Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
530 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 95 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. #10602396 | C2 | semidirect |
| 3. #10602395 | C2 | semidirect |
| 4. #10598127 | C2 | semidirect |
| 5. #10598113 | C2 | semidirect |
| 71. C24×C5 | M16 | semidirect |
| 109. C5×C22⋊C4 | M16 | semidirect |
| 266. C24 | #681 | semidirect |
| 308. C22⋊C4 | #681 | semidirect |
| 378. C5 | #11527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2321 | 2 |
| #10602396 | 2 |
| #10602395 | 2 |
| #10598127 | 2 |
| #10598113 | 2 |
| #11527 | 5 |