Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
258 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 103 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×Q8×D5 | C2 | semidirect |
| 3. C2×C5×Q16 | C2 | semidirect |
| 4. C2×#689 | C2 | semidirect |
| 5. C2×#688 | C2 | semidirect |
| 6. #4064 | C2 | direct (N × H) |
| 7. C2×#677 | C2 | semidirect |
| 8. C2×#676 | C2 | semidirect |
| 14. Q8×D5 | C22 | semidirect |
| 22. C5×Q16 | C22 | semidirect |
| 24. #689 | C22 | semidirect |
| 25. #688 | C22 | semidirect |
| 27. #677 | C22 | semidirect |
| 28. #676 | C22 | semidirect |
| 57. C2×Q16 | D5 | semidirect |
| 86. Q16 | C2×D5 | semidirect |
| 92. C2×C5 | #137 | semidirect |
| 119. C5 | C2×#137 | semidirect |
| 133. C2 | #4064 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#713 | 2 |
| C2×Q8×D5 | 2 |
| C2×C5×Q16 | 2 |
| C2×#689 | 2 |
| C2×#688 | 2 |
| #4064 | 2 |
| C2×#677 | 2 |
| C2×#676 | 2 |
| C2×#137 | 5 |