Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
219 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 219 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #11716371 | C2 | direct (N × H) |
| 66. C2×C25 | #101 | semidirect |
| 88. C25 | C2×#101 | semidirect |
| 144. C2 | #11716371 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic50 | 2 |
| C2×M16×C25 | 2 |
| C2×#87716 | 2 |
| #11716371 | 2 |
| C2×#3956 | 5 |