Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
794 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 105 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×#2541 | C2 | semidirect |
| 2. #10614897 | C2 | semidirect |
| 3. #10614038 | C2 | semidirect |
| 4. #10602552 | C2 | semidirect |
| 5. #10602390 | C2 | semidirect |
| 6. #10600262 | C2 | semidirect |
| 7. #10598111 | C2 | semidirect |
| 65. #4020 | D4 | semidirect |
| 68. #4015 | D4 | semidirect |
| 77. C4⋊#168 | D4 | semidirect |
| 78. C4⋊#168 | D4 | semidirect |
| 83. #2541 | D5 | semidirect |
| 110. C2×C5×D4 | D8 | semidirect |
| 343. C2×D4 | #686 | semidirect |
| 443. C5 | #10238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2541 | 2 |
| #10614897 | 2 |
| #10614038 | 2 |
| #10602552 | 2 |
| #10602390 | 2 |
| #10600262 | 2 |
| #10598111 | 2 |
| #10238 | 5 |