Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
188 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 70 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×D4×C11 | C2 | semidirect |
| 2. C2×C5×C22⋊D11 | C2 | semidirect |
| 3. C2×C5×C22⋊D11 | C2 | semidirect |
| 4. C22×C5×Dic11 | C2 | semidirect |
| 5. C5×C22⋊Dic11 | C2 | semidirect |
| 6. C5×(C2×D11)⋊C4 | C2 | semidirect |
| 7. C5×Dic11⋊C4 | C2 | semidirect |
| 19. #66992 | C5 | direct (N × H) |
| 25. C22×C5×C11 | D4 | semidirect |
| 33. C5×Dic11 | D4 | semidirect |
| 34. C2×D4×C11 | C2×C5 | semidirect |
| 35. C2×C22⋊D11 | C2×C5 | semidirect |
| 36. C2×C22⋊D11 | C2×C5 | semidirect |
| 37. C22×Dic11 | C2×C5 | semidirect |
| 38. C22⋊Dic11 | C2×C5 | semidirect |
| 39. (C2×D11)⋊C4 | C2×C5 | semidirect |
| 40. Dic11⋊C4 | C2×C5 | semidirect |
| 61. C2×C5×D4 | D11 | semidirect |
| 66. C5×C11 | #121 | semidirect |
| 72. C22×C11 | C5×D4 | semidirect |
| 80. Dic11 | C5×D4 | semidirect |
| 107. C22×C5 | C22⋊D11 | semidirect |
| 115. C2×D4 | C5×D11 | semidirect |
| 120. C11 | C5×#121 | semidirect |
| 138. C5 | #66992 | direct (N × H) |
| 147. C22 | C5×C22⋊D11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×C11 | 2 |
| C2×C5×C22⋊D11 | 2 |
| C22×C5×Dic11 | 2 |
| C5×C22⋊Dic11 | 2 |
| C5×(C2×D11)⋊C4 | 2 |
| C5×Dic11⋊C4 | 2 |
| #66992 | 5 |
| C5×#121 | 11 |