Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
260 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×#3990 | C2 | semidirect |
| 3. C22⋊#674 | C2 | semidirect |
| 4. #64887 | C2 | semidirect |
| 13. C2×#674 | C22 | semidirect |
| 75. C22×C5 | M32 | semidirect |
| 83. C2×D5 | M32 | semidirect |
| 138. C5 | #2112 | semidirect |
| 148. C22 | #3990 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D5 | 2 |
| C2×#3990 | 2 |
| C22⋊#674 | 2 |
| #64887 | 2 |
| #2112 | 5 |