Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
264 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 74 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×C4×D5×C11 | C2 | semidirect |
| 3. C2×D5×Dic11 | C2 | semidirect |
| 4. #11724932 | C2 | semidirect |
| 5. C5×(C2×D11)⋊C4 | C2 | semidirect |
| 6. #11724886 | C2 | semidirect |
| 7. (C2×D11)⋊Dic5 | C2 | semidirect |
| 13. C2×D5×D11 | C4 | semidirect |
| 14. C2×C4×C5×C11 | C22 | semidirect |
| 15. C2×Dic55 | C22 | semidirect |
| 16. C2×C11×Dic5 | C22 | semidirect |
| 18. C2×C5×Dic11 | C22 | semidirect |
| 24. C2×D55 | C2×C4 | semidirect |
| 30. C2×C5×D11 | C2×C4 | semidirect |
| 42. (C2×D11)⋊C4 | D5 | direct (N × H) |
| 49. D5×C11 | C22⋊C4 | semidirect |
| 58. C2×C4×C11 | C2×D5 | semidirect |
| 61. C2×Dic11 | C2×D5 | semidirect |
| 64. C2×C4×D5 | D11 | semidirect |
| 69. C5×C11 | C2×C22⋊C4 | semidirect |
| 80. C2×D11 | C4×D5 | semidirect |
| 92. C2×C4×C5 | C2×D11 | semidirect |
| 94. C2×Dic5 | C2×D11 | semidirect |
| 126. C11 | D5×C22⋊C4 | semidirect |
| 132. D5 | (C2×D11)⋊C4 | direct (N × H) |
| 144. C2×C4 | D5×D11 | semidirect |
| 145. C5 | C2×(C2×D11)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D5×D11 | 2 |
| C2×C4×D5×C11 | 2 |
| C2×D5×Dic11 | 2 |
| #11724932 | 2 |
| C5×(C2×D11)⋊C4 | 2 |
| #11724886 | 2 |
| (C2×D11)⋊Dic5 | 2 |
| C2×(C2×D11)⋊C4 | 5 |
| D5×C22⋊C4 | 11 |