Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
2016 conjugacy classes of subgroups; only the 568 normal subgroups are shown.
This group has 2016 conjugacy classes of subgroups — too many to draw. Only its 568 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D52 |
| commutator, cosocle | C2×C52 | C25 |
| Frattini | C2 | C23×D52 |
| Fitting | C22×C4×C52 | C22 |
| socle | C23×C52 | C23 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | C22×#41 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C4⋊(C5⋊D5) | C2 | semidirect |
| 2. C22×C4×C5×D5 | C2 | semidirect |
| 3. C22×C5×Dic10 | C2 | semidirect |
| 4. C22×#6038 | C2 | semidirect |
| 5. C22×#6036 | C2 | semidirect |
| 6. C2×#87874 | C2 | direct (N × H) |
| 10. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 13. C2×C4×C5×D5 | C22 | semidirect |
| 14. C2×C5×Dic10 | C22 | semidirect |
| 15. C2×#6038 | C22 | semidirect |
| 16. C2×#6036 | C22 | semidirect |
| 17. #87874 | C22 | direct (N × H) |
| 26. C4⋊(C5⋊D5) | C23 | semidirect |
| 29. C4×C5×D5 | C23 | semidirect |
| 30. C5×Dic10 | C23 | semidirect |
| 31. #6038 | C23 | semidirect |
| 32. #6036 | C23 | semidirect |
| 44. C22×C4×D5 | D5 | semidirect |
| 45. C22×Dic10 | D5 | semidirect |
| 46. C22×C52 | #41 | semidirect |
| 78. C2×C4×D5 | C2×D5 | semidirect |
| 79. C2×Dic10 | C2×D5 | semidirect |
| 81. C2×C52 | C2×#41 | semidirect |
| 114. C4×D5 | C22×D5 | semidirect |
| 115. Dic10 | C22×D5 | semidirect |
| 122. C52 | C22×#41 | semidirect |
| 127. C22×C5 | #709 | semidirect |
| 128. C22×C5 | #713 | semidirect |
| 160. C2×C5 | C2×#709 | semidirect |
| 161. C2×C5 | C2×#713 | semidirect |
| 182. C5 | C22×#709 | semidirect |
| 183. C5 | C22×#713 | semidirect |
| 188. C22 | #87874 | direct (N × H) |
| 195. C2 | C2×#87874 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C5⋊D5) | 2 |
| C22×C4×C5×D5 | 2 |
| C22×C5×Dic10 | 2 |
| C22×#6038 | 2 |
| C22×#6036 | 2 |
| C2×#87874 | 2 |
| C22×#713 | 5 |
| C22×#709 | 5 |