Subgroups — C₂₉×#2293 #16816007

Order 3712.

652 conjugacy classes of subgroups.

The subgroup lattice has 206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₄×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#117	C₂	1	2	yes	maximal, complemented
3	C₂₉×#390	C₂	1	2	yes	maximal
4	C₂₉×#389	C₂	1	2	yes	maximal, complemented
5	C₂₉×#388	C₂	1	4	yes	maximal, complemented
6	C₄×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₂²⋊C₄×C₂₉	C₂	1	2	yes	maximal, complemented
8	C₄³×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×D₄×C₂₉	C₂²	1	1	yes	characteristic
10	C₂³×C₄×C₂₉	C₂²	1	2	yes	—
11	C₄×D₄×C₂₉	C₄	1	8	yes	complemented
12	C₂₉×#117	—	2	8	no	—
13	C₂×C₄⋊C₄×C₂₉	C₂²	1	4	yes	—
14	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
15	C₂×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊C₄×C₂₉	C₂²	1	4	yes	—
17	C₂×C₂²⋊C₄×C₂₉	C₂²	1	4	yes	—
18	C₂×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
19	C₂×C₄²×C₂₉	C₂²	1	2	yes	—
20	C₂×C₄²×C₂₉	C₂²	1	2	yes	—
21	C₂×C₄²×C₂₉	C₂²	1	2	yes	—
22	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
23	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
24	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
25	C₂₉×#95	C₂²	1	4	yes	—
26	C₂₉×#95	C₂²	1	2	yes	—
27	C₂⁴×C₂₉	C₂³	1	2	yes	—
28	C₂×D₄×C₂₉	—	2	4	no	—
29	C₂×D₄×C₂₉	C₂×C₄	1	4	yes	—
30	C₂²×C₄×C₂₉	—	2	4	no	—
31	C₂²×C₄×C₂₉	—	2	4	no	—
32	C₂²×C₄×C₂₉	C₂×C₄	1	8	yes	—
33	C₂²×C₄×C₂₉	C₂³	1	4	yes	—
34	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
35	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
36	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
37	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
38	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
39	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
40	C₄⋊C₄×C₂₉	—	2	8	no	—
41	C₄⋊C₄×C₂₉	—	2	4	no	—
42	C₄⋊C₄×C₂₉	C₂×C₄	1	4	yes	—
43	C₂²⋊C₄×C₂₉	—	2	8	no	—
44	C₂²⋊C₄×C₂₉	—	2	8	no	—
45	C₂²⋊C₄×C₂₉	C₂×C₄	1	8	yes	—
46	C₄²×C₂₉	—	2	4	no	—
47	C₄²×C₂₉	—	2	4	no	—
48	C₄²×C₂₉	—	2	4	no	—
49	C₄²×C₂₉	—	2	2	no	—
50	C₄²×C₂₉	C₂×C₄	1	4	yes	—
51	C₄²×C₂₉	D₄	1	4	yes	complemented
52	C₂³×C₂₉	—	2	2	no	—
53	C₂³×C₂₉	—	2	4	no	—
54	C₂³×C₂₉	—	2	2	no	—
55	C₂³×C₂₉	—	2	4	no	—
56	C₂³×C₂₉	C₂²×C₄	1	4	yes	—
57	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
58	D₄×C₂₉	—	2	8	no	—
59	C₂×C₄×C₂₉	—	2	2	no	—
60	C₂×C₄×C₂₉	—	2	2	no	—
61	C₂×C₄×C₂₉	—	2	2	no	—
62	C₂×C₄×C₂₉	—	2	2	no	—
63	C₂×C₄×C₂₉	—	2	2	no	—
64	C₂×C₄×C₂₉	—	2	2	no	—
65	C₂×C₄×C₂₉	—	2	2	no	—
66	C₂×C₄×C₂₉	—	2	16	no	—
67	C₂×C₄×C₂₉	—	2	4	no	—
68	C₂×C₄×C₂₉	—	2	4	no	—
69	C₂×C₄×C₂₉	—	2	4	no	—
70	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
71	C₂×C₄×C₂₉	C₂²×C₄	1	4	yes	—
72	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
73	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
74	C₂×C₄×C₂₉	C₂×D₄	1	4	yes	—
75	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
76	C₂×C₄×C₂₉	#41	1	4	yes	—
77	C₂×C₄×C₂₉	#41	1	4	yes	—
78	C₂×C₄×C₂₉	#41	1	2	yes	—
79	#2293	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂²×C₂₉	—	2	4	no	—
81	C₂²×C₂₉	—	2	4	no	—
82	C₂²×C₂₉	—	2	4	no	—
83	C₂²×C₂₉	—	4	4	no	—
84	C₂²×C₂₉	—	4	4	no	—
85	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
86	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
87	C₂²×C₂₉	C₂×#41	1	2	yes	—
88	C₂²×C₂₉	C₂×#41	1	1	yes	characteristic
89	C₂²×C₂₉	C₂×#41	1	2	yes	—
90	C₄×C₂₉	—	2	4	no	—
91	C₄×C₂₉	—	2	2	no	—
92	C₄×C₂₉	—	2	4	no	—
93	C₄×C₂₉	—	2	4	no	—
94	C₄×C₂₉	—	4	4	no	—
95	C₄×C₂₉	#117	1	4	yes	complemented
96	C₄×C₂₉	C₄×D₄	1	4	yes	—
97	C₂×C₄×D₄	C₂×C₂₉	1	1	yes	characteristic
98	C₂×#117	C₂×C₂₉	1	2	yes	complemented
99	#390	C₂×C₂₉	1	2	yes	—
100	#389	C₂×C₂₉	1	2	yes	complemented
101	#388	C₂×C₂₉	1	4	yes	complemented
102	C₄×C₄⋊C₄	C₂×C₂₉	1	1	yes	characteristic, complemented
103	C₄×C₂²⋊C₄	C₂×C₂₉	1	2	yes	complemented
104	C₄³	C₂×C₂₉	1	1	yes	characteristic, complemented
105	C₂×C₂₉	—	4	4	no	—
106	C₂×C₂₉	C₂×#117	1	1	yes	characteristic
107	C₂×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
108	C₂×C₂₉	C₄×#41	1	1	yes	characteristic
109	C₂×C₂₉	#529	1	2	yes	—
110	C₂×C₂₉	#532	1	2	yes	—
111	C₂²×D₄	C₂²×C₂₉	1	1	yes	characteristic
112	C₂³×C₄	C₂²×C₂₉	1	2	yes	—
113	C₄×D₄	C₄×C₂₉	1	8	yes	complemented
114	#117	—	2	8	no	—
115	C₂×C₄⋊C₄	C₂²×C₂₉	1	4	yes	—
116	C₂×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
117	C₂×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
118	C₂×C₂²⋊C₄	C₂²×C₂₉	1	4	yes	—
119	C₂×C₂²⋊C₄	C₂²×C₂₉	1	4	yes	—
120	C₂×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
121	C₂×C₄²	C₂²×C₂₉	1	2	yes	—
122	C₂×C₄²	C₂²×C₂₉	1	1	yes	characteristic
123	C₂×C₄²	C₂²×C₂₉	1	2	yes	—
124	C₂×C₄²	C₂²×C₂₉	1	2	yes	—
125	C₂×C₄²	C₂²×C₂₉	1	1	yes	characteristic
126	C₂×C₄²	C₂²×C₂₉	1	1	yes	characteristic
127	#95	C₂²×C₂₉	1	4	yes	—
128	#95	C₂²×C₂₉	1	2	yes	—
129	C₂₉	#2293	1	1	yes	characteristic, direct product factor, Sylow
130	C₂⁴	C₂³×C₂₉	1	2	yes	—
131	C₂×D₄	—	2	4	no	—
132	C₂×D₄	C₂×C₄×C₂₉	1	4	yes	—
133	C₂²×C₄	—	2	4	no	—
134	C₂²×C₄	—	2	4	no	—
135	C₂²×C₄	C₂×C₄×C₂₉	1	8	yes	—
136	C₂²×C₄	C₂³×C₂₉	1	4	yes	—
137	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
138	C₂²×C₄	C₂³×C₂₉	1	2	yes	—
139	C₂²×C₄	C₂³×C₂₉	1	2	yes	—
140	C₂²×C₄	C₂³×C₂₉	1	2	yes	—
141	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
142	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
143	C₄⋊C₄	—	2	8	no	—
144	C₄⋊C₄	—	2	4	no	—
145	C₄⋊C₄	C₂×C₄×C₂₉	1	4	yes	—
146	C₂²⋊C₄	—	2	8	no	—
147	C₂²⋊C₄	—	2	8	no	—
148	C₂²⋊C₄	C₂×C₄×C₂₉	1	8	yes	—
149	C₄²	—	2	4	no	—
150	C₄²	—	2	4	no	—
151	C₄²	—	2	4	no	—
152	C₄²	—	2	2	no	—
153	C₄²	C₂×C₄×C₂₉	1	4	yes	—
154	C₄²	D₄×C₂₉	1	4	yes	complemented
155	C₂³	—	2	2	no	—
156	C₂³	—	2	4	no	—
157	C₂³	—	2	2	no	—
158	C₂³	—	2	4	no	—
159	C₂³	C₂²×C₄×C₂₉	1	4	yes	—
160	C₂³	C₂⁴×C₂₉	1	1	yes	characteristic
161	D₄	—	2	8	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	16	no	—
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	2	4	no	—
172	C₂×C₄	—	2	4	no	—
173	C₂×C₄	C₂²×C₄×C₂₉	1	2	yes	—
174	C₂×C₄	C₂²×C₄×C₂₉	1	4	yes	—
175	C₂×C₄	C₂²×C₄×C₂₉	1	2	yes	—
176	C₂×C₄	C₂²×C₄×C₂₉	1	2	yes	—
177	C₂×C₄	C₂×D₄×C₂₉	1	4	yes	—
178	C₂×C₄	C₂×D₄×C₂₉	1	2	yes	—
179	C₂×C₄	#41×C₂₉	1	4	yes	—
180	C₂×C₄	#41×C₂₉	1	4	yes	—
181	C₂×C₄	#41×C₂₉	1	2	yes	—
182	C₂²	—	2	4	no	—
183	C₂²	—	2	4	no	—
184	C₂²	—	2	4	no	—
185	C₂²	—	4	4	no	—
186	C₂²	—	4	4	no	—
187	C₂²	C₂³×C₄×C₂₉	1	1	yes	characteristic
188	C₂²	C₂²×D₄×C₂₉	1	1	yes	characteristic
189	C₂²	C₂×#41×C₂₉	1	2	yes	—
190	C₂²	C₂×#41×C₂₉	1	1	yes	characteristic
191	C₂²	C₂×#41×C₂₉	1	2	yes	—
192	C₄	—	2	4	no	—
193	C₄	—	2	2	no	—
194	C₄	—	2	4	no	—
195	C₄	—	2	4	no	—
196	C₄	—	4	4	no	—
197	C₄	C₂₉×#117	1	4	yes	complemented
198	C₄	C₄×D₄×C₂₉	1	4	yes	—
199	C₂	—	4	4	no	—
200	C₂	C₂×C₂₉×#117	1	1	yes	characteristic
201	C₂	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
202	C₂	C₄×#41×C₂₉	1	1	yes	characteristic
203	C₂	C₂₉×#529	1	2	yes	—
204	C₂	C₂₉×#532	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₉	C₂³
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁴×C₂₉
socle	C₂³×C₂₉	C₂⁴
prime radical	C₂²×D₄×C₂₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₉×#117	C₂	semidirect
4. C₂₉×#389	C₂	semidirect
5. C₂₉×#388	C₂	semidirect
6. C₄×C₄⋊C₄×C₂₉	C₂	semidirect
7. C₄×C₂²⋊C₄×C₂₉	C₂	semidirect
8. C₄³×C₂₉	C₂	semidirect
11. C₄×D₄×C₂₉	C₄	semidirect
51. C₄²×C₂₉	D₄	semidirect
79. #2293	C₂₉	direct (N × H)
95. C₄×C₂₉	#117	semidirect
98. C₂×#117	C₂×C₂₉	semidirect
100. #389	C₂×C₂₉	semidirect
101. #388	C₂×C₂₉	semidirect
102. C₄×C₄⋊C₄	C₂×C₂₉	semidirect
103. C₄×C₂²⋊C₄	C₂×C₂₉	semidirect
104. C₄³	C₂×C₂₉	semidirect
113. C₄×D₄	C₄×C₂₉	semidirect
129. C₂₉	#2293	direct (N × H)
154. C₄²	D₄×C₂₉	semidirect
197. C₄	C₂₉×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₄×C₂₉	2
C₂×C₂₉×#117	2
C₂₉×#390	2
C₂₉×#389	2
C₂₉×#388	2
C₄×C₄⋊C₄×C₂₉	2
C₄×C₂²⋊C₄×C₂₉	2
C₄³×C₂₉	2
#2293	29

Subgroups — C29×#2293 #16816007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#2293 #16816007