Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
228 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 67 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. #10599841 | C2 | semidirect |
| 3. #10599380 | C2 | semidirect |
| 5. C5×#1371 | C2 | semidirect |
| 6. #10597965 | C2 | semidirect |
| 50. #1371 | D5 | semidirect |
| 77. C5×C16 | SD16 | semidirect |
| 175. C16 | #677 | semidirect |
| 202. C5 | #12444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10599854 | 2 |
| #10599841 | 2 |
| #10599380 | 2 |
| #10599379 | 2 |
| C5×#1371 | 2 |
| #10597965 | 2 |
| #10597964 | 2 |
| #12444 | 5 |