Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
552 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 146 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 |
| prime radical | C23×C52 | C23 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | #533 |
| 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 |
|---|---|---|
| 5. #11717037 | C2 | semidirect |
| 6. #11716989 | C2 | semidirect |
| 7. #11716985 | C2 | semidirect |
| 8. #11716961 | C2 | semidirect |
| 9. #11716956 | C2 | semidirect |
| 33. C2×#1039 | Q8 | semidirect |
| 137. C52 | #533 | semidirect |
| 202. C5 | #65956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1039 | 2 |
| C5×#4070 | 2 |
| #11717100 | 2 |
| #11717075 | 2 |
| #11717037 | 2 |
| #11716989 | 2 |
| #11716985 | 2 |
| #11716961 | 2 |
| #11716956 | 2 |
| #65956 | 5 |