Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
470 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 99 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. C5×#1986 | C2 | semidirect |
| 3. #10602623 | C2 | semidirect |
| 5. #10600643 | C2 | semidirect |
| 7. #10598111 | C2 | semidirect |
| 71. #1986 | D5 | semidirect |
| 100. C5×M16 | SD16 | semidirect |
| 280. M16 | #688 | semidirect |
| 352. C5 | #10504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615086 | 2 |
| C5×#1986 | 2 |
| #10602623 | 2 |
| #10600669 | 2 |
| #10600643 | 2 |
| #10600280 | 2 |
| #10598111 | 2 |
| #10504 | 5 |