Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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. C22×C5×SD16 | C2 | semidirect |
| 2. C2×#4088 | C2 | semidirect |
| 4. C2×#3968 | C2 | semidirect |
| 5. C2×#3965 | C2 | semidirect |
| 6. #65399 | C2 | semidirect |
| 7. #64772 | C2 | semidirect |
| 72. C22×SD16 | D5 | semidirect |
| 232. C5 | #2019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×SD16 | 2 |
| C2×#4088 | 2 |
| C2×#4078 | 2 |
| C2×#3968 | 2 |
| C2×#3965 | 2 |
| #65399 | 2 |
| #64772 | 2 |
| #2019 | 5 |