Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
276 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 69 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×#424 | C2 | semidirect |
| 3. C2×#3956 | C2 | semidirect |
| 5. #65293 | C2 | semidirect |
| 7. #64772 | C2 | semidirect |
| 56. #424 | D5 | semidirect |
| 181. C5 | #2046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#677 | 2 |
| C5×#424 | 2 |
| C2×#3956 | 2 |
| C2×#3955 | 2 |
| #65293 | 2 |
| #65290 | 2 |
| #64772 | 2 |
| #2046 | 5 |