Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
760 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 360 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C52 | C23 |
| commutator | C22 | C22×C4×C52 |
| Frattini, cosocle | C2×C4 | C23×C52 |
| socle | C22×C52 | C22×C4 |
| prime radical | C24×C52 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C52 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C52×M16 | C2 | semidirect |
| 3. C52×C22⋊C8 | C2 | semidirect |
| 11. C2×C52×C8 | C22 | semidirect |
| 12. C5×#407 | C5 | direct (N × H) |
| 26. C2×C5×M16 | C2×C5 | semidirect |
| 27. C5×C22⋊C8 | C2×C5 | semidirect |
| 33. C22×C52 | M16 | semidirect |
| 45. C2×C5×C8 | C22×C5 | semidirect |
| 46. #407 | C52 | direct (N × H) |
| 64. C2×M16 | C2×C52 | semidirect |
| 65. C22⋊C8 | C2×C52 | semidirect |
| 66. C52 | #407 | direct (N × H) |
| 72. C22×C5 | C5×M16 | semidirect |
| 84. C2×C8 | C22×C52 | semidirect |
| 101. C5 | C5×#407 | direct (N × H) |
| 107. C22 | C52×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C52 | 2 |
| C2×C52×M16 | 2 |
| C52×C22⋊C8 | 2 |
| C5×#407 | 5 |