Subgroups — C₂₉×#28922 #20323822

Order 7424.

868 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×#488	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#468	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2427	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#2059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2034	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#2015	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2001	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1971	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1933	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1928	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1894	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1762	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×#125	C₂²	1	1	yes	characteristic
20	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
25	C₂₉×#488	—	2	4	no	—
26	C₂₉×#468	—	2	4	no	—
27	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×#103	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×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
40	C₂₉×#400	—	2	1	no	—
41	C₂₉×#397	—	2	1	no	—
42	C₂₉×#397	—	2	1	no	—
43	C₂₉×#394	—	2	1	no	—
44	C₂₉×#391	C₂²	1	1	yes	characteristic
45	C₂₉×#391	C₂²	1	1	yes	characteristic
46	C₂₉×#391	C₂²	1	1	yes	characteristic
47	C₂₉×#389	C₂²	1	1	yes	characteristic
48	C₂₉×#388	—	2	1	no	—
49	C₂₉×#386	—	2	1	no	—
50	C₂₉×#382	—	2	1	no	—
51	C₂₉×#380	—	2	1	no	—
52	C₂₉×#380	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
55	C₂₉×#340	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×#336	C₂²	1	1	yes	characteristic
60	C₂₉×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₂₉	—	2	1	no	—
64	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₂₉	—	2	1	no	—
66	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
67	C₂×Q₁₆×C₂₉	—	2	2	no	—
68	C₂×Q₁₆×C₂₉	—	4	1	no	—
69	C₂×Q₁₆×C₂₉	—	4	1	no	—
70	C₂×SD₁₆×C₂₉	—	2	2	no	—
71	C₂×SD₁₆×C₂₉	—	2	2	no	—
72	C₂×SD₁₆×C₂₉	—	4	1	no	—
73	C₂×M₁₆×C₂₉	—	2	2	no	—
74	C₂×M₁₆×C₂₉	—	2	2	no	—
75	C₂×M₁₆×C₂₉	—	4	1	no	—
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×#125	—	2	2	no	—
81	C₂₉×#125	—	4	1	no	—
82	C₂₉×#124	—	2	2	no	—
83	C₂₉×#124	—	4	1	no	—
84	C₂₉×C₂²⋊Q₈	—	2	2	no	—
85	C₂₉×C₂²⋊Q₈	—	2	2	no	—
86	C₂₉×C₂²⋊Q₈	—	4	1	no	—
87	C₂₉×C₂²⋊Q₈	—	4	1	no	—
88	C₂₉×#121	—	2	2	no	—
89	C₂₉×#121	—	4	1	no	—
90	C₄×D₄×C₂₉	—	2	2	no	—
91	C₄×D₄×C₂₉	—	4	1	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	—	2	1	no	—
96	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₂₉	—	2	1	no	—
112	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
114	C₂₉×#107	—	2	2	no	—
115	C₂₉×#106	—	4	1	no	—
116	C₂₉×#103	—	2	2	no	—
117	C₂₉×#103	—	2	2	no	—
118	C₂₉×#103	—	2	2	no	—
119	C₂₉×#103	—	2	2	no	—
120	C₂₉×#103	—	2	2	no	—
121	C₂₉×#102	—	2	2	no	—
122	C₂₉×#102	—	2	2	no	—
123	C₂₉×#102	D₄	1	4	yes	—
124	C₂₉×C₂²⋊C₈	—	2	2	no	—
125	C₂₉×#97	—	4	1	no	—
126	C₄×C₈×C₂₉	—	2	2	no	—
127	C₂₉×#95	—	2	1	no	—
128	C₂₉×#95	—	2	1	no	—
129	C₂₉×#95	—	2	1	no	—
130	C₂₉×#95	—	2	1	no	—
131	C₂₉×#95	—	2	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	D₄	1	1	yes	characteristic
137	C₂₉×#95	D₄	1	1	yes	characteristic
138	C₂⁴×C₂₉	—	2	1	no	—
139	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
140	C₂×Q₈×C₂₉	—	2	1	no	—
141	C₂×Q₈×C₂₉	—	2	1	no	—
142	C₂×Q₈×C₂₉	—	2	1	no	—
143	C₂×Q₈×C₂₉	—	2	1	no	—
144	C₂×Q₈×C₂₉	—	2	1	no	—
145	C₂×Q₈×C₂₉	—	2	1	no	—
146	C₂×Q₈×C₂₉	—	2	1	no	—
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×D₄×C₂₉	—	2	1	no	—
153	C₂×D₄×C₂₉	—	2	1	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	—	4	2	no	—
158	C₂×D₄×C₂₉	—	4	2	no	—
159	C₂×D₄×C₂₉	—	8	1	no	—
160	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
170	C₂²×C₄×C₂₉	—	2	1	no	—
171	C₂²×C₄×C₂₉	—	2	1	no	—
172	C₂²×C₄×C₂₉	—	2	1	no	—
173	C₂²×C₄×C₂₉	—	2	1	no	—
174	C₂²×C₄×C₂₉	—	4	2	no	—
175	C₂²×C₄×C₂₉	—	4	2	no	—
176	C₂²×C₄×C₂₉	—	8	1	no	—
177	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
183	Q₁₆×C₂₉	—	4	4	no	—
184	SD₁₆×C₂₉	—	4	4	no	—
185	M₁₆×C₂₉	—	4	4	no	—
186	C₂×C₈×C₂₉	—	2	1	no	—
187	C₂×C₈×C₂₉	—	2	1	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	C₂×D₄	1	2	yes	—
196	C₂×C₈×C₂₉	#41	1	2	yes	—
197	C₂×C₈×C₂₉	#41	1	2	yes	—
198	C₄⋊C₄×C₂₉	—	2	1	no	—
199	C₄⋊C₄×C₂₉	—	2	1	no	—
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	—	4	2	no	—
207	C₄⋊C₄×C₂₉	—	4	2	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	C₂×D₄	1	2	yes	—
212	C₄⋊C₄×C₂₉	#41	1	2	yes	—
213	C₂²⋊C₄×C₂₉	—	4	1	no	—
214	C₂²⋊C₄×C₂₉	—	4	1	no	—
215	C₂²⋊C₄×C₂₉	—	4	2	no	—
216	C₂²⋊C₄×C₂₉	—	4	2	no	—
217	C₂²⋊C₄×C₂₉	—	4	2	no	—
218	C₂²⋊C₄×C₂₉	—	4	2	no	—
219	C₂²⋊C₄×C₂₉	—	4	2	no	—
220	C₂²⋊C₄×C₂₉	—	4	2	no	—
221	C₂²⋊C₄×C₂₉	—	4	2	no	—
222	C₄²×C₂₉	—	2	1	no	—
223	C₄²×C₂₉	—	2	1	no	—
224	C₄²×C₂₉	—	2	1	no	—
225	C₄²×C₂₉	—	2	1	no	—
226	C₄²×C₂₉	—	4	2	no	—
227	#28922	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂³×C₂₉	—	2	1	no	—
229	C₂³×C₂₉	—	2	2	no	—
230	C₂³×C₂₉	—	2	1	no	—
231	C₂³×C₂₉	—	2	1	no	—
232	C₂³×C₂₉	—	2	1	no	—
233	C₂³×C₂₉	—	2	1	no	—
234	C₂³×C₂₉	—	2	1	no	—
235	C₂³×C₂₉	—	2	1	no	—
236	C₂³×C₂₉	—	4	1	no	—
237	C₂³×C₂₉	—	4	1	no	—
238	C₂³×C₂₉	—	4	1	no	—
239	C₂³×C₂₉	—	4	1	no	—
240	C₂³×C₂₉	—	4	1	no	—
241	C₂³×C₂₉	—	4	1	no	—
242	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
243	Q₈×C₂₉	—	4	1	no	—
244	Q₈×C₂₉	—	4	1	no	—
245	Q₈×C₂₉	—	4	1	no	—
246	Q₈×C₂₉	—	4	1	no	—
247	Q₈×C₂₉	—	4	1	no	—
248	Q₈×C₂₉	—	4	1	no	—
249	Q₈×C₂₉	—	4	1	no	—
250	Q₈×C₂₉	—	4	1	no	—
251	D₄×C₂₉	—	2	2	no	—
252	D₄×C₂₉	—	2	2	no	—
253	D₄×C₂₉	—	4	1	no	—
254	D₄×C₂₉	—	4	1	no	—
255	D₄×C₂₉	—	8	4	no	—
256	C₂×C₄×C₂₉	—	2	1	no	—
257	C₂×C₄×C₂₉	—	2	1	no	—
258	C₂×C₄×C₂₉	—	2	1	no	—
259	C₂×C₄×C₂₉	—	2	1	no	—
260	C₂×C₄×C₂₉	—	2	2	no	—
261	C₂×C₄×C₂₉	—	2	1	no	—
262	C₂×C₄×C₂₉	—	2	1	no	—
263	C₂×C₄×C₂₉	—	2	2	no	—
264	C₂×C₄×C₂₉	—	2	1	no	—
265	C₂×C₄×C₂₉	—	2	1	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	1	no	—
271	C₂×C₄×C₂₉	—	2	1	no	—
272	C₂×C₄×C₂₉	—	2	1	no	—
273	C₂×C₄×C₂₉	—	4	1	no	—
274	C₂×C₄×C₂₉	—	4	1	no	—
275	C₂×C₄×C₂₉	—	4	1	no	—
276	C₂×C₄×C₂₉	—	4	1	no	—
277	C₂×C₄×C₂₉	—	4	1	no	—
278	C₂×C₄×C₂₉	—	4	1	no	—
279	C₂×C₄×C₂₉	—	4	1	no	—
280	C₂×C₄×C₂₉	—	4	1	no	—
281	C₂×C₄×C₂₉	—	4	1	no	—
282	C₂×C₄×C₂₉	—	4	1	no	—
283	C₂×C₄×C₂₉	—	4	1	no	—
284	C₂×C₄×C₂₉	—	4	1	no	—
285	C₂×C₄×C₂₉	—	4	1	no	—
286	C₂×C₄×C₂₉	—	4	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	—	8	4	no	—
297	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
298	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
299	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
300	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
301	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
302	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
303	C₈×C₂₉	—	2	2	no	—
304	C₈×C₂₉	—	2	2	no	—
305	C₈×C₂₉	—	2	2	no	—
306	C₈×C₂₉	—	4	1	no	—
307	C₂×#488	C₂×C₂₉	1	1	yes	characteristic, complemented
308	C₂×#468	C₂×C₂₉	1	1	yes	characteristic
309	#2489	C₂×C₂₉	1	1	yes	characteristic, complemented
310	#2427	C₂×C₂₉	1	1	yes	characteristic
311	#2059	C₂×C₂₉	1	1	yes	characteristic, complemented
312	#2034	C₂×C₂₉	1	1	yes	characteristic
313	#2015	C₂×C₂₉	1	1	yes	characteristic, complemented
314	#2001	C₂×C₂₉	1	1	yes	characteristic, complemented
315	#1971	C₂×C₂₉	1	1	yes	characteristic, complemented
316	#1933	C₂×C₂₉	1	1	yes	characteristic, complemented
317	#1928	C₂×C₂₉	1	1	yes	characteristic, complemented
318	#1894	C₂×C₂₉	1	1	yes	characteristic, complemented
319	#1877	C₂×C₂₉	1	1	yes	characteristic, complemented
320	#1762	C₂×C₂₉	1	1	yes	characteristic, complemented
321	#1753	C₂×C₂₉	1	1	yes	characteristic, complemented
322	C₂²×C₂₉	—	4	1	no	—
323	C₂²×C₂₉	—	4	1	no	—
324	C₂²×C₂₉	—	4	1	no	—
325	C₂²×C₂₉	—	4	2	no	—
326	C₂²×C₂₉	—	4	1	no	—
327	C₂²×C₂₉	—	4	2	no	—
328	C₂²×C₂₉	—	4	1	no	—
329	C₂²×C₂₉	—	4	2	no	—
330	C₂²×C₂₉	—	4	1	no	—
331	C₂²×C₂₉	—	4	1	no	—
332	C₂²×C₂₉	—	8	1	no	—
333	C₂²×C₂₉	—	8	1	no	—
334	C₂²×C₂₉	—	8	1	no	—
335	C₂²×C₂₉	—	8	1	no	—
336	C₂²×C₂₉	#532	1	1	yes	characteristic
337	C₂²×C₂₉	D₄²	1	1	yes	characteristic
338	C₂²×C₂₉	#546	1	1	yes	characteristic
339	C₂²×C₂₉	#575	1	1	yes	characteristic
340	C₂²×C₂₉	#575	1	1	yes	characteristic
341	C₂²×C₂₉	#577	1	1	yes	characteristic
342	C₂²×C₂₉	#578	1	1	yes	characteristic
343	C₄×C₂₉	—	4	1	no	—
344	C₄×C₂₉	—	4	2	no	—
345	C₄×C₂₉	—	4	1	no	—
346	C₄×C₂₉	—	4	1	no	—
347	C₄×C₂₉	—	4	1	no	—
348	C₄×C₂₉	—	4	2	no	—
349	C₄×C₂₉	—	4	1	no	—
350	C₄×C₂₉	—	8	1	no	—
351	C₄×C₂₉	—	8	1	no	—
352	C₄×C₂₉	—	8	1	no	—
353	C₄×C₂₉	—	8	1	no	—
354	C₄×C₂₉	—	8	1	no	—
355	C₄×C₂₉	#532	1	1	yes	characteristic
356	C₄×C₂₉	#538	1	1	yes	characteristic
357	C₄×C₂₉	#546	1	1	yes	characteristic
358	C₄×C₂₉	#555	1	1	yes	characteristic
359	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
360	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
361	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
362	C₂×#125	C₂²×C₂₉	1	1	yes	characteristic
363	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
364	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
365	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
366	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic
367	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
368	#488	—	2	4	no	—
369	#468	—	2	4	no	—
370	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
371	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
372	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
373	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
374	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
375	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
376	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
377	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
378	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
379	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
380	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
381	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
382	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
383	#400	—	2	1	no	—
384	#397	—	2	1	no	—
385	#397	—	2	1	no	—
386	#394	—	2	1	no	—
387	#391	C₂²×C₂₉	1	1	yes	characteristic
388	#391	C₂²×C₂₉	1	1	yes	characteristic
389	#391	C₂²×C₂₉	1	1	yes	characteristic
390	#389	C₂²×C₂₉	1	1	yes	characteristic
391	#388	—	2	1	no	—
392	#386	—	2	1	no	—
393	#382	—	2	1	no	—
394	#380	—	2	1	no	—
395	#380	C₂²×C₂₉	1	1	yes	characteristic
396	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
397	C₄×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
398	#340	C₂²×C₂₉	1	1	yes	characteristic
399	#340	C₂²×C₂₉	1	1	yes	characteristic
400	#340	C₂²×C₂₉	1	1	yes	characteristic
401	#340	C₂²×C₂₉	1	1	yes	characteristic
402	#336	C₂²×C₂₉	1	1	yes	characteristic
403	#336	C₂²×C₂₉	1	1	yes	characteristic
404	C₂×C₂₉	—	8	1	no	—
405	C₂×C₂₉	—	8	2	no	—
406	C₂×C₂₉	#2555	1	1	yes	characteristic
407	C₂×C₂₉	#3178	1	1	yes	characteristic
408	C₂×C₂₉	#3183	1	1	yes	characteristic
409	C₂×C₂₉	#3267	1	1	yes	characteristic
410	C₂×C₂₉	#3269	1	1	yes	characteristic
411	C₂×C₂₉	#3323	1	1	yes	characteristic
412	C₂×C₂₉	#3327	1	1	yes	characteristic
413	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
414	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
415	C₂²×D₄	—	2	1	no	—
416	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
417	C₂³×C₄	—	2	1	no	—
418	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
419	C₂×Q₁₆	—	2	2	no	—
420	C₂×Q₁₆	—	4	1	no	—
421	C₂×Q₁₆	—	4	1	no	—
422	C₂×SD₁₆	—	2	2	no	—
423	C₂×SD₁₆	—	2	2	no	—
424	C₂×SD₁₆	—	4	1	no	—
425	C₂×M₁₆	—	2	2	no	—
426	C₂×M₁₆	—	2	2	no	—
427	C₂×M₁₆	—	4	1	no	—
428	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
429	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
430	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
431	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
432	#125	—	2	2	no	—
433	#125	—	4	1	no	—
434	#124	—	2	2	no	—
435	#124	—	4	1	no	—
436	C₂²⋊Q₈	—	2	2	no	—
437	C₂²⋊Q₈	—	2	2	no	—
438	C₂²⋊Q₈	—	4	1	no	—
439	C₂²⋊Q₈	—	4	1	no	—
440	#121	—	2	2	no	—
441	#121	—	4	1	no	—
442	C₄×D₄	—	2	2	no	—
443	C₄×D₄	—	4	1	no	—
444	C₂×C₄⋊C₄	—	2	1	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄⋊C₄	—	2	1	no	—
448	C₂×C₄⋊C₄	—	2	1	no	—
449	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	1	no	—
459	C₂×C₂²⋊C₄	—	2	1	no	—
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
463	C₂×C₄²	—	2	1	no	—
464	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
465	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
466	#107	—	2	2	no	—
467	#106	—	4	1	no	—
468	#103	—	2	2	no	—
469	#103	—	2	2	no	—
470	#103	—	2	2	no	—
471	#103	—	2	2	no	—
472	#103	—	2	2	no	—
473	#102	—	2	2	no	—
474	#102	—	2	2	no	—
475	#102	D₄×C₂₉	1	4	yes	—
476	C₂²⋊C₈	—	2	2	no	—
477	#97	—	4	1	no	—
478	C₄×C₈	—	2	2	no	—
479	#95	—	2	1	no	—
480	#95	—	2	1	no	—
481	#95	—	2	1	no	—
482	#95	—	2	1	no	—
483	#95	—	2	1	no	—
484	#95	—	2	1	no	—
485	#95	—	2	1	no	—
486	#95	—	2	1	no	—
487	#95	—	2	1	no	—
488	#95	D₄×C₂₉	1	1	yes	characteristic
489	#95	D₄×C₂₉	1	1	yes	characteristic
490	C₂₉	#28922	1	1	yes	characteristic, direct product factor, Sylow
491	C₂⁴	—	2	1	no	—
492	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	4	2	no	—
511	C₂×D₄	—	4	2	no	—
512	C₂×D₄	—	8	1	no	—
513	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	4	2	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	8	1	no	—
530	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
531	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
532	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
533	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
534	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
536	Q₁₆	—	4	4	no	—
537	SD₁₆	—	4	4	no	—
538	M₁₆	—	4	4	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
549	C₂×C₈	#41×C₂₉	1	2	yes	—
550	C₂×C₈	#41×C₂₉	1	2	yes	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	4	2	no	—
560	C₄⋊C₄	—	4	2	no	—
561	C₄⋊C₄	—	4	2	no	—
562	C₄⋊C₄	—	4	2	no	—
563	C₄⋊C₄	—	8	1	no	—
564	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
565	C₄⋊C₄	#41×C₂₉	1	2	yes	—
566	C₂²⋊C₄	—	4	1	no	—
567	C₂²⋊C₄	—	4	1	no	—
568	C₂²⋊C₄	—	4	2	no	—
569	C₂²⋊C₄	—	4	2	no	—
570	C₂²⋊C₄	—	4	2	no	—
571	C₂²⋊C₄	—	4	2	no	—
572	C₂²⋊C₄	—	4	2	no	—
573	C₂²⋊C₄	—	4	2	no	—
574	C₂²⋊C₄	—	4	2	no	—
575	C₄²	—	2	1	no	—
576	C₄²	—	2	1	no	—
577	C₄²	—	2	1	no	—
578	C₄²	—	2	1	no	—
579	C₄²	—	4	2	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	1	no	—
583	C₂³	—	2	1	no	—
584	C₂³	—	2	1	no	—
585	C₂³	—	2	1	no	—
586	C₂³	—	2	1	no	—
587	C₂³	—	2	1	no	—
588	C₂³	—	4	1	no	—
589	C₂³	—	4	1	no	—
590	C₂³	—	4	1	no	—
591	C₂³	—	4	1	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
595	Q₈	—	4	1	no	—
596	Q₈	—	4	1	no	—
597	Q₈	—	4	1	no	—
598	Q₈	—	4	1	no	—
599	Q₈	—	4	1	no	—
600	Q₈	—	4	1	no	—
601	Q₈	—	4	1	no	—
602	Q₈	—	4	1	no	—
603	D₄	—	2	2	no	—
604	D₄	—	2	2	no	—
605	D₄	—	4	1	no	—
606	D₄	—	4	1	no	—
607	D₄	—	8	4	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	8	4	no	—
649	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
650	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
651	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
652	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
653	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
654	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
655	C₈	—	2	2	no	—
656	C₈	—	2	2	no	—
657	C₈	—	2	2	no	—
658	C₈	—	4	1	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	2	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	4	2	no	—
664	C₂²	—	4	1	no	—
665	C₂²	—	4	2	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	8	1	no	—
670	C₂²	—	8	1	no	—
671	C₂²	—	8	1	no	—
672	C₂²	—	8	1	no	—
673	C₂²	C₂₉×#532	1	1	yes	characteristic
674	C₂²	D₄²×C₂₉	1	1	yes	characteristic
675	C₂²	C₂₉×#546	1	1	yes	characteristic
676	C₂²	C₂₉×#575	1	1	yes	characteristic
677	C₂²	C₂₉×#575	1	1	yes	characteristic
678	C₂²	C₂₉×#577	1	1	yes	characteristic
679	C₂²	C₂₉×#578	1	1	yes	characteristic
680	C₄	—	4	1	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	1	no	—
683	C₄	—	4	1	no	—
684	C₄	—	4	1	no	—
685	C₄	—	4	2	no	—
686	C₄	—	4	1	no	—
687	C₄	—	8	1	no	—
688	C₄	—	8	1	no	—
689	C₄	—	8	1	no	—
690	C₄	—	8	1	no	—
691	C₄	—	8	1	no	—
692	C₄	C₂₉×#532	1	1	yes	characteristic
693	C₄	C₂₉×#538	1	1	yes	characteristic
694	C₄	C₂₉×#546	1	1	yes	characteristic
695	C₄	C₂₉×#555	1	1	yes	characteristic
696	C₂	—	8	1	no	—
697	C₂	—	8	2	no	—
698	C₂	C₂₉×#2555	1	1	yes	characteristic
699	C₂	C₂₉×#3178	1	1	yes	characteristic
700	C₂	C₂₉×#3183	1	1	yes	characteristic
701	C₂	C₂₉×#3267	1	1	yes	characteristic
702	C₂	C₂₉×#3269	1	1	yes	characteristic
703	C₂	C₂₉×#3323	1	1	yes	characteristic
704	C₂	C₂₉×#3327	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#121	C₂²
LCS	G ▷ C₂²×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
1. C₂×C₂₉×#488	C₂	semidirect
3. C₂₉×#2489	C₂	semidirect
5. C₂₉×#2059	C₂	semidirect
7. C₂₉×#2015	C₂	semidirect
8. C₂₉×#2001	C₂	semidirect
9. C₂₉×#1971	C₂	semidirect
10. C₂₉×#1933	C₂	semidirect
11. C₂₉×#1928	C₂	semidirect
12. C₂₉×#1894	C₂	semidirect
13. C₂₉×#1877	C₂	semidirect
14. C₂₉×#1762	C₂	semidirect
15. C₂₉×#1753	C₂	semidirect
227. #28922	C₂₉	direct (N × H)
307. C₂×#488	C₂×C₂₉	semidirect
309. #2489	C₂×C₂₉	semidirect
311. #2059	C₂×C₂₉	semidirect
313. #2015	C₂×C₂₉	semidirect
314. #2001	C₂×C₂₉	semidirect
315. #1971	C₂×C₂₉	semidirect
316. #1933	C₂×C₂₉	semidirect
317. #1928	C₂×C₂₉	semidirect
318. #1894	C₂×C₂₉	semidirect
319. #1877	C₂×C₂₉	semidirect
320. #1762	C₂×C₂₉	semidirect
321. #1753	C₂×C₂₉	semidirect
490. C₂₉	#28922	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×#488	2
C₂×C₂₉×#468	2
C₂₉×#2489	2
C₂₉×#2427	2
C₂₉×#2059	2
C₂₉×#2034	2
C₂₉×#2015	2
C₂₉×#2001	2
C₂₉×#1971	2
C₂₉×#1933	2
C₂₉×#1928	2
C₂₉×#1894	2
C₂₉×#1877	2
C₂₉×#1762	2
C₂₉×#1753	2
#28922	29

Subgroups — C29×#28922 #20323822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#28922 #20323822