Subgroups — D₅×D₉×C₁₃₁ #37556052

Order 23580.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₅×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₉×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×D₅×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₅×C₁₃₁	—	3	1	no	maximal
5	C₅×C₉×C₁₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×D₉×C₁₃₁	—	5	1	no	maximal, Hall
7	D₁₅×C₁₃₁	—	3	1	no	—
8	C₅×D₃×C₁₃₁	—	3	1	no	—
9	C₃×D₅×C₁₃₁	D₃	1	1	yes	characteristic
10	C₂×D₅×C₁₃₁	—	9	1	no	Hall
11	D₉×C₁₃₁	—	5	1	no	—
12	D₉×C₁₃₁	D₅	1	1	yes	characteristic, direct product factor
13	C₂×C₉×C₁₃₁	—	5	1	no	—
14	C₃×C₅×C₁₃₁	C₂×D₃	1	1	yes	characteristic
15	C₂×D₃×C₁₃₁	—	15	1	no	—
16	C₂×C₅×C₁₃₁	—	9	1	no	—
17	D₅×C₁₃₁	—	9	1	no	—
18	D₅×C₁₃₁	D₉	1	1	yes	characteristic, direct product factor
19	C₉×C₁₃₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₁₃₁	—	5	1	no	—
21	D₃×C₁₃₁	—	3	1	no	—
22	D₃×C₁₃₁	—	15	1	no	—
23	C₅×C₁₃₁	C₂×D₉	1	1	yes	characteristic, complemented, Hall
24	C₂²×C₁₃₁	—	45	1	no	Hall
25	C₃×C₁₃₁	D₃×D₅	1	1	yes	characteristic
26	C₂×C₁₃₁	—	5	1	no	—
27	C₂×C₁₃₁	—	9	1	no	—
28	C₂×C₁₃₁	—	45	1	no	—
29	D₅×D₉	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₁₃₁	D₅×D₉	1	1	yes	characteristic, direct product factor, Sylow
31	D₄₅	C₂×C₁₃₁	1	1	yes	characteristic, complemented
32	C₉×D₅	C₂×C₁₃₁	1	1	yes	characteristic, complemented
33	C₅×D₉	C₂×C₁₃₁	1	1	yes	characteristic, complemented
34	D₃×D₅	—	3	1	no	—
35	C₅×C₉	C₂²×C₁₃₁	1	1	yes	characteristic, complemented, Hall
36	C₂×D₉	—	5	1	no	Hall
37	D₁₅	—	3	1	no	—
38	C₃×D₅	D₃×C₁₃₁	1	1	yes	characteristic
39	C₅×D₃	—	3	1	no	—
40	C₂×D₅	—	9	1	no	Hall
41	C₂×C₉	—	5	1	no	—
42	D₉	—	5	1	no	—
43	D₉	D₅×C₁₃₁	1	1	yes	characteristic, direct product factor
44	C₃×C₅	C₂×D₃×C₁₃₁	1	1	yes	characteristic
45	C₂×D₃	—	15	1	no	—
46	C₂×C₅	—	9	1	no	—
47	D₅	—	9	1	no	—
48	D₅	D₉×C₁₃₁	1	1	yes	characteristic, direct product factor
49	C₉	C₂×D₅×C₁₃₁	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	5	1	no	—
51	D₃	—	3	1	no	—
52	D₃	—	15	1	no	—
53	C₅	C₂×D₉×C₁₃₁	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	45	1	no	Sylow
55	C₃	D₃×D₅×C₁₃₁	1	1	yes	characteristic
56	C₂	—	5	1	no	—
57	C₂	—	9	1	no	—
58	C₂	—	45	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃₁	D₅×D₉
commutator, cosocle, hypocenter	C₅×C₉	C₂²×C₁₃₁
Frattini	C₃	D₃×D₅×C₁₃₁
Fitting	C₅×C₉×C₁₃₁	C₂²
socle	C₃×C₅×C₁₃₁	C₂×D₃
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₁₃₁

Complements

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

N	H ≅ G/N	type
1. D₄₅×C₁₃₁	C₂	semidirect
2. C₅×D₉×C₁₃₁	C₂	semidirect
3. C₉×D₅×C₁₃₁	C₂	semidirect
5. C₅×C₉×C₁₃₁	C₂²	semidirect
12. D₉×C₁₃₁	D₅	direct (N × H)
18. D₅×C₁₃₁	D₉	direct (N × H)
19. C₉×C₁₃₁	C₂×D₅	semidirect
23. C₅×C₁₃₁	C₂×D₉	semidirect
29. D₅×D₉	C₁₃₁	direct (N × H)
30. C₁₃₁	D₅×D₉	direct (N × H)
31. D₄₅	C₂×C₁₃₁	semidirect
32. C₉×D₅	C₂×C₁₃₁	semidirect
33. C₅×D₉	C₂×C₁₃₁	semidirect
35. C₅×C₉	C₂²×C₁₃₁	semidirect
43. D₉	D₅×C₁₃₁	direct (N × H)
48. D₅	D₉×C₁₃₁	direct (N × H)
49. C₉	C₂×D₅×C₁₃₁	semidirect
53. C₅	C₂×D₉×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
D₄₅×C₁₃₁	2
C₅×D₉×C₁₃₁	2
C₉×D₅×C₁₃₁	2
D₃×D₅×C₁₃₁	3
C₂×D₉×C₁₃₁	5
D₅×D₉	131

Subgroups — D5×D9×C131 #37556052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×D₉×C₁₃₁ #37556052