Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
148 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 148 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 |
|---|---|---|
| 2. C2×C11×Dic10 | C2 | semidirect |
| 3. C5×C11×C4⋊C4 | C2 | semidirect |
| 5. C11×C4⋊Dic5 | C2 | semidirect |
| 17. C2×D5×C11 | Q8 | semidirect |
| 25. C11×C4⋊C4 | D5 | semidirect |
| 27. #4043 | C11 | direct (N × H) |
| 40. C2×Dic10 | C2×C11 | semidirect |
| 41. C5×C4⋊C4 | C2×C11 | semidirect |
| 43. C4⋊Dic5 | C2×C11 | semidirect |
| 44. C5×C11 | C22⋊Q8 | semidirect |
| 68. C2×D5 | Q8×C11 | semidirect |
| 76. C4⋊C4 | D5×C11 | semidirect |
| 78. C11 | #4043 | direct (N × H) |
| 90. C5 | C11×C22⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D5×C11 | 2 |
| C2×C11×Dic10 | 2 |
| C5×C11×C4⋊C4 | 2 |
| C11×#685 | 2 |
| C11×C4⋊Dic5 | 2 |
| C11×C22⋊Q8 | 5 |
| #4043 | 11 |