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 |
|---|---|---|
| 1. C2×C5×Q8×D5 | C2 | semidirect |
| 3. C2×#87811 | C2 | semidirect |
| 4. C2×C5×#688 | C2 | semidirect |
| 5. D5×#688 | C2 | direct (N × H) |
| 6. C2×#87774 | C2 | semidirect |
| 7. C2×#87772 | C2 | semidirect |
| 8. C2×D5×#168 | C2 | semidirect |
| 10. C2×C52×Q8 | C22 | semidirect |
| 13. C5×Q8×D5 | C22 | semidirect |
| 18. C2×C5×Dic10 | C22 | semidirect |
| 22. #87811 | C22 | semidirect |
| 23. C2×#6029 | C22 | semidirect |
| 24. C5×#688 | C22 | semidirect |
| 25. C2×C5×#168 | C22 | semidirect |
| 26. #87774 | C22 | semidirect |
| 27. #87772 | C22 | semidirect |
| 28. D5×#168 | C22 | semidirect |
| 37. C52×Q8 | C23 | semidirect |
| 51. C5×Dic10 | C23 | semidirect |
| 53. #6029 | C23 | semidirect |
| 54. C5×#168 | C23 | semidirect |
| 56. C2×Q8×D5 | D5 | semidirect |
| 66. C2×#688 | D5 | direct (N × H) |
| 77. C2×C5×D5 | SD16 | semidirect |
| 92. C2×C5×Q8 | C2×D5 | semidirect |
| 93. C2×C5×Q8 | C2×D5 | semidirect |
| 99. Q8×D5 | C2×D5 | semidirect |
| 112. C2×Dic10 | C2×D5 | semidirect |
| 120. #688 | C2×D5 | direct (N × H) |
| 126. C2×#168 | C2×D5 | semidirect |
| 130. C2×C52 | C2×SD16 | semidirect |
| 134. C5×D5 | C2×SD16 | semidirect |
| 153. C5×Q8 | C22×D5 | semidirect |
| 154. C5×Q8 | C22×D5 | semidirect |
| 185. Dic10 | C22×D5 | semidirect |
| 190. #168 | C22×D5 | semidirect |
| 199. C52 | C22×SD16 | semidirect |
| 217. C2×D5 | #688 | direct (N × H) |
| 237. C2×Q8 | D52 | semidirect |
| 256. C2×C5 | D5×SD16 | semidirect |
| 257. C2×C5 | C2×#688 | semidirect |
| 264. D5 | C2×#688 | direct (N × H) |
| 274. Q8 | C2×D52 | semidirect |
| 290. C5 | C2×D5×SD16 | semidirect |
| 291. C5 | C22×#688 | semidirect |
| 308. C2 | D5×#688 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×D5 | 2 |
| C2×D5×D20 | 2 |
| C2×#87811 | 2 |
| C2×C5×#688 | 2 |
| D5×#688 | 2 |
| C2×#87774 | 2 |
| C2×#87772 | 2 |
| C2×D5×#168 | 2 |
| C22×#688 | 5 |
| C2×D5×SD16 | 5 |