Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
856 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 243 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. C52×C22⋊Q8 | C2 | semidirect |
| 2. #11717266 | C2 | semidirect |
| 3. Q8×#1039 | C2 | semidirect |
| 5. C2×C4⋊#1039 | C2 | semidirect |
| 6. #11717218 | C2 | semidirect |
| 7. #11717212 | C2 | semidirect |
| 8. #11717210 | C2 | semidirect |
| 9. #11717210 | C2 | semidirect |
| 11. #11717197 | C2 | semidirect |
| 52. C5×C22⋊Q8 | D5 | semidirect |
| 129. C22⋊Q8 | C5⋊D5 | semidirect |
| 135. C52 | #552 | semidirect |
| 196. C5 | #65976 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C22⋊Q8 | 2 |
| #11717266 | 2 |
| Q8×#1039 | 2 |
| C4×C22⋊(C5⋊D5) | 2 |
| C2×C4⋊#1039 | 2 |
| #11717218 | 2 |
| #11717212 | 2 |
| #11717210 | 2 |
| #11717206 | 2 |
| #11717197 | 2 |
| #65976 | 5 |