Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
416 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D53 |
| commutator, Fitting, socle, cosocle | C2×C53 | C23 |
| hypocenter | C53 | C2×D4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D5×C5⋊D5 | C2 | semidirect |
| 2. #11758757 | C2 | semidirect |
| 3. #11758751 | C2 | semidirect |
| 4. C5×#6038 | C2 | semidirect |
| 5. C5×#6037 | C2 | semidirect |
| 7. C2×C5×C5⋊D5 | C22 | semidirect |
| 8. C2×C52×D5 | C22 | semidirect |
| 10. C5×#1039 | C22 | semidirect |
| 11. C52×Dic5 | C22 | semidirect |
| 15. C5⋊(C5⋊D5) | D4 | semidirect |
| 27. #6038 | D5 | semidirect |
| 29. #6037 | D5 | semidirect |
| 32. C53 | C2×D4 | semidirect |
| 40. C2×C5⋊D5 | C2×D5 | semidirect |
| 45. C2×C5×D5 | C2×D5 | semidirect |
| 46. C2×C5×D5 | C2×D5 | semidirect |
| 51. #1039 | C2×D5 | semidirect |
| 55. C5×Dic5 | C2×D5 | semidirect |
| 93. C52 | D4×D5 | semidirect |
| 94. C52 | D4×D5 | semidirect |
| 111. C2×D5 | D52 | semidirect |
| 117. Dic5 | D52 | semidirect |
| 145. C5 | #87877 | semidirect |
| 146. C5 | #87886 | 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 |
| #11758757 | 2 |
| #11758751 | 2 |
| C5×#6038 | 2 |
| C5×#6037 | 2 |
| #87886 | 5 |
| #87877 | 5 |