Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
266 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 140 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. C2×#704 | C2 | semidirect |
| 3. C22×#170 | C2 | semidirect |
| 4. #4131 | C2 | direct (N × H) |
| 5. C2×#700 | C2 | semidirect |
| 6. C2×D5⋊C8 | C2 | semidirect |
| 14. #704 | C22 | semidirect |
| 18. C2×#170 | C22 | semidirect |
| 19. #700 | C22 | semidirect |
| 20. D5⋊C8 | C22 | semidirect |
| 67. C2×C5 | #131 | semidirect |
| 85. C5 | C2×#131 | semidirect |
| 97. C2 | #4131 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#711 | 2 |
| C2×#704 | 2 |
| C22×#170 | 2 |
| #4131 | 2 |
| C2×#700 | 2 |
| C2×D5⋊C8 | 2 |
| C2×#131 | 5 |