Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
276 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×#1042 |
| commutator, hypocenter | C53 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C53 | C2×C4 |
| prime radical | C2×C5×D52 | C2 |
| cosocle | C52×D5 | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#92559 | C2 | semidirect |
| 3. C2×C5×#1042 | C2 | semidirect |
| 4. D5×#1042 | C2 | direct (N × H) |
| 5. C2×C5×C5⋊D5 | C4 | semidirect |
| 6. C2×C52×D5 | C4 | semidirect |
| 8. C5×D52 | C4 | semidirect |
| 10. #92559 | C22 | semidirect |
| 11. C5×#1042 | C22 | semidirect |
| 15. C2×C53 | C2×C4 | semidirect |
| 16. C5×C5⋊D5 | C2×C4 | semidirect |
| 17. C52×D5 | C2×C4 | semidirect |
| 18. C52×D5 | C2×C4 | semidirect |
| 27. C2×#1042 | D5 | direct (N × H) |
| 33. C53 | C22×C4 | semidirect |
| 36. C2×C5⋊D5 | Dic5 | semidirect |
| 46. C2×C5×D5 | Dic5 | semidirect |
| 47. C2×C5×D5 | AGL(1,𝔽5) | semidirect |
| 50. D52 | Dic5 | semidirect |
| 55. #1042 | C2×D5 | direct (N × H) |
| 69. C2×C52 | C4×D5 | semidirect |
| 70. C2×C52 | C2×Dic5 | semidirect |
| 71. C2×C52 | C2×AGL(1,𝔽5) | semidirect |
| 72. C5⋊D5 | C2×Dic5 | semidirect |
| 79. C5×D5 | C4×D5 | semidirect |
| 80. C5×D5 | C2×Dic5 | semidirect |
| 81. C5×D5 | C2×Dic5 | semidirect |
| 82. C5×D5 | C2×AGL(1,𝔽5) | semidirect |
| 102. C52 | C2×C4×D5 | semidirect |
| 103. C52 | C22×Dic5 | semidirect |
| 104. C52 | C22×AGL(1,𝔽5) | semidirect |
| 121. C2×D5 | #1042 | direct (N × H) |
| 145. C2×C5 | D5×Dic5 | semidirect |
| 146. C2×C5 | D5×AGL(1,𝔽5) | semidirect |
| 147. C2×C5 | C2×#1042 | semidirect |
| 151. D5 | D5×Dic5 | semidirect |
| 152. D5 | C2×#1042 | direct (N × H) |
| 162. C5 | C2×D5×Dic5 | semidirect |
| 163. C5 | C2×D5×AGL(1,𝔽5) | semidirect |
| 164. C5 | C22×#1042 | semidirect |
| 176. C2 | D5×#1042 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D52 | 2 |
| C2×#92559 | 2 |
| C2×C5×#1042 | 2 |
| D5×#1042 | 2 |
| C22×#1042 | 5 |
| C2×D5×AGL(1,𝔽5) | 5 |
| C2×D5×Dic5 | 5 |