Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
480 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 480 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. C2×C5×#681 | C2 | semidirect |
| 3. C22×C5×#168 | C2 | semidirect |
| 4. C5×C22⋊#168 | C2 | semidirect |
| 17. #65523 | C5 | direct (N × H) |
| 37. C2×#681 | C2×C5 | semidirect |
| 38. C22×#168 | C2×C5 | semidirect |
| 40. C22⋊#168 | C2×C5 | semidirect |
| 128. C52 | #408 | semidirect |
| 194. C5 | #65523 | direct (N × H) |
| 195. C5 | C5×#408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×#41 | 2 |
| C2×C5×#681 | 2 |
| C22×C5×#168 | 2 |
| C5×C22⋊#168 | 2 |
| C5×#408 | 5 |
| #65523 | 5 |