Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
486 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 144 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 | C22×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C22×C4×C52 | C22 |
| prime radical | C23×C52 | C23 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | #544 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. #11716964 | C2 | semidirect |
| 7. #11716963 | C2 | semidirect |
| 8. #11716958 | C2 | semidirect |
| 9. #11716957 | C2 | semidirect |
| 41. C2×C5×Dic5 | Q8 | semidirect |
| 157. C2×Dic5 | Dic10 | semidirect |
| 177. C52 | #544 | semidirect |
| 259. C5 | #65834 | semidirect |
| 260. C5 | #65957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717244 | 2 |
| C5×#4070 | 2 |
| C2×C5×#683 | 2 |
| #11717082 | 2 |
| #11717073 | 2 |
| #11716964 | 2 |
| #11716963 | 2 |
| #11716958 | 2 |
| #11716957 | 2 |
| #65957 | 5 |
| #65834 | 5 |