Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
196 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 31 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 | #11758789 |
| commutator, Fitting, socle | C2×C53 | C2×C4 |
| prime radical | C2×#92566 | C2 |
| cosocle | C2×C5×C5⋊D5 | C22 |
| hypocenter | C53 | C22⋊C4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#92561 | C2 | semidirect |
| 3. C2×C5×#1044 | C2 | semidirect |
| 4. C2×C5×C5⋊D5 | C4 | semidirect |
| 18. C2×#1044 | D5 | semidirect |
| 23. C53 | C22⋊C4 | semidirect |
| 24. C2×C5⋊D5 | AGL(1,𝔽5) | semidirect |
| 67. C52 | #685 | semidirect |
| 68. C52 | C22⋊AGL(1,𝔽5) | semidirect |
| 107. C5 | (C2×AGL(1,𝔽5))⋊D5 | semidirect |
| 108. C5 | #87831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92566 | 2 |
| C2×#92561 | 2 |
| C2×C5×#1044 | 2 |
| #87831 | 5 |
| (C2×AGL(1,𝔽5))⋊D5 | 5 |