Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 4. #64970 | C2 | semidirect |
| 5. C5×#334 | C2 | semidirect |
| 6. #64706 | C2 | semidirect |
| 7. #64701 | C2 | semidirect |
| 45. #334 | D5 | semidirect |
| 134. C5 | #1703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65135 | 2 |
| #65131 | 2 |
| #64977 | 2 |
| #64970 | 2 |
| C5×#334 | 2 |
| #64706 | 2 |
| #64701 | 2 |
| #1703 | 5 |