Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
246 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 1. C5×#4088 | C2 | semidirect |
| 2. C2×C5×#688 | C2 | semidirect |
| 4. C5×#4053 | C2 | semidirect |
| 5. C52×#101 | C2 | semidirect |
| 6. C5×#3955 | C2 | semidirect |
| 7. C5×#3954 | C2 | semidirect |
| 24. #65043 | C5 | direct (N × H) |
| 45. #4088 | C2×C5 | semidirect |
| 46. C2×#688 | C2×C5 | semidirect |
| 48. #4053 | C2×C5 | semidirect |
| 51. C5×#101 | D5 | semidirect |
| 52. C5×#101 | C2×C5 | semidirect |
| 54. #3955 | C2×C5 | semidirect |
| 55. #3954 | C2×C5 | semidirect |
| 145. #101 | C5×D5 | semidirect |
| 147. C52 | #471 | semidirect |
| 210. C5 | #65043 | direct (N × H) |
| 211. C5 | C5×#471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4088 | 2 |
| C2×C5×#688 | 2 |
| C5×#4054 | 2 |
| C5×#4053 | 2 |
| C52×#101 | 2 |
| C5×#3955 | 2 |
| C5×#3954 | 2 |
| C5×#471 | 5 |
| #65043 | 5 |