Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
864 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 864 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×#124 | C2 |
| prime radical | #11717258 | C2 |
| hypercenter | #124 | C5⋊D5 |
| hypocenter | C52 | #542 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C52×#124 | C2 | semidirect |
| 2. #11717266 | C2 | semidirect |
| 3. Q8×#1039 | C2 | semidirect |
| 5. D4×#1039 | C2 | semidirect |
| 6. #11717206 | C2 | semidirect |
| 7. #11717205 | C2 | semidirect |
| 8. #11717199 | C2 | semidirect |
| 9. #11717198 | C2 | semidirect |
| 10. #11717192 | C2 | semidirect |
| 11. #11717189 | C2 | semidirect |
| 53. C5×#124 | D5 | semidirect |
| 129. #124 | C5⋊D5 | semidirect |
| 137. C52 | #542 | semidirect |
| 199. C5 | #66016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#124 | 2 |
| #11717266 | 2 |
| Q8×#1039 | 2 |
| #11717258 | 2 |
| D4×#1039 | 2 |
| #11717206 | 2 |
| #11717205 | 2 |
| #11717199 | 2 |
| #11717198 | 2 |
| #11717192 | 2 |
| #11717189 | 2 |
| #66016 | 5 |