Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
128 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 43 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 |
|---|---|---|
| 1. C2×C5×SD16 | C2 | semidirect |
| 2. Q8×Dic5 | C2 | semidirect |
| 3. C2×#688 | C2 | semidirect |
| 5. #3964 | C2 | semidirect |
| 6. #3953 | C2 | semidirect |
| 7. #3946 | C2 | semidirect |
| 25. C5×Q8 | D4 | semidirect |
| 40. C2×SD16 | D5 | semidirect |
| 58. Dic5 | SD16 | semidirect |
| 80. Q8 | C22⋊D5 | semidirect |
| 94. C5 | #460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×SD16 | 2 |
| Q8×Dic5 | 2 |
| C2×#688 | 2 |
| #4086 | 2 |
| #3964 | 2 |
| #3953 | 2 |
| #3946 | 2 |
| #460 | 5 |