Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
122 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 45 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. #11716841 | C2 | semidirect |
| 3. C2×#87763 | C2 | semidirect |
| 72. C52 | #350 | semidirect |
| 110. C5 | #64781 | semidirect |
| 111. C5 | #64898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4053 | 2 |
| #11716841 | 2 |
| C2×#87763 | 2 |
| #64898 | 5 |
| #64781 | 5 |