Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
240 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 240 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, prime radical, cosocle | C22×C53 | C22 |
| hypocenter | C53 | C4⋊C4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C5×#1039 | C4 | semidirect |
| 18. C53 | C4⋊C4 | semidirect |
| 25. #1039 | Dic5 | semidirect |
| 58. C52 | #683 | semidirect |
| 59. C52 | C4⋊Dic5 | semidirect |
| 93. C5 | #87780 | semidirect |
| 94. C5 | #87781 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#1039 | 2 |
| #87781 | 5 |
| #87780 | 5 |