Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1232 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 224 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×#127 |
| 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×C4×C5×Dic5 | C2 | semidirect |
| 5. #11717029 | C2 | direct (N × H) |
| 10. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 13. C2×C5×D20 | C22 | semidirect |
| 15. C2×#6038 | C22 | semidirect |
| 16. C4×C5×Dic5 | C22 | semidirect |
| 26. C2×C4×C52 | D4 | semidirect |
| 29. C2×C5×Dic5 | D4 | semidirect |
| 39. C22×D20 | D5 | semidirect |
| 42. C2×C4×Dic5 | D5 | semidirect |
| 53. C4×C52 | C2×D4 | semidirect |
| 54. C5×Dic5 | C2×D4 | semidirect |
| 78. C2×D20 | C2×D5 | semidirect |
| 80. C4×Dic5 | C2×D5 | semidirect |
| 82. C2×C52 | #127 | semidirect |
| 110. C2×C4×C5 | D20 | semidirect |
| 111. C2×C4×C5 | C22⋊D5 | semidirect |
| 115. C2×Dic5 | D20 | semidirect |
| 127. C52 | C2×#127 | semidirect |
| 154. C4×C5 | C2×D20 | semidirect |
| 155. C4×C5 | C2×C22⋊D5 | semidirect |
| 156. Dic5 | C2×D20 | semidirect |
| 172. C2×C5 | #4020 | semidirect |
| 173. C2×C5 | #4086 | semidirect |
| 194. C2×C4 | #6038 | semidirect |
| 197. C5 | C2×#4020 | semidirect |
| 198. C5 | C2×#4086 | semidirect |
| 209. C4 | C2×#6038 | semidirect |
| 212. C2 | #11717029 | 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×C4×C5×Dic5 | 2 |
| #11717029 | 2 |
| C2×#4086 | 5 |
| C2×#4020 | 5 |