Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
752 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×D4×D5 | C2 | semidirect |
| 2. C2×C52×D8 | C2 | semidirect |
| 3. C2×C5×#686 | C2 | semidirect |
| 4. C5×D5×D8 | C2 | direct (N × H) |
| 5. C2×C5×D40 | C2 | semidirect |
| 6. C2×C5×C8×D5 | C2 | semidirect |
| 8. C2×C52×D4 | C22 | semidirect |
| 11. C5×D4×D5 | C22 | semidirect |
| 12. C2×C5×D20 | C22 | semidirect |
| 14. C52×D8 | C22 | semidirect |
| 15. C2×C52×C8 | C22 | semidirect |
| 16. C5×#686 | C22 | semidirect |
| 17. C2×C5×#168 | C22 | semidirect |
| 18. C5×D40 | C22 | semidirect |
| 19. C5×C8×D5 | C22 | semidirect |
| 21. C2×D5×D8 | C5 | direct (N × H) |
| 28. C52×D4 | C23 | semidirect |
| 33. C5×D20 | C23 | semidirect |
| 36. C52×C8 | C23 | semidirect |
| 37. C5×#168 | C23 | semidirect |
| 39. C2×D4×D5 | C2×C5 | semidirect |
| 44. C2×C5×D8 | D5 | direct (N × H) |
| 45. C2×C5×D8 | C2×C5 | semidirect |
| 47. C2×#686 | C2×C5 | semidirect |
| 48. D5×D8 | C2×C5 | direct (N × H) |
| 49. C2×D40 | C2×C5 | semidirect |
| 50. C2×C8×D5 | C2×C5 | semidirect |
| 57. C2×C5×D5 | D8 | direct (N × H) |
| 69. C2×C5×D4 | C2×D5 | semidirect |
| 70. C2×C5×D4 | C22×C5 | semidirect |
| 74. D4×D5 | C22×C5 | semidirect |
| 75. C2×D20 | C22×C5 | semidirect |
| 80. C5×D8 | C2×D5 | direct (N × H) |
| 81. C5×D8 | C22×C5 | semidirect |
| 85. C2×C5×C8 | C2×D5 | semidirect |
| 86. C2×C5×C8 | C22×C5 | semidirect |
| 87. #686 | C22×C5 | semidirect |
| 88. C2×#168 | C22×C5 | semidirect |
| 89. D40 | C22×C5 | semidirect |
| 90. C8×D5 | C22×C5 | semidirect |
| 93. C2×C52 | C2×D8 | semidirect |
| 96. C5×D5 | C2×D8 | direct (N × H) |
| 115. C5×D4 | C22×D5 | semidirect |
| 116. C5×D4 | C23×C5 | semidirect |
| 126. D20 | C23×C5 | semidirect |
| 131. C5×C8 | C22×D5 | semidirect |
| 132. C5×C8 | C23×C5 | semidirect |
| 133. #168 | C23×C5 | semidirect |
| 138. C2×D8 | C5×D5 | direct (N × H) |
| 140. C52 | C22×D8 | semidirect |
| 158. C2×D5 | C5×D8 | direct (N × H) |
| 173. C2×D4 | C2×C5×D5 | semidirect |
| 177. D8 | C2×C5×D5 | direct (N × H) |
| 180. C2×C8 | C2×C5×D5 | semidirect |
| 188. C2×C5 | D5×D8 | direct (N × H) |
| 189. C2×C5 | C2×C5×D8 | semidirect |
| 193. D5 | C2×C5×D8 | direct (N × H) |
| 203. D4 | C22×C5×D5 | semidirect |
| 209. C8 | C22×C5×D5 | semidirect |
| 211. C5 | C2×D5×D8 | direct (N × H) |
| 212. C5 | C22×C5×D8 | semidirect |
| 227. C2 | C5×D5×D8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×D5 | 2 |
| C2×C52×D8 | 2 |
| C2×C5×#686 | 2 |
| C5×D5×D8 | 2 |
| C2×C5×D40 | 2 |
| C2×C5×C8×D5 | 2 |
| C22×C5×D8 | 5 |
| C2×D5×D8 | 5 |