Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
368 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 111 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. D5×#125 | C2 | semidirect |
| 3. C5×#490 | C2 | semidirect |
| 4. #65360 | C2 | semidirect |
| 5. #65354 | C2 | semidirect |
| 6. #65066 | C2 | semidirect |
| 7. #65063 | C2 | semidirect |
| 8. #65055 | C2 | semidirect |
| 9. #65052 | C2 | semidirect |
| 10. #64994 | C2 | semidirect |
| 11. #64991 | C2 | semidirect |
| 85. #490 | D5 | semidirect |
| 233. C5 | #3234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66050 | 2 |
| D5×#125 | 2 |
| C5×#490 | 2 |
| #65360 | 2 |
| #65354 | 2 |
| #65066 | 2 |
| #65063 | 2 |
| #65055 | 2 |
| #65052 | 2 |
| #64994 | 2 |
| #64991 | 2 |
| #3234 | 5 |