Subgroups — C₂₉×#23039 #20317939

Order 7424.

1082 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#469	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×#428	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2363	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2361	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1970	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1944	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×#1875	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1864	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1862	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂₉×#106	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₂₉	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₂₉	—	2	1	no	—
21	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
25	C₂₉×#469	C₄	1	8	yes	complemented
26	C₂₉×#442	—	2	4	no	—
27	C₂₉×#428	—	2	4	no	—
28	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
34	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
35	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
36	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
37	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
38	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
39	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
42	C₂₉×#390	—	2	1	no	—
43	C₂₉×#390	C₂²	1	1	yes	characteristic
44	C₂₉×#390	C₂²	1	1	yes	characteristic
45	C₂₉×#389	C₂²	1	1	yes	characteristic
46	C₂₉×#389	C₂²	1	1	yes	characteristic
47	C₂₉×#388	—	2	1	no	—
48	C₂₉×#388	—	2	1	no	—
49	C₂₉×#386	—	2	1	no	—
50	C₂₉×#386	—	2	1	no	—
51	C₂₉×#385	—	2	1	no	—
52	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₂₉	—	2	1	no	—
55	C₄×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
56	C₂₉×#340	C₂²	1	1	yes	characteristic
57	C₂₉×#340	C₂²	1	1	yes	characteristic
58	C₂₉×#340	C₂²	1	1	yes	characteristic
59	C₂₉×#340	C₂²	1	1	yes	characteristic
60	C₂₉×#336	C₂²	1	1	yes	characteristic
61	C₂₉×#336	C₂²	1	1	yes	characteristic
62	C₂²×D₄×C₂₉	—	2	1	no	—
63	C₂²×D₄×C₂₉	—	2	1	no	—
64	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₂₉	—	2	1	no	—
67	C₂³×C₄×C₂₉	—	2	1	no	—
68	C₂³×C₄×C₂₉	—	2	1	no	—
69	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
70	C₂×D₈×C₂₉	—	2	2	no	—
71	C₂×D₈×C₂₉	—	2	2	no	—
72	C₂×D₈×C₂₉	C₂×C₄	1	4	yes	complemented
73	C₂×M₁₆×C₂₉	—	2	2	no	—
74	C₂×M₁₆×C₂₉	—	2	2	no	—
75	C₂×M₁₆×C₂₉	C₂×C₄	1	4	yes	complemented
76	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
80	C₂₉×#121	—	2	2	no	—
81	C₂₉×#121	—	2	2	no	—
82	C₂₉×#121	C₂×C₄	1	4	yes	complemented
83	C₂₉×#121	C₂×C₄	1	4	yes	complemented
84	C₄×D₄×C₂₉	—	2	2	no	—
85	C₄×D₄×C₂₉	—	2	2	no	—
86	C₄×D₄×C₂₉	—	4	1	no	—
87	C₄×D₄×C₂₉	—	4	1	no	—
88	C₄×D₄×C₂₉	—	4	4	no	—
89	C₂₉×#117	—	2	2	no	—
90	C₂₉×#117	—	4	1	no	—
91	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
92	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
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×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
119	C₂₉×#107	—	2	2	no	—
120	C₂₉×#106	—	2	2	no	—
121	C₂₉×#106	C₂×C₄	1	4	yes	complemented
122	C₂₉×#106	D₄	1	4	yes	complemented
123	C₂₉×#102	—	2	2	no	—
124	C₂₉×#102	—	2	2	no	—
125	C₂₉×#102	—	4	1	no	—
126	C₂₉×#102	—	4	1	no	—
127	C₂₉×#102	C₂×C₄	1	4	yes	complemented
128	C₂₉×#102	C₂×C₄	1	4	yes	complemented
129	C₂₉×C₂²⋊C₈	—	2	2	no	—
130	C₂₉×#97	—	2	2	no	—
131	C₄×C₈×C₂₉	—	2	2	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	D₄	1	1	yes	characteristic
137	C₂₉×#95	D₄	1	1	yes	characteristic
138	C₂⁴×C₂₉	—	2	1	no	—
139	C₂⁴×C₂₉	—	2	1	no	—
140	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
141	C₂×D₄×C₂₉	—	2	4	no	—
142	C₂×D₄×C₂₉	—	2	4	no	—
143	C₂×D₄×C₂₉	—	2	1	no	—
144	C₂×D₄×C₂₉	—	2	1	no	—
145	C₂×D₄×C₂₉	—	2	1	no	—
146	C₂×D₄×C₂₉	—	2	1	no	—
147	C₂×D₄×C₂₉	—	2	1	no	—
148	C₂×D₄×C₂₉	—	2	1	no	—
149	C₂×D₄×C₂₉	—	2	1	no	—
150	C₂×D₄×C₂₉	—	2	1	no	—
151	C₂×D₄×C₂₉	—	2	1	no	—
152	C₂×D₄×C₂₉	—	2	1	no	—
153	C₂×D₄×C₂₉	—	4	2	no	—
154	C₂×D₄×C₂₉	—	4	2	no	—
155	C₂×D₄×C₂₉	—	8	1	no	—
156	C₂×D₄×C₂₉	—	8	1	no	—
157	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
158	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
159	C₂²×C₄×C₂₉	—	2	1	no	—
160	C₂²×C₄×C₂₉	—	2	1	no	—
161	C₂²×C₄×C₂₉	—	2	1	no	—
162	C₂²×C₄×C₂₉	—	2	1	no	—
163	C₂²×C₄×C₂₉	—	2	1	no	—
164	C₂²×C₄×C₂₉	—	2	1	no	—
165	C₂²×C₄×C₂₉	—	2	1	no	—
166	C₂²×C₄×C₂₉	—	2	1	no	—
167	C₂²×C₄×C₂₉	—	2	1	no	—
168	C₂²×C₄×C₂₉	—	2	1	no	—
169	C₂²×C₄×C₂₉	—	4	2	no	—
170	C₂²×C₄×C₂₉	—	4	2	no	—
171	C₂²×C₄×C₂₉	—	4	2	no	—
172	C₂²×C₄×C₂₉	—	4	2	no	—
173	C₂²×C₄×C₂₉	—	4	2	no	—
174	C₂²×C₄×C₂₉	—	4	2	no	—
175	C₂²×C₄×C₂₉	—	8	1	no	—
176	C₂²×C₄×C₂₉	—	8	1	no	—
177	C₂²×C₄×C₂₉	—	8	1	no	—
178	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
179	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₂₉	#41	1	2	yes	—
185	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
186	D₈×C₂₉	—	2	8	no	—
187	M₁₆×C₂₉	—	2	8	no	—
188	C₂×C₈×C₂₉	—	2	1	no	—
189	C₂×C₈×C₂₉	—	2	1	no	—
190	C₂×C₈×C₂₉	—	2	1	no	—
191	C₂×C₈×C₂₉	—	2	1	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	C₂²×C₄	1	2	yes	—
197	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
198	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
199	C₂×C₈×C₂₉	#41	1	2	yes	—
200	C₄⋊C₄×C₂₉	—	2	1	no	—
201	C₄⋊C₄×C₂₉	—	2	1	no	—
202	C₄⋊C₄×C₂₉	—	2	1	no	—
203	C₄⋊C₄×C₂₉	—	2	1	no	—
204	C₄⋊C₄×C₂₉	—	2	1	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	—	4	2	no	—
209	C₄⋊C₄×C₂₉	—	4	2	no	—
210	C₄⋊C₄×C₂₉	—	8	1	no	—
211	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
212	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
213	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
214	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
215	C₂²⋊C₄×C₂₉	—	2	4	no	—
216	C₂²⋊C₄×C₂₉	—	2	4	no	—
217	C₂²⋊C₄×C₂₉	—	2	2	no	—
218	C₂²⋊C₄×C₂₉	—	4	1	no	—
219	C₂²⋊C₄×C₂₉	—	4	2	no	—
220	C₂²⋊C₄×C₂₉	—	4	2	no	—
221	C₂²⋊C₄×C₂₉	—	4	2	no	—
222	C₂²⋊C₄×C₂₉	—	4	2	no	—
223	C₂²⋊C₄×C₂₉	—	4	2	no	—
224	C₂²⋊C₄×C₂₉	—	8	1	no	—
225	C₂²⋊C₄×C₂₉	—	8	1	no	—
226	C₄²×C₂₉	—	2	1	no	—
227	C₄²×C₂₉	—	2	1	no	—
228	C₄²×C₂₉	—	2	1	no	—
229	C₄²×C₂₉	—	2	1	no	—
230	C₄²×C₂₉	—	4	2	no	—
231	C₄²×C₂₉	—	4	2	no	—
232	C₄²×C₂₉	—	8	1	no	—
233	#23039	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂³×C₂₉	—	2	1	no	—
235	C₂³×C₂₉	—	2	1	no	—
236	C₂³×C₂₉	—	2	1	no	—
237	C₂³×C₂₉	—	2	1	no	—
238	C₂³×C₂₉	—	2	1	no	—
239	C₂³×C₂₉	—	2	1	no	—
240	C₂³×C₂₉	—	2	2	no	—
241	C₂³×C₂₉	—	2	2	no	—
242	C₂³×C₂₉	—	4	1	no	—
243	C₂³×C₂₉	—	4	1	no	—
244	C₂³×C₂₉	—	4	1	no	—
245	C₂³×C₂₉	—	4	1	no	—
246	C₂³×C₂₉	—	4	1	no	—
247	C₂³×C₂₉	—	4	1	no	—
248	C₂³×C₂₉	—	4	1	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	C₄×D₄	1	2	yes	—
255	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
256	D₄×C₂₉	—	2	2	no	—
257	D₄×C₂₉	—	2	2	no	—
258	D₄×C₂₉	—	2	2	no	—
259	D₄×C₂₉	—	2	2	no	—
260	D₄×C₂₉	—	4	8	no	—
261	D₄×C₂₉	—	4	1	no	—
262	D₄×C₂₉	—	4	1	no	—
263	D₄×C₂₉	—	4	1	no	—
264	D₄×C₂₉	—	4	1	no	—
265	D₄×C₂₉	—	8	4	no	—
266	C₂×C₄×C₂₉	—	2	1	no	—
267	C₂×C₄×C₂₉	—	2	1	no	—
268	C₂×C₄×C₂₉	—	2	1	no	—
269	C₂×C₄×C₂₉	—	2	1	no	—
270	C₂×C₄×C₂₉	—	2	2	no	—
271	C₂×C₄×C₂₉	—	2	2	no	—
272	C₂×C₄×C₂₉	—	2	2	no	—
273	C₂×C₄×C₂₉	—	2	2	no	—
274	C₂×C₄×C₂₉	—	2	2	no	—
275	C₂×C₄×C₂₉	—	2	2	no	—
276	C₂×C₄×C₂₉	—	2	1	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	1	no	—
282	C₂×C₄×C₂₉	—	2	1	no	—
283	C₂×C₄×C₂₉	—	2	1	no	—
284	C₂×C₄×C₂₉	—	2	1	no	—
285	C₂×C₄×C₂₉	—	2	1	no	—
286	C₂×C₄×C₂₉	—	2	1	no	—
287	C₂×C₄×C₂₉	—	4	1	no	—
288	C₂×C₄×C₂₉	—	4	1	no	—
289	C₂×C₄×C₂₉	—	4	1	no	—
290	C₂×C₄×C₂₉	—	4	1	no	—
291	C₂×C₄×C₂₉	—	4	1	no	—
292	C₂×C₄×C₂₉	—	4	1	no	—
293	C₂×C₄×C₂₉	—	4	1	no	—
294	C₂×C₄×C₂₉	—	4	1	no	—
295	C₂×C₄×C₂₉	—	4	1	no	—
296	C₂×C₄×C₂₉	—	4	1	no	—
297	C₂×C₄×C₂₉	—	4	1	no	—
298	C₂×C₄×C₂₉	—	4	1	no	—
299	C₂×C₄×C₂₉	—	4	1	no	—
300	C₂×C₄×C₂₉	—	4	1	no	—
301	C₂×C₄×C₂₉	—	8	4	no	—
302	C₂×C₄×C₂₉	—	8	4	no	—
303	C₂×C₄×C₂₉	—	8	4	no	—
304	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
305	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
306	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
307	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
310	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
311	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
312	C₈×C₂₉	—	2	2	no	—
313	C₈×C₂₉	—	4	1	no	—
314	C₈×C₂₉	—	4	1	no	—
315	C₈×C₂₉	C₄×D₄	1	4	yes	complemented
316	C₂×#469	C₂×C₂₉	1	1	yes	characteristic
317	C₂×#442	C₂×C₂₉	1	1	yes	characteristic, complemented
318	C₂×#428	C₂×C₂₉	1	1	yes	characteristic, complemented
319	#2363	C₂×C₂₉	1	1	yes	characteristic, complemented
320	#2361	C₂×C₂₉	1	1	yes	characteristic, complemented
321	#1970	C₂×C₂₉	1	1	yes	characteristic, complemented
322	#1944	C₂×C₂₉	1	1	yes	characteristic, complemented
323	#1926	C₂×C₂₉	1	1	yes	characteristic, complemented
324	#1925	C₂×C₂₉	1	1	yes	characteristic, complemented
325	#1875	C₂×C₂₉	1	1	yes	characteristic, complemented
326	#1874	C₂×C₂₉	1	1	yes	characteristic, complemented
327	#1864	C₂×C₂₉	1	1	yes	characteristic, complemented
328	#1862	C₂×C₂₉	1	1	yes	characteristic, complemented
329	C₄×#106	C₂×C₂₉	1	1	yes	characteristic, complemented
330	#1753	C₂×C₂₉	1	1	yes	characteristic, complemented
331	C₂²×C₂₉	—	2	2	no	—
332	C₂²×C₂₉	—	2	2	no	—
333	C₂²×C₂₉	—	2	2	no	—
334	C₂²×C₂₉	—	4	1	no	—
335	C₂²×C₂₉	—	4	1	no	—
336	C₂²×C₂₉	—	4	1	no	—
337	C₂²×C₂₉	—	4	1	no	—
338	C₂²×C₂₉	—	4	2	no	—
339	C₂²×C₂₉	—	4	2	no	—
340	C₂²×C₂₉	—	4	2	no	—
341	C₂²×C₂₉	—	4	2	no	—
342	C₂²×C₂₉	—	4	2	no	—
343	C₂²×C₂₉	—	4	2	no	—
344	C₂²×C₂₉	—	8	1	no	—
345	C₂²×C₂₉	—	8	1	no	—
346	C₂²×C₂₉	—	8	1	no	—
347	C₂²×C₂₉	—	8	1	no	—
348	C₂²×C₂₉	—	8	1	no	—
349	C₂²×C₂₉	—	8	1	no	—
350	C₂²×C₂₉	—	8	1	no	—
351	C₂²×C₂₉	—	8	1	no	—
352	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
353	C₂²×C₂₉	D₄²	1	1	yes	characteristic
354	C₂²×C₂₉	#547	1	1	yes	characteristic
355	C₂²×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
356	C₂²×C₂₉	#575	1	1	yes	characteristic
357	C₂²×C₂₉	#576	1	1	yes	characteristic
358	C₂²×C₂₉	#577	1	1	yes	characteristic
359	C₄×C₂₉	—	2	2	no	—
360	C₄×C₂₉	—	2	2	no	—
361	C₄×C₂₉	—	4	1	no	—
362	C₄×C₂₉	—	4	2	no	—
363	C₄×C₂₉	—	4	2	no	—
364	C₄×C₂₉	—	4	1	no	—
365	C₄×C₂₉	—	4	2	no	—
366	C₄×C₂₉	—	4	1	no	—
367	C₄×C₂₉	—	4	2	no	—
368	C₄×C₂₉	—	8	1	no	—
369	C₄×C₂₉	—	8	1	no	—
370	C₄×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
371	C₄×C₂₉	#520	1	1	yes	characteristic
372	C₄×C₂₉	#548	1	1	yes	characteristic
373	C₄×C₂₉	#553	1	1	yes	characteristic
374	C₂²×D₈	C₂²×C₂₉	1	1	yes	characteristic
375	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
376	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic
377	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic
378	C₂×C₄×D₄	—	2	1	no	—
379	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
380	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
381	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
382	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
383	#469	C₄×C₂₉	1	8	yes	complemented
384	#442	—	2	4	no	—
385	#428	—	2	4	no	—
386	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
387	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
388	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
389	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
390	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
391	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
392	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
393	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
394	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
395	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
396	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
397	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
398	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
399	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
400	#390	—	2	1	no	—
401	#390	C₂²×C₂₉	1	1	yes	characteristic
402	#390	C₂²×C₂₉	1	1	yes	characteristic
403	#389	C₂²×C₂₉	1	1	yes	characteristic
404	#389	C₂²×C₂₉	1	1	yes	characteristic
405	#388	—	2	1	no	—
406	#388	—	2	1	no	—
407	#386	—	2	1	no	—
408	#386	—	2	1	no	—
409	#385	—	2	1	no	—
410	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
411	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
412	C₄×C₂²⋊C₄	—	2	1	no	—
413	C₄×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
414	#340	C₂²×C₂₉	1	1	yes	characteristic
415	#340	C₂²×C₂₉	1	1	yes	characteristic
416	#340	C₂²×C₂₉	1	1	yes	characteristic
417	#340	C₂²×C₂₉	1	1	yes	characteristic
418	#336	C₂²×C₂₉	1	1	yes	characteristic
419	#336	C₂²×C₂₉	1	1	yes	characteristic
420	C₂×C₂₉	—	4	2	no	—
421	C₂×C₂₉	—	8	2	no	—
422	C₂×C₂₉	—	8	2	no	—
423	C₂×C₂₉	#2361	1	1	yes	characteristic
424	C₂×C₂₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
425	C₂×C₂₉	#2946	1	1	yes	characteristic
426	C₂×C₂₉	#3274	1	1	yes	characteristic
427	C₂×C₂₉	#3275	1	1	yes	characteristic
428	C₂×C₂₉	#3345	1	1	yes	characteristic
429	C₂×C₂₉	#3347	1	1	yes	characteristic
430	C₂²×D₄	—	2	1	no	—
431	C₂²×D₄	—	2	1	no	—
432	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
433	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
434	C₂³×C₄	—	2	1	no	—
435	C₂³×C₄	—	2	1	no	—
436	C₂³×C₄	—	2	1	no	—
437	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
438	C₂×D₈	—	2	2	no	—
439	C₂×D₈	—	2	2	no	—
440	C₂×D₈	C₂×C₄×C₂₉	1	4	yes	complemented
441	C₂×M₁₆	—	2	2	no	—
442	C₂×M₁₆	—	2	2	no	—
443	C₂×M₁₆	C₂×C₄×C₂₉	1	4	yes	complemented
444	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
445	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
446	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
447	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
448	#121	—	2	2	no	—
449	#121	—	2	2	no	—
450	#121	C₂×C₄×C₂₉	1	4	yes	complemented
451	#121	C₂×C₄×C₂₉	1	4	yes	complemented
452	C₄×D₄	—	2	2	no	—
453	C₄×D₄	—	2	2	no	—
454	C₄×D₄	—	4	1	no	—
455	C₄×D₄	—	4	1	no	—
456	C₄×D₄	—	4	4	no	—
457	#117	—	2	2	no	—
458	#117	—	4	1	no	—
459	C₂×C₄⋊C₄	—	2	2	no	—
460	C₂×C₄⋊C₄	—	2	1	no	—
461	C₂×C₄⋊C₄	—	2	1	no	—
462	C₂×C₄⋊C₄	—	2	1	no	—
463	C₂×C₄⋊C₄	—	4	1	no	—
464	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	—	2	1	no	—
471	C₂×C₂²⋊C₄	—	2	1	no	—
472	C₂×C₂²⋊C₄	—	2	1	no	—
473	C₂×C₂²⋊C₄	—	2	1	no	—
474	C₂×C₂²⋊C₄	—	2	1	no	—
475	C₂×C₂²⋊C₄	—	2	1	no	—
476	C₂×C₂²⋊C₄	—	2	1	no	—
477	C₂×C₂²⋊C₄	—	2	1	no	—
478	C₂×C₂²⋊C₄	—	2	1	no	—
479	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
480	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
481	C₂×C₄²	—	2	1	no	—
482	C₂×C₄²	—	2	1	no	—
483	C₂×C₄²	—	2	1	no	—
484	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
485	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
486	#107	—	2	2	no	—
487	#107	—	2	2	no	—
488	#106	—	2	2	no	—
489	#106	C₂×C₄×C₂₉	1	4	yes	complemented
490	#106	D₄×C₂₉	1	4	yes	complemented
491	#102	—	2	2	no	—
492	#102	—	2	2	no	—
493	#102	—	4	1	no	—
494	#102	—	4	1	no	—
495	#102	C₂×C₄×C₂₉	1	4	yes	complemented
496	#102	C₂×C₄×C₂₉	1	4	yes	complemented
497	C₂²⋊C₈	—	2	2	no	—
498	#97	—	2	2	no	—
499	C₄×C₈	—	2	2	no	—
500	#95	—	2	1	no	—
501	#95	—	2	1	no	—
502	#95	—	2	1	no	—
503	#95	—	2	1	no	—
504	#95	D₄×C₂₉	1	1	yes	characteristic
505	#95	D₄×C₂₉	1	1	yes	characteristic
506	C₂₉	#23039	1	1	yes	characteristic, direct product factor, Sylow
507	C₂⁴	—	2	1	no	—
508	C₂⁴	—	2	1	no	—
509	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
510	C₂×D₄	—	2	4	no	—
511	C₂×D₄	—	2	4	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	4	2	no	—
523	C₂×D₄	—	4	2	no	—
524	C₂×D₄	—	8	1	no	—
525	C₂×D₄	—	8	1	no	—
526	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
527	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	4	2	no	—
539	C₂²×C₄	—	4	2	no	—
540	C₂²×C₄	—	4	2	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	4	2	no	—
544	C₂²×C₄	—	8	1	no	—
545	C₂²×C₄	—	8	1	no	—
546	C₂²×C₄	—	8	1	no	—
547	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
548	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
549	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
550	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
551	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
552	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
553	C₂²×C₄	#41×C₂₉	1	2	yes	—
554	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
555	D₈	—	2	8	no	—
556	M₁₆	—	2	8	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
566	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
567	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
568	C₂×C₈	#41×C₂₉	1	2	yes	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	4	2	no	—
578	C₄⋊C₄	—	4	2	no	—
579	C₄⋊C₄	—	8	1	no	—
580	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
581	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
582	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
583	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	2	no	—
587	C₂²⋊C₄	—	4	1	no	—
588	C₂²⋊C₄	—	4	2	no	—
589	C₂²⋊C₄	—	4	2	no	—
590	C₂²⋊C₄	—	4	2	no	—
591	C₂²⋊C₄	—	4	2	no	—
592	C₂²⋊C₄	—	4	2	no	—
593	C₂²⋊C₄	—	8	1	no	—
594	C₂²⋊C₄	—	8	1	no	—
595	C₄²	—	2	1	no	—
596	C₄²	—	2	1	no	—
597	C₄²	—	2	1	no	—
598	C₄²	—	2	1	no	—
599	C₄²	—	4	2	no	—
600	C₄²	—	4	2	no	—
601	C₄²	—	8	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	1	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	1	no	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	2	no	—
610	C₂³	—	4	1	no	—
611	C₂³	—	4	1	no	—
612	C₂³	—	4	1	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	4	1	no	—
616	C₂³	—	4	1	no	—
617	C₂³	—	4	1	no	—
618	C₂³	—	4	1	no	—
619	C₂³	—	4	1	no	—
620	C₂³	—	4	1	no	—
621	C₂³	—	4	1	no	—
622	C₂³	C₄×D₄×C₂₉	1	2	yes	—
623	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
624	D₄	—	2	2	no	—
625	D₄	—	2	2	no	—
626	D₄	—	2	2	no	—
627	D₄	—	2	2	no	—
628	D₄	—	4	8	no	—
629	D₄	—	4	1	no	—
630	D₄	—	4	1	no	—
631	D₄	—	4	1	no	—
632	D₄	—	4	1	no	—
633	D₄	—	8	4	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	8	4	no	—
670	C₂×C₄	—	8	4	no	—
671	C₂×C₄	—	8	4	no	—
672	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
673	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
674	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
675	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
676	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
677	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
678	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
679	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
680	C₈	—	2	2	no	—
681	C₈	—	4	1	no	—
682	C₈	—	4	1	no	—
683	C₈	C₄×D₄×C₂₉	1	4	yes	complemented
684	C₂²	—	2	2	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	4	1	no	—
690	C₂²	—	4	1	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	8	1	no	—
698	C₂²	—	8	1	no	—
699	C₂²	—	8	1	no	—
700	C₂²	—	8	1	no	—
701	C₂²	—	8	1	no	—
702	C₂²	—	8	1	no	—
703	C₂²	—	8	1	no	—
704	C₂²	—	8	1	no	—
705	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
706	C₂²	D₄²×C₂₉	1	1	yes	characteristic
707	C₂²	C₂₉×#547	1	1	yes	characteristic
708	C₂²	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
709	C₂²	C₂₉×#575	1	1	yes	characteristic
710	C₂²	C₂₉×#576	1	1	yes	characteristic
711	C₂²	C₂₉×#577	1	1	yes	characteristic
712	C₄	—	2	2	no	—
713	C₄	—	2	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	1	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	1	no	—
721	C₄	—	8	1	no	—
722	C₄	—	8	1	no	—
723	C₄	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
724	C₄	C₂₉×#520	1	1	yes	characteristic
725	C₄	C₂₉×#548	1	1	yes	characteristic
726	C₄	C₂₉×#553	1	1	yes	characteristic
727	C₂	—	4	2	no	—
728	C₂	—	8	2	no	—
729	C₂	—	8	2	no	—
730	C₂	C₂₉×#2361	1	1	yes	characteristic
731	C₂	C₄×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
732	C₂	C₂₉×#2946	1	1	yes	characteristic
733	C₂	C₂₉×#3274	1	1	yes	characteristic
734	C₂	C₂₉×#3275	1	1	yes	characteristic
735	C₂	C₂₉×#3345	1	1	yes	characteristic
736	C₂	C₂₉×#3347	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	C₂×C₂₉×#469	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₄×C₂²⋊C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₉×#442	C₂	semidirect
3. C₂×C₂₉×#428	C₂	semidirect
4. C₂₉×#2363	C₂	semidirect
5. C₂₉×#2361	C₂	semidirect
6. C₂₉×#1970	C₂	semidirect
7. C₂₉×#1944	C₂	semidirect
8. C₂₉×#1926	C₂	semidirect
9. C₂₉×#1925	C₂	semidirect
10. C₂₉×#1875	C₂	semidirect
11. C₂₉×#1874	C₂	semidirect
12. C₂₉×#1864	C₂	semidirect
13. C₂₉×#1862	C₂	semidirect
14. C₄×C₂₉×#106	C₂	semidirect
15. C₂₉×#1753	C₂	semidirect
25. C₂₉×#469	C₄	semidirect
72. C₂×D₈×C₂₉	C₂×C₄	semidirect
75. C₂×M₁₆×C₂₉	C₂×C₄	semidirect
82. C₂₉×#121	C₂×C₄	semidirect
83. C₂₉×#121	C₂×C₄	semidirect
121. C₂₉×#106	C₂×C₄	semidirect
122. C₂₉×#106	D₄	semidirect
127. C₂₉×#102	C₂×C₄	semidirect
128. C₂₉×#102	C₂×C₄	semidirect
233. #23039	C₂₉	direct (N × H)
315. C₈×C₂₉	C₄×D₄	semidirect
317. C₂×#442	C₂×C₂₉	semidirect
318. C₂×#428	C₂×C₂₉	semidirect
319. #2363	C₂×C₂₉	semidirect
320. #2361	C₂×C₂₉	semidirect
321. #1970	C₂×C₂₉	semidirect
322. #1944	C₂×C₂₉	semidirect
323. #1926	C₂×C₂₉	semidirect
324. #1925	C₂×C₂₉	semidirect
325. #1875	C₂×C₂₉	semidirect
326. #1874	C₂×C₂₉	semidirect
327. #1864	C₂×C₂₉	semidirect
328. #1862	C₂×C₂₉	semidirect
329. C₄×#106	C₂×C₂₉	semidirect
330. #1753	C₂×C₂₉	semidirect
383. #469	C₄×C₂₉	semidirect
440. C₂×D₈	C₂×C₄×C₂₉	semidirect
443. C₂×M₁₆	C₂×C₄×C₂₉	semidirect
450. #121	C₂×C₄×C₂₉	semidirect
451. #121	C₂×C₄×C₂₉	semidirect
489. #106	C₂×C₄×C₂₉	semidirect
490. #106	D₄×C₂₉	semidirect
495. #102	C₂×C₄×C₂₉	semidirect
496. #102	C₂×C₄×C₂₉	semidirect
506. C₂₉	#23039	direct (N × H)
683. C₈	C₄×D₄×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#469	2
C₂×C₂₉×#442	2
C₂×C₂₉×#428	2
C₂₉×#2363	2
C₂₉×#2361	2
C₂₉×#1970	2
C₂₉×#1944	2
C₂₉×#1926	2
C₂₉×#1925	2
C₂₉×#1875	2
C₂₉×#1874	2
C₂₉×#1864	2
C₂₉×#1862	2
C₄×C₂₉×#106	2
C₂₉×#1753	2
#23039	29

Subgroups — C29×#23039 #20317939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#23039 #20317939