Subgroups — C₃×D₁₇×D₁₅₉ #44570002

Order 32436.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₁₇×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₇×D₁₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₇₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₇×D₁₅₉	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×D₁₇×D₅₃	—	3	1	no	maximal
6	C₃²×C₁₇×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₂₇₀₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₇×D₁₅₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×D₉₀₁	—	3	1	no	—
10	C₃×D₁₇×C₅₃	—	2	1	no	—
11	C₃×D₁₇×C₅₃	D₃	1	1	yes	characteristic, complemented
12	C₃×D₁₇×C₅₃	C₂×C₃	1	1	yes	characteristic, complemented
13	C₃×C₁₇×D₅₃	—	3	1	no	—
14	D₁₇×D₅₃	—	3	1	no	Hall
15	C₃×C₁₇×C₅₃	—	2	1	no	—
16	C₃×C₁₇×C₅₃	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₇×C₅₃	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₂×C₃×D₁₅₉	—	17	1	no	maximal, Hall
19	D₉₀₁	—	3	1	no	—
20	C₁₇×D₅₃	—	3	1	no	—
21	D₁₇×C₅₃	C₃×D₃	1	1	yes	characteristic, complemented
22	C₂×C₃²×C₅₃	—	17	1	no	—
23	C₃×D₁₅₉	—	17	1	no	—
24	C₃×D₁₅₉	D₁₇	1	1	yes	characteristic, direct product factor
25	C₁₇×C₅₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
26	C₂×D₁₅₉	—	17	1	no	—
27	C₂×C₃×D₅₃	—	51	1	no	—
28	C₃×D₃×D₁₇	—	53	1	no	maximal, Hall
29	C₃²×C₅₃	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₅₃	—	17	1	no	—
31	C₂×C₃×C₅₃	—	17	1	no	—
32	C₂×C₃×C₅₃	—	34	1	no	—
33	D₁₅₉	—	17	1	no	—
34	D₁₅₉	C₃×D₁₇	1	1	yes	characteristic, direct product factor
35	C₃×D₅₃	—	3	1	no	—
36	C₃×D₅₃	—	51	1	no	—
37	C₃×D₅₁	—	53	1	no	—
38	C₃×D₃×C₁₇	—	53	1	no	—
39	C₃²×D₁₇	D₅₃	1	1	yes	characteristic, complemented
40	C₂×D₅₃	—	51	1	no	Hall
41	C₂×C₃×D₁₇	—	159	1	no	—
42	D₃×D₁₇	—	53	1	no	—
43	C₃×C₅₃	—	2	1	no	—
44	C₃×C₅₃	D₃×D₁₇	1	1	yes	characteristic, complemented
45	C₃×C₅₃	C₂×C₃×D₁₇	1	1	yes	characteristic, complemented
46	C₃²×C₁₇	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
47	C₂×C₅₃	—	17	1	no	—
48	D₅₃	—	3	1	no	—
49	D₅₃	—	51	1	no	—
50	C₂×C₃×C₁₇	—	159	1	no	—
51	D₅₁	—	53	1	no	—
52	C₃×D₁₇	—	2	1	no	—
53	C₃×D₁₇	—	159	1	no	—
54	C₃×D₁₇	C₃×D₅₃	1	1	yes	characteristic, complemented
55	C₃×D₁₇	D₁₅₉	1	1	yes	characteristic, direct product factor
56	D₃×C₁₇	—	53	1	no	—
57	C₂×D₁₇	—	159	1	no	Hall
58	C₅₃	C₃×D₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
59	C₃×C₁₇	—	2	1	no	—
60	C₃×C₁₇	C₂×C₃×D₅₃	1	1	yes	characteristic, complemented
61	C₃×C₁₇	C₂×D₁₅₉	1	1	yes	characteristic, complemented
62	C₂×C₃×D₃	—	901	1	no	Hall
63	C₂×C₁₇	—	159	1	no	—
64	D₁₇	—	159	1	no	—
65	D₁₇	C₃×D₁₅₉	1	1	yes	characteristic, direct product factor
66	C₂×C₃²	—	17	1	no	—
67	C₃×D₃	—	53	1	no	—
68	C₃×D₃	—	901	1	no	—
69	C₁₇	C₂×C₃×D₁₅₉	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₃	—	2703	1	no	—
71	C₂×D₃	—	901	1	no	—
72	C₃²	D₁₇×D₅₃	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	17	1	no	—
74	C₂×C₃	—	17	1	no	—
75	C₂×C₃	—	34	1	no	—
76	C₂×C₃	—	2703	1	no	—
77	C₂×C₃	—	159	1	no	—
78	D₃	—	53	1	no	—
79	D₃	—	901	1	no	—
80	C₂²	—	2703	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	C₃×D₁₇×D₅₃	1	1	yes	characteristic, complemented
83	C₃	D₁₇×D₁₅₉	1	1	yes	characteristic, direct product factor
84	C₂	—	17	1	no	—
85	C₂	—	2703	1	no	—
86	C₂	—	159	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₁₇×D₁₅₉
commutator, cosocle, hypocenter	C₃×C₁₇×C₅₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇×C₅₃	C₂²
LCS	G ▷ C₃×C₁₇×C₅₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×D₁₇×C₅₃	C₂	semidirect
2. C₃×C₁₇×D₁₅₉	C₂	semidirect
3. C₃×D₂₇₀₃	C₂	semidirect
4. D₁₇×D₁₅₉	C₃	direct (N × H)
6. C₃²×C₁₇×C₅₃	C₂²	semidirect
7. D₂₇₀₃	C₂×C₃	semidirect
8. C₁₇×D₁₅₉	C₂×C₃	semidirect
11. C₃×D₁₇×C₅₃	D₃	semidirect
12. C₃×D₁₇×C₅₃	C₂×C₃	semidirect
16. C₃×C₁₇×C₅₃	C₂×D₃	semidirect
17. C₃×C₁₇×C₅₃	C₂²×C₃	semidirect
21. D₁₇×C₅₃	C₃×D₃	semidirect
24. C₃×D₁₅₉	D₁₇	direct (N × H)
25. C₁₇×C₅₃	C₂×C₃×D₃	semidirect
29. C₃²×C₅₃	C₂×D₁₇	semidirect
34. D₁₅₉	C₃×D₁₇	direct (N × H)
39. C₃²×D₁₇	D₅₃	semidirect
44. C₃×C₅₃	D₃×D₁₇	semidirect
45. C₃×C₅₃	C₂×C₃×D₁₇	semidirect
46. C₃²×C₁₇	C₂×D₅₃	semidirect
54. C₃×D₁₇	C₃×D₅₃	semidirect
55. C₃×D₁₇	D₁₅₉	direct (N × H)
58. C₅₃	C₃×D₃×D₁₇	semidirect
60. C₃×C₁₇	C₂×C₃×D₅₃	semidirect
61. C₃×C₁₇	C₂×D₁₅₉	semidirect
65. D₁₇	C₃×D₁₅₉	direct (N × H)
69. C₁₇	C₂×C₃×D₁₅₉	semidirect
72. C₃²	D₁₇×D₅₃	semidirect
82. C₃	C₃×D₁₇×D₅₃	semidirect
83. C₃	D₁₇×D₁₅₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×D₁₇×C₅₃	2
C₃×C₁₇×D₁₅₉	2
C₃×D₂₇₀₃	2
D₁₇×D₁₅₉	3
C₃×D₁₇×D₅₃	3
C₂×C₃×D₁₅₉	17
C₃×D₃×D₁₇	53

Subgroups — C3×D17×D159 #44570002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₁₇×D₁₅₉ #44570002