Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
2648 conjugacy classes of subgroups; only the 371 normal subgroups are shown.
This group has 2648 conjugacy classes of subgroups — too many to draw. Only its 371 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×C5⋊D5 |
| commutator, cosocle | C22×C52 | C24 |
| Frattini | C22 | C23×C5⋊D5 |
| Fitting | C22×C52×D4 | C2 |
| socle | C23×C52 | C23 |
| hypercenter | C22×D4 | C5⋊D5 |
| hypocenter | C52 | C2×#120 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×C5⋊D5 | C2 | semidirect |
| 2. C22×C52×D4 | C2 | semidirect |
| 3. C22×C22⋊(C5⋊D5) | C2 | semidirect |
| 4. C2×C22⋊#1039 | C2 | semidirect |
| 5. #11717257 | C2 | direct (N × H) |
| 6. C2×#87808 | C2 | semidirect |
| 8. C24×C52 | C22 | semidirect |
| 12. C23×C5⋊D5 | C22 | semidirect |
| 14. C2×C52×D4 | C22 | semidirect |
| 15. C22×C4×C52 | C22 | semidirect |
| 17. C2×C22⋊(C5⋊D5) | C22 | semidirect |
| 18. C22×#1039 | C22 | semidirect |
| 19. C22⋊#1039 | C22 | semidirect |
| 20. #87808 | C22 | semidirect |
| 25. C23×C52 | D4 | semidirect |
| 28. C23×C52 | C23 | semidirect |
| 34. C22×C5⋊D5 | D4 | semidirect |
| 38. C2×C4×C52 | C23 | semidirect |
| 41. C2×#1039 | C23 | semidirect |
| 43. C22×C5×D4 | D5 | semidirect |
| 55. C22×C52 | C2×D4 | semidirect |
| 61. C2×C5⋊D5 | C2×D4 | semidirect |
| 65. C24×C5 | C2×D5 | semidirect |
| 71. C2×C5×D4 | C2×D5 | semidirect |
| 72. C22×C4×C5 | C2×D5 | semidirect |
| 81. C2×C52 | #120 | semidirect |
| 88. C23×C5 | C22⋊D5 | semidirect |
| 91. C23×C5 | C22×D5 | semidirect |
| 101. C2×C4×C5 | C22×D5 | semidirect |
| 107. C22×D4 | C5⋊D5 | semidirect |
| 111. C52 | C2×#120 | semidirect |
| 119. C22×C5 | C2×C22⋊D5 | semidirect |
| 133. C24 | C2×C5⋊D5 | semidirect |
| 137. C2×D4 | C2×C5⋊D5 | semidirect |
| 139. C22×C4 | C2×C5⋊D5 | semidirect |
| 144. C2×C5 | #4083 | semidirect |
| 158. C23 | C22⋊(C5⋊D5) | semidirect |
| 161. C23 | C22×C5⋊D5 | semidirect |
| 167. C2×C4 | C22×C5⋊D5 | semidirect |
| 168. C5 | C2×#4083 | semidirect |
| 181. C22 | C2×C22⋊(C5⋊D5) | semidirect |
| 188. C2 | #11717257 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C5⋊D5 | 2 |
| C22×C52×D4 | 2 |
| C22×C22⋊(C5⋊D5) | 2 |
| C2×C22⋊#1039 | 2 |
| #11717257 | 2 |
| C2×#87808 | 2 |
| C2×#4083 | 5 |