Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
258 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 101 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×Q8×D5 | C2 | semidirect |
| 3. C5×#137 | C2 | semidirect |
| 4. #4097 | C2 | semidirect |
| 5. #4088 | C2 | semidirect |
| 6. #4064 | C2 | semidirect |
| 7. D5×Q16 | C2 | semidirect |
| 8. #4061 | C2 | semidirect |
| 9. D5×SD16 | C2 | semidirect |
| 10. #4055 | C2 | semidirect |
| 11. D5×M16 | C2 | semidirect |
| 13. C2×C5×Q8 | C22 | semidirect |
| 19. Q8×D5 | C22 | semidirect |
| 30. C2×Dic10 | C22 | semidirect |
| 31. C5×Q16 | C22 | semidirect |
| 32. C5×SD16 | C22 | semidirect |
| 33. C5×M16 | C22 | semidirect |
| 34. #689 | C22 | semidirect |
| 35. #689 | C22 | semidirect |
| 36. #688 | C22 | semidirect |
| 37. #687 | C22 | semidirect |
| 38. #681 | C22 | semidirect |
| 39. Dic20 | C22 | semidirect |
| 40. #677 | C22 | semidirect |
| 41. #676 | C22 | semidirect |
| 86. #137 | D5 | direct (N × H) |
| 118. C2×Q8 | C2×D5 | semidirect |
| 127. Q16 | C2×D5 | semidirect |
| 131. SD16 | C2×D5 | semidirect |
| 134. M16 | C2×D5 | semidirect |
| 141. D5 | #137 | direct (N × H) |
| 177. C5 | C2×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#41 | 2 |
| C2×Q8×D5 | 2 |
| C5×#137 | 2 |
| #4097 | 2 |
| #4088 | 2 |
| #4064 | 2 |
| D5×Q16 | 2 |
| #4061 | 2 |
| D5×SD16 | 2 |
| #4055 | 2 |
| D5×M16 | 2 |
| C2×#137 | 5 |