Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
632 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 195 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. C52×#117 | C2 | semidirect |
| 3. C22×#6029 | C2 | semidirect |
| 4. #11716677 | C2 | semidirect |
| 5. #11716676 | C2 | semidirect |
| 9. #87900 | C4 | semidirect |
| 35. C5×#117 | D5 | semidirect |
| 83. #117 | C5⋊D5 | semidirect |
| 86. C52 | #416 | semidirect |
| 128. C5 | #65291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87900 | 2 |
| C52×#117 | 2 |
| C22×#6029 | 2 |
| #11716677 | 2 |
| #11716676 | 2 |
| #65291 | 5 |