Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
576 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 132 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 | #11717098 | C2 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | #529 |
| 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 |
|---|---|---|
| 1. C2×C4×#1039 | C2 | semidirect |
| 2. C5×#4075 | C2 | semidirect |
| 3. #11717100 | C2 | semidirect |
| 5. #11717091 | C2 | semidirect |
| 6. #11717033 | C2 | semidirect |
| 7. #11717020 | C2 | semidirect |
| 8. #11716996 | C2 | semidirect |
| 9. #11716989 | C2 | semidirect |
| 10. #11716980 | C2 | semidirect |
| 11. #11716956 | C2 | semidirect |
| 57. #4075 | D5 | semidirect |
| 179. C52 | #529 | semidirect |
| 264. C5 | #65983 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1039 | 2 |
| C5×#4075 | 2 |
| #11717100 | 2 |
| #11717098 | 2 |
| #11717091 | 2 |
| #11717033 | 2 |
| #11717020 | 2 |
| #11716996 | 2 |
| #11716989 | 2 |
| #11716980 | 2 |
| #11716956 | 2 |
| #65983 | 5 |