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 | C52×C4⋊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. C52×C4⋊Q8 | C2 | semidirect |
| 3. Q8×#1039 | C2 | semidirect |
| 5. #11717209 | C2 | semidirect |
| 7. #11717190 | C2 | semidirect |
| 31. C5×C4⋊Q8 | D5 | semidirect |
| 73. C4⋊Q8 | C5⋊D5 | semidirect |
| 80. C52 | #541 | semidirect |
| 115. C5 | #66065 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C4⋊Q8 | 2 |
| #11717266 | 2 |
| Q8×#1039 | 2 |
| #11717218 | 2 |
| #11717209 | 2 |
| #11717192 | 2 |
| #11717190 | 2 |
| #66065 | 5 |