Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
266 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 70 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. #65758 | C2 | semidirect |
| 3. C4×#704 | C2 | semidirect |
| 4. Q8⋊#170 | C2 | semidirect |
| 5. D4⋊#170 | C2 | semidirect |
| 61. C5×Q8 | M16 | semidirect |
| 64. C5×D4 | M16 | semidirect |
| 157. Q8 | #704 | semidirect |
| 160. D4 | #704 | semidirect |
| 181. C5 | #1489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic5 | 2 |
| #65758 | 2 |
| C4×#704 | 2 |
| Q8⋊#170 | 2 |
| D4⋊#170 | 2 |
| #1489 | 5 |