Finite Group DatabasebetaFinite Group DatabasebetaOrder 2560.
276 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 276 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. #12011189 | C2 | semidirect |
| 3. #12011185 | C2 | semidirect |
| 4. #11986971 | C2 | semidirect |
| 5. #11986769 | C2 | semidirect |
| 6. #11986637 | C2 | semidirect |
| 7. C5×#7390 | C2 | semidirect |
| 36. #64740 | C8 | semidirect |
| 37. #64739 | C8 | semidirect |
| 50. #7390 | D5 | semidirect |
| 72. Dic40 | C2×C8 | semidirect |
| 74. D80 | C2×C8 | semidirect |
| 79. #3926 | C2×C8 | semidirect |
| 242. C5 | AGL(1,ℤ/32) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #12019923 | 2 |
| #12011189 | 2 |
| #12011185 | 2 |
| #11986971 | 2 |
| #11986769 | 2 |
| #11986637 | 2 |
| C5×#7390 | 2 |
| AGL(1,ℤ/32) | 5 |