Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
768 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 227 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 | C23×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C4×C52×Q8 | C2 |
| prime radical | C22×C5⋊D5 | C23 |
| hypercenter | C4×Q8 | C5⋊D5 |
| hypocenter | C52 | #541 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×C52×Q8 | C2 | semidirect |
| 3. #11717264 | C2 | semidirect |
| 6. #11717210 | C2 | semidirect |
| 7. #11717209 | C2 | semidirect |
| 10. #11717190 | C2 | semidirect |
| 11. C4×#6045 | C2 | semidirect |
| 50. C4×C5×Q8 | D5 | semidirect |
| 126. C4×Q8 | C5⋊D5 | semidirect |
| 128. C52 | #541 | semidirect |
| 184. C5 | #65917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C52×Q8 | 2 |
| #11717266 | 2 |
| #11717264 | 2 |
| #11717218 | 2 |
| #11717217 | 2 |
| #11717210 | 2 |
| #11717209 | 2 |
| #11717196 | 2 |
| #11717192 | 2 |
| #11717190 | 2 |
| C4×#6045 | 2 |
| #65917 | 5 |