Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
172 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 32 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 | D5×#1044 |
| commutator, Fitting, socle | C2×C53 | C2×C4 |
| prime radical, cosocle | C2×C5×C5⋊D5 | C22 |
| hypocenter | C53 | C4⋊C4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. #92553 | C4 | semidirect |
| 8. C52×Dic5 | C4 | semidirect |
| 21. C53 | C4⋊C4 | semidirect |
| 36. C5×Dic5 | AGL(1,𝔽5) | semidirect |
| 60. C52 | #683 | semidirect |
| 61. C52 | C4⋊AGL(1,𝔽5) | semidirect |
| 76. Dic5 | #1044 | semidirect |
| 95. C5 | #87825 | semidirect |
| 96. C5 | C4⋊#1044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92560 | 2 |
| C2×C5×#1044 | 2 |
| Dic5×C5⋊D5 | 2 |
| C4⋊#1044 | 5 |
| #87825 | 5 |