Subgroups — D₃×D₁₇×C₁₆₉ #46828151

Order 34476.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₁×C₁₆₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₁₇×C₁₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₇×C₁₆₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₇×C₁₆₉	—	3	1	no	maximal, Hall
5	C₃×C₁₇×C₁₆₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₇×C₁₆₉	—	3	1	no	—
7	D₁₇×C₁₆₉	D₃	1	1	yes	characteristic, direct product factor
8	C₂×C₁₇×C₁₆₉	—	3	1	no	—
9	C₁₇×C₁₆₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	D₃×C₁₃×D₁₇	C₁₃	1	1	yes	maximal, characteristic
11	C₂×D₃×C₁₆₉	—	17	1	no	maximal, Hall
12	C₁₃×D₅₁	C₂×C₁₃	1	1	yes	characteristic
13	D₃×C₁₃×C₁₇	C₂×C₁₃	1	1	yes	characteristic
14	C₃×C₁₃×D₁₇	C₂×C₁₃	1	1	yes	characteristic
15	C₂×C₃×C₁₆₉	—	17	1	no	—
16	D₃×C₁₆₉	—	17	1	no	—
17	D₃×C₁₆₉	D₁₇	1	1	yes	characteristic, direct product factor
18	C₂×C₁₃×D₁₇	—	3	1	no	—
19	C₂²×C₁₆₉	—	51	1	no	Hall
20	C₃×C₁₃×C₁₇	C₂²×C₁₃	1	1	yes	characteristic
21	C₃×C₁₆₉	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₁₃×C₁₇	—	3	1	no	—
23	C₁₃×D₁₇	—	3	1	no	—
24	C₁₃×D₁₇	D₃×C₁₃	1	1	yes	characteristic
25	C₂×C₁₆₉	—	3	1	no	—
26	C₂×C₁₆₉	—	17	1	no	—
27	C₂×C₁₆₉	—	51	1	no	—
28	C₁₃×C₁₇	C₂×D₃×C₁₃	1	1	yes	characteristic
29	D₃×D₁₇	C₁₆₉	1	1	yes	characteristic, direct product factor, Hall
30	C₁₆₉	D₃×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×D₃×C₁₃	—	17	1	no	—
32	D₅₁	C₂×C₁₆₉	1	1	yes	characteristic, complemented
33	C₃×D₁₇	C₂×C₁₆₉	1	1	yes	characteristic, complemented
34	D₃×C₁₇	C₂×C₁₆₉	1	1	yes	characteristic, complemented
35	C₂×C₃×C₁₃	—	17	1	no	—
36	D₃×C₁₃	—	17	1	no	—
37	D₃×C₁₃	C₁₃×D₁₇	1	1	yes	characteristic
38	C₂×D₁₇	—	3	1	no	Hall
39	C₂²×C₁₃	—	51	1	no	—
40	C₃×C₁₇	C₂²×C₁₆₉	1	1	yes	characteristic, complemented, Hall
41	C₃×C₁₃	C₂×C₁₃×D₁₇	1	1	yes	characteristic
42	C₂×C₁₇	—	3	1	no	—
43	D₁₇	—	3	1	no	—
44	D₁₇	D₃×C₁₆₉	1	1	yes	characteristic, direct product factor
45	C₂×C₁₃	—	3	1	no	—
46	C₂×C₁₃	—	17	1	no	—
47	C₂×C₁₃	—	51	1	no	—
48	C₁₇	C₂×D₃×C₁₆₉	1	1	yes	characteristic, complemented, Sylow
49	C₁₃	D₃×C₁₃×D₁₇	1	1	yes	characteristic
50	C₂×D₃	—	17	1	no	Hall
51	C₂×C₃	—	17	1	no	—
52	D₃	—	17	1	no	—
53	D₃	D₁₇×C₁₆₉	1	1	yes	characteristic, direct product factor
54	C₂²	—	51	1	no	Sylow
55	C₃	C₂×D₁₇×C₁₆₉	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	3	1	no	—
57	C₂	—	17	1	no	—
58	C₂	—	51	1	no	—

	subgroup	G/H
center, hypercenter	C₁₆₉	D₃×D₁₇
commutator, hypocenter	C₃×C₁₇	C₂²×C₁₆₉
Frattini	C₁₃	D₃×C₁₃×D₁₇
Fitting	C₃×C₁₇×C₁₆₉	C₂²
socle, cosocle	C₃×C₁₃×C₁₇	C₂²×C₁₃
prime radical	D₃×C₁₃×D₁₇	C₁₃
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₁₆₉

Complements

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

N	H ≅ G/N	type
1. D₅₁×C₁₆₉	C₂	semidirect
2. D₃×C₁₇×C₁₆₉	C₂	semidirect
3. C₃×D₁₇×C₁₆₉	C₂	semidirect
5. C₃×C₁₇×C₁₆₉	C₂²	semidirect
7. D₁₇×C₁₆₉	D₃	direct (N × H)
9. C₁₇×C₁₆₉	C₂×D₃	semidirect
17. D₃×C₁₆₉	D₁₇	direct (N × H)
21. C₃×C₁₆₉	C₂×D₁₇	semidirect
29. D₃×D₁₇	C₁₆₉	direct (N × H)
30. C₁₆₉	D₃×D₁₇	direct (N × H)
32. D₅₁	C₂×C₁₆₉	semidirect
33. C₃×D₁₇	C₂×C₁₆₉	semidirect
34. D₃×C₁₇	C₂×C₁₆₉	semidirect
40. C₃×C₁₇	C₂²×C₁₆₉	semidirect
44. D₁₇	D₃×C₁₆₉	direct (N × H)
48. C₁₇	C₂×D₃×C₁₆₉	semidirect
53. D₃	D₁₇×C₁₆₉	direct (N × H)
55. C₃	C₂×D₁₇×C₁₆₉	semidirect

Maximal subgroups

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

subgroup	index
D₅₁×C₁₆₉	2
D₃×C₁₇×C₁₆₉	2
C₃×D₁₇×C₁₆₉	2
C₂×D₁₇×C₁₆₉	3
D₃×C₁₃×D₁₇	13
C₂×D₃×C₁₆₉	17

Subgroups — D3×D17×C169 #46828151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₁₇×C₁₆₉ #46828151