Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
616 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 160 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, prime radical | C24×C52 | C22 |
| hypercenter | C24 | D52 |
| hypocenter | C52 | #543 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11717100 | C2 | semidirect |
| 4. #11717082 | C2 | semidirect |
| 8. C2×#6039 | C22 | semidirect |
| 12. #87781 | C22 | semidirect |
| 13. #87780 | C22 | semidirect |
| 16. C23×C52 | Q8 | semidirect |
| 66. C23×C5 | Dic10 | semidirect |
| 83. C52 | #543 | semidirect |
| 121. C23 | #6039 | semidirect |
| 130. C5 | #65817 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#1039 | 2 |
| C2×C5×C22⋊Dic5 | 2 |
| #11717100 | 2 |
| #11717082 | 2 |
| #65817 | 5 |