Subgroups — C₃×D₅×D₃₅ #14523639

Order 2100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×D₃₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₇×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₃₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅²×C₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×D₃₅	—	5	1	no	maximal
7	C₃×D₅×D₇	—	5	1	no	maximal
8	C₅⋊D₃₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₃₅	C₂×C₃	1	1	yes	characteristic, complemented
10	C₅×C₇×D₅	C₂×C₃	1	1	yes	characteristic, complemented
11	C₃×D₅²	—	7	1	no	maximal, Hall
12	C₂×C₃×C₅×C₇	—	5	1	no	—
13	C₃×D₃₅	—	5	1	no	—
14	C₃×D₃₅	—	5	1	no	—
15	C₃×D₃₅	—	10	2	no	—
16	C₃×D₃₅	D₅	1	1	yes	characteristic, direct product factor
17	C₃×C₇×D₅	D₅	1	1	yes	characteristic, complemented
18	C₃×C₅×D₇	—	5	1	no	—
19	C₅²×C₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
20	C₃×C₅⋊D₅	—	7	1	no	—
21	C₃×C₅×D₅	—	7	1	no	—
22	C₃×C₅×D₅	D₇	1	1	yes	characteristic, complemented
23	C₂×D₃₅	—	5	1	no	—
24	D₅×D₇	—	5	1	no	—
25	C₃×C₅×C₇	—	2	2	no	—
26	C₃×C₅×C₇	C₂×D₅	1	1	yes	characteristic, complemented
27	C₃×C₅×C₇	C₂×D₅	1	1	yes	characteristic, complemented
28	D₅²	—	7	1	no	Hall
29	C₂×C₃×D₇	—	25	1	no	Hall
30	C₃×C₅²	C₂×D₇	1	1	yes	characteristic, complemented, Hall
31	C₂×C₅×C₇	—	5	1	no	—
32	D₃₅	—	5	1	no	—
33	D₃₅	—	5	1	no	—
34	D₃₅	—	10	2	no	—
35	D₃₅	C₃×D₅	1	1	yes	characteristic, direct product factor
36	C₅×D₇	—	5	1	no	—
37	C₇×D₅	C₃×D₅	1	1	yes	characteristic, complemented
38	C₂×C₃×D₅	—	35	1	no	—
39	C₂×C₃×D₅	—	35	1	no	—
40	C₅⋊D₅	—	7	1	no	—
41	C₅×D₅	—	7	1	no	—
42	C₅×D₅	C₃×D₇	1	1	yes	characteristic, complemented
43	C₂×C₃×C₇	—	5	1	no	—
44	C₃×D₇	—	5	1	no	—
45	C₃×D₇	—	25	1	no	—
46	C₅×C₇	—	2	2	no	—
47	C₅×C₇	C₂×C₃×D₅	1	1	yes	characteristic, complemented
48	C₅×C₇	C₂×C₃×D₅	1	1	yes	characteristic, complemented
49	C₂×C₃×C₅	—	5	1	no	—
50	C₂×C₃×C₅	—	35	1	no	—
51	C₃×D₅	—	7	1	no	—
52	C₃×D₅	—	35	1	no	—
53	C₃×D₅	—	35	1	no	—
54	C₃×D₅	—	70	2	no	—
55	C₃×D₅	D₃₅	1	1	yes	characteristic, direct product factor
56	C₂×D₇	—	25	1	no	Hall
57	C₅²	C₂×C₃×D₇	1	1	yes	characteristic, complemented, Sylow
58	C₃×C₇	D₅²	1	1	yes	characteristic, complemented, Hall
59	C₂×D₅	—	35	1	no	—
60	C₂×D₅	—	35	1	no	—
61	C₃×C₅	—	2	2	no	—
62	C₃×C₅	D₅×D₇	1	1	yes	characteristic, complemented
63	C₃×C₅	C₂×D₃₅	1	1	yes	characteristic, complemented
64	C₂×C₇	—	5	1	no	—
65	D₇	—	5	1	no	—
66	D₇	—	25	1	no	—
67	C₂²×C₃	—	175	1	no	Hall
68	C₂×C₅	—	5	1	no	—
69	C₂×C₅	—	35	1	no	—
70	D₅	—	7	1	no	—
71	D₅	—	35	1	no	—
72	D₅	—	35	1	no	—
73	D₅	—	70	2	no	—
74	D₅	C₃×D₃₅	1	1	yes	characteristic, direct product factor
75	C₇	C₃×D₅²	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₃	—	5	1	no	—
77	C₂×C₃	—	35	1	no	—
78	C₂×C₃	—	175	1	no	—
79	C₅	—	2	2	no	—
80	C₅	C₃×D₅×D₇	1	1	yes	characteristic, complemented
81	C₅	C₂×C₃×D₃₅	1	1	yes	characteristic, complemented
82	C₂²	—	175	1	no	Sylow
83	C₃	D₅×D₃₅	1	1	yes	characteristic, direct product factor, Sylow
84	C₂	—	5	1	no	—
85	C₂	—	35	1	no	—
86	C₂	—	175	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₅×D₃₅
commutator, cosocle, hypocenter	C₅²×C₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇	C₂²
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅⋊D₃₅	C₂	semidirect
2. C₃×C₅×D₃₅	C₂	semidirect
3. C₃×C₅×C₇×D₅	C₂	semidirect
4. D₅×D₃₅	C₃	direct (N × H)
5. C₃×C₅²×C₇	C₂²	semidirect
8. C₅⋊D₃₅	C₂×C₃	semidirect
9. C₅×D₃₅	C₂×C₃	semidirect
10. C₅×C₇×D₅	C₂×C₃	semidirect
16. C₃×D₃₅	D₅	direct (N × H)
17. C₃×C₇×D₅	D₅	semidirect
19. C₅²×C₇	C₂²×C₃	semidirect
22. C₃×C₅×D₅	D₇	semidirect
26. C₃×C₅×C₇	C₂×D₅	semidirect
27. C₃×C₅×C₇	C₂×D₅	semidirect
30. C₃×C₅²	C₂×D₇	semidirect
35. D₃₅	C₃×D₅	direct (N × H)
37. C₇×D₅	C₃×D₅	semidirect
42. C₅×D₅	C₃×D₇	semidirect
47. C₅×C₇	C₂×C₃×D₅	semidirect
48. C₅×C₇	C₂×C₃×D₅	semidirect
55. C₃×D₅	D₃₅	direct (N × H)
57. C₅²	C₂×C₃×D₇	semidirect
58. C₃×C₇	D₅²	semidirect
62. C₃×C₅	D₅×D₇	semidirect
63. C₃×C₅	C₂×D₃₅	semidirect
74. D₅	C₃×D₃₅	direct (N × H)
75. C₇	C₃×D₅²	semidirect
80. C₅	C₃×D₅×D₇	semidirect
81. C₅	C₂×C₃×D₃₅	semidirect
83. C₃	D₅×D₃₅	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×C₅⋊D₃₅	2
C₃×C₅×D₃₅	2
C₃×C₅×C₇×D₅	2
D₅×D₃₅	3
C₂×C₃×D₃₅	5
C₃×D₅×D₇	5
C₃×D₅²	7

Subgroups — C3×D5×D35 #14523639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×D₃₅ #14523639