Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
816 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D5×C5⋊D5 |
| commutator, cosocle | C2×C53 | C23 |
| Frattini | C2 | C2×D5×C5⋊D5 |
| Fitting, socle | C22×C53 | C22 |
| hypocenter | C53 | C2×D4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C5⋊(C5⋊D5) | C2 | semidirect |
| 2. C22×C5×C5⋊D5 | C2 | semidirect |
| 3. C2×C52×Dic5 | C2 | semidirect |
| 4. #11758754 | C2 | direct (N × H) |
| 7. C2×C5⋊(C5⋊D5) | C22 | semidirect |
| 9. C2×C5×C5⋊D5 | C22 | semidirect |
| 10. C52×Dic5 | C22 | semidirect |
| 13. C2×C53 | D4 | semidirect |
| 20. C22×C5⋊D5 | D5 | semidirect |
| 24. C2×C5×Dic5 | D5 | semidirect |
| 26. C53 | C2×D4 | semidirect |
| 37. C2×C5⋊D5 | C2×D5 | semidirect |
| 41. C5×Dic5 | C2×D5 | semidirect |
| 46. C2×C52 | D20 | semidirect |
| 47. C2×C52 | C22⋊D5 | semidirect |
| 62. C2×Dic5 | C5⋊D5 | semidirect |
| 65. C52 | C2×D20 | semidirect |
| 66. C52 | C2×C22⋊D5 | semidirect |
| 81. Dic5 | C2×C5⋊D5 | semidirect |
| 86. C2×C5 | #6038 | semidirect |
| 87. C2×C5 | C4⋊(C5⋊D5) | semidirect |
| 99. C5 | C2×#6038 | semidirect |
| 100. C5 | C2×C4⋊(C5⋊D5) | semidirect |
| 109. C2 | #11758754 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5⋊(C5⋊D5) | 2 |
| C22×C5×C5⋊D5 | 2 |
| C2×C52×Dic5 | 2 |
| #11758754 | 2 |
| C2×C4⋊(C5⋊D5) | 5 |
| C2×#6038 | 5 |