Finite Group DatabasebetaFinite Group DatabasebetaOrder 3520.
260 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 260 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. #66991⋊C5 | C2 | semidirect |
| 2. C2×#4323⋊C5 | C2 | semidirect |
| 3. C2×#4313⋊C5 | C2 | semidirect |
| 4. #66948⋊C5 | C2 | semidirect |
| 5. #102×C11⋊C5 | C2 | semidirect |
| 6. #66885⋊C5 | C2 | semidirect |
| 7. #66872⋊C5 | C2 | semidirect |
| 21. #10622395 | C5 | semidirect |
| 38. (C11⋊C5)⋊C8 | D4 | semidirect |
| 39. #66991 | C2×C5 | semidirect |
| 40. C2×#4323 | C2×C5 | semidirect |
| 41. C2×#4313 | C2×C5 | semidirect |
| 42. #66948 | C2×C5 | semidirect |
| 43. C11×#102 | C2×C5 | semidirect |
| 44. #66885 | C2×C5 | semidirect |
| 45. #66872 | C2×C5 | semidirect |
| 104. C11⋊C8 | C5×D4 | semidirect |
| 119. C11⋊C5 | #469 | semidirect |
| 158. #102 | AGL(1,𝔽11) | semidirect |
| 193. C11 | C5×#469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66991⋊C5 | 2 |
| C2×#4323⋊C5 | 2 |
| C2×#4313⋊C5 | 2 |
| #66948⋊C5 | 2 |
| #102×C11⋊C5 | 2 |
| #66885⋊C5 | 2 |
| #66872⋊C5 | 2 |
| #10622395 | 5 |
| C5×#469 | 11 |