Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
366 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 65 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. #10601667 | C2 | semidirect |
| 3. #10600082 | C2 | semidirect |
| 4. #10599872 | C2 | semidirect |
| 5. C5×#1330 | C2 | semidirect |
| 6. #10598053 | C2 | semidirect |
| 7. #10598007 | C2 | semidirect |
| 18. #64971 | C22 | semidirect |
| 19. C5×C4⋊C16 | C22 | semidirect |
| 20. C5×#346 | C22 | semidirect |
| 26. #64677 | C22 | semidirect |
| 69. #1330 | D5 | semidirect |
| 126. C4⋊C16 | C2×D5 | semidirect |
| 130. #346 | C2×D5 | semidirect |
| 303. C5 | #12376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611280 | 2 |
| #10601667 | 2 |
| #10600082 | 2 |
| #10599872 | 2 |
| C5×#1330 | 2 |
| #10598053 | 2 |
| #10598007 | 2 |
| #12376 | 5 |