Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
306 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 87 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. C5×#2252 | C2 | semidirect |
| 2. #10602174 | C2 | semidirect |
| 3. #10602152 | C2 | semidirect |
| 5. C16×#168 | C2 | semidirect |
| 31. #2252 | D5 | semidirect |
| 50. C5×C16 | SD16 | semidirect |
| 75. #168 | D16 | semidirect |
| 114. C16 | #688 | semidirect |
| 133. C5 | #12503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2252 | 2 |
| #10602174 | 2 |
| #10602152 | 2 |
| #10599853 | 2 |
| C16×#168 | 2 |
| #12503 | 5 |