Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
432 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 146 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 | direct (N × H) |
| 9. C2×#704 | C4 | semidirect |
| 35. #704 | C2×C4 | semidirect |
| 126. C2×C5 | #343 | semidirect |
| 157. C5 | C2×#343 | semidirect |
| 179. C2 | #64919 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#704 | 2 |
| C22×#683 | 2 |
| #64919 | 2 |
| C2×#343 | 5 |