Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
258 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×D5 |
| commutator, socle | C2×C5 | C23×C4 |
| Fitting | C2×C5×M16 | C2 |
| prime radical | C2×#709 | C2 |
| cosocle | C4×C5 | C24 |
| hypercenter | C2×M16 | D5 |
| hypocenter | C5 | #568 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C4 ◁ C2×M16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C5×M16 | C2 | semidirect |
| 3. C2×#681 | C2 | semidirect |
| 4. #4053 | C2 | semidirect |
| 5. D5×M16 | C2 | semidirect |
| 6. #4047 | C2 | semidirect |
| 17. C5×M16 | C22 | semidirect |
| 18. C2×C5×C8 | C22 | semidirect |
| 20. #681 | C22 | semidirect |
| 21. C2×#168 | C22 | semidirect |
| 22. #676 | C22 | semidirect |
| 23. C8×D5 | C22 | semidirect |
| 49. C2×M16 | D5 | semidirect |
| 74. M16 | C2×D5 | semidirect |
| 77. C2×C8 | C2×D5 | semidirect |
| 102. C5 | #568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#709 | 2 |
| C2×C5×M16 | 2 |
| C2×#681 | 2 |
| #4053 | 2 |
| D5×M16 | 2 |
| #4047 | 2 |
| #568 | 5 |