Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 103 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×#713 | C2 | semidirect |
| 2. C2×D4×D5 | C2 | semidirect |
| 3. C2×C5×SD16 | C2 | semidirect |
| 4. C2×#688 | C2 | semidirect |
| 5. C2×#686 | C2 | semidirect |
| 6. #4060 | C2 | direct (N × H) |
| 7. C2×D40 | C2 | semidirect |
| 8. C2×#676 | C2 | semidirect |
| 10. C2×C5×Q8 | C22 | semidirect |
| 14. #713 | C22 | semidirect |
| 16. D4×D5 | C22 | semidirect |
| 19. C2×D20 | C22 | semidirect |
| 22. C5×SD16 | C22 | semidirect |
| 23. C2×C5×C8 | C22 | semidirect |
| 24. #688 | C22 | semidirect |
| 25. #686 | C22 | semidirect |
| 26. C2×#168 | C22 | semidirect |
| 27. D40 | C22 | semidirect |
| 28. #676 | C22 | semidirect |
| 37. C5×Q8 | C23 | semidirect |
| 48. D20 | C23 | semidirect |
| 52. C5×C8 | C23 | semidirect |
| 53. #168 | C23 | semidirect |
| 58. C2×SD16 | D5 | semidirect |
| 79. C2×Q8 | C2×D5 | semidirect |
| 90. SD16 | C2×D5 | semidirect |
| 95. C2×C8 | C2×D5 | semidirect |
| 97. C2×C5 | AGL(1,ℤ/8) | semidirect |
| 109. Q8 | C22×D5 | semidirect |
| 125. C8 | C22×D5 | semidirect |
| 126. C5 | C2×AGL(1,ℤ/8) | semidirect |
| 145. C2 | #4060 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#713 | 2 |
| C2×D4×D5 | 2 |
| C2×C5×SD16 | 2 |
| C2×#688 | 2 |
| C2×#686 | 2 |
| #4060 | 2 |
| C2×D40 | 2 |
| C2×#676 | 2 |
| C2×AGL(1,ℤ/8) | 5 |