Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
632 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #10605884 | C2 | semidirect |
| 3. #10601306 | C2 | semidirect |
| 4. #10601295 | C2 | semidirect |
| 5. #10600338 | C2 | semidirect |
| 6. C5×#1286 | C2 | semidirect |
| 7. #10598228 | C2 | semidirect |
| 21. #64984 | C4 | semidirect |
| 22. #64983 | C4 | semidirect |
| 50. #4020 | C2×C4 | semidirect |
| 54. #4015 | C2×C4 | semidirect |
| 59. C4×C5×C8 | C2×C4 | semidirect |
| 75. #1286 | D5 | semidirect |
| 129. C4×Dic5 | D8 | semidirect |
| 241. C4×C8 | C4×D5 | semidirect |
| 388. C5 | #9299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611034 | 2 |
| #10605884 | 2 |
| #10601306 | 2 |
| #10601295 | 2 |
| #10600338 | 2 |
| C5×#1286 | 2 |
| #10598228 | 2 |
| #9299 | 5 |