Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
278 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 67 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×#391 | C2 | semidirect |
| 3. C2×#3968 | C2 | semidirect |
| 5. #65253 | C2 | semidirect |
| 7. #64743 | C2 | semidirect |
| 69. #391 | D5 | semidirect |
| 216. C5 | #2038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66150 | 2 |
| C5×#391 | 2 |
| C2×#3968 | 2 |
| #65255 | 2 |
| #65253 | 2 |
| C2×#3937 | 2 |
| #64743 | 2 |
| #2038 | 5 |