Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
384 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C5 | C2×D52 |
| commutator, cosocle | C2×C52 | C23×C5 |
| Frattini | C2 | C2×C5×D52 |
| Fitting | C22×C53 | C22 |
| socle | C2×C53 | C23 |
| hypercenter | C22×C5 | D52 |
| hypocenter | C52 | C2×C5×D4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2×C5 ◁ C22×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C52×D5 | C2 | semidirect |
| 2. C2×C5×D52 | C2 | semidirect |
| 3. C5×C22⋊(C5⋊D5) | C2 | semidirect |
| 4. C52×C22⋊D5 | C2 | semidirect |
| 5. C5×#6038 | C2 | semidirect |
| 6. C5×#6037 | C2 | semidirect |
| 7. C5×D5×Dic5 | C2 | semidirect |
| 8. C22×C53 | C22 | semidirect |
| 9. C2×C5×C5⋊D5 | C22 | semidirect |
| 12. C2×C52×D5 | C22 | semidirect |
| 13. C2×C52×D5 | C22 | semidirect |
| 15. C5×#1039 | C22 | semidirect |
| 16. C52×Dic5 | C22 | semidirect |
| 19. D5×C22⋊D5 | C5 | direct (N × H) |
| 25. C52×D5 | D4 | semidirect |
| 30. C22×C5×D5 | D5 | semidirect |
| 31. C22×C5×D5 | C2×C5 | semidirect |
| 32. C2×D52 | C2×C5 | semidirect |
| 34. C22⋊(C5⋊D5) | C2×C5 | semidirect |
| 42. C5×C22⋊D5 | D5 | direct (N × H) |
| 43. C5×C22⋊D5 | C2×C5 | semidirect |
| 47. #6038 | C2×C5 | semidirect |
| 48. #6037 | C2×C5 | semidirect |
| 49. D5×Dic5 | C2×C5 | semidirect |
| 50. C53 | C2×D4 | semidirect |
| 59. C22×C52 | C2×D5 | semidirect |
| 60. C22×C52 | C2×D5 | semidirect |
| 61. C22×C52 | C22×C5 | semidirect |
| 62. C2×C5⋊D5 | C22×C5 | semidirect |
| 75. C2×C5×D5 | C2×D5 | semidirect |
| 76. C2×C5×D5 | C2×D5 | semidirect |
| 78. C2×C5×D5 | C22×C5 | semidirect |
| 79. C2×C5×D5 | C22×C5 | semidirect |
| 82. #1039 | C22×C5 | semidirect |
| 87. C5×Dic5 | C2×D5 | semidirect |
| 88. C5×Dic5 | C22×C5 | semidirect |
| 120. C5×D5 | C22⋊D5 | direct (N × H) |
| 121. C5×D5 | C5×D4 | semidirect |
| 128. C22×D5 | C5×D5 | semidirect |
| 142. C22⋊D5 | C5×D5 | direct (N × H) |
| 150. C52 | D4×D5 | semidirect |
| 151. C52 | C2×C22⋊D5 | semidirect |
| 152. C52 | C2×C5×D4 | semidirect |
| 171. C22×C5 | D52 | semidirect |
| 172. C22×C5 | C2×C5×D5 | semidirect |
| 173. C22×C5 | C2×C5×D5 | semidirect |
| 181. C2×D5 | C2×C5×D5 | semidirect |
| 182. C2×D5 | C2×C5×D5 | semidirect |
| 190. Dic5 | C2×C5×D5 | semidirect |
| 221. D5 | C5×C22⋊D5 | direct (N × H) |
| 233. C5 | D5×C22⋊D5 | direct (N × H) |
| 234. C5 | C5×D4×D5 | semidirect |
| 235. C5 | C2×C5×C22⋊D5 | semidirect |
| 242. C22 | C5×D52 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D5 | 2 |
| C2×C5×D52 | 2 |
| C5×C22⋊(C5⋊D5) | 2 |
| C52×C22⋊D5 | 2 |
| C5×#6038 | 2 |
| C5×#6037 | 2 |
| C5×D5×Dic5 | 2 |
| C2×C5×C22⋊D5 | 5 |
| C5×D4×D5 | 5 |
| D5×C22⋊D5 | 5 |