Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
340 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. #65901 | C2 | semidirect |
| 3. C5×#477 | C2 | semidirect |
| 4. #65382 | C2 | semidirect |
| 7. #65166 | C2 | semidirect |
| 9. #65120 | C2 | semidirect |
| 11. #65086 | C2 | semidirect |
| 79. #477 | D5 | semidirect |
| 213. C5 | #3372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66064 | 2 |
| #65901 | 2 |
| C5×#477 | 2 |
| #65382 | 2 |
| C4×#688 | 2 |
| #65178 | 2 |
| #65166 | 2 |
| #65130 | 2 |
| #65120 | 2 |
| #65107 | 2 |
| #65086 | 2 |
| #3372 | 5 |