Subgroups — C₂₉×#23083 #20317983

Order 7424.

1040 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₂₉×#121	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1954	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1954	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1939	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1923	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1869	C₂	1	2	yes	maximal, complemented
9	C₈×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₂²⋊C₄×C₂₉	C₂	1	2	yes	maximal, complemented
11	C₄×C₂₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₂₉	C₂²	1	2	yes	—
13	C₂×C₂₉×#121	C₄	1	1	yes	characteristic
14	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
16	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
17	C₈×D₄×C₂₉	—	2	4	no	—
18	C₂₉×#431	—	2	4	no	—
19	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₉×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₂×C₂₉×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₂₉	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₂₉	C₂²	1	2	yes	—
32	C₂₉×#390	C₄	1	1	yes	characteristic
33	C₂₉×#389	C₄	1	1	yes	characteristic
34	C₂₉×#388	C₄	1	2	yes	—
35	C₂₉×#386	C₄	1	2	yes	—
36	C₂₉×#380	C₄	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
39	C₂₉×#336	C₂²	1	1	yes	characteristic
40	C₂₉×#336	C₂²	1	2	yes	—
41	C₂₉×#336	C₂²	1	2	yes	—
42	C₂₉×#336	C₂²	1	1	yes	characteristic
43	C₂²×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₂₉	C₂×C₄	1	2	yes	—
45	C₂³×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
49	C₂²×C₈×C₂₉	—	2	4	no	—
50	C₂²×C₈×C₂₉	—	2	4	no	—
51	C₂²×C₈×C₂₉	—	4	2	no	—
52	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
55	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
58	C₂₉×#121	C₈	1	8	yes	complemented
59	C₄×D₄×C₂₉	—	2	2	no	—
60	C₄×D₄×C₂₉	—	2	2	no	—
61	C₄×D₄×C₂₉	—	4	2	no	—
62	C₄×D₄×C₂₉	—	4	2	no	—
63	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
68	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
69	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
70	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
71	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
72	C₂×C₄²×C₂₉	—	2	2	no	—
73	C₂×C₄²×C₂₉	—	2	2	no	—
74	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
78	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
79	C₂₉×C₄⋊C₈	—	2	2	no	—
80	C₂₉×C₄⋊C₈	—	4	2	no	—
81	C₂₉×C₄⋊C₈	D₄	1	4	yes	complemented
82	C₂₉×C₂²⋊C₈	—	2	4	no	—
83	C₂₉×C₂²⋊C₈	—	2	4	no	—
84	C₂₉×C₂²⋊C₈	—	2	2	no	—
85	C₂₉×C₂²⋊C₈	—	2	2	no	—
86	C₂₉×C₂²⋊C₈	—	2	4	no	—
87	C₂₉×C₂²⋊C₈	—	4	2	no	—
88	C₄×C₈×C₂₉	—	2	4	no	—
89	C₄×C₈×C₂₉	—	2	2	no	—
90	C₄×C₈×C₂₉	—	2	2	no	—
91	C₄×C₈×C₂₉	—	4	2	no	—
92	C₂₉×#95	C₂×C₄	1	2	yes	—
93	C₂₉×#95	C₂×C₄	1	2	yes	—
94	C₂₉×#95	C₂×C₄	1	2	yes	—
95	C₂⁴×C₂₉	C₂²×C₄	1	2	yes	—
96	C₂⁴×C₂₉	C₂²×C₄	1	1	yes	characteristic
97	C₂×D₄×C₂₉	—	2	2	no	—
98	C₂×D₄×C₂₉	—	2	2	no	—
99	C₂×D₄×C₂₉	—	4	2	no	—
100	C₂×D₄×C₂₉	—	4	2	no	—
101	C₂×D₄×C₂₉	C₂×C₈	1	4	yes	—
102	C₂×D₄×C₂₉	C₂×C₈	1	8	yes	complemented
103	C₂²×C₄×C₂₉	—	2	2	no	—
104	C₂²×C₄×C₂₉	—	2	2	no	—
105	C₂²×C₄×C₂₉	—	2	2	no	—
106	C₂²×C₄×C₂₉	—	2	2	no	—
107	C₂²×C₄×C₂₉	—	2	1	no	—
108	C₂²×C₄×C₂₉	—	2	2	no	—
109	C₂²×C₄×C₂₉	—	2	1	no	—
110	C₂²×C₄×C₂₉	—	2	2	no	—
111	C₂²×C₄×C₂₉	—	2	2	no	—
112	C₂²×C₄×C₂₉	—	2	1	no	—
113	C₂²×C₄×C₂₉	—	2	1	no	—
114	C₂²×C₄×C₂₉	—	2	2	no	—
115	C₂²×C₄×C₂₉	—	2	1	no	—
116	C₂²×C₄×C₂₉	—	2	1	no	—
117	C₂²×C₄×C₂₉	—	2	2	no	—
118	C₂²×C₄×C₂₉	—	2	2	no	—
119	C₂²×C₄×C₂₉	—	4	1	no	—
120	C₂²×C₄×C₂₉	C₂×C₈	1	4	yes	complemented
121	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
130	C₂×C₈×C₂₉	—	2	1	no	—
131	C₂×C₈×C₂₉	—	2	2	no	—
132	C₂×C₈×C₂₉	—	2	1	no	—
133	C₂×C₈×C₂₉	—	2	1	no	—
134	C₂×C₈×C₂₉	—	2	2	no	—
135	C₂×C₈×C₂₉	—	2	1	no	—
136	C₂×C₈×C₂₉	—	2	1	no	—
137	C₂×C₈×C₂₉	—	2	2	no	—
138	C₂×C₈×C₂₉	—	2	1	no	—
139	C₂×C₈×C₂₉	—	2	1	no	—
140	C₂×C₈×C₂₉	—	2	2	no	—
141	C₂×C₈×C₂₉	—	2	1	no	—
142	C₂×C₈×C₂₉	—	2	1	no	—
143	C₂×C₈×C₂₉	—	2	2	no	—
144	C₂×C₈×C₂₉	—	2	1	no	—
145	C₂×C₈×C₂₉	—	4	8	no	—
146	C₂×C₈×C₂₉	C₂×D₄	1	4	yes	—
147	C₂×C₈×C₂₉	#41	1	2	yes	—
148	C₂×C₈×C₂₉	#41	1	2	yes	—
149	C₄⋊C₄×C₂₉	—	2	2	no	—
150	C₄⋊C₄×C₂₉	—	2	2	no	—
151	C₄⋊C₄×C₂₉	—	4	2	no	—
152	C₄⋊C₄×C₂₉	C₂×C₈	1	4	yes	complemented
153	C₂²⋊C₄×C₂₉	—	2	4	no	—
154	C₂²⋊C₄×C₂₉	—	2	4	no	—
155	C₂²⋊C₄×C₂₉	—	4	2	no	—
156	C₂²⋊C₄×C₂₉	—	4	2	no	—
157	C₂²⋊C₄×C₂₉	C₂×C₈	1	8	yes	complemented
158	C₄²×C₂₉	—	2	2	no	—
159	C₄²×C₂₉	—	2	2	no	—
160	C₄²×C₂₉	—	2	1	no	—
161	C₄²×C₂₉	—	2	1	no	—
162	C₄²×C₂₉	—	2	2	no	—
163	C₄²×C₂₉	—	2	2	no	—
164	C₄²×C₂₉	C₂×D₄	1	2	yes	—
165	C₄²×C₂₉	#41	1	2	yes	—
166	#23083	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂³×C₂₉	—	2	2	no	—
168	C₂³×C₂₉	—	2	1	no	—
169	C₂³×C₂₉	—	2	2	no	—
170	C₂³×C₂₉	—	2	1	no	—
171	C₂³×C₂₉	—	2	1	no	—
172	C₂³×C₂₉	—	2	2	no	—
173	C₂³×C₂₉	—	2	2	no	—
174	C₂³×C₂₉	—	2	1	no	—
175	C₂³×C₂₉	—	2	1	no	—
176	C₂³×C₂₉	—	2	2	no	—
177	C₂³×C₂₉	—	2	1	no	—
178	C₂³×C₂₉	—	2	2	no	—
179	C₂³×C₂₉	C₂²×C₈	1	4	yes	—
180	C₂³×C₂₉	C₂²×C₈	1	2	yes	—
181	C₂³×C₂₉	C₂³×C₄	1	1	yes	characteristic
182	D₄×C₂₉	—	2	8	no	—
183	D₄×C₂₉	—	4	8	no	—
184	C₂×C₄×C₂₉	—	2	1	no	—
185	C₂×C₄×C₂₉	—	2	1	no	—
186	C₂×C₄×C₂₉	—	2	2	no	—
187	C₂×C₄×C₂₉	—	2	1	no	—
188	C₂×C₄×C₂₉	—	2	1	no	—
189	C₂×C₄×C₂₉	—	2	1	no	—
190	C₂×C₄×C₂₉	—	2	1	no	—
191	C₂×C₄×C₂₉	—	2	2	no	—
192	C₂×C₄×C₂₉	—	2	8	no	—
193	C₂×C₄×C₂₉	—	2	1	no	—
194	C₂×C₄×C₂₉	—	2	2	no	—
195	C₂×C₄×C₂₉	—	2	2	no	—
196	C₂×C₄×C₂₉	—	2	1	no	—
197	C₂×C₄×C₂₉	—	2	2	no	—
198	C₂×C₄×C₂₉	—	2	1	no	—
199	C₂×C₄×C₂₉	—	2	2	no	—
200	C₂×C₄×C₂₉	—	2	2	no	—
201	C₂×C₄×C₂₉	—	2	2	no	—
202	C₂×C₄×C₂₉	—	4	4	no	—
203	C₂×C₄×C₂₉	—	4	2	no	—
204	C₂×C₄×C₂₉	—	4	1	no	—
205	C₂×C₄×C₂₉	—	4	1	no	—
206	C₂×C₄×C₂₉	—	4	2	no	—
207	C₂×C₄×C₂₉	—	4	1	no	—
208	C₂×C₄×C₂₉	—	4	2	no	—
209	C₂×C₄×C₂₉	—	4	1	no	—
210	C₂×C₄×C₂₉	—	4	2	no	—
211	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
212	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
213	C₂×C₄×C₂₉	C₂²×C₈	1	2	yes	—
214	C₂×C₄×C₂₉	C₂²×C₈	1	4	yes	—
215	C₂×C₄×C₂₉	C₂²×C₈	1	2	yes	—
216	C₂×C₄×C₂₉	#131	1	2	yes	—
217	C₂×C₄×C₂₉	#131	1	2	yes	—
218	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
224	C₈×C₂₉	—	2	2	no	—
225	C₈×C₂₉	—	2	4	no	—
226	C₈×C₂₉	—	2	2	no	—
227	C₈×C₂₉	—	4	1	no	—
228	C₈×C₂₉	—	4	2	no	—
229	C₈×C₂₉	—	4	1	no	—
230	C₂×C₈×D₄	C₂×C₂₉	1	1	yes	characteristic, complemented
231	C₂×#431	C₂×C₂₉	1	1	yes	characteristic, complemented
232	C₄×#121	C₂×C₂₉	1	1	yes	characteristic
233	#1954	C₂×C₂₉	1	1	yes	characteristic, complemented
234	#1954	C₂×C₂₉	1	2	yes	complemented
235	#1939	C₂×C₂₉	1	1	yes	characteristic, complemented
236	#1923	C₂×C₂₉	1	2	yes	complemented
237	#1869	C₂×C₂₉	1	2	yes	complemented
238	C₈×C₄⋊C₄	C₂×C₂₉	1	1	yes	characteristic, complemented
239	C₈×C₂²⋊C₄	C₂×C₂₉	1	2	yes	complemented
240	C₄×C₂²⋊C₈	C₂×C₂₉	1	1	yes	characteristic, complemented
241	C₂²×C₂₉	—	2	2	no	—
242	C₂²×C₂₉	—	2	4	no	—
243	C₂²×C₂₉	—	2	4	no	—
244	C₂²×C₂₉	—	2	2	no	—
245	C₂²×C₂₉	—	2	2	no	—
246	C₂²×C₂₉	—	2	4	no	—
247	C₂²×C₂₉	—	4	2	no	—
248	C₂²×C₂₉	—	4	1	no	—
249	C₂²×C₂₉	—	4	1	no	—
250	C₂²×C₂₉	—	4	2	no	—
251	C₂²×C₂₉	—	4	1	no	—
252	C₂²×C₂₉	—	4	2	no	—
253	C₂²×C₂₉	—	4	1	no	—
254	C₂²×C₂₉	—	4	2	no	—
255	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
256	C₂²×C₂₉	C₄×#41	1	1	yes	characteristic
257	C₂²×C₂₉	#518	1	1	yes	characteristic
258	C₂²×C₂₉	C₂³×C₈	1	1	yes	characteristic
259	C₂²×C₂₉	C₂×#131	1	1	yes	characteristic
260	C₂²×C₂₉	C₂×#131	1	1	yes	characteristic
261	C₂²×C₂₉	#568	1	1	yes	characteristic
262	C₄×C₂₉	—	2	2	no	—
263	C₄×C₂₉	—	2	2	no	—
264	C₄×C₂₉	—	2	2	no	—
265	C₄×C₂₉	—	2	4	no	—
266	C₄×C₂₉	—	4	1	no	—
267	C₄×C₂₉	—	4	2	no	—
268	C₄×C₂₉	—	4	2	no	—
269	C₄×C₂₉	C₈×D₄	1	4	yes	—
270	C₄×C₂₉	#546	1	1	yes	characteristic
271	C₄×C₂₉	#550	1	1	yes	characteristic
272	C₄×C₂₉	#553	1	1	yes	characteristic
273	C₄×C₂₉	#555	1	1	yes	characteristic
274	C₂³×C₈	C₂²×C₂₉	1	2	yes	—
275	C₂×#121	C₄×C₂₉	1	1	yes	characteristic
276	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
277	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
278	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
279	C₈×D₄	—	2	4	no	—
280	#431	—	2	4	no	—
281	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
282	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
283	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
285	C₂×C₂²⋊C₈	C₂²×C₂₉	1	2	yes	—
286	C₂×C₂²⋊C₈	C₂²×C₂₉	1	2	yes	—
287	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
288	C₂×C₂²⋊C₈	C₂²×C₂₉	1	2	yes	—
289	C₂×C₂²⋊C₈	C₂²×C₂₉	1	2	yes	—
290	C₂×C₄×C₈	C₂²×C₂₉	1	2	yes	—
291	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
292	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
293	C₂×C₄×C₈	C₂²×C₂₉	1	2	yes	—
294	#390	C₄×C₂₉	1	1	yes	characteristic
295	#389	C₄×C₂₉	1	1	yes	characteristic
296	#388	C₄×C₂₉	1	2	yes	—
297	#386	C₄×C₂₉	1	2	yes	—
298	#380	C₄×C₂₉	1	1	yes	characteristic
299	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
300	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
301	#336	C₂²×C₂₉	1	2	yes	—
302	#336	C₂²×C₂₉	1	2	yes	—
303	#336	C₂²×C₂₉	1	1	yes	characteristic
304	#336	C₂²×C₂₉	1	1	yes	characteristic
305	C₂×C₂₉	—	4	2	no	—
306	C₂×C₂₉	—	4	4	no	—
307	C₂×C₂₉	#2363	1	1	yes	characteristic
308	C₂×C₂₉	C₂×C₈×D₄	1	1	yes	characteristic
309	C₂×C₂₉	#2933	1	1	yes	characteristic
310	C₂×C₂₉	C₈×#41	1	1	yes	characteristic
311	C₂×C₂₉	#2969	1	1	yes	characteristic
312	C₂×C₂₉	#2972	1	1	yes	characteristic
313	C₂×C₂₉	#2979	1	1	yes	characteristic
314	C₂²×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
315	C₂²×D₄	C₂×C₄×C₂₉	1	2	yes	—
316	C₂³×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
317	C₂³×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
318	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
319	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
320	C₂²×C₈	—	2	4	no	—
321	C₂²×C₈	—	2	4	no	—
322	C₂²×C₈	—	4	2	no	—
323	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
324	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
325	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
326	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
327	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
328	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
329	#121	C₈×C₂₉	1	8	yes	complemented
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	—	2	2	no	—
332	C₄×D₄	—	4	2	no	—
333	C₄×D₄	—	4	2	no	—
334	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
337	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
338	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
339	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
340	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
341	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
342	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
343	C₂×C₄²	—	2	2	no	—
344	C₂×C₄²	—	2	2	no	—
345	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
346	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
347	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
348	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
349	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
350	C₄⋊C₈	—	2	2	no	—
351	C₄⋊C₈	—	4	2	no	—
352	C₄⋊C₈	D₄×C₂₉	1	4	yes	complemented
353	C₂²⋊C₈	—	2	4	no	—
354	C₂²⋊C₈	—	2	4	no	—
355	C₂²⋊C₈	—	2	2	no	—
356	C₂²⋊C₈	—	2	4	no	—
357	C₂²⋊C₈	—	2	2	no	—
358	C₂²⋊C₈	—	4	2	no	—
359	C₄×C₈	—	2	4	no	—
360	C₄×C₈	—	2	2	no	—
361	C₄×C₈	—	2	2	no	—
362	C₄×C₈	—	4	2	no	—
363	#95	C₂×C₄×C₂₉	1	2	yes	—
364	#95	C₂×C₄×C₂₉	1	2	yes	—
365	#95	C₂×C₄×C₂₉	1	2	yes	—
366	C₂₉	#23083	1	1	yes	characteristic, direct product factor, Sylow
367	C₂⁴	C₂²×C₄×C₂₉	1	2	yes	—
368	C₂⁴	C₂²×C₄×C₂₉	1	1	yes	characteristic
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	C₂×C₈×C₂₉	1	4	yes	—
374	C₂×D₄	C₂×C₈×C₂₉	1	8	yes	complemented
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	4	1	no	—
392	C₂²×C₄	C₂×C₈×C₂₉	1	4	yes	complemented
393	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
394	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
395	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
396	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
397	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
398	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
399	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
400	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
401	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	4	8	no	—
418	C₂×C₈	C₂×D₄×C₂₉	1	4	yes	—
419	C₂×C₈	#41×C₂₉	1	2	yes	—
420	C₂×C₈	#41×C₂₉	1	2	yes	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	4	2	no	—
424	C₄⋊C₄	C₂×C₈×C₂₉	1	4	yes	complemented
425	C₂²⋊C₄	—	2	4	no	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	4	2	no	—
428	C₂²⋊C₄	—	4	2	no	—
429	C₂²⋊C₄	C₂×C₈×C₂₉	1	8	yes	complemented
430	C₄²	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	1	no	—
433	C₄²	—	2	1	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	2	no	—
436	C₄²	C₂×D₄×C₂₉	1	2	yes	—
437	C₄²	#41×C₂₉	1	2	yes	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	1	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	1	no	—
446	C₂³	—	2	1	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	2	no	—
450	C₂³	C₂²×C₈×C₂₉	1	4	yes	—
451	C₂³	C₂²×C₈×C₂₉	1	2	yes	—
452	C₂³	C₂³×C₄×C₂₉	1	1	yes	characteristic
453	D₄	—	2	8	no	—
454	D₄	—	4	8	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	8	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
483	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
484	C₂×C₄	C₂²×C₈×C₂₉	1	2	yes	—
485	C₂×C₄	C₂²×C₈×C₂₉	1	4	yes	—
486	C₂×C₄	C₂²×C₈×C₂₉	1	2	yes	—
487	C₂×C₄	C₂₉×#131	1	2	yes	—
488	C₂×C₄	C₂₉×#131	1	2	yes	—
489	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
490	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
491	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
492	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
493	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
494	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
495	C₈	—	2	2	no	—
496	C₈	—	2	4	no	—
497	C₈	—	2	2	no	—
498	C₈	—	4	1	no	—
499	C₈	—	4	2	no	—
500	C₈	—	4	1	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	4	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	4	1	no	—
515	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
516	C₂²	C₄×#41×C₂₉	1	1	yes	characteristic
517	C₂²	C₂₉×#518	1	1	yes	characteristic
518	C₂²	C₂³×C₈×C₂₉	1	1	yes	characteristic
519	C₂²	C₂×C₂₉×#131	1	1	yes	characteristic
520	C₂²	C₂×C₂₉×#131	1	1	yes	characteristic
521	C₂²	C₂₉×#568	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	2	4	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	2	no	—
529	C₄	C₈×D₄×C₂₉	1	4	yes	—
530	C₄	C₂₉×#546	1	1	yes	characteristic
531	C₄	C₂₉×#550	1	1	yes	characteristic
532	C₄	C₂₉×#553	1	1	yes	characteristic
533	C₄	C₂₉×#555	1	1	yes	characteristic
534	C₂	—	4	2	no	—
535	C₂	—	4	4	no	—
536	C₂	C₂₉×#2363	1	1	yes	characteristic
537	C₂	C₂×C₈×D₄×C₂₉	1	1	yes	characteristic
538	C₂	C₂₉×#2933	1	1	yes	characteristic
539	C₂	C₈×#41×C₂₉	1	1	yes	characteristic
540	C₂	C₂₉×#2969	1	1	yes	characteristic
541	C₂	C₂₉×#2972	1	1	yes	characteristic
542	C₂	C₂₉×#2979	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₉	C₂⁴
commutator	C₂²	C₂³×C₈×C₂₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
socle	C₂³×C₂₉	C₂³×C₄
prime radical	C₂×C₂₉×#121	C₄
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
1. C₂×C₈×D₄×C₂₉	C₂	semidirect
2. C₂×C₂₉×#431	C₂	semidirect
4. C₂₉×#1954	C₂	semidirect
5. C₂₉×#1954	C₂	semidirect
6. C₂₉×#1939	C₂	semidirect
7. C₂₉×#1923	C₂	semidirect
8. C₂₉×#1869	C₂	semidirect
9. C₈×C₄⋊C₄×C₂₉	C₂	semidirect
10. C₈×C₂²⋊C₄×C₂₉	C₂	semidirect
11. C₄×C₂₉×C₂²⋊C₈	C₂	semidirect
58. C₂₉×#121	C₈	semidirect
81. C₂₉×C₄⋊C₈	D₄	semidirect
102. C₂×D₄×C₂₉	C₂×C₈	semidirect
120. C₂²×C₄×C₂₉	C₂×C₈	semidirect
152. C₄⋊C₄×C₂₉	C₂×C₈	semidirect
157. C₂²⋊C₄×C₂₉	C₂×C₈	semidirect
166. #23083	C₂₉	direct (N × H)
230. C₂×C₈×D₄	C₂×C₂₉	semidirect
231. C₂×#431	C₂×C₂₉	semidirect
233. #1954	C₂×C₂₉	semidirect
234. #1954	C₂×C₂₉	semidirect
235. #1939	C₂×C₂₉	semidirect
236. #1923	C₂×C₂₉	semidirect
237. #1869	C₂×C₂₉	semidirect
238. C₈×C₄⋊C₄	C₂×C₂₉	semidirect
239. C₈×C₂²⋊C₄	C₂×C₂₉	semidirect
240. C₄×C₂²⋊C₈	C₂×C₂₉	semidirect
329. #121	C₈×C₂₉	semidirect
352. C₄⋊C₈	D₄×C₂₉	semidirect
366. C₂₉	#23083	direct (N × H)
374. C₂×D₄	C₂×C₈×C₂₉	semidirect
392. C₂²×C₄	C₂×C₈×C₂₉	semidirect
424. C₄⋊C₄	C₂×C₈×C₂₉	semidirect
429. C₂²⋊C₄	C₂×C₈×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₄×C₂₉	2
C₂×C₂₉×#431	2
C₄×C₂₉×#121	2
C₂₉×#1954	2
C₂₉×#1939	2
C₂₉×#1923	2
C₂₉×#1869	2
C₈×C₄⋊C₄×C₂₉	2
C₈×C₂²⋊C₄×C₂₉	2
C₄×C₂₉×C₂²⋊C₈	2
#23083	29

Subgroups — C29×#23083 #20317983

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#23083 #20317983