Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
176 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 49 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. #65377 | C2 | semidirect |
| 2. #65372 | C2 | semidirect |
| 4. #65127 | C2 | semidirect |
| 5. C5×#332 | C2 | semidirect |
| 6. #64705 | C2 | semidirect |
| 7. #64700 | C2 | semidirect |
| 48. #332 | D5 | semidirect |
| 149. C5 | #1701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65377 | 2 |
| #65372 | 2 |
| #65132 | 2 |
| #65127 | 2 |
| C5×#332 | 2 |
| #64705 | 2 |
| #64700 | 2 |
| #1701 | 5 |