Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
994 conjugacy classes of subgroups; only the 239 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 239 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. D5×#498 | C2 | semidirect |
| 3. C5×#1705 | C2 | semidirect |
| 4. #10602125 | C2 | semidirect |
| 5. #10602047 | C2 | semidirect |
| 6. #10598850 | C2 | semidirect |
| 7. C82×D5 | C2 | semidirect |
| 11. C5×#498 | C22 | semidirect |
| 15. #65368 | C22 | semidirect |
| 21. #64969 | C22 | semidirect |
| 22. C5×C82 | C22 | semidirect |
| 23. C8×#168 | C22 | semidirect |
| 53. #1705 | D5 | direct (N × H) |
| 77. C8×D5 | SD16 | semidirect |
| 84. #498 | C2×D5 | semidirect |
| 93. C82 | C2×D5 | semidirect |
| 110. C5×C8 | C2×SD16 | semidirect |
| 111. #168 | C2×SD16 | semidirect |
| 170. D5 | #1705 | direct (N × H) |
| 188. C8 | D5×SD16 | semidirect |
| 189. C5 | C2×#1705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#498 | 2 |
| D5×#492 | 2 |
| C5×#1705 | 2 |
| #10602125 | 2 |
| #10602047 | 2 |
| #10598850 | 2 |
| C82×D5 | 2 |
| C2×#1705 | 5 |