Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
174 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 59 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. #65161 | C2 | semidirect |
| 3. C5×#366 | C2 | semidirect |
| 4. C16×Dic5 | C2 | semidirect |
| 5. #64711 | C2 | semidirect |
| 13. D80 | C4 | semidirect |
| 23. D40 | C2×C4 | semidirect |
| 24. C5×C16 | C2×C4 | semidirect |
| 28. #366 | D5 | semidirect |
| 58. Dic5 | D16 | semidirect |
| 69. C16 | C4×D5 | semidirect |
| 85. C5 | C4×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D80 | 2 |
| #65161 | 2 |
| C5×#366 | 2 |
| C16×Dic5 | 2 |
| #64711 | 2 |
| C4×D16 | 5 |