Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
195 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 195 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11716351 | C2 | semidirect |
| 5. C4×#6014 | C2 | semidirect |
| 10. #87716 | C4 | semidirect |
| 11. C2×#6014 | C4 | semidirect |
| 64. C25 | #405 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×#117 | 2 |
| C2×#87716 | 2 |
| C22×#6014 | 2 |
| #11716351 | 2 |
| C4×#6014 | 2 |
| #65286 | 5 |