Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
256 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
| prime radical | C2×C52×D5 | C22 |
| hypocenter | C53 | C2×Q8 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11758758 | C2 | semidirect |
| 2. #11758755 | C2 | semidirect |
| 4. C5×#6039 | C2 | semidirect |
| 14. C52×D5 | Q8 | semidirect |
| 25. #6039 | D5 | direct (N × H) |
| 29. C53 | C2×Q8 | semidirect |
| 58. C5×D5 | Dic10 | semidirect |
| 76. C52 | C2×Dic10 | semidirect |
| 77. C52 | Q8×D5 | semidirect |
| 105. D5 | #6039 | direct (N × H) |
| 114. C5 | D5×Dic10 | semidirect |
| 115. C5 | C2×#6039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11758758 | 2 |
| #11758755 | 2 |
| D5×#1039 | 2 |
| C5×#6039 | 2 |
| C5×D5×Dic5 | 2 |
| C2×#6039 | 5 |
| D5×Dic10 | 5 |