Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
156 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 66 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. C22×C5×Dic11 | C2 | semidirect |
| 3. C5×C11×C22⋊C4 | C2 | semidirect |
| 4. C5×(C2×D11)⋊C4 | C2 | semidirect |
| 5. C5×C4⋊Dic11 | C2 | semidirect |
| 13. #66939 | C5 | direct (N × H) |
| 23. C22×Dic11 | C2×C5 | semidirect |
| 24. C11×C22⋊C4 | C2×C5 | semidirect |
| 25. (C2×D11)⋊C4 | C2×C5 | semidirect |
| 26. C4⋊Dic11 | C2×C5 | semidirect |
| 43. C5×C22⋊C4 | D11 | semidirect |
| 44. C5×C11 | #123 | semidirect |
| 77. C22⋊C4 | C5×D11 | semidirect |
| 78. C11 | C5×#123 | semidirect |
| 90. C5 | #66939 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C22⋊D11 | 2 |
| C22×C5×Dic11 | 2 |
| C5×C11×C22⋊C4 | 2 |
| C5×(C2×D11)⋊C4 | 2 |
| C5×C4⋊Dic11 | 2 |
| #66939 | 5 |
| C5×#123 | 11 |