Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
330 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 159 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×#117 | C2 | semidirect |
| 3. #4072 | C2 | semidirect |
| 4. #4038 | C2 | semidirect |
| 5. D5×C4⋊C4 | C2 | semidirect |
| 7. #4023 | C2 | semidirect |
| 8. #4018 | C2 | semidirect |
| 9. C42×D5 | C2 | semidirect |
| 13. C2×C4×D5 | C4 | semidirect |
| 19. C5×C4⋊C4 | C22 | semidirect |
| 21. C42×C5 | C22 | semidirect |
| 24. C4⋊Dic5 | C22 | semidirect |
| 25. #683 | C22 | semidirect |
| 26. C4×Dic5 | C22 | semidirect |
| 27. C4×Dic5 | C22 | semidirect |
| 34. C2×C4×C5 | C2×C4 | semidirect |
| 38. C2×Dic5 | C2×C4 | semidirect |
| 45. C4×D5 | C2×C4 | semidirect |
| 46. C4×D5 | C2×C4 | semidirect |
| 52. #117 | D5 | direct (N × H) |
| 81. C4⋊C4 | C2×D5 | semidirect |
| 87. C42 | C2×D5 | semidirect |
| 92. D5 | #117 | direct (N × H) |
| 107. C2×C4 | C4×D5 | semidirect |
| 111. C5 | C2×#117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D5 | 2 |
| C5×#117 | 2 |
| #4072 | 2 |
| #4038 | 2 |
| D5×C4⋊C4 | 2 |
| D5×C22⋊C4 | 2 |
| #4023 | 2 |
| #4018 | 2 |
| C42×D5 | 2 |
| C2×#117 | 5 |