Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
620 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 113 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. #10605959 | C2 | semidirect |
| 3. C5×#1517 | C2 | semidirect |
| 4. #10602604 | C2 | semidirect |
| 5. #10601550 | C2 | semidirect |
| 6. #10598237 | C2 | semidirect |
| 7. #10598122 | C2 | semidirect |
| 15. #65372 | C4 | semidirect |
| 16. #65361 | C4 | semidirect |
| 34. C5×C4⋊Q8 | C2×C4 | semidirect |
| 35. C5×#127 | C2×C4 | semidirect |
| 73. C4⋊#168 | C2×C4 | semidirect |
| 77. #1517 | D5 | semidirect |
| 219. C4⋊Q8 | C4×D5 | semidirect |
| 220. #127 | C4×D5 | semidirect |
| 395. C5 | #9179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615028 | 2 |
| #10605959 | 2 |
| C5×#1517 | 2 |
| #10602604 | 2 |
| #10601550 | 2 |
| #10598237 | 2 |
| #10598122 | 2 |
| #9179 | 5 |