Subgroups — D₅₉×C₃⋊D₅₁ #49115693

Order 36108.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×C₃⋊D₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊D₃₀₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅₁×D₅₉	—	3	4	no	maximal
5	C₃²×C₁₇×C₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃₀₀₉	—	3	4	no	—
7	C₅₉×D₅₁	—	3	4	no	—
8	C₃×C₁₇×D₅₉	D₃	1	4	yes	complemented
9	D₁₇×D₅₉	—	9	1	no	Hall
10	C₃×C₁₇×C₅₉	C₂×D₃	1	4	yes	complemented
11	C₃⋊D₃×D₅₉	—	17	1	no	maximal, Hall
12	D₁₀₀₃	—	9	1	no	—
13	C₁₇×D₅₉	C₃⋊D₃	1	1	yes	characteristic, complemented
14	D₁₇×C₅₉	—	9	1	no	—
15	C₃⋊D₁₇₇	—	17	1	no	—
16	C₃⋊D₃×C₅₉	—	17	1	no	—
17	C₃²×D₅₉	D₁₇	1	1	yes	characteristic, complemented
18	C₁₇×C₅₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
19	D₃×D₅₉	—	51	4	no	—
20	C₂×C₃⋊D₅₁	—	59	1	no	maximal, Hall
21	C₃²×C₅₉	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
22	D₁₇₇	—	51	4	no	—
23	C₃×D₅₉	D₅₁	1	4	yes	complemented
24	D₃×C₅₉	—	51	4	no	—
25	C₂×C₃²×C₁₇	—	59	1	no	—
26	C₃⋊D₅₁	—	59	1	no	—
27	C₃⋊D₅₁	D₅₉	1	1	yes	characteristic, direct product factor
28	C₂×D₅₉	—	153	1	no	Hall
29	C₂×D₅₁	—	177	4	no	—
30	C₃×C₅₉	C₂×D₅₁	1	4	yes	complemented
31	C₃²×C₁₇	C₂×D₅₉	1	1	yes	characteristic, complemented, Hall
32	C₂×C₅₉	—	153	1	no	—
33	D₅₉	—	153	1	no	—
34	D₅₉	C₃⋊D₅₁	1	1	yes	characteristic, direct product factor
35	C₂×C₃×C₁₇	—	59	4	no	—
36	D₅₁	—	3	4	no	—
37	D₅₁	—	177	4	no	—
38	C₂×D₁₇	—	531	1	no	Hall
39	C₅₉	C₂×C₃⋊D₅₁	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₁₇	D₃×D₅₉	1	4	yes	complemented
41	C₂×C₃⋊D₃	—	1003	1	no	Hall
42	C₂×C₁₇	—	59	1	no	—
43	D₁₇	—	9	1	no	—
44	D₁₇	—	531	1	no	—
45	C₂×C₃²	—	59	1	no	—
46	C₃⋊D₃	—	17	1	no	—
47	C₃⋊D₃	—	1003	1	no	—
48	C₁₇	C₃⋊D₃×D₅₉	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₃	—	3009	4	no	—
50	C₃²	D₁₇×D₅₉	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	59	4	no	—
52	D₃	—	51	4	no	—
53	D₃	—	3009	4	no	—
54	C₂²	—	9027	1	no	Sylow
55	C₃	D₅₁×D₅₉	1	4	yes	complemented
56	C₂	—	59	1	no	—
57	C₂	—	9027	1	no	—
58	C₂	—	153	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₇×D₅₉	C₂	semidirect
2. C₅₉×C₃⋊D₅₁	C₂	semidirect
3. C₃⋊D₃₀₀₉	C₂	semidirect
5. C₃²×C₁₇×C₅₉	C₂²	semidirect
8. C₃×C₁₇×D₅₉	D₃	semidirect
10. C₃×C₁₇×C₅₉	C₂×D₃	semidirect
13. C₁₇×D₅₉	C₃⋊D₃	semidirect
17. C₃²×D₅₉	D₁₇	semidirect
18. C₁₇×C₅₉	C₂×C₃⋊D₃	semidirect
21. C₃²×C₅₉	C₂×D₁₇	semidirect
23. C₃×D₅₉	D₅₁	semidirect
27. C₃⋊D₅₁	D₅₉	direct (N × H)
30. C₃×C₅₉	C₂×D₅₁	semidirect
31. C₃²×C₁₇	C₂×D₅₉	semidirect
34. D₅₉	C₃⋊D₅₁	direct (N × H)
39. C₅₉	C₂×C₃⋊D₅₁	semidirect
40. C₃×C₁₇	D₃×D₅₉	semidirect
48. C₁₇	C₃⋊D₃×D₅₉	semidirect
50. C₃²	D₁₇×D₅₉	semidirect
55. C₃	D₅₁×D₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₁₇×D₅₉	2
C₅₉×C₃⋊D₅₁	2
C₃⋊D₃₀₀₉	2
D₅₁×D₅₉	3
C₃⋊D₃×D₅₉	17
C₂×C₃⋊D₅₁	59

Subgroups — D59×C3⋊D51 #49115693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₉×C₃⋊D₅₁ #49115693