Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
672 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 153 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 | C2×C5×#117 | C2 |
| prime radical | C24×D5 | C22 |
| hypercenter | C2×#117 | D5 |
| hypocenter | C5 | #2482 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ C2×#117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#117 | C2 | semidirect |
| 3. #65500 | C2 | semidirect |
| 4. #65282 | C2 | semidirect |
| 5. #65281 | C2 | semidirect |
| 7. #65235 | C2 | semidirect |
| 8. #65229 | C2 | semidirect |
| 13. C2×C5×C4⋊C4 | C22 | semidirect |
| 14. C2×C5×C4⋊C4 | C22 | semidirect |
| 16. C2×C42×C5 | C22 | semidirect |
| 23. C2×#683 | C22 | semidirect |
| 24. #3963 | C22 | semidirect |
| 25. #3963 | C22 | semidirect |
| 26. #3963 | C22 | semidirect |
| 54. C2×#117 | D5 | semidirect |
| 96. C2×C4⋊C4 | C2×D5 | semidirect |
| 97. C2×C4⋊C4 | C2×D5 | semidirect |
| 105. C2×C42 | C2×D5 | semidirect |
| 190. C5 | #2482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#117 | 2 |
| C22×#685 | 2 |
| #65500 | 2 |
| #65282 | 2 |
| #65281 | 2 |
| #65244 | 2 |
| #65235 | 2 |
| #65229 | 2 |
| #2482 | 5 |