Subgroups — C₂×C₁₇×D₉×C₅₉ #49115646

Order 36108.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×D₉×C₅₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₁₇×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₁₇×C₅₉	—	3	1	no	maximal
4	C₉×C₁₇×C₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃×C₁₇×C₅₉	—	3	2	no	—
6	C₂×C₃×C₁₇×C₅₉	D₃	1	1	yes	characteristic
7	C₂²×C₁₇×C₅₉	—	9	1	no	Hall
8	C₃×C₁₇×C₅₉	C₂×D₃	1	1	yes	characteristic
9	C₂×D₉×C₅₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₇×C₅₉	—	9	2	no	—
11	C₂×C₁₇×C₅₉	D₉	1	1	yes	characteristic, direct product factor
12	C₂×C₉×C₅₉	C₂×C₁₇	1	1	yes	characteristic, complemented
13	D₉×C₅₉	C₂×C₁₇	1	2	yes	direct product factor
14	C₁₇×C₅₉	C₂×D₉	1	1	yes	characteristic, direct product factor, Hall
15	C₂×D₃×C₅₉	—	3	1	no	—
16	C₂×C₁₇×D₉	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₉×C₅₉	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₅₉	D₃×C₁₇	1	1	yes	characteristic
19	D₃×C₅₉	—	3	2	no	—
20	C₂×C₉×C₁₇	C₂×C₅₉	1	1	yes	characteristic, complemented
21	C₁₇×D₉	C₂×C₅₉	1	2	yes	direct product factor
22	C₂²×C₅₉	—	9	1	no	Hall
23	C₂×D₃×C₁₇	—	3	1	no	—
24	C₃×C₅₉	C₂×D₃×C₁₇	1	1	yes	characteristic
25	C₉×C₁₇	C₂²×C₅₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅₉	—	9	2	no	—
27	C₂×C₅₉	C₁₇×D₉	1	1	yes	characteristic, direct product factor
28	C₂×C₃×C₁₇	D₃×C₅₉	1	1	yes	characteristic
29	D₃×C₁₇	—	3	2	no	—
30	C₂²×C₁₇	—	9	1	no	Hall
31	C₅₉	C₂×C₁₇×D₉	1	1	yes	characteristic, direct product factor, Sylow
32	C₃×C₁₇	C₂×D₃×C₅₉	1	1	yes	characteristic
33	C₂×D₉	C₁₇×C₅₉	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₁₇	—	9	2	no	—
35	C₂×C₁₇	D₉×C₅₉	1	1	yes	characteristic, direct product factor
36	C₂×C₉	C₂×C₁₇×C₅₉	1	1	yes	characteristic, complemented
37	D₉	C₂×C₁₇×C₅₉	1	2	yes	direct product factor
38	C₁₇	C₂×D₉×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×D₃	—	3	1	no	—
40	C₉	C₂²×C₁₇×C₅₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₃×C₁₇×C₅₉	1	1	yes	characteristic
42	D₃	—	3	2	no	—
43	C₂²	—	9	1	no	Sylow
44	C₃	C₂×D₃×C₁₇×C₅₉	1	1	yes	characteristic
45	C₂	—	9	2	no	—
46	C₂	C₁₇×D₉×C₅₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇×C₅₉	D₉
commutator, cosocle, hypocenter	C₉	C₂²×C₁₇×C₅₉
Frattini	C₃	C₂×D₃×C₁₇×C₅₉
Fitting	C₂×C₉×C₁₇×C₅₉	C₂
socle	C₂×C₃×C₁₇×C₅₉	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₁₇×C₅₉

Complements

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

N	H ≅ G/N	type
1. C₁₇×D₉×C₅₉	C₂	direct (N × H)
2. C₂×C₉×C₁₇×C₅₉	C₂	semidirect
4. C₉×C₁₇×C₅₉	C₂²	semidirect
9. C₂×D₉×C₅₉	C₁₇	direct (N × H)
11. C₂×C₁₇×C₅₉	D₉	direct (N × H)
12. C₂×C₉×C₅₉	C₂×C₁₇	semidirect
13. D₉×C₅₉	C₂×C₁₇	direct (N × H)
14. C₁₇×C₅₉	C₂×D₉	direct (N × H)
16. C₂×C₁₇×D₉	C₅₉	direct (N × H)
17. C₉×C₅₉	C₂²×C₁₇	semidirect
20. C₂×C₉×C₁₇	C₂×C₅₉	semidirect
21. C₁₇×D₉	C₂×C₅₉	direct (N × H)
25. C₉×C₁₇	C₂²×C₅₉	semidirect
27. C₂×C₅₉	C₁₇×D₉	direct (N × H)
31. C₅₉	C₂×C₁₇×D₉	direct (N × H)
33. C₂×D₉	C₁₇×C₅₉	direct (N × H)
35. C₂×C₁₇	D₉×C₅₉	direct (N × H)
36. C₂×C₉	C₂×C₁₇×C₅₉	semidirect
37. D₉	C₂×C₁₇×C₅₉	direct (N × H)
38. C₁₇	C₂×D₉×C₅₉	direct (N × H)
40. C₉	C₂²×C₁₇×C₅₉	semidirect
46. C₂	C₁₇×D₉×C₅₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×D₉×C₅₉	2
C₂×C₉×C₁₇×C₅₉	2
C₂×D₃×C₁₇×C₅₉	3
C₂×D₉×C₅₉	17
C₂×C₁₇×D₉	59

Subgroups — C2×C17×D9×C59 #49115646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×D₉×C₅₉ #49115646