Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1104 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 1104 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, Frattini | C22 | C22×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C42×C52 | C22 |
| hypercenter | C42 | D52 |
| hypocenter | C52 | C2×#127 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D5×D20 | C2 | semidirect |
| 2. #11717194 | C2 | semidirect |
| 3. C5×#4020 | C2 | semidirect |
| 4. C42×C5×D5 | C2 | semidirect |
| 5. #11717029 | C2 | semidirect |
| 7. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 8. C2×C5×D20 | C22 | semidirect |
| 10. C2×#6038 | C22 | semidirect |
| 12. C42×C52 | C22 | semidirect |
| 13. C4×C5×Dic5 | C22 | semidirect |
| 24. C4×C5×D5 | D4 | semidirect |
| 35. #4020 | D5 | direct (N × H) |
| 36. C42×D5 | D5 | semidirect |
| 42. C4×C52 | C2×D4 | semidirect |
| 43. C5×Dic5 | C2×D4 | semidirect |
| 55. C2×D20 | C2×D5 | semidirect |
| 59. C42×C5 | C2×D5 | semidirect |
| 60. C42×C5 | C2×D5 | semidirect |
| 61. C4×Dic5 | C2×D5 | semidirect |
| 66. C5×D5 | #127 | semidirect |
| 89. C4×D5 | D20 | semidirect |
| 95. C52 | C2×#127 | semidirect |
| 110. C4×C5 | C2×D20 | semidirect |
| 111. C4×C5 | D4×D5 | semidirect |
| 112. Dic5 | C2×D20 | semidirect |
| 120. C42 | D52 | semidirect |
| 130. D5 | #4020 | direct (N × H) |
| 142. C5 | C2×#4020 | semidirect |
| 143. C5 | D5×#127 | semidirect |
| 150. C4 | D5×D20 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×D20 | 2 |
| #11717194 | 2 |
| C5×#4020 | 2 |
| C42×C5×D5 | 2 |
| #11717029 | 2 |
| D5×#127 | 5 |
| C2×#4020 | 5 |