Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
442 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 79 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. #10599899 | C2 | semidirect |
| 3. #10599732 | C2 | semidirect |
| 4. C5×#1349 | C2 | semidirect |
| 5. #10598266 | C2 | semidirect |
| 6. #10598018 | C2 | semidirect |
| 7. #10597978 | C2 | semidirect |
| 22. C5×C22⋊C16 | C22 | semidirect |
| 23. C5×#341 | C22 | semidirect |
| 24. #64772 | C22 | semidirect |
| 25. C22⋊#672 | C22 | semidirect |
| 71. #1349 | D5 | semidirect |
| 137. C22⋊C16 | C2×D5 | semidirect |
| 139. #341 | C2×D5 | semidirect |
| 343. C5 | #11895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#466 | 2 |
| #10599899 | 2 |
| #10599732 | 2 |
| C5×#1349 | 2 |
| #10598266 | 2 |
| #10598018 | 2 |
| #10597978 | 2 |
| #11895 | 5 |