Subgroups — C₂₉×#22052 #20316952

Order 7424.

1080 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#450	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2323	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#2309	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1973	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1968	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1936	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1934	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1926	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1925	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1786	C₂	1	1	yes	maximal, characteristic
15	C₂₉×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₂₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
23	C₂₉×#450	C₄	1	8	yes	complemented
24	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
34	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
38	C₂₉×#391	C₂²	1	1	yes	characteristic, complemented
39	C₂₉×#390	—	2	1	no	—
40	C₂₉×#390	—	2	1	no	—
41	C₂₉×#390	C₂²	1	1	yes	characteristic
42	C₂₉×#390	C₂²	1	1	yes	characteristic
43	C₂₉×#390	C₂²	1	1	yes	characteristic
44	C₂₉×#390	C₂²	1	1	yes	characteristic
45	C₂₉×#389	—	2	1	no	—
46	C₂₉×#389	C₂²	1	1	yes	characteristic, complemented
47	C₂₉×#388	—	2	1	no	—
48	C₂₉×#388	—	2	1	no	—
49	C₂₉×#387	—	2	1	no	—
50	C₂₉×#380	C₂²	1	1	yes	characteristic
51	C₂₉×#379	—	2	1	no	—
52	C₂₉×#379	—	2	1	no	—
53	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
54	C₂₉×#340	C₂²	1	1	yes	characteristic, complemented
55	C₂₉×#340	C₂²	1	1	yes	characteristic, complemented
56	C₂₉×#340	C₂²	1	1	yes	characteristic, complemented
57	C₂₉×#340	C₂²	1	1	yes	characteristic, complemented
58	C₂₉×#336	C₂²	1	1	yes	characteristic, complemented
59	C₂₉×#336	C₂²	1	1	yes	characteristic, complemented
60	C₂⁵×C₂₉	—	2	1	no	—
61	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₂₉	—	2	1	no	—
63	C₂²×D₄×C₂₉	—	2	2	no	—
64	C₂²×D₄×C₂₉	—	4	1	no	—
65	C₂²×D₄×C₂₉	—	4	1	no	—
66	C₂²×D₄×C₂₉	—	4	1	no	—
67	C₂²×D₄×C₂₉	—	4	1	no	—
68	C₂²×D₄×C₂₉	C₂×C₄	1	4	yes	—
69	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
72	C₂×SD₁₆×C₂₉	—	4	1	no	—
73	C₂×SD₁₆×C₂₉	—	4	1	no	—
74	C₂×SD₁₆×C₂₉	—	4	1	no	—
75	C₂×SD₁₆×C₂₉	—	4	1	no	—
76	C₂×SD₁₆×C₂₉	C₂×C₄	1	4	yes	—
77	C₂×SD₁₆×C₂₉	C₂×C₄	1	4	yes	—
78	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
82	C₂₉×C₂²⋊Q₈	—	2	2	no	—
83	C₂₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
84	C₄×Q₈×C₂₉	—	4	1	no	—
85	C₄×Q₈×C₂₉	—	4	1	no	—
86	C₂₉×#117	—	4	1	no	—
87	C₂₉×#117	—	4	1	no	—
88	C₂₉×#117	—	4	1	no	—
89	C₂₉×#117	—	4	1	no	—
90	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
112	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
113	C₂×C₄²×C₂₉	—	2	1	no	—
114	C₂×C₄²×C₂₉	—	2	1	no	—
115	C₂×C₄²×C₂₉	—	2	1	no	—
116	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
118	C₂₉×#107	—	4	1	no	—
119	C₂₉×#106	—	4	1	no	—
120	C₂₉×#103	—	4	1	no	—
121	C₂₉×#103	—	4	1	no	—
122	C₂₉×#102	—	4	1	no	—
123	C₂₉×#102	—	4	1	no	—
124	C₂₉×#102	—	4	1	no	—
125	C₂₉×#102	—	4	1	no	—
126	C₂₉×#102	C₂×C₄	1	4	yes	—
127	C₂₉×#102	C₂×C₄	1	4	yes	—
128	C₂₉×C₂²⋊C₈	—	2	2	no	—
129	C₂₉×C₂²⋊C₈	C₂×C₄	1	4	yes	—
130	C₂₉×#97	—	4	1	no	—
131	C₄×C₈×C₂₉	—	4	1	no	—
132	C₂₉×#95	—	2	1	no	—
133	C₂₉×#95	—	2	1	no	—
134	C₂₉×#95	—	2	1	no	—
135	C₂₉×#95	—	2	1	no	—
136	C₂₉×#95	—	2	1	no	—
137	C₂⁴×C₂₉	—	2	1	no	—
138	C₂⁴×C₂₉	—	2	1	no	—
139	C₂⁴×C₂₉	—	2	4	no	—
140	C₂⁴×C₂₉	—	4	2	no	—
141	C₂⁴×C₂₉	—	4	2	no	—
142	C₂⁴×C₂₉	—	8	1	no	—
143	C₂⁴×C₂₉	—	8	1	no	—
144	C₂⁴×C₂₉	—	8	1	no	—
145	C₂⁴×C₂₉	—	8	1	no	—
146	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
147	C₂×Q₈×C₂₉	—	2	1	no	—
148	C₂×Q₈×C₂₉	—	2	1	no	—
149	C₂×Q₈×C₂₉	—	2	1	no	—
150	C₂×Q₈×C₂₉	—	2	1	no	—
151	C₂×Q₈×C₂₉	—	2	1	no	—
152	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
153	C₂×D₄×C₂₉	—	2	4	no	—
154	C₂×D₄×C₂₉	—	2	1	no	—
155	C₂×D₄×C₂₉	—	2	1	no	—
156	C₂×D₄×C₂₉	—	2	1	no	—
157	C₂×D₄×C₂₉	—	2	1	no	—
158	C₂×D₄×C₂₉	—	2	1	no	—
159	C₂×D₄×C₂₉	—	2	1	no	—
160	C₂×D₄×C₂₉	—	2	1	no	—
161	C₂×D₄×C₂₉	—	2	1	no	—
162	C₂×D₄×C₂₉	—	2	1	no	—
163	C₂×D₄×C₂₉	—	2	1	no	—
164	C₂×D₄×C₂₉	—	4	4	no	—
165	C₂×D₄×C₂₉	—	4	4	no	—
166	C₂×D₄×C₂₉	—	4	2	no	—
167	C₂×D₄×C₂₉	—	4	2	no	—
168	C₂×D₄×C₂₉	—	4	4	no	—
169	C₂×D₄×C₂₉	—	4	4	no	—
170	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
171	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
172	C₂²×C₄×C₂₉	—	2	1	no	—
173	C₂²×C₄×C₂₉	—	2	1	no	—
174	C₂²×C₄×C₂₉	—	2	1	no	—
175	C₂²×C₄×C₂₉	—	2	1	no	—
176	C₂²×C₄×C₂₉	—	2	1	no	—
177	C₂²×C₄×C₂₉	—	2	1	no	—
178	C₂²×C₄×C₂₉	—	2	1	no	—
179	C₂²×C₄×C₂₉	—	2	1	no	—
180	C₂²×C₄×C₂₉	—	2	1	no	—
181	C₂²×C₄×C₂₉	—	2	1	no	—
182	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
183	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₂₉	#41	1	2	yes	—
189	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
190	SD₁₆×C₂₉	—	4	4	no	—
191	SD₁₆×C₂₉	—	4	4	no	—
192	C₂×C₈×C₂₉	—	2	1	no	—
193	C₂×C₈×C₂₉	—	2	1	no	—
194	C₂×C₈×C₂₉	—	2	1	no	—
195	C₂×C₈×C₂₉	—	2	1	no	—
196	C₂×C₈×C₂₉	—	2	1	no	—
197	C₂×C₈×C₂₉	—	2	1	no	—
198	C₂×C₈×C₂₉	—	2	1	no	—
199	C₂×C₈×C₂₉	—	2	1	no	—
200	C₂×C₈×C₂₉	—	2	1	no	—
201	C₂×C₈×C₂₉	—	2	1	no	—
202	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
203	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
204	C₄⋊C₄×C₂₉	—	2	4	no	—
205	C₄⋊C₄×C₂₉	—	2	1	no	—
206	C₄⋊C₄×C₂₉	—	2	1	no	—
207	C₄⋊C₄×C₂₉	—	2	1	no	—
208	C₄⋊C₄×C₂₉	—	2	1	no	—
209	C₄⋊C₄×C₂₉	—	2	1	no	—
210	C₄⋊C₄×C₂₉	—	2	1	no	—
211	C₄⋊C₄×C₂₉	—	2	1	no	—
212	C₄⋊C₄×C₂₉	—	2	1	no	—
213	C₄⋊C₄×C₂₉	—	2	1	no	—
214	C₄⋊C₄×C₂₉	—	4	1	no	—
215	C₄⋊C₄×C₂₉	—	4	1	no	—
216	C₄⋊C₄×C₂₉	—	4	2	no	—
217	C₄⋊C₄×C₂₉	—	8	1	no	—
218	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
219	C₂²⋊C₄×C₂₉	—	2	4	no	—
220	C₂²⋊C₄×C₂₉	—	4	1	no	—
221	C₂²⋊C₄×C₂₉	—	4	1	no	—
222	C₂²⋊C₄×C₂₉	—	4	2	no	—
223	C₂²⋊C₄×C₂₉	—	8	1	no	—
224	C₂²⋊C₄×C₂₉	—	8	1	no	—
225	C₂²⋊C₄×C₂₉	—	8	1	no	—
226	C₂²⋊C₄×C₂₉	—	8	1	no	—
227	C₂²⋊C₄×C₂₉	—	8	1	no	—
228	C₂²⋊C₄×C₂₉	—	8	1	no	—
229	C₂²⋊C₄×C₂₉	—	8	1	no	—
230	C₂²⋊C₄×C₂₉	—	8	1	no	—
231	C₂²⋊C₄×C₂₉	—	8	1	no	—
232	C₄²×C₂₉	—	2	1	no	—
233	C₄²×C₂₉	—	2	1	no	—
234	C₄²×C₂₉	—	2	1	no	—
235	C₄²×C₂₉	—	2	1	no	—
236	C₄²×C₂₉	—	4	2	no	—
237	C₄²×C₂₉	—	4	2	no	—
238	C₄²×C₂₉	—	8	1	no	—
239	#22052	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂³×C₂₉	—	2	1	no	—
241	C₂³×C₂₉	—	2	1	no	—
242	C₂³×C₂₉	—	2	1	no	—
243	C₂³×C₂₉	—	2	1	no	—
244	C₂³×C₂₉	—	2	1	no	—
245	C₂³×C₂₉	—	2	1	no	—
246	C₂³×C₂₉	—	2	2	no	—
247	C₂³×C₂₉	—	2	2	no	—
248	C₂³×C₂₉	—	4	8	no	—
249	C₂³×C₂₉	—	4	1	no	—
250	C₂³×C₂₉	—	4	1	no	—
251	C₂³×C₂₉	—	4	1	no	—
252	C₂³×C₂₉	—	4	1	no	—
253	C₂³×C₂₉	—	4	1	no	—
254	C₂³×C₂₉	—	4	1	no	—
255	C₂³×C₂₉	—	4	1	no	—
256	C₂³×C₂₉	—	4	1	no	—
257	C₂³×C₂₉	—	4	1	no	—
258	C₂³×C₂₉	—	4	1	no	—
259	C₂³×C₂₉	—	4	1	no	—
260	C₂³×C₂₉	—	4	1	no	—
261	C₂³×C₂₉	—	8	4	no	—
262	C₂³×C₂₉	—	8	4	no	—
263	C₂³×C₂₉	—	8	4	no	—
264	C₂³×C₂₉	—	8	4	no	—
265	C₂³×C₂₉	—	8	4	no	—
266	C₂³×C₂₉	—	8	4	no	—
267	C₂³×C₂₉	C₄×D₄	1	2	yes	—
268	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
269	Q₈×C₂₉	—	2	2	no	—
270	Q₈×C₂₉	—	2	2	no	—
271	Q₈×C₂₉	—	4	1	no	—
272	Q₈×C₂₉	—	4	1	no	—
273	D₄×C₂₉	—	2	2	no	—
274	D₄×C₂₉	—	2	2	no	—
275	D₄×C₂₉	—	2	2	no	—
276	D₄×C₂₉	—	2	2	no	—
277	D₄×C₂₉	—	4	8	no	—
278	D₄×C₂₉	—	4	1	no	—
279	D₄×C₂₉	—	4	1	no	—
280	D₄×C₂₉	—	4	1	no	—
281	D₄×C₂₉	—	4	1	no	—
282	C₂×C₄×C₂₉	—	2	1	no	—
283	C₂×C₄×C₂₉	—	2	1	no	—
284	C₂×C₄×C₂₉	—	2	2	no	—
285	C₂×C₄×C₂₉	—	2	2	no	—
286	C₂×C₄×C₂₉	—	2	2	no	—
287	C₂×C₄×C₂₉	—	2	2	no	—
288	C₂×C₄×C₂₉	—	2	2	no	—
289	C₂×C₄×C₂₉	—	2	2	no	—
290	C₂×C₄×C₂₉	—	2	1	no	—
291	C₂×C₄×C₂₉	—	2	1	no	—
292	C₂×C₄×C₂₉	—	2	1	no	—
293	C₂×C₄×C₂₉	—	2	1	no	—
294	C₂×C₄×C₂₉	—	2	1	no	—
295	C₂×C₄×C₂₉	—	2	1	no	—
296	C₂×C₄×C₂₉	—	2	1	no	—
297	C₂×C₄×C₂₉	—	2	1	no	—
298	C₂×C₄×C₂₉	—	2	1	no	—
299	C₂×C₄×C₂₉	—	2	1	no	—
300	C₂×C₄×C₂₉	—	2	1	no	—
301	C₂×C₄×C₂₉	—	2	1	no	—
302	C₂×C₄×C₂₉	—	4	1	no	—
303	C₂×C₄×C₂₉	—	4	1	no	—
304	C₂×C₄×C₂₉	—	4	1	no	—
305	C₂×C₄×C₂₉	—	4	1	no	—
306	C₂×C₄×C₂₉	—	4	1	no	—
307	C₂×C₄×C₂₉	—	4	1	no	—
308	C₂×C₄×C₂₉	—	4	1	no	—
309	C₂×C₄×C₂₉	—	4	1	no	—
310	C₂×C₄×C₂₉	—	4	1	no	—
311	C₂×C₄×C₂₉	—	4	1	no	—
312	C₂×C₄×C₂₉	—	4	1	no	—
313	C₂×C₄×C₂₉	—	4	1	no	—
314	C₂×C₄×C₂₉	—	4	1	no	—
315	C₂×C₄×C₂₉	—	4	1	no	—
316	C₂×C₄×C₂₉	—	4	1	no	—
317	C₂×C₄×C₂₉	—	4	1	no	—
318	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
319	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
320	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
321	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
322	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
323	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
324	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
325	C₈×C₂₉	—	2	2	no	—
326	C₈×C₂₉	—	2	2	no	—
327	C₈×C₂₉	—	4	1	no	—
328	C₈×C₂₉	—	4	1	no	—
329	C₂×#450	C₂×C₂₉	1	1	yes	characteristic
330	#2323	C₂×C₂₉	1	1	yes	characteristic, complemented
331	#2309	C₂×C₂₉	1	1	yes	characteristic
332	#1973	C₂×C₂₉	1	1	yes	characteristic, complemented
333	#1968	C₂×C₂₉	1	1	yes	characteristic, complemented
334	#1936	C₂×C₂₉	1	1	yes	characteristic, complemented
335	#1934	C₂×C₂₉	1	1	yes	characteristic, complemented
336	#1926	C₂×C₂₉	1	1	yes	characteristic, complemented
337	#1925	C₂×C₂₉	1	1	yes	characteristic, complemented
338	#1880	C₂×C₂₉	1	1	yes	characteristic, complemented
339	#1880	C₂×C₂₉	1	1	yes	characteristic, complemented
340	#1873	C₂×C₂₉	1	1	yes	characteristic, complemented
341	#1854	C₂×C₂₉	1	1	yes	characteristic, complemented
342	#1786	C₂×C₂₉	1	1	yes	characteristic
343	#1750	C₂×C₂₉	1	1	yes	characteristic, complemented
344	C₂²×C₂₉	—	2	2	no	—
345	C₂²×C₂₉	—	2	2	no	—
346	C₂²×C₂₉	—	2	2	no	—
347	C₂²×C₂₉	—	4	1	no	—
348	C₂²×C₂₉	—	4	1	no	—
349	C₂²×C₂₉	—	4	1	no	—
350	C₂²×C₂₉	—	4	1	no	—
351	C₂²×C₂₉	—	4	2	no	—
352	C₂²×C₂₉	—	4	2	no	—
353	C₂²×C₂₉	—	4	2	no	—
354	C₂²×C₂₉	—	4	2	no	—
355	C₂²×C₂₉	—	4	2	no	—
356	C₂²×C₂₉	—	4	2	no	—
357	C₂²×C₂₉	—	8	16	no	—
358	C₂²×C₂₉	—	8	1	no	—
359	C₂²×C₂₉	—	8	1	no	—
360	C₂²×C₂₉	—	8	1	no	—
361	C₂²×C₂₉	—	8	1	no	—
362	C₂²×C₂₉	—	8	1	no	—
363	C₂²×C₂₉	—	8	1	no	—
364	C₂²×C₂₉	—	8	1	no	—
365	C₂²×C₂₉	—	8	1	no	—
366	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
367	C₂²×C₂₉	#534	1	1	yes	characteristic
368	C₂²×C₂₉	#535	1	1	yes	characteristic
369	C₂²×C₂₉	#576	1	1	yes	characteristic
370	C₂²×C₂₉	#577	1	1	yes	characteristic
371	C₂²×C₂₉	#577	1	1	yes	characteristic
372	C₂²×C₂₉	#577	1	1	yes	characteristic
373	C₄×C₂₉	—	2	2	no	—
374	C₄×C₂₉	—	4	2	no	—
375	C₄×C₂₉	—	4	1	no	—
376	C₄×C₂₉	—	4	1	no	—
377	C₄×C₂₉	—	4	1	no	—
378	C₄×C₂₉	—	4	1	no	—
379	C₄×C₂₉	—	4	2	no	—
380	C₄×C₂₉	—	8	1	no	—
381	C₄×C₂₉	—	8	1	no	—
382	C₄×C₂₉	—	8	1	no	—
383	C₄×C₂₉	—	8	1	no	—
384	C₄×C₂₉	#518	1	1	yes	characteristic
385	C₄×C₂₉	#518	1	1	yes	characteristic
386	C₄×C₂₉	#538	1	1	yes	characteristic
387	C₄×C₂₉	#538	1	1	yes	characteristic
388	C₂³×D₄	C₂²×C₂₉	1	1	yes	characteristic
389	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
390	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
391	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
392	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
393	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
394	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
395	#450	C₄×C₂₉	1	8	yes	complemented
396	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic, complemented
397	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic, complemented
398	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic, complemented
399	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic, complemented
400	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
401	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
402	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
403	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
404	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
405	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
406	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
407	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
408	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic, complemented
409	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
410	#391	C₂²×C₂₉	1	1	yes	characteristic, complemented
411	#390	—	2	1	no	—
412	#390	—	2	1	no	—
413	#390	C₂²×C₂₉	1	1	yes	characteristic
414	#390	C₂²×C₂₉	1	1	yes	characteristic
415	#390	C₂²×C₂₉	1	1	yes	characteristic
416	#390	C₂²×C₂₉	1	1	yes	characteristic
417	#389	—	2	1	no	—
418	#389	C₂²×C₂₉	1	1	yes	characteristic, complemented
419	#388	—	2	1	no	—
420	#388	—	2	1	no	—
421	#387	—	2	1	no	—
422	#380	C₂²×C₂₉	1	1	yes	characteristic
423	#379	—	2	1	no	—
424	#379	—	2	1	no	—
425	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
426	#340	C₂²×C₂₉	1	1	yes	characteristic, complemented
427	#340	C₂²×C₂₉	1	1	yes	characteristic, complemented
428	#340	C₂²×C₂₉	1	1	yes	characteristic, complemented
429	#340	C₂²×C₂₉	1	1	yes	characteristic, complemented
430	#336	C₂²×C₂₉	1	1	yes	characteristic, complemented
431	#336	C₂²×C₂₉	1	1	yes	characteristic, complemented
432	C₂×C₂₉	—	4	2	no	—
433	C₂×C₂₉	—	8	2	no	—
434	C₂×C₂₉	—	8	2	no	—
435	C₂×C₂₉	#2321	1	1	yes	characteristic
436	C₂×C₂₉	#2946	1	1	yes	characteristic
437	C₂×C₂₉	#2949	1	1	yes	characteristic
438	C₂×C₂₉	#3198	1	1	yes	characteristic
439	C₂×C₂₉	#3200	1	1	yes	characteristic
440	C₂×C₂₉	#3222	1	1	yes	characteristic
441	C₂×C₂₉	#3224	1	1	yes	characteristic
442	C₂⁵	—	2	1	no	—
443	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
444	C₂²×D₄	—	2	1	no	—
445	C₂²×D₄	—	2	2	no	—
446	C₂²×D₄	—	4	1	no	—
447	C₂²×D₄	—	4	1	no	—
448	C₂²×D₄	—	4	1	no	—
449	C₂²×D₄	—	4	1	no	—
450	C₂²×D₄	C₂×C₄×C₂₉	1	4	yes	—
451	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
452	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
454	C₂×SD₁₆	—	4	1	no	—
455	C₂×SD₁₆	—	4	1	no	—
456	C₂×SD₁₆	—	4	1	no	—
457	C₂×SD₁₆	—	4	1	no	—
458	C₂×SD₁₆	C₂×C₄×C₂₉	1	4	yes	—
459	C₂×SD₁₆	C₂×C₄×C₂₉	1	4	yes	—
460	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
461	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
462	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
463	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
464	C₂²⋊Q₈	—	2	2	no	—
465	C₂²⋊Q₈	C₂×C₄×C₂₉	1	4	yes	—
466	C₄×Q₈	—	4	1	no	—
467	C₄×Q₈	—	4	1	no	—
468	#117	—	4	1	no	—
469	#117	—	4	1	no	—
470	#117	—	4	1	no	—
471	#117	—	4	1	no	—
472	C₂×C₄⋊C₄	—	2	1	no	—
473	C₂×C₄⋊C₄	—	2	1	no	—
474	C₂×C₄⋊C₄	—	2	1	no	—
475	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
476	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
478	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
479	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
482	C₂×C₂²⋊C₄	—	2	1	no	—
483	C₂×C₂²⋊C₄	—	2	1	no	—
484	C₂×C₂²⋊C₄	—	2	1	no	—
485	C₂×C₂²⋊C₄	—	2	1	no	—
486	C₂×C₂²⋊C₄	—	2	1	no	—
487	C₂×C₂²⋊C₄	—	2	1	no	—
488	C₂×C₂²⋊C₄	—	2	1	no	—
489	C₂×C₂²⋊C₄	—	2	1	no	—
490	C₂×C₂²⋊C₄	—	2	1	no	—
491	C₂×C₂²⋊C₄	—	2	1	no	—
492	C₂×C₂²⋊C₄	—	2	1	no	—
493	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
494	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
495	C₂×C₄²	—	2	1	no	—
496	C₂×C₄²	—	2	1	no	—
497	C₂×C₄²	—	2	1	no	—
498	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
499	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
500	#107	—	4	1	no	—
501	#106	—	4	1	no	—
502	#103	—	4	1	no	—
503	#103	—	4	1	no	—
504	#102	—	4	1	no	—
505	#102	—	4	1	no	—
506	#102	—	4	1	no	—
507	#102	—	4	1	no	—
508	#102	C₂×C₄×C₂₉	1	4	yes	—
509	#102	C₂×C₄×C₂₉	1	4	yes	—
510	C₂²⋊C₈	—	2	2	no	—
511	C₂²⋊C₈	C₂×C₄×C₂₉	1	4	yes	—
512	#97	—	4	1	no	—
513	C₄×C₈	—	4	1	no	—
514	#95	—	2	1	no	—
515	#95	—	2	1	no	—
516	#95	—	2	1	no	—
517	#95	—	2	1	no	—
518	#95	—	2	1	no	—
519	C₂₉	#22052	1	1	yes	characteristic, direct product factor, Sylow
520	C₂⁴	—	2	1	no	—
521	C₂⁴	—	2	1	no	—
522	C₂⁴	—	2	4	no	—
523	C₂⁴	—	4	2	no	—
524	C₂⁴	—	4	2	no	—
525	C₂⁴	—	8	1	no	—
526	C₂⁴	—	8	1	no	—
527	C₂⁴	—	8	1	no	—
528	C₂⁴	—	8	1	no	—
529	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	—	2	1	no	—
534	C₂×Q₈	—	2	1	no	—
535	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	4	4	no	—
548	C₂×D₄	—	4	4	no	—
549	C₂×D₄	—	4	2	no	—
550	C₂×D₄	—	4	2	no	—
551	C₂×D₄	—	4	4	no	—
552	C₂×D₄	—	4	4	no	—
553	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
554	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
566	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
567	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
568	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
569	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
570	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
571	C₂²×C₄	#41×C₂₉	1	2	yes	—
572	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
573	SD₁₆	—	4	4	no	—
574	SD₁₆	—	4	4	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
586	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	4	1	no	—
598	C₄⋊C₄	—	4	1	no	—
599	C₄⋊C₄	—	4	2	no	—
600	C₄⋊C₄	—	8	1	no	—
601	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	4	1	no	—
604	C₂²⋊C₄	—	4	1	no	—
605	C₂²⋊C₄	—	4	2	no	—
606	C₂²⋊C₄	—	8	1	no	—
607	C₂²⋊C₄	—	8	1	no	—
608	C₂²⋊C₄	—	8	1	no	—
609	C₂²⋊C₄	—	8	1	no	—
610	C₂²⋊C₄	—	8	1	no	—
611	C₂²⋊C₄	—	8	1	no	—
612	C₂²⋊C₄	—	8	1	no	—
613	C₂²⋊C₄	—	8	1	no	—
614	C₂²⋊C₄	—	8	1	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	2	1	no	—
617	C₄²	—	2	1	no	—
618	C₄²	—	2	1	no	—
619	C₄²	—	4	2	no	—
620	C₄²	—	4	2	no	—
621	C₄²	—	8	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	4	8	no	—
631	C₂³	—	4	1	no	—
632	C₂³	—	4	1	no	—
633	C₂³	—	4	1	no	—
634	C₂³	—	4	1	no	—
635	C₂³	—	4	1	no	—
636	C₂³	—	4	1	no	—
637	C₂³	—	4	1	no	—
638	C₂³	—	4	1	no	—
639	C₂³	—	4	1	no	—
640	C₂³	—	4	1	no	—
641	C₂³	—	4	1	no	—
642	C₂³	—	4	1	no	—
643	C₂³	—	8	4	no	—
644	C₂³	—	8	4	no	—
645	C₂³	—	8	4	no	—
646	C₂³	—	8	4	no	—
647	C₂³	—	8	4	no	—
648	C₂³	—	8	4	no	—
649	C₂³	C₄×D₄×C₂₉	1	2	yes	—
650	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
651	Q₈	—	2	2	no	—
652	Q₈	—	2	2	no	—
653	Q₈	—	4	1	no	—
654	Q₈	—	4	1	no	—
655	D₄	—	2	2	no	—
656	D₄	—	2	2	no	—
657	D₄	—	2	2	no	—
658	D₄	—	2	2	no	—
659	D₄	—	4	8	no	—
660	D₄	—	4	1	no	—
661	D₄	—	4	1	no	—
662	D₄	—	4	1	no	—
663	D₄	—	4	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
701	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
702	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
703	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
704	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
705	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
706	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
707	C₈	—	2	2	no	—
708	C₈	—	2	2	no	—
709	C₈	—	4	1	no	—
710	C₈	—	4	1	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	4	1	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	8	16	no	—
725	C₂²	—	8	1	no	—
726	C₂²	—	8	1	no	—
727	C₂²	—	8	1	no	—
728	C₂²	—	8	1	no	—
729	C₂²	—	8	1	no	—
730	C₂²	—	8	1	no	—
731	C₂²	—	8	1	no	—
732	C₂²	—	8	1	no	—
733	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
734	C₂²	C₂₉×#534	1	1	yes	characteristic
735	C₂²	C₂₉×#535	1	1	yes	characteristic
736	C₂²	C₂₉×#576	1	1	yes	characteristic
737	C₂²	C₂₉×#577	1	1	yes	characteristic
738	C₂²	C₂₉×#577	1	1	yes	characteristic
739	C₂²	C₂₉×#577	1	1	yes	characteristic
740	C₄	—	2	2	no	—
741	C₄	—	4	1	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	1	no	—
744	C₄	—	4	1	no	—
745	C₄	—	4	2	no	—
746	C₄	—	4	2	no	—
747	C₄	—	8	1	no	—
748	C₄	—	8	1	no	—
749	C₄	—	8	1	no	—
750	C₄	—	8	1	no	—
751	C₄	C₂₉×#518	1	1	yes	characteristic
752	C₄	C₂₉×#518	1	1	yes	characteristic
753	C₄	C₂₉×#538	1	1	yes	characteristic
754	C₄	C₂₉×#538	1	1	yes	characteristic
755	C₂	—	4	2	no	—
756	C₂	—	8	2	no	—
757	C₂	—	8	2	no	—
758	C₂	C₂₉×#2321	1	1	yes	characteristic
759	C₂	C₂₉×#2946	1	1	yes	characteristic
760	C₂	C₂₉×#2949	1	1	yes	characteristic
761	C₂	C₂₉×#3198	1	1	yes	characteristic
762	C₂	C₂₉×#3200	1	1	yes	characteristic
763	C₂	C₂₉×#3222	1	1	yes	characteristic
764	C₂	C₂₉×#3224	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂³×D₄×C₂₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₂₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#2323	C₂	semidirect
4. C₂₉×#1973	C₂	semidirect
5. C₂₉×#1968	C₂	semidirect
6. C₂₉×#1936	C₂	semidirect
7. C₂₉×#1934	C₂	semidirect
8. C₂₉×#1926	C₂	semidirect
9. C₂₉×#1925	C₂	semidirect
10. C₂₉×#1880	C₂	semidirect
11. C₂₉×#1880	C₂	semidirect
12. C₂₉×#1873	C₂	semidirect
13. C₂₉×#1854	C₂	semidirect
15. C₂₉×#1750	C₂	semidirect
20. C₂×C₄×Q₈×C₂₉	C₂²	semidirect
23. C₂₉×#450	C₄	semidirect
24. C₂×C₂₉×#107	C₂²	semidirect
25. C₂×C₂₉×#106	C₂²	semidirect
26. C₂×C₂₉×#103	C₂²	semidirect
27. C₂×C₂₉×#103	C₂²	semidirect
36. C₂×C₂₉×#97	C₂²	semidirect
37. C₂×C₄×C₈×C₂₉	C₂²	semidirect
38. C₂₉×#391	C₂²	semidirect
46. C₂₉×#389	C₂²	semidirect
53. C₄×C₄⋊C₄×C₂₉	C₂²	semidirect
54. C₂₉×#340	C₂²	semidirect
55. C₂₉×#340	C₂²	semidirect
56. C₂₉×#340	C₂²	semidirect
57. C₂₉×#340	C₂²	semidirect
58. C₂₉×#336	C₂²	semidirect
59. C₂₉×#336	C₂²	semidirect
239. #22052	C₂₉	direct (N × H)
330. #2323	C₂×C₂₉	semidirect
332. #1973	C₂×C₂₉	semidirect
333. #1968	C₂×C₂₉	semidirect
334. #1936	C₂×C₂₉	semidirect
335. #1934	C₂×C₂₉	semidirect
336. #1926	C₂×C₂₉	semidirect
337. #1925	C₂×C₂₉	semidirect
338. #1880	C₂×C₂₉	semidirect
339. #1880	C₂×C₂₉	semidirect
340. #1873	C₂×C₂₉	semidirect
341. #1854	C₂×C₂₉	semidirect
343. #1750	C₂×C₂₉	semidirect
392. C₂×C₄×Q₈	C₂²×C₂₉	semidirect
395. #450	C₄×C₂₉	semidirect
396. C₂×#107	C₂²×C₂₉	semidirect
397. C₂×#106	C₂²×C₂₉	semidirect
398. C₂×#103	C₂²×C₂₉	semidirect
399. C₂×#103	C₂²×C₂₉	semidirect
408. C₂×#97	C₂²×C₂₉	semidirect
409. C₂×C₄×C₈	C₂²×C₂₉	semidirect
410. #391	C₂²×C₂₉	semidirect
418. #389	C₂²×C₂₉	semidirect
425. C₄×C₄⋊C₄	C₂²×C₂₉	semidirect
426. #340	C₂²×C₂₉	semidirect
427. #340	C₂²×C₂₉	semidirect
428. #340	C₂²×C₂₉	semidirect
429. #340	C₂²×C₂₉	semidirect
430. #336	C₂²×C₂₉	semidirect
431. #336	C₂²×C₂₉	semidirect
519. C₂₉	#22052	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#450	2
C₂₉×#2323	2
C₂₉×#2309	2
C₂₉×#1973	2
C₂₉×#1968	2
C₂₉×#1936	2
C₂₉×#1934	2
C₂₉×#1926	2
C₂₉×#1925	2
C₂₉×#1880	2
C₂₉×#1873	2
C₂₉×#1854	2
C₂₉×#1786	2
C₂₉×#1750	2
#22052	29

Subgroups — C29×#22052 #20316952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#22052 #20316952