Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
272 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C5 | C2×D52 |
| commutator, cosocle | C2×C52 | C23×C5 |
| Frattini | C2 | C2×C5×D52 |
| Fitting | C4×C53 | C22 |
| socle | C2×C53 | C23 |
| hypercenter | C4×C5 | D52 |
| hypocenter | C52 | C5×#41 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2×C5 ◁ C4×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#6045 | C2 | semidirect |
| 2. C52×D20 | C2 | semidirect |
| 3. C4×C52×D5 | C2 | semidirect |
| 4. C5×#6037 | C2 | semidirect |
| 5. C5×D5×Dic5 | C2 | semidirect |
| 13. #87870 | C5 | direct (N × H) |
| 19. #6045 | C2×C5 | semidirect |
| 24. C5×D20 | D5 | semidirect |
| 25. C5×D20 | C2×C5 | semidirect |
| 28. C4×C5×D5 | D5 | semidirect |
| 29. C4×C5×D5 | C2×C5 | semidirect |
| 33. #6037 | C2×C5 | semidirect |
| 34. D5×Dic5 | C2×C5 | semidirect |
| 35. C53 | #41 | semidirect |
| 89. D20 | C5×D5 | semidirect |
| 91. C4×D5 | C5×D5 | semidirect |
| 99. C52 | #709 | semidirect |
| 100. C52 | #711 | semidirect |
| 101. C52 | C5×#41 | semidirect |
| 150. C5 | #87870 | direct (N × H) |
| 151. C5 | C5×#709 | semidirect |
| 152. C5 | C5×#711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#6045 | 2 |
| C52×D20 | 2 |
| C4×C52×D5 | 2 |
| C5×#6037 | 2 |
| C5×D5×Dic5 | 2 |
| C5×#711 | 5 |
| C5×#709 | 5 |
| #87870 | 5 |