Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 1. C22×C5×Q8 | C2 | semidirect |
| 3. C2×#689 | C2 | semidirect |
| 4. #4088 | C2 | direct (N × H) |
| 5. C2×#688 | C2 | semidirect |
| 6. C2×#681 | C2 | semidirect |
| 10. C2×C5×Q8 | C22 | semidirect |
| 19. #689 | C22 | semidirect |
| 20. #688 | C22 | semidirect |
| 21. #681 | C22 | semidirect |
| 44. C22×Q8 | D5 | semidirect |
| 65. C2×Q8 | C2×D5 | semidirect |
| 76. C2×C5 | #137 | semidirect |
| 98. C5 | C2×#137 | semidirect |
| 111. C2 | #4088 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Q8 | 2 |
| C2×#709 | 2 |
| C2×#689 | 2 |
| #4088 | 2 |
| C2×#688 | 2 |
| C2×#681 | 2 |
| C2×#137 | 5 |