Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
494 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 160 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, prime radical, cosocle | C22×C52 | C24 |
| Fitting | C42×C52 | C22 |
| hypercenter | C42 | D52 |
| hypocenter | C52 | Q82 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 32. #6045 | Q8 | semidirect |
| 37. C5×Dic10 | Q8 | semidirect |
| 135. Dic10 | Dic10 | semidirect |
| 144. C52 | Q82 | semidirect |
| 207. C5 | Q8×Dic10 | semidirect |
| 208. C5 | #66056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6045 | 2 |
| C5×#4015 | 2 |
| C4×C5×Dic10 | 2 |
| #11717037 | 2 |
| #11717036 | 2 |
| #11716962 | 2 |
| #11716961 | 2 |
| #11716957 | 2 |
| #66056 | 5 |
| Q8×Dic10 | 5 |