Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
896 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 896 conjugacy classes of subgroups — too many to draw. Only its 232 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. C2×#87781 | C2 | semidirect |
| 4. #11717075 | C2 | direct (N × H) |
| 5. C2×Dic52 | C2 | semidirect |
| 7. C22×#1039 | C4 | semidirect |
| 13. #87781 | C22 | semidirect |
| 14. Dic52 | C22 | semidirect |
| 22. C2×#1039 | C2×C4 | semidirect |
| 61. C2×C52 | #117 | semidirect |
| 91. C52 | C2×#117 | semidirect |
| 124. C2×C5 | #4023 | semidirect |
| 139. C5 | C2×#4023 | semidirect |
| 150. C2 | #11717075 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1039 | 2 |
| C2×C5×C22⋊Dic5 | 2 |
| C2×#87781 | 2 |
| #11717075 | 2 |
| C2×Dic52 | 2 |
| C2×#4023 | 5 |