Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
944 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 215 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×#123 | C2 |
| prime radical | #11717260 | C2 |
| hypercenter | #123 | C5⋊D5 |
| hypocenter | C52 | #559 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C52×#123 | C2 | semidirect |
| 3. #11717255 | C2 | semidirect |
| 4. C4×C22⋊(C5⋊D5) | C2 | semidirect |
| 5. #11717214 | C2 | semidirect |
| 6. #11717207 | C2 | semidirect |
| 7. #11717205 | C2 | semidirect |
| 8. #11717205 | C2 | semidirect |
| 9. #11717201 | C2 | semidirect |
| 49. C5×#123 | D5 | semidirect |
| 121. #123 | C5⋊D5 | semidirect |
| 125. C52 | #559 | semidirect |
| 183. C5 | #65998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#123 | 2 |
| #11717260 | 2 |
| #11717255 | 2 |
| C4×C22⋊(C5⋊D5) | 2 |
| #11717214 | 2 |
| #11717207 | 2 |
| #11717205 | 2 |
| #11717201 | 2 |
| #65998 | 5 |