Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
160 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 1. C2×#3932 | C2 | semidirect |
| 2. C2×#3930 | C2 | semidirect |
| 3. #65176 | C2 | semidirect |
| 5. C5×#366 | C2 | semidirect |
| 6. #64712 | C2 | semidirect |
| 7. #64711 | C2 | semidirect |
| 39. C5×C16 | D4 | semidirect |
| 45. #366 | D5 | semidirect |
| 109. C16 | D20 | semidirect |
| 132. C5 | #2220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3932 | 2 |
| C2×#3930 | 2 |
| #65176 | 2 |
| #65172 | 2 |
| C5×#366 | 2 |
| #64712 | 2 |
| #64711 | 2 |
| #2220 | 5 |