Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
262 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 4. C2×#3956 | C2 | semidirect |
| 5. C2×#3954 | C2 | semidirect |
| 6. C2×#3942 | C2 | semidirect |
| 7. #64750 | C2 | semidirect |
| 197. C5 | #2052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4097 | 2 |
| C5×#417 | 2 |
| #65523 | 2 |
| C2×#3956 | 2 |
| C2×#3954 | 2 |
| C2×#3942 | 2 |
| #64750 | 2 |
| #2052 | 5 |