Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
696 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 160 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 | C2×C5×#709 | C2 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | #536 |
| 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. C22×#6045 | C2 | semidirect |
| 3. C5×#4072 | C2 | semidirect |
| 4. #11717080 | C2 | semidirect |
| 5. #11716983 | C2 | semidirect |
| 6. #11716979 | C2 | semidirect |
| 7. #11716975 | C2 | semidirect |
| 49. #4072 | D5 | semidirect |
| 150. C52 | #536 | semidirect |
| 219. C5 | #65860 | semidirect |
| 220. C5 | #66159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6045 | 2 |
| C2×C5×#709 | 2 |
| C5×#4072 | 2 |
| #11717080 | 2 |
| #11716983 | 2 |
| #11716979 | 2 |
| #11716975 | 2 |
| #66159 | 5 |
| #65860 | 5 |