Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
566 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 130 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 | C22×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C22×C4×C52 | C22 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | #555 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×C22⋊(C5⋊D5) | C2 | semidirect |
| 2. C5×#4076 | C2 | semidirect |
| 3. C5×#4072 | C2 | semidirect |
| 4. #11717089 | C2 | semidirect |
| 5. #11717077 | C2 | semidirect |
| 6. #11717037 | C2 | semidirect |
| 7. #11717034 | C2 | semidirect |
| 8. #11717017 | C2 | semidirect |
| 9. #11716995 | C2 | semidirect |
| 10. #11716970 | C2 | semidirect |
| 11. #11716967 | C2 | semidirect |
| 62. #4076 | D5 | semidirect |
| 66. #4072 | D5 | semidirect |
| 216. C52 | #555 | semidirect |
| 325. C5 | #65866 | semidirect |
| 326. C5 | #65950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C22⋊(C5⋊D5) | 2 |
| C5×#4076 | 2 |
| C5×#4072 | 2 |
| #11717089 | 2 |
| #11717077 | 2 |
| #11717037 | 2 |
| #11717034 | 2 |
| #11717017 | 2 |
| #11716995 | 2 |
| #11716970 | 2 |
| #11716967 | 2 |
| #65950 | 5 |
| #65866 | 5 |