Subgroups — C₂×C₅×C₇×D₉×C₂₉ #49141315

Order 36540.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×D₉×C₂₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇×C₉×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₃×C₇×C₂₉	—	3	1	no	maximal
4	C₅×C₇×C₉×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×D₉×C₂₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×D₃×C₇×C₂₉	—	3	2	no	—
7	C₂×C₃×C₅×C₇×C₂₉	D₃	1	1	yes	characteristic
8	C₂×C₅×D₉×C₂₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₅×C₇×C₂₉	—	9	1	no	Hall
10	C₇×D₉×C₂₉	C₂×C₅	1	2	yes	direct product factor
11	C₂×C₇×C₉×C₂₉	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃×C₅×C₇×C₂₉	C₂×D₃	1	1	yes	characteristic
13	C₅×D₉×C₂₉	C₂×C₇	1	2	yes	direct product factor
14	C₂×C₅×C₉×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented
15	C₂×D₃×C₇×C₂₉	—	3	1	no	—
16	C₂×C₅×C₇×C₂₉	—	9	2	no	—
17	C₂×C₅×C₇×C₂₉	D₉	1	1	yes	characteristic, direct product factor
18	C₇×C₉×C₂₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅×D₃×C₂₉	—	3	1	no	—
20	C₅×C₉×C₂₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅×C₇×D₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₃×C₇×C₂₉	C₅×D₃	1	1	yes	characteristic
23	D₃×C₇×C₂₉	—	3	2	no	—
24	C₂×D₉×C₂₉	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
25	C₅×C₇×C₂₉	C₂×D₉	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₃×C₅×C₂₉	D₃×C₇	1	1	yes	characteristic
27	C₅×D₃×C₂₉	—	3	2	no	—
28	C₂²×C₇×C₂₉	—	9	1	no	Hall
29	C₂×C₅×C₇×C₉	C₂×C₂₉	1	1	yes	characteristic, complemented
30	C₅×C₇×D₉	C₂×C₂₉	1	2	yes	direct product factor
31	C₃×C₇×C₂₉	C₂×C₅×D₃	1	1	yes	characteristic
32	C₂²×C₅×C₂₉	—	9	1	no	Hall
33	C₂×C₉×C₂₉	C₂×C₅×C₇	1	1	yes	characteristic, complemented
34	D₉×C₂₉	C₂×C₅×C₇	1	2	yes	direct product factor
35	C₃×C₅×C₂₉	C₂×D₃×C₇	1	1	yes	characteristic
36	C₂×C₅×D₃×C₇	—	3	1	no	—
37	C₂×C₇×C₂₉	—	9	2	no	—
38	C₂×C₇×C₂₉	C₅×D₉	1	1	yes	characteristic, direct product factor
39	C₂×D₃×C₂₉	—	3	1	no	—
40	C₅×C₇×C₉	C₂²×C₂₉	1	1	yes	characteristic, complemented, Hall
41	C₂×C₅×C₂₉	—	9	2	no	—
42	C₂×C₅×C₂₉	C₇×D₉	1	1	yes	characteristic, direct product factor
43	C₉×C₂₉	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Hall
44	C₂×C₇×D₉	C₅×C₂₉	1	1	yes	characteristic, direct product factor, Hall
45	C₂×C₃×C₅×C₇	D₃×C₂₉	1	1	yes	characteristic
46	C₅×D₃×C₇	—	3	2	no	—
47	C₇×C₂₉	C₂×C₅×D₉	1	1	yes	characteristic, direct product factor, Hall
48	C₂×C₅×D₉	C₇×C₂₉	1	1	yes	characteristic, direct product factor, Hall
49	C₂×C₃×C₂₉	C₅×D₃×C₇	1	1	yes	characteristic
50	D₃×C₂₉	—	3	2	no	—
51	C₅×C₂₉	C₂×C₇×D₉	1	1	yes	characteristic, direct product factor, Hall
52	C₂²×C₅×C₇	—	9	1	no	Hall
53	C₂×C₇×C₉	C₂×C₅×C₂₉	1	1	yes	characteristic, complemented
54	C₇×D₉	C₂×C₅×C₂₉	1	2	yes	direct product factor
55	C₂²×C₂₉	—	9	1	no	Hall
56	C₃×C₅×C₇	C₂×D₃×C₂₉	1	1	yes	characteristic
57	C₂×C₅×C₉	C₂×C₇×C₂₉	1	1	yes	characteristic, complemented
58	C₅×D₉	C₂×C₇×C₂₉	1	2	yes	direct product factor
59	C₃×C₂₉	C₂×C₅×D₃×C₇	1	1	yes	characteristic
60	C₂×D₃×C₇	—	3	1	no	—
61	C₂×C₅×C₇	—	9	2	no	—
62	C₂×C₅×C₇	D₉×C₂₉	1	1	yes	characteristic, direct product factor
63	C₇×C₉	C₂²×C₅×C₂₉	1	1	yes	characteristic, complemented, Hall
64	C₂×C₅×D₃	—	3	1	no	—
65	C₂×C₂₉	—	9	2	no	—
66	C₂×C₂₉	C₅×C₇×D₉	1	1	yes	characteristic, direct product factor
67	C₅×C₉	C₂²×C₇×C₂₉	1	1	yes	characteristic, complemented, Hall
68	C₂×C₃×C₇	C₅×D₃×C₂₉	1	1	yes	characteristic
69	D₃×C₇	—	3	2	no	—
70	C₂×D₉	C₅×C₇×C₂₉	1	1	yes	characteristic, direct product factor, Hall
71	C₅×C₇	C₂×D₉×C₂₉	1	1	yes	characteristic, direct product factor, Hall
72	C₂×C₃×C₅	D₃×C₇×C₂₉	1	1	yes	characteristic
73	C₅×D₃	—	3	2	no	—
74	C₂₉	C₂×C₅×C₇×D₉	1	1	yes	characteristic, direct product factor, Sylow
75	C₂²×C₇	—	9	1	no	Hall
76	C₃×C₇	C₂×C₅×D₃×C₂₉	1	1	yes	characteristic
77	C₂²×C₅	—	9	1	no	Hall
78	C₂×C₉	C₂×C₅×C₇×C₂₉	1	1	yes	characteristic, complemented
79	D₉	C₂×C₅×C₇×C₂₉	1	2	yes	direct product factor
80	C₃×C₅	C₂×D₃×C₇×C₂₉	1	1	yes	characteristic
81	C₂×C₇	—	9	2	no	—
82	C₂×C₇	C₅×D₉×C₂₉	1	1	yes	characteristic, direct product factor
83	C₂×D₃	—	3	1	no	—
84	C₂×C₅	—	9	2	no	—
85	C₂×C₅	C₇×D₉×C₂₉	1	1	yes	characteristic, direct product factor
86	C₉	C₂²×C₅×C₇×C₂₉	1	1	yes	characteristic, complemented, Sylow
87	C₇	C₂×C₅×D₉×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
88	C₂×C₃	C₅×D₃×C₇×C₂₉	1	1	yes	characteristic
89	D₃	—	3	2	no	—
90	C₅	C₂×C₇×D₉×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
91	C₂²	—	9	1	no	Sylow
92	C₃	C₂×C₅×D₃×C₇×C₂₉	1	1	yes	characteristic
93	C₂	—	9	2	no	—
94	C₂	C₅×C₇×D₉×C₂₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₇×C₂₉	D₉
commutator, cosocle, hypocenter	C₉	C₂²×C₅×C₇×C₂₉
Frattini	C₃	C₂×C₅×D₃×C₇×C₂₉
Fitting	C₂×C₅×C₇×C₉×C₂₉	C₂
socle	C₂×C₃×C₅×C₇×C₂₉	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₅×C₇×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×D₉×C₂₉	C₂	direct (N × H)
2. C₂×C₅×C₇×C₉×C₂₉	C₂	semidirect
4. C₅×C₇×C₉×C₂₉	C₂²	semidirect
5. C₂×C₇×D₉×C₂₉	C₅	direct (N × H)
8. C₂×C₅×D₉×C₂₉	C₇	direct (N × H)
10. C₇×D₉×C₂₉	C₂×C₅	direct (N × H)
11. C₂×C₇×C₉×C₂₉	C₂×C₅	semidirect
13. C₅×D₉×C₂₉	C₂×C₇	direct (N × H)
14. C₂×C₅×C₉×C₂₉	C₂×C₇	semidirect
17. C₂×C₅×C₇×C₂₉	D₉	direct (N × H)
18. C₇×C₉×C₂₉	C₂²×C₅	semidirect
20. C₅×C₉×C₂₉	C₂²×C₇	semidirect
21. C₂×C₅×C₇×D₉	C₂₉	direct (N × H)
24. C₂×D₉×C₂₉	C₅×C₇	direct (N × H)
25. C₅×C₇×C₂₉	C₂×D₉	direct (N × H)
29. C₂×C₅×C₇×C₉	C₂×C₂₉	semidirect
30. C₅×C₇×D₉	C₂×C₂₉	direct (N × H)
33. C₂×C₉×C₂₉	C₂×C₅×C₇	semidirect
34. D₉×C₂₉	C₂×C₅×C₇	direct (N × H)
38. C₂×C₇×C₂₉	C₅×D₉	direct (N × H)
40. C₅×C₇×C₉	C₂²×C₂₉	semidirect
42. C₂×C₅×C₂₉	C₇×D₉	direct (N × H)
43. C₉×C₂₉	C₂²×C₅×C₇	semidirect
44. C₂×C₇×D₉	C₅×C₂₉	direct (N × H)
47. C₇×C₂₉	C₂×C₅×D₉	direct (N × H)
48. C₂×C₅×D₉	C₇×C₂₉	direct (N × H)
51. C₅×C₂₉	C₂×C₇×D₉	direct (N × H)
53. C₂×C₇×C₉	C₂×C₅×C₂₉	semidirect
54. C₇×D₉	C₂×C₅×C₂₉	direct (N × H)
57. C₂×C₅×C₉	C₂×C₇×C₂₉	semidirect
58. C₅×D₉	C₂×C₇×C₂₉	direct (N × H)
62. C₂×C₅×C₇	D₉×C₂₉	direct (N × H)
63. C₇×C₉	C₂²×C₅×C₂₉	semidirect
66. C₂×C₂₉	C₅×C₇×D₉	direct (N × H)
67. C₅×C₉	C₂²×C₇×C₂₉	semidirect
70. C₂×D₉	C₅×C₇×C₂₉	direct (N × H)
71. C₅×C₇	C₂×D₉×C₂₉	direct (N × H)
74. C₂₉	C₂×C₅×C₇×D₉	direct (N × H)
78. C₂×C₉	C₂×C₅×C₇×C₂₉	semidirect
79. D₉	C₂×C₅×C₇×C₂₉	direct (N × H)
82. C₂×C₇	C₅×D₉×C₂₉	direct (N × H)
85. C₂×C₅	C₇×D₉×C₂₉	direct (N × H)
86. C₉	C₂²×C₅×C₇×C₂₉	semidirect
87. C₇	C₂×C₅×D₉×C₂₉	direct (N × H)
90. C₅	C₂×C₇×D₉×C₂₉	direct (N × H)
94. C₂	C₅×C₇×D₉×C₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₇×D₉×C₂₉	2
C₂×C₅×C₇×C₉×C₂₉	2
C₂×C₅×D₃×C₇×C₂₉	3
C₂×C₇×D₉×C₂₉	5
C₂×C₅×D₉×C₂₉	7
C₂×C₅×C₇×D₉	29

Subgroups — C2×C5×C7×D9×C29 #49141315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₇×D₉×C₂₉ #49141315