Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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. M16×Dic5 | C2 | semidirect |
| 4. C5×#343 | C2 | semidirect |
| 5. #64750 | C2 | semidirect |
| 15. #3955 | C4 | semidirect |
| 32. C5×M16 | C2×C4 | semidirect |
| 39. #681 | C2×C4 | semidirect |
| 45. #343 | D5 | semidirect |
| 96. Dic5 | #100 | semidirect |
| 112. M16 | C4×D5 | semidirect |
| 148. C5 | C4×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4039 | 2 |
| C2×#3955 | 2 |
| M16×Dic5 | 2 |
| C5×#343 | 2 |
| #64750 | 2 |
| C4×#100 | 5 |