Subgroups — C₂×C₃×C₃₁×C₅⋊D₅ #22604942

Order 9300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁×C₅⋊D₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅²×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×D₅×C₃₁	—	5	6	no	maximal
6	C₂×C₅²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃₁×C₅⋊D₅	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₅×C₃₁	D₅	1	6	yes	complemented
9	C₃×D₅×C₃₁	—	5	12	no	—
10	C₅²×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₅×C₃₁	—	5	6	no	—
12	C₃×C₅×C₃₁	C₂×D₅	1	6	yes	complemented
13	C₂²×C₃×C₃₁	—	25	1	no	Hall
14	C₂×C₅×C₃₁	C₃×D₅	1	6	yes	complemented
15	D₅×C₃₁	—	5	12	no	—
16	C₂×C₃×C₅⋊D₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₃₁	—	25	2	no	—
18	C₂×C₃×C₃₁	C₅⋊D₅	1	1	yes	characteristic, direct product factor
19	C₅×C₃₁	C₂×C₃×D₅	1	6	yes	complemented
20	C₂×C₃×C₅²	C₂×C₃₁	1	1	yes	characteristic, complemented
21	C₃×C₅⋊D₅	C₂×C₃₁	1	2	yes	direct product factor
22	C₂²×C₃₁	—	25	1	no	Hall
23	C₂×C₅⋊D₅	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₃₁	C₂×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₅²	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃₁	—	25	2	no	—
27	C₂×C₃₁	C₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor
28	C₂×C₃×D₅	—	5	6	no	—
29	C₂×C₅²	C₂×C₃×C₃₁	1	1	yes	characteristic, complemented
30	C₅⋊D₅	C₂×C₃×C₃₁	1	2	yes	direct product factor
31	C₃₁	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×C₃×C₅	D₅×C₃₁	1	6	yes	complemented
33	C₃×D₅	—	5	12	no	—
34	C₅²	C₂²×C₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
35	C₂×D₅	—	5	6	no	—
36	C₃×C₅	C₂×D₅×C₃₁	1	6	yes	complemented
37	C₂²×C₃	—	25	1	no	Hall
38	C₂×C₅	C₃×D₅×C₃₁	1	6	yes	complemented
39	D₅	—	5	12	no	—
40	C₂×C₃	—	25	2	no	—
41	C₂×C₃	C₃₁×C₅⋊D₅	1	1	yes	characteristic, direct product factor
42	C₅	C₂×C₃×D₅×C₃₁	1	6	yes	complemented
43	C₂²	—	25	1	no	Sylow
44	C₃	C₂×C₃₁×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	—	25	2	no	—
46	C₂	C₃×C₃₁×C₅⋊D₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₃₁	C₅⋊D₅
commutator, hypocenter	C₅²	C₂²×C₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₃₁	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₃×C₃₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×C₃₁×C₅⋊D₅	C₂	direct (N × H)
2. C₂×C₃×C₅²×C₃₁	C₂	semidirect
3. C₂×C₃₁×C₅⋊D₅	C₃	direct (N × H)
4. C₃×C₅²×C₃₁	C₂²	semidirect
6. C₂×C₅²×C₃₁	C₂×C₃	semidirect
7. C₃₁×C₅⋊D₅	C₂×C₃	direct (N × H)
8. C₂×C₃×C₅×C₃₁	D₅	semidirect
10. C₅²×C₃₁	C₂²×C₃	semidirect
12. C₃×C₅×C₃₁	C₂×D₅	semidirect
14. C₂×C₅×C₃₁	C₃×D₅	semidirect
16. C₂×C₃×C₅⋊D₅	C₃₁	direct (N × H)
18. C₂×C₃×C₃₁	C₅⋊D₅	direct (N × H)
19. C₅×C₃₁	C₂×C₃×D₅	semidirect
20. C₂×C₃×C₅²	C₂×C₃₁	semidirect
21. C₃×C₅⋊D₅	C₂×C₃₁	direct (N × H)
23. C₂×C₅⋊D₅	C₃×C₃₁	direct (N × H)
24. C₃×C₃₁	C₂×C₅⋊D₅	direct (N × H)
25. C₃×C₅²	C₂²×C₃₁	semidirect
27. C₂×C₃₁	C₃×C₅⋊D₅	direct (N × H)
29. C₂×C₅²	C₂×C₃×C₃₁	semidirect
30. C₅⋊D₅	C₂×C₃×C₃₁	direct (N × H)
31. C₃₁	C₂×C₃×C₅⋊D₅	direct (N × H)
32. C₂×C₃×C₅	D₅×C₃₁	semidirect
34. C₅²	C₂²×C₃×C₃₁	semidirect
36. C₃×C₅	C₂×D₅×C₃₁	semidirect
38. C₂×C₅	C₃×D₅×C₃₁	semidirect
41. C₂×C₃	C₃₁×C₅⋊D₅	direct (N × H)
42. C₅	C₂×C₃×D₅×C₃₁	semidirect
44. C₃	C₂×C₃₁×C₅⋊D₅	direct (N × H)
46. C₂	C₃×C₃₁×C₅⋊D₅	direct (N × H)

Subgroups — C2×C3×C31×C5⋊D5 #22604942

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₃₁×C₅⋊D₅ #22604942