Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
566 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 566 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 |
| hypercenter | C4⋊C4 | D52 |
| hypocenter | C52 | #555 |
| 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. #11717215 | C2 | semidirect |
| 2. C5×#4038 | C2 | semidirect |
| 3. C5×#4034 | C2 | semidirect |
| 4. #11717028 | C2 | semidirect |
| 5. #11717027 | C2 | semidirect |
| 6. #11717025 | C2 | semidirect |
| 7. C4×#6038 | C2 | semidirect |
| 8. #11717013 | C2 | semidirect |
| 9. #11716982 | C2 | semidirect |
| 10. #11716967 | C2 | semidirect |
| 11. #11716954 | C2 | semidirect |
| 71. #4038 | D5 | semidirect |
| 72. #4034 | D5 | semidirect |
| 212. C52 | #555 | semidirect |
| 319. C5 | #65866 | semidirect |
| 320. C5 | #66068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717215 | 2 |
| C5×#4038 | 2 |
| C5×#4034 | 2 |
| #11717028 | 2 |
| #11717027 | 2 |
| #11717025 | 2 |
| C4×#6038 | 2 |
| #11717013 | 2 |
| #11716982 | 2 |
| #11716967 | 2 |
| #11716954 | 2 |
| #66068 | 5 |
| #65866 | 5 |