Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
714 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 171 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. C22×D80 | C2 | semidirect |
| 2. C2×#65190 | C2 | semidirect |
| 3. #10610914 | C2 | semidirect |
| 4. C5×#2158 | C2 | semidirect |
| 5. #10601445 | C2 | semidirect |
| 6. #10600141 | C2 | semidirect |
| 7. #10600120 | C2 | semidirect |
| 19. C2×#3930 | C22 | semidirect |
| 20. C2×D5×C16 | C22 | semidirect |
| 21. #65172 | C22 | semidirect |
| 23. C5×#367 | C22 | semidirect |
| 24. C5×#366 | C22 | semidirect |
| 25. #64711 | C22 | semidirect |
| 44. C2×C5×C16 | D4 | semidirect |
| 61. #2158 | D5 | semidirect |
| 110. #367 | C2×D5 | semidirect |
| 111. #366 | C2×D5 | semidirect |
| 160. C2×C16 | D20 | semidirect |
| 240. C5 | #33607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D80 | 2 |
| C2×#65190 | 2 |
| #10610914 | 2 |
| C5×#2158 | 2 |
| #10601445 | 2 |
| #10600141 | 2 |
| #10600120 | 2 |
| #33607 | 5 |