Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
327 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 327 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 |
| prime radical | C5×#121 | D5 |
| hypercenter | #121 | D25 |
| hypocenter | C25 | #539 |
| LCS | G ▷ C22×C25 ▷ C25 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11716497 | C2 | semidirect |
| 3. #11716497 | C2 | semidirect |
| 4. D4×Dic25 | C2 | semidirect |
| 5. #11716486 | C2 | semidirect |
| 6. C2×#87718 | C2 | semidirect |
| 7. #11716451 | C2 | semidirect |
| 8. #11716441 | C2 | semidirect |
| 9. #11716440 | C2 | semidirect |
| 123. C25 | #539 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×#121 | 2 |
| #11716497 | 2 |
| D4×Dic25 | 2 |
| #11716486 | 2 |
| C2×#87718 | 2 |
| #11716451 | 2 |
| #11716441 | 2 |
| #11716440 | 2 |
| #65936 | 5 |