Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
512 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 123 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. C4×C5×#101 | C2 | semidirect |
| 3. C4×#3968 | C2 | semidirect |
| 5. #10598190 | C2 | semidirect |
| 23. #64697 | C4 | semidirect |
| 53. C5×#101 | C2×C4 | semidirect |
| 57. #3968 | C2×C4 | semidirect |
| 67. C4×#101 | D5 | semidirect |
| 209. #101 | C4×D5 | semidirect |
| 340. C5 | #12632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614186 | 2 |
| C4×C5×#101 | 2 |
| C4×#3968 | 2 |
| C2×#64697 | 2 |
| #10598190 | 2 |
| #12632 | 5 |