Subgroups — C₃×D₃₅⋊D₃₇ #29509670

Order 15540.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₇×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₇×D₁₈₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₂₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₅⋊D₃₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₇×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₇×D₃₇	—	5	1	no	maximal, Hall
7	C₃₇×D₃₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×D₁₈₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₂₅₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₅×D₃₇	—	7	1	no	maximal, Hall
11	C₃×D₂₅₉	D₅	1	1	yes	characteristic, complemented
12	C₃×D₇×C₃₇	—	5	1	no	—
13	C₃×C₇×D₃₇	—	5	1	no	—
14	C₅×C₇×C₃₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
15	C₃×D₁₈₅	D₇	1	1	yes	characteristic, complemented
16	C₃×D₅×C₃₇	—	7	1	no	—
17	C₃×C₅×D₃₇	—	7	1	no	—
18	D₇×D₃₇	—	5	1	no	Hall
19	C₃×C₇×C₃₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	D₅×D₃₇	—	7	1	no	Hall
21	C₃×C₅×C₃₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	D₂₅₉	C₃×D₅	1	1	yes	characteristic, complemented
23	C₇×D₃₇	—	5	1	no	—
24	D₇×C₃₇	—	5	1	no	—
25	C₂×C₃×D₃₇	—	35	1	no	Hall
26	C₃×D₅×D₇	—	37	1	no	maximal, Hall
27	D₁₈₅	C₃×D₇	1	1	yes	characteristic, complemented
28	C₅×D₃₇	—	7	1	no	—
29	D₅×C₃₇	—	7	1	no	—
30	C₇×C₃₇	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
31	C₂×C₃×C₃₇	—	35	1	no	—
32	C₃×D₃₇	—	5	1	no	—
33	C₃×D₃₇	—	7	1	no	—
34	C₃×D₃₅	D₃₇	1	1	yes	characteristic, complemented
35	C₃×C₇×D₅	—	37	1	no	—
36	C₃×C₅×D₇	—	37	1	no	—
37	C₅×C₃₇	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Hall
38	C₂×D₃₇	—	35	1	no	Hall
39	D₅×D₇	—	37	1	no	Hall
40	C₃×C₃₇	D₅×D₇	1	1	yes	characteristic, complemented, Hall
41	C₃×C₅×C₇	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
42	C₂×C₃×D₇	—	185	1	no	Hall
43	C₂×C₃₇	—	35	1	no	—
44	D₃₇	—	5	1	no	—
45	D₃₇	—	7	1	no	—
46	D₃₅	C₃×D₃₇	1	1	yes	characteristic, complemented
47	C₅×D₇	—	37	1	no	—
48	C₇×D₅	—	37	1	no	—
49	C₂×C₃×D₅	—	259	1	no	Hall
50	C₂×C₃×C₇	—	185	1	no	—
51	C₃×D₇	—	5	1	no	—
52	C₃×D₇	—	37	1	no	—
53	C₃₇	C₃×D₅×D₇	1	1	yes	characteristic, complemented, Sylow
54	C₅×C₇	C₂×C₃×D₃₇	1	1	yes	characteristic, complemented, Hall
55	C₂×C₃×C₅	—	259	1	no	—
56	C₃×D₅	—	7	1	no	—
57	C₃×D₅	—	37	1	no	—
58	C₂×D₇	—	185	1	no	Hall
59	C₃×C₇	D₅×D₃₇	1	1	yes	characteristic, complemented, Hall
60	C₂×D₅	—	259	1	no	Hall
61	C₃×C₅	D₇×D₃₇	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇	—	185	1	no	—
63	D₇	—	5	1	no	—
64	D₇	—	37	1	no	—
65	C₂²×C₃	—	1295	1	no	Hall
66	C₂×C₅	—	259	1	no	—
67	D₅	—	7	1	no	—
68	D₅	—	37	1	no	—
69	C₇	C₃×D₅×D₃₇	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	259	1	no	—
71	C₂×C₃	—	35	1	no	—
72	C₂×C₃	—	185	1	no	—
73	C₅	C₃×D₇×D₃₇	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	1295	1	no	Sylow
75	C₃	D₃₅⋊D₃₇	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	259	1	no	—
77	C₂	—	35	1	no	—
78	C₂	—	185	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₃₅⋊D₃₇
commutator, cosocle, hypocenter	C₅×C₇×C₃₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₃₇	C₂²
LCS	G ▷ C₅×C₇×C₃₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₃₇×D₃₅	C₂	semidirect
2. C₃×C₇×D₁₈₅	C₂	semidirect
3. C₃×C₅×D₂₅₉	C₂	semidirect
4. D₃₅⋊D₃₇	C₃	direct (N × H)
5. C₃×C₅×C₇×C₃₇	C₂²	semidirect
7. C₃₇×D₃₅	C₂×C₃	semidirect
8. C₇×D₁₈₅	C₂×C₃	semidirect
9. C₅×D₂₅₉	C₂×C₃	semidirect
11. C₃×D₂₅₉	D₅	semidirect
14. C₅×C₇×C₃₇	C₂²×C₃	semidirect
15. C₃×D₁₈₅	D₇	semidirect
19. C₃×C₇×C₃₇	C₂×D₅	semidirect
21. C₃×C₅×C₃₇	C₂×D₇	semidirect
22. D₂₅₉	C₃×D₅	semidirect
27. D₁₈₅	C₃×D₇	semidirect
30. C₇×C₃₇	C₂×C₃×D₅	semidirect
34. C₃×D₃₅	D₃₇	semidirect
37. C₅×C₃₇	C₂×C₃×D₇	semidirect
40. C₃×C₃₇	D₅×D₇	semidirect
41. C₃×C₅×C₇	C₂×D₃₇	semidirect
46. D₃₅	C₃×D₃₇	semidirect
53. C₃₇	C₃×D₅×D₇	semidirect
54. C₅×C₇	C₂×C₃×D₃₇	semidirect
59. C₃×C₇	D₅×D₃₇	semidirect
61. C₃×C₅	D₇×D₃₇	semidirect
69. C₇	C₃×D₅×D₃₇	semidirect
73. C₅	C₃×D₇×D₃₇	semidirect
75. C₃	D₃₅⋊D₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₃₇×D₃₅	2
C₃×C₇×D₁₈₅	2
C₃×C₅×D₂₅₉	2
D₃₅⋊D₃₇	3
C₃×D₇×D₃₇	5
C₃×D₅×D₃₇	7
C₃×D₅×D₇	37

Subgroups — C3×D35⋊D37 #29509670

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃₅⋊D₃₇ #29509670