Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
566 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 136 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 | C42×C52 | C22 |
| hypercenter | C42 | D52 |
| hypocenter | C52 | #555 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×C4⋊(C5⋊D5) | C2 | semidirect |
| 2. C4×C5×D20 | C2 | semidirect |
| 3. C5×#4015 | C2 | semidirect |
| 4. #11717034 | C2 | semidirect |
| 5. #11717027 | C2 | semidirect |
| 6. #11717025 | C2 | semidirect |
| 7. #11716967 | C2 | semidirect |
| 8. #11716959 | C2 | semidirect |
| 56. C4×D20 | D5 | semidirect |
| 57. #4015 | D5 | semidirect |
| 157. C52 | #555 | semidirect |
| 237. C5 | #65897 | semidirect |
| 238. C5 | #66068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C5⋊D5) | 2 |
| C4×C5×D20 | 2 |
| C5×#4015 | 2 |
| #11717034 | 2 |
| #11717027 | 2 |
| #11717025 | 2 |
| #11716967 | 2 |
| #11716959 | 2 |
| #66068 | 5 |
| #65897 | 5 |