Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
140 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 4. #64724 | C2 | semidirect |
| 5. #64723 | C2 | semidirect |
| 96. C5 | #2236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65405 | 2 |
| C2×#3950 | 2 |
| C5×C22⋊C16 | 2 |
| #64724 | 2 |
| #64723 | 2 |
| #2236 | 5 |