Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
740 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 101 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. #10615086 | C2 | semidirect |
| 2. #10615081 | C2 | semidirect |
| 4. C5×#1503 | C2 | semidirect |
| 5. #10601567 | C2 | semidirect |
| 6. #10601550 | C2 | semidirect |
| 7. #10598111 | C2 | semidirect |
| 38. C5×C4⋊Q8 | D4 | semidirect |
| 39. C5×C4⋊Q8 | D4 | semidirect |
| 76. C4⋊#168 | D4 | semidirect |
| 77. C4⋊#168 | D4 | semidirect |
| 83. #1503 | D5 | semidirect |
| 115. C2×D20 | SD16 | semidirect |
| 226. C4⋊Q8 | D20 | semidirect |
| 227. C4⋊Q8 | D20 | semidirect |
| 408. C5 | #10246 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615086 | 2 |
| #10615081 | 2 |
| #10605530 | 2 |
| C5×#1503 | 2 |
| #10601567 | 2 |
| #10601550 | 2 |
| #10598111 | 2 |
| #10246 | 5 |