Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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. C5×#477 | C2 | semidirect |
| 4. #65380 | C2 | semidirect |
| 5. #65320 | C2 | semidirect |
| 7. #65164 | C2 | semidirect |
| 8. #65138 | C2 | semidirect |
| 11. #65082 | C2 | semidirect |
| 86. #477 | D5 | semidirect |
| 112. C4×D5 | Q16 | semidirect |
| 237. C5 | #3249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66062 | 2 |
| #65912 | 2 |
| C5×#477 | 2 |
| #65380 | 2 |
| #65320 | 2 |
| #65176 | 2 |
| #65164 | 2 |
| #65138 | 2 |
| D5×C4⋊C8 | 2 |
| #65102 | 2 |
| #65082 | 2 |
| #3249 | 5 |