Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
122 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 59 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. Q8×Dic5 | C2 | semidirect |
| 4. #3967 | C2 | semidirect |
| 6. #3949 | C2 | semidirect |
| 7. C8×Dic5 | C2 | semidirect |
| 11. C5×SD16 | C4 | semidirect |
| 23. C5×Q8 | C2×C4 | semidirect |
| 33. C5×C8 | C2×C4 | semidirect |
| 52. Dic5 | SD16 | direct (N × H) |
| 56. SD16 | Dic5 | direct (N × H) |
| 71. Q8 | C2×Dic5 | semidirect |
| 82. C8 | C2×Dic5 | semidirect |
| 83. C5 | C4×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×SD16 | 2 |
| Q8×Dic5 | 2 |
| D4×Dic5 | 2 |
| #3967 | 2 |
| #3964 | 2 |
| #3949 | 2 |
| C8×Dic5 | 2 |
| C4×SD16 | 5 |