Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
392 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 112 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. C22×#6029 | C2 | semidirect |
| 3. C2×C5×#681 | C2 | semidirect |
| 4. #11716597 | C2 | semidirect |
| 35. C2×#681 | D5 | semidirect |
| 118. C52 | #408 | semidirect |
| 180. C5 | #65418 | semidirect |
| 181. C5 | #65523 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#709 | 2 |
| C22×#6029 | 2 |
| C2×C5×#681 | 2 |
| #11716597 | 2 |
| #65523 | 5 |
| #65418 | 5 |