Subgroups — C₂₉×#17797 #20312697

Order 7424.

712 conjugacy classes of subgroups.

The subgroup lattice has 380 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×C₄×M₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1569	C₂	1	4	yes	maximal, complemented
5	C₂₉×#1568	C₂	1	4	yes	maximal, complemented
6	C₂₉×#1565	C₂	1	4	yes	maximal, complemented
7	C₂²×M₁₆×C₂₉	C₄	1	2	yes	—
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	C₂²	1	2	yes	—
17	C₂₉×#423	C₂²	1	2	yes	—
18	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂₉×#407	—	2	1	no	—
20	C₂×C₂₉×C₂²⋊C₈	—	2	1	no	—
21	C₄×M₁₆×C₂₉	—	2	1	no	—
22	C₄×M₁₆×C₂₉	C₄	1	2	yes	—
23	C₄×M₁₆×C₂₉	C₄	1	1	yes	characteristic
24	C₄×M₁₆×C₂₉	C₄	1	1	yes	characteristic
25	C₄×M₁₆×C₂₉	C₂²	1	2	yes	—
26	C₄×M₁₆×C₂₉	C₂²	1	2	yes	—
27	C₂×C₂₉×#97	—	2	1	no	—
28	C₂×C₂₉×#97	C₄	1	2	yes	—
29	C₂×C₄×C₈×C₂₉	C₂²	1	2	yes	—
30	C₂₉×#335	C₂²	1	8	yes	complemented
31	C₂₉×#334	C₂²	1	8	yes	complemented
32	C₂³×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₂₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₂₉	Q₈	1	1	yes	characteristic
35	C₂×M₁₆×C₂₉	—	2	8	no	—
36	C₂×M₁₆×C₂₉	—	2	2	no	—
37	C₂×M₁₆×C₂₉	C₂×C₄	1	2	yes	—
38	C₂×M₁₆×C₂₉	C₂×C₄	1	4	yes	—
39	C₂×M₁₆×C₂₉	C₂×C₄	1	2	yes	—
40	C₂²×C₈×C₂₉	—	2	2	no	—
41	C₂²×C₈×C₂₉	C₂×C₄	1	4	yes	—
42	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₂₉	Q₈	1	1	yes	characteristic
49	C₂×C₄²×C₂₉	Q₈	1	1	yes	characteristic
50	C₂×C₄²×C₂₉	Q₈	1	1	yes	characteristic
51	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
54	C₂₉×C₄⋊C₈	—	2	2	no	—
55	C₂₉×C₄⋊C₈	—	2	2	no	—
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×#97	—	2	2	no	—
63	C₂₉×#97	—	2	2	no	—
64	C₂₉×#97	—	2	2	no	—
65	C₂₉×#97	C₂×C₄	1	2	yes	—
66	C₂₉×#97	C₂×C₄	1	4	yes	—
67	C₂₉×#97	C₂×C₄	1	2	yes	—
68	C₄×C₈×C₂₉	—	2	2	no	—
69	C₄×C₈×C₂₉	C₂×C₄	1	2	yes	—
70	C₄×C₈×C₂₉	C₂×C₄	1	2	yes	—
71	C₄×C₈×C₂₉	C₂³	1	4	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	—	2	4	no	—
95	M₁₆×C₂₉	—	2	8	no	—
96	M₁₆×C₂₉	—	4	4	no	—
97	M₁₆×C₂₉	M₁₆	1	8	yes	complemented
98	C₂×C₈×C₂₉	—	2	8	no	—
99	C₂×C₈×C₂₉	—	2	4	no	—
100	C₂×C₈×C₂₉	—	2	4	no	—
101	C₂×C₈×C₂₉	—	4	4	no	—
102	C₂×C₈×C₂₉	C₂²×C₄	1	4	yes	—
103	C₂×C₈×C₂₉	C₂²×C₄	1	4	yes	—
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	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₂₉	C₂×Q₈	1	1	yes	characteristic
117	C₄²×C₂₉	C₂×Q₈	1	1	yes	characteristic
118	C₄²×C₂₉	C₂×Q₈	1	1	yes	characteristic
119	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
120	#17797	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂³×C₂₉	—	2	2	no	—
122	C₂³×C₂₉	—	2	2	no	—
123	C₂³×C₂₉	—	4	1	no	—
124	C₂³×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₂³×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₂³×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
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	—	2	2	no	—
135	C₂×C₄×C₂₉	—	2	2	no	—
136	C₂×C₄×C₂₉	—	2	2	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	—	4	1	no	—
142	C₂×C₄×C₂₉	—	4	1	no	—
143	C₂×C₄×C₂₉	—	4	1	no	—
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	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₂₉	C₂×M₁₆	1	4	yes	—
154	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
157	C₈×C₂₉	—	2	4	no	—
158	C₈×C₂₉	—	4	4	no	—
159	C₈×C₂₉	—	4	4	no	—
160	C₈×C₂₉	C₂×M₁₆	1	8	yes	—
161	#2920	C₂×C₂₉	1	1	yes	characteristic
162	C₂×#432	C₂×C₂₉	1	1	yes	characteristic
163	C₂×C₄×M₁₆	C₂×C₂₉	1	1	yes	characteristic
164	#1569	C₂×C₂₉	1	4	yes	complemented
165	#1568	C₂×C₂₉	1	4	yes	complemented
166	#1565	C₂×C₂₉	1	4	yes	complemented
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	—	2	1	no	—
173	C₂²×C₂₉	—	2	1	no	—
174	C₂²×C₂₉	—	4	4	no	—
175	C₂²×C₂₉	#423	1	2	yes	—
176	C₂²×C₂₉	#430	1	2	yes	—
177	C₂²×C₂₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
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	—	2	1	no	—
186	C₄×C₂₉	—	2	1	no	—
187	C₄×C₂₉	#423	1	2	yes	—
188	C₄×C₂₉	C₂²×M₁₆	1	2	yes	—
189	C₄×C₂₉	#575	1	2	yes	—
190	C₂²×M₁₆	C₄×C₂₉	1	2	yes	—
191	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
192	#432	—	2	1	no	—
193	#432	—	2	1	no	—
194	#432	—	2	1	no	—
195	#432	C₂²×C₂₉	1	2	yes	—
196	#432	C₂²×C₂₉	1	2	yes	—
197	#432	C₂²×C₂₉	1	2	yes	—
198	#431	—	2	1	no	—
199	#431	C₂²×C₂₉	1	2	yes	—
200	#423	C₂²×C₂₉	1	2	yes	—
201	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
202	#407	—	2	1	no	—
203	C₂×C₂²⋊C₈	—	2	1	no	—
204	C₄×M₁₆	—	2	1	no	—
205	C₄×M₁₆	C₄×C₂₉	1	1	yes	characteristic
206	C₄×M₁₆	C₄×C₂₉	1	2	yes	—
207	C₄×M₁₆	C₄×C₂₉	1	1	yes	characteristic
208	C₄×M₁₆	C₂²×C₂₉	1	2	yes	—
209	C₄×M₁₆	C₂²×C₂₉	1	2	yes	—
210	C₂×#97	—	2	1	no	—
211	C₂×#97	C₄×C₂₉	1	2	yes	—
212	C₂×C₄×C₈	C₂²×C₂₉	1	2	yes	—
213	#335	C₂²×C₂₉	1	8	yes	complemented
214	#334	C₂²×C₂₉	1	8	yes	complemented
215	C₂×C₂₉	—	2	2	no	—
216	C₂×C₂₉	—	2	2	no	—
217	C₂×C₂₉	—	4	1	no	—
218	C₂×C₂₉	C₂×#423	1	1	yes	characteristic
219	C₂×C₂₉	#2911	1	1	yes	characteristic
220	C₂×C₂₉	C₂×#430	1	1	yes	characteristic
221	C₂³×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
222	C₂³×C₄	D₄×C₂₉	1	1	yes	characteristic
223	C₂³×C₄	Q₈×C₂₉	1	1	yes	characteristic
224	C₂×M₁₆	—	2	8	no	—
225	C₂×M₁₆	—	2	2	no	—
226	C₂×M₁₆	C₂×C₄×C₂₉	1	2	yes	—
227	C₂×M₁₆	C₂×C₄×C₂₉	1	4	yes	—
228	C₂×M₁₆	C₂×C₄×C₂₉	1	2	yes	—
229	C₂²×C₈	—	2	2	no	—
230	C₂²×C₈	C₂×C₄×C₂₉	1	4	yes	—
231	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
232	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
233	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
234	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
235	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
236	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
237	C₂×C₄²	Q₈×C₂₉	1	1	yes	characteristic
238	C₂×C₄²	Q₈×C₂₉	1	1	yes	characteristic
239	C₂×C₄²	Q₈×C₂₉	1	1	yes	characteristic
240	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
241	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
242	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
243	C₄⋊C₈	—	2	2	no	—
244	C₄⋊C₈	—	2	2	no	—
245	C₄⋊C₈	C₂³×C₂₉	1	4	yes	—
246	C₄⋊C₈	C₂³×C₂₉	1	4	yes	—
247	C₂²⋊C₈	—	2	2	no	—
248	C₂²⋊C₈	—	2	2	no	—
249	C₂²⋊C₈	—	2	2	no	—
250	C₂²⋊C₈	—	2	2	no	—
251	#97	—	2	2	no	—
252	#97	—	2	2	no	—
253	#97	—	2	2	no	—
254	#97	C₂×C₄×C₂₉	1	2	yes	—
255	#97	C₂×C₄×C₂₉	1	4	yes	—
256	#97	C₂×C₄×C₂₉	1	2	yes	—
257	C₄×C₈	—	2	2	no	—
258	C₄×C₈	C₂×C₄×C₂₉	1	2	yes	—
259	C₄×C₈	C₂×C₄×C₂₉	1	2	yes	—
260	C₄×C₈	C₂³×C₂₉	1	4	yes	—
261	C₂₉	#17797	1	1	yes	characteristic, direct product factor, Sylow
262	C₂⁴	C₄⋊C₄×C₂₉	1	1	yes	characteristic
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	—	4	2	no	—
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	C₄⋊C₄×C₂₉	1	1	yes	characteristic
273	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
274	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
275	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
276	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
277	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
279	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
281	C₂²×C₄	C₂×Q₈×C₂₉	1	1	yes	characteristic
282	C₂²×C₄	C₂×Q₈×C₂₉	1	1	yes	characteristic
283	C₂²×C₄	C₂×Q₈×C₂₉	1	1	yes	characteristic
284	M₁₆	—	2	4	no	—
285	M₁₆	—	2	8	no	—
286	M₁₆	—	4	4	no	—
287	M₁₆	M₁₆×C₂₉	1	8	yes	complemented
288	C₂×C₈	—	2	8	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	—	4	4	no	—
292	C₂×C₈	C₂²×C₄×C₂₉	1	4	yes	—
293	C₂×C₈	C₂²×C₄×C₂₉	1	4	yes	—
294	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
295	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
296	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
297	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
298	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
299	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
300	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
301	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
302	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
303	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
304	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
305	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
306	C₄²	C₂×Q₈×C₂₉	1	1	yes	characteristic
307	C₄²	C₂×Q₈×C₂₉	1	1	yes	characteristic
308	C₄²	C₂×Q₈×C₂₉	1	1	yes	characteristic
309	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
310	C₂³	—	2	2	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	4	1	no	—
313	C₂³	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
314	C₂³	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
315	C₂³	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
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	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
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	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
337	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
338	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
339	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
340	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
341	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
342	C₂×C₄	C₂×M₁₆×C₂₉	1	4	yes	—
343	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
344	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
345	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
346	C₈	—	2	4	no	—
347	C₈	—	4	4	no	—
348	C₈	—	4	4	no	—
349	C₈	C₂×M₁₆×C₂₉	1	8	yes	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	4	4	no	—
358	C₂²	C₂₉×#423	1	2	yes	—
359	C₂²	C₂₉×#430	1	2	yes	—
360	C₂²	C₂²×C₄⋊C₄×C₂₉	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	C₂₉×#423	1	2	yes	—
371	C₄	C₂²×M₁₆×C₂₉	1	2	yes	—
372	C₄	C₂₉×#575	1	2	yes	—
373	C₂	—	2	2	no	—
374	C₂	—	2	2	no	—
375	C₂	—	4	1	no	—
376	C₂	C₂×C₂₉×#423	1	1	yes	characteristic
377	C₂	C₂₉×#2911	1	1	yes	characteristic
378	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×#1569	C₂	semidirect
5. C₂₉×#1568	C₂	semidirect
6. C₂₉×#1565	C₂	semidirect
30. C₂₉×#335	C₂²	semidirect
31. C₂₉×#334	C₂²	semidirect
97. M₁₆×C₂₉	M₁₆	semidirect
120. #17797	C₂₉	direct (N × H)
164. #1569	C₂×C₂₉	semidirect
165. #1568	C₂×C₂₉	semidirect
166. #1565	C₂×C₂₉	semidirect
213. #335	C₂²×C₂₉	semidirect
214. #334	C₂²×C₂₉	semidirect
261. C₂₉	#17797	direct (N × H)
287. M₁₆	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×#2920	2
C₂×C₂₉×#432	2
C₂×C₄×M₁₆×C₂₉	2
C₂₉×#1569	2
C₂₉×#1568	2
C₂₉×#1565	2
#17797	29

Subgroups — C29×#17797 #20312697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#17797 #20312697