Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
472 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 117 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 | C23×D5 |
| commutator, socle, cosocle | C23×C5 | C24 |
| Fitting, prime radical | C5×#392 | C2 |
| hypercenter | #392 | D5 |
| hypocenter | C5 | #2824 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #392 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #65511 | C2 | semidirect |
| 3. #65511 | C2 | semidirect |
| 4. #65509 | C2 | semidirect |
| 5. #65241 | C2 | semidirect |
| 6. #65236 | C2 | semidirect |
| 7. #65236 | C2 | semidirect |
| 8. #65235 | C2 | semidirect |
| 9. #64947 | C2 | semidirect |
| 221. C5 | #2824 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#392 | 2 |
| #65511 | 2 |
| #65509 | 2 |
| #65241 | 2 |
| #65236 | 2 |
| #65235 | 2 |
| #64947 | 2 |
| #2824 | 5 |