Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
464 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 83 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. #10599899 | C2 | semidirect |
| 3. #10599661 | C2 | semidirect |
| 4. C5×#1347 | C2 | semidirect |
| 5. #10598265 | C2 | semidirect |
| 6. #10598017 | C2 | semidirect |
| 7. #10597976 | C2 | semidirect |
| 8. C2×D5×D8 | C4 | semidirect |
| 12. #65446 | C4 | semidirect |
| 18. #65172 | C4 | semidirect |
| 19. D5×#107 | C4 | semidirect |
| 22. C5×C22⋊C16 | C22 | semidirect |
| 23. C5×#340 | C22 | semidirect |
| 24. #64771 | C22 | semidirect |
| 25. C22⋊#672 | C22 | semidirect |
| 71. #1347 | D5 | semidirect |
| 139. C22⋊C16 | C2×D5 | semidirect |
| 141. #340 | C2×D5 | semidirect |
| 366. C5 | #11888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#466 | 2 |
| #10599899 | 2 |
| #10599661 | 2 |
| C5×#1347 | 2 |
| #10598265 | 2 |
| #10598017 | 2 |
| #10597976 | 2 |
| #11888 | 5 |