Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
332 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 170 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. C11×#713 | C2 | semidirect |
| 3. D4×D5×C11 | C2 | semidirect |
| 4. C11×#709 | C2 | semidirect |
| 5. C2×C11×D20 | C2 | semidirect |
| 6. C22×D5×C11 | C22 | semidirect |
| 7. C5×Q8×C11 | C22 | semidirect |
| 8. C5×D4×C11 | C22 | semidirect |
| 9. C2×C4×C5×C11 | C22 | semidirect |
| 10. C11×C22⋊D5 | C22 | semidirect |
| 11. C11×D20 | C22 | semidirect |
| 12. C11×D20 | C22 | semidirect |
| 13. C4×D5×C11 | C22 | semidirect |
| 14. C11×Dic10 | C22 | semidirect |
| 24. C11×#41 | D5 | semidirect |
| 27. #4149 | C11 | direct (N × H) |
| 33. Q8×C11 | C2×D5 | semidirect |
| 37. D4×C11 | C2×D5 | semidirect |
| 39. C2×C4×C11 | C2×D5 | semidirect |
| 40. C5×#41 | C2×C11 | semidirect |
| 41. #713 | C2×C11 | semidirect |
| 42. D4×D5 | C2×C11 | semidirect |
| 43. #709 | C2×C11 | semidirect |
| 44. C2×D20 | C2×C11 | semidirect |
| 45. C5×C11 | H(5,𝔽2) | semidirect |
| 52. C22×D5 | C22×C11 | semidirect |
| 53. C5×Q8 | C22×C11 | semidirect |
| 54. C5×D4 | C22×C11 | semidirect |
| 55. C2×C4×C5 | C22×C11 | semidirect |
| 56. C22⋊D5 | C22×C11 | semidirect |
| 57. D20 | C22×C11 | semidirect |
| 58. D20 | C22×C11 | semidirect |
| 59. C4×D5 | C22×C11 | semidirect |
| 60. Dic10 | C22×C11 | semidirect |
| 73. #41 | D5×C11 | semidirect |
| 76. C11 | #4149 | direct (N × H) |
| 82. Q8 | C2×D5×C11 | semidirect |
| 86. D4 | C2×D5×C11 | semidirect |
| 88. C2×C4 | C2×D5×C11 | semidirect |
| 89. C5 | C11×H(5,𝔽2) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C11×#41 | 2 |
| C11×#713 | 2 |
| D4×D5×C11 | 2 |
| C11×#709 | 2 |
| C2×C11×D20 | 2 |
| C11×H(5,𝔽2) | 5 |
| #4149 | 11 |