Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
186 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 63 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×C5×M16 | C2 | semidirect |
| 3. C2×#681 | C2 | semidirect |
| 4. #3955 | C2 | direct (N × H) |
| 14. C5×M16 | C22 | semidirect |
| 17. #681 | C22 | semidirect |
| 39. C2×M16 | D5 | semidirect |
| 64. M16 | C2×D5 | semidirect |
| 69. C2×C5 | #100 | semidirect |
| 89. C5 | C2×#100 | semidirect |
| 105. C2 | #3955 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D20 | 2 |
| C2×C5×M16 | 2 |
| C2×#681 | 2 |
| #3955 | 2 |
| C2×#100 | 5 |