Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 53 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×C22⋊C4 | C2 | semidirect |
| 3. C5×#99 | C2 | semidirect |
| 4. #3966 | C2 | semidirect |
| 5. #3938 | C2 | semidirect |
| 6. C23×D5 | C4 | semidirect |
| 9. C2×C22⋊D5 | C4 | semidirect |
| 13. C2×D20 | C4 | semidirect |
| 15. C2×C4×D5 | C4 | semidirect |
| 16. C5×C22⋊C4 | C22 | semidirect |
| 17. C22⋊Dic5 | C22 | semidirect |
| 20. C23×C5 | C2×C4 | semidirect |
| 28. C22×D5 | C2×C4 | semidirect |
| 33. C2×C4×C5 | C2×C4 | semidirect |
| 37. C2×Dic5 | C2×C4 | semidirect |
| 46. #99 | D5 | direct (N × H) |
| 79. C22⋊C4 | C2×D5 | semidirect |
| 87. D5 | #99 | direct (N × H) |
| 97. C23 | C4×D5 | semidirect |
| 109. C2×C4 | C4×D5 | semidirect |
| 110. C5 | C2×#99 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D5 | 2 |
| D5×C22⋊C4 | 2 |
| C5×#99 | 2 |
| #3966 | 2 |
| #3938 | 2 |
| C2×#99 | 5 |