Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
106 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 40 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. #4133 | C2 | semidirect |
| 2. #4131 | C2 | semidirect |
| 4. #4010 | C2 | semidirect |
| 5. #4008 | C2 | semidirect |
| 6. #3995 | C2 | semidirect |
| 7. C8×AGL(1,𝔽5) | C2 | semidirect |
| 18. C5×SD16 | C4 | semidirect |
| 19. #689 | C4 | semidirect |
| 20. #686 | C4 | semidirect |
| 21. #677 | C4 | semidirect |
| 59. SD16 | AGL(1,𝔽5) | semidirect |
| 90. C5 | #443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4133 | 2 |
| #4131 | 2 |
| #4062 | 2 |
| #4010 | 2 |
| #4008 | 2 |
| #3995 | 2 |
| C8×AGL(1,𝔽5) | 2 |
| #443 | 5 |