Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
340 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 85 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. #66153 | C2 | semidirect |
| 3. C5×#413 | C2 | semidirect |
| 4. C2×#3955 | C2 | semidirect |
| 5. #64776 | C2 | semidirect |
| 43. #681 | D4 | semidirect |
| 48. #413 | D5 | semidirect |
| 152. C5 | #1914 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #66164 | 2 |
| #66153 | 2 |
| C5×#413 | 2 |
| C2×#3955 | 2 |
| #64776 | 2 |
| #1914 | 5 |