Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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. C2×C5×Q32 | C2 | semidirect |
| 4. C2×#3961 | C2 | semidirect |
| 5. #64784 | C2 | semidirect |
| 7. #64723 | C2 | semidirect |
| 50. C2×Q32 | D5 | semidirect |
| 93. C2×D5 | Q32 | semidirect |
| 149. C5 | #2188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×Q16 | 2 |
| C2×C5×Q32 | 2 |
| #65477 | 2 |
| C2×#3961 | 2 |
| #64784 | 2 |
| #64727 | 2 |
| #64723 | 2 |
| #2188 | 5 |