Subgroups — C₂₉×#8161 #20303061

Order 7424.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#435	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₉×#99	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#1752	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×C₂²⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1459	C₂	1	1	yes	maximal, characteristic
6	C₂₉×#1282	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1282	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×M₁₆×C₂₉	C₄	1	1	yes	characteristic, complemented
9	C₂³×C₈×C₂₉	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
11	C₂₉×#435	—	2	1	no	—
12	C₂₉×#435	—	2	1	no	—
13	C₂₉×#435	—	2	1	no	—
14	C₂₉×#435	—	2	1	no	—
15	C₂×C₂₉×C₄⋊C₈	C₄	1	1	yes	characteristic, complemented
16	C₂×C₂₉×#99	C₄	1	2	yes	—
17	C₂×C₂₉×C₂²⋊C₈	C₄	1	1	yes	characteristic, complemented
18	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#97	—	2	1	no	—
22	C₂×C₂₉×#97	C₄	1	1	yes	characteristic, complemented
23	C₂×C₄×C₈×C₂₉	—	2	1	no	—
24	C₄×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
25	C₄×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
26	C₂₉×#342	C₄	1	2	yes	—
27	C₂₉×#336	—	2	1	no	—
28	C₂₉×#336	—	2	1	no	—
29	C₂₉×#324	C₄	1	2	yes	complemented
30	C₂₉×#323	C₄	1	2	yes	complemented
31	C₂²×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
34	C₂×M₁₆×C₂₉	—	2	1	no	—
35	C₂×M₁₆×C₂₉	—	2	1	no	—
36	C₂×M₁₆×C₂₉	—	4	2	no	—
37	C₂²×C₈×C₂₉	—	2	1	no	—
38	C₂²×C₈×C₂₉	—	2	1	no	—
39	C₂²×C₈×C₂₉	—	4	2	no	—
40	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
48	C₄×D₄×C₂₉	—	2	1	no	—
49	C₄×D₄×C₂₉	—	2	1	no	—
50	C₄×D₄×C₂₉	—	2	1	no	—
51	C₄×D₄×C₂₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
54	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₂₉	—	2	1	no	—
58	C₂×C₄²×C₂₉	—	2	1	no	—
59	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
60	C₂₉×C₄⋊C₈	—	2	1	no	—
61	C₂₉×C₄⋊C₈	—	2	1	no	—
62	C₂₉×#99	—	2	4	no	—
63	C₂₉×C₂²⋊C₈	—	2	1	no	—
64	C₂₉×C₂²⋊C₈	—	2	1	no	—
65	C₂₉×C₂²⋊C₈	—	2	1	no	—
66	C₂₉×C₂²⋊C₈	—	2	1	no	—
67	C₂₉×C₂²⋊C₈	—	2	1	no	—
68	C₂₉×C₂²⋊C₈	—	2	1	no	—
69	C₂₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
70	C₂₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
71	C₂₉×#97	—	2	1	no	—
72	C₂₉×#97	—	2	1	no	—
73	C₂₉×#97	—	4	2	no	—
74	C₄×C₈×C₂₉	—	4	2	no	—
75	C₂₉×#95	—	2	1	no	—
76	C₂₉×#95	—	2	1	no	—
77	C₂⁴×C₂₉	C₄²	1	1	yes	characteristic
78	C₂⁴×C₂₉	C₂²×C₄	1	1	yes	characteristic
79	C₂×D₄×C₂₉	—	2	1	no	—
80	C₂×D₄×C₂₉	—	2	1	no	—
81	C₂×D₄×C₂₉	—	2	2	no	—
82	C₂×D₄×C₂₉	—	2	2	no	—
83	C₂²×C₄×C₂₉	—	2	2	no	—
84	C₂²×C₄×C₂₉	—	2	1	no	—
85	C₂²×C₄×C₂₉	—	2	1	no	—
86	C₂²×C₄×C₂₉	—	2	2	no	—
87	C₂²×C₄×C₂₉	—	4	1	no	—
88	C₂²×C₄×C₂₉	—	4	1	no	—
89	C₂²×C₄×C₂₉	—	4	1	no	—
90	C₂²×C₄×C₂₉	—	4	1	no	—
91	C₂²×C₄×C₂₉	C₄²	1	1	yes	characteristic
92	C₂²×C₄×C₂₉	C₄²	1	1	yes	characteristic
93	C₂²×C₄×C₂₉	C₄²	1	1	yes	characteristic
94	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
99	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
100	M₁₆×C₂₉	—	4	2	no	—
101	M₁₆×C₂₉	—	4	2	no	—
102	C₂×C₈×C₂₉	—	2	2	no	—
103	C₂×C₈×C₂₉	—	2	2	no	—
104	C₂×C₈×C₂₉	—	2	2	no	—
105	C₂×C₈×C₂₉	—	2	1	no	—
106	C₂×C₈×C₂₉	—	2	1	no	—
107	C₂×C₈×C₂₉	—	2	2	no	—
108	C₂×C₈×C₂₉	—	2	2	no	—
109	C₂×C₈×C₂₉	—	4	1	no	—
110	C₂×C₈×C₂₉	—	4	1	no	—
111	C₂×C₈×C₂₉	—	4	1	no	—
112	C₂×C₈×C₂₉	—	4	1	no	—
113	C₂×C₈×C₂₉	—	4	1	no	—
114	C₂×C₈×C₂₉	—	4	1	no	—
115	C₂×C₈×C₂₉	—	4	1	no	—
116	C₂×C₈×C₂₉	—	4	1	no	—
117	C₂×C₈×C₂₉	—	4	1	no	—
118	C₂×C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
119	C₂×C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
122	C₄⋊C₄×C₂₉	—	2	1	no	—
123	C₄⋊C₄×C₂₉	—	2	1	no	—
124	C₂²⋊C₄×C₂₉	—	2	1	no	—
125	C₂²⋊C₄×C₂₉	—	2	1	no	—
126	C₂²⋊C₄×C₂₉	—	2	2	no	—
127	C₂²⋊C₄×C₂₉	—	2	1	no	—
128	C₂²⋊C₄×C₂₉	—	2	1	no	—
129	C₂²⋊C₄×C₂₉	—	2	2	no	—
130	C₂²⋊C₄×C₂₉	—	2	2	no	—
131	C₂²⋊C₄×C₂₉	M₁₆	1	4	yes	complemented
132	C₄²×C₂₉	—	2	1	no	—
133	C₄²×C₂₉	—	2	1	no	—
134	C₄²×C₂₉	—	4	1	no	—
135	C₄²×C₂₉	—	4	1	no	—
136	C₄²×C₂₉	—	4	1	no	—
137	C₄²×C₂₉	—	4	1	no	—
138	#8161	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₂₉	—	2	1	no	—
140	C₂³×C₂₉	—	2	1	no	—
141	C₂³×C₂₉	—	2	1	no	—
142	C₂³×C₂₉	—	4	1	no	—
143	C₂³×C₂₉	—	4	1	no	—
144	C₂³×C₂₉	—	4	1	no	—
145	C₂³×C₂₉	—	4	1	no	—
146	C₂³×C₂₉	C₂×C₄²	1	1	yes	characteristic
147	C₂³×C₂₉	C₄×D₄	1	1	yes	characteristic
148	C₂³×C₂₉	C₄×D₄	1	1	yes	characteristic
149	C₂³×C₂₉	C₂×M₁₆	1	2	yes	—
150	C₂³×C₂₉	#131	1	2	yes	—
151	D₄×C₂₉	—	4	2	no	—
152	D₄×C₂₉	—	4	2	no	—
153	C₂×C₄×C₂₉	—	2	1	no	—
154	C₂×C₄×C₂₉	—	2	1	no	—
155	C₂×C₄×C₂₉	—	2	1	no	—
156	C₂×C₄×C₂₉	—	2	1	no	—
157	C₂×C₄×C₂₉	—	2	1	no	—
158	C₂×C₄×C₂₉	—	2	1	no	—
159	C₂×C₄×C₂₉	—	2	1	no	—
160	C₂×C₄×C₂₉	—	2	1	no	—
161	C₂×C₄×C₂₉	—	2	1	no	—
162	C₂×C₄×C₂₉	—	2	1	no	—
163	C₂×C₄×C₂₉	—	2	1	no	—
164	C₂×C₄×C₂₉	—	2	4	no	—
165	C₂×C₄×C₂₉	—	4	1	no	—
166	C₂×C₄×C₂₉	—	4	1	no	—
167	C₂×C₄×C₂₉	—	4	1	no	—
168	C₂×C₄×C₂₉	—	4	2	no	—
169	C₂×C₄×C₂₉	—	4	2	no	—
170	C₂×C₄×C₂₉	—	4	2	no	—
171	C₂×C₄×C₂₉	—	4	1	no	—
172	C₂×C₄×C₂₉	—	4	1	no	—
173	C₂×C₄×C₂₉	—	4	1	no	—
174	C₂×C₄×C₂₉	—	4	1	no	—
175	C₂×C₄×C₂₉	—	4	2	no	—
176	C₂×C₄×C₂₉	—	4	2	no	—
177	C₂×C₄×C₂₉	—	4	2	no	—
178	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₂₉	#117	1	1	yes	characteristic
180	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
182	C₈×C₂₉	—	2	1	no	—
183	C₈×C₂₉	—	2	1	no	—
184	C₈×C₂₉	—	2	1	no	—
185	C₈×C₂₉	—	4	2	no	—
186	C₈×C₂₉	—	4	2	no	—
187	C₈×C₂₉	—	4	1	no	—
188	C₈×C₂₉	—	4	1	no	—
189	C₈×C₂₉	#99	1	2	yes	complemented
190	C₂×#435	C₂×C₂₉	1	1	yes	characteristic
191	C₄×#99	C₂×C₂₉	1	1	yes	characteristic
192	#1752	C₂×C₂₉	1	1	yes	characteristic, complemented
193	C₈×C₂²⋊C₄	C₂×C₂₉	1	1	yes	characteristic, complemented
194	#1459	C₂×C₂₉	1	1	yes	characteristic
195	#1282	C₂×C₂₉	1	1	yes	characteristic, complemented
196	#1282	C₂×C₂₉	1	1	yes	characteristic, complemented
197	C₂²×C₂₉	—	2	1	no	—
198	C₂²×C₂₉	—	2	1	no	—
199	C₂²×C₂₉	—	2	1	no	—
200	C₂²×C₂₉	—	2	1	no	—
201	C₂²×C₂₉	—	2	1	no	—
202	C₂²×C₂₉	—	2	1	no	—
203	C₂²×C₂₉	—	4	2	no	—
204	C₂²×C₂₉	—	4	2	no	—
205	C₂²×C₂₉	—	4	1	no	—
206	C₂²×C₂₉	—	4	1	no	—
207	C₂²×C₂₉	—	4	1	no	—
208	C₂²×C₂₉	—	8	1	no	—
209	C₂²×C₂₉	—	8	1	no	—
210	C₂²×C₂₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²×C₂₉	C₄×M₁₆	1	1	yes	characteristic
212	C₂²×C₂₉	#405	1	1	yes	characteristic
213	C₂²×C₂₉	#435	1	2	yes	—
214	C₂²×C₂₉	#436	1	2	yes	—
215	C₄×C₂₉	—	2	1	no	—
216	C₄×C₂₉	—	2	1	no	—
217	C₄×C₂₉	—	2	1	no	—
218	C₄×C₂₉	—	4	4	no	—
219	C₄×C₂₉	—	4	1	no	—
220	C₄×C₂₉	—	4	1	no	—
221	C₄×C₂₉	—	4	1	no	—
222	C₄×C₂₉	—	8	2	no	—
223	C₄×C₂₉	C₂×#99	1	1	yes	characteristic
224	C₄×C₂₉	#410	1	1	yes	characteristic
225	C₂²×M₁₆	C₄×C₂₉	1	1	yes	characteristic, complemented
226	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic
227	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
228	#435	—	2	1	no	—
229	#435	—	2	1	no	—
230	#435	—	2	1	no	—
231	#435	—	2	1	no	—
232	C₂×C₄⋊C₈	C₄×C₂₉	1	1	yes	characteristic, complemented
233	C₂×#99	C₄×C₂₉	1	2	yes	—
234	C₂×C₂²⋊C₈	C₄×C₂₉	1	1	yes	characteristic, complemented
235	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
236	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
237	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
238	C₂×#97	—	2	1	no	—
239	C₂×#97	C₄×C₂₉	1	1	yes	characteristic, complemented
240	C₂×C₄×C₈	—	2	1	no	—
241	C₄×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
242	C₄×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
243	#342	C₄×C₂₉	1	2	yes	—
244	#336	—	2	1	no	—
245	#336	—	2	1	no	—
246	#324	C₄×C₂₉	1	2	yes	complemented
247	#323	C₄×C₂₉	1	2	yes	complemented
248	C₂×C₂₉	—	2	2	no	—
249	C₂×C₂₉	—	2	2	no	—
250	C₂×C₂₉	—	2	1	no	—
251	C₂×C₂₉	—	2	1	no	—
252	C₂×C₂₉	—	8	1	no	—
253	C₂×C₂₉	#1753	1	1	yes	characteristic
254	C₂×C₂₉	C₄×#99	1	1	yes	characteristic
255	C₂×C₂₉	#1757	1	1	yes	characteristic
256	C₂²×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
257	C₂³×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
258	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
259	C₂×M₁₆	—	2	1	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	4	2	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	4	2	no	—
265	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
266	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
267	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
268	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
269	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
270	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
271	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
272	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
273	C₄×D₄	—	2	1	no	—
274	C₄×D₄	—	2	1	no	—
275	C₄×D₄	—	2	1	no	—
276	C₄×D₄	—	2	1	no	—
277	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
279	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	—	2	1	no	—
287	#99	—	2	4	no	—
288	C₂²⋊C₈	—	2	1	no	—
289	C₂²⋊C₈	—	2	1	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	C₂²⋊C₈	—	2	1	no	—
292	C₂²⋊C₈	—	2	1	no	—
293	C₂²⋊C₈	—	2	1	no	—
294	C₂²⋊C₈	C₂×C₄×C₂₉	1	2	yes	—
295	C₂²⋊C₈	C₂×C₄×C₂₉	1	2	yes	—
296	#97	—	2	1	no	—
297	#97	—	2	1	no	—
298	#97	—	4	2	no	—
299	C₄×C₈	—	4	2	no	—
300	#95	—	2	1	no	—
301	#95	—	2	1	no	—
302	C₂₉	#8161	1	1	yes	characteristic, direct product factor, Sylow
303	C₂⁴	C₄²×C₂₉	1	1	yes	characteristic
304	C₂⁴	C₂²×C₄×C₂₉	1	1	yes	characteristic
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	4	1	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	C₄²×C₂₉	1	1	yes	characteristic
318	C₂²×C₄	C₄²×C₂₉	1	1	yes	characteristic
319	C₂²×C₄	C₄²×C₂₉	1	1	yes	characteristic
320	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
321	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
324	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
325	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
326	M₁₆	—	4	2	no	—
327	M₁₆	—	4	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
345	C₂×C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
346	C₂×C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
347	C₂×C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₂²⋊C₄	—	2	1	no	—
351	C₂²⋊C₄	—	2	1	no	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	2	no	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₂²⋊C₄	M₁₆×C₂₉	1	4	yes	complemented
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	4	1	no	—
361	C₄²	—	4	1	no	—
362	C₄²	—	4	1	no	—
363	C₄²	—	4	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	1	no	—
371	C₂³	C₂×C₄²×C₂₉	1	1	yes	characteristic
372	C₂³	C₄×D₄×C₂₉	1	1	yes	characteristic
373	C₂³	C₄×D₄×C₂₉	1	1	yes	characteristic
374	C₂³	C₂×M₁₆×C₂₉	1	2	yes	—
375	C₂³	C₂₉×#131	1	2	yes	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
404	C₂×C₄	C₂₉×#117	1	1	yes	characteristic
405	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
406	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
407	C₈	—	2	1	no	—
408	C₈	—	2	1	no	—
409	C₈	—	2	1	no	—
410	C₈	—	4	2	no	—
411	C₈	—	4	2	no	—
412	C₈	—	4	1	no	—
413	C₈	—	4	1	no	—
414	C₈	C₂₉×#99	1	2	yes	complemented
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	C₄×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
429	C₂²	C₄×M₁₆×C₂₉	1	1	yes	characteristic
430	C₂²	C₂₉×#405	1	1	yes	characteristic
431	C₂²	C₂₉×#435	1	2	yes	—
432	C₂²	C₂₉×#436	1	2	yes	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	4	4	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	8	2	no	—
441	C₄	C₂×C₂₉×#99	1	1	yes	characteristic
442	C₄	C₂₉×#410	1	1	yes	characteristic
443	C₂	—	2	2	no	—
444	C₂	—	2	2	no	—
445	C₂	—	2	1	no	—
446	C₂	—	2	1	no	—
447	C₂	—	8	1	no	—
448	C₂	C₂₉×#1753	1	1	yes	characteristic
449	C₂	C₄×C₂₉×#99	1	1	yes	characteristic
450	C₂	C₂₉×#1757	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂×C₄²×C₂₉
Frattini, cosocle	C₂³×C₄	C₂³×C₂₉
socle	C₂²×C₂₉	C₄×C₂²⋊C₄
prime radical	C₂²×D₄×C₂₉	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂³×C₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₉×#1752	C₂	semidirect
4. C₈×C₂²⋊C₄×C₂₉	C₂	semidirect
6. C₂₉×#1282	C₂	semidirect
7. C₂₉×#1282	C₂	semidirect
8. C₂²×M₁₆×C₂₉	C₄	semidirect
15. C₂×C₂₉×C₄⋊C₈	C₄	semidirect
17. C₂×C₂₉×C₂²⋊C₈	C₄	semidirect
22. C₂×C₂₉×#97	C₄	semidirect
29. C₂₉×#324	C₄	semidirect
30. C₂₉×#323	C₄	semidirect
131. C₂²⋊C₄×C₂₉	M₁₆	semidirect
138. #8161	C₂₉	direct (N × H)
189. C₈×C₂₉	#99	semidirect
192. #1752	C₂×C₂₉	semidirect
193. C₈×C₂²⋊C₄	C₂×C₂₉	semidirect
195. #1282	C₂×C₂₉	semidirect
196. #1282	C₂×C₂₉	semidirect
225. C₂²×M₁₆	C₄×C₂₉	semidirect
232. C₂×C₄⋊C₈	C₄×C₂₉	semidirect
234. C₂×C₂²⋊C₈	C₄×C₂₉	semidirect
239. C₂×#97	C₄×C₂₉	semidirect
246. #324	C₄×C₂₉	semidirect
247. #323	C₄×C₂₉	semidirect
302. C₂₉	#8161	direct (N × H)
357. C₂²⋊C₄	M₁₆×C₂₉	semidirect
414. C₈	C₂₉×#99	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#435	2
C₄×C₂₉×#99	2
C₂₉×#1752	2
C₈×C₂²⋊C₄×C₂₉	2
C₂₉×#1459	2
C₂₉×#1282	2
#8161	29

Subgroups — C29×#8161 #20303061

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#8161 #20303061