Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
154 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 48 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×#700 | C2 | semidirect |
| 4. #4010 | C2 | semidirect |
| 5. #4008 | C2 | semidirect |
| 6. C5×#41 | C4 | semidirect |
| 8. Q8×D5 | C4 | semidirect |
| 12. D4×D5 | C4 | semidirect |
| 14. #709 | C4 | semidirect |
| 20. C4×AGL(1,𝔽5) | C22 | semidirect |
| 22. #700 | C22 | semidirect |
| 73. #41 | AGL(1,𝔽5) | semidirect |
| 116. C5 | #421 | 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×#700 | 2 |
| #4010 | 2 |
| #4008 | 2 |
| #421 | 5 |