Subgroups — C₂²×C₄×C₅×C₈×C₂₉ #72196366

Order 18560.

1520 conjugacy classes of subgroups.

The subgroup lattice has 168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²×C₅×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₅×C₈×C₂₉	C₂	1	2	yes	maximal
3	C₂×C₄×C₅×C₈×C₂₉	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₄×C₅×C₂₉	C₄	1	2	yes	—
5	C₂³×C₄×C₅×C₂₉	C₂²	1	1	yes	characteristic
6	C₂²×C₅×C₈×C₂₉	C₄	1	16	yes	direct product factor
7	C₂²×C₅×C₈×C₂₉	C₂²	1	12	yes	—
8	C₂×C₄²×C₅×C₂₉	C₄	1	6	yes	—
9	C₂×C₄²×C₅×C₂₉	C₂²	1	6	yes	—
10	C₄×C₅×C₈×C₂₉	C₂²	1	16	yes	direct product factor
11	C₂⁴×C₅×C₂₉	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄×C₅×C₂₉	C₈	1	16	yes	direct product factor
13	C₂²×C₄×C₅×C₂₉	C₂×C₄	1	3	yes	—
14	C₂²×C₄×C₅×C₂₉	C₂×C₄	1	8	yes	—
15	C₂²×C₄×C₅×C₂₉	C₂×C₄	1	12	yes	—
16	C₂²×C₄×C₅×C₂₉	C₂³	1	3	yes	—
17	C₄²×C₅×C₂₉	C₂×C₄	1	12	yes	—
18	C₄²×C₅×C₂₉	C₂³	1	4	yes	—
19	C₂×C₅×C₈×C₂₉	C₂×C₄	1	48	yes	direct product factor
20	C₂×C₅×C₈×C₂₉	C₂³	1	8	yes	—
21	C₂²×C₄×C₈×C₂₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂³×C₈×C₂₉	C₂×C₅	1	2	yes	—
23	C₂²×C₄²×C₂₉	C₂×C₅	1	1	yes	characteristic
24	C₂×C₄×C₈×C₂₉	C₂×C₅	1	12	yes	direct product factor
25	C₂³×C₅×C₂₉	C₄²	1	4	yes	—
26	C₂³×C₅×C₂₉	C₂×C₈	1	8	yes	—
27	C₂³×C₅×C₂₉	C₂²×C₄	1	3	yes	—
28	C₂×C₄×C₅×C₂₉	C₄²	1	12	yes	—
29	C₂×C₄×C₅×C₂₉	C₂×C₈	1	48	yes	direct product factor
30	C₂×C₄×C₅×C₂₉	C₂²×C₄	1	3	yes	—
31	C₂×C₄×C₅×C₂₉	C₂²×C₄	1	8	yes	—
32	C₂×C₄×C₅×C₂₉	C₂²×C₄	1	12	yes	—
33	C₂×C₄×C₅×C₂₉	C₂⁴	1	1	yes	characteristic
34	C₅×C₈×C₂₉	C₂²×C₄	1	16	yes	direct product factor
35	C₂³×C₄×C₂₉	C₄×C₅	1	2	yes	—
36	C₂³×C₄×C₂₉	C₂²×C₅	1	1	yes	characteristic
37	C₂²×C₈×C₂₉	C₄×C₅	1	16	yes	direct product factor
38	C₂²×C₈×C₂₉	C₂²×C₅	1	12	yes	—
39	C₂×C₄²×C₂₉	C₄×C₅	1	6	yes	—
40	C₂×C₄²×C₂₉	C₂²×C₅	1	6	yes	—
41	C₄×C₈×C₂₉	C₂²×C₅	1	16	yes	direct product factor
42	C₂²×C₄×C₅×C₈	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₂²×C₅×C₂₉	C₄×C₈	1	16	yes	direct product factor
44	C₂²×C₅×C₂₉	C₂×C₄²	1	6	yes	—
45	C₂²×C₅×C₂₉	C₂²×C₈	1	12	yes	—
46	C₂²×C₅×C₂₉	C₂³×C₄	1	1	yes	characteristic
47	C₄×C₅×C₂₉	C₂×C₄²	1	6	yes	—
48	C₄×C₅×C₂₉	C₂²×C₈	1	16	yes	direct product factor
49	C₄×C₅×C₂₉	C₂³×C₄	1	2	yes	—
50	C₂⁴×C₂₉	C₂×C₄×C₅	1	1	yes	characteristic
51	C₂²×C₄×C₂₉	C₅×C₈	1	16	yes	direct product factor
52	C₂²×C₄×C₂₉	C₂×C₄×C₅	1	3	yes	—
53	C₂²×C₄×C₂₉	C₂×C₄×C₅	1	8	yes	—
54	C₂²×C₄×C₂₉	C₂×C₄×C₅	1	12	yes	—
55	C₂²×C₄×C₂₉	C₂³×C₅	1	3	yes	—
56	C₂×C₈×C₂₉	C₂×C₄×C₅	1	48	yes	direct product factor
57	C₂×C₈×C₂₉	C₂³×C₅	1	8	yes	—
58	C₄²×C₂₉	C₂×C₄×C₅	1	12	yes	—
59	C₄²×C₂₉	C₂³×C₅	1	4	yes	—
60	C₂³×C₅×C₈	C₂×C₂₉	1	2	yes	—
61	C₂²×C₄²×C₅	C₂×C₂₉	1	1	yes	characteristic
62	C₂×C₄×C₅×C₈	C₂×C₂₉	1	12	yes	direct product factor
63	C₂×C₅×C₂₉	C₂×C₄×C₈	1	12	yes	direct product factor
64	C₂×C₅×C₂₉	C₂²×C₄²	1	1	yes	characteristic
65	C₂×C₅×C₂₉	C₂³×C₈	1	2	yes	—
66	C₂³×C₂₉	C₄²×C₅	1	4	yes	—
67	C₂³×C₂₉	C₂×C₅×C₈	1	8	yes	—
68	C₂³×C₂₉	C₂²×C₄×C₅	1	3	yes	—
69	C₂×C₄×C₂₉	C₄²×C₅	1	12	yes	—
70	C₂×C₄×C₂₉	C₂×C₅×C₈	1	48	yes	direct product factor
71	C₂×C₄×C₂₉	C₂²×C₄×C₅	1	3	yes	—
72	C₂×C₄×C₂₉	C₂²×C₄×C₅	1	8	yes	—
73	C₂×C₄×C₂₉	C₂²×C₄×C₅	1	12	yes	—
74	C₂×C₄×C₂₉	C₂⁴×C₅	1	1	yes	characteristic
75	C₈×C₂₉	C₂²×C₄×C₅	1	16	yes	direct product factor
76	C₂³×C₄×C₅	C₄×C₂₉	1	2	yes	—
77	C₂³×C₄×C₅	C₂²×C₂₉	1	1	yes	characteristic
78	C₂²×C₅×C₈	C₄×C₂₉	1	16	yes	direct product factor
79	C₂²×C₅×C₈	C₂²×C₂₉	1	12	yes	—
80	C₂×C₄²×C₅	C₄×C₂₉	1	6	yes	—
81	C₂×C₄²×C₅	C₂²×C₂₉	1	6	yes	—
82	C₄×C₅×C₈	C₂²×C₂₉	1	16	yes	direct product factor
83	C₅×C₂₉	C₂²×C₄×C₈	1	1	yes	characteristic, direct product factor, Hall
84	C₂²×C₄×C₈	C₅×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
85	C₂²×C₂₉	C₄×C₅×C₈	1	16	yes	direct product factor
86	C₂²×C₂₉	C₂×C₄²×C₅	1	6	yes	—
87	C₂²×C₂₉	C₂²×C₅×C₈	1	12	yes	—
88	C₂²×C₂₉	C₂³×C₄×C₅	1	1	yes	characteristic
89	C₄×C₂₉	C₂×C₄²×C₅	1	6	yes	—
90	C₄×C₂₉	C₂²×C₅×C₈	1	16	yes	direct product factor
91	C₄×C₂₉	C₂³×C₄×C₅	1	2	yes	—
92	C₂⁴×C₅	C₂×C₄×C₂₉	1	1	yes	characteristic
93	C₂²×C₄×C₅	C₈×C₂₉	1	16	yes	direct product factor
94	C₂²×C₄×C₅	C₂×C₄×C₂₉	1	3	yes	—
95	C₂²×C₄×C₅	C₂×C₄×C₂₉	1	8	yes	—
96	C₂²×C₄×C₅	C₂×C₄×C₂₉	1	12	yes	—
97	C₂²×C₄×C₅	C₂³×C₂₉	1	3	yes	—
98	C₂×C₅×C₈	C₂×C₄×C₂₉	1	48	yes	direct product factor
99	C₂×C₅×C₈	C₂³×C₂₉	1	8	yes	—
100	C₄²×C₅	C₂×C₄×C₂₉	1	12	yes	—
101	C₄²×C₅	C₂³×C₂₉	1	4	yes	—
102	C₂³×C₈	C₂×C₅×C₂₉	1	2	yes	—
103	C₂²×C₄²	C₂×C₅×C₂₉	1	1	yes	characteristic
104	C₂×C₄×C₈	C₂×C₅×C₂₉	1	12	yes	direct product factor
105	C₂×C₂₉	C₂×C₄×C₅×C₈	1	12	yes	direct product factor
106	C₂×C₂₉	C₂²×C₄²×C₅	1	1	yes	characteristic
107	C₂×C₂₉	C₂³×C₅×C₈	1	2	yes	—
108	C₂³×C₅	C₄²×C₂₉	1	4	yes	—
109	C₂³×C₅	C₂×C₈×C₂₉	1	8	yes	—
110	C₂³×C₅	C₂²×C₄×C₂₉	1	3	yes	—
111	C₂×C₄×C₅	C₄²×C₂₉	1	12	yes	—
112	C₂×C₄×C₅	C₂×C₈×C₂₉	1	48	yes	direct product factor
113	C₂×C₄×C₅	C₂²×C₄×C₂₉	1	3	yes	—
114	C₂×C₄×C₅	C₂²×C₄×C₂₉	1	8	yes	—
115	C₂×C₄×C₅	C₂²×C₄×C₂₉	1	12	yes	—
116	C₂×C₄×C₅	C₂⁴×C₂₉	1	1	yes	characteristic
117	C₅×C₈	C₂²×C₄×C₂₉	1	16	yes	direct product factor
118	C₂³×C₄	C₄×C₅×C₂₉	1	2	yes	—
119	C₂³×C₄	C₂²×C₅×C₂₉	1	1	yes	characteristic
120	C₂²×C₈	C₄×C₅×C₂₉	1	16	yes	direct product factor
121	C₂²×C₈	C₂²×C₅×C₂₉	1	12	yes	—
122	C₂×C₄²	C₄×C₅×C₂₉	1	6	yes	—
123	C₂×C₄²	C₂²×C₅×C₂₉	1	6	yes	—
124	C₄×C₈	C₂²×C₅×C₂₉	1	16	yes	direct product factor
125	C₂₉	C₂²×C₄×C₅×C₈	1	1	yes	characteristic, direct product factor, Sylow
126	C₂²×C₅	C₄×C₈×C₂₉	1	16	yes	direct product factor
127	C₂²×C₅	C₂×C₄²×C₂₉	1	6	yes	—
128	C₂²×C₅	C₂²×C₈×C₂₉	1	12	yes	—
129	C₂²×C₅	C₂³×C₄×C₂₉	1	1	yes	characteristic
130	C₄×C₅	C₂×C₄²×C₂₉	1	6	yes	—
131	C₄×C₅	C₂²×C₈×C₂₉	1	16	yes	direct product factor
132	C₄×C₅	C₂³×C₄×C₂₉	1	2	yes	—
133	C₂⁴	C₂×C₄×C₅×C₂₉	1	1	yes	characteristic
134	C₂²×C₄	C₅×C₈×C₂₉	1	16	yes	direct product factor
135	C₂²×C₄	C₂×C₄×C₅×C₂₉	1	3	yes	—
136	C₂²×C₄	C₂×C₄×C₅×C₂₉	1	8	yes	—
137	C₂²×C₄	C₂×C₄×C₅×C₂₉	1	12	yes	—
138	C₂²×C₄	C₂³×C₅×C₂₉	1	3	yes	—
139	C₂×C₈	C₂×C₄×C₅×C₂₉	1	48	yes	direct product factor
140	C₂×C₈	C₂³×C₅×C₂₉	1	8	yes	—
141	C₄²	C₂×C₄×C₅×C₂₉	1	12	yes	—
142	C₄²	C₂³×C₅×C₂₉	1	4	yes	—
143	C₂×C₅	C₂×C₄×C₈×C₂₉	1	12	yes	direct product factor
144	C₂×C₅	C₂²×C₄²×C₂₉	1	1	yes	characteristic
145	C₂×C₅	C₂³×C₈×C₂₉	1	2	yes	—
146	C₂³	C₂×C₅×C₈×C₂₉	1	8	yes	—
147	C₂³	C₄²×C₅×C₂₉	1	4	yes	—
148	C₂³	C₂²×C₄×C₅×C₂₉	1	3	yes	—
149	C₂×C₄	C₂×C₅×C₈×C₂₉	1	48	yes	direct product factor
150	C₂×C₄	C₄²×C₅×C₂₉	1	12	yes	—
151	C₂×C₄	C₂²×C₄×C₅×C₂₉	1	3	yes	—
152	C₂×C₄	C₂²×C₄×C₅×C₂₉	1	8	yes	—
153	C₂×C₄	C₂²×C₄×C₅×C₂₉	1	12	yes	—
154	C₂×C₄	C₂⁴×C₅×C₂₉	1	1	yes	characteristic
155	C₈	C₂²×C₄×C₅×C₂₉	1	16	yes	direct product factor
156	C₅	C₂²×C₄×C₈×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
157	C₂²	C₄×C₅×C₈×C₂₉	1	16	yes	direct product factor
158	C₂²	C₂×C₄²×C₅×C₂₉	1	6	yes	—
159	C₂²	C₂²×C₅×C₈×C₂₉	1	12	yes	—
160	C₂²	C₂³×C₄×C₅×C₂₉	1	1	yes	characteristic
161	C₄	C₂×C₄²×C₅×C₂₉	1	6	yes	—
162	C₄	C₂²×C₅×C₈×C₂₉	1	16	yes	direct product factor
163	C₄	C₂³×C₄×C₅×C₂₉	1	2	yes	—
164	C₂	C₂×C₄×C₅×C₈×C₂₉	1	12	yes	direct product factor
165	C₂	C₂³×C₅×C₈×C₂₉	1	2	yes	—
166	C₂	C₂²×C₄²×C₅×C₂₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂⁴×C₅×C₂₉
socle, prime radical	C₂⁴×C₅×C₂₉	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₅×C₈×C₂₉	C₂	direct (N × H)
6. C₂²×C₅×C₈×C₂₉	C₄	direct (N × H)
10. C₄×C₅×C₈×C₂₉	C₂²	direct (N × H)
12. C₂²×C₄×C₅×C₂₉	C₈	direct (N × H)
19. C₂×C₅×C₈×C₂₉	C₂×C₄	direct (N × H)
21. C₂²×C₄×C₈×C₂₉	C₅	direct (N × H)
24. C₂×C₄×C₈×C₂₉	C₂×C₅	direct (N × H)
29. C₂×C₄×C₅×C₂₉	C₂×C₈	direct (N × H)
34. C₅×C₈×C₂₉	C₂²×C₄	direct (N × H)
37. C₂²×C₈×C₂₉	C₄×C₅	direct (N × H)
41. C₄×C₈×C₂₉	C₂²×C₅	direct (N × H)
42. C₂²×C₄×C₅×C₈	C₂₉	direct (N × H)
43. C₂²×C₅×C₂₉	C₄×C₈	direct (N × H)
48. C₄×C₅×C₂₉	C₂²×C₈	direct (N × H)
51. C₂²×C₄×C₂₉	C₅×C₈	direct (N × H)
56. C₂×C₈×C₂₉	C₂×C₄×C₅	direct (N × H)
62. C₂×C₄×C₅×C₈	C₂×C₂₉	direct (N × H)
63. C₂×C₅×C₂₉	C₂×C₄×C₈	direct (N × H)
70. C₂×C₄×C₂₉	C₂×C₅×C₈	direct (N × H)
75. C₈×C₂₉	C₂²×C₄×C₅	direct (N × H)
78. C₂²×C₅×C₈	C₄×C₂₉	direct (N × H)
82. C₄×C₅×C₈	C₂²×C₂₉	direct (N × H)
83. C₅×C₂₉	C₂²×C₄×C₈	direct (N × H)
84. C₂²×C₄×C₈	C₅×C₂₉	direct (N × H)
85. C₂²×C₂₉	C₄×C₅×C₈	direct (N × H)
90. C₄×C₂₉	C₂²×C₅×C₈	direct (N × H)
93. C₂²×C₄×C₅	C₈×C₂₉	direct (N × H)
98. C₂×C₅×C₈	C₂×C₄×C₂₉	direct (N × H)
104. C₂×C₄×C₈	C₂×C₅×C₂₉	direct (N × H)
105. C₂×C₂₉	C₂×C₄×C₅×C₈	direct (N × H)
112. C₂×C₄×C₅	C₂×C₈×C₂₉	direct (N × H)
117. C₅×C₈	C₂²×C₄×C₂₉	direct (N × H)
120. C₂²×C₈	C₄×C₅×C₂₉	direct (N × H)
124. C₄×C₈	C₂²×C₅×C₂₉	direct (N × H)
125. C₂₉	C₂²×C₄×C₅×C₈	direct (N × H)
126. C₂²×C₅	C₄×C₈×C₂₉	direct (N × H)
131. C₄×C₅	C₂²×C₈×C₂₉	direct (N × H)
134. C₂²×C₄	C₅×C₈×C₂₉	direct (N × H)
139. C₂×C₈	C₂×C₄×C₅×C₂₉	direct (N × H)
143. C₂×C₅	C₂×C₄×C₈×C₂₉	direct (N × H)
149. C₂×C₄	C₂×C₅×C₈×C₂₉	direct (N × H)
155. C₈	C₂²×C₄×C₅×C₂₉	direct (N × H)
156. C₅	C₂²×C₄×C₈×C₂₉	direct (N × H)
157. C₂²	C₄×C₅×C₈×C₂₉	direct (N × H)
162. C₄	C₂²×C₅×C₈×C₂₉	direct (N × H)
164. C₂	C₂×C₄×C₅×C₈×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
C₂²×C₄²×C₅×C₂₉	2
C₂³×C₅×C₈×C₂₉	2
C₂×C₄×C₅×C₈×C₂₉	2
C₂²×C₄×C₈×C₂₉	5
C₂²×C₄×C₅×C₈	29

Subgroups — C22×C4×C5×C8×C29 #72196366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×C₅×C₈×C₂₉ #72196366