Finite Group DatabasebetaFinite Group DatabasebetaOrder 3520.
524 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 524 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. C2×#4339⋊C5 | C2 | semidirect |
| 2. C2×M16×C11⋊C5 | C2 | semidirect |
| 3. #66962⋊C5 | C2 | semidirect |
| 4. #66961⋊C5 | C2 | semidirect |
| 5. #66957⋊C5 | C2 | semidirect |
| 11. #4339⋊C5 | C22 | semidirect |
| 12. C2×C4⋊AGL(1,𝔽11) | C22 | semidirect |
| 14. C2×(C11⋊C5)⋊Q8 | C22 | semidirect |
| 15. M16×C11⋊C5 | C22 | semidirect |
| 16. C2×C8×C11⋊C5 | C22 | semidirect |
| 17. Dic44⋊C5 | C22 | semidirect |
| 18. D88⋊C5 | C22 | semidirect |
| 19. #4314⋊C5 | C22 | semidirect |
| 20. #10623279 | C5 | semidirect |
| 37. C2×#4339 | C2×C5 | semidirect |
| 38. C2×C11×M16 | C2×C5 | semidirect |
| 39. #66962 | C2×C5 | semidirect |
| 40. #66961 | C2×C5 | semidirect |
| 41. #66957 | C2×C5 | semidirect |
| 57. #4339 | C22×C5 | semidirect |
| 58. C2×D44 | C22×C5 | semidirect |
| 60. C2×Dic22 | C22×C5 | semidirect |
| 61. C11×M16 | C22×C5 | semidirect |
| 62. C2×C8×C11 | C22×C5 | semidirect |
| 63. Dic44 | C22×C5 | semidirect |
| 64. D88 | C22×C5 | semidirect |
| 65. #4314 | C22×C5 | semidirect |
| 106. C11⋊C5 | #575 | semidirect |
| 136. C2×M16 | AGL(1,𝔽11) | semidirect |
| 162. M16 | C2×AGL(1,𝔽11) | semidirect |
| 163. C2×C8 | C2×AGL(1,𝔽11) | semidirect |
| 164. C11 | C5×#575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4339⋊C5 | 2 |
| C2×M16×C11⋊C5 | 2 |
| #66962⋊C5 | 2 |
| #66961⋊C5 | 2 |
| #66957⋊C5 | 2 |
| #10623279 | 5 |
| C5×#575 | 11 |