Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
848 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 229 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×#124 | C2 |
| prime radical | C2×C52×D4 | C22 |
| hypercenter | #124 | C5⋊D5 |
| hypocenter | C52 | #556 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×#1039 | C2 | semidirect |
| 3. #11717264 | C2 | semidirect |
| 6. #11717199 | C2 | semidirect |
| 7. #11717199 | C2 | semidirect |
| 8. #11717198 | C2 | semidirect |
| 9. #11717197 | C2 | semidirect |
| 10. C4×#6045 | C2 | semidirect |
| 11. C4×#6045 | C2 | semidirect |
| 132. C52 | #556 | semidirect |
| 190. C5 | #66005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#124 | 2 |
| Q8×#1039 | 2 |
| #11717264 | 2 |
| #11717256 | 2 |
| D4×#1039 | 2 |
| #11717199 | 2 |
| #11717198 | 2 |
| #11717197 | 2 |
| C4×#6045 | 2 |
| #66005 | 5 |