Subgroups — C₂₉×#2321 #16816035

Order 3712.

808 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#120	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂²⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#390	C₂	1	2	yes	maximal, complemented
5	C₂₉×#388	C₂	1	2	yes	maximal, complemented
6	C₂₉×#388	C₂	1	2	yes	maximal, complemented
7	C₂₉×#386	C₂	1	2	yes	maximal, complemented
8	C₂₉×#386	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#385	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#379	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₂²⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁵×C₂₉	C₂²	1	1	yes	characteristic
13	C₂²×D₄×C₂₉	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₂₉	C₂²	1	2	yes	—
15	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
18	C₂₉×#120	C₄	1	8	yes	complemented
19	C₄×D₄×C₂₉	—	2	4	no	—
20	C₂×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	complemented
22	C₂×C₂²⋊C₄×C₂₉	—	2	4	no	—
23	C₂×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
28	C₂×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	complemented
33	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄²×C₂₉	C₂²	1	2	yes	complemented
35	C₂₉×#95	C₂²	1	2	yes	complemented
36	C₂₉×#95	C₂²	1	2	yes	complemented
37	C₂₉×#95	C₂²	1	2	yes	complemented
38	C₂⁴×C₂₉	—	2	2	no	—
39	C₂⁴×C₂₉	—	2	2	no	—
40	C₂⁴×C₂₉	—	4	2	no	—
41	C₂⁴×C₂₉	—	4	2	no	—
42	C₂⁴×C₂₉	C₂×C₄	1	4	yes	complemented
43	C₂⁴×C₂₉	C₂³	1	2	yes	—
44	C₂⁴×C₂₉	C₂³	1	1	yes	characteristic
45	C₂⁴×C₂₉	C₂³	1	1	yes	characteristic
46	C₂×D₄×C₂₉	—	2	2	no	—
47	C₂×D₄×C₂₉	—	2	2	no	—
48	C₂×D₄×C₂₉	—	4	2	no	—
49	C₂×D₄×C₂₉	—	4	2	no	—
50	C₂×D₄×C₂₉	C₂×C₄	1	4	yes	—
51	C₂×D₄×C₂₉	C₂×C₄	1	8	yes	complemented
52	C₂²×C₄×C₂₉	—	2	2	no	—
53	C₂²×C₄×C₂₉	—	2	2	no	—
54	C₂²×C₄×C₂₉	—	4	2	no	—
55	C₂²×C₄×C₂₉	—	4	2	no	—
56	C₂²×C₄×C₂₉	—	4	2	no	—
57	C₂²×C₄×C₂₉	D₄	1	4	yes	complemented
58	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
60	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
62	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
64	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
66	C₄⋊C₄×C₂₉	—	2	2	no	—
67	C₄⋊C₄×C₂₉	—	4	2	no	—
68	C₂²⋊C₄×C₂₉	—	2	2	no	—
69	C₂²⋊C₄×C₂₉	—	2	2	no	—
70	C₂²⋊C₄×C₂₉	—	2	4	no	—
71	C₂²⋊C₄×C₂₉	—	2	4	no	—
72	C₂²⋊C₄×C₂₉	—	2	2	no	—
73	C₂²⋊C₄×C₂₉	—	4	2	no	—
74	C₂²⋊C₄×C₂₉	—	4	2	no	—
75	C₂²⋊C₄×C₂₉	—	4	2	no	—
76	C₂²⋊C₄×C₂₉	C₂×C₄	1	8	yes	complemented
77	C₂²⋊C₄×C₂₉	C₂×C₄	1	4	yes	complemented
78	C₄²×C₂₉	—	2	2	no	—
79	C₄²×C₂₉	—	4	2	no	—
80	C₂³×C₂₉	—	2	2	no	—
81	C₂³×C₂₉	—	2	2	no	—
82	C₂³×C₂₉	—	2	8	no	—
83	C₂³×C₂₉	—	2	2	no	—
84	C₂³×C₂₉	—	2	1	no	—
85	C₂³×C₂₉	—	2	1	no	—
86	C₂³×C₂₉	—	2	2	no	—
87	C₂³×C₂₉	—	2	2	no	—
88	C₂³×C₂₉	—	2	2	no	—
89	C₂³×C₂₉	—	2	2	no	—
90	C₂³×C₂₉	—	2	2	no	—
91	C₂³×C₂₉	—	2	2	no	—
92	C₂³×C₂₉	—	2	2	no	—
93	C₂³×C₂₉	—	4	8	no	—
94	C₂³×C₂₉	—	4	4	no	—
95	C₂³×C₂₉	—	4	4	no	—
96	C₂³×C₂₉	—	4	8	no	—
97	C₂³×C₂₉	C₂²×C₄	1	4	yes	—
98	C₂³×C₂₉	C₂²×C₄	1	2	yes	—
99	C₂³×C₂₉	C₂²×C₄	1	2	yes	—
100	C₂³×C₂₉	C₂×D₄	1	2	yes	—
101	C₂³×C₂₉	#41	1	2	yes	—
102	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
103	D₄×C₂₉	—	2	8	no	—
104	D₄×C₂₉	—	4	8	no	—
105	C₂×C₄×C₂₉	—	2	1	no	—
106	C₂×C₄×C₂₉	—	2	1	no	—
107	C₂×C₄×C₂₉	—	2	2	no	—
108	C₂×C₄×C₂₉	—	2	2	no	—
109	C₂×C₄×C₂₉	—	2	2	no	—
110	C₂×C₄×C₂₉	—	2	2	no	—
111	C₂×C₄×C₂₉	—	2	1	no	—
112	C₂×C₄×C₂₉	—	2	2	no	—
113	C₂×C₄×C₂₉	—	2	1	no	—
114	C₂×C₄×C₂₉	—	2	2	no	—
115	C₂×C₄×C₂₉	—	2	2	no	—
116	C₂×C₄×C₂₉	—	2	2	no	—
117	C₂×C₄×C₂₉	—	2	2	no	—
118	C₂×C₄×C₂₉	—	2	2	no	—
119	C₂×C₄×C₂₉	—	2	2	no	—
120	C₂×C₄×C₂₉	—	2	2	no	—
121	C₂×C₄×C₂₉	—	4	4	no	—
122	C₂×C₄×C₂₉	—	4	4	no	—
123	C₂×C₄×C₂₉	—	4	4	no	—
124	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
125	C₂×C₄×C₂₉	C₂²×C₄	1	4	yes	—
126	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
127	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
128	#2321	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂²×C₂₉	—	2	4	no	—
130	C₂²×C₂₉	—	2	2	no	—
131	C₂²×C₂₉	—	2	2	no	—
132	C₂²×C₂₉	—	2	4	no	—
133	C₂²×C₂₉	—	2	2	no	—
134	C₂²×C₂₉	—	2	4	no	—
135	C₂²×C₂₉	—	2	4	no	—
136	C₂²×C₂₉	—	2	4	no	—
137	C₂²×C₂₉	—	2	4	no	—
138	C₂²×C₂₉	—	4	16	no	—
139	C₂²×C₂₉	—	4	1	no	—
140	C₂²×C₂₉	—	4	2	no	—
141	C₂²×C₂₉	—	4	1	no	—
142	C₂²×C₂₉	—	4	2	no	—
143	C₂²×C₂₉	—	4	2	no	—
144	C₂²×C₂₉	—	4	2	no	—
145	C₂²×C₂₉	—	4	2	no	—
146	C₂²×C₂₉	C₄×D₄	1	4	yes	—
147	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
148	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
149	C₂²×C₂₉	C₂×#41	1	1	yes	characteristic
150	C₂²×C₂₉	H(5,𝔽₂)	1	2	yes	—
151	C₂²×C₂₉	H(5,𝔽₂)	1	2	yes	—
152	C₄×C₂₉	—	2	2	no	—
153	C₄×C₂₉	—	2	4	no	—
154	C₄×C₂₉	—	2	2	no	—
155	C₄×C₂₉	—	2	2	no	—
156	C₄×C₂₉	—	4	1	no	—
157	C₄×C₂₉	—	4	1	no	—
158	C₄×C₂₉	—	4	2	no	—
159	C₄×C₂₉	—	4	2	no	—
160	C₂×#120	C₂×C₂₉	1	1	yes	characteristic
161	C₂×C₄×D₄	C₂×C₂₉	1	1	yes	characteristic, complemented
162	C₂²×C₂²⋊C₄	C₂×C₂₉	1	1	yes	characteristic, complemented
163	#390	C₂×C₂₉	1	2	yes	complemented
164	#388	C₂×C₂₉	1	2	yes	complemented
165	#388	C₂×C₂₉	1	2	yes	complemented
166	#386	C₂×C₂₉	1	2	yes	complemented
167	#386	C₂×C₂₉	1	1	yes	characteristic, complemented
168	#385	C₂×C₂₉	1	1	yes	characteristic, complemented
169	#379	C₂×C₂₉	1	1	yes	characteristic, complemented
170	C₄×C₂²⋊C₄	C₂×C₂₉	1	1	yes	characteristic, complemented
171	C₂×C₂₉	—	2	4	no	—
172	C₂×C₂₉	—	4	2	no	—
173	C₂×C₂₉	—	4	4	no	—
174	C₂×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
175	C₂×C₂₉	#518	1	2	yes	—
176	C₂×C₂₉	#534	1	1	yes	characteristic
177	C₂×C₂₉	#535	1	1	yes	characteristic
178	C₂×C₂₉	#538	1	2	yes	—
179	C₂⁵	C₂²×C₂₉	1	1	yes	characteristic
180	C₂²×D₄	C₂²×C₂₉	1	1	yes	characteristic
181	C₂²×D₄	C₂²×C₂₉	1	2	yes	—
182	C₂³×C₄	C₂²×C₂₉	1	1	yes	characteristic
183	C₂³×C₄	C₂²×C₂₉	1	1	yes	characteristic
184	C₂³×C₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
185	#120	C₄×C₂₉	1	8	yes	complemented
186	C₄×D₄	—	2	4	no	—
187	C₂×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
188	C₂×C₄⋊C₄	C₂²×C₂₉	1	2	yes	complemented
189	C₂×C₂²⋊C₄	—	2	4	no	—
190	C₂×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
191	C₂×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
192	C₂×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
193	C₂×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
194	C₂×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
195	C₂×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
196	C₂×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
197	C₂×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
198	C₂×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
199	C₂×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	complemented
200	C₂×C₄²	C₂²×C₂₉	1	1	yes	characteristic, complemented
201	C₂×C₄²	C₂²×C₂₉	1	2	yes	complemented
202	#95	C₂²×C₂₉	1	2	yes	complemented
203	#95	C₂²×C₂₉	1	2	yes	complemented
204	#95	C₂²×C₂₉	1	2	yes	complemented
205	C₂₉	#2321	1	1	yes	characteristic, direct product factor, Sylow
206	C₂⁴	—	2	2	no	—
207	C₂⁴	—	2	2	no	—
208	C₂⁴	—	4	2	no	—
209	C₂⁴	—	4	2	no	—
210	C₂⁴	C₂×C₄×C₂₉	1	4	yes	complemented
211	C₂⁴	C₂³×C₂₉	1	2	yes	—
212	C₂⁴	C₂³×C₂₉	1	1	yes	characteristic
213	C₂⁴	C₂³×C₂₉	1	1	yes	characteristic
214	C₂×D₄	—	2	2	no	—
215	C₂×D₄	—	2	2	no	—
216	C₂×D₄	—	4	2	no	—
217	C₂×D₄	—	4	2	no	—
218	C₂×D₄	C₂×C₄×C₂₉	1	4	yes	—
219	C₂×D₄	C₂×C₄×C₂₉	1	8	yes	complemented
220	C₂²×C₄	—	2	2	no	—
221	C₂²×C₄	—	2	2	no	—
222	C₂²×C₄	—	4	2	no	—
223	C₂²×C₄	—	4	2	no	—
224	C₂²×C₄	—	4	2	no	—
225	C₂²×C₄	D₄×C₂₉	1	4	yes	complemented
226	C₂²×C₄	C₂³×C₂₉	1	2	yes	—
227	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
228	C₂²×C₄	C₂³×C₂₉	1	2	yes	—
229	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
230	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
231	C₂²×C₄	C₂³×C₂₉	1	2	yes	—
232	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
233	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
234	C₄⋊C₄	—	2	2	no	—
235	C₄⋊C₄	—	4	2	no	—
236	C₂²⋊C₄	—	2	2	no	—
237	C₂²⋊C₄	—	2	2	no	—
238	C₂²⋊C₄	—	2	4	no	—
239	C₂²⋊C₄	—	2	4	no	—
240	C₂²⋊C₄	—	2	2	no	—
241	C₂²⋊C₄	—	4	2	no	—
242	C₂²⋊C₄	—	4	2	no	—
243	C₂²⋊C₄	—	4	2	no	—
244	C₂²⋊C₄	C₂×C₄×C₂₉	1	8	yes	complemented
245	C₂²⋊C₄	C₂×C₄×C₂₉	1	4	yes	complemented
246	C₄²	—	2	2	no	—
247	C₄²	—	4	2	no	—
248	C₂³	—	2	2	no	—
249	C₂³	—	2	2	no	—
250	C₂³	—	2	8	no	—
251	C₂³	—	2	2	no	—
252	C₂³	—	2	1	no	—
253	C₂³	—	2	1	no	—
254	C₂³	—	2	2	no	—
255	C₂³	—	2	2	no	—
256	C₂³	—	2	2	no	—
257	C₂³	—	2	2	no	—
258	C₂³	—	2	2	no	—
259	C₂³	—	2	2	no	—
260	C₂³	—	2	2	no	—
261	C₂³	—	4	8	no	—
262	C₂³	—	4	4	no	—
263	C₂³	—	4	4	no	—
264	C₂³	—	4	8	no	—
265	C₂³	C₂²×C₄×C₂₉	1	4	yes	—
266	C₂³	C₂²×C₄×C₂₉	1	2	yes	—
267	C₂³	C₂²×C₄×C₂₉	1	2	yes	—
268	C₂³	C₂×D₄×C₂₉	1	2	yes	—
269	C₂³	#41×C₂₉	1	2	yes	—
270	C₂³	C₂⁴×C₂₉	1	1	yes	characteristic
271	D₄	—	2	8	no	—
272	D₄	—	4	8	no	—
273	C₂×C₄	—	2	1	no	—
274	C₂×C₄	—	2	1	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	1	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	4	4	no	—
290	C₂×C₄	—	4	4	no	—
291	C₂×C₄	—	4	4	no	—
292	C₂×C₄	C₂²×C₄×C₂₉	1	2	yes	—
293	C₂×C₄	C₂²×C₄×C₂₉	1	4	yes	—
294	C₂×C₄	C₂×D₄×C₂₉	1	2	yes	—
295	C₂×C₄	C₂×D₄×C₂₉	1	2	yes	—
296	C₂²	—	2	4	no	—
297	C₂²	—	2	2	no	—
298	C₂²	—	2	2	no	—
299	C₂²	—	2	4	no	—
300	C₂²	—	2	2	no	—
301	C₂²	—	2	4	no	—
302	C₂²	—	2	4	no	—
303	C₂²	—	2	4	no	—
304	C₂²	—	2	4	no	—
305	C₂²	—	4	16	no	—
306	C₂²	—	4	1	no	—
307	C₂²	—	4	2	no	—
308	C₂²	—	4	2	no	—
309	C₂²	—	4	1	no	—
310	C₂²	—	4	2	no	—
311	C₂²	—	4	2	no	—
312	C₂²	—	4	2	no	—
313	C₂²	C₄×D₄×C₂₉	1	4	yes	—
314	C₂²	C₂³×C₄×C₂₉	1	1	yes	characteristic
315	C₂²	C₂²×D₄×C₂₉	1	1	yes	characteristic
316	C₂²	C₂×#41×C₂₉	1	1	yes	characteristic
317	C₂²	C₂₉×H(5,𝔽₂)	1	2	yes	—
318	C₂²	C₂₉×H(5,𝔽₂)	1	2	yes	—
319	C₄	—	2	2	no	—
320	C₄	—	2	4	no	—
321	C₄	—	2	2	no	—
322	C₄	—	2	2	no	—
323	C₄	—	4	1	no	—
324	C₄	—	4	2	no	—
325	C₄	—	4	1	no	—
326	C₄	—	4	2	no	—
327	C₂	—	2	4	no	—
328	C₂	—	4	4	no	—
329	C₂	—	4	2	no	—
330	C₂	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
331	C₂	C₂₉×#518	1	2	yes	—
332	C₂	C₂₉×#534	1	1	yes	characteristic
333	C₂	C₂₉×#535	1	1	yes	characteristic
334	C₂	C₂₉×#538	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#120	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₄×C₂₉	C₂	semidirect
3. C₂²×C₂²⋊C₄×C₂₉	C₂	semidirect
4. C₂₉×#390	C₂	semidirect
5. C₂₉×#388	C₂	semidirect
6. C₂₉×#388	C₂	semidirect
7. C₂₉×#386	C₂	semidirect
8. C₂₉×#386	C₂	semidirect
9. C₂₉×#385	C₂	semidirect
10. C₂₉×#379	C₂	semidirect
11. C₄×C₂²⋊C₄×C₂₉	C₂	semidirect
17. C₂³×C₄×C₂₉	C₂²	semidirect
18. C₂₉×#120	C₄	semidirect
20. C₂×C₄⋊C₄×C₂₉	C₂²	semidirect
21. C₂×C₄⋊C₄×C₂₉	C₂²	semidirect
31. C₂×C₂²⋊C₄×C₂₉	C₂²	semidirect
32. C₂×C₂²⋊C₄×C₂₉	C₂²	semidirect
33. C₂×C₄²×C₂₉	C₂²	semidirect
34. C₂×C₄²×C₂₉	C₂²	semidirect
35. C₂₉×#95	C₂²	semidirect
36. C₂₉×#95	C₂²	semidirect
37. C₂₉×#95	C₂²	semidirect
42. C₂⁴×C₂₉	C₂×C₄	semidirect
51. C₂×D₄×C₂₉	C₂×C₄	semidirect
57. C₂²×C₄×C₂₉	D₄	semidirect
76. C₂²⋊C₄×C₂₉	C₂×C₄	semidirect
77. C₂²⋊C₄×C₂₉	C₂×C₄	semidirect
128. #2321	C₂₉	direct (N × H)
161. C₂×C₄×D₄	C₂×C₂₉	semidirect
162. C₂²×C₂²⋊C₄	C₂×C₂₉	semidirect
163. #390	C₂×C₂₉	semidirect
164. #388	C₂×C₂₉	semidirect
165. #388	C₂×C₂₉	semidirect
166. #386	C₂×C₂₉	semidirect
167. #386	C₂×C₂₉	semidirect
168. #385	C₂×C₂₉	semidirect
169. #379	C₂×C₂₉	semidirect
170. C₄×C₂²⋊C₄	C₂×C₂₉	semidirect
184. C₂³×C₄	C₂²×C₂₉	semidirect
185. #120	C₄×C₂₉	semidirect
187. C₂×C₄⋊C₄	C₂²×C₂₉	semidirect
188. C₂×C₄⋊C₄	C₂²×C₂₉	semidirect
198. C₂×C₂²⋊C₄	C₂²×C₂₉	semidirect
199. C₂×C₂²⋊C₄	C₂²×C₂₉	semidirect
200. C₂×C₄²	C₂²×C₂₉	semidirect
201. C₂×C₄²	C₂²×C₂₉	semidirect
202. #95	C₂²×C₂₉	semidirect
203. #95	C₂²×C₂₉	semidirect
204. #95	C₂²×C₂₉	semidirect
205. C₂₉	#2321	direct (N × H)
210. C₂⁴	C₂×C₄×C₂₉	semidirect
219. C₂×D₄	C₂×C₄×C₂₉	semidirect
225. C₂²×C₄	D₄×C₂₉	semidirect
244. C₂²⋊C₄	C₂×C₄×C₂₉	semidirect
245. C₂²⋊C₄	C₂×C₄×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#120	2
C₂×C₄×D₄×C₂₉	2
C₂²×C₂²⋊C₄×C₂₉	2
C₂₉×#390	2
C₂₉×#388	2
C₂₉×#386	2
C₂₉×#385	2
C₂₉×#379	2
C₄×C₂²⋊C₄×C₂₉	2
#2321	29

Subgroups — C29×#2321 #16816035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#2321 #16816035