Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
248 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 94 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×#4047 | C2 | semidirect |
| 3. C52×#97 | C2 | semidirect |
| 4. C5×#3951 | C2 | semidirect |
| 5. C5×#3937 | C2 | semidirect |
| 11. C5×Dic20 | C4 | semidirect |
| 12. C5×D40 | C4 | semidirect |
| 13. C5×#677 | C4 | semidirect |
| 17. #65006 | C5 | direct (N × H) |
| 31. #4047 | C2×C5 | semidirect |
| 35. C5×#97 | D5 | semidirect |
| 36. C5×#97 | C2×C5 | semidirect |
| 37. #3951 | C2×C5 | semidirect |
| 38. #3937 | C2×C5 | semidirect |
| 63. Dic20 | C4×C5 | semidirect |
| 64. D40 | C4×C5 | semidirect |
| 65. #677 | C4×C5 | semidirect |
| 101. #97 | C5×D5 | semidirect |
| 102. C52 | #444 | semidirect |
| 148. C5 | #65006 | direct (N × H) |
| 149. C5 | C5×#444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4050 | 2 |
| C5×#4047 | 2 |
| C52×#97 | 2 |
| C5×#3951 | 2 |
| C5×#3937 | 2 |
| C5×#444 | 5 |
| #65006 | 5 |