Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
703 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 703 conjugacy classes of subgroups — too many to draw. Only its 290 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 | D5×AGL(1,𝔽5) |
| commutator, hypocenter | C52 | C23×C8 |
| Frattini | C2 | C22×D5×AGL(1,𝔽5) |
| Fitting, socle | C23×C52 | C2×C4 |
| prime radical | C23×C5×D5 | C4 |
| cosocle | C5×Dic5 | C24 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#6032 | C2 | semidirect |
| 3. C22×C5×#170 | C2 | semidirect |
| 4. C2×D5×#170 | C2 | direct (N × H) |
| 10. C2×#6032 | C22 | semidirect |
| 11. C2×C5×#170 | C22 | semidirect |
| 12. D5×#170 | C22 | direct (N × H) |
| 16. C22×C5×D5 | C8 | semidirect |
| 23. #6032 | C23 | semidirect |
| 24. C5×#170 | C23 | semidirect |
| 29. C22×#170 | D5 | direct (N × H) |
| 33. C22×C52 | C2×C8 | semidirect |
| 35. C2×C5×D5 | C2×C8 | semidirect |
| 53. C2×#170 | C2×D5 | direct (N × H) |
| 58. C2×C52 | C22×C8 | semidirect |
| 60. C5×D5 | C22×C8 | semidirect |
| 66. C22×D5 | #170 | direct (N × H) |
| 80. #170 | C22×D5 | direct (N × H) |
| 87. C52 | C23×C8 | semidirect |
| 92. C22×C5 | C8×D5 | semidirect |
| 93. C22×C5 | C2×#170 | semidirect |
| 96. C2×D5 | C2×#170 | direct (N × H) |
| 116. C2×C5 | C2×C8×D5 | semidirect |
| 117. C2×C5 | C22×#170 | semidirect |
| 120. D5 | C22×#170 | direct (N × H) |
| 132. C5 | C22×C8×D5 | semidirect |
| 133. C5 | C23×#170 | semidirect |
| 136. C22 | D5×#170 | direct (N × H) |
| 142. C2 | C2×D5×#170 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D5×Dic5 | 2 |
| C22×#6032 | 2 |
| C22×C5×#170 | 2 |
| C2×D5×#170 | 2 |
| C23×#170 | 5 |
| C22×C8×D5 | 5 |