Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
2032 conjugacy classes of subgroups; only the 536 normal subgroups are shown.
This group has 2032 conjugacy classes of subgroups — too many to draw. Only its 536 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D52 |
| commutator, cosocle | C2×C52 | C25 |
| Frattini | C2 | C23×D52 |
| Fitting | C24×C52 | C22 |
| socle | C22×C52 | C24 |
| hypercenter | C24 | D52 |
| hypocenter | C52 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ 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. #11717495 | C2 | direct (N × H) |
| 4. C2×#87886 | C2 | semidirect |
| 5. C2×D5×C22⋊D5 | C2 | semidirect |
| 6. C2×#87880 | C2 | semidirect |
| 7. C2×#87879 | C2 | semidirect |
| 8. C24×C52 | C22 | semidirect |
| 9. C23×C5⋊D5 | C22 | semidirect |
| 10. C23×C5×D5 | C22 | semidirect |
| 11. C22×D52 | C22 | semidirect |
| 12. C2×C22⋊(C5⋊D5) | C22 | semidirect |
| 13. C2×C22⋊(C5⋊D5) | C22 | semidirect |
| 14. C22×#1039 | C22 | semidirect |
| 15. C2×C5×C22⋊D5 | C22 | semidirect |
| 16. C2×C5×C22⋊D5 | C22 | semidirect |
| 17. C2×C5×C22⋊D5 | C22 | semidirect |
| 18. C22×C5×Dic5 | C22 | semidirect |
| 19. #87886 | C22 | semidirect |
| 20. D5×C22⋊D5 | C22 | semidirect |
| 21. C2×#6039 | C22 | semidirect |
| 22. C2×#6038 | C22 | semidirect |
| 23. C2×#6037 | C22 | semidirect |
| 24. C2×#6036 | C22 | semidirect |
| 25. #87880 | C22 | semidirect |
| 26. #87879 | C22 | semidirect |
| 27. C2×D5×Dic5 | C22 | semidirect |
| 32. C23×C52 | C23 | semidirect |
| 35. C22×C5⋊D5 | C23 | semidirect |
| 38. C22×C5×D5 | C23 | semidirect |
| 40. C2×D52 | C23 | semidirect |
| 41. C22⋊(C5⋊D5) | C23 | semidirect |
| 43. C2×#1039 | C23 | semidirect |
| 44. C5×C22⋊D5 | C23 | semidirect |
| 45. C5×C22⋊D5 | C23 | semidirect |
| 47. C2×C5×Dic5 | C23 | semidirect |
| 48. #6039 | C23 | semidirect |
| 49. #6038 | C23 | semidirect |
| 50. #6037 | C23 | semidirect |
| 51. #6036 | C23 | semidirect |
| 52. D5×Dic5 | C23 | semidirect |
| 57. C22×C22⋊D5 | D5 | semidirect |
| 81. C24×C5 | C2×D5 | semidirect |
| 85. C23×D5 | C2×D5 | semidirect |
| 98. C2×C22⋊D5 | C2×D5 | semidirect |
| 99. C2×C22⋊D5 | C2×D5 | semidirect |
| 100. C2×C22⋊D5 | C2×D5 | semidirect |
| 104. C22×Dic5 | C2×D5 | semidirect |
| 117. C2×C52 | H(5,𝔽2) | semidirect |
| 132. C23×C5 | C22×D5 | semidirect |
| 143. C22×D5 | C22×D5 | semidirect |
| 153. C22⋊D5 | C22×D5 | semidirect |
| 154. C22⋊D5 | C22×D5 | semidirect |
| 161. C2×Dic5 | C22×D5 | semidirect |
| 173. C52 | C2×H(5,𝔽2) | semidirect |
| 208. C24 | D52 | semidirect |
| 233. C2×C5 | #4144 | semidirect |
| 249. C23 | C2×D52 | semidirect |
| 263. C5 | C2×#4144 | semidirect |
| 283. C2 | #11717495 | 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 |
| #11717495 | 2 |
| C2×#87886 | 2 |
| C2×D5×C22⋊D5 | 2 |
| C2×#87880 | 2 |
| C2×#87879 | 2 |
| C2×#4144 | 5 |