Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
256 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 142 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. C5×#3944 | C2 | direct (N × H) |
| 3. C2×C5×#672 | C2 | semidirect |
| 9. C5×#672 | C22 | semidirect |
| 11. C2×#3944 | C5 | direct (N × H) |
| 25. #3944 | C2×C5 | direct (N × H) |
| 26. C2×#672 | C2×C5 | semidirect |
| 49. #672 | C22×C5 | semidirect |
| 52. C2×C52 | M32 | semidirect |
| 81. C52 | C2×M32 | semidirect |
| 111. C2×C5 | #3944 | direct (N × H) |
| 112. C2×C5 | C5×M32 | semidirect |
| 124. C5 | C2×#3944 | direct (N × H) |
| 125. C5 | C2×C5×M32 | semidirect |
| 133. C2 | C5×#3944 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×C8 | 2 |
| C5×#3944 | 2 |
| C2×C5×#672 | 2 |
| C2×C5×M32 | 5 |
| C2×#3944 | 5 |