Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
824 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 235 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C52×#125 | C2 |
| prime radical | C22×C5⋊D5 | C23 |
| hypercenter | #125 | C5⋊D5 |
| hypocenter | C52 | #544 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C52×#125 | C2 | semidirect |
| 6. #11717210 | C2 | semidirect |
| 7. #11717209 | C2 | semidirect |
| 8. #11717208 | C2 | semidirect |
| 9. #11717208 | C2 | semidirect |
| 11. #11717189 | C2 | semidirect |
| 48. C4×C5⋊D5 | Q8 | semidirect |
| 51. C5×#125 | D5 | semidirect |
| 124. #125 | C5⋊D5 | semidirect |
| 130. C52 | #544 | semidirect |
| 187. C5 | #66023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#125 | 2 |
| #11717217 | 2 |
| #11717216 | 2 |
| #11717212 | 2 |
| C4⋊C4×C5⋊D5 | 2 |
| #11717210 | 2 |
| #11717209 | 2 |
| #11717208 | 2 |
| #11717192 | 2 |
| #11717189 | 2 |
| #66023 | 5 |