Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
296 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 296 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. #11758756 | C2 | semidirect |
| 2. #11758754 | C2 | semidirect |
| 3. #11758753 | C2 | semidirect |
| 4. #11758751 | C2 | semidirect |
| 5. C5×#6039 | C2 | semidirect |
| 6. C5×#6038 | C2 | semidirect |
| 7. C5×D5×Dic5 | C2 | semidirect |
| 31. #6039 | D5 | semidirect |
| 38. #6038 | D5 | semidirect |
| 45. D5×Dic5 | D5 | semidirect |
| 46. C53 | #41 | semidirect |
| 131. C52 | #709 | semidirect |
| 132. C52 | #711 | semidirect |
| 133. C52 | #713 | semidirect |
| 199. C5 | #87871 | semidirect |
| 200. C5 | #87874 | semidirect |
| 201. C5 | #87879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11758756 | 2 |
| #11758754 | 2 |
| #11758753 | 2 |
| #11758751 | 2 |
| C5×#6039 | 2 |
| C5×#6038 | 2 |
| C5×D5×Dic5 | 2 |
| #87879 | 5 |
| #87874 | 5 |
| #87871 | 5 |