Subgroups — C₂×C₅×C₉×D₁₃₁ #37556063

Order 23580.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×D₁₃₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₉×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×D₁₃₁	C₃	1	1	yes	maximal, characteristic
4	C₅×C₉×C₁₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₉×D₁₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×D₁₃₁	C₂×C₃	1	2	yes	—
7	C₂×C₃×C₅×C₁₃₁	C₂×C₃	1	1	yes	characteristic
8	C₂×C₅×D₁₃₁	C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₉×D₁₃₁	C₂×C₅	1	2	yes	direct product factor
10	C₂×C₉×C₁₃₁	C₂×C₅	1	1	yes	characteristic, complemented
11	C₃×C₅×C₁₃₁	C₂²×C₃	1	1	yes	characteristic
12	C₂×C₃×D₁₃₁	C₃×C₅	1	1	yes	characteristic
13	C₂×C₅×C₁₃₁	C₂×C₉	1	1	yes	characteristic, complemented
14	C₅×D₁₃₁	C₂×C₉	1	2	yes	direct product factor
15	C₉×C₁₃₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₁₃₁	C₂×C₃×C₅	1	1	yes	characteristic
17	C₃×D₁₃₁	C₂×C₃×C₅	1	2	yes	—
18	C₅×C₁₃₁	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
19	C₂×D₁₃₁	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₁₃₁	C₂²×C₃×C₅	1	1	yes	characteristic
21	C₂×C₁₃₁	C₂×C₅×C₉	1	1	yes	characteristic, complemented
22	D₁₃₁	C₂×C₅×C₉	1	2	yes	direct product factor
23	C₂²×C₅×C₉	—	131	1	no	maximal, Hall
24	C₁₃₁	C₂²×C₅×C₉	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₅×C₉	—	131	2	no	—
26	C₂×C₅×C₉	D₁₃₁	1	1	yes	characteristic, direct product factor
27	C₂²×C₃×C₅	—	131	1	no	—
28	C₅×C₉	C₂×D₁₃₁	1	1	yes	characteristic, direct product factor, Hall
29	C₂²×C₉	—	131	1	no	Hall
30	C₂×C₃×C₅	—	131	2	no	—
31	C₂×C₃×C₅	C₃×D₁₃₁	1	1	yes	characteristic
32	C₂²×C₅	—	131	1	no	Hall
33	C₂×C₉	—	131	2	no	—
34	C₂×C₉	C₅×D₁₃₁	1	1	yes	characteristic, direct product factor
35	C₃×C₅	C₂×C₃×D₁₃₁	1	1	yes	characteristic
36	C₂²×C₃	—	131	1	no	—
37	C₂×C₅	—	131	2	no	—
38	C₂×C₅	C₉×D₁₃₁	1	1	yes	characteristic, direct product factor
39	C₉	C₂×C₅×D₁₃₁	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₃	—	131	2	no	—
41	C₂×C₃	C₃×C₅×D₁₃₁	1	1	yes	characteristic
42	C₅	C₂×C₉×D₁₃₁	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²	—	131	1	no	Sylow
44	C₃	C₂×C₃×C₅×D₁₃₁	1	1	yes	characteristic
45	C₂	—	131	2	no	—
46	C₂	C₅×C₉×D₁₃₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₉	D₁₃₁
commutator, hypocenter	C₁₃₁	C₂²×C₅×C₉
Frattini	C₃	C₂×C₃×C₅×D₁₃₁
Fitting	C₂×C₅×C₉×C₁₃₁	C₂
socle	C₂×C₃×C₅×C₁₃₁	C₂×C₃
prime radical	C₂×C₃×C₅×D₁₃₁	C₃
cosocle	C₃×C₁₃₁	C₂²×C₃×C₅
LCS	G ▷ C₁₃₁
UCS	C₁ ◁ C₂×C₅×C₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×D₁₃₁	C₂	direct (N × H)
2. C₂×C₅×C₉×C₁₃₁	C₂	semidirect
4. C₅×C₉×C₁₃₁	C₂²	semidirect
5. C₂×C₉×D₁₃₁	C₅	direct (N × H)
8. C₂×C₅×D₁₃₁	C₉	direct (N × H)
9. C₉×D₁₃₁	C₂×C₅	direct (N × H)
10. C₂×C₉×C₁₃₁	C₂×C₅	semidirect
13. C₂×C₅×C₁₃₁	C₂×C₉	semidirect
14. C₅×D₁₃₁	C₂×C₉	direct (N × H)
15. C₉×C₁₃₁	C₂²×C₅	semidirect
18. C₅×C₁₃₁	C₂²×C₉	semidirect
19. C₂×D₁₃₁	C₅×C₉	direct (N × H)
21. C₂×C₁₃₁	C₂×C₅×C₉	semidirect
22. D₁₃₁	C₂×C₅×C₉	direct (N × H)
24. C₁₃₁	C₂²×C₅×C₉	semidirect
26. C₂×C₅×C₉	D₁₃₁	direct (N × H)
28. C₅×C₉	C₂×D₁₃₁	direct (N × H)
34. C₂×C₉	C₅×D₁₃₁	direct (N × H)
38. C₂×C₅	C₉×D₁₃₁	direct (N × H)
39. C₉	C₂×C₅×D₁₃₁	direct (N × H)
42. C₅	C₂×C₉×D₁₃₁	direct (N × H)
46. C₂	C₅×C₉×D₁₃₁	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×C₉×D₁₃₁	2
C₂×C₅×C₉×C₁₃₁	2
C₂×C₃×C₅×D₁₃₁	3
C₂×C₉×D₁₃₁	5
C₂²×C₅×C₉	131

Subgroups — C2×C5×C9×D131 #37556063

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₉×D₁₃₁ #37556063