Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
196 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 40 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×#1042 |
| commutator, Fitting, socle | C2×C53 | C2×C4 |
| prime radical | C2×C5×D52 | C2 |
| cosocle | C2×C52×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×#92559 | C2 | semidirect |
| 3. C2×C5×#1042 | C2 | semidirect |
| 4. C2×C5×C5⋊D5 | C4 | semidirect |
| 5. C2×C52×D5 | C4 | semidirect |
| 25. C2×#1042 | D5 | semidirect |
| 29. C53 | C22⋊C4 | semidirect |
| 32. C2×C5⋊D5 | Dic5 | semidirect |
| 42. C2×C5×D5 | Dic5 | semidirect |
| 43. C2×C5×D5 | AGL(1,𝔽5) | semidirect |
| 95. C52 | #685 | semidirect |
| 96. C52 | C22⋊Dic5 | semidirect |
| 97. C52 | C22⋊AGL(1,𝔽5) | semidirect |
| 114. C2×D5 | #1042 | semidirect |
| 154. C5 | #87778 | semidirect |
| 155. C5 | (C2×AGL(1,𝔽5))⋊D5 | semidirect |
| 156. C5 | C22⋊#1042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D52 | 2 |
| C2×#92559 | 2 |
| C2×C5×#1042 | 2 |
| C22⋊#1042 | 5 |
| (C2×AGL(1,𝔽5))⋊D5 | 5 |
| #87778 | 5 |