Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
384 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 3. #65352 | C2 | direct (N × H) |
| 147. C2×C5 | #479 | semidirect |
| 173. C5 | C2×#479 | semidirect |
| 187. C2 | #65352 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#125 | 2 |
| C2×C4×Dic10 | 2 |
| #65352 | 2 |
| C2×#3942 | 2 |
| C2×#3940 | 2 |
| C2×#3939 | 2 |
| C2×C4⋊#168 | 2 |
| C2×#479 | 5 |