Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
1104 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 269 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 | C22×C5 | C23×C4 |
| Fitting | C2×C5×#117 | C2 |
| socle, cosocle | C23×C5 | C24 |
| prime radical | C23×D20 | C2 |
| hypercenter | C2×#117 | D5 |
| hypocenter | C5 | #2309 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ C2×#117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C5×#117 | C2 | semidirect |
| 3. C2×#4072 | C2 | semidirect |
| 4. #65277 | C2 | semidirect |
| 5. #65244 | C2 | semidirect |
| 6. #65228 | C2 | semidirect |
| 11. C22×D20 | C4 | semidirect |
| 15. C2×C5×C4⋊C4 | C22 | semidirect |
| 17. C2×C42×C5 | C22 | semidirect |
| 19. C2×#685 | C22 | semidirect |
| 21. C2×C4⋊Dic5 | C22 | semidirect |
| 22. C2×C4×Dic5 | C22 | semidirect |
| 53. C2×#117 | D5 | semidirect |
| 72. C2×C4×C5 | C22⋊C4 | semidirect |
| 93. C2×C4⋊C4 | C2×D5 | semidirect |
| 98. C2×C42 | C2×D5 | semidirect |
| 168. C2×C4 | #685 | semidirect |
| 175. C5 | #2309 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D20 | 2 |
| C2×C5×#117 | 2 |
| C2×#4072 | 2 |
| #65277 | 2 |
| #65244 | 2 |
| #65228 | 2 |
| #2309 | 5 |