Subgroups — C₂₉×#21122 #20316022

Order 7424.

1042 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#442	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2293	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×D₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#1926	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1925	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1920	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1919	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1879	C₂	1	1	yes	maximal, characteristic
9	C₂₉×#1879	C₂	1	1	yes	maximal, characteristic
10	C₂₉×#1864	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1862	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1776	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1762	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1762	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1745	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₂₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#117	—	2	1	no	—
22	C₂²×C₄²×C₂₉	—	2	1	no	—
23	C₂₉×#442	C₄	1	8	yes	complemented
24	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
25	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
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×#97	C₂²	1	1	yes	characteristic
34	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
35	C₂₉×#390	C₂²	1	1	yes	characteristic
36	C₂₉×#390	C₂²	1	1	yes	characteristic
37	C₂₉×#389	C₂²	1	1	yes	characteristic
38	C₂₉×#389	C₂²	1	1	yes	characteristic
39	C₂₉×#388	—	2	1	no	—
40	C₂₉×#388	—	2	1	no	—
41	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
45	C₄×C₂²⋊C₄×C₂₉	—	2	1	no	—
46	C₄×C₂²⋊C₄×C₂₉	—	2	1	no	—
47	C₄×C₂²⋊C₄×C₂₉	—	2	1	no	—
48	C₄×C₂²⋊C₄×C₂₉	—	2	1	no	—
49	C₄³×C₂₉	C₂²	1	1	yes	characteristic
50	C₂₉×#340	C₂²	1	1	yes	characteristic
51	C₂₉×#340	C₂²	1	1	yes	characteristic
52	C₂₉×#340	C₂²	1	1	yes	characteristic
53	C₂₉×#340	C₂²	1	1	yes	characteristic
54	C₂₉×#340	C₂²	1	1	yes	characteristic
55	C₂₉×#340	C₂²	1	1	yes	characteristic
56	C₂₉×#336	C₂²	1	1	yes	characteristic
57	C₂₉×#336	C₂²	1	1	yes	characteristic
58	C₂₉×#336	C₂²	1	1	yes	characteristic
59	C₂₉×#336	C₂²	1	1	yes	characteristic
60	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₂₉	—	2	1	no	—
63	C₂³×C₄×C₂₉	—	2	1	no	—
64	C₂³×C₄×C₂₉	—	2	1	no	—
65	C₂³×C₄×C₂₉	—	2	1	no	—
66	C₂×D₈×C₂₉	—	2	2	no	—
67	C₂×D₈×C₂₉	—	2	2	no	—
68	C₂×D₈×C₂₉	C₂×C₄	1	4	yes	—
69	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
73	C₄×D₄×C₂₉	—	2	2	no	—
74	C₄×D₄×C₂₉	—	2	2	no	—
75	C₄×D₄×C₂₉	—	2	2	no	—
76	C₄×D₄×C₂₉	—	2	2	no	—
77	C₄×D₄×C₂₉	—	2	2	no	—
78	C₄×D₄×C₂₉	—	2	2	no	—
79	C₄×D₄×C₂₉	C₂×C₄	1	4	yes	—
80	C₄×D₄×C₂₉	C₂×C₄	1	4	yes	complemented
81	C₂₉×#117	—	4	4	no	—
82	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
98	C₂×C₄²×C₂₉	—	2	1	no	—
99	C₂×C₄²×C₂₉	—	2	1	no	—
100	C₂×C₄²×C₂₉	—	2	1	no	—
101	C₂×C₄²×C₂₉	—	2	1	no	—
102	C₂×C₄²×C₂₉	—	4	4	no	—
103	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
110	C₂₉×#107	—	2	2	no	—
111	C₂₉×#106	—	2	2	no	—
112	C₂₉×#106	C₂×C₄	1	4	yes	complemented
113	C₂₉×#102	—	2	2	no	—
114	C₂₉×#102	—	2	2	no	—
115	C₂₉×#102	—	2	2	no	—
116	C₂₉×#102	—	2	2	no	—
117	C₂₉×#102	C₂×C₄	1	4	yes	—
118	C₂₉×#102	C₂×C₄	1	4	yes	complemented
119	C₂₉×#97	—	2	2	no	—
120	C₂₉×#97	C₂×C₄	1	4	yes	complemented
121	C₂₉×#95	—	2	1	no	—
122	C₂₉×#95	—	2	1	no	—
123	C₂₉×#95	—	2	1	no	—
124	C₂₉×#95	—	2	1	no	—
125	C₂₉×#95	—	2	1	no	—
126	C₂₉×#95	—	2	1	no	—
127	C₂⁴×C₂₉	—	2	1	no	—
128	C₂⁴×C₂₉	—	2	1	no	—
129	C₂×D₄×C₂₉	—	2	1	no	—
130	C₂×D₄×C₂₉	—	2	1	no	—
131	C₂×D₄×C₂₉	—	2	1	no	—
132	C₂×D₄×C₂₉	—	2	1	no	—
133	C₂×D₄×C₂₉	—	2	1	no	—
134	C₂×D₄×C₂₉	—	2	1	no	—
135	C₂×D₄×C₂₉	—	2	1	no	—
136	C₂×D₄×C₂₉	—	2	1	no	—
137	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
138	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
139	C₂×D₄×C₂₉	#41	1	2	yes	—
140	C₂×D₄×C₂₉	#41	1	2	yes	—
141	C₂²×C₄×C₂₉	—	2	4	no	—
142	C₂²×C₄×C₂₉	—	2	4	no	—
143	C₂²×C₄×C₂₉	—	2	1	no	—
144	C₂²×C₄×C₂₉	—	2	1	no	—
145	C₂²×C₄×C₂₉	—	2	1	no	—
146	C₂²×C₄×C₂₉	—	2	1	no	—
147	C₂²×C₄×C₂₉	—	2	4	no	—
148	C₂²×C₄×C₂₉	—	2	4	no	—
149	C₂²×C₄×C₂₉	—	2	1	no	—
150	C₂²×C₄×C₂₉	—	2	1	no	—
151	C₂²×C₄×C₂₉	—	4	2	no	—
152	C₂²×C₄×C₂₉	—	4	2	no	—
153	C₂²×C₄×C₂₉	—	4	2	no	—
154	C₂²×C₄×C₂₉	—	4	2	no	—
155	C₂²×C₄×C₂₉	—	4	2	no	—
156	C₂²×C₄×C₂₉	—	4	2	no	—
157	C₂²×C₄×C₂₉	—	4	2	no	—
158	C₂²×C₄×C₂₉	—	4	2	no	—
159	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
166	D₈×C₂₉	—	2	8	no	—
167	C₂×C₈×C₂₉	—	2	1	no	—
168	C₂×C₈×C₂₉	—	2	1	no	—
169	C₂×C₈×C₂₉	—	2	1	no	—
170	C₂×C₈×C₂₉	—	2	1	no	—
171	C₂×C₈×C₂₉	—	2	1	no	—
172	C₂×C₈×C₂₉	—	2	1	no	—
173	C₂×C₈×C₂₉	—	2	1	no	—
174	C₂×C₈×C₂₉	—	2	1	no	—
175	C₂×C₈×C₂₉	—	2	1	no	—
176	C₂×C₈×C₂₉	—	2	1	no	—
177	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
178	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
179	C₄⋊C₄×C₂₉	—	2	1	no	—
180	C₄⋊C₄×C₂₉	—	2	1	no	—
181	C₄⋊C₄×C₂₉	—	2	1	no	—
182	C₄⋊C₄×C₂₉	—	2	1	no	—
183	C₄⋊C₄×C₂₉	—	2	1	no	—
184	C₄⋊C₄×C₂₉	—	2	1	no	—
185	C₄⋊C₄×C₂₉	—	2	1	no	—
186	C₄⋊C₄×C₂₉	—	2	1	no	—
187	C₄⋊C₄×C₂₉	—	4	2	no	—
188	C₄⋊C₄×C₂₉	—	4	2	no	—
189	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
190	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
191	C₄⋊C₄×C₂₉	#41	1	2	yes	—
192	C₄⋊C₄×C₂₉	#41	1	2	yes	—
193	C₂²⋊C₄×C₂₉	—	2	4	no	—
194	C₂²⋊C₄×C₂₉	—	2	4	no	—
195	C₂²⋊C₄×C₂₉	—	2	4	no	—
196	C₂²⋊C₄×C₂₉	—	2	4	no	—
197	C₂²⋊C₄×C₂₉	—	4	2	no	—
198	C₂²⋊C₄×C₂₉	—	4	2	no	—
199	C₂²⋊C₄×C₂₉	—	4	2	no	—
200	C₂²⋊C₄×C₂₉	—	4	2	no	—
201	C₄²×C₂₉	—	2	2	no	—
202	C₄²×C₂₉	—	2	2	no	—
203	C₄²×C₂₉	—	2	1	no	—
204	C₄²×C₂₉	—	2	1	no	—
205	C₄²×C₂₉	—	2	1	no	—
206	C₄²×C₂₉	—	2	1	no	—
207	C₄²×C₂₉	—	4	1	no	—
208	C₄²×C₂₉	—	4	1	no	—
209	C₄²×C₂₉	—	4	2	no	—
210	C₄²×C₂₉	—	4	2	no	—
211	C₄²×C₂₉	—	4	2	no	—
212	C₄²×C₂₉	—	4	2	no	—
213	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
214	C₄²×C₂₉	#41	1	2	yes	—
215	#21122	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂³×C₂₉	—	2	2	no	—
217	C₂³×C₂₉	—	2	2	no	—
218	C₂³×C₂₉	—	2	2	no	—
219	C₂³×C₂₉	—	2	2	no	—
220	C₂³×C₂₉	—	4	1	no	—
221	C₂³×C₂₉	—	4	1	no	—
222	C₂³×C₂₉	—	4	1	no	—
223	C₂³×C₂₉	—	4	1	no	—
224	C₂³×C₂₉	—	4	1	no	—
225	C₂³×C₂₉	—	4	1	no	—
226	C₂³×C₂₉	—	4	1	no	—
227	C₂³×C₂₉	—	4	1	no	—
228	C₂³×C₂₉	—	4	1	no	—
229	C₂³×C₂₉	—	4	1	no	—
230	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
231	D₄×C₂₉	—	2	2	no	—
232	D₄×C₂₉	—	2	2	no	—
233	D₄×C₂₉	—	2	2	no	—
234	D₄×C₂₉	—	2	2	no	—
235	D₄×C₂₉	—	2	2	no	—
236	D₄×C₂₉	—	4	1	no	—
237	D₄×C₂₉	—	4	1	no	—
238	D₄×C₂₉	#117	1	4	yes	complemented
239	C₂×C₄×C₂₉	—	2	1	no	—
240	C₂×C₄×C₂₉	—	2	1	no	—
241	C₂×C₄×C₂₉	—	2	1	no	—
242	C₂×C₄×C₂₉	—	2	1	no	—
243	C₂×C₄×C₂₉	—	2	1	no	—
244	C₂×C₄×C₂₉	—	2	1	no	—
245	C₂×C₄×C₂₉	—	2	1	no	—
246	C₂×C₄×C₂₉	—	2	1	no	—
247	C₂×C₄×C₂₉	—	2	2	no	—
248	C₂×C₄×C₂₉	—	2	2	no	—
249	C₂×C₄×C₂₉	—	2	1	no	—
250	C₂×C₄×C₂₉	—	2	1	no	—
251	C₂×C₄×C₂₉	—	2	2	no	—
252	C₂×C₄×C₂₉	—	2	2	no	—
253	C₂×C₄×C₂₉	—	2	1	no	—
254	C₂×C₄×C₂₉	—	2	1	no	—
255	C₂×C₄×C₂₉	—	2	1	no	—
256	C₂×C₄×C₂₉	—	2	1	no	—
257	C₂×C₄×C₂₉	—	4	8	no	—
258	C₂×C₄×C₂₉	—	4	8	no	—
259	C₂×C₄×C₂₉	—	4	8	no	—
260	C₂×C₄×C₂₉	—	4	8	no	—
261	C₂×C₄×C₂₉	—	4	1	no	—
262	C₂×C₄×C₂₉	—	4	1	no	—
263	C₂×C₄×C₂₉	—	4	1	no	—
264	C₂×C₄×C₂₉	—	4	1	no	—
265	C₂×C₄×C₂₉	—	4	1	no	—
266	C₂×C₄×C₂₉	—	4	1	no	—
267	C₂×C₄×C₂₉	—	4	1	no	—
268	C₂×C₄×C₂₉	—	4	1	no	—
269	C₂×C₄×C₂₉	—	4	1	no	—
270	C₂×C₄×C₂₉	—	4	1	no	—
271	C₂×C₄×C₂₉	—	4	1	no	—
272	C₂×C₄×C₂₉	—	4	1	no	—
273	C₂×C₄×C₂₉	—	4	1	no	—
274	C₂×C₄×C₂₉	—	4	1	no	—
275	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
276	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
277	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
278	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
279	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
280	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
281	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
282	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
283	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
285	C₈×C₂₉	—	2	2	no	—
286	C₈×C₂₉	—	2	2	no	—
287	C₈×C₂₉	—	4	1	no	—
288	C₈×C₂₉	—	4	1	no	—
289	C₂×#442	C₂×C₂₉	1	1	yes	characteristic
290	#2293	C₂×C₂₉	1	1	yes	characteristic, complemented
291	C₄²×D₄	C₂×C₂₉	1	1	yes	characteristic, complemented
292	#1926	C₂×C₂₉	1	1	yes	characteristic, complemented
293	#1925	C₂×C₂₉	1	1	yes	characteristic, complemented
294	#1920	C₂×C₂₉	1	1	yes	characteristic, complemented
295	#1919	C₂×C₂₉	1	1	yes	characteristic, complemented
296	#1879	C₂×C₂₉	1	1	yes	characteristic
297	#1879	C₂×C₂₉	1	1	yes	characteristic
298	#1864	C₂×C₂₉	1	1	yes	characteristic, complemented
299	#1862	C₂×C₂₉	1	1	yes	characteristic, complemented
300	#1776	C₂×C₂₉	1	1	yes	characteristic, complemented
301	#1762	C₂×C₂₉	1	1	yes	characteristic, complemented
302	#1762	C₂×C₂₉	1	1	yes	characteristic, complemented
303	#1745	C₂×C₂₉	1	1	yes	characteristic, complemented
304	C₂²×C₂₉	—	2	4	no	—
305	C₂²×C₂₉	—	4	2	no	—
306	C₂²×C₂₉	—	4	2	no	—
307	C₂²×C₂₉	—	4	2	no	—
308	C₂²×C₂₉	—	4	2	no	—
309	C₂²×C₂₉	—	4	2	no	—
310	C₂²×C₂₉	—	4	2	no	—
311	C₂²×C₂₉	—	4	2	no	—
312	C₂²×C₂₉	—	4	2	no	—
313	C₂²×C₂₉	—	4	2	no	—
314	C₂²×C₂₉	—	8	1	no	—
315	C₂²×C₂₉	—	8	1	no	—
316	C₂²×C₂₉	—	8	1	no	—
317	C₂²×C₂₉	—	8	1	no	—
318	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
319	C₂²×C₂₉	#525	1	1	yes	characteristic
320	C₂²×C₂₉	#525	1	1	yes	characteristic
321	C₂²×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
322	C₂²×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
323	C₂²×C₂₉	#575	1	1	yes	characteristic
324	C₂²×C₂₉	#575	1	1	yes	characteristic
325	C₄×C₂₉	—	2	2	no	—
326	C₄×C₂₉	—	2	2	no	—
327	C₄×C₂₉	—	2	2	no	—
328	C₄×C₂₉	—	2	2	no	—
329	C₄×C₂₉	—	4	2	no	—
330	C₄×C₂₉	—	4	1	no	—
331	C₄×C₂₉	—	4	2	no	—
332	C₄×C₂₉	—	4	1	no	—
333	C₄×C₂₉	—	4	2	no	—
334	C₄×C₂₉	—	4	2	no	—
335	C₄×C₂₉	—	8	1	no	—
336	C₄×C₂₉	—	8	1	no	—
337	C₄×C₂₉	C₂×#117	1	1	yes	characteristic
338	C₄×C₂₉	C₄×#41	1	1	yes	characteristic
339	C₄×C₂₉	#529	1	1	yes	characteristic
340	C₄×C₂₉	#529	1	1	yes	characteristic
341	C₂²×D₈	C₂²×C₂₉	1	1	yes	characteristic
342	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
343	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
344	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
345	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
346	C₂×#117	—	2	1	no	—
347	C₂²×C₄²	—	2	1	no	—
348	#442	C₄×C₂₉	1	8	yes	complemented
349	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
350	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
351	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
352	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
353	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
354	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
355	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
356	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
357	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
358	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
359	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
360	#390	C₂²×C₂₉	1	1	yes	characteristic
361	#390	C₂²×C₂₉	1	1	yes	characteristic
362	#389	C₂²×C₂₉	1	1	yes	characteristic
363	#389	C₂²×C₂₉	1	1	yes	characteristic
364	#388	—	2	1	no	—
365	#388	—	2	1	no	—
366	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
367	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
368	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
369	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
370	C₄×C₂²⋊C₄	—	2	1	no	—
371	C₄×C₂²⋊C₄	—	2	1	no	—
372	C₄×C₂²⋊C₄	—	2	1	no	—
373	C₄×C₂²⋊C₄	—	2	1	no	—
374	C₄³	C₂²×C₂₉	1	1	yes	characteristic
375	#340	C₂²×C₂₉	1	1	yes	characteristic
376	#340	C₂²×C₂₉	1	1	yes	characteristic
377	#340	C₂²×C₂₉	1	1	yes	characteristic
378	#340	C₂²×C₂₉	1	1	yes	characteristic
379	#340	C₂²×C₂₉	1	1	yes	characteristic
380	#340	C₂²×C₂₉	1	1	yes	characteristic
381	#336	C₂²×C₂₉	1	1	yes	characteristic
382	#336	C₂²×C₂₉	1	1	yes	characteristic
383	#336	C₂²×C₂₉	1	1	yes	characteristic
384	#336	C₂²×C₂₉	1	1	yes	characteristic
385	C₂×C₂₉	—	4	4	no	—
386	C₂×C₂₉	—	8	2	no	—
387	C₂×C₂₉	#2290	1	1	yes	characteristic
388	C₂×C₂₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
389	C₂×C₂₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
390	C₂×C₂₉	#3109	1	1	yes	characteristic
391	C₂×C₂₉	#3111	1	1	yes	characteristic
392	C₂×C₂₉	#3114	1	1	yes	characteristic
393	C₂×C₂₉	#3115	1	1	yes	characteristic
394	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
395	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
396	C₂³×C₄	—	2	1	no	—
397	C₂³×C₄	—	2	1	no	—
398	C₂³×C₄	—	2	1	no	—
399	C₂³×C₄	—	2	1	no	—
400	C₂×D₈	—	2	2	no	—
401	C₂×D₈	—	2	2	no	—
402	C₂×D₈	C₂×C₄×C₂₉	1	4	yes	—
403	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
404	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
405	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
406	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	—	2	2	no	—
411	C₄×D₄	—	2	2	no	—
412	C₄×D₄	—	2	2	no	—
413	C₄×D₄	C₂×C₄×C₂₉	1	4	yes	—
414	C₄×D₄	C₂×C₄×C₂₉	1	4	yes	complemented
415	#117	—	4	4	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₄²	—	2	1	no	—
433	C₂×C₄²	—	2	1	no	—
434	C₂×C₄²	—	2	1	no	—
435	C₂×C₄²	—	2	1	no	—
436	C₂×C₄²	—	4	4	no	—
437	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
438	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
439	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
440	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
442	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
444	#107	—	2	2	no	—
445	#106	—	2	2	no	—
446	#106	C₂×C₄×C₂₉	1	4	yes	complemented
447	#102	—	2	2	no	—
448	#102	—	2	2	no	—
449	#102	—	2	2	no	—
450	#102	—	2	2	no	—
451	#102	C₂×C₄×C₂₉	1	4	yes	—
452	#102	C₂×C₄×C₂₉	1	4	yes	complemented
453	#97	—	2	2	no	—
454	#97	C₂×C₄×C₂₉	1	4	yes	complemented
455	#95	—	2	1	no	—
456	#95	—	2	1	no	—
457	#95	—	2	1	no	—
458	#95	—	2	1	no	—
459	#95	—	2	1	no	—
460	#95	—	2	1	no	—
461	C₂₉	#21122	1	1	yes	characteristic, direct product factor, Sylow
462	C₂⁴	—	2	1	no	—
463	C₂⁴	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
473	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
474	C₂×D₄	#41×C₂₉	1	2	yes	—
475	C₂×D₄	#41×C₂₉	1	2	yes	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	4	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	4	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	4	2	no	—
487	C₂²×C₄	—	4	2	no	—
488	C₂²×C₄	—	4	2	no	—
489	C₂²×C₄	—	4	2	no	—
490	C₂²×C₄	—	4	2	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	—	4	2	no	—
494	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
496	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
500	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
501	D₈	—	2	8	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
513	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	4	2	no	—
523	C₄⋊C₄	—	4	2	no	—
524	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
525	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
526	C₄⋊C₄	#41×C₂₉	1	2	yes	—
527	C₄⋊C₄	#41×C₂₉	1	2	yes	—
528	C₂²⋊C₄	—	2	4	no	—
529	C₂²⋊C₄	—	2	4	no	—
530	C₂²⋊C₄	—	2	4	no	—
531	C₂²⋊C₄	—	2	4	no	—
532	C₂²⋊C₄	—	4	2	no	—
533	C₂²⋊C₄	—	4	2	no	—
534	C₂²⋊C₄	—	4	2	no	—
535	C₂²⋊C₄	—	4	2	no	—
536	C₄²	—	2	2	no	—
537	C₄²	—	2	2	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	4	1	no	—
543	C₄²	—	4	1	no	—
544	C₄²	—	4	2	no	—
545	C₄²	—	4	2	no	—
546	C₄²	—	4	2	no	—
547	C₄²	—	4	2	no	—
548	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
549	C₄²	#41×C₂₉	1	2	yes	—
550	C₂³	—	2	2	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	2	2	no	—
553	C₂³	—	2	2	no	—
554	C₂³	—	4	1	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	4	1	no	—
559	C₂³	—	4	1	no	—
560	C₂³	—	4	1	no	—
561	C₂³	—	4	1	no	—
562	C₂³	—	4	1	no	—
563	C₂³	—	4	1	no	—
564	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
565	D₄	—	2	2	no	—
566	D₄	—	2	2	no	—
567	D₄	—	2	2	no	—
568	D₄	—	2	2	no	—
569	D₄	—	2	2	no	—
570	D₄	—	4	1	no	—
571	D₄	—	4	1	no	—
572	D₄	C₂₉×#117	1	4	yes	complemented
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	4	8	no	—
592	C₂×C₄	—	4	8	no	—
593	C₂×C₄	—	4	8	no	—
594	C₂×C₄	—	4	8	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
610	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
611	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
612	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
613	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
614	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
615	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
616	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
617	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
618	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
619	C₈	—	2	2	no	—
620	C₈	—	2	2	no	—
621	C₈	—	4	1	no	—
622	C₈	—	4	1	no	—
623	C₂²	—	2	4	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	4	2	no	—
626	C₂²	—	4	2	no	—
627	C₂²	—	4	2	no	—
628	C₂²	—	4	2	no	—
629	C₂²	—	4	2	no	—
630	C₂²	—	4	2	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	4	2	no	—
633	C₂²	—	8	1	no	—
634	C₂²	—	8	1	no	—
635	C₂²	—	8	1	no	—
636	C₂²	—	8	1	no	—
637	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
638	C₂²	C₂₉×#525	1	1	yes	characteristic
639	C₂²	C₂₉×#525	1	1	yes	characteristic
640	C₂²	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
641	C₂²	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
642	C₂²	C₂₉×#575	1	1	yes	characteristic
643	C₂²	C₂₉×#575	1	1	yes	characteristic
644	C₄	—	2	2	no	—
645	C₄	—	2	2	no	—
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	4	2	no	—
649	C₄	—	4	2	no	—
650	C₄	—	4	2	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	2	no	—
653	C₄	—	4	1	no	—
654	C₄	—	8	1	no	—
655	C₄	—	8	1	no	—
656	C₄	C₂×C₂₉×#117	1	1	yes	characteristic
657	C₄	C₄×#41×C₂₉	1	1	yes	characteristic
658	C₄	C₂₉×#529	1	1	yes	characteristic
659	C₄	C₂₉×#529	1	1	yes	characteristic
660	C₂	—	4	4	no	—
661	C₂	—	8	2	no	—
662	C₂	C₂₉×#2290	1	1	yes	characteristic
663	C₂	C₄×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
664	C₂	C₄×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
665	C₂	C₂₉×#3109	1	1	yes	characteristic
666	C₂	C₂₉×#3111	1	1	yes	characteristic
667	C₂	C₂₉×#3114	1	1	yes	characteristic
668	C₂	C₂₉×#3115	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	C₂²×D₈×C₂₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₄³×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#2293	C₂	semidirect
3. C₄²×D₄×C₂₉	C₂	semidirect
4. C₂₉×#1926	C₂	semidirect
5. C₂₉×#1925	C₂	semidirect
6. C₂₉×#1920	C₂	semidirect
7. C₂₉×#1919	C₂	semidirect
10. C₂₉×#1864	C₂	semidirect
11. C₂₉×#1862	C₂	semidirect
12. C₂₉×#1776	C₂	semidirect
13. C₂₉×#1762	C₂	semidirect
14. C₂₉×#1762	C₂	semidirect
15. C₂₉×#1745	C₂	semidirect
23. C₂₉×#442	C₄	semidirect
80. C₄×D₄×C₂₉	C₂×C₄	semidirect
112. C₂₉×#106	C₂×C₄	semidirect
118. C₂₉×#102	C₂×C₄	semidirect
120. C₂₉×#97	C₂×C₄	semidirect
215. #21122	C₂₉	direct (N × H)
238. D₄×C₂₉	#117	semidirect
290. #2293	C₂×C₂₉	semidirect
291. C₄²×D₄	C₂×C₂₉	semidirect
292. #1926	C₂×C₂₉	semidirect
293. #1925	C₂×C₂₉	semidirect
294. #1920	C₂×C₂₉	semidirect
295. #1919	C₂×C₂₉	semidirect
298. #1864	C₂×C₂₉	semidirect
299. #1862	C₂×C₂₉	semidirect
300. #1776	C₂×C₂₉	semidirect
301. #1762	C₂×C₂₉	semidirect
302. #1762	C₂×C₂₉	semidirect
303. #1745	C₂×C₂₉	semidirect
348. #442	C₄×C₂₉	semidirect
414. C₄×D₄	C₂×C₄×C₂₉	semidirect
446. #106	C₂×C₄×C₂₉	semidirect
452. #102	C₂×C₄×C₂₉	semidirect
454. #97	C₂×C₄×C₂₉	semidirect
461. C₂₉	#21122	direct (N × H)
572. D₄	C₂₉×#117	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#442	2
C₂₉×#2293	2
C₄²×D₄×C₂₉	2
C₂₉×#1926	2
C₂₉×#1925	2
C₂₉×#1920	2
C₂₉×#1919	2
C₂₉×#1879	2
C₂₉×#1864	2
C₂₉×#1862	2
C₂₉×#1776	2
C₂₉×#1762	2
C₂₉×#1745	2
#21122	29

Subgroups — C29×#21122 #20316022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#21122 #20316022