Subgroups — C₃²×C₇×C₅⋊D₃₅ #36348066

Order 22050.

528 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×C₇²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×C₅⋊D₃₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₇×D₃₅	—	5	6	no	maximal
4	C₃×C₅²×C₇²	C₂×C₃	1	4	yes	complemented
5	C₃²×C₅⋊D₃₅	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₃²×C₇×C₅⋊D₅	—	7	1	no	maximal
7	C₇×C₅⋊D₃₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₃²×C₅×C₇²	D₅	1	6	yes	complemented
9	C₃²×C₅²×C₇	—	2	3	no	—
10	C₃²×C₅²×C₇	D₇	1	1	yes	characteristic, complemented
11	C₃²×C₅²×C₇	C₂×C₇	1	1	yes	characteristic, complemented
12	C₃×C₇×D₃₅	—	5	24	no	—
13	C₅²×C₇²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅⋊D₃₅	C₃×C₇	1	4	yes	direct product factor
15	C₃×C₇×C₅⋊D₅	—	7	4	no	—
16	C₃²×C₇×D₇	—	25	1	no	Hall
17	C₃×C₅×C₇²	C₃×D₅	1	24	yes	complemented
18	C₃²×D₃₅	—	5	6	no	—
19	C₃²×C₇×D₅	—	35	6	no	—
20	C₃×C₅²×C₇	—	2	12	no	—
21	C₃×C₅²×C₇	C₃×D₇	1	4	yes	complemented
22	C₃×C₅²×C₇	C₂×C₃×C₇	1	4	yes	complemented
23	C₇×D₃₅	—	5	6	no	—
24	C₃²×C₅⋊D₅	—	7	1	no	Hall
25	C₃²×C₇²	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
26	C₅⋊D₃₅	C₃²×C₇	1	1	yes	characteristic, direct product factor
27	C₇×C₅⋊D₅	—	7	1	no	—
28	C₃²×C₅×C₇	—	2	18	no	—
29	C₃²×C₅×C₇	C₇×D₅	1	6	yes	complemented
30	C₃²×C₅×C₇	D₃₅	1	6	yes	complemented
31	C₃×C₇×D₇	—	25	4	no	—
32	C₅×C₇²	C₃²×D₅	1	6	yes	complemented
33	C₃²×C₅²	C₇×D₇	1	1	yes	characteristic, complemented, Hall
34	C₃×D₃₅	—	5	24	no	—
35	C₃×C₇×D₅	—	35	24	no	—
36	C₅²×C₇	—	2	3	no	—
37	C₅²×C₇	C₃²×D₇	1	1	yes	characteristic, complemented
38	C₅²×C₇	C₂×C₃²×C₇	1	1	yes	characteristic, complemented
39	C₃×C₅⋊D₅	—	7	4	no	—
40	C₃×C₇²	C₃×C₅⋊D₅	1	4	yes	complemented
41	C₂×C₃²×C₇	—	175	1	no	—
42	C₃²×D₇	—	25	1	no	—
43	C₃×C₅×C₇	—	2	72	no	—
44	C₃×C₅×C₇	C₃×C₇×D₅	1	24	yes	complemented
45	C₃×C₅×C₇	C₃×D₃₅	1	24	yes	complemented
46	C₇×D₇	—	25	1	no	Hall
47	C₃²×D₅	—	35	6	no	—
48	C₃×C₅²	C₃×C₇×D₇	1	4	yes	complemented
49	D₃₅	—	5	6	no	—
50	C₇×D₅	—	35	6	no	—
51	C₃²×C₇	—	2	3	no	—
52	C₃²×C₇	C₇×C₅⋊D₅	1	1	yes	characteristic, complemented
53	C₃²×C₇	C₅⋊D₃₅	1	1	yes	characteristic, direct product factor
54	C₅⋊D₅	—	7	1	no	Hall
55	C₇²	C₃²×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
56	C₃²×C₅	C₇×D₃₅	1	6	yes	complemented
57	C₂×C₃×C₇	—	175	4	no	—
58	C₃×D₇	—	25	4	no	—
59	C₅×C₇	—	2	18	no	—
60	C₅×C₇	C₃²×C₇×D₅	1	6	yes	complemented
61	C₅×C₇	C₃²×D₃₅	1	6	yes	complemented
62	C₃×D₅	—	35	24	no	—
63	C₅²	C₃²×C₇×D₇	1	1	yes	characteristic, complemented, Sylow
64	C₃×C₇	—	2	12	no	—
65	C₃×C₇	C₃×C₇×C₅⋊D₅	1	4	yes	complemented
66	C₃×C₇	C₃×C₅⋊D₃₅	1	4	yes	direct product factor
67	C₂×C₃²	—	175	1	no	Hall
68	C₃×C₅	C₃×C₇×D₃₅	1	24	yes	complemented
69	C₂×C₇	—	175	1	no	—
70	D₇	—	25	1	no	—
71	D₅	—	35	6	no	—
72	C₃²	C₇×C₅⋊D₃₅	1	1	yes	characteristic, direct product factor, Sylow
73	C₇	—	2	3	no	—
74	C₇	C₃²×C₇×C₅⋊D₅	1	1	yes	characteristic, complemented
75	C₇	C₃²×C₅⋊D₃₅	1	1	yes	characteristic, direct product factor
76	C₂×C₃	—	175	4	no	—
77	C₅	C₃²×C₇×D₃₅	1	6	yes	complemented
78	C₃	C₃×C₇×C₅⋊D₃₅	1	4	yes	direct product factor
79	C₂	—	175	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₇	C₅⋊D₃₅
commutator, cosocle, hypocenter	C₅²×C₇	C₂×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₇²	C₂
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₃²×C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×C₇²	C₂	semidirect
2. C₃×C₇×C₅⋊D₃₅	C₃	direct (N × H)
4. C₃×C₅²×C₇²	C₂×C₃	semidirect
5. C₃²×C₅⋊D₃₅	C₇	direct (N × H)
7. C₇×C₅⋊D₃₅	C₃²	direct (N × H)
8. C₃²×C₅×C₇²	D₅	semidirect
10. C₃²×C₅²×C₇	D₇	semidirect
11. C₃²×C₅²×C₇	C₂×C₇	semidirect
13. C₅²×C₇²	C₂×C₃²	semidirect
14. C₃×C₅⋊D₃₅	C₃×C₇	direct (N × H)
17. C₃×C₅×C₇²	C₃×D₅	semidirect
21. C₃×C₅²×C₇	C₃×D₇	semidirect
22. C₃×C₅²×C₇	C₂×C₃×C₇	semidirect
25. C₃²×C₇²	C₅⋊D₅	semidirect
26. C₅⋊D₃₅	C₃²×C₇	direct (N × H)
29. C₃²×C₅×C₇	C₇×D₅	semidirect
30. C₃²×C₅×C₇	D₃₅	semidirect
32. C₅×C₇²	C₃²×D₅	semidirect
33. C₃²×C₅²	C₇×D₇	semidirect
37. C₅²×C₇	C₃²×D₇	semidirect
38. C₅²×C₇	C₂×C₃²×C₇	semidirect
40. C₃×C₇²	C₃×C₅⋊D₅	semidirect
44. C₃×C₅×C₇	C₃×C₇×D₅	semidirect
45. C₃×C₅×C₇	C₃×D₃₅	semidirect
48. C₃×C₅²	C₃×C₇×D₇	semidirect
52. C₃²×C₇	C₇×C₅⋊D₅	semidirect
53. C₃²×C₇	C₅⋊D₃₅	direct (N × H)
55. C₇²	C₃²×C₅⋊D₅	semidirect
56. C₃²×C₅	C₇×D₃₅	semidirect
60. C₅×C₇	C₃²×C₇×D₅	semidirect
61. C₅×C₇	C₃²×D₃₅	semidirect
63. C₅²	C₃²×C₇×D₇	semidirect
65. C₃×C₇	C₃×C₇×C₅⋊D₅	semidirect
66. C₃×C₇	C₃×C₅⋊D₃₅	direct (N × H)
68. C₃×C₅	C₃×C₇×D₃₅	semidirect
72. C₃²	C₇×C₅⋊D₃₅	direct (N × H)
74. C₇	C₃²×C₇×C₅⋊D₅	semidirect
75. C₇	C₃²×C₅⋊D₃₅	direct (N × H)
77. C₅	C₃²×C₇×D₃₅	semidirect
78. C₃	C₃×C₇×C₅⋊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
C₃²×C₅²×C₇²	2
C₃×C₇×C₅⋊D₃₅	3
C₃²×C₇×D₃₅	5
C₃²×C₅⋊D₃₅	7
C₃²×C₇×C₅⋊D₅	7

Subgroups — C32×C7×C5⋊D35 #36348066

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₇×C₅⋊D₃₅ #36348066