Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
280 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 280 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 |
|---|---|---|
| 1. #10599858 | C2 | semidirect |
| 4. #10599837 | C2 | semidirect |
| 5. #10598856 | C2 | semidirect |
| 7. C5×#1311 | C2 | semidirect |
| 52. #1311 | D5 | semidirect |
| 76. C5×C16 | SD16 | semidirect |
| 167. C16 | #677 | semidirect |
| 191. C5 | #12508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10599858 | 2 |
| #10599854 | 2 |
| #10599851 | 2 |
| #10599837 | 2 |
| #10598856 | 2 |
| #10598851 | 2 |
| C5×#1311 | 2 |
| #12508 | 5 |