Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
686 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 686 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 |
|---|---|---|
| 1. C5×#3100 | C2 | semidirect |
| 2. #10615028 | C2 | semidirect |
| 3. #10614146 | C2 | semidirect |
| 4. #10602607 | C2 | semidirect |
| 5. #10602391 | C2 | semidirect |
| 6. #10601550 | C2 | semidirect |
| 7. #10598229 | C2 | semidirect |
| 41. C5×C4⋊Q8 | D4 | semidirect |
| 42. C5×#127 | D4 | semidirect |
| 76. C4×C5×C8 | D4 | semidirect |
| 85. C4⋊#168 | D4 | semidirect |
| 87. #3100 | D5 | semidirect |
| 129. C2×D20 | D8 | semidirect |
| 261. C4⋊Q8 | C22⋊D5 | semidirect |
| 262. #127 | C22⋊D5 | semidirect |
| 298. C4×C8 | C22⋊D5 | semidirect |
| 472. C5 | #9996 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3100 | 2 |
| #10615028 | 2 |
| #10614146 | 2 |
| #10602607 | 2 |
| #10602391 | 2 |
| #10601550 | 2 |
| #10598229 | 2 |
| #9996 | 5 |