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×#709 | C2 | semidirect |
| 2. C22×D20 | C2 | semidirect |
| 3. C2×C5×M16 | C2 | semidirect |
| 4. #4054 | C2 | direct (N × H) |
| 5. C2×D40 | C2 | semidirect |
| 6. C2×#677 | C2 | semidirect |
| 11. #709 | C22 | semidirect |
| 15. C2×D20 | C22 | semidirect |
| 16. C2×D20 | C22 | semidirect |
| 18. C2×Dic10 | C22 | semidirect |
| 19. C5×M16 | C22 | semidirect |
| 20. C2×C5×C8 | C22 | semidirect |
| 21. D40 | C22 | semidirect |
| 22. #677 | C22 | semidirect |
| 39. D20 | C23 | semidirect |
| 42. Dic10 | C23 | semidirect |
| 43. C5×C8 | C23 | semidirect |
| 49. C2×M16 | D5 | semidirect |
| 76. M16 | C2×D5 | semidirect |
| 77. C2×C8 | C2×D5 | semidirect |
| 79. C2×C5 | AGL(1,ℤ/8) | semidirect |
| 102. C8 | C22×D5 | semidirect |
| 103. C5 | C2×AGL(1,ℤ/8) | semidirect |
| 119. C2 | #4054 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#709 | 2 |
| C22×D20 | 2 |
| C2×C5×M16 | 2 |
| #4054 | 2 |
| C2×D40 | 2 |
| C2×#677 | 2 |
| C2×AGL(1,ℤ/8) | 5 |