Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
560 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D52 |
| commutator, socle, cosocle | C23×C52 | C23 |
| Fitting | C22×C4×C52 | C22 |
| prime radical | C23×C5×D5 | C22 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | #393 |
| LCS | G ▷ C23×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#6045 | C2 | semidirect |
| 4. C5×#3963 | C2 | semidirect |
| 5. #11716620 | C2 | semidirect |
| 22. C22×C5×D5 | Q8 | semidirect |
| 44. #3963 | D5 | semidirect |
| 100. C22×D5 | Dic10 | semidirect |
| 134. C52 | #393 | semidirect |
| 214. C5 | #64962 | semidirect |
| 215. C5 | #65236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6045 | 2 |
| C2×C5×#685 | 2 |
| C2×#87778 | 2 |
| C5×#3963 | 2 |
| #11716620 | 2 |
| #65236 | 5 |
| #64962 | 5 |