Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
180 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | #1042 |
| commutator, hypocenter | C52 | C2×C5×C8 |
| Frattini | C2 | C2×C5×#1042 |
| Fitting, socle, prime radical | C22×C53 | C4 |
| cosocle | C5×Dic5 | C22×C5 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#6032 | C2 | direct (N × H) |
| 6. C2×#6032 | C5 | direct (N × H) |
| 9. C2×C53 | C8 | semidirect |
| 15. #6032 | C2×C5 | direct (N × H) |
| 18. C53 | C2×C8 | semidirect |
| 45. C2×C52 | #168 | semidirect |
| 46. C2×C52 | C5×C8 | semidirect |
| 47. C2×C52 | #170 | semidirect |
| 62. C52 | C2×#168 | semidirect |
| 63. C52 | C2×C5×C8 | semidirect |
| 64. C52 | C2×#170 | semidirect |
| 89. C2×C5 | C5×#168 | semidirect |
| 90. C2×C5 | C5×#170 | semidirect |
| 91. C2×C5 | #6032 | direct (N × H) |
| 101. C5 | C2×C5×#168 | semidirect |
| 102. C5 | C2×C5×#170 | semidirect |
| 103. C5 | C2×#6032 | direct (N × H) |
| 107. C2 | C5×#6032 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×Dic5 | 2 |
| C5×#6032 | 2 |
| C2×#6032 | 5 |
| C2×C5×#170 | 5 |
| C2×C5×#168 | 5 |