Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 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. C5×C11×#41 | C2 | semidirect |
| 2. C2×C5×D44 | C2 | semidirect |
| 3. C5×#4325 | C2 | semidirect |
| 4. C5×#4323 | C2 | semidirect |
| 5. C5×#4318 | C2 | semidirect |
| 7. C5×Q8×C11 | C22 | semidirect |
| 9. C5×D4×C11 | C22 | semidirect |
| 14. C5×C11⋊C8 | C22 | semidirect |
| 15. #67002 | C5 | direct (N × H) |
| 23. C11×#41 | C2×C5 | semidirect |
| 24. C2×D44 | C2×C5 | semidirect |
| 25. #4325 | C2×C5 | semidirect |
| 26. #4323 | C2×C5 | semidirect |
| 27. #4318 | C2×C5 | semidirect |
| 34. Q8×C11 | C22×C5 | semidirect |
| 36. D4×C11 | C22×C5 | semidirect |
| 41. C11⋊C8 | C22×C5 | semidirect |
| 42. C5×#41 | D11 | semidirect |
| 47. C5×C11 | AGL(1,ℤ/8) | semidirect |
| 56. C5×Q8 | C2×D11 | semidirect |
| 60. C5×D4 | C2×D11 | semidirect |
| 76. #41 | C5×D11 | semidirect |
| 81. C11 | C5×AGL(1,ℤ/8) | semidirect |
| 87. Q8 | C2×C5×D11 | semidirect |
| 91. D4 | C2×C5×D11 | semidirect |
| 95. C5 | #67002 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C11×#41 | 2 |
| C2×C5×D44 | 2 |
| C5×#4325 | 2 |
| C5×#4323 | 2 |
| C5×#4318 | 2 |
| #67002 | 5 |
| C5×AGL(1,ℤ/8) | 11 |