Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
5314 conjugacy classes of subgroups; only the 1444 normal subgroups are shown.
This group has 5314 conjugacy classes of subgroups — too many to draw. Only its 1444 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | D52 |
| commutator, hypocenter | C52 | C24×C8 |
| Frattini | C4 | C23×D52 |
| Fitting | C23×C4×C52 | C22 |
| socle | C24×C52 | C2×C4 |
| prime radical | C24×C5⋊D5 | C4 |
| cosocle | C4×C52 | C25 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C23×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×C5×#168 | C2 | semidirect |
| 3. C22×#87767 | C2 | direct (N × H) |
| 9. C22×C5×#168 | C22 | semidirect |
| 10. C2×#87767 | C22 | direct (N × H) |
| 13. C23×C5⋊D5 | C8 | semidirect |
| 20. C2×C5×#168 | C23 | semidirect |
| 21. #87767 | C23 | direct (N × H) |
| 25. C23×#168 | D5 | semidirect |
| 27. C23×C52 | C2×C8 | semidirect |
| 29. C22×C5⋊D5 | C2×C8 | semidirect |
| 36. C5×#168 | C24 | semidirect |
| 48. C22×#168 | C2×D5 | semidirect |
| 51. C22×C52 | C22×C8 | semidirect |
| 53. C2×C5⋊D5 | C22×C8 | semidirect |
| 75. C2×#168 | C22×D5 | semidirect |
| 80. C2×C52 | C23×C8 | semidirect |
| 82. C5⋊D5 | C23×C8 | semidirect |
| 85. C23×C5 | C8×D5 | semidirect |
| 102. #168 | C23×D5 | semidirect |
| 110. C52 | C24×C8 | semidirect |
| 113. C22×C5 | C2×C8×D5 | semidirect |
| 137. C2×C5 | C22×C8×D5 | semidirect |
| 143. C23 | #87767 | direct (N × H) |
| 152. C5 | C23×C8×D5 | semidirect |
| 155. C22 | C2×#87767 | direct (N × H) |
| 161. C2 | C22×#87767 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C5⋊D5 | 2 |
| C23×C5×#168 | 2 |
| C22×#87767 | 2 |
| C23×C8×D5 | 5 |