Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
196 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 1. C5×#4050 | C2 | semidirect |
| 2. C2×#87756 | C2 | semidirect |
| 3. #11716591 | C2 | semidirect |
| 4. #11716588 | C2 | semidirect |
| 5. #11716586 | C2 | semidirect |
| 22. #4050 | D5 | semidirect |
| 71. C52 | #508 | semidirect |
| 103. C5 | #65483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4050 | 2 |
| C2×#87756 | 2 |
| #11716591 | 2 |
| #11716588 | 2 |
| #11716586 | 2 |
| #65483 | 5 |