Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
184 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 3. C5×C11×C4⋊C4 | C2 | semidirect |
| 4. C11×C4⋊Dic5 | C2 | semidirect |
| 5. C11×#683 | C2 | semidirect |
| 12. C4×D5×C11 | C4 | semidirect |
| 19. C4×C5×C11 | C2×C4 | semidirect |
| 21. C11×Dic5 | C2×C4 | semidirect |
| 26. C11×C4⋊C4 | D5 | direct (N × H) |
| 27. D5×C4⋊C4 | C11 | direct (N × H) |
| 31. D5×C11 | C4⋊C4 | direct (N × H) |
| 41. C5×C4⋊C4 | C2×C11 | semidirect |
| 42. C4⋊Dic5 | C2×C11 | semidirect |
| 43. #683 | C2×C11 | semidirect |
| 44. C5×C11 | C2×C4⋊C4 | semidirect |
| 52. C4×C11 | C4×D5 | semidirect |
| 59. C4×D5 | C4×C11 | semidirect |
| 70. C4×C5 | C2×C4×C11 | semidirect |
| 72. Dic5 | C2×C4×C11 | semidirect |
| 77. C4⋊C4 | D5×C11 | direct (N × H) |
| 78. C11 | D5×C4⋊C4 | direct (N × H) |
| 82. D5 | C11×C4⋊C4 | direct (N × H) |
| 90. C5 | C2×C11×C4⋊C4 | semidirect |
| 98. C4 | C4×D5×C11 | 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 |
| C5×C11×C4⋊C4 | 2 |
| C11×C4⋊Dic5 | 2 |
| C11×#683 | 2 |
| C2×C11×C4⋊C4 | 5 |
| D5×C4⋊C4 | 11 |