Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
222 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D5 |
| commutator, socle, cosocle | C22×C5 | C24 |
| Fitting | C5×C22⋊Q8 | C2 |
| prime radical | C23×C5 | C23 |
| hypercenter | C22⋊Q8 | D5 |
| hypocenter | C5 | #533 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×Dic5 | C2 | semidirect |
| 3. #4090 | C2 | semidirect |
| 6. #4035 | C2 | semidirect |
| 7. #4034 | C2 | semidirect |
| 8. #4033 | C2 | semidirect |
| 9. #4033 | C2 | semidirect |
| 44. C2×Dic5 | Q8 | semidirect |
| 122. C5 | #533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C22⋊Q8 | 2 |
| Q8×Dic5 | 2 |
| #4090 | 2 |
| #4070 | 2 |
| C2×C4×Dic5 | 2 |
| #4035 | 2 |
| #4034 | 2 |
| #4033 | 2 |
| #4024 | 2 |
| #4023 | 2 |
| #533 | 5 |