Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1336 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1336 conjugacy classes of subgroups — too many to draw. Only its 235 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C52×#127 | C2 |
| hypercenter | #127 | C5⋊D5 |
| hypocenter | C52 | #535 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87902 | C2 | semidirect |
| 2. C2×D4×C5⋊D5 | C2 | semidirect |
| 3. C52×#127 | C2 | semidirect |
| 4. #11717260 | C2 | semidirect |
| 5. #11717259 | C2 | semidirect |
| 6. #11717257 | C2 | semidirect |
| 7. #11717256 | C2 | semidirect |
| 8. #11717195 | C2 | semidirect |
| 9. #11717192 | C2 | semidirect |
| 12. C2×C52×D4 | C22 | semidirect |
| 13. C2×C52×D4 | C22 | semidirect |
| 16. C2×C22⋊(C5⋊D5) | C22 | semidirect |
| 17. C22×#1039 | C22 | semidirect |
| 22. C2×#6045 | C22 | semidirect |
| 23. C42×C52 | C22 | semidirect |
| 24. C22⋊#1039 | C22 | semidirect |
| 26. #87808 | C22 | semidirect |
| 27. #87806 | C22 | semidirect |
| 28. C4×#1039 | C22 | semidirect |
| 49. C4×C5⋊D5 | D4 | semidirect |
| 53. C5×#127 | D5 | semidirect |
| 77. C2×C5×D4 | C2×D5 | semidirect |
| 78. C2×C5×D4 | C2×D5 | semidirect |
| 88. C42×C5 | C2×D5 | semidirect |
| 125. #127 | C5⋊D5 | semidirect |
| 131. C52 | #535 | semidirect |
| 156. C2×D4 | C2×C5⋊D5 | semidirect |
| 157. C2×D4 | C2×C5⋊D5 | semidirect |
| 165. C42 | C2×C5⋊D5 | semidirect |
| 193. C5 | #66049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87902 | 2 |
| C2×D4×C5⋊D5 | 2 |
| C52×#127 | 2 |
| #11717260 | 2 |
| #11717259 | 2 |
| #11717257 | 2 |
| #11717256 | 2 |
| #11717195 | 2 |
| #11717192 | 2 |
| #66049 | 5 |