Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
984 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 192 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 | C24×C52 | C22 |
| socle | C23×C52 | C23 |
| hypercenter | C24 | D52 |
| hypocenter | C52 | C2×#121 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C5×C22⋊D5 | C2 | semidirect |
| 2. C22×C5×C22⋊D5 | C2 | semidirect |
| 3. C22×#6037 | C2 | semidirect |
| 4. C22×D5×Dic5 | C2 | semidirect |
| 5. C2×C22⋊#1039 | C2 | semidirect |
| 6. #11717088 | C2 | direct (N × H) |
| 7. C2×#87780 | C2 | semidirect |
| 8. C2×#87778 | C2 | semidirect |
| 16. C2×C5×C22⋊D5 | C22 | semidirect |
| 17. C2×C5×C22⋊D5 | C22 | semidirect |
| 21. C2×#6037 | C22 | semidirect |
| 23. C2×D5×Dic5 | C22 | semidirect |
| 24. C22⋊#1039 | C22 | semidirect |
| 25. #87780 | C22 | semidirect |
| 26. #87778 | C22 | semidirect |
| 39. C22×C5×D5 | D4 | semidirect |
| 49. C2×C5×Dic5 | D4 | semidirect |
| 58. C22×C22⋊D5 | D5 | semidirect |
| 59. C22×C22⋊D5 | D5 | semidirect |
| 86. C2×C5×D5 | C2×D4 | semidirect |
| 90. C5×Dic5 | C2×D4 | semidirect |
| 110. C2×C22⋊D5 | C2×D5 | semidirect |
| 111. C2×C22⋊D5 | C2×D5 | semidirect |
| 133. C2×C52 | #121 | semidirect |
| 167. C22×D5 | C22⋊D5 | semidirect |
| 194. C2×Dic5 | C22⋊D5 | semidirect |
| 206. C52 | C2×#121 | semidirect |
| 246. C2×D5 | C2×C22⋊D5 | semidirect |
| 256. Dic5 | C2×C22⋊D5 | semidirect |
| 284. C2×C5 | #4084 | semidirect |
| 285. C2×C5 | #4085 | semidirect |
| 320. C5 | C2×#4084 | semidirect |
| 321. C5 | C2×#4085 | semidirect |
| 345. C2 | #11717088 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C22⋊D5 | 2 |
| C22×#6037 | 2 |
| C22×D5×Dic5 | 2 |
| C2×C22⋊#1039 | 2 |
| #11717088 | 2 |
| C2×#87780 | 2 |
| C2×#87778 | 2 |
| C2×#4085 | 5 |
| C2×#4084 | 5 |