Subgroups — C₂×C₃²×C₅×C₇×D₂₉ #49141673

Order 36540.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇×D₂₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×C₇×D₂₉	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₅×C₇×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃²×C₇×D₂₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×C₇×D₂₉	C₂×C₃	1	8	yes	direct product factor
7	C₂×C₃×C₅×C₇×C₂₉	C₂×C₃	1	4	yes	complemented
8	C₂×C₃²×C₅×D₂₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₅×C₇×D₂₉	C₃²	1	1	yes	characteristic, direct product factor, Hall
10	C₃²×C₇×D₂₉	C₂×C₅	1	2	yes	direct product factor
11	C₂×C₃²×C₇×C₂₉	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃×C₅×C₇×C₂₉	C₂²×C₃	1	4	yes	complemented
13	C₃²×C₅×D₂₉	C₂×C₇	1	2	yes	direct product factor
14	C₂×C₃²×C₅×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented
15	C₂×C₃×C₇×D₂₉	C₃×C₅	1	4	yes	direct product factor
16	C₅×C₇×D₂₉	C₂×C₃²	1	2	yes	direct product factor
17	C₂×C₅×C₇×C₂₉	C₂×C₃²	1	1	yes	characteristic, complemented
18	C₃²×C₇×C₂₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₅×D₂₉	C₃×C₇	1	4	yes	direct product factor
20	C₃²×C₅×C₂₉	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
21	C₂²×C₃²×C₅×C₇	—	29	1	no	maximal, Hall
22	C₂×C₃×C₇×C₂₉	C₂×C₃×C₅	1	4	yes	complemented
23	C₃×C₇×D₂₉	C₂×C₃×C₅	1	8	yes	direct product factor
24	C₂×C₃²×D₂₉	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
25	C₅×C₇×C₂₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₅×C₂₉	C₂×C₃×C₇	1	4	yes	complemented
27	C₃×C₅×D₂₉	C₂×C₃×C₇	1	8	yes	direct product factor
28	C₂×C₇×D₂₉	C₃²×C₅	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₃²×C₅×C₇	—	29	2	no	—
30	C₂×C₃²×C₅×C₇	D₂₉	1	1	yes	characteristic, direct product factor
31	C₃×C₇×C₂₉	C₂²×C₃×C₅	1	4	yes	complemented
32	C₂×C₅×D₂₉	C₃²×C₇	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₃²×C₂₉	C₂×C₅×C₇	1	1	yes	characteristic, complemented
34	C₃²×D₂₉	C₂×C₅×C₇	1	2	yes	direct product factor
35	C₃×C₅×C₂₉	C₂²×C₃×C₇	1	4	yes	complemented
36	C₂²×C₃×C₅×C₇	—	29	4	no	—
37	C₂×C₇×C₂₉	C₂×C₃²×C₅	1	1	yes	characteristic, complemented
38	C₇×D₂₉	C₂×C₃²×C₅	1	2	yes	direct product factor
39	C₂×C₃×D₂₉	C₃×C₅×C₇	1	4	yes	direct product factor
40	C₃²×C₅×C₇	C₂×D₂₉	1	1	yes	characteristic, direct product factor, Hall
41	C₂×C₅×C₂₉	C₂×C₃²×C₇	1	1	yes	characteristic, complemented
42	C₅×D₂₉	C₂×C₃²×C₇	1	2	yes	direct product factor
43	C₃²×C₂₉	C₂²×C₅×C₇	1	1	yes	characteristic, complemented, Hall
44	C₂²×C₃²×C₇	—	29	1	no	Hall
45	C₂×C₃×C₅×C₇	—	29	8	no	—
46	C₂×C₃×C₅×C₇	C₃×D₂₉	1	4	yes	direct product factor
47	C₇×C₂₉	C₂²×C₃²×C₅	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₃²×C₅	—	29	1	no	Hall
49	C₂×C₃×C₂₉	C₂×C₃×C₅×C₇	1	4	yes	complemented
50	C₃×D₂₉	C₂×C₃×C₅×C₇	1	8	yes	direct product factor
51	C₅×C₂₉	C₂²×C₃²×C₇	1	1	yes	characteristic, complemented, Hall
52	C₂²×C₅×C₇	—	29	1	no	Hall
53	C₂×C₃²×C₇	—	29	2	no	—
54	C₂×C₃²×C₇	C₅×D₂₉	1	1	yes	characteristic, direct product factor
55	C₂×D₂₉	C₃²×C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
56	C₃×C₅×C₇	C₂×C₃×D₂₉	1	4	yes	direct product factor
57	C₂×C₃²×C₅	—	29	2	no	—
58	C₂×C₃²×C₅	C₇×D₂₉	1	1	yes	characteristic, direct product factor
59	C₃×C₂₉	C₂²×C₃×C₅×C₇	1	4	yes	complemented
60	C₂²×C₃×C₇	—	29	4	no	—
61	C₂×C₅×C₇	—	29	2	no	—
62	C₂×C₅×C₇	C₃²×D₂₉	1	1	yes	characteristic, direct product factor
63	C₃²×C₇	C₂×C₅×D₂₉	1	1	yes	characteristic, direct product factor, Hall
64	C₂²×C₃×C₅	—	29	4	no	—
65	C₂×C₂₉	C₂×C₃²×C₅×C₇	1	1	yes	characteristic, complemented
66	D₂₉	C₂×C₃²×C₅×C₇	1	2	yes	direct product factor
67	C₃²×C₅	C₂×C₇×D₂₉	1	1	yes	characteristic, direct product factor, Hall
68	C₂×C₃×C₇	—	29	8	no	—
69	C₂×C₃×C₇	C₃×C₅×D₂₉	1	4	yes	direct product factor
70	C₂²×C₃²	—	29	1	no	Hall
71	C₅×C₇	C₂×C₃²×D₂₉	1	1	yes	characteristic, direct product factor, Hall
72	C₂×C₃×C₅	—	29	8	no	—
73	C₂×C₃×C₅	C₃×C₇×D₂₉	1	4	yes	direct product factor
74	C₂₉	C₂²×C₃²×C₅×C₇	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₇	—	29	1	no	Hall
76	C₃×C₇	C₂×C₃×C₅×D₂₉	1	4	yes	direct product factor
77	C₂²×C₅	—	29	1	no	Hall
78	C₂×C₃²	—	29	2	no	—
79	C₂×C₃²	C₅×C₇×D₂₉	1	1	yes	characteristic, direct product factor
80	C₃×C₅	C₂×C₃×C₇×D₂₉	1	4	yes	direct product factor
81	C₂×C₇	—	29	2	no	—
82	C₂×C₇	C₃²×C₅×D₂₉	1	1	yes	characteristic, direct product factor
83	C₂²×C₃	—	29	4	no	—
84	C₂×C₅	—	29	2	no	—
85	C₂×C₅	C₃²×C₇×D₂₉	1	1	yes	characteristic, direct product factor
86	C₃²	C₂×C₅×C₇×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
87	C₇	C₂×C₃²×C₅×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
88	C₂×C₃	—	29	8	no	—
89	C₂×C₃	C₃×C₅×C₇×D₂₉	1	4	yes	direct product factor
90	C₅	C₂×C₃²×C₇×D₂₉	1	1	yes	characteristic, direct product factor, Sylow
91	C₂²	—	29	1	no	Sylow
92	C₃	C₂×C₃×C₅×C₇×D₂₉	1	4	yes	direct product factor
93	C₂	—	29	2	no	—
94	C₂	C₃²×C₅×C₇×D₂₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₅×C₇	D₂₉
commutator, cosocle, hypocenter	C₂₉	C₂²×C₃²×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₇×C₂₉	C₂
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂×C₃²×C₅×C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₇×D₂₉	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₇×C₂₉	C₂	semidirect
3. C₂×C₃×C₅×C₇×D₂₉	C₃	direct (N × H)
4. C₃²×C₅×C₇×C₂₉	C₂²	semidirect
5. C₂×C₃²×C₇×D₂₉	C₅	direct (N × H)
6. C₃×C₅×C₇×D₂₉	C₂×C₃	direct (N × H)
7. C₂×C₃×C₅×C₇×C₂₉	C₂×C₃	semidirect
8. C₂×C₃²×C₅×D₂₉	C₇	direct (N × H)
9. C₂×C₅×C₇×D₂₉	C₃²	direct (N × H)
10. C₃²×C₇×D₂₉	C₂×C₅	direct (N × H)
11. C₂×C₃²×C₇×C₂₉	C₂×C₅	semidirect
12. C₃×C₅×C₇×C₂₉	C₂²×C₃	semidirect
13. C₃²×C₅×D₂₉	C₂×C₇	direct (N × H)
14. C₂×C₃²×C₅×C₂₉	C₂×C₇	semidirect
15. C₂×C₃×C₇×D₂₉	C₃×C₅	direct (N × H)
16. C₅×C₇×D₂₉	C₂×C₃²	direct (N × H)
17. C₂×C₅×C₇×C₂₉	C₂×C₃²	semidirect
18. C₃²×C₇×C₂₉	C₂²×C₅	semidirect
19. C₂×C₃×C₅×D₂₉	C₃×C₇	direct (N × H)
20. C₃²×C₅×C₂₉	C₂²×C₇	semidirect
22. C₂×C₃×C₇×C₂₉	C₂×C₃×C₅	semidirect
23. C₃×C₇×D₂₉	C₂×C₃×C₅	direct (N × H)
24. C₂×C₃²×D₂₉	C₅×C₇	direct (N × H)
25. C₅×C₇×C₂₉	C₂²×C₃²	semidirect
26. C₂×C₃×C₅×C₂₉	C₂×C₃×C₇	semidirect
27. C₃×C₅×D₂₉	C₂×C₃×C₇	direct (N × H)
28. C₂×C₇×D₂₉	C₃²×C₅	direct (N × H)
30. C₂×C₃²×C₅×C₇	D₂₉	direct (N × H)
31. C₃×C₇×C₂₉	C₂²×C₃×C₅	semidirect
32. C₂×C₅×D₂₉	C₃²×C₇	direct (N × H)
33. C₂×C₃²×C₂₉	C₂×C₅×C₇	semidirect
34. C₃²×D₂₉	C₂×C₅×C₇	direct (N × H)
35. C₃×C₅×C₂₉	C₂²×C₃×C₇	semidirect
37. C₂×C₇×C₂₉	C₂×C₃²×C₅	semidirect
38. C₇×D₂₉	C₂×C₃²×C₅	direct (N × H)
39. C₂×C₃×D₂₉	C₃×C₅×C₇	direct (N × H)
40. C₃²×C₅×C₇	C₂×D₂₉	direct (N × H)
41. C₂×C₅×C₂₉	C₂×C₃²×C₇	semidirect
42. C₅×D₂₉	C₂×C₃²×C₇	direct (N × H)
43. C₃²×C₂₉	C₂²×C₅×C₇	semidirect
46. C₂×C₃×C₅×C₇	C₃×D₂₉	direct (N × H)
47. C₇×C₂₉	C₂²×C₃²×C₅	semidirect
49. C₂×C₃×C₂₉	C₂×C₃×C₅×C₇	semidirect
50. C₃×D₂₉	C₂×C₃×C₅×C₇	direct (N × H)
51. C₅×C₂₉	C₂²×C₃²×C₇	semidirect
54. C₂×C₃²×C₇	C₅×D₂₉	direct (N × H)
55. C₂×D₂₉	C₃²×C₅×C₇	direct (N × H)
56. C₃×C₅×C₇	C₂×C₃×D₂₉	direct (N × H)
58. C₂×C₃²×C₅	C₇×D₂₉	direct (N × H)
59. C₃×C₂₉	C₂²×C₃×C₅×C₇	semidirect
62. C₂×C₅×C₇	C₃²×D₂₉	direct (N × H)
63. C₃²×C₇	C₂×C₅×D₂₉	direct (N × H)
65. C₂×C₂₉	C₂×C₃²×C₅×C₇	semidirect
66. D₂₉	C₂×C₃²×C₅×C₇	direct (N × H)
67. C₃²×C₅	C₂×C₇×D₂₉	direct (N × H)
69. C₂×C₃×C₇	C₃×C₅×D₂₉	direct (N × H)
71. C₅×C₇	C₂×C₃²×D₂₉	direct (N × H)
73. C₂×C₃×C₅	C₃×C₇×D₂₉	direct (N × H)
74. C₂₉	C₂²×C₃²×C₅×C₇	semidirect
76. C₃×C₇	C₂×C₃×C₅×D₂₉	direct (N × H)
79. C₂×C₃²	C₅×C₇×D₂₉	direct (N × H)
80. C₃×C₅	C₂×C₃×C₇×D₂₉	direct (N × H)
82. C₂×C₇	C₃²×C₅×D₂₉	direct (N × H)
85. C₂×C₅	C₃²×C₇×D₂₉	direct (N × H)
86. C₃²	C₂×C₅×C₇×D₂₉	direct (N × H)
87. C₇	C₂×C₃²×C₅×D₂₉	direct (N × H)
89. C₂×C₃	C₃×C₅×C₇×D₂₉	direct (N × H)
90. C₅	C₂×C₃²×C₇×D₂₉	direct (N × H)
92. C₃	C₂×C₃×C₅×C₇×D₂₉	direct (N × H)
94. C₂	C₃²×C₅×C₇×D₂₉	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×C₅×C₇×D₂₉	2
C₂×C₃²×C₅×C₇×C₂₉	2
C₂×C₃×C₅×C₇×D₂₉	3
C₂×C₃²×C₇×D₂₉	5
C₂×C₃²×C₅×D₂₉	7
C₂²×C₃²×C₅×C₇	29

Subgroups — C2×C32×C5×C7×D29 #49141673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₅×C₇×D₂₉ #49141673