Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
266 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 151 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×C5×C8 | C2 | semidirect |
| 3. C2×#681 | C2 | semidirect |
| 4. #4047 | C2 | direct (N × H) |
| 5. C2×#676 | C2 | semidirect |
| 6. C2×C8×D5 | C2 | semidirect |
| 16. C2×C5×C8 | C22 | semidirect |
| 17. #681 | C22 | semidirect |
| 19. #676 | C22 | semidirect |
| 20. C8×D5 | C22 | semidirect |
| 42. C22×C8 | D5 | semidirect |
| 65. C2×C8 | C2×D5 | semidirect |
| 67. C2×C5 | #131 | semidirect |
| 85. C5 | C2×#131 | semidirect |
| 97. C2 | #4047 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#709 | 2 |
| C22×C5×C8 | 2 |
| C2×#681 | 2 |
| #4047 | 2 |
| C2×#676 | 2 |
| C2×C8×D5 | 2 |
| C2×#131 | 5 |