Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
1382 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1382 conjugacy classes of subgroups — too many to draw. Only its 291 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. C22×C5×#101 | C2 | semidirect |
| 3. C22×#3968 | C2 | semidirect |
| 4. C2×#64697 | C2 | direct (N × H) |
| 17. C2×C5×#101 | C22 | semidirect |
| 19. C2×#3968 | C22 | semidirect |
| 20. #64697 | C22 | direct (N × H) |
| 55. C5×#101 | C23 | semidirect |
| 57. #3968 | C23 | semidirect |
| 60. C22×#101 | D5 | semidirect |
| 126. C2×#101 | C2×D5 | semidirect |
| 202. #101 | C22×D5 | semidirect |
| 205. C22×C5 | #355 | semidirect |
| 272. C2×C5 | C2×#355 | semidirect |
| 314. C5 | C22×#355 | semidirect |
| 321. C22 | #64697 | direct (N × H) |
| 335. C2 | C2×#64697 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4093 | 2 |
| C22×C5×#101 | 2 |
| C22×#3968 | 2 |
| C2×#64697 | 2 |
| C22×#355 | 5 |