Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
150 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 150 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 |
|---|---|---|
| 4. #4009 | C2 | semidirect |
| 5. C2×C5×Q8 | C4 | semidirect |
| 8. Q8×D5 | C4 | semidirect |
| 13. C2×Dic10 | C4 | semidirect |
| 61. C2×Q8 | AGL(1,𝔽5) | semidirect |
| 93. C5 | #419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D5 | 2 |
| #4130 | 2 |
| D5⋊M16 | 2 |
| #4009 | 2 |
| #419 | 5 |