Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
336 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 78 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×#4150 | C2 | semidirect |
| 2. C5×#4095 | C2 | semidirect |
| 3. C5×#4054 | C2 | semidirect |
| 4. C5×#4021 | C2 | semidirect |
| 5. C52×#104 | C2 | semidirect |
| 6. C5×#3956 | C2 | semidirect |
| 7. C5×#3937 | C2 | semidirect |
| 26. #65116 | C5 | direct (N × H) |
| 50. #4150 | C2×C5 | semidirect |
| 54. #4095 | C2×C5 | semidirect |
| 55. #4054 | C2×C5 | semidirect |
| 56. #4021 | C2×C5 | semidirect |
| 59. C5×#104 | D5 | semidirect |
| 60. C5×#104 | C2×C5 | semidirect |
| 62. #3956 | C2×C5 | semidirect |
| 63. #3937 | C2×C5 | semidirect |
| 174. #104 | C5×D5 | semidirect |
| 176. C52 | #454 | semidirect |
| 258. C5 | #65116 | direct (N × H) |
| 259. C5 | C5×#454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4150 | 2 |
| C5×#4095 | 2 |
| C5×#4054 | 2 |
| C5×#4021 | 2 |
| C52×#104 | 2 |
| C5×#3956 | 2 |
| C5×#3937 | 2 |
| C5×#454 | 5 |
| #65116 | 5 |