Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
484 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 484 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 | C52×C4⋊C4 | C22 |
| prime radical | C2×#6037 | C22 |
| hypercenter | C4⋊C4 | D52 |
| hypocenter | C52 | #552 |
| 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 |
|---|---|---|
| 1. #11717210 | C2 | semidirect |
| 2. C5×#4043 | C2 | semidirect |
| 3. C5×#4038 | C2 | semidirect |
| 5. D5×C4⋊Dic5 | C2 | semidirect |
| 7. #11716995 | C2 | semidirect |
| 8. #11716988 | C2 | semidirect |
| 9. #11716976 | C2 | semidirect |
| 10. #11716974 | C2 | semidirect |
| 11. #11716961 | C2 | semidirect |
| 62. #4043 | D5 | semidirect |
| 63. #4038 | D5 | semidirect |
| 197. C52 | #552 | semidirect |
| 289. C5 | #65863 | semidirect |
| 290. C5 | #65976 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717210 | 2 |
| C5×#4043 | 2 |
| C5×#4038 | 2 |
| C4×#6037 | 2 |
| D5×C4⋊Dic5 | 2 |
| #11717003 | 2 |
| #11716995 | 2 |
| #11716988 | 2 |
| #11716976 | 2 |
| #11716974 | 2 |
| #11716961 | 2 |
| #65976 | 5 |
| #65863 | 5 |