Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
452 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. #10601629 | C2 | semidirect |
| 5. #10600655 | C2 | semidirect |
| 6. C5×#1291 | C2 | semidirect |
| 7. #10598239 | C2 | semidirect |
| 16. #65139 | C4 | semidirect |
| 17. #65138 | C4 | semidirect |
| 18. #65131 | C4 | semidirect |
| 19. #65130 | C4 | semidirect |
| 89. #1291 | D5 | semidirect |
| 363. C5 | #9159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611079 | 2 |
| #10611059 | 2 |
| #10601629 | 2 |
| #10600659 | 2 |
| #10600655 | 2 |
| C5×#1291 | 2 |
| #10598239 | 2 |
| #9159 | 5 |