Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
316 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 3. #64919 | C2 | semidirect |
| 127. C5 | #1821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#683 | 2 |
| #65798 | 2 |
| #64919 | 2 |
| #1821 | 5 |