Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
148 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 148 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 |
|---|---|---|
| 2. C2×C5×Dic22 | C2 | semidirect |
| 5. C5×C4⋊Dic11 | C2 | semidirect |
| 6. C5×Dic11⋊C4 | C2 | semidirect |
| 7. C5×Dic11⋊C4 | C2 | semidirect |
| 17. #66931 | C5 | direct (N × H) |
| 20. C22×C5×C11 | Q8 | semidirect |
| 29. C2×Dic22 | C2×C5 | semidirect |
| 32. C4⋊Dic11 | C2×C5 | semidirect |
| 33. Dic11⋊C4 | C2×C5 | semidirect |
| 34. Dic11⋊C4 | C2×C5 | semidirect |
| 56. C5×C11 | C22⋊Q8 | semidirect |
| 59. C22×C11 | C5×Q8 | semidirect |
| 83. C22×C5 | Dic22 | semidirect |
| 98. C11 | C5×C22⋊Q8 | semidirect |
| 112. C5 | #66931 | direct (N × H) |
| 115. C22 | C5×Dic22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Dic11 | 2 |
| C2×C5×Dic22 | 2 |
| C5×C11×C22⋊C4 | 2 |
| C5×C22⋊Dic11 | 2 |
| C5×C4⋊Dic11 | 2 |
| C5×Dic11⋊C4 | 2 |
| #66931 | 5 |
| C5×C22⋊Q8 | 11 |