Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
936 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 245 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C52×C22⋊Q8 | C2 |
| prime radical | #11717250 | C2 |
| hypercenter | C22⋊Q8 | C5⋊D5 |
| hypocenter | C52 | #529 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C52×C22⋊Q8 | C2 | semidirect |
| 2. #11717267 | C2 | semidirect |
| 3. Q8×#1039 | C2 | semidirect |
| 5. C2×C4×#1039 | C2 | semidirect |
| 6. #11717218 | C2 | semidirect |
| 7. #11717213 | C2 | semidirect |
| 8. #11717212 | C2 | semidirect |
| 9. #11717210 | C2 | semidirect |
| 10. #11717206 | C2 | semidirect |
| 11. #11717201 | C2 | semidirect |
| 54. C5×C22⋊Q8 | D5 | semidirect |
| 132. C22⋊Q8 | C5⋊D5 | semidirect |
| 139. C52 | #529 | semidirect |
| 202. C5 | #65958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C22⋊Q8 | 2 |
| #11717267 | 2 |
| Q8×#1039 | 2 |
| #11717250 | 2 |
| C2×C4×#1039 | 2 |
| #11717218 | 2 |
| #11717213 | 2 |
| #11717212 | 2 |
| #11717210 | 2 |
| #11717206 | 2 |
| #11717201 | 2 |
| #65958 | 5 |