Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
237 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 237 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C25 | C22⋊C4 |
| commutator | C22 | C22×C4×C25 |
| Frattini, cosocle | C23×C5 | C23×C5 |
| socle | C2×C5 | C2×C5×C22⋊C4 |
| prime radical | C2×C5×#41 | C2×C5 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C25 ◁ C22×C4×C25 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C25×#117 | C2 | semidirect |
| 3. C25×#99 | C2 | semidirect |
| 6. C2×Q8×C25 | C4 | semidirect |
| 7. C2×D4×C25 | C4 | semidirect |
| 9. C22×C4×C25 | C4 | semidirect |
| 51. #410 | C25 | direct (N × H) |
| 70. #117 | C2×C25 | semidirect |
| 71. #99 | C2×C25 | semidirect |
| 72. C25 | #410 | direct (N × H) |
| 85. C2×Q8 | C4×C25 | semidirect |
| 86. C2×D4 | C4×C25 | semidirect |
| 88. C22×C4 | C4×C25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×C25 | 2 |
| C25×#117 | 2 |
| C25×#99 | 2 |
| C5×#410 | 5 |