Subgroups — C₂₉×#18726 #20313626

Order 7424.

892 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3247	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3247	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1638	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1637	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1636	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1635	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1628	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1627	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1626	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1625	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₉×#332	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1483	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1483	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#563	—	2	2	no	—
17	C₂₉×#557	C₂²	1	1	yes	characteristic
18	C₂₉×#556	C₂²	1	1	yes	characteristic
19	C₂₉×#554	—	2	1	no	—
20	C₂₉×#553	—	2	1	no	—
21	D₄×Q₈×C₂₉	—	2	1	no	—
22	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
23	C₂₉×#548	—	2	1	no	—
24	C₂₉×#547	C₂²	1	1	yes	characteristic
25	C₂₉×#544	—	2	1	no	—
26	C₂₉×#542	—	2	1	no	—
27	C₂₉×#541	—	2	1	no	—
28	C₂₉×#539	—	2	2	no	—
29	C₂₉×#536	—	2	1	no	—
30	C₂₉×#532	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂₉×#529	C₂²	1	1	yes	characteristic
33	C₂₉×#529	C₂²	1	1	yes	characteristic
34	C₂₉×#489	—	2	2	no	—
35	C₂₉×#487	C₂²	1	1	yes	characteristic
36	C₂₉×#487	C₂²	1	1	yes	characteristic
37	C₂₉×#486	C₂²	1	1	yes	characteristic
38	C₂₉×#486	C₂²	1	1	yes	characteristic
39	C₂₉×#478	—	2	1	no	—
40	C₂₉×#478	—	2	1	no	—
41	C₂₉×#477	C₂²	1	1	yes	characteristic
42	C₂₉×#477	C₂²	1	1	yes	characteristic
43	C₂₉×#476	C₂²	1	1	yes	characteristic
44	C₂₉×#476	C₂²	1	1	yes	characteristic
45	C₂₉×#466	—	2	1	no	—
46	C₂₉×#466	—	2	1	no	—
47	C₂₉×#465	—	2	1	no	—
48	C₂₉×#465	—	2	1	no	—
49	C₂₉×#463	—	2	1	no	—
50	C₂₉×#463	—	2	1	no	—
51	C₂₉×#460	C₂²	1	1	yes	characteristic
52	C₂₉×#460	C₂²	1	1	yes	characteristic
53	C₂₉×#459	C₂²	1	1	yes	characteristic
54	C₂₉×#459	C₂²	1	1	yes	characteristic
55	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
56	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
57	C₂₉×#417	—	2	2	no	—
58	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
59	C₂₉×#332	C₂²	1	1	yes	characteristic
60	C₂₉×#332	C₂²	1	1	yes	characteristic
61	C₂₉×#332	C₂²	1	1	yes	characteristic
62	C₂₉×#332	C₂²	1	1	yes	characteristic
63	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
67	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
69	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	C₂×#41×C₂₉	—	2	1	no	—
72	C₂×#41×C₂₉	—	2	1	no	—
73	C₂²×Q₈×C₂₉	—	2	1	no	—
74	C₂²×Q₈×C₂₉	—	2	1	no	—
75	C₂×SD₁₆×C₂₉	—	2	1	no	—
76	C₂×SD₁₆×C₂₉	—	2	1	no	—
77	C₂×D₈×C₂₉	—	2	1	no	—
78	C₂×D₈×C₂₉	—	2	1	no	—
79	C₂×M₁₆×C₂₉	—	2	1	no	—
80	C₂²×C₈×C₂₉	—	2	1	no	—
81	C₂²×C₈×C₂₉	—	2	1	no	—
82	C₂₉×C₄⋊Q₈	—	2	2	no	—
83	C₂₉×C₄⋊Q₈	—	2	1	no	—
84	C₂₉×C₄⋊Q₈	—	2	1	no	—
85	C₂₉×C₄⋊Q₈	—	2	1	no	—
86	C₂₉×C₄⋊Q₈	—	2	1	no	—
87	C₂₉×C₄⋊Q₈	D₄	1	2	yes	—
88	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
90	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
91	C₂₉×#127	C₂³	1	1	yes	characteristic
92	C₂₉×#126	—	2	2	no	—
93	C₂₉×#126	—	2	2	no	—
94	C₂₉×#126	—	2	2	no	—
95	C₂₉×#126	—	2	1	no	—
96	C₂₉×#126	—	2	1	no	—
97	C₂₉×#125	—	2	2	no	—
98	C₂₉×#125	—	2	2	no	—
99	C₂₉×#125	—	2	2	no	—
100	C₂₉×#125	—	2	1	no	—
101	C₂₉×#125	D₄	1	1	yes	characteristic
102	C₂₉×#125	D₄	1	1	yes	characteristic
103	C₂₉×#124	—	2	2	no	—
104	C₂₉×#124	—	2	1	no	—
105	C₂₉×#124	—	2	1	no	—
106	C₂₉×#124	D₄	1	1	yes	characteristic
107	C₂₉×#124	D₄	1	1	yes	characteristic
108	C₂₉×#123	—	2	2	no	—
109	C₂₉×#123	—	2	2	no	—
110	C₂₉×#123	—	2	1	no	—
111	C₂₉×#123	—	2	1	no	—
112	C₂₉×#123	—	2	2	no	—
113	C₂₉×C₂²⋊Q₈	—	2	2	no	—
114	C₂₉×C₂²⋊Q₈	—	2	2	no	—
115	C₂₉×C₂²⋊Q₈	—	2	2	no	—
116	C₂₉×C₂²⋊Q₈	—	2	2	no	—
117	C₂₉×C₂²⋊Q₈	—	2	2	no	—
118	C₂₉×C₂²⋊Q₈	—	2	1	no	—
119	C₂₉×C₂²⋊Q₈	—	2	2	no	—
120	C₂₉×C₂²⋊Q₈	—	2	1	no	—
121	C₂₉×C₂²⋊Q₈	—	2	1	no	—
122	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
123	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
124	C₂₉×#121	—	2	2	no	—
125	C₂₉×#121	—	2	1	no	—
126	C₂₉×#121	—	2	1	no	—
127	C₂₉×#121	—	2	1	no	—
128	C₂₉×#121	D₄	1	1	yes	characteristic
129	C₂₉×#121	D₄	1	1	yes	characteristic
130	C₄×Q₈×C₂₉	—	2	1	no	—
131	C₄×Q₈×C₂₉	—	2	1	no	—
132	C₄×Q₈×C₂₉	—	2	1	no	—
133	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
134	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
135	C₄×D₄×C₂₉	—	2	2	no	—
136	C₄×D₄×C₂₉	—	2	2	no	—
137	C₄×D₄×C₂₉	—	2	1	no	—
138	C₄×D₄×C₂₉	—	2	1	no	—
139	C₄×D₄×C₂₉	—	2	1	no	—
140	C₄×D₄×C₂₉	—	2	1	no	—
141	C₄×D₄×C₂₉	—	2	1	no	—
142	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
143	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
144	C₂₉×#117	—	2	1	no	—
145	C₂₉×#117	—	2	1	no	—
146	C₂₉×#117	—	2	1	no	—
147	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
148	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
149	C₂×C₄⋊C₄×C₂₉	D₄	1	2	yes	—
150	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
151	C₂₉×#107	—	2	1	no	—
152	C₂₉×#107	—	2	1	no	—
153	C₂₉×#106	—	2	1	no	—
154	C₂₉×#106	—	2	1	no	—
155	C₂₉×C₄⋊C₈	—	2	1	no	—
156	C₂₉×C₄⋊C₈	—	2	1	no	—
157	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₂₉×#103	—	2	1	no	—
162	C₂₉×#103	—	2	1	no	—
163	C₂₉×#103	—	2	2	no	—
164	C₂₉×#103	—	2	2	no	—
165	C₂₉×#102	—	2	1	no	—
166	C₂₉×#102	—	2	1	no	—
167	C₂₉×#102	—	2	1	no	—
168	C₂₉×#102	—	2	1	no	—
169	C₂₉×#102	—	2	1	no	—
170	C₂₉×#102	—	2	1	no	—
171	C₂₉×#102	—	2	2	no	—
172	C₂₉×#102	—	2	2	no	—
173	C₂₉×#97	—	2	1	no	—
174	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
175	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
176	#41×C₂₉	—	4	4	no	—
177	#41×C₂₉	—	8	1	no	—
178	#41×C₂₉	—	8	1	no	—
179	C₂×Q₈×C₂₉	—	2	2	no	—
180	C₂×Q₈×C₂₉	—	2	2	no	—
181	C₂×Q₈×C₂₉	—	2	1	no	—
182	C₂×Q₈×C₂₉	—	2	1	no	—
183	C₂×Q₈×C₂₉	—	2	1	no	—
184	C₂×Q₈×C₂₉	—	8	1	no	—
185	C₂×Q₈×C₂₉	—	8	1	no	—
186	C₂×Q₈×C₂₉	—	8	1	no	—
187	C₂×Q₈×C₂₉	—	8	1	no	—
188	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
189	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
190	C₂×D₄×C₂₉	—	2	1	no	—
191	C₂×D₄×C₂₉	—	2	1	no	—
192	C₂×D₄×C₂₉	—	2	2	no	—
193	C₂×D₄×C₂₉	—	2	1	no	—
194	C₂×D₄×C₂₉	—	2	1	no	—
195	C₂×D₄×C₂₉	—	2	1	no	—
196	C₂×D₄×C₂₉	—	4	1	no	—
197	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
198	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₂₉	—	2	2	no	—
200	C₂²×C₄×C₂₉	—	2	2	no	—
201	C₂²×C₄×C₂₉	—	2	2	no	—
202	C₂²×C₄×C₂₉	—	2	1	no	—
203	C₂²×C₄×C₂₉	—	2	1	no	—
204	C₂²×C₄×C₂₉	—	4	1	no	—
205	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
208	SD₁₆×C₂₉	—	8	1	no	—
209	SD₁₆×C₂₉	—	8	1	no	—
210	D₈×C₂₉	—	8	1	no	—
211	D₈×C₂₉	—	8	1	no	—
212	M₁₆×C₂₉	—	4	2	no	—
213	C₂×C₈×C₂₉	—	2	1	no	—
214	C₂×C₈×C₂₉	—	2	1	no	—
215	C₂×C₈×C₂₉	—	2	1	no	—
216	C₂×C₈×C₂₉	—	2	1	no	—
217	C₂×C₈×C₂₉	—	2	1	no	—
218	C₂×C₈×C₂₉	—	2	1	no	—
219	C₂×C₈×C₂₉	—	8	1	no	—
220	C₂×C₈×C₂₉	—	8	1	no	—
221	C₄⋊C₄×C₂₉	—	2	2	no	—
222	C₄⋊C₄×C₂₉	—	2	2	no	—
223	C₄⋊C₄×C₂₉	—	2	2	no	—
224	C₄⋊C₄×C₂₉	—	2	2	no	—
225	C₄⋊C₄×C₂₉	—	2	2	no	—
226	C₄⋊C₄×C₂₉	—	2	2	no	—
227	C₄⋊C₄×C₂₉	—	2	2	no	—
228	C₄⋊C₄×C₂₉	—	2	2	no	—
229	C₄⋊C₄×C₂₉	—	2	1	no	—
230	C₄⋊C₄×C₂₉	—	2	1	no	—
231	C₄⋊C₄×C₂₉	—	2	1	no	—
232	C₄⋊C₄×C₂₉	—	2	1	no	—
233	C₄⋊C₄×C₂₉	—	2	1	no	—
234	C₄⋊C₄×C₂₉	—	2	1	no	—
235	C₄⋊C₄×C₂₉	—	2	1	no	—
236	C₄⋊C₄×C₂₉	—	2	1	no	—
237	C₄⋊C₄×C₂₉	—	2	1	no	—
238	C₄⋊C₄×C₂₉	—	2	1	no	—
239	C₄⋊C₄×C₂₉	—	2	1	no	—
240	C₄⋊C₄×C₂₉	—	2	1	no	—
241	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
242	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
243	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
244	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
245	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
246	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
247	C₂²⋊C₄×C₂₉	—	2	2	no	—
248	C₂²⋊C₄×C₂₉	—	2	2	no	—
249	C₂²⋊C₄×C₂₉	—	2	2	no	—
250	C₂²⋊C₄×C₂₉	—	2	2	no	—
251	C₂²⋊C₄×C₂₉	—	2	1	no	—
252	C₂²⋊C₄×C₂₉	—	2	1	no	—
253	C₂²⋊C₄×C₂₉	—	2	1	no	—
254	C₂²⋊C₄×C₂₉	—	2	1	no	—
255	C₂²⋊C₄×C₂₉	—	2	1	no	—
256	C₂²⋊C₄×C₂₉	—	2	1	no	—
257	C₂²⋊C₄×C₂₉	—	2	1	no	—
258	C₂²⋊C₄×C₂₉	—	2	1	no	—
259	C₂²⋊C₄×C₂₉	—	2	1	no	—
260	C₂²⋊C₄×C₂₉	—	2	1	no	—
261	C₂²⋊C₄×C₂₉	—	4	1	no	—
262	C₂²⋊C₄×C₂₉	—	4	1	no	—
263	C₄²×C₂₉	—	2	2	no	—
264	C₄²×C₂₉	—	2	2	no	—
265	C₄²×C₂₉	—	2	1	no	—
266	C₄²×C₂₉	—	2	1	no	—
267	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
268	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
269	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
270	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
271	#18726	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
272	C₂³×C₂₉	—	2	1	no	—
273	C₂³×C₂₉	—	2	1	no	—
274	C₂³×C₂₉	—	4	1	no	—
275	C₂³×C₂₉	#120	1	1	yes	characteristic
276	Q₈×C₂₉	—	2	1	no	—
277	Q₈×C₂₉	—	2	1	no	—
278	Q₈×C₂₉	—	2	1	no	—
279	Q₈×C₂₉	—	2	1	no	—
280	Q₈×C₂₉	—	4	2	no	—
281	Q₈×C₂₉	—	4	1	no	—
282	Q₈×C₂₉	—	4	1	no	—
283	Q₈×C₂₉	—	4	1	no	—
284	Q₈×C₂₉	—	4	1	no	—
285	Q₈×C₂₉	—	8	2	no	—
286	Q₈×C₂₉	—	8	2	no	—
287	D₄×C₂₉	—	2	1	no	—
288	D₄×C₂₉	—	2	1	no	—
289	D₄×C₂₉	—	2	1	no	—
290	D₄×C₂₉	—	2	1	no	—
291	D₄×C₂₉	—	4	2	no	—
292	D₄×C₂₉	—	4	2	no	—
293	D₄×C₂₉	—	4	2	no	—
294	D₄×C₂₉	—	4	1	no	—
295	D₄×C₂₉	—	4	1	no	—
296	D₄×C₂₉	—	4	1	no	—
297	D₄×C₂₉	—	4	1	no	—
298	D₄×C₂₉	—	8	2	no	—
299	D₄×C₂₉	—	8	2	no	—
300	C₂×C₄×C₂₉	—	2	2	no	—
301	C₂×C₄×C₂₉	—	2	1	no	—
302	C₂×C₄×C₂₉	—	2	1	no	—
303	C₂×C₄×C₂₉	—	2	1	no	—
304	C₂×C₄×C₂₉	—	2	1	no	—
305	C₂×C₄×C₂₉	—	2	1	no	—
306	C₂×C₄×C₂₉	—	2	1	no	—
307	C₂×C₄×C₂₉	—	2	1	no	—
308	C₂×C₄×C₂₉	—	2	1	no	—
309	C₂×C₄×C₂₉	—	2	1	no	—
310	C₂×C₄×C₂₉	—	2	2	no	—
311	C₂×C₄×C₂₉	—	2	2	no	—
312	C₂×C₄×C₂₉	—	2	1	no	—
313	C₂×C₄×C₂₉	—	4	1	no	—
314	C₂×C₄×C₂₉	—	4	1	no	—
315	C₂×C₄×C₂₉	—	4	1	no	—
316	C₂×C₄×C₂₉	—	4	1	no	—
317	C₂×C₄×C₂₉	—	4	1	no	—
318	C₂×C₄×C₂₉	—	8	2	no	—
319	C₂×C₄×C₂₉	—	8	2	no	—
320	C₂×C₄×C₂₉	—	8	2	no	—
321	C₂×C₄×C₂₉	—	8	2	no	—
322	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
323	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
324	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
325	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
328	C₈×C₂₉	—	4	1	no	—
329	C₈×C₂₉	—	4	1	no	—
330	C₈×C₂₉	—	4	1	no	—
331	C₈×C₂₉	—	4	1	no	—
332	C₈×C₂₉	—	4	1	no	—
333	C₈×C₂₉	—	4	1	no	—
334	#3552	C₂×C₂₉	1	1	yes	characteristic, complemented
335	#3247	C₂×C₂₉	1	1	yes	characteristic, complemented
336	#3247	C₂×C₂₉	1	1	yes	characteristic, complemented
337	#3141	C₂×C₂₉	1	1	yes	characteristic, complemented
338	#1638	C₂×C₂₉	1	1	yes	characteristic, complemented
339	#1637	C₂×C₂₉	1	1	yes	characteristic, complemented
340	#1636	C₂×C₂₉	1	1	yes	characteristic, complemented
341	#1635	C₂×C₂₉	1	1	yes	characteristic, complemented
342	#1628	C₂×C₂₉	1	1	yes	characteristic, complemented
343	#1627	C₂×C₂₉	1	1	yes	characteristic, complemented
344	#1626	C₂×C₂₉	1	1	yes	characteristic, complemented
345	#1625	C₂×C₂₉	1	1	yes	characteristic, complemented
346	C₂×#332	C₂×C₂₉	1	1	yes	characteristic, complemented
347	#1483	C₂×C₂₉	1	1	yes	characteristic, complemented
348	#1483	C₂×C₂₉	1	1	yes	characteristic, complemented
349	C₂²×C₂₉	—	2	1	no	—
350	C₂²×C₂₉	—	2	1	no	—
351	C₂²×C₂₉	—	4	1	no	—
352	C₂²×C₂₉	—	4	1	no	—
353	C₂²×C₂₉	—	4	1	no	—
354	C₂²×C₂₉	—	4	1	no	—
355	C₂²×C₂₉	—	4	1	no	—
356	C₂²×C₂₉	—	4	1	no	—
357	C₂²×C₂₉	—	8	1	no	—
358	C₂²×C₂₉	—	8	1	no	—
359	C₂²×C₂₉	—	8	1	no	—
360	C₂²×C₂₉	#454	1	2	yes	—
361	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
362	C₄×C₂₉	—	2	1	no	—
363	C₄×C₂₉	—	2	1	no	—
364	C₄×C₂₉	—	2	1	no	—
365	C₄×C₂₉	—	2	1	no	—
366	C₄×C₂₉	—	4	1	no	—
367	C₄×C₂₉	—	4	2	no	—
368	C₄×C₂₉	—	4	1	no	—
369	C₄×C₂₉	—	4	2	no	—
370	C₄×C₂₉	—	4	1	no	—
371	C₄×C₂₉	—	4	1	no	—
372	C₄×C₂₉	—	4	1	no	—
373	C₄×C₂₉	—	4	1	no	—
374	C₄×C₂₉	—	8	1	no	—
375	C₄×C₂₉	#576	1	1	yes	characteristic
376	C₄×C₂₉	#577	1	1	yes	characteristic
377	C₄×C₂₉	#577	1	1	yes	characteristic
378	C₄×C₂₉	#578	1	1	yes	characteristic
379	#563	—	2	2	no	—
380	#557	C₂²×C₂₉	1	1	yes	characteristic
381	#556	C₂²×C₂₉	1	1	yes	characteristic
382	#554	—	2	1	no	—
383	#553	—	2	1	no	—
384	D₄×Q₈	—	2	1	no	—
385	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
386	#548	—	2	1	no	—
387	#547	C₂²×C₂₉	1	1	yes	characteristic
388	#544	—	2	1	no	—
389	#542	—	2	1	no	—
390	#541	—	2	1	no	—
391	#539	—	2	2	no	—
392	#536	—	2	1	no	—
393	#532	C₂²×C₂₉	1	1	yes	characteristic
394	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
395	#529	C₂²×C₂₉	1	1	yes	characteristic
396	#529	C₂²×C₂₉	1	1	yes	characteristic
397	#489	—	2	2	no	—
398	#487	C₂²×C₂₉	1	1	yes	characteristic
399	#487	C₂²×C₂₉	1	1	yes	characteristic
400	#486	C₂²×C₂₉	1	1	yes	characteristic
401	#486	C₂²×C₂₉	1	1	yes	characteristic
402	#478	—	2	1	no	—
403	#478	—	2	1	no	—
404	#477	C₂²×C₂₉	1	1	yes	characteristic
405	#477	C₂²×C₂₉	1	1	yes	characteristic
406	#476	C₂²×C₂₉	1	1	yes	characteristic
407	#476	C₂²×C₂₉	1	1	yes	characteristic
408	#466	—	2	1	no	—
409	#466	—	2	1	no	—
410	#465	—	2	1	no	—
411	#465	—	2	1	no	—
412	#463	—	2	1	no	—
413	#463	—	2	1	no	—
414	#460	C₂²×C₂₉	1	1	yes	characteristic
415	#460	C₂²×C₂₉	1	1	yes	characteristic
416	#459	C₂²×C₂₉	1	1	yes	characteristic
417	#459	C₂²×C₂₉	1	1	yes	characteristic
418	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
419	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
420	#417	—	2	2	no	—
421	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
422	#332	C₂²×C₂₉	1	1	yes	characteristic
423	#332	C₂²×C₂₉	1	1	yes	characteristic
424	#332	C₂²×C₂₉	1	1	yes	characteristic
425	#332	C₂²×C₂₉	1	1	yes	characteristic
426	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
427	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
428	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
429	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
430	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
431	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
432	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
433	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
434	C₂×C₂₉	—	2	2	no	—
435	C₂×C₂₉	—	8	1	no	—
436	C₂×C₂₉	—	8	1	no	—
437	C₂×C₂₉	—	16	1	no	—
438	C₂×C₂₉	#3012	1	1	yes	characteristic
439	C₂×C₂₉	#3013	1	1	yes	characteristic
440	C₂×C₂₉	C₂×#454	1	1	yes	characteristic
441	C₂×#41	—	2	1	no	—
442	C₂×#41	—	2	1	no	—
443	C₂²×Q₈	—	2	1	no	—
444	C₂²×Q₈	—	2	1	no	—
445	C₂×SD₁₆	—	2	1	no	—
446	C₂×SD₁₆	—	2	1	no	—
447	C₂×D₈	—	2	1	no	—
448	C₂×D₈	—	2	1	no	—
449	C₂×M₁₆	—	2	1	no	—
450	C₂²×C₈	—	2	1	no	—
451	C₂²×C₈	—	2	1	no	—
452	C₄⋊Q₈	—	2	2	no	—
453	C₄⋊Q₈	—	2	1	no	—
454	C₄⋊Q₈	—	2	1	no	—
455	C₄⋊Q₈	—	2	1	no	—
456	C₄⋊Q₈	—	2	1	no	—
457	C₄⋊Q₈	D₄×C₂₉	1	2	yes	—
458	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
459	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
460	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
461	#127	C₂³×C₂₉	1	1	yes	characteristic
462	#126	—	2	2	no	—
463	#126	—	2	2	no	—
464	#126	—	2	2	no	—
465	#126	—	2	1	no	—
466	#126	—	2	1	no	—
467	#125	—	2	2	no	—
468	#125	—	2	2	no	—
469	#125	—	2	2	no	—
470	#125	—	2	1	no	—
471	#125	D₄×C₂₉	1	1	yes	characteristic
472	#125	D₄×C₂₉	1	1	yes	characteristic
473	#124	—	2	2	no	—
474	#124	—	2	1	no	—
475	#124	—	2	1	no	—
476	#124	D₄×C₂₉	1	1	yes	characteristic
477	#124	D₄×C₂₉	1	1	yes	characteristic
478	#123	—	2	2	no	—
479	#123	—	2	2	no	—
480	#123	—	2	1	no	—
481	#123	—	2	1	no	—
482	#123	—	2	2	no	—
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	—	2	2	no	—
488	C₂²⋊Q₈	—	2	1	no	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	—	2	1	no	—
491	C₂²⋊Q₈	—	2	1	no	—
492	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
493	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
494	#121	—	2	2	no	—
495	#121	—	2	1	no	—
496	#121	—	2	1	no	—
497	#121	—	2	1	no	—
498	#121	D₄×C₂₉	1	1	yes	characteristic
499	#121	D₄×C₂₉	1	1	yes	characteristic
500	C₄×Q₈	—	2	1	no	—
501	C₄×Q₈	—	2	1	no	—
502	C₄×Q₈	—	2	1	no	—
503	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
504	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	—	2	1	no	—
508	C₄×D₄	—	2	1	no	—
509	C₄×D₄	—	2	1	no	—
510	C₄×D₄	—	2	1	no	—
511	C₄×D₄	—	2	1	no	—
512	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
513	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
514	#117	—	2	1	no	—
515	#117	—	2	1	no	—
516	#117	—	2	1	no	—
517	C₂×C₄⋊C₄	—	2	1	no	—
518	C₂×C₄⋊C₄	—	2	1	no	—
519	C₂×C₄⋊C₄	D₄×C₂₉	1	2	yes	—
520	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
521	#107	—	2	1	no	—
522	#107	—	2	1	no	—
523	#106	—	2	1	no	—
524	#106	—	2	1	no	—
525	C₄⋊C₈	—	2	1	no	—
526	C₄⋊C₈	—	2	1	no	—
527	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
528	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
529	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
530	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
531	#103	—	2	1	no	—
532	#103	—	2	1	no	—
533	#103	—	2	2	no	—
534	#103	—	2	2	no	—
535	#102	—	2	1	no	—
536	#102	—	2	1	no	—
537	#102	—	2	2	no	—
538	#102	—	2	2	no	—
539	#102	—	2	1	no	—
540	#102	—	2	1	no	—
541	#102	—	2	1	no	—
542	#102	—	2	1	no	—
543	#97	—	2	1	no	—
544	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
545	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
546	C₂₉	#18726	1	1	yes	characteristic, direct product factor, Sylow
547	#41	—	4	4	no	—
548	#41	—	8	1	no	—
549	#41	—	8	1	no	—
550	C₂×Q₈	—	2	2	no	—
551	C₂×Q₈	—	2	2	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	8	1	no	—
556	C₂×Q₈	—	8	1	no	—
557	C₂×Q₈	—	8	1	no	—
558	C₂×Q₈	—	8	1	no	—
559	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
560	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	4	1	no	—
568	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
569	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	4	1	no	—
576	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
577	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
578	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
579	SD₁₆	—	8	1	no	—
580	SD₁₆	—	8	1	no	—
581	D₈	—	8	1	no	—
582	D₈	—	8	1	no	—
583	M₁₆	—	4	2	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	8	1	no	—
591	C₂×C₈	—	8	1	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
613	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
614	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
615	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
616	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
617	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	2	2	no	—
620	C₂²⋊C₄	—	2	2	no	—
621	C₂²⋊C₄	—	2	2	no	—
622	C₂²⋊C₄	—	2	1	no	—
623	C₂²⋊C₄	—	2	1	no	—
624	C₂²⋊C₄	—	2	1	no	—
625	C₂²⋊C₄	—	2	1	no	—
626	C₂²⋊C₄	—	2	1	no	—
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	2	1	no	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	2	1	no	—
631	C₂²⋊C₄	—	2	1	no	—
632	C₂²⋊C₄	—	4	1	no	—
633	C₂²⋊C₄	—	4	1	no	—
634	C₄²	—	2	2	no	—
635	C₄²	—	2	2	no	—
636	C₄²	—	2	1	no	—
637	C₄²	—	2	1	no	—
638	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
639	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
640	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
641	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
642	C₂³	—	2	1	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	4	1	no	—
645	C₂³	C₂₉×#120	1	1	yes	characteristic
646	Q₈	—	2	1	no	—
647	Q₈	—	2	1	no	—
648	Q₈	—	2	1	no	—
649	Q₈	—	2	1	no	—
650	Q₈	—	4	2	no	—
651	Q₈	—	4	1	no	—
652	Q₈	—	4	1	no	—
653	Q₈	—	4	1	no	—
654	Q₈	—	4	1	no	—
655	Q₈	—	8	2	no	—
656	Q₈	—	8	2	no	—
657	D₄	—	2	1	no	—
658	D₄	—	2	1	no	—
659	D₄	—	2	1	no	—
660	D₄	—	2	1	no	—
661	D₄	—	4	2	no	—
662	D₄	—	4	2	no	—
663	D₄	—	4	2	no	—
664	D₄	—	4	1	no	—
665	D₄	—	4	1	no	—
666	D₄	—	4	1	no	—
667	D₄	—	4	1	no	—
668	D₄	—	8	2	no	—
669	D₄	—	8	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	8	2	no	—
689	C₂×C₄	—	8	2	no	—
690	C₂×C₄	—	8	2	no	—
691	C₂×C₄	—	8	2	no	—
692	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
693	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
694	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
695	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
696	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
697	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
698	C₈	—	4	1	no	—
699	C₈	—	4	1	no	—
700	C₈	—	4	1	no	—
701	C₈	—	4	1	no	—
702	C₈	—	4	1	no	—
703	C₈	—	4	1	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	2	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	8	1	no	—
713	C₂²	—	8	1	no	—
714	C₂²	—	8	1	no	—
715	C₂²	C₂₉×#454	1	2	yes	—
716	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
717	C₄	—	2	1	no	—
718	C₄	—	2	1	no	—
719	C₄	—	2	1	no	—
720	C₄	—	2	1	no	—
721	C₄	—	4	1	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	2	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	1	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	1	no	—
729	C₄	—	8	1	no	—
730	C₄	C₂₉×#576	1	1	yes	characteristic
731	C₄	C₂₉×#577	1	1	yes	characteristic
732	C₄	C₂₉×#577	1	1	yes	characteristic
733	C₄	C₂₉×#578	1	1	yes	characteristic
734	C₂	—	2	2	no	—
735	C₂	—	8	1	no	—
736	C₂	—	8	1	no	—
737	C₂	—	16	1	no	—
738	C₂	C₂₉×#3012	1	1	yes	characteristic
739	C₂	C₂₉×#3013	1	1	yes	characteristic
740	C₂	C₂×C₂₉×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3552	C₂	semidirect
2. C₂₉×#3247	C₂	semidirect
3. C₂₉×#3247	C₂	semidirect
4. C₂₉×#3141	C₂	semidirect
5. C₂₉×#1638	C₂	semidirect
6. C₂₉×#1637	C₂	semidirect
7. C₂₉×#1636	C₂	semidirect
8. C₂₉×#1635	C₂	semidirect
9. C₂₉×#1628	C₂	semidirect
10. C₂₉×#1627	C₂	semidirect
11. C₂₉×#1626	C₂	semidirect
12. C₂₉×#1625	C₂	semidirect
13. C₂×C₂₉×#332	C₂	semidirect
14. C₂₉×#1483	C₂	semidirect
15. C₂₉×#1483	C₂	semidirect
271. #18726	C₂₉	direct (N × H)
334. #3552	C₂×C₂₉	semidirect
335. #3247	C₂×C₂₉	semidirect
336. #3247	C₂×C₂₉	semidirect
337. #3141	C₂×C₂₉	semidirect
338. #1638	C₂×C₂₉	semidirect
339. #1637	C₂×C₂₉	semidirect
340. #1636	C₂×C₂₉	semidirect
341. #1635	C₂×C₂₉	semidirect
342. #1628	C₂×C₂₉	semidirect
343. #1627	C₂×C₂₉	semidirect
344. #1626	C₂×C₂₉	semidirect
345. #1625	C₂×C₂₉	semidirect
346. C₂×#332	C₂×C₂₉	semidirect
347. #1483	C₂×C₂₉	semidirect
348. #1483	C₂×C₂₉	semidirect
546. C₂₉	#18726	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×#3552	2
C₂₉×#3247	2
C₂₉×#3141	2
C₂₉×#1638	2
C₂₉×#1637	2
C₂₉×#1636	2
C₂₉×#1635	2
C₂₉×#1628	2
C₂₉×#1627	2
C₂₉×#1626	2
C₂₉×#1625	2
C₂×C₂₉×#332	2
C₂₉×#1483	2
#18726	29

Subgroups — C29×#18726 #20313626

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18726 #20313626