Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1088 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D52 |
| commutator, cosocle | C22×C52 | C24 |
| Frattini | C22 | C22×D52 |
| Fitting | C24×C52 | C22 |
| socle | C23×C52 | C23 |
| hypercenter | C24 | D52 |
| hypocenter | C52 | C2×#121 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#1039 | C2 | semidirect |
| 2. C22×C5×C22⋊D5 | C2 | semidirect |
| 3. C22×#6037 | C2 | semidirect |
| 4. #11717098 | C2 | direct (N × H) |
| 5. C2×#87781 | C2 | semidirect |
| 6. C2×#87778 | C2 | semidirect |
| 12. C22×#1039 | C22 | semidirect |
| 14. C2×C5×C22⋊D5 | C22 | semidirect |
| 17. C2×#6037 | C22 | semidirect |
| 18. #87781 | C22 | semidirect |
| 19. #87778 | C22 | semidirect |
| 23. C23×C52 | D4 | semidirect |
| 32. C2×#1039 | D4 | semidirect |
| 41. C22×C22⋊D5 | D5 | semidirect |
| 53. C22×C52 | C2×D4 | semidirect |
| 61. #1039 | C2×D4 | semidirect |
| 73. C2×C22⋊D5 | C2×D5 | semidirect |
| 88. C2×C52 | #121 | semidirect |
| 104. C23×C5 | C22⋊D5 | semidirect |
| 134. C52 | C2×#121 | semidirect |
| 153. C22×C5 | C2×C22⋊D5 | semidirect |
| 185. C2×C5 | #4085 | semidirect |
| 196. C23 | #6037 | semidirect |
| 209. C5 | C2×#4085 | semidirect |
| 219. C22 | C2×#6037 | semidirect |
| 227. C2 | #11717098 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1039 | 2 |
| C22×C5×C22⋊D5 | 2 |
| C22×#6037 | 2 |
| #11717098 | 2 |
| C2×#87781 | 2 |
| C2×#87778 | 2 |
| C2×#4085 | 5 |