Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
632 conjugacy classes of subgroups; only the 312 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 312 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C52 | C22⋊C4 |
| commutator | C22 | C22×C4×C52 |
| Frattini, cosocle | C23 | C23×C52 |
| socle | C2×C52 | C2×C22⋊C4 |
| prime radical | C2×C52×#41 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C52 ◁ C22×C4×C52 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C52×#117 | C2 | semidirect |
| 3. C52×#99 | C2 | semidirect |
| 6. C2×C52×Q8 | C4 | semidirect |
| 7. C2×C52×D4 | C4 | semidirect |
| 9. C22×C4×C52 | C4 | semidirect |
| 14. C5×#410 | C5 | direct (N × H) |
| 29. C5×#117 | C2×C5 | semidirect |
| 30. C5×#99 | C2×C5 | semidirect |
| 43. C2×C5×Q8 | C4×C5 | semidirect |
| 44. C2×C5×D4 | C4×C5 | semidirect |
| 46. C22×C4×C5 | C4×C5 | semidirect |
| 51. #410 | C52 | direct (N × H) |
| 70. #117 | C2×C52 | semidirect |
| 71. #99 | C2×C52 | semidirect |
| 72. C52 | #410 | direct (N × H) |
| 85. C2×Q8 | C4×C52 | semidirect |
| 86. C2×D4 | C4×C52 | semidirect |
| 88. C22×C4 | C4×C52 | semidirect |
| 110. C5 | C5×#410 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×#41 | 2 |
| C52×#117 | 2 |
| C52×#99 | 2 |
| C5×#410 | 5 |