Subgroups — C₅₉×C₃⋊Dic₅₁ #49115652

Order 36108.

72 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	—	3	4	no	maximal
3	C₃²×C₁₇×C₅₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₇×C₅₉	D₃	1	4	yes	—
5	C₅₉×Dic₁₇	—	9	1	no	Hall
6	C₃×C₁₇×C₅₉	Dic₃	1	4	yes	complemented
7	C₃⋊Dic₃×C₅₉	—	17	1	no	maximal, Hall
8	C₂×C₁₇×C₅₉	C₃⋊D₃	1	1	yes	characteristic
9	C₂×C₃²×C₅₉	D₁₇	1	1	yes	characteristic
10	C₁₇×C₅₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
11	Dic₃×C₅₉	—	51	4	no	—
12	C₃⋊Dic₅₁	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃²×C₅₉	Dic₁₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×C₅₉	D₅₁	1	4	yes	—
15	C₂×C₃²×C₁₇	C₂×C₅₉	1	1	yes	characteristic
16	C₄×C₅₉	—	153	1	no	Hall
17	Dic₅₁	—	3	4	no	—
18	C₃×C₅₉	Dic₅₁	1	4	yes	complemented
19	C₃²×C₁₇	C₄×C₅₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅₉	C₃⋊D₅₁	1	1	yes	characteristic
21	C₂×C₃×C₁₇	D₃×C₅₉	1	4	yes	—
22	Dic₁₇	—	9	1	no	Hall
23	C₅₉	C₃⋊Dic₅₁	1	1	yes	characteristic, direct product factor, Sylow
24	C₃×C₁₇	Dic₃×C₅₉	1	4	yes	complemented
25	C₃⋊Dic₃	—	17	1	no	Hall
26	C₂×C₁₇	C₃⋊D₃×C₅₉	1	1	yes	characteristic
27	C₂×C₃²	D₁₇×C₅₉	1	1	yes	characteristic
28	C₁₇	C₃⋊Dic₃×C₅₉	1	1	yes	characteristic, complemented, Sylow
29	Dic₃	—	51	4	no	—
30	C₃²	C₅₉×Dic₁₇	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	C₅₉×D₅₁	1	4	yes	—
32	C₄	—	153	1	no	Sylow
33	C₃	C₅₉×Dic₅₁	1	4	yes	complemented
34	C₂	C₅₉×C₃⋊D₅₁	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₃²×C₁₇×C₅₉	C₄	semidirect
6. C₃×C₁₇×C₅₉	Dic₃	semidirect
10. C₁₇×C₅₉	C₃⋊Dic₃	semidirect
12. C₃⋊Dic₅₁	C₅₉	direct (N × H)
13. C₃²×C₅₉	Dic₁₇	semidirect
18. C₃×C₅₉	Dic₅₁	semidirect
19. C₃²×C₁₇	C₄×C₅₉	semidirect
23. C₅₉	C₃⋊Dic₅₁	direct (N × H)
24. C₃×C₁₇	Dic₃×C₅₉	semidirect
28. C₁₇	C₃⋊Dic₃×C₅₉	semidirect
30. C₃²	C₅₉×Dic₁₇	semidirect
33. C₃	C₅₉×Dic₅₁	semidirect

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⋊Dic₃×C₅₉	17
C₃⋊Dic₅₁	59

Subgroups — C59×C3⋊Dic51 #49115652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×C₃⋊Dic₅₁ #49115652