Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
206 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×D52 |
| commutator, socle | C2×C52 | C22×C8 |
| Fitting | C52×C16 | C22 |
| prime radical | C2×D52 | C8 |
| cosocle | C52×C8 | C23 |
| hypercenter | C16 | D52 |
| hypocenter | C52 | C2×M32 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C8 ◁ C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11716665 | C2 | semidirect |
| 3. C5×#3930 | C2 | semidirect |
| 4. C5×D5×C16 | C2 | semidirect |
| 5. #11716585 | C2 | semidirect |
| 6. #11716584 | C2 | semidirect |
| 7. D5×#672 | C2 | semidirect |
| 15. C52×C16 | C22 | semidirect |
| 16. #87756 | C22 | semidirect |
| 17. C5×#672 | C22 | semidirect |
| 18. C5×#672 | C22 | semidirect |
| 44. #3930 | D5 | direct (N × H) |
| 46. D5×C16 | D5 | semidirect |
| 73. C5×C16 | C2×D5 | semidirect |
| 74. C5×C16 | C2×D5 | semidirect |
| 78. #672 | C2×D5 | semidirect |
| 79. #672 | C2×D5 | semidirect |
| 84. C5×D5 | M32 | semidirect |
| 117. C52 | C2×M32 | semidirect |
| 147. C16 | D52 | semidirect |
| 157. D5 | #3930 | direct (N × H) |
| 170. C5 | C2×#3930 | semidirect |
| 171. C5 | D5×M32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×D52 | 2 |
| #11716665 | 2 |
| C5×#3930 | 2 |
| C5×D5×C16 | 2 |
| #11716585 | 2 |
| #11716584 | 2 |
| D5×#672 | 2 |
| D5×M32 | 5 |
| C2×#3930 | 5 |