Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
422 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D5 |
| commutator, socle | C22×C5 | C23×C4 |
| Fitting | C5×#433 | C2 |
| prime radical | #65858 | C2 |
| cosocle | C2×C4×C5 | C24 |
| hypercenter | #433 | D5 |
| hypocenter | C5 | #2977 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C4 ◁ #433 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#433 | C2 | semidirect |
| 3. #65289 | C2 | semidirect |
| 4. #65125 | C2 | semidirect |
| 5. #65123 | C2 | semidirect |
| 6. #65016 | C2 | semidirect |
| 7. D5×C22⋊C8 | C2 | semidirect |
| 8. #64995 | C2 | semidirect |
| 9. C8×D20 | C2 | semidirect |
| 13. C2×#676 | C22 | semidirect |
| 16. C2×C8×D5 | C22 | semidirect |
| 23. C5×C4⋊C8 | C22 | semidirect |
| 25. C5×#97 | C22 | semidirect |
| 26. C4×C5×C8 | C22 | semidirect |
| 30. #3952 | C22 | semidirect |
| 31. #3952 | C22 | semidirect |
| 32. C4⋊#168 | C22 | semidirect |
| 33. #3935 | C22 | semidirect |
| 34. C4×#168 | C22 | semidirect |
| 73. #433 | D5 | semidirect |
| 117. C4⋊C8 | C2×D5 | semidirect |
| 125. #97 | C2×D5 | semidirect |
| 127. C4×C8 | C2×D5 | semidirect |
| 207. C5 | #2977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #65858 | 2 |
| C5×#433 | 2 |
| #65289 | 2 |
| #65125 | 2 |
| #65123 | 2 |
| #65016 | 2 |
| D5×C22⋊C8 | 2 |
| #64995 | 2 |
| C8×D20 | 2 |
| #2977 | 5 |