Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
328 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 107 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×#87802 | C2 | semidirect |
| 3. #11716696 | C2 | semidirect |
| 4. #11716694 | C2 | semidirect |
| 5. #11716679 | C2 | semidirect |
| 65. C52 | #510 | semidirect |
| 94. C5 | #65484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#135 | 2 |
| C2×#87802 | 2 |
| #11716696 | 2 |
| #11716694 | 2 |
| #11716679 | 2 |
| #65484 | 5 |