Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
680 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#1044 |
| commutator, socle | C2×C52 | C23×C4 |
| Fitting | C52×#41 | C4 |
| prime radical | #41×C5⋊D5 | C2 |
| cosocle | #1039 | C24 |
| hypercenter | #41 | #1044 |
| hypocenter | C52 | #568 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11717454 | C2 | semidirect |
| 3. #11717452 | C2 | semidirect |
| 4. #11717448 | C2 | semidirect |
| 5. C2×#87863 | C2 | semidirect |
| 13. #87867 | C22 | semidirect |
| 14. C2×#6034 | C22 | semidirect |
| 17. #87863 | C22 | semidirect |
| 18. #87862 | C22 | semidirect |
| 104. C52 | #568 | semidirect |
| 157. C5 | #66264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×C5⋊D5 | 2 |
| #11717454 | 2 |
| #11717452 | 2 |
| #11717448 | 2 |
| C2×#87863 | 2 |
| #66264 | 5 |