Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
158 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 50 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. #4130 | C2 | semidirect |
| 3. C2×D5⋊C8 | C2 | semidirect |
| 4. #4009 | C2 | semidirect |
| 5. #4007 | C2 | semidirect |
| 6. C5×#41 | C4 | semidirect |
| 7. #713 | C4 | semidirect |
| 10. #711 | C4 | semidirect |
| 14. #709 | C4 | semidirect |
| 73. #41 | AGL(1,𝔽5) | semidirect |
| 116. C5 | #416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×#41 | 2 |
| #4130 | 2 |
| C2×D5⋊C8 | 2 |
| #4009 | 2 |
| #4007 | 2 |
| #416 | 5 |