Finite Group DatabasebetaFinite Group DatabasebetaOrder 3600.
840 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 155 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 | #11744719 |
| commutator, cosocle | C2×C32×C52 | C23 |
| Frattini | C2 | C2×#11744719 |
| Fitting, socle | C22×C32×C52 | C22 |
| hypocenter | C32×C52 | C2×D4 |
| LCS | G ▷ C2×C32×C52 ▷ C32×C52 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C32×C5⋊D5 | C2 | semidirect |
| 2. C22×C5×C3⋊D15 | C2 | semidirect |
| 3. C2×C5×C3⋊Dic15 | C2 | semidirect |
| 4. #14268269 | C2 | direct (N × H) |
| 8. C2×C5×C3⋊D15 | C22 | semidirect |
| 10. C2×C32×C5⋊D5 | C22 | semidirect |
| 11. C5×C3⋊Dic15 | C22 | semidirect |
| 15. C22×C3×C5⋊D5 | D3 | semidirect |
| 18. C2×C32×C52 | D4 | semidirect |
| 23. C22×C3⋊D15 | D5 | semidirect |
| 28. C2×C3⋊Dic15 | D5 | semidirect |
| 36. C2×C3×C5⋊D5 | C2×D3 | semidirect |
| 40. C32×C52 | C2×D4 | semidirect |
| 41. C22×C5⋊D5 | C3⋊D3 | semidirect |
| 49. C2×C3⋊D15 | C2×D5 | semidirect |
| 59. C3⋊Dic15 | C2×D5 | semidirect |
| 61. C2×C3×C52 | #67 | semidirect |
| 77. C2×C5⋊D5 | C2×C3⋊D3 | semidirect |
| 83. C2×C32×C5 | D20 | semidirect |
| 84. C2×C32×C5 | C22⋊D5 | semidirect |
| 95. C3×C52 | C2×#67 | semidirect |
| 116. C2×C52 | #638 | semidirect |
| 122. C32×C5 | C2×D20 | semidirect |
| 123. C32×C5 | C2×C22⋊D5 | semidirect |
| 141. C2×C3×C5 | #1201 | semidirect |
| 142. C2×C3×C5 | #1202 | semidirect |
| 151. C52 | C2×#638 | semidirect |
| 173. C2×C32 | #6038 | semidirect |
| 178. C3×C5 | C2×#1201 | semidirect |
| 179. C3×C5 | C2×#1202 | semidirect |
| 189. C2×C5 | #67138 | semidirect |
| 190. C2×C5 | #67139 | semidirect |
| 198. C32 | C2×#6038 | semidirect |
| 204. C2×C3 | #10597127 | semidirect |
| 208. C5 | C2×#67138 | semidirect |
| 209. C5 | C2×#67139 | semidirect |
| 216. C3 | C2×#10597127 | semidirect |
| 219. C2 | #14268269 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C5⋊D5 | 2 |
| C22×C5×C3⋊D15 | 2 |
| C2×C5×C3⋊Dic15 | 2 |
| #14268269 | 2 |
| C2×#10597127 | 3 |
| C2×#67139 | 5 |
| C2×#67138 | 5 |