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×C5×#41 | C2 | semidirect |
| 2. C22×D20 | C2 | semidirect |
| 3. #4095 | C2 | direct (N × H) |
| 4. C2×#688 | C2 | semidirect |
| 5. C2×#686 | C2 | semidirect |
| 6. C2×#681 | C2 | semidirect |
| 9. C5×#41 | C22 | semidirect |
| 10. C2×C5×Q8 | C22 | semidirect |
| 12. C2×C5×D4 | C22 | semidirect |
| 18. C2×D20 | C22 | semidirect |
| 19. #688 | C22 | semidirect |
| 20. #686 | C22 | semidirect |
| 21. #681 | C22 | semidirect |
| 22. C2×#168 | C22 | semidirect |
| 30. C5×Q8 | C23 | semidirect |
| 33. C5×D4 | C23 | semidirect |
| 43. #168 | C23 | semidirect |
| 44. C2×#41 | D5 | semidirect |
| 64. #41 | C2×D5 | semidirect |
| 65. C2×Q8 | C2×D5 | semidirect |
| 71. C2×D4 | C2×D5 | semidirect |
| 80. C2×C5 | AGL(1,ℤ/8) | semidirect |
| 89. Q8 | C22×D5 | semidirect |
| 95. D4 | C22×D5 | semidirect |
| 103. C5 | C2×AGL(1,ℤ/8) | semidirect |
| 119. C2 | #4095 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#41 | 2 |
| C22×D20 | 2 |
| #4095 | 2 |
| C2×#688 | 2 |
| C2×#686 | 2 |
| C2×#681 | 2 |
| C2×AGL(1,ℤ/8) | 5 |