Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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×#124 | C2 |
| prime radical | #4084 | C2 |
| hypercenter | #124 | D5 |
| hypocenter | C5 | #529 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#124 | C2 | semidirect |
| 2. #4092 | C2 | semidirect |
| 3. Q8×Dic5 | C2 | semidirect |
| 5. D4×Dic5 | C2 | semidirect |
| 6. #4029 | C2 | semidirect |
| 7. #4027 | C2 | semidirect |
| 8. #4025 | C2 | semidirect |
| 9. #4023 | C2 | semidirect |
| 10. C42×D5 | C2 | semidirect |
| 11. #4016 | C2 | semidirect |
| 56. #124 | D5 | semidirect |
| 127. C5 | #529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#124 | 2 |
| #4092 | 2 |
| Q8×Dic5 | 2 |
| #4084 | 2 |
| D4×Dic5 | 2 |
| #4029 | 2 |
| #4027 | 2 |
| #4025 | 2 |
| #4023 | 2 |
| C42×D5 | 2 |
| #4016 | 2 |
| #529 | 5 |