Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
220 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 78 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×#3998 | C2 | semidirect |
| 3. C2×#3998 | C2 | semidirect |
| 4. #64898 | C2 | semidirect |
| 17. #3998 | C22 | semidirect |
| 19. C2×#674 | C22 | semidirect |
| 148. C5 | #2117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4053 | 2 |
| C2×#3998 | 2 |
| #64898 | 2 |
| #2117 | 5 |