Subgroups — C₂₉×#17816 #20312716

Order 7424.

640 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#2920	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#432	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×#431	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1572	C₂	1	4	yes	maximal, complemented
5	C₂₉×#1571	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1570	C₂	1	2	yes	maximal, complemented
7	C₂₉×#1568	C₂	1	4	yes	maximal, complemented
8	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
9	C₂₉×#432	—	2	1	no	—
10	C₂₉×#432	—	2	1	no	—
11	C₂₉×#432	—	2	1	no	—
12	C₂₉×#432	C₂²	1	2	yes	—
13	C₂₉×#432	C₂²	1	2	yes	—
14	C₂₉×#432	C₂²	1	2	yes	—
15	C₂₉×#431	—	2	1	no	—
16	C₂₉×#431	C₄	1	2	yes	—
17	C₂₉×#431	C₄	1	2	yes	—
18	C₂₉×#431	C₂²	1	2	yes	—
19	C₂₉×#431	C₂²	1	1	yes	characteristic
20	C₂₉×#431	C₂²	1	1	yes	characteristic
21	C₂₉×#431	C₂²	1	2	yes	—
22	C₂₉×#423	C₂²	1	2	yes	—
23	C₂×C₂₉×C₄⋊C₈	C₄	1	2	yes	—
24	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂₉×#407	—	2	1	no	—
26	C₂×C₂₉×C₂²⋊C₈	—	2	1	no	—
27	C₂×C₂₉×C₂²⋊C₈	C₄	1	2	yes	—
28	C₄×M₁₆×C₂₉	—	2	1	no	—
29	C₂×C₂₉×#97	—	2	1	no	—
30	C₂×C₄×C₈×C₂₉	C₂²	1	2	yes	—
31	C₂₉×#335	C₂²	1	8	yes	complemented
32	C₂₉×#334	C₂²	1	8	yes	complemented
33	C₂³×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₂₉	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₂₉	Q₈	1	1	yes	characteristic
36	C₂×M₁₆×C₂₉	—	2	2	no	—
37	C₂²×C₈×C₂₉	—	2	2	no	—
38	C₂²×C₈×C₂₉	C₂×C₄	1	4	yes	—
39	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₂₉	Q₈	1	1	yes	characteristic
46	C₂×C₄²×C₂₉	Q₈	1	1	yes	characteristic
47	C₂×C₄²×C₂₉	Q₈	1	1	yes	characteristic
48	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
49	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
50	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
51	C₂₉×C₄⋊C₈	—	2	2	no	—
52	C₂₉×C₄⋊C₈	—	2	2	no	—
53	C₂₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
54	C₂₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
55	C₂₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
56	C₂₉×C₄⋊C₈	C₂³	1	4	yes	—
57	C₂₉×C₄⋊C₈	C₂³	1	4	yes	—
58	C₂₉×C₂²⋊C₈	—	2	2	no	—
59	C₂₉×C₂²⋊C₈	—	2	2	no	—
60	C₂₉×C₂²⋊C₈	—	2	2	no	—
61	C₂₉×C₂²⋊C₈	—	2	2	no	—
62	C₂₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
63	C₂₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
64	C₂₉×C₂²⋊C₈	C₂×C₄	1	4	yes	—
65	C₂₉×#97	—	2	2	no	—
66	C₂₉×#97	—	2	2	no	—
67	C₂₉×#97	—	2	2	no	—
68	C₄×C₈×C₂₉	—	2	2	no	—
69	C₄×C₈×C₂₉	C₂×C₄	1	4	yes	—
70	C₄×C₈×C₂₉	C₂³	1	2	yes	—
71	C₄×C₈×C₂₉	C₂³	1	2	yes	—
72	C₂⁴×C₂₉	C₄⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₂₉	—	2	4	no	—
74	C₂²×C₄×C₂₉	—	4	2	no	—
75	C₂²×C₄×C₂₉	—	4	2	no	—
76	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
94	M₁₆×C₂₉	—	4	4	no	—
95	C₂×C₈×C₂₉	—	2	4	no	—
96	C₂×C₈×C₂₉	—	2	4	no	—
97	C₂×C₈×C₂₉	—	4	4	no	—
98	C₂×C₈×C₂₉	—	4	4	no	—
99	C₂×C₈×C₂₉	C₂²×C₄	1	4	yes	—
100	C₂×C₈×C₂₉	C₂²×C₄	1	4	yes	—
101	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₂₉	C₂×Q₈	1	1	yes	characteristic
114	C₄²×C₂₉	C₂×Q₈	1	1	yes	characteristic
115	C₄²×C₂₉	C₂×Q₈	1	1	yes	characteristic
116	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
117	#17816	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂³×C₂₉	—	2	2	no	—
119	C₂³×C₂₉	—	2	2	no	—
120	C₂³×C₂₉	—	4	1	no	—
121	C₂³×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂³×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
123	C₂³×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₄×C₂₉	—	2	2	no	—
125	C₂×C₄×C₂₉	—	2	2	no	—
126	C₂×C₄×C₂₉	—	2	2	no	—
127	C₂×C₄×C₂₉	—	2	2	no	—
128	C₂×C₄×C₂₉	—	2	2	no	—
129	C₂×C₄×C₂₉	—	2	2	no	—
130	C₂×C₄×C₂₉	—	2	2	no	—
131	C₂×C₄×C₂₉	—	2	2	no	—
132	C₂×C₄×C₂₉	—	2	2	no	—
133	C₂×C₄×C₂₉	—	2	2	no	—
134	C₂×C₄×C₂₉	—	4	1	no	—
135	C₂×C₄×C₂₉	—	4	1	no	—
136	C₂×C₄×C₂₉	—	4	1	no	—
137	C₂×C₄×C₂₉	—	4	1	no	—
138	C₂×C₄×C₂₉	—	4	1	no	—
139	C₂×C₄×C₂₉	—	4	1	no	—
140	C₂×C₄×C₂₉	—	4	1	no	—
141	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₂₉	#135	1	4	yes	—
151	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
154	C₈×C₂₉	—	2	4	no	—
155	C₈×C₂₉	—	2	4	no	—
156	C₈×C₂₉	—	4	4	no	—
157	C₈×C₂₉	—	4	4	no	—
158	#2920	C₂×C₂₉	1	1	yes	characteristic
159	C₂×#432	C₂×C₂₉	1	1	yes	characteristic
160	C₂×#431	C₂×C₂₉	1	1	yes	characteristic
161	#1572	C₂×C₂₉	1	4	yes	complemented
162	#1571	C₂×C₂₉	1	2	yes	complemented
163	#1570	C₂×C₂₉	1	2	yes	complemented
164	#1568	C₂×C₂₉	1	4	yes	complemented
165	C₂²×C₂₉	—	2	1	no	—
166	C₂²×C₂₉	—	2	1	no	—
167	C₂²×C₂₉	—	2	1	no	—
168	C₂²×C₂₉	—	2	1	no	—
169	C₂²×C₂₉	—	2	1	no	—
170	C₂²×C₂₉	—	2	1	no	—
171	C₂²×C₂₉	—	2	1	no	—
172	C₂²×C₂₉	—	4	4	no	—
173	C₂²×C₂₉	#427	1	2	yes	—
174	C₂²×C₂₉	#430	1	2	yes	—
175	C₂²×C₂₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
176	C₄×C₂₉	—	2	1	no	—
177	C₄×C₂₉	—	2	1	no	—
178	C₄×C₂₉	—	2	1	no	—
179	C₄×C₂₉	—	2	1	no	—
180	C₄×C₂₉	—	2	1	no	—
181	C₄×C₂₉	—	2	1	no	—
182	C₄×C₂₉	—	2	1	no	—
183	C₄×C₂₉	—	2	1	no	—
184	C₄×C₂₉	—	2	1	no	—
185	C₄×C₂₉	#427	1	2	yes	—
186	C₄×C₂₉	#568	1	2	yes	—
187	C₄×C₂₉	C₂×#135	1	2	yes	—
188	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
189	#432	—	2	1	no	—
190	#432	—	2	1	no	—
191	#432	—	2	1	no	—
192	#432	C₂²×C₂₉	1	2	yes	—
193	#432	C₂²×C₂₉	1	2	yes	—
194	#432	C₂²×C₂₉	1	2	yes	—
195	#431	—	2	1	no	—
196	#431	C₄×C₂₉	1	2	yes	—
197	#431	C₄×C₂₉	1	2	yes	—
198	#431	C₂²×C₂₉	1	2	yes	—
199	#431	C₂²×C₂₉	1	1	yes	characteristic
200	#431	C₂²×C₂₉	1	1	yes	characteristic
201	#431	C₂²×C₂₉	1	2	yes	—
202	#423	C₂²×C₂₉	1	2	yes	—
203	C₂×C₄⋊C₈	C₄×C₂₉	1	2	yes	—
204	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
205	#407	—	2	1	no	—
206	C₂×C₂²⋊C₈	—	2	1	no	—
207	C₂×C₂²⋊C₈	C₄×C₂₉	1	2	yes	—
208	C₄×M₁₆	—	2	1	no	—
209	C₂×#97	—	2	1	no	—
210	C₂×C₄×C₈	C₂²×C₂₉	1	2	yes	—
211	#335	C₂²×C₂₉	1	8	yes	complemented
212	#334	C₂²×C₂₉	1	8	yes	complemented
213	C₂×C₂₉	—	2	2	no	—
214	C₂×C₂₉	—	2	2	no	—
215	C₂×C₂₉	—	4	1	no	—
216	C₂×C₂₉	#2905	1	1	yes	characteristic
217	C₂×C₂₉	C₂×#427	1	1	yes	characteristic
218	C₂×C₂₉	C₂×#430	1	1	yes	characteristic
219	C₂³×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
220	C₂³×C₄	D₄×C₂₉	1	1	yes	characteristic
221	C₂³×C₄	Q₈×C₂₉	1	1	yes	characteristic
222	C₂×M₁₆	—	2	2	no	—
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	C₂×C₄×C₂₉	1	4	yes	—
225	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
226	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
227	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
228	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
229	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
230	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
231	C₂×C₄²	Q₈×C₂₉	1	1	yes	characteristic
232	C₂×C₄²	Q₈×C₂₉	1	1	yes	characteristic
233	C₂×C₄²	Q₈×C₂₉	1	1	yes	characteristic
234	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
235	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
236	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
237	C₄⋊C₈	—	2	2	no	—
238	C₄⋊C₈	—	2	2	no	—
239	C₄⋊C₈	C₂×C₄×C₂₉	1	2	yes	—
240	C₄⋊C₈	C₂×C₄×C₂₉	1	2	yes	—
241	C₄⋊C₈	C₂×C₄×C₂₉	1	4	yes	—
242	C₄⋊C₈	C₂³×C₂₉	1	4	yes	—
243	C₄⋊C₈	C₂³×C₂₉	1	4	yes	—
244	C₂²⋊C₈	—	2	2	no	—
245	C₂²⋊C₈	—	2	2	no	—
246	C₂²⋊C₈	—	2	2	no	—
247	C₂²⋊C₈	—	2	2	no	—
248	C₂²⋊C₈	C₂×C₄×C₂₉	1	2	yes	—
249	C₂²⋊C₈	C₂×C₄×C₂₉	1	2	yes	—
250	C₂²⋊C₈	C₂×C₄×C₂₉	1	4	yes	—
251	#97	—	2	2	no	—
252	#97	—	2	2	no	—
253	#97	—	2	2	no	—
254	C₄×C₈	—	2	2	no	—
255	C₄×C₈	C₂×C₄×C₂₉	1	4	yes	—
256	C₄×C₈	C₂³×C₂₉	1	2	yes	—
257	C₄×C₈	C₂³×C₂₉	1	2	yes	—
258	C₂₉	#17816	1	1	yes	characteristic, direct product factor, Sylow
259	C₂⁴	C₄⋊C₄×C₂₉	1	1	yes	characteristic
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
264	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
265	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
266	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
269	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
270	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
271	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
272	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
273	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
278	C₂²×C₄	C₂×Q₈×C₂₉	1	1	yes	characteristic
279	C₂²×C₄	C₂×Q₈×C₂₉	1	1	yes	characteristic
280	C₂²×C₄	C₂×Q₈×C₂₉	1	1	yes	characteristic
281	M₁₆	—	4	4	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	4	4	no	—
285	C₂×C₈	—	4	4	no	—
286	C₂×C₈	C₂²×C₄×C₂₉	1	4	yes	—
287	C₂×C₈	C₂²×C₄×C₂₉	1	4	yes	—
288	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
289	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
290	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
291	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
292	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
293	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
294	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
295	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
296	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
297	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
298	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
299	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
300	C₄²	C₂×Q₈×C₂₉	1	1	yes	characteristic
301	C₄²	C₂×Q₈×C₂₉	1	1	yes	characteristic
302	C₄²	C₂×Q₈×C₂₉	1	1	yes	characteristic
303	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
304	C₂³	—	2	2	no	—
305	C₂³	—	2	2	no	—
306	C₂³	—	4	1	no	—
307	C₂³	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
308	C₂³	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
309	C₂³	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
328	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
329	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
330	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
331	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
332	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
333	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
334	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
335	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
336	C₂×C₄	C₂₉×#135	1	4	yes	—
337	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
338	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
339	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
340	C₈	—	2	4	no	—
341	C₈	—	2	4	no	—
342	C₈	—	4	4	no	—
343	C₈	—	4	4	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	4	4	no	—
352	C₂²	C₂₉×#427	1	2	yes	—
353	C₂²	C₂₉×#430	1	2	yes	—
354	C₂²	C₂²×C₄⋊C₄×C₂₉	1	1	yes	characteristic
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	C₂₉×#427	1	2	yes	—
365	C₄	C₂₉×#568	1	2	yes	—
366	C₄	C₂×C₂₉×#135	1	2	yes	—
367	C₂	—	2	2	no	—
368	C₂	—	2	2	no	—
369	C₂	—	4	1	no	—
370	C₂	C₂₉×#2905	1	1	yes	characteristic
371	C₂	C₂×C₂₉×#427	1	1	yes	characteristic
372	C₂	C₂×C₂₉×#430	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	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₂₉	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂²×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₉×#1572	C₂	semidirect
5. C₂₉×#1571	C₂	semidirect
6. C₂₉×#1570	C₂	semidirect
7. C₂₉×#1568	C₂	semidirect
31. C₂₉×#335	C₂²	semidirect
32. C₂₉×#334	C₂²	semidirect
117. #17816	C₂₉	direct (N × H)
161. #1572	C₂×C₂₉	semidirect
162. #1571	C₂×C₂₉	semidirect
163. #1570	C₂×C₂₉	semidirect
164. #1568	C₂×C₂₉	semidirect
211. #335	C₂²×C₂₉	semidirect
212. #334	C₂²×C₂₉	semidirect
258. C₂₉	#17816	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×#2920	2
C₂×C₂₉×#432	2
C₂×C₂₉×#431	2
C₂₉×#1572	2
C₂₉×#1571	2
C₂₉×#1570	2
C₂₉×#1568	2
#17816	29

Subgroups — C29×#17816 #20312716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#17816 #20312716