Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
298 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 159 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×C5×M16 | C2 | semidirect |
| 3. C2×#681 | C2 | semidirect |
| 4. D5×M16 | C2 | direct (N × H) |
| 5. C2×#676 | C2 | semidirect |
| 6. C2×C8×D5 | C2 | semidirect |
| 16. C5×M16 | C22 | semidirect |
| 17. C2×C5×C8 | C22 | semidirect |
| 18. #681 | C22 | semidirect |
| 19. C2×#168 | C22 | semidirect |
| 20. #676 | C22 | semidirect |
| 21. C8×D5 | C22 | semidirect |
| 41. C5×C8 | C23 | semidirect |
| 42. #168 | C23 | semidirect |
| 47. C2×M16 | D5 | direct (N × H) |
| 54. C2×D5 | M16 | direct (N × H) |
| 73. M16 | C2×D5 | direct (N × H) |
| 76. C2×C8 | C2×D5 | semidirect |
| 78. C2×C5 | C2×M16 | semidirect |
| 81. D5 | C2×M16 | direct (N × H) |
| 101. C8 | C22×D5 | semidirect |
| 102. C5 | C22×M16 | semidirect |
| 119. C2 | D5×M16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D5 | 2 |
| C2×C5×M16 | 2 |
| C2×#681 | 2 |
| D5×M16 | 2 |
| C2×#676 | 2 |
| C2×C8×D5 | 2 |
| C22×M16 | 5 |