Subgroups — C₂₉×#34331 #20329231

Order 7424.

2436 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#559	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2367	C₂	1	2	yes	maximal, complemented
3	C₂₉×#2367	C₂	1	2	yes	maximal, complemented
4	C₂₉×#2366	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#2359	C₂	1	4	yes	maximal, complemented
6	C₂₉×#2355	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2354	C₂	1	2	yes	maximal, complemented
8	Q₈×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#2349	C₂	1	2	yes	maximal, complemented
10	C₂₉×#2335	C₂	1	4	yes	maximal, complemented
11	C₂₉×#2326	C₂	1	2	yes	maximal, complemented
12	C₄×C₂₉×#127	C₂	1	1	yes	maximal, characteristic
13	C₄×C₂₉×#124	C₂	1	2	yes	maximal, complemented
14	C₂₉×#2295	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#2293	C₂	1	2	yes	maximal, complemented
16	C₂₉×#2275	C₂	1	2	yes	maximal, complemented
17	C₄²×Q₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₉×#559	C₄	1	16	yes	complemented
19	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
20	C₂×C₂₉×#124	C₂²	1	2	yes	—
21	C₂×C₂₉×#124	C₂²	1	2	yes	—
22	C₂×C₂₉×#123	C₂²	1	4	yes	—
23	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
35	C₂×C₂₉×#117	C₂²	1	4	yes	—
36	C₂₉×#391	C₂²	1	1	yes	characteristic
37	C₂₉×#391	C₂²	1	1	yes	characteristic
38	C₂₉×#391	C₂²	1	2	yes	—
39	C₂₉×#390	C₂²	1	2	yes	—
40	C₂₉×#390	C₂²	1	2	yes	—
41	C₂₉×#390	C₂²	1	2	yes	—
42	C₂₉×#390	C₂²	1	2	yes	—
43	C₂₉×#390	C₂²	1	2	yes	—
44	C₂₉×#389	C₂²	1	1	yes	characteristic
45	C₂₉×#389	C₂²	1	2	yes	—
46	C₂₉×#389	C₂²	1	1	yes	characteristic
47	C₂₉×#389	C₂²	1	4	yes	—
48	C₂₉×#388	C₂²	1	4	yes	—
49	C₂₉×#388	C₂²	1	4	yes	—
50	C₂₉×#388	C₂²	1	4	yes	—
51	C₂₉×#388	C₂²	1	4	yes	—
52	C₂₉×#388	C₂²	1	4	yes	—
53	C₂₉×#388	C₂²	1	4	yes	—
54	C₂₉×#387	C₂²	1	2	yes	—
55	C₂₉×#387	C₂²	1	2	yes	—
56	C₂₉×#387	C₂²	1	4	yes	—
57	C₂₉×#386	C₂²	1	4	yes	—
58	C₂₉×#385	C₂²	1	4	yes	—
59	C₂₉×#385	C₂²	1	4	yes	—
60	C₂₉×#385	C₂²	1	4	yes	—
61	C₂₉×#384	C₂²	1	1	yes	characteristic
62	C₂₉×#384	C₂²	1	2	yes	—
63	C₂₉×#382	C₂²	1	2	yes	—
64	C₂₉×#380	C₂²	1	4	yes	—
65	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
66	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
67	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
69	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
70	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
72	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
75	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊C₄×C₂₉	C₂²	1	4	yes	—
77	C₄×C₂²⋊C₄×C₂₉	C₂²	1	4	yes	—
78	C₄×C₂²⋊C₄×C₂₉	C₂²	1	4	yes	—
79	C₄×C₂²⋊C₄×C₂₉	C₂²	1	4	yes	—
80	C₂₉×#376	C₂²	1	2	yes	—
81	C₂×C₂₉×#95	C₂²	1	4	yes	—
82	C₄³×C₂₉	C₂²	1	2	yes	—
83	C₄³×C₂₉	C₂²	1	1	yes	characteristic
84	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
87	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
89	C₂³×C₄×C₂₉	C₂³	1	4	yes	—
90	C₂³×C₄×C₂₉	C₂³	1	4	yes	—
91	C₂³×C₄×C₂₉	C₂³	1	4	yes	—
92	C₂₉×#127	C₂×C₄	1	8	yes	—
93	C₂₉×#124	C₂×C₄	1	16	yes	complemented
94	C₂₉×#124	C₂×C₄	1	16	yes	complemented
95	C₂₉×#123	C₂×C₄	1	32	yes	complemented
96	C₄×Q₈×C₂₉	—	2	4	no	—
97	C₄×Q₈×C₂₉	—	2	4	no	—
98	C₄×Q₈×C₂₉	—	4	4	no	—
99	C₄×Q₈×C₂₉	C₂×C₄	1	8	yes	complemented
100	C₄×Q₈×C₂₉	C₂×C₄	1	8	yes	complemented
101	C₄×D₄×C₂₉	—	2	8	no	—
102	C₄×D₄×C₂₉	—	2	8	no	—
103	C₄×D₄×C₂₉	—	4	4	no	—
104	C₄×D₄×C₂₉	—	4	4	no	—
105	C₄×D₄×C₂₉	—	4	4	no	—
106	C₄×D₄×C₂₉	C₂×C₄	1	16	yes	complemented
107	C₄×D₄×C₂₉	C₂×C₄	1	16	yes	complemented
108	C₂₉×#117	—	4	8	no	—
109	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
126	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
135	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
136	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
139	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
140	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
141	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
143	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
145	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
146	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
147	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
149	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
150	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
152	C₂₉×#95	C₂³	1	2	yes	—
153	C₂₉×#95	C₂³	1	2	yes	—
154	C₂₉×#95	C₂³	1	4	yes	—
155	C₂₉×#95	C₂³	1	4	yes	—
156	C₂₉×#95	C₂³	1	2	yes	—
157	C₂₉×#95	C₂³	1	2	yes	—
158	C₂₉×#95	C₂³	1	2	yes	—
159	C₂₉×#95	C₂³	1	2	yes	—
160	C₂₉×#95	C₂³	1	4	yes	—
161	C₂₉×#95	C₂³	1	2	yes	—
162	C₂₉×#95	C₂³	1	2	yes	—
163	C₂₉×#95	C₂³	1	4	yes	—
164	C₂₉×#95	C₂³	1	2	yes	—
165	C₂₉×#95	C₂³	1	2	yes	—
166	C₂⁴×C₂₉	C₂⁴	1	4	yes	—
167	C₂×Q₈×C₂₉	—	2	2	no	—
168	C₂×Q₈×C₂₉	—	2	2	no	—
169	C₂×Q₈×C₂₉	—	2	2	no	—
170	C₂×Q₈×C₂₉	—	2	2	no	—
171	C₂×Q₈×C₂₉	C₂²×C₄	1	4	yes	—
172	C₂×Q₈×C₂₉	C₂²×C₄	1	4	yes	—
173	C₂×D₄×C₂₉	—	2	4	no	—
174	C₂×D₄×C₂₉	—	2	4	no	—
175	C₂×D₄×C₂₉	—	2	4	no	—
176	C₂×D₄×C₂₉	—	2	4	no	—
177	C₂×D₄×C₂₉	—	4	2	no	—
178	C₂×D₄×C₂₉	—	4	2	no	—
179	C₂×D₄×C₂₉	C₂²×C₄	1	8	yes	—
180	C₂×D₄×C₂₉	C₂²×C₄	1	8	yes	—
181	C₂×D₄×C₂₉	C₂²×C₄	1	8	yes	—
182	C₂²×C₄×C₂₉	—	2	8	no	—
183	C₂²×C₄×C₂₉	—	2	8	no	—
184	C₂²×C₄×C₂₉	—	4	4	no	—
185	C₂²×C₄×C₂₉	—	4	4	no	—
186	C₂²×C₄×C₂₉	—	4	4	no	—
187	C₂²×C₄×C₂₉	—	4	4	no	—
188	C₂²×C₄×C₂₉	—	4	4	no	—
189	C₂²×C₄×C₂₉	—	4	4	no	—
190	C₂²×C₄×C₂₉	C₂²×C₄	1	16	yes	—
191	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
207	C₄⋊C₄×C₂₉	—	2	4	no	—
208	C₄⋊C₄×C₂₉	—	2	4	no	—
209	C₄⋊C₄×C₂₉	—	2	4	no	—
210	C₄⋊C₄×C₂₉	—	2	2	no	—
211	C₄⋊C₄×C₂₉	—	2	4	no	—
212	C₄⋊C₄×C₂₉	—	2	2	no	—
213	C₄⋊C₄×C₂₉	—	2	4	no	—
214	C₄⋊C₄×C₂₉	—	2	2	no	—
215	C₄⋊C₄×C₂₉	—	4	2	no	—
216	C₄⋊C₄×C₂₉	—	4	4	no	—
217	C₄⋊C₄×C₂₉	—	4	2	no	—
218	C₄⋊C₄×C₂₉	—	4	4	no	—
219	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
220	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
221	C₄⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
222	C₄⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
223	C₄⋊C₄×C₂₉	#41	1	4	yes	—
224	C₂²⋊C₄×C₂₉	—	2	8	no	—
225	C₂²⋊C₄×C₂₉	—	2	8	no	—
226	C₂²⋊C₄×C₂₉	—	2	8	no	—
227	C₂²⋊C₄×C₂₉	—	4	4	no	—
228	C₂²⋊C₄×C₂₉	—	4	4	no	—
229	C₂²⋊C₄×C₂₉	—	4	4	no	—
230	C₂²⋊C₄×C₂₉	C₂²×C₄	1	16	yes	—
231	C₂²⋊C₄×C₂₉	C₂²×C₄	1	16	yes	—
232	C₂²⋊C₄×C₂₉	C₂²×C₄	1	16	yes	—
233	C₄²×C₂₉	—	2	4	no	—
234	C₄²×C₂₉	—	2	4	no	—
235	C₄²×C₂₉	—	2	2	no	—
236	C₄²×C₂₉	—	2	4	no	—
237	C₄²×C₂₉	—	2	4	no	—
238	C₄²×C₂₉	—	2	2	no	—
239	C₄²×C₂₉	—	2	2	no	—
240	C₄²×C₂₉	—	2	4	no	—
241	C₄²×C₂₉	—	2	2	no	—
242	C₄²×C₂₉	—	4	2	no	—
243	C₄²×C₂₉	—	4	1	no	—
244	C₄²×C₂₉	—	4	4	no	—
245	C₄²×C₂₉	—	4	4	no	—
246	C₄²×C₂₉	C₂²×C₄	1	8	yes	—
247	C₄²×C₂₉	C₂²×C₄	1	8	yes	—
248	C₄²×C₂₉	C₂²×C₄	1	4	yes	—
249	C₄²×C₂₉	#41	1	4	yes	—
250	#34331	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
251	C₂³×C₂₉	—	2	4	no	—
252	C₂³×C₂₉	—	2	4	no	—
253	C₂³×C₂₉	—	2	4	no	—
254	C₂³×C₂₉	—	2	4	no	—
255	C₂³×C₂₉	—	2	4	no	—
256	C₂³×C₂₉	—	2	4	no	—
257	C₂³×C₂₉	C₂³×C₄	1	8	yes	—
258	C₂³×C₂₉	C₂⁵	1	1	yes	characteristic
259	Q₈×C₂₉	—	2	8	no	—
260	Q₈×C₂₉	—	2	8	no	—
261	D₄×C₂₉	—	2	16	no	—
262	D₄×C₂₉	—	2	16	no	—
263	D₄×C₂₉	—	4	8	no	—
264	C₂×C₄×C₂₉	—	2	1	no	—
265	C₂×C₄×C₂₉	—	2	2	no	—
266	C₂×C₄×C₂₉	—	2	2	no	—
267	C₂×C₄×C₂₉	—	2	2	no	—
268	C₂×C₄×C₂₉	—	2	2	no	—
269	C₂×C₄×C₂₉	—	2	1	no	—
270	C₂×C₄×C₂₉	—	2	1	no	—
271	C₂×C₄×C₂₉	—	2	1	no	—
272	C₂×C₄×C₂₉	—	2	2	no	—
273	C₂×C₄×C₂₉	—	2	2	no	—
274	C₂×C₄×C₂₉	—	2	1	no	—
275	C₂×C₄×C₂₉	—	2	1	no	—
276	C₂×C₄×C₂₉	—	2	2	no	—
277	C₂×C₄×C₂₉	—	2	1	no	—
278	C₂×C₄×C₂₉	—	2	2	no	—
279	C₂×C₄×C₂₉	—	2	2	no	—
280	C₂×C₄×C₂₉	—	2	1	no	—
281	C₂×C₄×C₂₉	—	2	2	no	—
282	C₂×C₄×C₂₉	—	2	2	no	—
283	C₂×C₄×C₂₉	—	2	2	no	—
284	C₂×C₄×C₂₉	—	2	1	no	—
285	C₂×C₄×C₂₉	—	2	2	no	—
286	C₂×C₄×C₂₉	—	2	4	no	—
287	C₂×C₄×C₂₉	—	2	1	no	—
288	C₂×C₄×C₂₉	—	2	2	no	—
289	C₂×C₄×C₂₉	—	2	2	no	—
290	C₂×C₄×C₂₉	—	2	2	no	—
291	C₂×C₄×C₂₉	—	2	4	no	—
292	C₂×C₄×C₂₉	—	2	4	no	—
293	C₂×C₄×C₂₉	—	2	2	no	—
294	C₂×C₄×C₂₉	—	2	2	no	—
295	C₂×C₄×C₂₉	—	2	1	no	—
296	C₂×C₄×C₂₉	—	2	2	no	—
297	C₂×C₄×C₂₉	—	4	16	no	—
298	C₂×C₄×C₂₉	—	8	8	no	—
299	C₂×C₄×C₂₉	—	8	8	no	—
300	C₂×C₄×C₂₉	C₂³×C₄	1	4	yes	—
301	C₂×C₄×C₂₉	C₂³×C₄	1	4	yes	—
302	C₂×C₄×C₂₉	C₂³×C₄	1	4	yes	—
303	C₂×C₄×C₂₉	C₂³×C₄	1	4	yes	—
304	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
305	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
306	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
307	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
308	C₂×C₄×C₂₉	C₂×#41	1	4	yes	—
309	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
310	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
311	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
312	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
313	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
314	C₂×C₄×C₂₉	2₋¹⁺⁴	1	2	yes	—
315	C₂×#559	C₂×C₂₉	1	1	yes	characteristic
316	#2367	C₂×C₂₉	1	2	yes	complemented
317	#2367	C₂×C₂₉	1	2	yes	complemented
318	#2366	C₂×C₂₉	1	1	yes	characteristic
319	#2359	C₂×C₂₉	1	4	yes	complemented
320	#2355	C₂×C₂₉	1	1	yes	characteristic, complemented
321	#2354	C₂×C₂₉	1	2	yes	complemented
322	Q₈×C₄⋊C₄	C₂×C₂₉	1	1	yes	characteristic, complemented
323	#2349	C₂×C₂₉	1	2	yes	complemented
324	#2335	C₂×C₂₉	1	4	yes	complemented
325	#2326	C₂×C₂₉	1	2	yes	complemented
326	C₄×#127	C₂×C₂₉	1	1	yes	characteristic
327	C₄×#124	C₂×C₂₉	1	2	yes	complemented
328	#2295	C₂×C₂₉	1	1	yes	characteristic, complemented
329	#2293	C₂×C₂₉	1	2	yes	complemented
330	#2275	C₂×C₂₉	1	2	yes	complemented
331	C₄²×Q₈	C₂×C₂₉	1	1	yes	characteristic, complemented
332	C₂²×C₂₉	—	2	8	no	—
333	C₂²×C₂₉	—	2	8	no	—
334	C₂²×C₂₉	—	2	8	no	—
335	C₂²×C₂₉	—	4	4	no	—
336	C₂²×C₂₉	—	4	4	no	—
337	C₂²×C₂₉	—	4	4	no	—
338	C₂²×C₂₉	—	4	4	no	—
339	C₂²×C₂₉	C₂⁴×C₄	1	1	yes	characteristic
340	C₂²×C₂₉	C₂²×#41	1	1	yes	characteristic
341	C₂²×C₂₉	C₂²×#41	1	1	yes	characteristic
342	C₂²×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
343	C₂²×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
344	C₂²×C₂₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
345	C₂²×C₂₉	#585	1	1	yes	characteristic
346	C₄×C₂₉	—	2	4	no	—
347	C₄×C₂₉	—	2	4	no	—
348	C₄×C₂₉	—	2	4	no	—
349	C₄×C₂₉	—	2	4	no	—
350	C₄×C₂₉	—	2	2	no	—
351	C₄×C₂₉	—	2	2	no	—
352	C₄×C₂₉	—	2	2	no	—
353	C₄×C₂₉	—	2	4	no	—
354	C₄×C₂₉	—	2	2	no	—
355	C₄×C₂₉	—	4	2	no	—
356	C₄×C₂₉	—	4	4	no	—
357	C₄×C₂₉	—	4	1	no	—
358	C₄×C₂₉	—	4	2	no	—
359	C₄×C₂₉	—	4	2	no	—
360	C₄×C₂₉	C₄×#41	1	4	yes	—
361	C₄×C₂₉	#520	1	4	yes	—
362	#559	C₄×C₂₉	1	16	yes	complemented
363	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
364	C₂×#124	C₂²×C₂₉	1	2	yes	—
365	C₂×#124	C₂²×C₂₉	1	2	yes	—
366	C₂×#123	C₂²×C₂₉	1	4	yes	—
367	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
368	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
369	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	—
370	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
371	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
372	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
373	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
374	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
375	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
376	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
377	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
378	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
379	C₂×#117	C₂²×C₂₉	1	4	yes	—
380	#391	C₂²×C₂₉	1	2	yes	—
381	#391	C₂²×C₂₉	1	1	yes	characteristic
382	#391	C₂²×C₂₉	1	1	yes	characteristic
383	#390	C₂²×C₂₉	1	2	yes	—
384	#390	C₂²×C₂₉	1	2	yes	—
385	#390	C₂²×C₂₉	1	2	yes	—
386	#390	C₂²×C₂₉	1	2	yes	—
387	#390	C₂²×C₂₉	1	2	yes	—
388	#389	C₂²×C₂₉	1	4	yes	—
389	#389	C₂²×C₂₉	1	1	yes	characteristic
390	#389	C₂²×C₂₉	1	2	yes	—
391	#389	C₂²×C₂₉	1	1	yes	characteristic
392	#388	C₂²×C₂₉	1	4	yes	—
393	#388	C₂²×C₂₉	1	4	yes	—
394	#388	C₂²×C₂₉	1	4	yes	—
395	#388	C₂²×C₂₉	1	4	yes	—
396	#388	C₂²×C₂₉	1	4	yes	—
397	#388	C₂²×C₂₉	1	4	yes	—
398	#387	C₂²×C₂₉	1	2	yes	—
399	#387	C₂²×C₂₉	1	4	yes	—
400	#387	C₂²×C₂₉	1	2	yes	—
401	#386	C₂²×C₂₉	1	4	yes	—
402	#385	C₂²×C₂₉	1	4	yes	—
403	#385	C₂²×C₂₉	1	4	yes	—
404	#385	C₂²×C₂₉	1	4	yes	—
405	#384	C₂²×C₂₉	1	1	yes	characteristic
406	#384	C₂²×C₂₉	1	2	yes	—
407	#382	C₂²×C₂₉	1	2	yes	—
408	#380	C₂²×C₂₉	1	4	yes	—
409	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
410	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
411	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
412	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
413	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
414	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
415	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
416	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
417	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
418	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
419	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
420	C₄×C₂²⋊C₄	C₂²×C₂₉	1	4	yes	—
421	C₄×C₂²⋊C₄	C₂²×C₂₉	1	4	yes	—
422	C₄×C₂²⋊C₄	C₂²×C₂₉	1	4	yes	—
423	C₄×C₂²⋊C₄	C₂²×C₂₉	1	4	yes	—
424	#376	C₂²×C₂₉	1	2	yes	—
425	C₂×#95	C₂²×C₂₉	1	4	yes	—
426	C₄³	C₂²×C₂₉	1	1	yes	characteristic
427	C₄³	C₂²×C₂₉	1	2	yes	—
428	C₂×C₂₉	—	4	8	no	—
429	C₂×C₂₉	C₂×C₄×#41	1	1	yes	characteristic
430	C₂×C₂₉	C₂×#520	1	1	yes	characteristic
431	C₂×C₂₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic
432	C₂×C₂₉	#3507	1	1	yes	characteristic
433	C₂×C₂₉	#3508	1	1	yes	characteristic
434	C₂×C₂₉	#3514	1	1	yes	characteristic
435	C₂×C₂₉	#3522	1	1	yes	characteristic
436	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
437	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
438	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
439	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
440	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
441	C₂³×C₄	C₂³×C₂₉	1	4	yes	—
442	C₂³×C₄	C₂³×C₂₉	1	4	yes	—
443	C₂³×C₄	C₂³×C₂₉	1	4	yes	—
444	#127	C₂×C₄×C₂₉	1	8	yes	—
445	#124	C₂×C₄×C₂₉	1	16	yes	complemented
446	#124	C₂×C₄×C₂₉	1	16	yes	complemented
447	#123	C₂×C₄×C₂₉	1	32	yes	complemented
448	C₄×Q₈	—	2	4	no	—
449	C₄×Q₈	—	2	4	no	—
450	C₄×Q₈	—	4	4	no	—
451	C₄×Q₈	C₂×C₄×C₂₉	1	8	yes	complemented
452	C₄×Q₈	C₂×C₄×C₂₉	1	8	yes	complemented
453	C₄×D₄	—	2	8	no	—
454	C₄×D₄	—	2	8	no	—
455	C₄×D₄	—	4	4	no	—
456	C₄×D₄	—	4	4	no	—
457	C₄×D₄	—	4	4	no	—
458	C₄×D₄	C₂×C₄×C₂₉	1	16	yes	complemented
459	C₄×D₄	C₂×C₄×C₂₉	1	16	yes	complemented
460	#117	—	4	8	no	—
461	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
462	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
463	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
470	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
472	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
478	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
487	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
488	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
489	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
490	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
491	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
492	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
493	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
495	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
497	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
498	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
499	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
500	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
501	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
502	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
503	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
504	#95	C₂³×C₂₉	1	2	yes	—
505	#95	C₂³×C₂₉	1	2	yes	—
506	#95	C₂³×C₂₉	1	4	yes	—
507	#95	C₂³×C₂₉	1	4	yes	—
508	#95	C₂³×C₂₉	1	2	yes	—
509	#95	C₂³×C₂₉	1	2	yes	—
510	#95	C₂³×C₂₉	1	2	yes	—
511	#95	C₂³×C₂₉	1	2	yes	—
512	#95	C₂³×C₂₉	1	4	yes	—
513	#95	C₂³×C₂₉	1	2	yes	—
514	#95	C₂³×C₂₉	1	2	yes	—
515	#95	C₂³×C₂₉	1	4	yes	—
516	#95	C₂³×C₂₉	1	2	yes	—
517	#95	C₂³×C₂₉	1	2	yes	—
518	C₂₉	#34331	1	1	yes	characteristic, direct product factor, Sylow
519	C₂⁴	C₂⁴×C₂₉	1	4	yes	—
520	C₂×Q₈	—	2	2	no	—
521	C₂×Q₈	—	2	2	no	—
522	C₂×Q₈	—	2	2	no	—
523	C₂×Q₈	—	2	2	no	—
524	C₂×Q₈	C₂²×C₄×C₂₉	1	4	yes	—
525	C₂×Q₈	C₂²×C₄×C₂₉	1	4	yes	—
526	C₂×D₄	—	2	4	no	—
527	C₂×D₄	—	2	4	no	—
528	C₂×D₄	—	2	4	no	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	4	2	no	—
531	C₂×D₄	—	4	2	no	—
532	C₂×D₄	C₂²×C₄×C₂₉	1	8	yes	—
533	C₂×D₄	C₂²×C₄×C₂₉	1	8	yes	—
534	C₂×D₄	C₂²×C₄×C₂₉	1	8	yes	—
535	C₂²×C₄	—	2	8	no	—
536	C₂²×C₄	—	2	8	no	—
537	C₂²×C₄	—	4	4	no	—
538	C₂²×C₄	—	4	4	no	—
539	C₂²×C₄	—	4	4	no	—
540	C₂²×C₄	—	4	4	no	—
541	C₂²×C₄	—	4	4	no	—
542	C₂²×C₄	—	4	4	no	—
543	C₂²×C₄	C₂²×C₄×C₂₉	1	16	yes	—
544	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
547	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
548	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
557	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
558	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
560	C₄⋊C₄	—	2	4	no	—
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	—	2	4	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	4	4	no	—
569	C₄⋊C₄	—	4	2	no	—
570	C₄⋊C₄	—	4	4	no	—
571	C₄⋊C₄	—	4	2	no	—
572	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
573	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
574	C₄⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
575	C₄⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
576	C₄⋊C₄	#41×C₂₉	1	4	yes	—
577	C₂²⋊C₄	—	2	8	no	—
578	C₂²⋊C₄	—	2	8	no	—
579	C₂²⋊C₄	—	2	8	no	—
580	C₂²⋊C₄	—	4	4	no	—
581	C₂²⋊C₄	—	4	4	no	—
582	C₂²⋊C₄	—	4	4	no	—
583	C₂²⋊C₄	C₂²×C₄×C₂₉	1	16	yes	—
584	C₂²⋊C₄	C₂²×C₄×C₂₉	1	16	yes	—
585	C₂²⋊C₄	C₂²×C₄×C₂₉	1	16	yes	—
586	C₄²	—	2	4	no	—
587	C₄²	—	2	4	no	—
588	C₄²	—	2	2	no	—
589	C₄²	—	2	4	no	—
590	C₄²	—	2	4	no	—
591	C₄²	—	2	2	no	—
592	C₄²	—	2	2	no	—
593	C₄²	—	2	4	no	—
594	C₄²	—	2	2	no	—
595	C₄²	—	4	4	no	—
596	C₄²	—	4	4	no	—
597	C₄²	—	4	2	no	—
598	C₄²	—	4	1	no	—
599	C₄²	C₂²×C₄×C₂₉	1	8	yes	—
600	C₄²	C₂²×C₄×C₂₉	1	8	yes	—
601	C₄²	C₂²×C₄×C₂₉	1	4	yes	—
602	C₄²	#41×C₂₉	1	4	yes	—
603	C₂³	—	2	4	no	—
604	C₂³	—	2	4	no	—
605	C₂³	—	2	4	no	—
606	C₂³	—	2	4	no	—
607	C₂³	—	2	4	no	—
608	C₂³	—	2	4	no	—
609	C₂³	C₂³×C₄×C₂₉	1	8	yes	—
610	C₂³	C₂⁵×C₂₉	1	1	yes	characteristic
611	Q₈	—	2	8	no	—
612	Q₈	—	2	8	no	—
613	D₄	—	2	16	no	—
614	D₄	—	2	16	no	—
615	D₄	—	4	8	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	4	16	no	—
650	C₂×C₄	—	8	8	no	—
651	C₂×C₄	—	8	8	no	—
652	C₂×C₄	C₂³×C₄×C₂₉	1	4	yes	—
653	C₂×C₄	C₂³×C₄×C₂₉	1	4	yes	—
654	C₂×C₄	C₂³×C₄×C₂₉	1	4	yes	—
655	C₂×C₄	C₂³×C₄×C₂₉	1	4	yes	—
656	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
657	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
658	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
659	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
660	C₂×C₄	C₂×#41×C₂₉	1	4	yes	—
661	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
662	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
663	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
664	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
665	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
666	C₂×C₄	C₂₉×2₋¹⁺⁴	1	2	yes	—
667	C₂²	—	2	8	no	—
668	C₂²	—	2	8	no	—
669	C₂²	—	2	8	no	—
670	C₂²	—	4	4	no	—
671	C₂²	—	4	4	no	—
672	C₂²	—	4	4	no	—
673	C₂²	—	4	4	no	—
674	C₂²	C₂⁴×C₄×C₂₉	1	1	yes	characteristic
675	C₂²	C₂²×#41×C₂₉	1	1	yes	characteristic
676	C₂²	C₂²×#41×C₂₉	1	1	yes	characteristic
677	C₂²	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
678	C₂²	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
679	C₂²	C₂×C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
680	C₂²	C₂₉×#585	1	1	yes	characteristic
681	C₄	—	2	2	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	4	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	4	no	—
686	C₄	—	2	4	no	—
687	C₄	—	2	4	no	—
688	C₄	—	2	4	no	—
689	C₄	—	2	2	no	—
690	C₄	—	4	4	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	2	no	—
693	C₄	—	4	1	no	—
694	C₄	—	4	2	no	—
695	C₄	C₄×#41×C₂₉	1	4	yes	—
696	C₄	C₂₉×#520	1	4	yes	—
697	C₂	—	4	8	no	—
698	C₂	C₂×C₄×#41×C₂₉	1	1	yes	characteristic
699	C₂	C₂×C₂₉×#520	1	1	yes	characteristic
700	C₂	C₄×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
701	C₂	C₂₉×#3507	1	1	yes	characteristic
702	C₂	C₂₉×#3508	1	1	yes	characteristic
703	C₂	C₂₉×#3514	1	1	yes	characteristic
704	C₂	C₂₉×#3522	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁵×C₂₉
prime radical	C₂×C₂₉×#127	C₂²
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. C₂₉×#2367	C₂	semidirect
3. C₂₉×#2367	C₂	semidirect
5. C₂₉×#2359	C₂	semidirect
6. C₂₉×#2355	C₂	semidirect
7. C₂₉×#2354	C₂	semidirect
8. Q₈×C₄⋊C₄×C₂₉	C₂	semidirect
9. C₂₉×#2349	C₂	semidirect
10. C₂₉×#2335	C₂	semidirect
11. C₂₉×#2326	C₂	semidirect
13. C₄×C₂₉×#124	C₂	semidirect
14. C₂₉×#2295	C₂	semidirect
15. C₂₉×#2293	C₂	semidirect
16. C₂₉×#2275	C₂	semidirect
17. C₄²×Q₈×C₂₉	C₂	semidirect
18. C₂₉×#559	C₄	semidirect
93. C₂₉×#124	C₂×C₄	semidirect
94. C₂₉×#124	C₂×C₄	semidirect
95. C₂₉×#123	C₂×C₄	semidirect
99. C₄×Q₈×C₂₉	C₂×C₄	semidirect
100. C₄×Q₈×C₂₉	C₂×C₄	semidirect
106. C₄×D₄×C₂₉	C₂×C₄	semidirect
107. C₄×D₄×C₂₉	C₂×C₄	semidirect
250. #34331	C₂₉	direct (N × H)
316. #2367	C₂×C₂₉	semidirect
317. #2367	C₂×C₂₉	semidirect
319. #2359	C₂×C₂₉	semidirect
320. #2355	C₂×C₂₉	semidirect
321. #2354	C₂×C₂₉	semidirect
322. Q₈×C₄⋊C₄	C₂×C₂₉	semidirect
323. #2349	C₂×C₂₉	semidirect
324. #2335	C₂×C₂₉	semidirect
325. #2326	C₂×C₂₉	semidirect
327. C₄×#124	C₂×C₂₉	semidirect
328. #2295	C₂×C₂₉	semidirect
329. #2293	C₂×C₂₉	semidirect
330. #2275	C₂×C₂₉	semidirect
331. C₄²×Q₈	C₂×C₂₉	semidirect
362. #559	C₄×C₂₉	semidirect
445. #124	C₂×C₄×C₂₉	semidirect
446. #124	C₂×C₄×C₂₉	semidirect
447. #123	C₂×C₄×C₂₉	semidirect
451. C₄×Q₈	C₂×C₄×C₂₉	semidirect
452. C₄×Q₈	C₂×C₄×C₂₉	semidirect
458. C₄×D₄	C₂×C₄×C₂₉	semidirect
459. C₄×D₄	C₂×C₄×C₂₉	semidirect
518. C₂₉	#34331	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×#559	2
C₂₉×#2367	2
C₂₉×#2366	2
C₂₉×#2359	2
C₂₉×#2355	2
C₂₉×#2354	2
Q₈×C₄⋊C₄×C₂₉	2
C₂₉×#2349	2
C₂₉×#2335	2
C₂₉×#2326	2
C₄×C₂₉×#127	2
C₄×C₂₉×#124	2
C₂₉×#2295	2
C₂₉×#2293	2
C₂₉×#2275	2
C₄²×Q₈×C₂₉	2
#34331	29

Subgroups — C29×#34331 #20329231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#34331 #20329231