Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
512 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C52 | C2×D5 |
| commutator, cosocle | C2×C5 | C23×C52 |
| Frattini | C2 | C22×C52×D5 |
| Fitting | C2×C4×C53 | C2 |
| socle | C2×C53 | C23 |
| hypercenter | C2×C4×C52 | D5 |
| hypocenter | C5 | C52×#41 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C4×C52 ◁ C2×C4×C52 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4×C53 | C2 | semidirect |
| 2. C52×C22⋊D5 | C2 | semidirect |
| 3. C52×D20 | C2 | semidirect |
| 4. C4×C52×D5 | C2 | semidirect |
| 5. C52×Dic10 | C2 | semidirect |
| 12. C5×#709 | C5 | direct (N × H) |
| 21. C2×C4×C52 | D5 | semidirect |
| 22. C2×C4×C52 | C2×C5 | semidirect |
| 23. C5×C22⋊D5 | C2×C5 | semidirect |
| 24. C5×D20 | C2×C5 | semidirect |
| 25. C4×C5×D5 | C2×C5 | semidirect |
| 26. C5×Dic10 | C2×C5 | semidirect |
| 27. C53 | #41 | semidirect |
| 42. #709 | C52 | direct (N × H) |
| 56. C2×C4×C5 | C5×D5 | semidirect |
| 57. C2×C4×C5 | C2×C52 | semidirect |
| 58. C22⋊D5 | C2×C52 | semidirect |
| 59. D20 | C2×C52 | semidirect |
| 60. C4×D5 | C2×C52 | semidirect |
| 61. Dic10 | C2×C52 | semidirect |
| 63. C52 | #709 | direct (N × H) |
| 64. C52 | C5×#41 | semidirect |
| 91. C2×C4 | C52×D5 | semidirect |
| 93. C5 | C5×#709 | direct (N × H) |
| 94. C5 | C52×#41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C53 | 2 |
| C52×C22⋊D5 | 2 |
| C52×D20 | 2 |
| C4×C52×D5 | 2 |
| C52×Dic10 | 2 |
| C52×#41 | 5 |
| C5×#709 | 5 |