Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
324 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 60. #689 | Q8 | semidirect |
| 202. C5 | #3383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#557 | 2 |
| #65901 | 2 |
| #65383 | 2 |
| #65367 | 2 |
| #65353 | 2 |
| #65352 | 2 |
| C4×#689 | 2 |
| Q8×#168 | 2 |
| #65311 | 2 |
| #65309 | 2 |
| #3383 | 5 |