Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
286 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D5 |
| commutator | C22×C5 | C22×C4 |
| Fitting, prime radical | C22×C5×D4 | C2 |
| socle, cosocle | C23×C5 | C23 |
| hypercenter | C22×D4 | D5 |
| hypocenter | C5 | #386 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×Dic5 | C2 | semidirect |
| 3. C2×C22⋊Dic5 | C2 | semidirect |
| 4. C2×C22⋊Dic5 | C2 | semidirect |
| 5. #3963 | C2 | semidirect |
| 10. C2×C5×D4 | C4 | semidirect |
| 26. C23×C5 | C2×C4 | semidirect |
| 33. C2×C4×C5 | C2×C4 | semidirect |
| 40. C2×Dic5 | D4 | semidirect |
| 55. C22×C5 | C22⋊C4 | semidirect |
| 68. C2×D4 | Dic5 | semidirect |
| 90. C23 | C2×Dic5 | semidirect |
| 104. C2×C4 | C2×Dic5 | semidirect |
| 105. C5 | #386 | semidirect |
| 115. C22 | C22⋊Dic5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D4 | 2 |
| C23×Dic5 | 2 |
| C2×C22⋊Dic5 | 2 |
| #3963 | 2 |
| #386 | 5 |