Subgroups — C₂₉×#24935 #20319835

Order 7424.

834 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#2487	C₂	1	1	yes	maximal, characteristic
2	D₄×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2099	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2084	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2077	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2077	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1920	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1920	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1869	C₂	1	1	yes	maximal, characteristic
10	C₂₉×#1853	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1853	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1824	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1823	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1807	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₈×C₂₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₂₉	—	2	1	no	—
18	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
24	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
25	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂₉×#400	—	2	1	no	—
30	C₂₉×#399	—	2	1	no	—
31	C₂₉×#389	—	2	1	no	—
32	C₂₉×#389	C₂²	1	1	yes	characteristic
33	C₂₉×#389	C₂²	1	1	yes	characteristic
34	C₂₉×#386	—	2	1	no	—
35	C₂₉×#385	—	2	1	no	—
36	C₂₉×#385	—	2	1	no	—
37	C₂₉×#385	—	2	1	no	—
38	C₂₉×#384	C₂²	1	1	yes	characteristic
39	C₂₉×#380	C₂²	1	1	yes	characteristic
40	C₂₉×#380	C₂²	1	1	yes	characteristic
41	C₂₉×#380	C₂²	1	1	yes	characteristic
42	C₂₉×#380	C₂²	1	1	yes	characteristic
43	C₂₉×#380	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
45	C₂₉×#340	C₂²	1	1	yes	characteristic
46	C₂₉×#340	C₂²	1	1	yes	characteristic
47	C₂₉×#340	C₂²	1	1	yes	characteristic
48	C₂₉×#340	C₂²	1	1	yes	characteristic
49	C₂₉×#340	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×#340	C₂²	1	1	yes	characteristic
57	C₂₉×#336	C₂²	1	1	yes	characteristic
58	C₂₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₂₉	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₂₉	—	2	1	no	—
61	C₂³×C₄×C₂₉	—	2	1	no	—
62	C₂³×C₄×C₂₉	—	2	1	no	—
63	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₂₉	—	2	2	no	—
66	C₂²×C₈×C₂₉	—	2	2	no	—
67	C₂²×C₈×C₂₉	—	4	1	no	—
68	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
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	C₄×D₄×C₂₉	—	2	2	no	—
73	C₄×D₄×C₂₉	—	2	2	no	—
74	C₄×D₄×C₂₉	—	4	4	no	—
75	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
77	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
78	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
79	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
87	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
88	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₂₉	C₂³	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×C₂²⋊C₄×C₂₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₂₉	—	2	1	no	—
105	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
106	C₂₉×#106	—	2	2	no	—
107	C₂₉×#106	—	2	2	no	—
108	C₂₉×#106	—	4	1	no	—
109	C₂₉×#106	—	4	1	no	—
110	C₂₉×C₂²⋊C₈	—	2	2	no	—
111	C₂₉×C₂²⋊C₈	—	2	2	no	—
112	C₂₉×C₂²⋊C₈	—	4	1	no	—
113	C₂₉×#95	—	2	1	no	—
114	C₂₉×#95	—	2	1	no	—
115	C₂₉×#95	—	2	1	no	—
116	C₂₉×#95	—	2	1	no	—
117	C₂₉×#95	—	2	1	no	—
118	C₂₉×#95	—	2	1	no	—
119	C₂₉×#95	—	2	1	no	—
120	C₂₉×#95	—	2	1	no	—
121	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
122	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
123	C₂×D₄×C₂₉	—	2	2	no	—
124	C₂×D₄×C₂₉	—	2	2	no	—
125	C₂×D₄×C₂₉	SD₁₆	1	4	yes	—
126	C₂²×C₄×C₂₉	—	2	1	no	—
127	C₂²×C₄×C₂₉	—	2	1	no	—
128	C₂²×C₄×C₂₉	—	2	1	no	—
129	C₂²×C₄×C₂₉	—	2	1	no	—
130	C₂²×C₄×C₂₉	—	2	1	no	—
131	C₂²×C₄×C₂₉	—	2	1	no	—
132	C₂²×C₄×C₂₉	—	2	1	no	—
133	C₂²×C₄×C₂₉	—	2	1	no	—
134	C₂²×C₄×C₂₉	—	2	1	no	—
135	C₂²×C₄×C₂₉	—	2	1	no	—
136	C₂²×C₄×C₂₉	—	2	1	no	—
137	C₂²×C₄×C₂₉	—	2	1	no	—
138	C₂²×C₄×C₂₉	—	2	1	no	—
139	C₂²×C₄×C₂₉	—	2	1	no	—
140	C₂²×C₄×C₂₉	—	2	1	no	—
141	C₂²×C₄×C₂₉	—	2	1	no	—
142	C₂²×C₄×C₂₉	—	2	1	no	—
143	C₂²×C₄×C₂₉	—	2	1	no	—
144	C₂²×C₄×C₂₉	—	4	2	no	—
145	C₂²×C₄×C₂₉	—	4	2	no	—
146	C₂²×C₄×C₂₉	—	4	2	no	—
147	C₂²×C₄×C₂₉	—	4	2	no	—
148	C₂²×C₄×C₂₉	—	4	2	no	—
149	C₂²×C₄×C₂₉	—	8	1	no	—
150	C₂²×C₄×C₂₉	—	8	1	no	—
151	C₂²×C₄×C₂₉	—	8	1	no	—
152	C₂²×C₄×C₂₉	—	8	1	no	—
153	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₂₉	#41	1	2	yes	—
158	C₂²×C₄×C₂₉	#41	1	2	yes	—
159	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
160	C₂×C₈×C₂₉	—	2	1	no	—
161	C₂×C₈×C₂₉	—	2	1	no	—
162	C₂×C₈×C₂₉	—	2	1	no	—
163	C₂×C₈×C₂₉	—	2	1	no	—
164	C₂×C₈×C₂₉	—	2	1	no	—
165	C₂×C₈×C₂₉	—	2	1	no	—
166	C₂×C₈×C₂₉	—	2	1	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	—	4	4	no	—
172	C₂×C₈×C₂₉	#41	1	2	yes	—
173	C₄⋊C₄×C₂₉	—	2	2	no	—
174	C₄⋊C₄×C₂₉	—	2	1	no	—
175	C₄⋊C₄×C₂₉	—	2	1	no	—
176	C₄⋊C₄×C₂₉	—	2	1	no	—
177	C₄⋊C₄×C₂₉	—	2	1	no	—
178	C₄⋊C₄×C₂₉	—	2	1	no	—
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	—	2	1	no	—
188	C₄⋊C₄×C₂₉	—	2	1	no	—
189	C₄⋊C₄×C₂₉	—	4	2	no	—
190	C₄⋊C₄×C₂₉	—	4	2	no	—
191	C₄⋊C₄×C₂₉	—	4	2	no	—
192	C₄⋊C₄×C₂₉	—	4	2	no	—
193	C₄⋊C₄×C₂₉	—	8	1	no	—
194	C₄⋊C₄×C₂₉	—	8	1	no	—
195	C₄⋊C₄×C₂₉	—	8	1	no	—
196	C₄⋊C₄×C₂₉	#41	1	2	yes	—
197	C₂²⋊C₄×C₂₉	—	2	2	no	—
198	C₂²⋊C₄×C₂₉	—	2	2	no	—
199	C₂²⋊C₄×C₂₉	—	4	2	no	—
200	C₂²⋊C₄×C₂₉	—	4	2	no	—
201	C₂²⋊C₄×C₂₉	—	4	2	no	—
202	C₂²⋊C₄×C₂₉	—	8	1	no	—
203	C₂²⋊C₄×C₂₉	—	8	1	no	—
204	C₄²×C₂₉	—	2	1	no	—
205	C₄²×C₂₉	—	2	1	no	—
206	C₄²×C₂₉	—	4	2	no	—
207	#24935	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂³×C₂₉	—	2	1	no	—
209	C₂³×C₂₉	—	2	1	no	—
210	C₂³×C₂₉	—	2	1	no	—
211	C₂³×C₂₉	—	2	1	no	—
212	C₂³×C₂₉	—	2	1	no	—
213	C₂³×C₂₉	—	2	1	no	—
214	C₂³×C₂₉	—	2	1	no	—
215	C₂³×C₂₉	—	2	1	no	—
216	C₂³×C₂₉	—	2	1	no	—
217	C₂³×C₂₉	—	2	1	no	—
218	C₂³×C₂₉	#123	1	2	yes	—
219	C₂³×C₂₉	C₂×SD₁₆	1	2	yes	—
220	C₂³×C₂₉	C₂×SD₁₆	1	2	yes	—
221	C₂³×C₂₉	#137	1	2	yes	—
222	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
223	D₄×C₂₉	—	2	8	no	—
224	C₂×C₄×C₂₉	—	2	1	no	—
225	C₂×C₄×C₂₉	—	2	1	no	—
226	C₂×C₄×C₂₉	—	2	1	no	—
227	C₂×C₄×C₂₉	—	2	1	no	—
228	C₂×C₄×C₂₉	—	2	2	no	—
229	C₂×C₄×C₂₉	—	2	2	no	—
230	C₂×C₄×C₂₉	—	2	2	no	—
231	C₂×C₄×C₂₉	—	2	2	no	—
232	C₂×C₄×C₂₉	—	2	1	no	—
233	C₂×C₄×C₂₉	—	2	1	no	—
234	C₂×C₄×C₂₉	—	2	2	no	—
235	C₂×C₄×C₂₉	—	2	1	no	—
236	C₂×C₄×C₂₉	—	2	1	no	—
237	C₂×C₄×C₂₉	—	2	1	no	—
238	C₂×C₄×C₂₉	—	2	1	no	—
239	C₂×C₄×C₂₉	—	4	1	no	—
240	C₂×C₄×C₂₉	—	4	1	no	—
241	C₂×C₄×C₂₉	—	4	1	no	—
242	C₂×C₄×C₂₉	—	4	1	no	—
243	C₂×C₄×C₂₉	—	4	1	no	—
244	C₂×C₄×C₂₉	—	4	1	no	—
245	C₂×C₄×C₂₉	—	4	1	no	—
246	C₂×C₄×C₂₉	—	4	1	no	—
247	C₂×C₄×C₂₉	—	4	1	no	—
248	C₂×C₄×C₂₉	—	4	1	no	—
249	C₂×C₄×C₂₉	—	4	1	no	—
250	C₂×C₄×C₂₉	—	4	1	no	—
251	C₂×C₄×C₂₉	—	4	1	no	—
252	C₂×C₄×C₂₉	—	4	1	no	—
253	C₂×C₄×C₂₉	—	4	1	no	—
254	C₂×C₄×C₂₉	—	4	1	no	—
255	C₂×C₄×C₂₉	—	4	1	no	—
256	C₂×C₄×C₂₉	—	4	1	no	—
257	C₂×C₄×C₂₉	—	4	1	no	—
258	C₂×C₄×C₂₉	—	4	1	no	—
259	C₂×C₄×C₂₉	—	4	1	no	—
260	C₂×C₄×C₂₉	—	4	1	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	—	8	4	no	—
267	C₂×C₄×C₂₉	—	8	4	no	—
268	C₂×C₄×C₂₉	—	8	4	no	—
269	C₂×C₄×C₂₉	#123	1	2	yes	—
270	C₂×C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
271	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
272	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
273	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
274	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
275	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
276	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
277	C₈×C₂₉	—	2	2	no	—
278	C₈×C₂₉	—	4	1	no	—
279	C₈×C₂₉	—	4	1	no	—
280	C₈×C₂₉	—	4	1	no	—
281	#2487	C₂×C₂₉	1	1	yes	characteristic
282	D₄×C₄⋊C₄	C₂×C₂₉	1	1	yes	characteristic
283	#2099	C₂×C₂₉	1	1	yes	characteristic, complemented
284	#2084	C₂×C₂₉	1	1	yes	characteristic, complemented
285	#2077	C₂×C₂₉	1	1	yes	characteristic, complemented
286	#2077	C₂×C₂₉	1	1	yes	characteristic, complemented
287	#1920	C₂×C₂₉	1	1	yes	characteristic, complemented
288	#1920	C₂×C₂₉	1	1	yes	characteristic, complemented
289	#1869	C₂×C₂₉	1	1	yes	characteristic
290	#1853	C₂×C₂₉	1	1	yes	characteristic, complemented
291	#1853	C₂×C₂₉	1	1	yes	characteristic, complemented
292	#1824	C₂×C₂₉	1	1	yes	characteristic, complemented
293	#1823	C₂×C₂₉	1	1	yes	characteristic, complemented
294	#1807	C₂×C₂₉	1	1	yes	characteristic, complemented
295	C₂×#340	C₂×C₂₉	1	1	yes	characteristic, complemented
296	C₂²×C₂₉	—	2	2	no	—
297	C₂²×C₂₉	—	2	2	no	—
298	C₂²×C₂₉	—	2	2	no	—
299	C₂²×C₂₉	—	2	2	no	—
300	C₂²×C₂₉	—	2	2	no	—
301	C₂²×C₂₉	—	2	2	no	—
302	C₂²×C₂₉	—	2	2	no	—
303	C₂²×C₂₉	—	2	2	no	—
304	C₂²×C₂₉	—	2	2	no	—
305	C₂²×C₂₉	—	4	1	no	—
306	C₂²×C₂₉	—	4	1	no	—
307	C₂²×C₂₉	—	4	1	no	—
308	C₂²×C₂₉	—	4	1	no	—
309	C₂²×C₂₉	#483	1	4	yes	—
310	C₂²×C₂₉	C₂×#123	1	1	yes	characteristic
311	C₂²×C₂₉	#546	1	1	yes	characteristic
312	C₂²×C₂₉	#547	1	1	yes	characteristic
313	C₂²×C₂₉	C₂²×SD₁₆	1	1	yes	characteristic
314	C₂²×C₂₉	C₂×#137	1	1	yes	characteristic
315	C₂²×C₂₉	#576	1	1	yes	characteristic
316	C₂²×C₂₉	#577	1	1	yes	characteristic
317	C₄×C₂₉	—	2	2	no	—
318	C₄×C₂₉	—	2	2	no	—
319	C₄×C₂₉	—	4	1	no	—
320	C₄×C₂₉	—	4	1	no	—
321	C₄×C₂₉	—	4	2	no	—
322	C₄×C₂₉	—	8	1	no	—
323	C₄×C₂₉	—	8	1	no	—
324	C₄×C₂₉	—	8	1	no	—
325	C₄×C₂₉	—	8	1	no	—
326	C₄×C₂₉	—	8	1	no	—
327	C₄×C₂₉	—	8	1	no	—
328	C₄×C₂₉	—	8	1	no	—
329	C₄×C₂₉	#529	1	1	yes	characteristic
330	C₄×C₂₉	#539	1	1	yes	characteristic
331	C₄×C₂₉	#551	1	1	yes	characteristic
332	C₄×C₂₉	#552	1	1	yes	characteristic
333	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic
334	C₂×C₄×D₄	—	2	1	no	—
335	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
336	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
337	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
338	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
339	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
340	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
341	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
342	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
343	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
344	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
345	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
346	#400	—	2	1	no	—
347	#399	—	2	1	no	—
348	#389	—	2	1	no	—
349	#389	C₂²×C₂₉	1	1	yes	characteristic
350	#389	C₂²×C₂₉	1	1	yes	characteristic
351	#386	—	2	1	no	—
352	#385	—	2	1	no	—
353	#385	—	2	1	no	—
354	#385	—	2	1	no	—
355	#384	C₂²×C₂₉	1	1	yes	characteristic
356	#380	C₂²×C₂₉	1	1	yes	characteristic
357	#380	C₂²×C₂₉	1	1	yes	characteristic
358	#380	C₂²×C₂₉	1	1	yes	characteristic
359	#380	C₂²×C₂₉	1	1	yes	characteristic
360	#380	C₂²×C₂₉	1	1	yes	characteristic
361	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
362	#340	C₂²×C₂₉	1	1	yes	characteristic
363	#340	C₂²×C₂₉	1	1	yes	characteristic
364	#340	C₂²×C₂₉	1	1	yes	characteristic
365	#340	C₂²×C₂₉	1	1	yes	characteristic
366	#340	C₂²×C₂₉	1	1	yes	characteristic
367	#340	C₂²×C₂₉	1	1	yes	characteristic
368	#340	C₂²×C₂₉	1	1	yes	characteristic
369	#340	C₂²×C₂₉	1	1	yes	characteristic
370	#340	C₂²×C₂₉	1	1	yes	characteristic
371	#340	C₂²×C₂₉	1	1	yes	characteristic
372	#340	C₂²×C₂₉	1	1	yes	characteristic
373	#340	C₂²×C₂₉	1	1	yes	characteristic
374	#336	C₂²×C₂₉	1	1	yes	characteristic
375	#336	C₂²×C₂₉	1	1	yes	characteristic
376	C₂×C₂₉	—	2	4	no	—
377	C₂×C₂₉	—	4	2	no	—
378	C₂×C₂₉	#2419	1	1	yes	characteristic
379	C₂×C₂₉	C₂×#483	1	1	yes	characteristic
380	C₂×C₂₉	#3096	1	1	yes	characteristic
381	C₂×C₂₉	#3295	1	1	yes	characteristic
382	C₂×C₂₉	#3320	1	1	yes	characteristic
383	C₂×C₂₉	#3335	1	1	yes	characteristic
384	C₂×C₂₉	#3346	1	1	yes	characteristic
385	C₂²×D₄	D₄×C₂₉	1	1	yes	characteristic
386	C₂³×C₄	—	2	1	no	—
387	C₂³×C₄	—	2	1	no	—
388	C₂³×C₄	—	2	1	no	—
389	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
390	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
391	C₂²×C₈	—	2	2	no	—
392	C₂²×C₈	—	2	2	no	—
393	C₂²×C₈	—	4	1	no	—
394	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
395	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
396	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
397	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	—	2	2	no	—
400	C₄×D₄	—	4	4	no	—
401	C₂×C₄⋊C₄	—	2	2	no	—
402	C₂×C₄⋊C₄	—	2	2	no	—
403	C₂×C₄⋊C₄	—	2	2	no	—
404	C₂×C₄⋊C₄	—	2	2	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	4	1	no	—
413	C₂×C₄⋊C₄	—	4	1	no	—
414	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
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	D₄×C₂₉	1	1	yes	characteristic
429	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
430	C₂×C₄²	—	2	1	no	—
431	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
432	#106	—	2	2	no	—
433	#106	—	2	2	no	—
434	#106	—	4	1	no	—
435	#106	—	4	1	no	—
436	C₂²⋊C₈	—	2	2	no	—
437	C₂²⋊C₈	—	2	2	no	—
438	C₂²⋊C₈	—	4	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	C₂₉	#24935	1	1	yes	characteristic, direct product factor, Sylow
448	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
449	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	SD₁₆×C₂₉	1	4	yes	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	4	2	no	—
473	C₂²×C₄	—	4	2	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	—	4	2	no	—
476	C₂²×C₄	—	8	1	no	—
477	C₂²×C₄	—	8	1	no	—
478	C₂²×C₄	—	8	1	no	—
479	C₂²×C₄	—	8	1	no	—
480	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
484	C₂²×C₄	#41×C₂₉	1	2	yes	—
485	C₂²×C₄	#41×C₂₉	1	2	yes	—
486	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	4	4	no	—
499	C₂×C₈	#41×C₂₉	1	2	yes	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	4	2	no	—
517	C₄⋊C₄	—	4	2	no	—
518	C₄⋊C₄	—	4	2	no	—
519	C₄⋊C₄	—	4	2	no	—
520	C₄⋊C₄	—	8	1	no	—
521	C₄⋊C₄	—	8	1	no	—
522	C₄⋊C₄	—	8	1	no	—
523	C₄⋊C₄	#41×C₂₉	1	2	yes	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	4	2	no	—
527	C₂²⋊C₄	—	4	2	no	—
528	C₂²⋊C₄	—	4	2	no	—
529	C₂²⋊C₄	—	8	1	no	—
530	C₂²⋊C₄	—	8	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	2	1	no	—
533	C₄²	—	4	2	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	1	no	—
541	C₂³	—	2	1	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	2	1	no	—
544	C₂³	C₂₉×#123	1	2	yes	—
545	C₂³	C₂×SD₁₆×C₂₉	1	2	yes	—
546	C₂³	C₂×SD₁₆×C₂₉	1	2	yes	—
547	C₂³	C₂₉×#137	1	2	yes	—
548	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
549	D₄	—	2	8	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	8	4	no	—
593	C₂×C₄	—	8	4	no	—
594	C₂×C₄	—	8	4	no	—
595	C₂×C₄	C₂₉×#123	1	2	yes	—
596	C₂×C₄	C₂×SD₁₆×C₂₉	1	2	yes	—
597	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
598	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
599	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
600	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
601	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
602	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
603	C₈	—	2	2	no	—
604	C₈	—	4	1	no	—
605	C₈	—	4	1	no	—
606	C₈	—	4	1	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	4	1	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	C₂₉×#483	1	4	yes	—
621	C₂²	C₂×C₂₉×#123	1	1	yes	characteristic
622	C₂²	C₂₉×#546	1	1	yes	characteristic
623	C₂²	C₂₉×#547	1	1	yes	characteristic
624	C₂²	C₂²×SD₁₆×C₂₉	1	1	yes	characteristic
625	C₂²	C₂×C₂₉×#137	1	1	yes	characteristic
626	C₂²	C₂₉×#576	1	1	yes	characteristic
627	C₂²	C₂₉×#577	1	1	yes	characteristic
628	C₄	—	2	2	no	—
629	C₄	—	2	2	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	2	no	—
632	C₄	—	4	1	no	—
633	C₄	—	8	1	no	—
634	C₄	—	8	1	no	—
635	C₄	—	8	1	no	—
636	C₄	—	8	1	no	—
637	C₄	—	8	1	no	—
638	C₄	—	8	1	no	—
639	C₄	—	8	1	no	—
640	C₄	C₂₉×#529	1	1	yes	characteristic
641	C₄	C₂₉×#539	1	1	yes	characteristic
642	C₄	C₂₉×#551	1	1	yes	characteristic
643	C₄	C₂₉×#552	1	1	yes	characteristic
644	C₂	—	2	4	no	—
645	C₂	—	4	2	no	—
646	C₂	C₂₉×#2419	1	1	yes	characteristic
647	C₂	C₂×C₂₉×#483	1	1	yes	characteristic
648	C₂	C₂₉×#3096	1	1	yes	characteristic
649	C₂	C₂₉×#3295	1	1	yes	characteristic
650	C₂	C₂₉×#3320	1	1	yes	characteristic
651	C₂	C₂₉×#3335	1	1	yes	characteristic
652	C₂	C₂₉×#3346	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₂₉×#2099	C₂	semidirect
4. C₂₉×#2084	C₂	semidirect
5. C₂₉×#2077	C₂	semidirect
6. C₂₉×#2077	C₂	semidirect
7. C₂₉×#1920	C₂	semidirect
8. C₂₉×#1920	C₂	semidirect
10. C₂₉×#1853	C₂	semidirect
11. C₂₉×#1853	C₂	semidirect
12. C₂₉×#1824	C₂	semidirect
13. C₂₉×#1823	C₂	semidirect
14. C₂₉×#1807	C₂	semidirect
15. C₂×C₂₉×#340	C₂	semidirect
207. #24935	C₂₉	direct (N × H)
283. #2099	C₂×C₂₉	semidirect
284. #2084	C₂×C₂₉	semidirect
285. #2077	C₂×C₂₉	semidirect
286. #2077	C₂×C₂₉	semidirect
287. #1920	C₂×C₂₉	semidirect
288. #1920	C₂×C₂₉	semidirect
290. #1853	C₂×C₂₉	semidirect
291. #1853	C₂×C₂₉	semidirect
292. #1824	C₂×C₂₉	semidirect
293. #1823	C₂×C₂₉	semidirect
294. #1807	C₂×C₂₉	semidirect
295. C₂×#340	C₂×C₂₉	semidirect
447. C₂₉	#24935	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×#2487	2
D₄×C₄⋊C₄×C₂₉	2
C₂₉×#2099	2
C₂₉×#2084	2
C₂₉×#2077	2
C₂₉×#1920	2
C₂₉×#1869	2
C₂₉×#1853	2
C₂₉×#1824	2
C₂₉×#1823	2
C₂₉×#1807	2
C₂×C₂₉×#340	2
#24935	29

Subgroups — C29×#24935 #20319835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#24935 #20319835