Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
152 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 66 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×C5×D44 | C2 | semidirect |
| 3. C5×#4323 | C2 | direct (N × H) |
| 4. C2×C5×C11⋊C8 | C2 | semidirect |
| 8. C5×D4×C11 | C22 | semidirect |
| 11. C5×D44 | C22 | semidirect |
| 12. C5×C11⋊C8 | C22 | semidirect |
| 13. C2×#4323 | C5 | direct (N × H) |
| 21. C2×D4×C11 | C2×C5 | semidirect |
| 22. C2×D44 | C2×C5 | semidirect |
| 23. #4323 | C2×C5 | direct (N × H) |
| 24. C2×C11⋊C8 | C2×C5 | semidirect |
| 27. C2×C5×C11 | D8 | semidirect |
| 33. D4×C11 | C22×C5 | semidirect |
| 36. D44 | C22×C5 | semidirect |
| 37. C11⋊C8 | C22×C5 | semidirect |
| 39. C2×C5×D4 | D11 | semidirect |
| 42. C5×C11 | C2×D8 | semidirect |
| 55. C5×D4 | C2×D11 | semidirect |
| 60. C2×C11 | C5×D8 | semidirect |
| 71. C2×D4 | C5×D11 | semidirect |
| 74. C11 | C2×C5×D8 | semidirect |
| 77. C2×C5 | #4323 | direct (N × H) |
| 84. D4 | C2×C5×D11 | semidirect |
| 87. C5 | C2×#4323 | direct (N × H) |
| 97. C2 | C5×#4323 | direct (N × H) |
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×C5×D44 | 2 |
| C5×#4323 | 2 |
| C2×C5×C11⋊C8 | 2 |
| C2×#4323 | 5 |
| C2×C5×D8 | 11 |