Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
188 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 188 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 |
|---|---|---|
| 1. C2×C5×D4×C11 | C2 | semidirect |
| 2. C2×C11×C22⋊D5 | C2 | semidirect |
| 3. C2×C4×D5×C11 | C2 | semidirect |
| 4. C11×C22⋊Dic5 | C2 | semidirect |
| 5. C11×C4⋊Dic5 | C2 | semidirect |
| 21. C2×D5×C11 | D4 | semidirect |
| 22. C4×C5×C11 | D4 | semidirect |
| 26. C2×D4×C11 | D5 | semidirect |
| 30. #4084 | C11 | direct (N × H) |
| 44. C2×C5×D4 | C2×C11 | semidirect |
| 45. C2×C22⋊D5 | C2×C11 | semidirect |
| 46. C2×C4×D5 | C2×C11 | semidirect |
| 47. C22⋊Dic5 | C2×C11 | semidirect |
| 48. C4⋊Dic5 | C2×C11 | semidirect |
| 49. C5×C11 | #121 | semidirect |
| 59. C4×C11 | C22⋊D5 | semidirect |
| 80. C2×D5 | D4×C11 | semidirect |
| 81. C4×C5 | D4×C11 | semidirect |
| 85. C2×D4 | D5×C11 | semidirect |
| 89. C11 | #4084 | direct (N × H) |
| 103. C5 | C11×#121 | semidirect |
| 113. C4 | C11×C22⋊D5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×C11 | 2 |
| C2×C11×C22⋊D5 | 2 |
| C2×C4×D5×C11 | 2 |
| C11×C22⋊Dic5 | 2 |
| C11×C4⋊Dic5 | 2 |
| C11×#121 | 5 |
| #4084 | 11 |