Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
254 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 63 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×#419 | C2 | semidirect |
| 3. C2×#3968 | C2 | semidirect |
| 5. #65413 | C2 | semidirect |
| 7. #64753 | C2 | semidirect |
| 62. #419 | D5 | semidirect |
| 192. C5 | #2049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4088 | 2 |
| C5×#419 | 2 |
| C2×#3968 | 2 |
| #65421 | 2 |
| #65413 | 2 |
| #65294 | 2 |
| #64753 | 2 |
| #2049 | 5 |