Finite Group DatabasebetaFinite Group DatabasebetaOrder 1800.
136 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D3×D15 |
| commutator, cosocle | C2×C32×C5 | C22×C5 |
| Frattini | C2 | C5×D3×D15 |
| Fitting, socle, prime radical | C2×C32×C52 | C22 |
| hypocenter | C32×C5 | C5×Q8 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C2×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. #67153 | C5 | direct (N × H) |
| 16. C32×C52 | Q8 | semidirect |
| 39. C3×C52 | Dic6 | semidirect |
| 40. C3×C52 | Dic6 | semidirect |
| 60. C32×C5 | Dic10 | semidirect |
| 61. C32×C5 | C5×Q8 | semidirect |
| 76. C52 | #627 | semidirect |
| 92. C3×C5 | #1204 | semidirect |
| 93. C3×C5 | C5×Dic6 | semidirect |
| 94. C3×C5 | C5×Dic6 | semidirect |
| 95. C3×C5 | Dic30 | semidirect |
| 106. C32 | C5×Dic10 | semidirect |
| 112. C5 | C5×#627 | semidirect |
| 113. C5 | #67153 | direct (N × H) |
| 118. C3 | C5×#1204 | semidirect |
| 119. C3 | C5×Dic30 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C3⋊Dic15 | 2 |
| C3×C5×Dic15 | 2 |
| C3×C52×Dic3 | 2 |
| C5×Dic30 | 3 |
| C5×#1204 | 3 |
| #67153 | 5 |
| C5×#627 | 5 |