Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
154 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 67 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. #4072 | C2 | semidirect |
| 3. C2×#681 | C2 | semidirect |
| 4. #3969 | C2 | semidirect |
| 7. C5×#41 | C4 | semidirect |
| 9. C2×C5×Q8 | C4 | semidirect |
| 11. C2×C5×D4 | C4 | semidirect |
| 16. C4×Dic5 | C22 | semidirect |
| 18. #681 | C22 | semidirect |
| 58. #41 | Dic5 | semidirect |
| 60. C2×Q8 | Dic5 | semidirect |
| 62. C2×D4 | Dic5 | semidirect |
| 95. C5 | #421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#41 | 2 |
| #4072 | 2 |
| C2×#681 | 2 |
| #3969 | 2 |
| #421 | 5 |