Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
2016 conjugacy classes of subgroups; only the 568 normal subgroups are shown.
This group has 2016 conjugacy classes of subgroups — too many to draw. Only its 568 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 | C2×C52 | C25 |
| Frattini | C2 | C23×D52 |
| Fitting | C24×C52 | C22 |
| socle | C23×C52 | C23 |
| hypercenter | C24 | D52 |
| hypocenter | C52 | C22×#41 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C22⋊(C5⋊D5) | C2 | semidirect |
| 2. C22×C5×C22⋊D5 | C2 | semidirect |
| 3. C23×C5×Dic5 | C2 | semidirect |
| 4. C22×#6039 | C2 | semidirect |
| 5. C22×#6038 | C2 | semidirect |
| 6. C22×#6036 | C2 | semidirect |
| 7. C2×#87879 | C2 | direct (N × H) |
| 8. C22×D5×Dic5 | C2 | semidirect |
| 12. C2×C22⋊(C5⋊D5) | C22 | semidirect |
| 14. C2×C5×C22⋊D5 | C22 | semidirect |
| 18. C22×C5×Dic5 | C22 | semidirect |
| 19. C2×#6039 | C22 | semidirect |
| 20. C2×#6038 | C22 | semidirect |
| 21. C2×#6036 | C22 | semidirect |
| 22. #87879 | C22 | direct (N × H) |
| 23. C2×D5×Dic5 | C22 | semidirect |
| 33. C22⋊(C5⋊D5) | C23 | semidirect |
| 35. C5×C22⋊D5 | C23 | semidirect |
| 39. C2×C5×Dic5 | C23 | semidirect |
| 40. #6039 | C23 | semidirect |
| 41. #6038 | C23 | semidirect |
| 42. #6036 | C23 | semidirect |
| 43. D5×Dic5 | C23 | semidirect |
| 50. C22×C22⋊D5 | D5 | semidirect |
| 52. C23×Dic5 | D5 | semidirect |
| 62. C22×C52 | #41 | semidirect |
| 90. C2×C22⋊D5 | C2×D5 | semidirect |
| 98. C22×Dic5 | C2×D5 | semidirect |
| 109. C2×C52 | C2×#41 | semidirect |
| 141. C22⋊D5 | C22×D5 | semidirect |
| 149. C2×Dic5 | C22×D5 | semidirect |
| 164. C52 | C22×#41 | semidirect |
| 173. C22×C5 | #709 | semidirect |
| 174. C22×C5 | #711 | semidirect |
| 217. C2×C5 | C2×#709 | semidirect |
| 218. C2×C5 | C2×#711 | semidirect |
| 244. C5 | C22×#709 | semidirect |
| 245. C5 | C22×#711 | semidirect |
| 251. C22 | #87879 | direct (N × H) |
| 261. C2 | C2×#87879 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊(C5⋊D5) | 2 |
| C22×C5×C22⋊D5 | 2 |
| C23×C5×Dic5 | 2 |
| C22×#6039 | 2 |
| C22×#6038 | 2 |
| C22×#6036 | 2 |
| C2×#87879 | 2 |
| C22×D5×Dic5 | 2 |
| C22×#711 | 5 |
| C22×#709 | 5 |