Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
152 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 39 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. C5×#137 | C2 | semidirect |
| 3. #4093 | C2 | semidirect |
| 4. #4088 | C2 | semidirect |
| 5. #3969 | C2 | semidirect |
| 6. #3957 | C2 | semidirect |
| 7. #3955 | C2 | semidirect |
| 9. C2×C5×Q8 | C22 | semidirect |
| 19. C5×M16 | C22 | semidirect |
| 23. C4×Dic5 | C22 | semidirect |
| 24. #681 | C22 | semidirect |
| 50. #137 | D5 | semidirect |
| 71. C2×Q8 | C2×D5 | semidirect |
| 81. M16 | C2×D5 | semidirect |
| 111. C5 | #455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4149 | 2 |
| C5×#137 | 2 |
| #4093 | 2 |
| #4088 | 2 |
| #3969 | 2 |
| #3957 | 2 |
| #3955 | 2 |
| #455 | 5 |