Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
412 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 164 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. #65788 | C2 | semidirect |
| 3. #65705 | C2 | semidirect |
| 4. #65704 | C2 | semidirect |
| 5. #65680 | C2 | semidirect |
| 6. #65678 | C2 | semidirect |
| 7. C4×#700 | C2 | semidirect |
| 8. C4×D5⋊C8 | C2 | semidirect |
| 88. C4×D5 | M16 | semidirect |
| 91. #170 | #41 | semidirect |
| 187. C5 | #2965 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#713 | 2 |
| #65788 | 2 |
| #65705 | 2 |
| #65704 | 2 |
| #65680 | 2 |
| #65678 | 2 |
| C4×#700 | 2 |
| C4×D5⋊C8 | 2 |
| #2965 | 5 |