | semidirect |
| 2. C5×#4339 | C2 | semidirect |
| 3. C5×#4326 | C2 | semidirect |
| 4. C5×#4325 | C2 | semidirect |
| 5. C5×#4324 | C2 | semidirect |
| 6. C5×#4323 | C2 | semidirect |
| 7. C2×C5×C11⋊C8 | C2 | semidirect |
| 19. #67003 | C5 | direct (N × H) |
| 27. C11×#41 | C2×C5 | semidirect |
| 28. #4339 | C2×C5 | semidirect |
| 29. #4326 | C2×C5 | semidirect |
| 30. #4325 | C2×C5 | semidirect |
| 31. #4324 | C2×C5 | semidirect |
| 32. #4323 | C2×C5 | semidirect |
| 33. C2×C11⋊C8 | C2×C5 | semidirect |
| 51. C5×#41 | D11 | semidirect |
| 57. C5×C11 | #135 | semidirect |
| 89. #41 | C5×D11 | semidirect |
| 95. C11 | C5×#135 | semidirect |
| 111. C5 | #67003 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C11×#41 | 2 |
| C5×#4339 | 2 |
| C5×#4326 | 2 |
| C5×#4325 | 2 |
| C5×#4324 | 2 |
| C5×#4323 | 2 |
| C2×C5×C11⋊C8 | 2 |
| #67003 | 5 |
| C5×#135 | 11 |