Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
376 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 131 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. #65309 | C2 | semidirect |
| 7. #65166 | C2 | semidirect |
| 8. #65140 | C2 | semidirect |
| 11. #65088 | C2 | semidirect |
| 47. Q8×D5 | Q8 | semidirect |
| 87. #477 | D5 | semidirect |
| 239. C5 | #3078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66062 | 2 |
| C4×Q8×D5 | 2 |
| C5×#477 | 2 |
| #65380 | 2 |
| #65309 | 2 |
| #65170 | 2 |
| #65166 | 2 |
| #65140 | 2 |
| #65126 | 2 |
| #65091 | 2 |
| #65088 | 2 |
| #3078 | 5 |