Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
260 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 260 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 |
|---|---|---|
| 1. C23×C5×D11 | C2 | semidirect |
| 2. C2×C5×C22⋊D11 | C2 | semidirect |
| 3. C2×C5×D44 | C2 | semidirect |
| 4. C5×C11×C22⋊C4 | C2 | semidirect |
| 5. C5×(C2×D11)⋊C4 | C2 | semidirect |
| 10. C22×C5×D11 | C22 | semidirect |
| 11. C2×C4×C5×C11 | C22 | semidirect |
| 13. C2×C5×Dic11 | C22 | semidirect |
| 15. #66935 | C5 | direct (N × H) |
| 17. C22×C5×C11 | D4 | semidirect |
| 24. C2×C5×D11 | D4 | semidirect |
| 27. C23×D11 | C2×C5 | semidirect |
| 28. C2×C22⋊D11 | C2×C5 | semidirect |
| 29. C2×D44 | C2×C5 | semidirect |
| 30. C11×C22⋊C4 | C2×C5 | semidirect |
| 31. (C2×D11)⋊C4 | C2×C5 | semidirect |
| 42. C22×D11 | C22×C5 | semidirect |
| 43. C2×C4×C11 | C22×C5 | semidirect |
| 45. C2×Dic11 | C22×C5 | semidirect |
| 51. C5×C22⋊C4 | D11 | semidirect |
| 52. C5×C11 | #120 | semidirect |
| 54. C22×C11 | C5×D4 | semidirect |
| 61. C2×D11 | C5×D4 | semidirect |
| 72. C2×C4×C5 | C2×D11 | semidirect |
| 86. C22×C5 | D44 | semidirect |
| 94. C22⋊C4 | C5×D11 | semidirect |
| 95. C11 | C5×#120 | semidirect |
| 109. C2×C4 | C2×C5×D11 | semidirect |
| 110. C5 | #66935 | direct (N × H) |
| 118. C22 | C5×D44 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×D11 | 2 |
| C2×C5×C22⋊D11 | 2 |
| C2×C5×D44 | 2 |
| C5×C11×C22⋊C4 | 2 |
| C5×(C2×D11)⋊C4 | 2 |
| #66935 | 5 |
| C5×#120 | 11 |