Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
315 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 315 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C25 | C22⋊C4 |
| commutator | C22 | C22×C4×C25 |
| Frattini, cosocle | C23×C5 | C23×C5 |
| socle | C22×C5 | C5×C22⋊C4 |
| prime radical | C22×C5×D4 | C2×C5 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C25 ◁ C24×C25 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊C4×C25 | C2 | semidirect |
| 3. C25×#99 | C2 | direct (N × H) |
| 4. C24×C25 | C4 | semidirect |
| 8. C2×D4×C25 | C4 | semidirect |
| 11. C22×C4×C25 | C4 | semidirect |
| 13. C22⋊C4×C25 | C22 | semidirect |
| 21. C23×C25 | C2×C4 | semidirect |
| 31. C2×C4×C25 | C2×C4 | semidirect |
| 61. C2×#99 | C25 | direct (N × H) |
| 67. C2×C25 | #99 | direct (N × H) |
| 87. C2×C22⋊C4 | C2×C25 | semidirect |
| 88. #99 | C2×C25 | direct (N × H) |
| 89. C25 | C2×#99 | direct (N × H) |
| 106. C24 | C4×C25 | semidirect |
| 110. C2×D4 | C4×C25 | semidirect |
| 113. C22×C4 | C4×C25 | semidirect |
| 115. C22⋊C4 | C22×C25 | semidirect |
| 129. C23 | C2×C4×C25 | semidirect |
| 139. C2×C4 | C2×C4×C25 | semidirect |
| 162. C2 | C25×#99 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×C25 | 2 |
| C2×C22⋊C4×C25 | 2 |
| C25×#99 | 2 |
| C2×C5×#99 | 5 |