Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
512 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 86 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 | #41 |
| 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. C4⋊(C5⋊(C5⋊D5)) | C2 | semidirect |
| 2. C4×C5×C5⋊D5 | C2 | semidirect |
| 3. C52×Dic10 | C2 | semidirect |
| 4. #11758754 | C2 | semidirect |
| 5. #11758751 | C2 | semidirect |
| 22. C4×C5⋊D5 | D5 | semidirect |
| 24. C5×Dic10 | D5 | semidirect |
| 27. C53 | #41 | semidirect |
| 60. Dic10 | C5⋊D5 | semidirect |
| 62. C52 | #709 | semidirect |
| 63. C52 | #713 | semidirect |
| 91. C5 | #87874 | semidirect |
| 92. C5 | #87904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊(C5⋊(C5⋊D5)) | 2 |
| C4×C5×C5⋊D5 | 2 |
| C52×Dic10 | 2 |
| #11758754 | 2 |
| #11758751 | 2 |
| #87904 | 5 |
| #87874 | 5 |