Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
656 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 94 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 | D5×C5⋊D5 |
| 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 |
| 3. C2×C52×Dic5 | C2 | semidirect |
| 7. C2×C5⋊(C5⋊D5) | C4 | semidirect |
| 20. C2×#1039 | D5 | semidirect |
| 22. C2×C5×Dic5 | D5 | semidirect |
| 23. C53 | C22⋊C4 | semidirect |
| 60. C2×Dic5 | C5⋊D5 | semidirect |
| 62. C52 | #685 | semidirect |
| 63. C52 | #685 | semidirect |
| 97. C5 | #87779 | semidirect |
| 98. C5 | #87808 | 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 |
| C2×C52×Dic5 | 2 |
| #87808 | 5 |
| #87779 | 5 |