Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1560 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1560 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×C22⋊(C5⋊D5) | C2 | semidirect |
| 3. C22×#6038 | C2 | semidirect |
| 4. C2×C5×C22⋊Dic5 | C2 | semidirect |
| 5. #11717095 | C2 | direct (N × H) |
| 6. C2×#87778 | C2 | semidirect |
| 8. C23×C5⋊D5 | C22 | semidirect |
| 12. C23×C5×D5 | C22 | semidirect |
| 14. C2×C22⋊(C5⋊D5) | C22 | semidirect |
| 15. C22×#1039 | C22 | semidirect |
| 16. C22×C5×Dic5 | C22 | semidirect |
| 18. C2×#6038 | C22 | semidirect |
| 19. C5×C22⋊Dic5 | C22 | semidirect |
| 20. #87778 | C22 | semidirect |
| 24. C23×C52 | D4 | semidirect |
| 29. C22×C5⋊D5 | C23 | semidirect |
| 35. C22×C5×D5 | D4 | semidirect |
| 39. C2×#1039 | C23 | semidirect |
| 41. C2×C5×Dic5 | C23 | semidirect |
| 44. C24×D5 | D5 | semidirect |
| 53. C2×C22⋊Dic5 | D5 | semidirect |
| 60. C22×C52 | C2×D4 | semidirect |
| 69. C2×C5×D5 | C2×D4 | semidirect |
| 85. C23×D5 | C2×D5 | semidirect |
| 98. C22×Dic5 | C2×D5 | semidirect |
| 103. C22⋊Dic5 | C2×D5 | semidirect |
| 107. C2×C52 | #120 | semidirect |
| 125. C23×C5 | D20 | semidirect |
| 126. C23×C5 | C22⋊D5 | semidirect |
| 145. C22×D5 | C22⋊D5 | semidirect |
| 160. C2×Dic5 | C22×D5 | semidirect |
| 168. C52 | C2×#120 | semidirect |
| 185. C22×C5 | C2×D20 | semidirect |
| 189. C22×C5 | C2×C22⋊D5 | semidirect |
| 205. C2×D5 | C2×C22⋊D5 | semidirect |
| 232. C2×C5 | #4028 | semidirect |
| 233. C2×C5 | #4099 | semidirect |
| 253. C23 | #6038 | semidirect |
| 263. C5 | C2×#4028 | semidirect |
| 264. C5 | C2×#4099 | semidirect |
| 276. C22 | C2×#6038 | semidirect |
| 284. C2 | #11717095 | 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×C22⋊(C5⋊D5) | 2 |
| C22×#6038 | 2 |
| C2×C5×C22⋊Dic5 | 2 |
| #11717095 | 2 |
| C2×#87778 | 2 |
| C2×#4099 | 5 |
| C2×#4028 | 5 |