Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D25 |
| commutator, cosocle | C22×C25 | C24 |
| Frattini, socle | C22×C5 | C23×D5 |
| Fitting | C25×#121 | C2 |
| hypercenter | #121 | D25 |
| hypocenter | C25 | #540 |
| LCS | G ▷ C22×C25 ▷ C25 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×#121 | C2 | semidirect |
| 2. #11716502 | C2 | semidirect |
| 3. #11716501 | C2 | semidirect |
| 4. #11716500 | C2 | semidirect |
| 5. D4×Dic25 | C2 | semidirect |
| 6. #11716492 | C2 | semidirect |
| 7. #11716488 | C2 | semidirect |
| 8. #11716455 | C2 | semidirect |
| 9. #11716452 | C2 | semidirect |
| 10. #11716448 | C2 | semidirect |
| 11. #11716445 | C2 | semidirect |
| 142. #121 | D25 | semidirect |
| 146. C25 | #540 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×#121 | 2 |
| #11716502 | 2 |
| #11716501 | 2 |
| #11716500 | 2 |
| D4×Dic25 | 2 |
| #11716492 | 2 |
| #11716488 | 2 |
| #11716455 | 2 |
| #11716452 | 2 |
| #11716448 | 2 |
| #11716445 | 2 |
| #65953 | 5 |