Finite Group DatabasebetaFinite Group DatabasebetaOrder 3520.
180 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 180 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. C2×D8×C11⋊C5 | C2 | semidirect |
| 2. #66957⋊C5 | C2 | semidirect |
| 3. #66891⋊C5 | C2 | semidirect |
| 4. #66890⋊C5 | C2 | semidirect |
| 5. #66876⋊C5 | C2 | semidirect |
| 11. Dic44⋊C5 | C22 | semidirect |
| 12. D88⋊C5 | C22 | semidirect |
| 14. (C11⋊C5)⋊C16 | C22 | semidirect |
| 15. #10622760 | C5 | semidirect |
| 26. C2×C11×D8 | C2×C5 | semidirect |
| 27. #66957 | C2×C5 | semidirect |
| 28. #66891 | C2×C5 | semidirect |
| 29. #66890 | C2×C5 | semidirect |
| 30. #66876 | C2×C5 | semidirect |
| 44. Dic44 | C22×C5 | semidirect |
| 45. D88 | C22×C5 | semidirect |
| 47. C11⋊C16 | C22×C5 | semidirect |
| 77. C11⋊C5 | #509 | semidirect |
| 96. C2×D8 | AGL(1,𝔽11) | semidirect |
| 120. C11 | C5×#509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×C11⋊C5 | 2 |
| #66957⋊C5 | 2 |
| #66891⋊C5 | 2 |
| #66890⋊C5 | 2 |
| #66876⋊C5 | 2 |
| #10622760 | 5 |
| C5×#509 | 11 |