Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
338 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×#3956 | C2 | semidirect |
| 4. C2×#3956 | C2 | semidirect |
| 6. C5×#343 | C2 | semidirect |
| 7. #64750 | C2 | semidirect |
| 75. #343 | D5 | semidirect |
| 147. C2×D5 | #101 | semidirect |
| 240. C5 | #1901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×M16 | 2 |
| C2×#4043 | 2 |
| C2×#3956 | 2 |
| #65415 | 2 |
| C5×#343 | 2 |
| #64750 | 2 |
| #1901 | 5 |