Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1456 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1456 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 | C24×C52 | C22 |
| socle | C23×C52 | C23 |
| hypercenter | C24 | D52 |
| hypocenter | C52 | C2×#120 |
| 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. C24×C5×D5 | C2 | semidirect |
| 2. C22×C5×C22⋊D5 | C2 | semidirect |
| 3. C22×#6037 | C2 | semidirect |
| 4. C2×C22⋊#1039 | C2 | semidirect |
| 5. #11717094 | C2 | direct (N × H) |
| 6. C2×#87778 | C2 | semidirect |
| 11. C23×C5×D5 | C22 | semidirect |
| 12. C23×C5×D5 | C22 | semidirect |
| 13. C22×#1039 | C22 | semidirect |
| 15. C2×C5×C22⋊D5 | C22 | semidirect |
| 16. C22×C5×Dic5 | C22 | semidirect |
| 18. C2×#6037 | C22 | semidirect |
| 19. C22⋊#1039 | C22 | semidirect |
| 20. #87778 | C22 | semidirect |
| 24. C23×C52 | D4 | semidirect |
| 34. C22×C5×D5 | D4 | semidirect |
| 36. C22×C5×D5 | C23 | semidirect |
| 38. C2×#1039 | C23 | semidirect |
| 41. C2×C5×Dic5 | C23 | semidirect |
| 44. C24×D5 | D5 | semidirect |
| 48. C22×C22⋊D5 | D5 | semidirect |
| 60. C22×C52 | C2×D4 | semidirect |
| 69. C2×C5×D5 | C2×D4 | semidirect |
| 83. C23×D5 | C2×D5 | semidirect |
| 84. C23×D5 | C2×D5 | semidirect |
| 93. C2×C22⋊D5 | C2×D5 | semidirect |
| 97. C22×Dic5 | C2×D5 | semidirect |
| 105. C2×C52 | #120 | semidirect |
| 126. C23×C5 | C22⋊D5 | semidirect |
| 127. C23×C5 | C22⋊D5 | semidirect |
| 139. C22×D5 | C22⋊D5 | semidirect |
| 141. C22×D5 | C22×D5 | semidirect |
| 155. C2×Dic5 | C22×D5 | semidirect |
| 162. C52 | C2×#120 | semidirect |
| 185. C22×C5 | C2×C22⋊D5 | semidirect |
| 186. C22×C5 | C2×C22⋊D5 | semidirect |
| 196. C2×D5 | C2×C22⋊D5 | semidirect |
| 224. C2×C5 | #4083 | semidirect |
| 225. C2×C5 | #4099 | semidirect |
| 243. C23 | #6037 | semidirect |
| 253. C5 | C2×#4083 | semidirect |
| 254. C5 | C2×#4099 | semidirect |
| 266. C22 | C2×#6037 | semidirect |
| 274. C2 | #11717094 | 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×C5×C22⋊D5 | 2 |
| C22×#6037 | 2 |
| C2×C22⋊#1039 | 2 |
| #11717094 | 2 |
| C2×#87778 | 2 |
| C2×#4099 | 5 |
| C2×#4083 | 5 |