Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1744 conjugacy classes of subgroups; only the 536 normal subgroups are shown.
This group has 1744 conjugacy classes of subgroups — too many to draw. Only its 536 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D52 |
| commutator, cosocle | C2×C52 | C25 |
| Frattini | C2 | C23×D52 |
| Fitting | C22×C4×C52 | C22 |
| socle | C22×C52 | C24 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | C2×2−1+4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#6045 | C2 | semidirect |
| 2. C2×C5×#709 | C2 | semidirect |
| 3. C2×#87880 | C2 | semidirect |
| 4. #11717463 | C2 | direct (N × H) |
| 5. C2×#87870 | C2 | semidirect |
| 6. C2×D5×Dic10 | C2 | semidirect |
| 10. C2×#6045 | C22 | semidirect |
| 12. C5×#709 | C22 | semidirect |
| 18. #87880 | C22 | semidirect |
| 20. #87870 | C22 | semidirect |
| 21. D5×Dic10 | C22 | semidirect |
| 44. C2×#709 | D5 | semidirect |
| 72. #709 | C2×D5 | semidirect |
| 86. C2×C52 | 2−1+4 | semidirect |
| 125. C52 | C2×2−1+4 | semidirect |
| 163. C2×C5 | #4150 | semidirect |
| 182. C5 | C2×#4150 | semidirect |
| 193. C2 | #11717463 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6045 | 2 |
| C2×C5×#709 | 2 |
| C2×#87880 | 2 |
| #11717463 | 2 |
| C2×#87870 | 2 |
| C2×D5×Dic10 | 2 |
| C2×#4150 | 5 |