Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
280 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 46 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 | #41 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11758757 | C2 | semidirect |
| 2. Dic5×C5⋊D5 | C2 | semidirect |
| 3. D5×#1039 | C2 | semidirect |
| 4. C5×#6039 | C2 | semidirect |
| 5. C5×#6038 | C2 | semidirect |
| 21. #6039 | D5 | semidirect |
| 23. #6038 | D5 | semidirect |
| 30. C53 | #41 | semidirect |
| 81. C52 | #711 | semidirect |
| 82. C52 | #713 | semidirect |
| 123. C5 | #87871 | semidirect |
| 124. C5 | #87880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11758757 | 2 |
| Dic5×C5⋊D5 | 2 |
| D5×#1039 | 2 |
| C5×#6039 | 2 |
| C5×#6038 | 2 |
| #87880 | 5 |
| #87871 | 5 |