Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
447 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 447 conjugacy classes of subgroups — too many to draw. Only its 120 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×#704 | C2 | semidirect |
| 3. C5×C22⋊#170 | C2 | semidirect |
| 11. C2×C5×#170 | C22 | semidirect |
| 12. #65798 | C5 | direct (N × H) |
| 28. C2×#704 | C2×C5 | semidirect |
| 30. C22⋊#170 | C2×C5 | semidirect |
| 37. C22×C52 | M16 | semidirect |
| 56. C2×#170 | C22×C5 | semidirect |
| 95. C52 | #407 | semidirect |
| 112. C22×C5 | C5×M16 | semidirect |
| 113. C22×C5 | #704 | semidirect |
| 156. C5 | C5×#407 | semidirect |
| 157. C5 | #65798 | direct (N × H) |
| 162. C22 | C5×#704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×Dic5 | 2 |
| C2×C5×#704 | 2 |
| C5×C22⋊#170 | 2 |
| #65798 | 5 |
| C5×#407 | 5 |