Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
890 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 155 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. C5×#2113 | C2 | semidirect |
| 3. #10602800 | C2 | semidirect |
| 4. #10602231 | C2 | semidirect |
| 5. C2×#64728 | C2 | semidirect |
| 15. C2×C5×M32 | C22 | semidirect |
| 16. C22×C5×C16 | C22 | semidirect |
| 17. C2×#3944 | C22 | semidirect |
| 67. #2113 | D5 | semidirect |
| 129. C2×M32 | C2×D5 | semidirect |
| 130. C22×C16 | C2×D5 | semidirect |
| 310. C5 | #12685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619061 | 2 |
| C5×#2113 | 2 |
| #10602800 | 2 |
| #10602231 | 2 |
| C2×#64728 | 2 |
| #12685 | 5 |