Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
576 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
| prime radical | #11717034 | C2 |
| hypercenter | C42 | D52 |
| hypocenter | C52 | #529 |
| 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. C42×C5⋊D5 | C2 | semidirect |
| 2. C5×#4021 | C2 | semidirect |
| 3. C5×#4016 | C2 | semidirect |
| 5. #11717017 | C2 | semidirect |
| 6. #11716999 | C2 | semidirect |
| 7. #11716996 | C2 | semidirect |
| 8. #11716990 | C2 | semidirect |
| 9. #11716980 | C2 | semidirect |
| 10. #11716971 | C2 | semidirect |
| 11. #11716961 | C2 | semidirect |
| 73. #4021 | D5 | semidirect |
| 77. #4016 | D5 | semidirect |
| 210. C52 | #529 | semidirect |
| 309. C5 | #66014 | semidirect |
| 310. C5 | #66025 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C5⋊D5 | 2 |
| C5×#4021 | 2 |
| C5×#4016 | 2 |
| #11717034 | 2 |
| #11717017 | 2 |
| #11716999 | 2 |
| #11716996 | 2 |
| #11716990 | 2 |
| #11716980 | 2 |
| #11716971 | 2 |
| #11716961 | 2 |
| #66025 | 5 |
| #66014 | 5 |