Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
504 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 504 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×#6038 | 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. #11717212 | C2 | semidirect |
| 2. C5×#4043 | C2 | semidirect |
| 3. C5×#4036 | C2 | semidirect |
| 6. D5×C4⋊Dic5 | C2 | semidirect |
| 7. #11716996 | C2 | semidirect |
| 8. #11716991 | C2 | semidirect |
| 9. #11716990 | C2 | semidirect |
| 10. #11716966 | C2 | semidirect |
| 11. Dic5×Dic10 | C2 | semidirect |
| 62. #4043 | D5 | semidirect |
| 71. #4036 | D5 | semidirect |
| 198. C52 | #552 | semidirect |
| 293. C5 | #65976 | semidirect |
| 294. C5 | #66028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717212 | 2 |
| C5×#4043 | 2 |
| C5×#4036 | 2 |
| C4×#6038 | 2 |
| #11717011 | 2 |
| D5×C4⋊Dic5 | 2 |
| #11716996 | 2 |
| #11716991 | 2 |
| #11716990 | 2 |
| #11716966 | 2 |
| Dic5×Dic10 | 2 |
| #66028 | 5 |
| #65976 | 5 |