Subgroups — C₃×C₅₉×Dic₅₁ #49115656

Order 36108.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₇×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₅₉×Dic₅₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₅₉×Dic₁₇	—	3	1	no	maximal
4	C₃²×C₁₇×C₅₉	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₇×C₅₉	—	2	1	no	—
6	C₂×C₃×C₁₇×C₅₉	D₃	1	1	yes	characteristic
7	C₂×C₃×C₁₇×C₅₉	C₂×C₃	1	1	yes	characteristic
8	C₅₉×Dic₁₇	—	3	1	no	Hall
9	C₃×C₁₇×C₅₉	—	2	1	no	—
10	C₃×C₁₇×C₅₉	Dic₃	1	1	yes	characteristic, complemented
11	C₃×C₁₇×C₅₉	C₃×C₄	1	1	yes	characteristic, complemented
12	C₃×Dic₃×C₅₉	—	17	1	no	maximal, Hall
13	C₂×C₁₇×C₅₉	C₃×D₃	1	1	yes	characteristic
14	C₂×C₃²×C₅₉	D₁₇	1	1	yes	characteristic
15	C₁₇×C₅₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
16	C₃×C₄×C₅₉	—	51	1	no	—
17	Dic₃×C₅₉	—	17	1	no	—
18	C₃×Dic₅₁	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₃²×C₅₉	Dic₁₇	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₅₉	—	2	1	no	—
21	C₂×C₃×C₅₉	C₃×D₁₇	1	1	yes	characteristic
22	C₂×C₃×C₅₉	D₅₁	1	1	yes	characteristic
23	C₂×C₃²×C₁₇	C₂×C₅₉	1	1	yes	characteristic
24	C₄×C₅₉	—	51	1	no	Hall
25	Dic₅₁	C₃×C₅₉	1	1	yes	characteristic, direct product factor
26	C₃×Dic₁₇	—	3	1	no	—
27	C₃×C₅₉	—	2	1	no	—
28	C₃×C₅₉	C₃×Dic₁₇	1	1	yes	characteristic, complemented
29	C₃×C₅₉	Dic₅₁	1	1	yes	characteristic, direct product factor
30	C₃²×C₁₇	C₄×C₅₉	1	1	yes	characteristic, complemented, Hall
31	C₂×C₅₉	C₃×D₅₁	1	1	yes	characteristic
32	C₂×C₃×C₁₇	—	2	1	no	—
33	C₂×C₃×C₁₇	D₃×C₅₉	1	1	yes	characteristic
34	C₂×C₃×C₁₇	C₂×C₃×C₅₉	1	1	yes	characteristic
35	Dic₁₇	—	3	1	no	Hall
36	C₅₉	C₃×Dic₅₁	1	1	yes	characteristic, direct product factor, Sylow
37	C₃×C₁₇	—	2	1	no	—
38	C₃×C₁₇	Dic₃×C₅₉	1	1	yes	characteristic, complemented
39	C₃×C₁₇	C₃×C₄×C₅₉	1	1	yes	characteristic, complemented
40	C₃×Dic₃	—	17	1	no	Hall
41	C₂×C₁₇	C₃×D₃×C₅₉	1	1	yes	characteristic
42	C₂×C₃²	D₁₇×C₅₉	1	1	yes	characteristic
43	C₁₇	C₃×Dic₃×C₅₉	1	1	yes	characteristic, complemented, Sylow
44	C₃×C₄	—	51	1	no	—
45	Dic₃	—	17	1	no	—
46	C₃²	C₅₉×Dic₁₇	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	—	2	1	no	—
48	C₂×C₃	C₃×D₁₇×C₅₉	1	1	yes	characteristic
49	C₂×C₃	C₅₉×D₅₁	1	1	yes	characteristic
50	C₄	—	51	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×C₅₉×Dic₁₇	1	1	yes	characteristic, complemented
53	C₃	C₅₉×Dic₅₁	1	1	yes	characteristic, direct product factor
54	C₂	C₃×C₅₉×D₅₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅₉	D₅₁
commutator, hypocenter	C₃×C₁₇	C₃×C₄×C₅₉
Frattini	C₂	C₃×C₅₉×D₅₁
Fitting, socle, prime radical	C₂×C₃²×C₁₇×C₅₉	C₂
cosocle	C₂×C₃×C₁₇	C₂×C₃×C₅₉
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₂×C₃×C₅₉

Complements

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

N	H ≅ G/N	type
2. C₅₉×Dic₅₁	C₃	direct (N × H)
4. C₃²×C₁₇×C₅₉	C₄	semidirect
10. C₃×C₁₇×C₅₉	Dic₃	semidirect
11. C₃×C₁₇×C₅₉	C₃×C₄	semidirect
15. C₁₇×C₅₉	C₃×Dic₃	semidirect
18. C₃×Dic₅₁	C₅₉	direct (N × H)
19. C₃²×C₅₉	Dic₁₇	semidirect
25. Dic₅₁	C₃×C₅₉	direct (N × H)
28. C₃×C₅₉	C₃×Dic₁₇	semidirect
29. C₃×C₅₉	Dic₅₁	direct (N × H)
30. C₃²×C₁₇	C₄×C₅₉	semidirect
36. C₅₉	C₃×Dic₅₁	direct (N × H)
38. C₃×C₁₇	Dic₃×C₅₉	semidirect
39. C₃×C₁₇	C₃×C₄×C₅₉	semidirect
43. C₁₇	C₃×Dic₃×C₅₉	semidirect
46. C₃²	C₅₉×Dic₁₇	semidirect
52. C₃	C₃×C₅₉×Dic₁₇	semidirect
53. C₃	C₅₉×Dic₅₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₁₇×C₅₉	2
C₅₉×Dic₅₁	3
C₃×C₅₉×Dic₁₇	3
C₃×Dic₃×C₅₉	17
C₃×Dic₅₁	59

Subgroups — C3×C59×Dic51 #49115656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅₉×Dic₅₁ #49115656