Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
664 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 160 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 |
|---|---|---|
| 2. C2×D5×Dic10 | C2 | semidirect |
| 3. C2×#87800 | C2 | semidirect |
| 4. C2×C5×#677 | C2 | semidirect |
| 5. C2×C5×C8×D5 | C2 | semidirect |
| 6. C2×#87774 | C2 | semidirect |
| 7. C2×#87773 | C2 | semidirect |
| 8. D5×#677 | C2 | direct (N × H) |
| 11. C2×#6045 | C22 | semidirect |
| 14. C2×C5×Dic10 | C22 | semidirect |
| 21. D5×Dic10 | C22 | semidirect |
| 22. C2×C52×C8 | C22 | semidirect |
| 23. #87800 | C22 | semidirect |
| 24. C2×C5×#168 | C22 | semidirect |
| 25. C5×#677 | C22 | semidirect |
| 26. C5×C8×D5 | C22 | semidirect |
| 27. #87774 | C22 | semidirect |
| 28. #87773 | C22 | semidirect |
| 41. #6045 | C23 | semidirect |
| 49. C5×Dic10 | C23 | semidirect |
| 53. C52×C8 | C23 | semidirect |
| 54. C5×#168 | C23 | semidirect |
| 70. C2×#677 | D5 | direct (N × H) |
| 71. C2×C8×D5 | D5 | semidirect |
| 77. C2×C5×D5 | SD16 | semidirect |
| 112. C2×Dic10 | C2×D5 | semidirect |
| 117. C2×C5×C8 | C2×D5 | semidirect |
| 118. C2×C5×C8 | C2×D5 | semidirect |
| 121. C2×#168 | C2×D5 | semidirect |
| 127. #677 | C2×D5 | direct (N × H) |
| 128. C8×D5 | C2×D5 | semidirect |
| 130. C2×C52 | C2×SD16 | semidirect |
| 134. C5×D5 | C2×SD16 | semidirect |
| 185. Dic10 | C22×D5 | semidirect |
| 188. C5×C8 | C22×D5 | semidirect |
| 189. C5×C8 | C22×D5 | semidirect |
| 190. #168 | C22×D5 | semidirect |
| 199. C52 | C22×SD16 | semidirect |
| 217. C2×D5 | #677 | direct (N × H) |
| 251. C2×C8 | D52 | semidirect |
| 256. C2×C5 | C2×#677 | semidirect |
| 257. C2×C5 | D5×SD16 | semidirect |
| 264. D5 | C2×#677 | direct (N × H) |
| 288. C8 | C2×D52 | semidirect |
| 290. C5 | C22×#677 | semidirect |
| 291. C5 | C2×D5×SD16 | semidirect |
| 308. C2 | D5×#677 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×D20 | 2 |
| C2×D5×Dic10 | 2 |
| C2×#87800 | 2 |
| C2×C5×#677 | 2 |
| C2×C5×C8×D5 | 2 |
| C2×#87774 | 2 |
| C2×#87773 | 2 |
| D5×#677 | 2 |
| C2×D5×SD16 | 5 |
| C22×#677 | 5 |