Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
177 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 177 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. #11716356 | C2 | semidirect |
| 5. #11716355 | C2 | semidirect |
| 14. #87716 | C4 | semidirect |
| 26. #6014 | C2×C4 | semidirect |
| 72. C25 | #428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×#117 | 2 |
| C2×C4⋊Dic25 | 2 |
| C2×#87716 | 2 |
| #11716356 | 2 |
| #11716355 | 2 |
| #65284 | 5 |