Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
158 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 158 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. #4011 | C2 | semidirect |
| 4. #3999 | C2 | semidirect |
| 5. C22×C4×C5 | C4 | semidirect |
| 6. C2×C22⋊D5 | C4 | semidirect |
| 11. C2×C4×D5 | C4 | semidirect |
| 13. C2×Dic10 | C4 | semidirect |
| 61. C22×C4 | AGL(1,𝔽5) | semidirect |
| 88. C5 | #410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#709 | 2 |
| #4130 | 2 |
| #4011 | 2 |
| #3999 | 2 |
| #410 | 5 |