Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
784 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 211 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×#123 | C2 |
| prime radical | C2×C52×D4 | C22 |
| hypercenter | #123 | C5⋊D5 |
| hypocenter | C52 | #563 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #11717244 | C2 | semidirect |
| 5. #11717209 | C2 | semidirect |
| 6. #11717208 | C2 | semidirect |
| 7. #11717199 | C2 | semidirect |
| 8. #11717199 | C2 | semidirect |
| 9. #11717198 | C2 | semidirect |
| 116. C52 | #563 | semidirect |
| 168. C5 | #65985 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#123 | 2 |
| #11717256 | 2 |
| #11717255 | 2 |
| #11717244 | 2 |
| #11717209 | 2 |
| #11717208 | 2 |
| #11717199 | 2 |
| #11717198 | 2 |
| #65985 | 5 |