Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1088 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 200 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 | C22×C52 | C24 |
| Frattini | C22 | C22×D52 |
| Fitting | C22×C4×C52 | C22 |
| socle | C23×C52 | C23 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | C2×#121 |
| LCS | G ▷ C22×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×C5×D20 | C2 | semidirect |
| 3. C22×#6038 | C2 | semidirect |
| 4. C2×C5×C4⋊Dic5 | C2 | semidirect |
| 5. C2×#87778 | C2 | semidirect |
| 6. #11717034 | C2 | direct (N × H) |
| 12. C2×C4×C5⋊D5 | C22 | semidirect |
| 15. C2×C5×D20 | C22 | semidirect |
| 17. C2×#6038 | C22 | semidirect |
| 18. C5×C4⋊Dic5 | C22 | semidirect |
| 19. #87778 | C22 | semidirect |
| 25. C22×C5⋊D5 | D4 | semidirect |
| 31. C2×C4×C52 | D4 | semidirect |
| 43. C22×D20 | D5 | semidirect |
| 51. C2×C4⋊Dic5 | D5 | semidirect |
| 60. C2×C5⋊D5 | C2×D4 | semidirect |
| 65. C4×C52 | C2×D4 | semidirect |
| 88. C2×D20 | C2×D5 | semidirect |
| 98. C4⋊Dic5 | C2×D5 | semidirect |
| 100. C2×C52 | #121 | semidirect |
| 134. C2×C4×C5 | D20 | semidirect |
| 135. C2×C4×C5 | C22⋊D5 | semidirect |
| 158. C52 | C2×#121 | semidirect |
| 193. C4×C5 | C2×D20 | semidirect |
| 194. C4×C5 | C2×C22⋊D5 | semidirect |
| 217. C2×C5 | #4041 | semidirect |
| 218. C2×C5 | #4084 | semidirect |
| 245. C2×C4 | #6038 | semidirect |
| 248. C5 | C2×#4041 | semidirect |
| 249. C5 | C2×#4084 | semidirect |
| 264. C4 | C2×#6038 | semidirect |
| 267. C2 | #11717034 | 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×C5×D20 | 2 |
| C22×#6038 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C2×#87778 | 2 |
| #11717034 | 2 |
| C2×#4084 | 5 |
| C2×#4041 | 5 |