Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
616 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 136 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×C22⋊C4 | C22 |
| prime radical | C2×#87880 | C2 |
| hypercenter | C22⋊C4 | D52 |
| hypocenter | C52 | #536 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#6039 | C2 | semidirect |
| 3. #11717197 | C2 | semidirect |
| 4. C5×#4032 | C2 | semidirect |
| 5. #11717079 | C2 | semidirect |
| 6. #11717037 | C2 | semidirect |
| 7. #11717033 | C2 | semidirect |
| 8. #11717014 | C2 | semidirect |
| 51. #4032 | D5 | semidirect |
| 138. C52 | #536 | semidirect |
| 204. C5 | #65982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6039 | 2 |
| C2×#87880 | 2 |
| #11717197 | 2 |
| C5×#4032 | 2 |
| #11717079 | 2 |
| #11717037 | 2 |
| #11717033 | 2 |
| #11717014 | 2 |
| #65982 | 5 |