Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
704 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 209 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. #66079 | C2 | semidirect |
| 3. C2×C5×#101 | C2 | semidirect |
| 4. C2×#3968 | C2 | semidirect |
| 5. #65421 | C2 | semidirect |
| 6. #65040 | C2 | semidirect |
| 7. D5×#101 | C2 | semidirect |
| 70. C2×#101 | D5 | semidirect |
| 205. C5 | #2889 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4147 | 2 |
| #66079 | 2 |
| C2×C5×#101 | 2 |
| C2×#3968 | 2 |
| #65421 | 2 |
| #65040 | 2 |
| D5×#101 | 2 |
| #2889 | 5 |