Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
624 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D5×C5⋊D5 |
| commutator, socle, cosocle | C2×C53 | C23 |
| Fitting | C4×C53 | C22 |
| hypercenter | C4 | D5×C5⋊D5 |
| hypocenter | C53 | C2×D4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D5×C5⋊D5 | C2 | semidirect |
| 2. C4⋊(C5⋊(C5⋊D5)) | C2 | semidirect |
| 3. C5×C4⋊(C5⋊D5) | C2 | semidirect |
| 4. C4×C52×D5 | C2 | semidirect |
| 5. #11758754 | C2 | semidirect |
| 6. C2×C5⋊(C5⋊D5) | C22 | semidirect |
| 7. C2×C5×C5⋊D5 | C22 | semidirect |
| 10. C4×C53 | C22 | semidirect |
| 11. C52×Dic5 | C22 | semidirect |
| 17. C52×D5 | D4 | semidirect |
| 25. C4⋊(C5⋊D5) | D5 | direct (N × H) |
| 27. C4×C5×D5 | D5 | semidirect |
| 29. C53 | C2×D4 | semidirect |
| 35. C2×C5⋊D5 | C2×D5 | semidirect |
| 41. C4×C52 | C2×D5 | semidirect |
| 42. C4×C52 | C2×D5 | semidirect |
| 43. C5×Dic5 | C2×D5 | semidirect |
| 55. C5×D5 | D20 | semidirect |
| 66. C4×D5 | C5⋊D5 | semidirect |
| 68. C52 | C2×D20 | semidirect |
| 69. C52 | D4×D5 | semidirect |
| 81. C4×C5 | D52 | semidirect |
| 82. C4×C5 | C2×C5⋊D5 | semidirect |
| 83. Dic5 | C2×C5⋊D5 | semidirect |
| 94. D5 | C4⋊(C5⋊D5) | direct (N × H) |
| 101. C5 | D5×D20 | semidirect |
| 102. C5 | C2×C4⋊(C5⋊D5) | semidirect |
| 108. C4 | D5×C5⋊D5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×C5⋊D5 | 2 |
| C4⋊(C5⋊(C5⋊D5)) | 2 |
| C5×C4⋊(C5⋊D5) | 2 |
| C4×C52×D5 | 2 |
| #11758754 | 2 |
| C2×C4⋊(C5⋊D5) | 5 |
| D5×D20 | 5 |