Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
452 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 452 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. #65756 | C2 | semidirect |
| 3. #65748 | C2 | semidirect |
| 4. #65705 | C2 | semidirect |
| 7. C2×#700 | C22 | semidirect |
| 14. #4003 | C22 | semidirect |
| 15. C4⋊#170 | C22 | semidirect |
| 16. C4×#170 | C22 | semidirect |
| 44. C2×C4×C5 | M16 | semidirect |
| 116. C2×C4 | #700 | semidirect |
| 120. C5 | #2975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4039 | 2 |
| #65756 | 2 |
| #65748 | 2 |
| #65705 | 2 |
| #2975 | 5 |