Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 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. C22×Dic10 | C2 | semidirect |
| 5. C2×C4⋊Dic5 | C2 | semidirect |
| 6. C2×#683 | C2 | semidirect |
| 7. C2×#683 | C2 | semidirect |
| 8. #4024 | C2 | direct (N × H) |
| 19. C2×Dic10 | C22 | semidirect |
| 22. C4⋊Dic5 | C22 | semidirect |
| 23. #683 | C22 | semidirect |
| 24. #683 | C22 | semidirect |
| 28. C23×C5 | Q8 | semidirect |
| 58. C22×C5 | C2×Q8 | semidirect |
| 84. C2×C5 | C22⋊Q8 | semidirect |
| 90. C23 | Dic10 | semidirect |
| 107. C5 | C2×C22⋊Q8 | semidirect |
| 112. C22 | C2×Dic10 | semidirect |
| 123. C2 | #4024 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic5 | 2 |
| C22×Dic10 | 2 |
| C2×C5×C22⋊C4 | 2 |
| C2×C22⋊Dic5 | 2 |
| C2×C4⋊Dic5 | 2 |
| C2×#683 | 2 |
| #4024 | 2 |
| C2×C22⋊Q8 | 5 |