Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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×Q8×D5 | C2 | semidirect |
| 3. C2×C5×SD16 | C2 | semidirect |
| 4. C2×#688 | C2 | semidirect |
| 5. C2×#687 | C2 | semidirect |
| 6. D5×SD16 | C2 | direct (N × H) |
| 7. C2×#677 | C2 | semidirect |
| 8. C2×C8×D5 | C2 | semidirect |
| 10. C2×C5×Q8 | C22 | semidirect |
| 14. Q8×D5 | C22 | semidirect |
| 21. C2×Dic10 | C22 | semidirect |
| 22. C5×SD16 | C22 | semidirect |
| 23. C2×C5×C8 | C22 | semidirect |
| 24. #688 | C22 | semidirect |
| 25. #687 | C22 | semidirect |
| 26. C2×#168 | C22 | semidirect |
| 27. #677 | C22 | semidirect |
| 28. C8×D5 | C22 | semidirect |
| 36. C5×Q8 | C23 | semidirect |
| 51. Dic10 | C23 | semidirect |
| 52. C5×C8 | C23 | semidirect |
| 53. #168 | C23 | semidirect |
| 60. C2×SD16 | D5 | direct (N × H) |
| 68. C2×D5 | SD16 | direct (N × H) |
| 80. C2×Q8 | C2×D5 | semidirect |
| 91. SD16 | C2×D5 | direct (N × H) |
| 94. C2×C8 | C2×D5 | semidirect |
| 96. C2×C5 | C2×SD16 | semidirect |
| 99. D5 | C2×SD16 | direct (N × H) |
| 109. Q8 | C22×D5 | semidirect |
| 123. C8 | C22×D5 | semidirect |
| 124. C5 | C22×SD16 | semidirect |
| 141. C2 | D5×SD16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D5 | 2 |
| C2×D4×D5 | 2 |
| C2×C5×SD16 | 2 |
| C2×#688 | 2 |
| C2×#687 | 2 |
| D5×SD16 | 2 |
| C2×#677 | 2 |
| C2×C8×D5 | 2 |
| C22×SD16 | 5 |