Subgroups — C₂×C₅×D₉×C₁₃₁ #37556060

Order 23580.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₉×C₁₃₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₉×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₃×C₁₃₁	—	3	1	no	maximal
4	C₅×C₉×C₁₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₉×C₁₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₃×C₁₃₁	—	3	2	no	—
7	C₂×C₃×C₅×C₁₃₁	D₃	1	1	yes	characteristic
8	C₂²×C₅×C₁₃₁	—	9	1	no	Hall
9	D₉×C₁₃₁	C₂×C₅	1	2	yes	direct product factor
10	C₂×C₉×C₁₃₁	C₂×C₅	1	1	yes	characteristic, complemented
11	C₃×C₅×C₁₃₁	C₂×D₃	1	1	yes	characteristic
12	C₂×D₃×C₁₃₁	—	3	1	no	—
13	C₂×C₅×C₁₃₁	—	9	2	no	—
14	C₂×C₅×C₁₃₁	D₉	1	1	yes	characteristic, direct product factor
15	C₉×C₁₃₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₁₃₁	C₅×D₃	1	1	yes	characteristic
17	D₃×C₁₃₁	—	3	2	no	—
18	C₅×C₁₃₁	C₂×D₉	1	1	yes	characteristic, direct product factor, Hall
19	C₂²×C₁₃₁	—	9	1	no	Hall
20	C₃×C₁₃₁	C₂×C₅×D₃	1	1	yes	characteristic
21	C₂×C₁₃₁	—	9	2	no	—
22	C₂×C₁₃₁	C₅×D₉	1	1	yes	characteristic, direct product factor
23	C₂×C₅×D₉	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₁₃₁	C₂×C₅×D₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₅×C₉	C₂×C₁₃₁	1	1	yes	characteristic, complemented
26	C₅×D₉	C₂×C₁₃₁	1	2	yes	direct product factor
27	C₂×C₅×D₃	—	3	1	no	—
28	C₅×C₉	C₂²×C₁₃₁	1	1	yes	characteristic, complemented, Hall
29	C₂×D₉	C₅×C₁₃₁	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₃×C₅	D₃×C₁₃₁	1	1	yes	characteristic
31	C₅×D₃	—	3	2	no	—
32	C₂²×C₅	—	9	1	no	Hall
33	C₂×C₉	C₂×C₅×C₁₃₁	1	1	yes	characteristic, complemented
34	D₉	C₂×C₅×C₁₃₁	1	2	yes	direct product factor
35	C₃×C₅	C₂×D₃×C₁₃₁	1	1	yes	characteristic
36	C₂×D₃	—	3	1	no	—
37	C₂×C₅	—	9	2	no	—
38	C₂×C₅	D₉×C₁₃₁	1	1	yes	characteristic, direct product factor
39	C₉	C₂²×C₅×C₁₃₁	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃	C₅×D₃×C₁₃₁	1	1	yes	characteristic
41	D₃	—	3	2	no	—
42	C₅	C₂×D₉×C₁₃₁	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²	—	9	1	no	Sylow
44	C₃	C₂×C₅×D₃×C₁₃₁	1	1	yes	characteristic
45	C₂	—	9	2	no	—
46	C₂	C₅×D₉×C₁₃₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₃₁	D₉
commutator, cosocle, hypocenter	C₉	C₂²×C₅×C₁₃₁
Frattini	C₃	C₂×C₅×D₃×C₁₃₁
Fitting	C₂×C₅×C₉×C₁₃₁	C₂
socle	C₂×C₃×C₅×C₁₃₁	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₅×C₁₃₁

Complements

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

N	H ≅ G/N	type
1. C₅×D₉×C₁₃₁	C₂	direct (N × H)
2. C₂×C₅×C₉×C₁₃₁	C₂	semidirect
4. C₅×C₉×C₁₃₁	C₂²	semidirect
5. C₂×D₉×C₁₃₁	C₅	direct (N × H)
9. D₉×C₁₃₁	C₂×C₅	direct (N × H)
10. C₂×C₉×C₁₃₁	C₂×C₅	semidirect
14. C₂×C₅×C₁₃₁	D₉	direct (N × H)
15. C₉×C₁₃₁	C₂²×C₅	semidirect
18. C₅×C₁₃₁	C₂×D₉	direct (N × H)
22. C₂×C₁₃₁	C₅×D₉	direct (N × H)
23. C₂×C₅×D₉	C₁₃₁	direct (N × H)
24. C₁₃₁	C₂×C₅×D₉	direct (N × H)
25. C₂×C₅×C₉	C₂×C₁₃₁	semidirect
26. C₅×D₉	C₂×C₁₃₁	direct (N × H)
28. C₅×C₉	C₂²×C₁₃₁	semidirect
29. C₂×D₉	C₅×C₁₃₁	direct (N × H)
33. C₂×C₉	C₂×C₅×C₁₃₁	semidirect
34. D₉	C₂×C₅×C₁₃₁	direct (N × H)
38. C₂×C₅	D₉×C₁₃₁	direct (N × H)
39. C₉	C₂²×C₅×C₁₃₁	semidirect
42. C₅	C₂×D₉×C₁₃₁	direct (N × H)
46. C₂	C₅×D₉×C₁₃₁	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×D₉×C₁₃₁	2
C₂×C₅×C₉×C₁₃₁	2
C₂×C₅×D₃×C₁₃₁	3
C₂×D₉×C₁₃₁	5
C₂×C₅×D₉	131

Subgroups — C2×C5×D9×C131 #37556060

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₉×C₁₃₁ #37556060