Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
408 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 93 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. C5×#380 | C2 | semidirect |
| 3. C4×C22⋊Dic5 | C2 | semidirect |
| 4. C2×#3938 | C2 | semidirect |
| 7. C22×D20 | C4 | semidirect |
| 15. C2×#685 | C4 | semidirect |
| 16. C2×C4⋊Dic5 | C4 | semidirect |
| 44. C22⋊Dic5 | D4 | semidirect |
| 52. #380 | D5 | semidirect |
| 125. C4×C5 | #99 | semidirect |
| 198. C5 | #1964 | semidirect |
| 222. C4 | #3938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4076 | 2 |
| C5×#380 | 2 |
| C4×C22⋊Dic5 | 2 |
| C2×#3938 | 2 |
| #1964 | 5 |