Subgroups — C₂₉×#17799 #20312699

Order 7424.

666 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#2989	C₂	1	2	yes	maximal
2	C₄×C₂₉×#131	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#1569	C₂	1	4	yes	maximal, complemented
4	C₂₉×#1568	C₂	1	2	yes	maximal, complemented
5	C₂₉×#1567	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1565	C₂	1	2	yes	maximal, complemented
7	C₂₉×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₉×#335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₉×#131	C₄	1	1	yes	characteristic
10	C₂×C₂₉×#131	C₄	1	1	yes	characteristic
11	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
12	C₂₉×#446	—	2	2	no	—
13	C₂₉×#436	—	2	2	no	—
14	C₂₉×#435	—	2	4	no	—
15	C₂₉×#432	C₂²	1	4	yes	—
16	C₂₉×#431	C₂²	1	2	yes	—
17	C₂₉×#423	C₂²	1	4	yes	—
18	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂₉×#405	C₄	1	2	yes	—
20	C₂₉×#405	C₄	1	2	yes	—
21	C₂₉×#405	C₄	1	1	yes	characteristic
22	C₂₉×#405	C₄	1	1	yes	characteristic
23	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
24	C₄×M₁₆×C₂₉	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₂₉	C₂²	1	2	yes	—
27	C₂₉×#335	C₂²	1	2	yes	—
28	C₂₉×#335	C₂²	1	2	yes	—
29	C₂₉×#335	C₂²	1	1	yes	characteristic
30	C₂₉×#335	C₂²	1	1	yes	characteristic
31	C₂₉×#335	C₂²	1	4	yes	—
32	C₂₉×#334	C₂²	1	2	yes	—
33	C₂₉×#334	C₂²	1	4	yes	—
34	C₂×#41×C₂₉	C₂×C₄	1	1	yes	characteristic
35	C₂₉×#131	—	2	4	no	—
36	C₂₉×#131	—	2	4	no	—
37	C₂×M₁₆×C₂₉	—	2	4	no	—
38	C₂×M₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
39	C₂×M₁₆×C₂₉	C₂×C₄	1	2	yes	—
40	C₂×M₁₆×C₂₉	C₂×C₄	1	2	yes	—
41	C₂×M₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₈×C₂₉	—	2	2	no	—
43	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₂₉	C₂×C₄	1	2	yes	—
45	C₂²×C₈×C₂₉	C₂×C₄	1	2	yes	—
46	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
47	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
48	C₄×Q₈×C₂₉	Q₈	1	1	yes	characteristic
49	C₄×D₄×C₂₉	D₄	1	2	yes	—
50	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
51	C₄×D₄×C₂₉	Q₈	1	2	yes	—
52	C₄×D₄×C₂₉	Q₈	1	1	yes	characteristic
53	C₂₉×#117	C₂×C₄	1	2	yes	—
54	C₂₉×#117	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
57	C₂₉×C₄⋊C₈	—	2	4	no	—
58	C₂₉×C₄⋊C₈	—	2	2	no	—
59	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
60	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
61	C₂₉×C₄⋊C₈	C₂³	1	4	yes	—
62	C₂₉×C₂²⋊C₈	—	2	2	no	—
63	C₂₉×C₂²⋊C₈	—	2	4	no	—
64	C₂₉×#97	—	2	4	no	—
65	C₂₉×#97	C₂×C₄	1	2	yes	—
66	C₂₉×#97	C₂×C₄	1	2	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	1	yes	characteristic
71	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
72	C₄×C₈×C₂₉	C₂×C₄	1	2	yes	—
73	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₂₉	C₂³	1	2	yes	—
75	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
76	#41×C₂₉	—	2	2	no	—
77	#41×C₂₉	—	2	2	no	—
78	C₂×Q₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
79	C₂×D₄×C₂₉	C₄⋊C₄	1	2	yes	—
80	C₂×D₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₂₉	C₂×Q₈	1	2	yes	—
86	C₂²×C₄×C₂₉	C₂×Q₈	1	1	yes	characteristic
87	M₁₆×C₂₉	—	2	2	no	—
88	M₁₆×C₂₉	—	2	4	no	—
89	M₁₆×C₂₉	—	2	4	no	—
90	M₁₆×C₂₉	—	8	4	no	—
91	M₁₆×C₂₉	M₁₆	1	4	yes	complemented
92	C₂×C₈×C₂₉	—	2	2	no	—
93	C₂×C₈×C₂₉	—	2	4	no	—
94	C₂×C₈×C₂₉	—	2	4	no	—
95	C₂×C₈×C₂₉	—	2	4	no	—
96	C₂×C₈×C₂₉	—	2	2	no	—
97	C₂×C₈×C₂₉	—	2	2	no	—
98	C₂×C₈×C₂₉	—	8	2	no	—
99	C₂×C₈×C₂₉	M₁₆	1	4	yes	complemented
100	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
103	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
106	C₄⋊C₄×C₂₉	C₄⋊C₄	1	2	yes	—
107	C₄⋊C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
108	C₄⋊C₄×C₂₉	C₄⋊C₄	1	2	yes	—
109	C₄⋊C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
110	C₂²⋊C₄×C₂₉	C₄⋊C₄	1	2	yes	—
111	C₂²⋊C₄×C₂₉	C₄⋊C₄	1	2	yes	—
112	C₂²⋊C₄×C₂₉	C₄⋊C₄	1	2	yes	—
113	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
115	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₂₉	C₂×D₄	1	2	yes	—
117	C₄²×C₂₉	C₂×Q₈	1	2	yes	—
118	C₄²×C₂₉	C₂×Q₈	1	1	yes	characteristic
119	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
120	#17799	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂³×C₂₉	C₂×C₄⋊C₄	1	2	yes	—
122	C₂³×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
123	Q₈×C₂₉	—	2	2	no	—
124	D₄×C₂₉	—	2	4	no	—
125	D₄×C₂₉	—	2	2	no	—
126	C₂×C₄×C₂₉	—	2	2	no	—
127	C₂×C₄×C₂₉	—	2	2	no	—
128	C₂×C₄×C₂₉	—	2	1	no	—
129	C₂×C₄×C₂₉	—	2	2	no	—
130	C₂×C₄×C₂₉	—	2	1	no	—
131	C₂×C₄×C₂₉	—	2	2	no	—
132	C₂×C₄×C₂₉	—	4	1	no	—
133	C₂×C₄×C₂₉	—	4	2	no	—
134	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	2	yes	—
136	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	2	yes	—
138	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	2	yes	—
139	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₂₉	C₂×M₁₆	1	2	yes	—
141	C₂×C₄×C₂₉	C₂×M₁₆	1	2	yes	—
142	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
143	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
144	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
145	C₈×C₂₉	—	2	1	no	—
146	C₈×C₂₉	—	2	1	no	—
147	C₈×C₂₉	—	2	2	no	—
148	C₈×C₂₉	—	4	4	no	—
149	C₈×C₂₉	—	4	2	no	—
150	C₈×C₂₉	—	4	2	no	—
151	C₈×C₂₉	C₂×M₁₆	1	2	yes	—
152	C₈×C₂₉	C₂×M₁₆	1	4	yes	—
153	C₈×C₂₉	C₂×M₁₆	1	2	yes	—
154	#2989	C₂×C₂₉	1	2	yes	—
155	C₄×#131	C₂×C₂₉	1	1	yes	characteristic
156	#1569	C₂×C₂₉	1	4	yes	complemented
157	#1568	C₂×C₂₉	1	2	yes	complemented
158	#1567	C₂×C₂₉	1	2	yes	complemented
159	#1565	C₂×C₂₉	1	2	yes	complemented
160	#1564	C₂×C₂₉	1	1	yes	characteristic, complemented
161	C₂×#335	C₂×C₂₉	1	1	yes	characteristic, complemented
162	C₂²×C₂₉	—	2	1	no	—
163	C₂²×C₂₉	—	2	1	no	—
164	C₂²×C₂₉	—	2	2	no	—
165	C₂²×C₂₉	—	2	2	no	—
166	C₂²×C₂₉	—	2	2	no	—
167	C₂²×C₂₉	#423	1	2	yes	—
168	C₂²×C₂₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
169	C₄×C₂₉	—	2	2	no	—
170	C₄×C₂₉	—	2	1	no	—
171	C₄×C₂₉	—	2	2	no	—
172	C₄×C₂₉	—	2	1	no	—
173	C₄×C₂₉	—	2	1	no	—
174	C₄×C₂₉	—	2	2	no	—
175	C₄×C₂₉	#423	1	2	yes	—
176	C₄×C₂₉	C₂²×M₁₆	1	1	yes	characteristic
177	C₄×C₂₉	C₂²×M₁₆	1	1	yes	characteristic
178	C₄×C₂₉	#576	1	1	yes	characteristic
179	C₄×C₂₉	#578	1	1	yes	characteristic
180	C₂×#131	C₄×C₂₉	1	1	yes	characteristic
181	C₂×#131	C₄×C₂₉	1	1	yes	characteristic
182	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
183	#446	—	2	2	no	—
184	#436	—	2	2	no	—
185	#435	—	2	4	no	—
186	#432	C₂²×C₂₉	1	4	yes	—
187	#431	C₂²×C₂₉	1	2	yes	—
188	#423	C₂²×C₂₉	1	4	yes	—
189	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
190	#405	C₄×C₂₉	1	1	yes	characteristic
191	#405	C₄×C₂₉	1	2	yes	—
192	#405	C₄×C₂₉	1	2	yes	—
193	#405	C₄×C₂₉	1	1	yes	characteristic
194	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
195	C₄×M₁₆	C₂²×C₂₉	1	2	yes	—
196	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
197	C₂×C₄×C₈	C₂²×C₂₉	1	2	yes	—
198	#335	C₂²×C₂₉	1	2	yes	—
199	#335	C₂²×C₂₉	1	2	yes	—
200	#335	C₂²×C₂₉	1	1	yes	characteristic
201	#335	C₂²×C₂₉	1	1	yes	characteristic
202	#335	C₂²×C₂₉	1	4	yes	—
203	#334	C₂²×C₂₉	1	2	yes	—
204	#334	C₂²×C₂₉	1	4	yes	—
205	C₂×C₂₉	—	2	2	no	—
206	C₂×C₂₉	—	4	2	no	—
207	C₂×C₂₉	C₂×#423	1	1	yes	characteristic
208	C₂×C₂₉	#2913	1	1	yes	characteristic
209	C₂×C₂₉	#2916	1	1	yes	characteristic
210	C₂×#41	C₂×C₄×C₂₉	1	1	yes	characteristic
211	#131	—	2	4	no	—
212	#131	—	2	4	no	—
213	C₂×M₁₆	—	2	4	no	—
214	C₂×M₁₆	C₂×C₄×C₂₉	1	1	yes	characteristic
215	C₂×M₁₆	C₂×C₄×C₂₉	1	2	yes	—
216	C₂×M₁₆	C₂×C₄×C₂₉	1	2	yes	—
217	C₂×M₁₆	C₂×C₄×C₂₉	1	1	yes	characteristic
218	C₂²×C₈	—	2	2	no	—
219	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
220	C₂²×C₈	C₂×C₄×C₂₉	1	2	yes	—
221	C₂²×C₈	C₂×C₄×C₂₉	1	2	yes	—
222	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
223	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
224	C₄×Q₈	Q₈×C₂₉	1	1	yes	characteristic
225	C₄×D₄	D₄×C₂₉	1	2	yes	—
226	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
227	C₄×D₄	Q₈×C₂₉	1	2	yes	—
228	C₄×D₄	Q₈×C₂₉	1	1	yes	characteristic
229	#117	C₂×C₄×C₂₉	1	2	yes	—
230	#117	C₂×C₄×C₂₉	1	1	yes	characteristic
231	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
232	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
233	C₄⋊C₈	—	2	2	no	—
234	C₄⋊C₈	—	2	4	no	—
235	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
236	C₄⋊C₈	C₂³×C₂₉	1	4	yes	—
237	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
238	C₂²⋊C₈	—	2	2	no	—
239	C₂²⋊C₈	—	2	4	no	—
240	#97	—	2	4	no	—
241	#97	C₂×C₄×C₂₉	1	2	yes	—
242	#97	C₂×C₄×C₂₉	1	2	yes	—
243	#97	C₂×C₄×C₂₉	1	2	yes	—
244	C₄×C₈	—	2	2	no	—
245	C₄×C₈	C₂×C₄×C₂₉	1	2	yes	—
246	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
247	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
248	C₄×C₈	C₂×C₄×C₂₉	1	2	yes	—
249	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
250	C₄×C₈	C₂³×C₂₉	1	2	yes	—
251	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
252	C₂₉	#17799	1	1	yes	characteristic, direct product factor, Sylow
253	#41	—	2	2	no	—
254	#41	—	2	2	no	—
255	C₂×Q₈	C₄⋊C₄×C₂₉	1	1	yes	characteristic
256	C₂×D₄	C₄⋊C₄×C₂₉	1	2	yes	—
257	C₂×D₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
258	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
259	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
260	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
261	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
262	C₂²×C₄	C₂×Q₈×C₂₉	1	2	yes	—
263	C₂²×C₄	C₂×Q₈×C₂₉	1	1	yes	characteristic
264	M₁₆	—	2	2	no	—
265	M₁₆	—	2	4	no	—
266	M₁₆	—	2	4	no	—
267	M₁₆	—	8	4	no	—
268	M₁₆	M₁₆×C₂₉	1	4	yes	complemented
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	4	no	—
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	—	8	2	no	—
276	C₂×C₈	M₁₆×C₂₉	1	4	yes	complemented
277	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
278	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
279	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
280	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
281	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
282	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
283	C₄⋊C₄	C₄⋊C₄×C₂₉	1	2	yes	—
284	C₄⋊C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
285	C₄⋊C₄	C₄⋊C₄×C₂₉	1	2	yes	—
286	C₄⋊C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
287	C₂²⋊C₄	C₄⋊C₄×C₂₉	1	2	yes	—
288	C₂²⋊C₄	C₄⋊C₄×C₂₉	1	2	yes	—
289	C₂²⋊C₄	C₄⋊C₄×C₂₉	1	2	yes	—
290	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
291	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
292	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
293	C₄²	C₂×D₄×C₂₉	1	2	yes	—
294	C₄²	C₂×Q₈×C₂₉	1	2	yes	—
295	C₄²	C₂×Q₈×C₂₉	1	1	yes	characteristic
296	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
297	C₂³	C₂×C₄⋊C₄×C₂₉	1	2	yes	—
298	C₂³	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
299	Q₈	—	2	2	no	—
300	D₄	—	2	4	no	—
301	D₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	4	1	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
311	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	2	yes	—
312	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
313	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	2	yes	—
314	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	2	yes	—
315	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
316	C₂×C₄	C₂×M₁₆×C₂₉	1	2	yes	—
317	C₂×C₄	C₂×M₁₆×C₂₉	1	2	yes	—
318	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
319	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
320	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
321	C₈	—	2	1	no	—
322	C₈	—	2	1	no	—
323	C₈	—	2	2	no	—
324	C₈	—	4	4	no	—
325	C₈	—	4	2	no	—
326	C₈	—	4	2	no	—
327	C₈	C₂×M₁₆×C₂₉	1	2	yes	—
328	C₈	C₂×M₁₆×C₂₉	1	4	yes	—
329	C₈	C₂×M₁₆×C₂₉	1	2	yes	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	1	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	2	no	—
335	C₂²	C₂₉×#423	1	2	yes	—
336	C₂²	C₂²×C₄⋊C₄×C₂₉	1	1	yes	characteristic
337	C₄	—	2	2	no	—
338	C₄	—	2	1	no	—
339	C₄	—	2	2	no	—
340	C₄	—	2	1	no	—
341	C₄	—	2	1	no	—
342	C₄	—	2	2	no	—
343	C₄	C₂₉×#423	1	2	yes	—
344	C₄	C₂²×M₁₆×C₂₉	1	1	yes	characteristic
345	C₄	C₂²×M₁₆×C₂₉	1	1	yes	characteristic
346	C₄	C₂₉×#576	1	1	yes	characteristic
347	C₄	C₂₉×#578	1	1	yes	characteristic
348	C₂	—	2	2	no	—
349	C₂	—	4	2	no	—
350	C₂	C₂×C₂₉×#423	1	1	yes	characteristic
351	C₂	C₂₉×#2913	1	1	yes	characteristic
352	C₂	C₂₉×#2916	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	C₂×#41×C₂₉	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₄×#41×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₉×#1569	C₂	semidirect
4. C₂₉×#1568	C₂	semidirect
5. C₂₉×#1567	C₂	semidirect
6. C₂₉×#1565	C₂	semidirect
7. C₂₉×#1564	C₂	semidirect
8. C₂×C₂₉×#335	C₂	semidirect
91. M₁₆×C₂₉	M₁₆	semidirect
99. C₂×C₈×C₂₉	M₁₆	semidirect
120. #17799	C₂₉	direct (N × H)
156. #1569	C₂×C₂₉	semidirect
157. #1568	C₂×C₂₉	semidirect
158. #1567	C₂×C₂₉	semidirect
159. #1565	C₂×C₂₉	semidirect
160. #1564	C₂×C₂₉	semidirect
161. C₂×#335	C₂×C₂₉	semidirect
252. C₂₉	#17799	direct (N × H)
268. M₁₆	M₁₆×C₂₉	semidirect
276. C₂×C₈	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×#2989	2
C₄×C₂₉×#131	2
C₂₉×#1569	2
C₂₉×#1568	2
C₂₉×#1567	2
C₂₉×#1565	2
C₂₉×#1564	2
C₂×C₂₉×#335	2
#17799	29

Subgroups — C29×#17799 #20312699

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#17799 #20312699