Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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. D5×M16 | C2 | semidirect |
| 3. #4018 | C2 | semidirect |
| 4. C5×#104 | C2 | semidirect |
| 5. #3969 | C2 | semidirect |
| 6. #3957 | C2 | semidirect |
| 7. #3937 | C2 | semidirect |
| 9. #713 | C4 | semidirect |
| 10. Q8×D5 | C4 | semidirect |
| 12. #711 | C4 | semidirect |
| 14. D4×D5 | C4 | semidirect |
| 19. C5×M16 | C22 | semidirect |
| 20. C42×C5 | C22 | semidirect |
| 23. C4×Dic5 | C22 | semidirect |
| 24. #681 | C22 | semidirect |
| 61. #104 | D5 | semidirect |
| 90. M16 | C2×D5 | semidirect |
| 95. C42 | C2×D5 | semidirect |
| 129. C5 | #421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#41 | 2 |
| D5×M16 | 2 |
| #4018 | 2 |
| C5×#104 | 2 |
| #3969 | 2 |
| #3957 | 2 |
| #3937 | 2 |
| #421 | 5 |