Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
188 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 86 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×C11×Dic5 | C2 | semidirect |
| 3. C2×C4×D5×C11 | C2 | semidirect |
| 4. C5×C11×C22⋊C4 | C2 | semidirect |
| 5. C11×#685 | C2 | semidirect |
| 6. C11×#683 | C2 | semidirect |
| 7. C4×C11×Dic5 | C2 | semidirect |
| 12. C11×C22⋊D5 | C4 | semidirect |
| 21. C22×C5×C11 | C2×C4 | semidirect |
| 25. C2×D5×C11 | C2×C4 | semidirect |
| 29. C11×Dic5 | C2×C4 | semidirect |
| 30. C11×Dic5 | D4 | semidirect |
| 36. C11×C22⋊C4 | D5 | semidirect |
| 38. #4027 | C11 | direct (N × H) |
| 55. C22×Dic5 | C2×C11 | semidirect |
| 56. C2×C4×D5 | C2×C11 | semidirect |
| 57. C5×C22⋊C4 | C2×C11 | semidirect |
| 58. #685 | C2×C11 | semidirect |
| 59. #683 | C2×C11 | semidirect |
| 60. C4×Dic5 | C2×C11 | semidirect |
| 61. C5×C11 | C4×D4 | semidirect |
| 67. C22×C11 | C4×D5 | semidirect |
| 78. C22⋊D5 | C4×C11 | semidirect |
| 92. C22×C5 | C2×C4×C11 | semidirect |
| 96. C2×D5 | C2×C4×C11 | semidirect |
| 100. Dic5 | C2×C4×C11 | semidirect |
| 101. Dic5 | D4×C11 | semidirect |
| 107. C22⋊C4 | D5×C11 | semidirect |
| 109. C11 | #4027 | direct (N × H) |
| 125. C5 | C4×D4×C11 | semidirect |
| 131. C22 | C4×D5×C11 | 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 |
| C22×C11×Dic5 | 2 |
| C2×C4×D5×C11 | 2 |
| C5×C11×C22⋊C4 | 2 |
| C11×#685 | 2 |
| C11×#683 | 2 |
| C4×C11×Dic5 | 2 |
| C4×D4×C11 | 5 |
| #4027 | 11 |