Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
550 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 140 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×C4⋊(C5⋊D5) | C22 |
| hypercenter | C4⋊C4 | D52 |
| hypocenter | C52 | #554 |
| 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 |
|---|---|---|
| 2. C5×#4036 | C2 | semidirect |
| 3. C5×#4034 | C2 | semidirect |
| 4. C4×#6039 | C2 | semidirect |
| 7. #11717009 | C2 | semidirect |
| 8. #11717008 | C2 | semidirect |
| 9. #11717001 | C2 | semidirect |
| 10. #11716991 | C2 | semidirect |
| 11. #11716990 | C2 | semidirect |
| 42. C4⋊(C5⋊D5) | Q8 | semidirect |
| 71. #4036 | D5 | semidirect |
| 72. #4034 | D5 | semidirect |
| 199. C52 | #554 | semidirect |
| 289. C5 | #66024 | semidirect |
| 290. C5 | #66064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717213 | 2 |
| C5×#4036 | 2 |
| C5×#4034 | 2 |
| C4×#6039 | 2 |
| #11717013 | 2 |
| #11717009 | 2 |
| #11717008 | 2 |
| #11717001 | 2 |
| #11716991 | 2 |
| #11716990 | 2 |
| #66064 | 5 |
| #66024 | 5 |