Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
358 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 90 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. C2×C5×Q8×D5 | C2 | semidirect |
| 2. C2×C5×#688 | C2 | semidirect |
| 3. C2×C5×#677 | C2 | semidirect |
| 5. C52×#103 | C2 | semidirect |
| 6. C5×#3952 | C2 | semidirect |
| 7. C5×#3942 | C2 | semidirect |
| 24. #65095 | C5 | direct (N × H) |
| 28. C52×Q8 | D4 | semidirect |
| 42. C5×Dic10 | D4 | semidirect |
| 46. C2×Q8×D5 | C2×C5 | semidirect |
| 50. C2×#688 | C2×C5 | semidirect |
| 51. C2×#677 | C2×C5 | semidirect |
| 55. C5×#103 | D5 | semidirect |
| 56. C5×#103 | C2×C5 | semidirect |
| 58. #3952 | C2×C5 | semidirect |
| 59. #3942 | C2×C5 | semidirect |
| 66. C2×C5×D5 | SD16 | semidirect |
| 123. C5×Q8 | D20 | semidirect |
| 124. C5×Q8 | C5×D4 | semidirect |
| 152. Dic10 | C5×D4 | semidirect |
| 163. #103 | C5×D5 | semidirect |
| 165. C52 | #448 | semidirect |
| 180. C2×D5 | C5×SD16 | semidirect |
| 231. Q8 | C5×D20 | semidirect |
| 246. C5 | #65095 | direct (N × H) |
| 247. C5 | C5×#448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×D5 | 2 |
| C2×C5×#688 | 2 |
| C2×C5×#677 | 2 |
| C5×#4041 | 2 |
| C52×#103 | 2 |
| C5×#3952 | 2 |
| C5×#3942 | 2 |
| C5×#448 | 5 |
| #65095 | 5 |