Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
402 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 197 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×D83 |
| commutator, socle | C22×C83 | C23×C4 |
| Fitting, prime radical | #525×C83 | C2 |
| cosocle | C2×C4×C83 | C24 |
| hypercenter | #525 | D83 |
| hypocenter | C83 | #2978 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19127779 | C2 | semidirect |
| 2. #19127773 | C2 | semidirect |
| 3. #19127762 | C2 | semidirect |
| 4. #19127668 | C2 | semidirect |
| 5. #19127665 | C2 | semidirect |
| 8. C2×#13050574 | C22 | semidirect |
| 9. C22×C83⋊C8 | C22 | semidirect |
| 10. C4⋊(C83⋊C8) | C22 | semidirect |
| 14. C22⋊(C83⋊C8) | C22 | semidirect |
| 15. #14581703 | C22 | semidirect |
| 16. C4×C83⋊C8 | C22 | semidirect |
| 90. C83 | #2978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19127779 | 2 |
| #19127773 | 2 |
| #19127762 | 2 |
| #19127668 | 2 |
| #19127665 | 2 |
| #525×C83 | 2 |
| #2978 | 83 |