Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
703 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 703 conjugacy classes of subgroups — too many to draw. Only its 341 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | #1042 |
| commutator, hypocenter | C52 | C23×C8 |
| Frattini | C2 | C23×#1042 |
| Fitting | C22×C4×C52 | C4 |
| socle | C23×C52 | C2×C4 |
| prime radical | C23×C5×D5 | C4 |
| cosocle | C5×Dic5 | C24 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#6032 | C2 | semidirect |
| 3. C2×D5⋊#168 | C2 | direct (N × H) |
| 9. C2×#6032 | C22 | semidirect |
| 10. D5⋊#168 | C22 | direct (N × H) |
| 14. C22×C5×D5 | C8 | semidirect |
| 21. #6032 | C23 | semidirect |
| 28. C22×C52 | C2×C8 | semidirect |
| 30. C2×C5×D5 | C2×C8 | semidirect |
| 51. C2×C52 | C22×C8 | semidirect |
| 53. C5×D5 | C22×C8 | semidirect |
| 59. C22×D5 | #168 | semidirect |
| 77. C52 | C23×C8 | semidirect |
| 82. C22×C5 | C2×#168 | semidirect |
| 83. C22×C5 | D5⋊C8 | semidirect |
| 86. C2×D5 | C2×#168 | semidirect |
| 105. C2×C5 | C22×#168 | semidirect |
| 106. C2×C5 | C2×D5⋊C8 | semidirect |
| 109. D5 | C22×#168 | semidirect |
| 120. C5 | C23×#168 | semidirect |
| 121. C5 | C22×D5⋊C8 | semidirect |
| 124. C22 | D5⋊#168 | direct (N × H) |
| 130. C2 | C2×D5⋊#168 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×D5 | 2 |
| C22×#6032 | 2 |
| C2×D5⋊#168 | 2 |
| C22×D5⋊C8 | 5 |
| C23×#168 | 5 |