Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
224 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 1. C5×#405 | C2 | semidirect |
| 3. C2×#3954 | C2 | semidirect |
| 6. #64770 | C2 | semidirect |
| 7. #64752 | C2 | semidirect |
| 21. #3942 | C4 | semidirect |
| 22. #3942 | C4 | semidirect |
| 23. #3941 | C4 | semidirect |
| 24. #3941 | C4 | semidirect |
| 60. #405 | D5 | semidirect |
| 188. C5 | #1929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#405 | 2 |
| C2×#3957 | 2 |
| C2×#3954 | 2 |
| #65399 | 2 |
| #65291 | 2 |
| #64770 | 2 |
| #64752 | 2 |
| #1929 | 5 |