Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
285 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 285 conjugacy classes of subgroups — too many to draw. Only its 71 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×#87735 | C2 | semidirect |
| 3. C22⋊#6016 | C2 | semidirect |
| 4. #11716418 | C2 | semidirect |
| 13. C2×#6016 | C22 | semidirect |
| 39. C22×C25 | M16 | semidirect |
| 47. C2×D25 | M16 | semidirect |
| 90. C25 | #407 | semidirect |
| 149. C22 | #87735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D25 | 2 |
| C2×#87735 | 2 |
| C22⋊#6016 | 2 |
| #11716418 | 2 |
| #65756 | 5 |