Finite Group DatabasebetaFinite Group DatabasebetaOrder 3520.
536 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 186 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. #67042⋊C5 | C2 | semidirect |
| 2. #131×C11⋊C5 | C2 | semidirect |
| 3. #66961⋊C5 | C2 | semidirect |
| 4. #66957⋊C5 | C2 | semidirect |
| 5. C2×D88⋊C5 | C2 | semidirect |
| 9. #4339⋊C5 | C22 | semidirect |
| 10. C2×C4⋊AGL(1,𝔽11) | C22 | semidirect |
| 11. M16×C11⋊C5 | C22 | semidirect |
| 12. C2×C8×C11⋊C5 | C22 | semidirect |
| 13. Dic44⋊C5 | C22 | semidirect |
| 14. D88⋊C5 | C22 | semidirect |
| 15. D88⋊C5 | C22 | semidirect |
| 16. #4314⋊C5 | C22 | semidirect |
| 17. #10623283 | C5 | semidirect |
| 29. #67042 | C2×C5 | semidirect |
| 30. C11×#131 | C2×C5 | semidirect |
| 31. #66961 | C2×C5 | semidirect |
| 32. #66957 | C2×C5 | semidirect |
| 33. C2×D88 | C2×C5 | semidirect |
| 44. #4339 | C22×C5 | semidirect |
| 45. C2×D44 | C22×C5 | semidirect |
| 46. C11×M16 | C22×C5 | semidirect |
| 47. C2×C8×C11 | C22×C5 | semidirect |
| 48. Dic44 | C22×C5 | semidirect |
| 49. D88 | C22×C5 | semidirect |
| 50. D88 | C22×C5 | semidirect |
| 51. #4314 | C22×C5 | semidirect |
| 83. C11⋊C5 | #576 | semidirect |
| 105. #131 | AGL(1,𝔽11) | semidirect |
| 124. M16 | C2×AGL(1,𝔽11) | semidirect |
| 125. C2×C8 | C2×AGL(1,𝔽11) | semidirect |
| 126. C11 | C5×#576 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #67042⋊C5 | 2 |
| #131×C11⋊C5 | 2 |
| #66961⋊C5 | 2 |
| #66957⋊C5 | 2 |
| C2×D88⋊C5 | 2 |
| #10623283 | 5 |
| C5×#576 | 11 |