Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 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×#689 | C2 | semidirect |
| 3. C2×Dic20 | C2 | semidirect |
| 5. C5×#103 | C2 | semidirect |
| 7. #3942 | C2 | semidirect |
| 48. #103 | D5 | semidirect |
| 53. C2×D5 | Q16 | semidirect |
| 99. C5 | #451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D5 | 2 |
| C2×#689 | 2 |
| C2×Dic20 | 2 |
| #4043 | 2 |
| C5×#103 | 2 |
| #3952 | 2 |
| #3942 | 2 |
| #451 | 5 |