Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
304 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 51 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 | C22 | #92566 |
| commutator | C2×C53 | C2×C4 |
| Fitting, socle, cosocle | C22×C53 | C22 |
| prime radical | C22×C5×C5⋊D5 | C2 |
| hypocenter | C53 | C22⋊C4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C5×#1039 | C2 | semidirect |
| 5. C2×C5×C5⋊D5 | C4 | semidirect |
| 15. C2×#1039 | D5 | semidirect |
| 19. C53 | C22⋊C4 | semidirect |
| 26. C2×C5⋊D5 | Dic5 | semidirect |
| 63. C52 | #685 | semidirect |
| 64. C52 | C22⋊Dic5 | semidirect |
| 102. C5 | #87778 | semidirect |
| 103. C5 | #87779 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C5⋊D5 | 2 |
| C2×C5×#1039 | 2 |
| #87779 | 5 |
| #87778 | 5 |