Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
172 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C5×#6032 | C2 | semidirect |
| 6. #87853 | C5 | direct (N × H) |
| 15. #6032 | C2×C5 | semidirect |
| 18. C53 | M16 | semidirect |
| 62. C52 | #681 | semidirect |
| 63. C52 | C5×M16 | semidirect |
| 64. C52 | #704 | semidirect |
| 101. C5 | C5×#681 | semidirect |
| 102. C5 | C5×#704 | semidirect |
| 103. C5 | #87853 | 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 |
| #87853 | 5 |
| C5×#704 | 5 |
| C5×#681 | 5 |