Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1232 conjugacy classes of subgroups; only the 552 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 552 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D52 |
| commutator, hypocenter | C52 | C22×C42 |
| Frattini | C22 | C22×D52 |
| Fitting, socle, prime radical | C24×C52 | C22 |
| cosocle | C22×C52 | C24 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×Dic52 | C2 | direct (N × H) |
| 5. C22×#1039 | C4 | semidirect |
| 7. C22×C5×Dic5 | C4 | semidirect |
| 9. Dic52 | C22 | direct (N × H) |
| 14. C2×#1039 | C2×C4 | semidirect |
| 16. C2×C5×Dic5 | C2×C4 | semidirect |
| 23. C22×C52 | C42 | semidirect |
| 27. #1039 | C22×C4 | semidirect |
| 28. C5×Dic5 | C22×C4 | semidirect |
| 37. C22×Dic5 | Dic5 | direct (N × H) |
| 41. C2×C52 | C2×C42 | semidirect |
| 57. C2×Dic5 | C2×Dic5 | direct (N × H) |
| 62. C52 | C22×C42 | semidirect |
| 67. C22×C5 | C4×Dic5 | semidirect |
| 75. Dic5 | C22×Dic5 | direct (N × H) |
| 85. C2×C5 | C2×C4×Dic5 | semidirect |
| 97. C5 | C22×C4×Dic5 | semidirect |
| 98. C22 | Dic52 | direct (N × H) |
| 104. C2 | C2×Dic52 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1039 | 2 |
| C23×C5×Dic5 | 2 |
| C2×Dic52 | 2 |
| C22×C4×Dic5 | 5 |