Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
303 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 303 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D25 |
| commutator, cosocle | C23×C25 | C23 |
| Frattini, socle | C23×C5 | C22×D5 |
| Fitting | C25×#95 | C2 |
| prime radical | C23×D25 | C22 |
| hypercenter | #95 | D25 |
| hypocenter | C25 | #393 |
| LCS | G ▷ C23×C25 ▷ C25 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Dic50 | C2 | semidirect |
| 4. C25×#95 | C2 | semidirect |
| 5. #11716379 | C2 | semidirect |
| 21. C22×D25 | Q8 | semidirect |
| 89. #95 | D25 | semidirect |
| 90. C25 | #393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic50 | 2 |
| C2×#87720 | 2 |
| C25×#95 | 2 |
| #11716379 | 2 |
| #64962 | 5 |