Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
488 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 136 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 | C52×C4⋊C4 | C22 |
| prime radical | C22×C5⋊D5 | C23 |
| hypercenter | C4⋊C4 | D52 |
| hypocenter | C52 | #544 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#4034 | C2 | semidirect |
| 6. #11716989 | C2 | semidirect |
| 7. #11716988 | C2 | semidirect |
| 8. #11716985 | C2 | semidirect |
| 31. C4×C5⋊D5 | Q8 | semidirect |
| 46. #4034 | D5 | semidirect |
| 122. C52 | #544 | semidirect |
| 181. C5 | #66063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717212 | 2 |
| C5×#4034 | 2 |
| #11717018 | 2 |
| #11717008 | 2 |
| #11716992 | 2 |
| #11716989 | 2 |
| #11716988 | 2 |
| #11716985 | 2 |
| #66063 | 5 |