Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
184 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. C5×#446 | C2 | semidirect |
| 2. #65316 | C2 | semidirect |
| 4. #64705 | C2 | semidirect |
| 5. #64677 | C2 | semidirect |
| 35. #446 | D5 | semidirect |
| 52. C5×C8 | SD16 | semidirect |
| 109. C8 | #688 | semidirect |
| 110. C5 | #1688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#446 | 2 |
| #65316 | 2 |
| #64984 | 2 |
| #64705 | 2 |
| #64677 | 2 |
| #1688 | 5 |