Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1584 conjugacy classes of subgroups; only the 432 normal subgroups are shown.
This group has 1584 conjugacy classes of subgroups — too many to draw. Only its 432 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D52 |
| commutator | C2×C52 | C23×C4 |
| Frattini | C22 | C22×D52 |
| Fitting, socle | C24×C52 | C22 |
| prime radical | C24×C5×D5 | C2 |
| cosocle | C22×C52 | C24 |
| hypocenter | C52 | C22×C22⋊C4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#1039 | C2 | semidirect |
| 3. C23×C5×Dic5 | C2 | semidirect |
| 4. C2×#87778 | C2 | direct (N × H) |
| 8. C23×C5×D5 | C4 | semidirect |
| 11. C22×#1039 | C22 | semidirect |
| 13. C22×C5×Dic5 | C22 | semidirect |
| 14. #87778 | C22 | direct (N × H) |
| 24. C22×C5×D5 | C2×C4 | semidirect |
| 27. C2×#1039 | C23 | semidirect |
| 29. C2×C5×Dic5 | C23 | semidirect |
| 36. C23×Dic5 | D5 | semidirect |
| 39. C22×C52 | C22⋊C4 | semidirect |
| 47. C2×C5×D5 | C22×C4 | semidirect |
| 59. C23×D5 | Dic5 | semidirect |
| 70. C22×Dic5 | C2×D5 | semidirect |
| 74. C2×C52 | C2×C22⋊C4 | semidirect |
| 99. C22×D5 | C2×Dic5 | semidirect |
| 110. C2×Dic5 | C22×D5 | semidirect |
| 115. C52 | C22×C22⋊C4 | semidirect |
| 125. C22×C5 | #685 | semidirect |
| 126. C22×C5 | C22⋊Dic5 | semidirect |
| 138. C2×D5 | C22×Dic5 | semidirect |
| 159. C2×C5 | C2×#685 | semidirect |
| 160. C2×C5 | C2×C22⋊Dic5 | semidirect |
| 182. C5 | C22×#685 | semidirect |
| 183. C5 | C22×C22⋊Dic5 | semidirect |
| 188. C22 | #87778 | direct (N × H) |
| 196. C2 | C2×#87778 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C5×D5 | 2 |
| C23×#1039 | 2 |
| C23×C5×Dic5 | 2 |
| C2×#87778 | 2 |
| C22×C22⋊Dic5 | 5 |
| C22×#685 | 5 |