Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
992 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 219 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. #11717523 | C2 | semidirect |
| 2. C52×#135 | C2 | semidirect |
| 3. #11717271 | C2 | semidirect |
| 4. Q16×C5⋊D5 | C2 | semidirect |
| 5. #11717235 | C2 | semidirect |
| 6. #11717232 | C2 | semidirect |
| 7. C2×#87802 | C2 | semidirect |
| 8. #11717221 | C2 | semidirect |
| 49. C5×#135 | D5 | semidirect |
| 111. #135 | C5⋊D5 | semidirect |
| 115. C52 | #578 | semidirect |
| 166. C5 | #66105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717523 | 2 |
| C52×#135 | 2 |
| #11717271 | 2 |
| Q16×C5⋊D5 | 2 |
| #11717235 | 2 |
| #11717232 | 2 |
| C2×#87802 | 2 |
| #11717221 | 2 |
| #66105 | 5 |