Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
224 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | D52 |
| commutator, hypocenter | C52 | C22×C16 |
| Frattini | C8 | C2×D52 |
| Fitting | C52×C16 | C22 |
| socle | C2×C52 | C22×C8 |
| prime radical | C2×D52 | C8 |
| cosocle | C52×C8 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C16×C5⋊D5 | C2 | semidirect |
| 3. C5×D5×C16 | C2 | semidirect |
| 4. #11716583 | C2 | semidirect |
| 5. D5×#672 | C2 | semidirect |
| 11. C52×C16 | C22 | semidirect |
| 12. #87756 | C22 | semidirect |
| 13. C5×#672 | C22 | semidirect |
| 30. D5×C16 | D5 | direct (N × H) |
| 33. D52 | C16 | direct (N × H) |
| 47. C5×C16 | C2×D5 | semidirect |
| 50. #672 | C2×D5 | semidirect |
| 53. C5⋊D5 | C2×C16 | semidirect |
| 54. C5×D5 | C2×C16 | semidirect |
| 74. C52 | C22×C16 | semidirect |
| 93. C16 | D52 | direct (N × H) |
| 99. D5 | D5×C16 | direct (N × H) |
| 109. C5 | C2×D5×C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×D52 | 2 |
| C16×C5⋊D5 | 2 |
| C5×D5×C16 | 2 |
| #11716583 | 2 |
| D5×#672 | 2 |
| C2×D5×C16 | 5 |