Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
578 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 214 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. C5×#4150 | C2 | semidirect |
| 2. C5×#4149 | C2 | semidirect |
| 3. C52×#131 | C2 | semidirect |
| 4. C5×#4055 | C2 | semidirect |
| 5. C5×#4054 | C2 | semidirect |
| 6. C5×#4050 | C2 | semidirect |
| 7. C2×C5×#677 | C2 | semidirect |
| 14. C5×#709 | C22 | semidirect |
| 16. C2×C5×Dic10 | C22 | semidirect |
| 17. C52×M16 | C22 | semidirect |
| 18. C2×C52×C8 | C22 | semidirect |
| 19. C5×Dic20 | C22 | semidirect |
| 20. C5×D40 | C22 | semidirect |
| 21. C5×#677 | C22 | semidirect |
| 22. C5×#677 | C22 | semidirect |
| 23. C5×#677 | C22 | semidirect |
| 25. #66085 | C5 | direct (N × H) |
| 45. #4150 | C2×C5 | semidirect |
| 46. #4149 | C2×C5 | semidirect |
| 52. C5×#131 | D5 | semidirect |
| 53. C5×#131 | C2×C5 | semidirect |
| 54. #4055 | C2×C5 | semidirect |
| 55. #4054 | C2×C5 | semidirect |
| 56. #4050 | C2×C5 | semidirect |
| 57. C2×#677 | C2×C5 | semidirect |
| 82. #709 | C22×C5 | semidirect |
| 84. C2×Dic10 | C22×C5 | semidirect |
| 91. C5×M16 | C2×D5 | semidirect |
| 92. C5×M16 | C22×C5 | semidirect |
| 94. C2×C5×C8 | C2×D5 | semidirect |
| 95. C2×C5×C8 | C22×C5 | semidirect |
| 96. Dic20 | C22×C5 | semidirect |
| 97. D40 | C22×C5 | semidirect |
| 98. #677 | C22×C5 | semidirect |
| 99. #677 | C22×C5 | semidirect |
| 100. #677 | C22×C5 | semidirect |
| 151. #131 | C5×D5 | semidirect |
| 152. C52 | #577 | semidirect |
| 186. M16 | C2×C5×D5 | semidirect |
| 187. C2×C8 | C2×C5×D5 | semidirect |
| 216. C5 | #66085 | direct (N × H) |
| 217. C5 | C5×#577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4150 | 2 |
| C5×#4149 | 2 |
| C52×#131 | 2 |
| C5×#4055 | 2 |
| C5×#4054 | 2 |
| C5×#4050 | 2 |
| C2×C5×#677 | 2 |
| C5×#577 | 5 |
| #66085 | 5 |