Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
992 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 243 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 | C23×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting, prime radical | C52×#120 | C2 |
| hypercenter | #120 | C5⋊D5 |
| hypocenter | C52 | #551 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊#1039 | C2 | semidirect |
| 3. #11717256 | C2 | semidirect |
| 4. #11717255 | C2 | semidirect |
| 5. #11717255 | C2 | semidirect |
| 6. D4×#1039 | C2 | semidirect |
| 7. #11717199 | C2 | semidirect |
| 8. #11717198 | C2 | semidirect |
| 9. #11717197 | C2 | semidirect |
| 15. C22×#1039 | C22 | semidirect |
| 16. C2×#6045 | C22 | semidirect |
| 23. C22⋊#1039 | C22 | semidirect |
| 24. C22⋊#1039 | C22 | semidirect |
| 25. C4⋊#1039 | C22 | semidirect |
| 26. #87806 | C22 | semidirect |
| 27. #87806 | C22 | semidirect |
| 28. #87806 | C22 | semidirect |
| 29. C4×#1039 | C22 | semidirect |
| 30. C4×#1039 | C22 | semidirect |
| 126. C52 | #551 | semidirect |
| 185. C5 | #65921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#120 | 2 |
| C2×C22⋊#1039 | 2 |
| #11717256 | 2 |
| #11717255 | 2 |
| D4×#1039 | 2 |
| #11717199 | 2 |
| #11717198 | 2 |
| #11717197 | 2 |
| #65921 | 5 |