Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
152 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 2. C2×C11×Dic10 | C2 | semidirect |
| 3. C5×C11×C22⋊C4 | C2 | semidirect |
| 4. C11×C22⋊Dic5 | C2 | semidirect |
| 5. C11×#685 | C2 | semidirect |
| 6. C11×#685 | C2 | semidirect |
| 7. C4×C11×Dic5 | C2 | semidirect |
| 35. C11×C22⋊C4 | D5 | semidirect |
| 37. #4031 | C11 | direct (N × H) |
| 53. C2×Dic10 | C2×C11 | semidirect |
| 54. C5×C22⋊C4 | C2×C11 | semidirect |
| 55. C22⋊Dic5 | C2×C11 | semidirect |
| 56. #685 | C2×C11 | semidirect |
| 57. #685 | C2×C11 | semidirect |
| 58. C4×Dic5 | C2×C11 | semidirect |
| 59. C5×C11 | #124 | semidirect |
| 104. C22⋊C4 | D5×C11 | semidirect |
| 106. C11 | #4031 | direct (N × H) |
| 121. C5 | C11×#124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×C22⋊D5 | 2 |
| C2×C11×Dic10 | 2 |
| C5×C11×C22⋊C4 | 2 |
| C11×C22⋊Dic5 | 2 |
| C11×#685 | 2 |
| C4×C11×Dic5 | 2 |
| C11×#124 | 5 |
| #4031 | 11 |