Subgroups — C₂₉×#17877 #20312777

Order 7424.

726 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#2975	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#2972	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₈×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1586	C₂	1	4	yes	maximal, complemented
5	C₂₉×#1581	C₂	1	4	yes	maximal, complemented
6	C₂₉×#1564	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1478	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1452	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×C₂₉	C₄	1	1	yes	characteristic
11	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
13	C₄×D₈×C₂₉	C₄	1	2	yes	—
14	C₄×D₈×C₂₉	C₄	1	2	yes	—
15	C₄×D₈×C₂₉	C₂²	1	2	yes	—
16	C₄×D₈×C₂₉	C₂²	1	2	yes	—
17	C₂₉×#436	—	2	2	no	—
18	C₂₉×#436	C₂²	1	4	yes	complemented
19	C₈×D₄×C₂₉	—	2	2	no	—
20	C₈×D₄×C₂₉	C₂²	1	4	yes	complemented
21	C₂₉×#431	C₂²	1	1	yes	characteristic
22	C₂₉×#431	C₂²	1	1	yes	characteristic
23	C₂₉×#431	C₂²	1	1	yes	characteristic
24	C₂₉×#431	C₂²	1	1	yes	characteristic
25	C₂×C₂₉×#107	C₄	1	1	yes	characteristic
26	C₂×C₂₉×#102	C₄	1	1	yes	characteristic
27	C₂×C₂₉×#102	C₄	1	1	yes	characteristic
28	C₂₉×#407	—	2	2	no	—
29	C₂×C₂₉×C₂²⋊C₈	—	2	2	no	—
30	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
31	C₂₉×#335	C₂²	1	2	yes	complemented
32	C₂₉×#334	C₂²	1	2	yes	complemented
33	C₂₉×D₄⋊C₈	C₂²	1	4	yes	complemented
34	C₂₉×D₄⋊C₈	C₂²	1	4	yes	complemented
35	C₂₉×#322	C₂²	1	2	yes	complemented
36	C₂₉×#322	C₂²	1	2	yes	complemented
37	C₂²×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
38	C₂²×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₂₉	—	2	1	no	—
40	C₂³×C₄×C₂₉	—	2	1	no	—
41	C₂×D₈×C₂₉	—	2	4	no	—
42	C₂×D₈×C₂₉	C₂×C₄	1	2	yes	—
43	C₂×D₈×C₂₉	C₂×C₄	1	2	yes	—
44	C₂×M₁₆×C₂₉	—	2	4	no	—
45	C₂²×C₈×C₂₉	—	2	4	no	—
46	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₈×C₂₉	C₂×C₄	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	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
53	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
54	C₄×D₄×C₂₉	C₂³	1	2	yes	—
55	C₄×D₄×C₂₉	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
60	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
61	C₂₉×#107	C₂×C₄	1	2	yes	—
62	C₂₉×#107	C₂×C₄	1	2	yes	—
63	C₂₉×C₄⋊C₈	—	2	1	no	—
64	C₂₉×C₄⋊C₈	D₄	1	2	yes	—
65	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
66	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
67	C₂₉×#102	C₂×C₄	1	2	yes	—
68	C₂₉×#102	C₂×C₄	1	2	yes	—
69	C₂₉×#102	C₂×C₄	1	2	yes	—
70	C₂₉×#102	C₂×C₄	1	2	yes	—
71	C₂₉×C₂²⋊C₈	—	2	1	no	—
72	C₂₉×C₂²⋊C₈	—	2	1	no	—
73	C₂₉×C₂²⋊C₈	—	2	1	no	—
74	C₂₉×C₂²⋊C₈	—	2	4	no	—
75	C₂₉×C₂²⋊C₈	—	2	4	no	—
76	C₂₉×C₂²⋊C₈	D₄	1	2	yes	—
77	C₄×C₈×C₂₉	—	2	1	no	—
78	C₄×C₈×C₂₉	—	2	1	no	—
79	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₂₉	C₂³	1	2	yes	—
82	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
83	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
84	C₄×C₈×C₂₉	C₂³	1	2	yes	—
85	C₂⁴×C₂₉	—	2	1	no	—
86	C₂⁴×C₂₉	—	2	1	no	—
87	C₂×D₄×C₂₉	—	2	1	no	—
88	C₂×D₄×C₂₉	—	2	1	no	—
89	C₂×D₄×C₂₉	—	2	2	no	—
90	C₂×D₄×C₂₉	—	2	2	no	—
91	C₂×D₄×C₂₉	—	2	2	no	—
92	C₂×D₄×C₂₉	M₁₆	1	4	yes	complemented
93	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
94	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₂₉	—	2	1	no	—
96	C₂²×C₄×C₂₉	—	2	1	no	—
97	C₂²×C₄×C₂₉	—	2	2	no	—
98	C₂²×C₄×C₂₉	—	2	2	no	—
99	C₂²×C₄×C₂₉	—	2	2	no	—
100	C₂²×C₄×C₂₉	—	2	2	no	—
101	C₂²×C₄×C₂₉	—	8	2	no	—
102	C₂²×C₄×C₂₉	—	8	2	no	—
103	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
106	D₈×C₂₉	—	2	4	no	—
107	D₈×C₂₉	—	2	4	no	—
108	M₁₆×C₂₉	—	8	4	no	—
109	C₂×C₈×C₂₉	—	2	2	no	—
110	C₂×C₈×C₂₉	—	2	2	no	—
111	C₂×C₈×C₂₉	—	2	2	no	—
112	C₂×C₈×C₂₉	—	2	2	no	—
113	C₂×C₈×C₂₉	—	2	2	no	—
114	C₂×C₈×C₂₉	—	8	4	no	—
115	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₂₉	C₂×D₄	1	4	yes	—
120	C₄⋊C₄×C₂₉	—	2	1	no	—
121	C₄⋊C₄×C₂₉	—	2	1	no	—
122	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
123	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
124	C₂²⋊C₄×C₂₉	—	2	2	no	—
125	C₂²⋊C₄×C₂₉	—	2	2	no	—
126	C₂²⋊C₄×C₂₉	—	2	2	no	—
127	C₂²⋊C₄×C₂₉	—	2	2	no	—
128	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₂₉	#41	1	1	yes	characteristic
131	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
132	#17877	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₂₉	—	2	2	no	—
134	C₂³×C₂₉	—	2	4	no	—
135	C₂³×C₂₉	—	2	2	no	—
136	C₂³×C₂₉	—	4	2	no	—
137	C₂³×C₂₉	—	8	1	no	—
138	C₂³×C₂₉	—	8	1	no	—
139	C₂³×C₂₉	—	8	1	no	—
140	C₂³×C₂₉	—	8	1	no	—
141	C₂³×C₂₉	C₄×D₄	1	1	yes	characteristic
142	D₄×C₂₉	—	2	2	no	—
143	D₄×C₂₉	—	2	2	no	—
144	D₄×C₂₉	—	2	2	no	—
145	D₄×C₂₉	—	2	4	no	—
146	D₄×C₂₉	—	4	2	no	—
147	D₄×C₂₉	C₂×M₁₆	1	4	yes	—
148	C₂×C₄×C₂₉	—	2	2	no	—
149	C₂×C₄×C₂₉	—	2	2	no	—
150	C₂×C₄×C₂₉	—	2	2	no	—
151	C₂×C₄×C₂₉	—	4	1	no	—
152	C₂×C₄×C₂₉	—	4	4	no	—
153	C₂×C₄×C₂₉	—	4	4	no	—
154	C₂×C₄×C₂₉	—	8	2	no	—
155	C₂×C₄×C₂₉	—	8	2	no	—
156	C₂×C₄×C₂₉	—	8	1	no	—
157	C₂×C₄×C₂₉	—	8	1	no	—
158	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₂₉	C₂×M₁₆	1	2	yes	—
162	C₂×C₄×C₂₉	#131	1	2	yes	—
163	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
166	C₈×C₂₉	—	2	1	no	—
167	C₈×C₂₉	—	2	1	no	—
168	C₈×C₂₉	—	2	1	no	—
169	C₈×C₂₉	—	2	1	no	—
170	C₈×C₂₉	—	2	4	no	—
171	C₈×C₂₉	—	4	2	no	—
172	C₈×C₂₉	—	4	2	no	—
173	C₈×C₂₉	—	4	2	no	—
174	#2975	C₂×C₂₉	1	1	yes	characteristic, complemented
175	#2972	C₂×C₂₉	1	1	yes	characteristic, complemented
176	C₂×C₄×D₈	C₂×C₂₉	1	1	yes	characteristic
177	#1586	C₂×C₂₉	1	4	yes	complemented
178	#1581	C₂×C₂₉	1	4	yes	complemented
179	#1564	C₂×C₂₉	1	1	yes	characteristic, complemented
180	#1478	C₂×C₂₉	1	1	yes	characteristic, complemented
181	#1478	C₂×C₂₉	1	1	yes	characteristic, complemented
182	#1452	C₂×C₂₉	1	1	yes	characteristic, complemented
183	C₂²×C₂₉	—	2	1	no	—
184	C₂²×C₂₉	—	2	1	no	—
185	C₂²×C₂₉	—	2	4	no	—
186	C₂²×C₂₉	—	4	2	no	—
187	C₂²×C₂₉	—	4	2	no	—
188	C₂²×C₂₉	—	4	2	no	—
189	C₂²×C₂₉	—	4	2	no	—
190	C₂²×C₂₉	—	4	2	no	—
191	C₂²×C₂₉	—	8	4	no	—
192	C₂²×C₂₉	—	8	4	no	—
193	C₂²×C₂₉	#435	1	2	yes	—
194	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
195	C₄×C₂₉	—	2	1	no	—
196	C₄×C₂₉	—	2	1	no	—
197	C₄×C₂₉	—	2	1	no	—
198	C₄×C₂₉	—	4	2	no	—
199	C₄×C₂₉	—	4	2	no	—
200	C₄×C₂₉	#435	1	2	yes	—
201	C₄×C₂₉	C₂²×M₁₆	1	1	yes	characteristic
202	C₄×C₂₉	C₂×#131	1	1	yes	characteristic
203	C₄×C₂₉	#576	1	2	yes	—
204	C₂²×D₈	C₄×C₂₉	1	1	yes	characteristic
205	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
206	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
207	C₄×D₈	C₄×C₂₉	1	2	yes	—
208	C₄×D₈	C₄×C₂₉	1	2	yes	—
209	C₄×D₈	C₂²×C₂₉	1	2	yes	—
210	C₄×D₈	C₂²×C₂₉	1	2	yes	—
211	#436	—	2	2	no	—
212	#436	C₂²×C₂₉	1	4	yes	complemented
213	C₈×D₄	—	2	2	no	—
214	C₈×D₄	C₂²×C₂₉	1	4	yes	complemented
215	#431	C₂²×C₂₉	1	1	yes	characteristic
216	#431	C₂²×C₂₉	1	1	yes	characteristic
217	#431	C₂²×C₂₉	1	1	yes	characteristic
218	#431	C₂²×C₂₉	1	1	yes	characteristic
219	C₂×#107	C₄×C₂₉	1	1	yes	characteristic
220	C₂×#102	C₄×C₂₉	1	1	yes	characteristic
221	C₂×#102	C₄×C₂₉	1	1	yes	characteristic
222	#407	—	2	2	no	—
223	C₂×C₂²⋊C₈	—	2	2	no	—
224	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
225	#335	C₂²×C₂₉	1	2	yes	complemented
226	#334	C₂²×C₂₉	1	2	yes	complemented
227	D₄⋊C₈	C₂²×C₂₉	1	4	yes	complemented
228	D₄⋊C₈	C₂²×C₂₉	1	4	yes	complemented
229	#322	C₂²×C₂₉	1	2	yes	complemented
230	#322	C₂²×C₂₉	1	2	yes	complemented
231	C₂×C₂₉	—	2	2	no	—
232	C₂×C₂₉	—	4	4	no	—
233	C₂×C₂₉	—	8	2	no	—
234	C₂×C₂₉	C₂×#435	1	1	yes	characteristic
235	C₂×C₂₉	#2948	1	1	yes	characteristic
236	C₂×C₂₉	#2957	1	1	yes	characteristic
237	C₂²×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
238	C₂²×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
239	C₂³×C₄	—	2	1	no	—
240	C₂³×C₄	—	2	1	no	—
241	C₂×D₈	—	2	4	no	—
242	C₂×D₈	C₂×C₄×C₂₉	1	2	yes	—
243	C₂×D₈	C₂×C₄×C₂₉	1	2	yes	—
244	C₂×M₁₆	—	2	4	no	—
245	C₂²×C₈	—	2	4	no	—
246	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
247	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	1	no	—
250	C₄×D₄	—	2	1	no	—
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
253	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
254	C₄×D₄	C₂³×C₂₉	1	2	yes	—
255	C₄×D₄	C₂³×C₂₉	1	2	yes	—
256	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
258	C₂×C₂²⋊C₄	—	2	1	no	—
259	C₂×C₂²⋊C₄	—	2	1	no	—
260	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
261	#107	C₂×C₄×C₂₉	1	2	yes	—
262	#107	C₂×C₄×C₂₉	1	2	yes	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	D₄×C₂₉	1	2	yes	—
265	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
266	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
267	#102	C₂×C₄×C₂₉	1	2	yes	—
268	#102	C₂×C₄×C₂₉	1	2	yes	—
269	#102	C₂×C₄×C₂₉	1	2	yes	—
270	#102	C₂×C₄×C₂₉	1	2	yes	—
271	C₂²⋊C₈	—	2	1	no	—
272	C₂²⋊C₈	—	2	1	no	—
273	C₂²⋊C₈	—	2	1	no	—
274	C₂²⋊C₈	—	2	4	no	—
275	C₂²⋊C₈	—	2	4	no	—
276	C₂²⋊C₈	D₄×C₂₉	1	2	yes	—
277	C₄×C₈	—	2	1	no	—
278	C₄×C₈	—	2	1	no	—
279	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
280	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
281	C₄×C₈	C₂³×C₂₉	1	2	yes	—
282	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
283	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₂₉	1	2	yes	—
285	C₂₉	#17877	1	1	yes	characteristic, direct product factor, Sylow
286	C₂⁴	—	2	1	no	—
287	C₂⁴	—	2	1	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	M₁₆×C₂₉	1	4	yes	complemented
294	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
295	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	8	2	no	—
303	C₂²×C₄	—	8	2	no	—
304	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
306	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
307	D₈	—	2	4	no	—
308	D₈	—	2	4	no	—
309	M₁₆	—	8	4	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	8	4	no	—
316	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
317	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
318	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
319	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
320	C₂×C₈	C₂×D₄×C₂₉	1	4	yes	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
324	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
330	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
331	C₄²	#41×C₂₉	1	1	yes	characteristic
332	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
333	C₂³	—	2	2	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	8	1	no	—
338	C₂³	—	8	1	no	—
339	C₂³	—	8	1	no	—
340	C₂³	—	8	1	no	—
341	C₂³	C₄×D₄×C₂₉	1	1	yes	characteristic
342	D₄	—	2	4	no	—
343	D₄	—	2	2	no	—
344	D₄	—	2	2	no	—
345	D₄	—	2	2	no	—
346	D₄	—	4	2	no	—
347	D₄	C₂×M₁₆×C₂₉	1	4	yes	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	8	2	no	—
355	C₂×C₄	—	8	2	no	—
356	C₂×C₄	—	8	1	no	—
357	C₂×C₄	—	8	1	no	—
358	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
359	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
360	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
361	C₂×C₄	C₂×M₁₆×C₂₉	1	2	yes	—
362	C₂×C₄	C₂₉×#131	1	2	yes	—
363	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
364	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
365	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	—	2	1	no	—
369	C₈	—	2	1	no	—
370	C₈	—	2	4	no	—
371	C₈	—	4	2	no	—
372	C₈	—	4	2	no	—
373	C₈	—	4	2	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	4	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	8	4	no	—
383	C₂²	—	8	4	no	—
384	C₂²	C₂₉×#435	1	2	yes	—
385	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	4	2	no	—
390	C₄	—	4	2	no	—
391	C₄	C₂₉×#435	1	2	yes	—
392	C₄	C₂²×M₁₆×C₂₉	1	1	yes	characteristic
393	C₄	C₂×C₂₉×#131	1	1	yes	characteristic
394	C₄	C₂₉×#576	1	2	yes	—
395	C₂	—	2	2	no	—
396	C₂	—	4	4	no	—
397	C₂	—	8	2	no	—
398	C₂	C₂×C₂₉×#435	1	1	yes	characteristic
399	C₂	C₂₉×#2948	1	1	yes	characteristic
400	C₂	C₂₉×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₄²	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂×C₄×D₄
prime radical	C₂²×D₈×C₂₉	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂₉×#431 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#2975	C₂	semidirect
2. C₂₉×#2972	C₂	semidirect
4. C₂₉×#1586	C₂	semidirect
5. C₂₉×#1581	C₂	semidirect
6. C₂₉×#1564	C₂	semidirect
7. C₂₉×#1478	C₂	semidirect
8. C₂₉×#1478	C₂	semidirect
9. C₂₉×#1452	C₂	semidirect
18. C₂₉×#436	C₂²	semidirect
20. C₈×D₄×C₂₉	C₂²	semidirect
31. C₂₉×#335	C₂²	semidirect
32. C₂₉×#334	C₂²	semidirect
33. C₂₉×D₄⋊C₈	C₂²	semidirect
34. C₂₉×D₄⋊C₈	C₂²	semidirect
35. C₂₉×#322	C₂²	semidirect
36. C₂₉×#322	C₂²	semidirect
92. C₂×D₄×C₂₉	M₁₆	semidirect
132. #17877	C₂₉	direct (N × H)
174. #2975	C₂×C₂₉	semidirect
175. #2972	C₂×C₂₉	semidirect
177. #1586	C₂×C₂₉	semidirect
178. #1581	C₂×C₂₉	semidirect
179. #1564	C₂×C₂₉	semidirect
180. #1478	C₂×C₂₉	semidirect
181. #1478	C₂×C₂₉	semidirect
182. #1452	C₂×C₂₉	semidirect
212. #436	C₂²×C₂₉	semidirect
214. C₈×D₄	C₂²×C₂₉	semidirect
225. #335	C₂²×C₂₉	semidirect
226. #334	C₂²×C₂₉	semidirect
227. D₄⋊C₈	C₂²×C₂₉	semidirect
228. D₄⋊C₈	C₂²×C₂₉	semidirect
229. #322	C₂²×C₂₉	semidirect
230. #322	C₂²×C₂₉	semidirect
285. C₂₉	#17877	direct (N × H)
293. C₂×D₄	M₁₆×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#2975	2
C₂₉×#2972	2
C₂×C₄×D₈×C₂₉	2
C₂₉×#1586	2
C₂₉×#1581	2
C₂₉×#1564	2
C₂₉×#1478	2
C₂₉×#1452	2
#17877	29

Subgroups — C29×#17877 #20312777

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#17877 #20312777