Subgroups — C₂×C₅₉×C₃⋊D₅₁ #49115708

Order 36108.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×C₃⋊D₅₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₇×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×D₅₁	—	3	4	no	maximal
4	C₃²×C₁₇×C₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₅₉×D₅₁	—	3	8	no	—
6	C₂×C₃×C₁₇×C₅₉	D₃	1	4	yes	complemented
7	C₂×D₁₇×C₅₉	—	9	1	no	Hall
8	C₃×C₁₇×C₅₉	C₂×D₃	1	4	yes	complemented
9	C₂×C₃⋊D₃×C₅₉	—	17	1	no	maximal, Hall
10	C₂×C₁₇×C₅₉	C₃⋊D₃	1	1	yes	characteristic, complemented
11	D₁₇×C₅₉	—	9	2	no	—
12	C₂×C₃²×C₅₉	D₁₇	1	1	yes	characteristic, complemented
13	C₃⋊D₃×C₅₉	—	17	2	no	—
14	C₁₇×C₅₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
15	C₂×D₃×C₅₉	—	51	4	no	—
16	C₂×C₃⋊D₅₁	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₃²×C₅₉	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₅₉	D₅₁	1	4	yes	complemented
19	D₃×C₅₉	—	51	8	no	—
20	C₂×C₃²×C₁₇	C₂×C₅₉	1	1	yes	characteristic, complemented
21	C₃⋊D₅₁	C₂×C₅₉	1	2	yes	direct product factor
22	C₂²×C₅₉	—	153	1	no	Hall
23	C₂×D₅₁	—	3	4	no	—
24	C₃×C₅₉	C₂×D₅₁	1	4	yes	complemented
25	C₃²×C₁₇	C₂²×C₅₉	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅₉	—	153	2	no	—
27	C₂×C₅₉	C₃⋊D₅₁	1	1	yes	characteristic, direct product factor
28	C₂×C₃×C₁₇	D₃×C₅₉	1	4	yes	complemented
29	D₅₁	—	3	8	no	—
30	C₂×D₁₇	—	9	1	no	Hall
31	C₅₉	C₂×C₃⋊D₅₁	1	1	yes	characteristic, direct product factor, Sylow
32	C₃×C₁₇	C₂×D₃×C₅₉	1	4	yes	complemented
33	C₂×C₃⋊D₃	—	17	1	no	Hall
34	C₂×C₁₇	C₃⋊D₃×C₅₉	1	1	yes	characteristic, complemented
35	D₁₇	—	9	2	no	—
36	C₂×C₃²	D₁₇×C₅₉	1	1	yes	characteristic, complemented
37	C₃⋊D₃	—	17	2	no	—
38	C₁₇	C₂×C₃⋊D₃×C₅₉	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₃	—	51	4	no	—
40	C₃²	C₂×D₁₇×C₅₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	C₅₉×D₅₁	1	4	yes	complemented
42	D₃	—	51	8	no	—
43	C₂²	—	153	1	no	Sylow
44	C₃	C₂×C₅₉×D₅₁	1	4	yes	complemented
45	C₂	—	153	2	no	—
46	C₂	C₅₉×C₃⋊D₅₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅₉	C₃⋊D₅₁
commutator, cosocle, hypocenter	C₃²×C₁₇	C₂²×C₅₉
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₇×C₅₉	C₂
LCS	G ▷ C₃²×C₁₇
UCS	C₁ ◁ C₂×C₅₉

Complements

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

N	H ≅ G/N	type
1. C₅₉×C₃⋊D₅₁	C₂	direct (N × H)
2. C₂×C₃²×C₁₇×C₅₉	C₂	semidirect
4. C₃²×C₁₇×C₅₉	C₂²	semidirect
6. C₂×C₃×C₁₇×C₅₉	D₃	semidirect
8. C₃×C₁₇×C₅₉	C₂×D₃	semidirect
10. C₂×C₁₇×C₅₉	C₃⋊D₃	semidirect
12. C₂×C₃²×C₅₉	D₁₇	semidirect
14. C₁₇×C₅₉	C₂×C₃⋊D₃	semidirect
16. C₂×C₃⋊D₅₁	C₅₉	direct (N × H)
17. C₃²×C₅₉	C₂×D₁₇	semidirect
18. C₂×C₃×C₅₉	D₅₁	semidirect
20. C₂×C₃²×C₁₇	C₂×C₅₉	semidirect
21. C₃⋊D₅₁	C₂×C₅₉	direct (N × H)
24. C₃×C₅₉	C₂×D₅₁	semidirect
25. C₃²×C₁₇	C₂²×C₅₉	semidirect
27. C₂×C₅₉	C₃⋊D₅₁	direct (N × H)
28. C₂×C₃×C₁₇	D₃×C₅₉	semidirect
31. C₅₉	C₂×C₃⋊D₅₁	direct (N × H)
32. C₃×C₁₇	C₂×D₃×C₅₉	semidirect
34. C₂×C₁₇	C₃⋊D₃×C₅₉	semidirect
36. C₂×C₃²	D₁₇×C₅₉	semidirect
38. C₁₇	C₂×C₃⋊D₃×C₅₉	semidirect
40. C₃²	C₂×D₁₇×C₅₉	semidirect
41. C₂×C₃	C₅₉×D₅₁	semidirect
44. C₃	C₂×C₅₉×D₅₁	semidirect
46. C₂	C₅₉×C₃⋊D₅₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₉×C₃⋊D₅₁	2
C₂×C₃²×C₁₇×C₅₉	2
C₂×C₅₉×D₅₁	3
C₂×C₃⋊D₃×C₅₉	17
C₂×C₃⋊D₅₁	59

Subgroups — C2×C59×C3⋊D51 #49115708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₉×C₃⋊D₅₁ #49115708