Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
452 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 128 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 | C42×C52 | C22 |
| prime radical | C22×C5×D5 | C23 |
| hypercenter | C42 | D52 |
| hypocenter | C52 | #541 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11717189 | C2 | semidirect |
| 3. C5×#4016 | C2 | semidirect |
| 6. #11716963 | C2 | semidirect |
| 7. #11716962 | C2 | semidirect |
| 42. #4016 | D5 | semidirect |
| 118. C52 | #541 | semidirect |
| 172. C5 | #65852 | semidirect |
| 173. C5 | #66031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717189 | 2 |
| C5×#4018 | 2 |
| C5×#4016 | 2 |
| #11716977 | 2 |
| #11716975 | 2 |
| #11716963 | 2 |
| #11716962 | 2 |
| #66031 | 5 |
| #65852 | 5 |