Subgroups — C₂₉×#21506 #20316406

Order 7424.

972 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#462	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#441	C₂	1	2	yes	maximal
3	C₄×C₂₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₄²×Q₈×C₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#1981	C₂	1	1	yes	maximal, characteristic
6	C₂₉×#1948	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#1927	C₂	1	2	yes	maximal
8	C₂₉×#1878	C₂	1	2	yes	maximal
9	C₂₉×#1803	C₂	1	1	yes	maximal, characteristic
10	C₂₉×#1767	C₂	1	1	yes	maximal, characteristic
11	C₂₉×#1763	C₂	1	2	yes	maximal
12	C₂²×Q₁₆×C₂₉	C₂²	1	2	yes	—
13	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
18	C₂₉×#462	C₄	1	8	yes	complemented
19	C₂₉×#441	—	2	8	no	—
20	C₂×C₂₉×#106	C₂²	1	2	yes	—
21	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×#103	C₂²	1	2	yes	—
24	C₂×C₂₉×#103	C₂²	1	2	yes	—
25	C₂×C₂₉×#103	C₂²	1	2	yes	—
26	C₂×C₂₉×#103	C₂²	1	2	yes	—
27	C₂×C₂₉×#97	C₂²	1	2	yes	—
28	C₂₉×#391	C₂²	1	2	yes	—
29	C₂₉×#389	—	2	1	no	—
30	C₂₉×#389	—	2	1	no	—
31	C₂₉×#384	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₂₉	—	2	1	no	—
33	C₄×C₄⋊C₄×C₂₉	—	2	1	no	—
34	C₄×C₄⋊C₄×C₂₉	—	2	1	no	—
35	C₄×C₄⋊C₄×C₂₉	—	2	1	no	—
36	C₄×C₄⋊C₄×C₂₉	—	2	1	no	—
37	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
40	C₄³×C₂₉	—	2	1	no	—
41	C₄³×C₂₉	C₂²	1	1	yes	characteristic
42	C₂₉×#340	C₂²	1	2	yes	—
43	C₂₉×#340	C₂²	1	2	yes	—
44	C₂₉×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
46	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
47	C₂×Q₁₆×C₂₉	—	2	4	no	—
48	C₂×Q₁₆×C₂₉	—	2	4	no	—
49	C₂×Q₁₆×C₂₉	C₂×C₄	1	8	yes	—
50	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
52	C₂₉×C₄⋊Q₈	—	2	2	no	—
53	C₂₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
54	C₄×Q₈×C₂₉	—	2	2	no	—
55	C₄×Q₈×C₂₉	—	2	2	no	—
56	C₄×Q₈×C₂₉	—	2	2	no	—
57	C₄×Q₈×C₂₉	—	2	2	no	—
58	C₄×Q₈×C₂₉	—	2	4	no	—
59	C₄×Q₈×C₂₉	—	2	4	no	—
60	C₄×Q₈×C₂₉	C₂×C₄	1	4	yes	—
61	C₄×Q₈×C₂₉	D₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₂₉	—	2	1	no	—
75	C₂×C₄²×C₂₉	—	2	1	no	—
76	C₂×C₄²×C₂₉	—	2	1	no	—
77	C₂×C₄²×C₂₉	—	2	2	no	—
78	C₂×C₄²×C₂₉	—	2	1	no	—
79	C₂×C₄²×C₂₉	—	2	1	no	—
80	C₂×C₄²×C₂₉	—	2	1	no	—
81	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
88	C₂₉×#106	—	2	4	no	—
89	C₂₉×C₄⋊C₈	—	2	2	no	—
90	C₂₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
91	C₂₉×#103	—	2	4	no	—
92	C₂₉×#103	—	2	4	no	—
93	C₂₉×#103	—	2	4	no	—
94	C₂₉×#103	C₂×C₄	1	8	yes	—
95	C₂₉×#97	—	2	4	no	—
96	C₂₉×#95	—	2	1	no	—
97	C₂₉×#95	—	2	1	no	—
98	C₂₉×#95	—	2	1	no	—
99	C₂₉×#95	—	2	2	no	—
100	C₂₉×#95	—	2	2	no	—
101	C₂×Q₈×C₂₉	—	2	1	no	—
102	C₂×Q₈×C₂₉	—	2	1	no	—
103	C₂×Q₈×C₂₉	—	2	1	no	—
104	C₂×Q₈×C₂₉	—	2	2	no	—
105	C₂×Q₈×C₂₉	—	2	2	no	—
106	C₂×Q₈×C₂₉	—	2	2	no	—
107	C₂×Q₈×C₂₉	—	2	2	no	—
108	C₂×Q₈×C₂₉	—	2	2	no	—
109	C₂×Q₈×C₂₉	C₂²×C₄	1	4	yes	—
110	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
111	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
112	C₂×Q₈×C₂₉	#41	1	2	yes	—
113	C₂²×C₄×C₂₉	—	2	1	no	—
114	C₂²×C₄×C₂₉	—	2	1	no	—
115	C₂²×C₄×C₂₉	—	2	1	no	—
116	C₂²×C₄×C₂₉	—	2	1	no	—
117	C₂²×C₄×C₂₉	—	2	2	no	—
118	C₂²×C₄×C₂₉	—	2	2	no	—
119	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
126	Q₁₆×C₂₉	—	2	16	no	—
127	C₂×C₈×C₂₉	—	2	2	no	—
128	C₂×C₈×C₂₉	—	2	2	no	—
129	C₂×C₈×C₂₉	—	2	2	no	—
130	C₂×C₈×C₂₉	—	2	2	no	—
131	C₂×C₈×C₂₉	—	2	2	no	—
132	C₂×C₈×C₂₉	C₂²×C₄	1	4	yes	—
133	C₄⋊C₄×C₂₉	—	2	4	no	—
134	C₄⋊C₄×C₂₉	—	2	4	no	—
135	C₄⋊C₄×C₂₉	—	2	4	no	—
136	C₄⋊C₄×C₂₉	—	2	4	no	—
137	C₄⋊C₄×C₂₉	—	2	4	no	—
138	C₄⋊C₄×C₂₉	—	2	1	no	—
139	C₄⋊C₄×C₂₉	—	2	1	no	—
140	C₄⋊C₄×C₂₉	—	2	1	no	—
141	C₄⋊C₄×C₂₉	—	2	2	no	—
142	C₄⋊C₄×C₂₉	—	2	2	no	—
143	C₄⋊C₄×C₂₉	—	4	2	no	—
144	C₄⋊C₄×C₂₉	—	4	4	no	—
145	C₄⋊C₄×C₂₉	—	4	2	no	—
146	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
147	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
148	C₄⋊C₄×C₂₉	#41	1	2	yes	—
149	C₄²×C₂₉	—	2	4	no	—
150	C₄²×C₂₉	—	2	4	no	—
151	C₄²×C₂₉	—	2	4	no	—
152	C₄²×C₂₉	—	2	2	no	—
153	C₄²×C₂₉	—	2	2	no	—
154	C₄²×C₂₉	—	2	2	no	—
155	C₄²×C₂₉	—	2	1	no	—
156	C₄²×C₂₉	—	2	1	no	—
157	C₄²×C₂₉	—	4	1	no	—
158	C₄²×C₂₉	—	4	2	no	—
159	C₄²×C₂₉	—	4	4	no	—
160	C₄²×C₂₉	—	4	2	no	—
161	C₄²×C₂₉	—	4	2	no	—
162	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
163	C₄²×C₂₉	C₂×D₄	1	2	yes	—
164	C₄²×C₂₉	#41	1	2	yes	—
165	C₄²×C₂₉	#41	1	2	yes	—
166	#21506	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
168	Q₈×C₂₉	—	2	2	no	—
169	Q₈×C₂₉	—	2	2	no	—
170	Q₈×C₂₉	—	2	2	no	—
171	Q₈×C₂₉	—	2	4	no	—
172	Q₈×C₂₉	—	2	4	no	—
173	Q₈×C₂₉	—	4	2	no	—
174	Q₈×C₂₉	—	4	2	no	—
175	Q₈×C₂₉	C₄×D₄	1	4	yes	—
176	C₂×C₄×C₂₉	—	2	2	no	—
177	C₂×C₄×C₂₉	—	2	2	no	—
178	C₂×C₄×C₂₉	—	2	1	no	—
179	C₂×C₄×C₂₉	—	2	2	no	—
180	C₂×C₄×C₂₉	—	2	1	no	—
181	C₂×C₄×C₂₉	—	2	1	no	—
182	C₂×C₄×C₂₉	—	2	1	no	—
183	C₂×C₄×C₂₉	—	2	1	no	—
184	C₂×C₄×C₂₉	—	2	1	no	—
185	C₂×C₄×C₂₉	—	2	1	no	—
186	C₂×C₄×C₂₉	—	2	1	no	—
187	C₂×C₄×C₂₉	—	2	2	no	—
188	C₂×C₄×C₂₉	—	2	4	no	—
189	C₂×C₄×C₂₉	—	2	2	no	—
190	C₂×C₄×C₂₉	—	2	1	no	—
191	C₂×C₄×C₂₉	—	2	2	no	—
192	C₂×C₄×C₂₉	—	2	1	no	—
193	C₂×C₄×C₂₉	—	2	1	no	—
194	C₂×C₄×C₂₉	—	4	2	no	—
195	C₂×C₄×C₂₉	—	4	2	no	—
196	C₂×C₄×C₂₉	—	4	1	no	—
197	C₂×C₄×C₂₉	—	4	1	no	—
198	C₂×C₄×C₂₉	—	4	1	no	—
199	C₂×C₄×C₂₉	—	4	1	no	—
200	C₂×C₄×C₂₉	—	4	1	no	—
201	C₂×C₄×C₂₉	—	4	1	no	—
202	C₂×C₄×C₂₉	—	4	2	no	—
203	C₂×C₄×C₂₉	—	4	2	no	—
204	C₂×C₄×C₂₉	—	4	2	no	—
205	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
206	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
207	C₂×C₄×C₂₉	#121	1	2	yes	—
208	C₂×C₄×C₂₉	#121	1	2	yes	—
209	C₂×C₄×C₂₉	#137	1	2	yes	—
210	C₂×C₄×C₂₉	#137	1	2	yes	—
211	C₂×C₄×C₂₉	#137	1	2	yes	—
212	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
218	C₈×C₂₉	—	2	4	no	—
219	C₈×C₂₉	—	4	2	no	—
220	C₂×#462	C₂×C₂₉	1	1	yes	characteristic
221	C₂×#441	C₂×C₂₉	1	2	yes	—
222	C₄×C₄⋊Q₈	C₂×C₂₉	1	1	yes	characteristic
223	C₄²×Q₈	C₂×C₂₉	1	1	yes	characteristic
224	#1981	C₂×C₂₉	1	1	yes	characteristic
225	#1948	C₂×C₂₉	1	1	yes	characteristic
226	#1927	C₂×C₂₉	1	2	yes	—
227	#1878	C₂×C₂₉	1	2	yes	—
228	#1803	C₂×C₂₉	1	1	yes	characteristic
229	#1767	C₂×C₂₉	1	1	yes	characteristic
230	#1763	C₂×C₂₉	1	2	yes	—
231	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
232	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
233	C₂²×C₂₉	#525	1	1	yes	characteristic
234	C₂²×C₂₉	C₂×#137	1	1	yes	characteristic
235	C₂²×C₂₉	C₂×#137	1	1	yes	characteristic
236	C₂²×C₂₉	C₂×#137	1	1	yes	characteristic
237	C₂²×C₂₉	#575	1	1	yes	characteristic
238	C₄×C₂₉	—	2	2	no	—
239	C₄×C₂₉	—	2	2	no	—
240	C₄×C₂₉	—	2	2	no	—
241	C₄×C₂₉	—	2	2	no	—
242	C₄×C₂₉	—	2	4	no	—
243	C₄×C₂₉	—	4	1	no	—
244	C₄×C₂₉	—	4	2	no	—
245	C₄×C₂₉	—	4	2	no	—
246	C₄×C₂₉	—	4	2	no	—
247	C₄×C₂₉	—	4	4	no	—
248	C₄×C₂₉	—	8	2	no	—
249	C₄×C₂₉	#441	1	4	yes	complemented
250	C₄×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
251	C₄×C₂₉	C₄×#41	1	1	yes	characteristic
252	C₄×C₂₉	#529	1	1	yes	characteristic
253	C₄×C₂₉	#532	1	1	yes	characteristic
254	C₂²×Q₁₆	C₂²×C₂₉	1	2	yes	—
255	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
256	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	—
257	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
258	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
259	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
260	#462	C₄×C₂₉	1	8	yes	complemented
261	#441	—	2	8	no	—
262	C₂×#106	C₂²×C₂₉	1	2	yes	—
263	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
265	C₂×#103	C₂²×C₂₉	1	2	yes	—
266	C₂×#103	C₂²×C₂₉	1	2	yes	—
267	C₂×#103	C₂²×C₂₉	1	2	yes	—
268	C₂×#103	C₂²×C₂₉	1	2	yes	—
269	C₂×#97	C₂²×C₂₉	1	2	yes	—
270	#391	C₂²×C₂₉	1	2	yes	—
271	#389	—	2	1	no	—
272	#389	—	2	1	no	—
273	#384	C₂²×C₂₉	1	1	yes	characteristic
274	C₄×C₄⋊C₄	—	2	1	no	—
275	C₄×C₄⋊C₄	—	2	1	no	—
276	C₄×C₄⋊C₄	—	2	1	no	—
277	C₄×C₄⋊C₄	—	2	1	no	—
278	C₄×C₄⋊C₄	—	2	1	no	—
279	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
280	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
281	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
282	C₄³	—	2	1	no	—
283	C₄³	C₂²×C₂₉	1	1	yes	characteristic
284	#340	C₂²×C₂₉	1	2	yes	—
285	#340	C₂²×C₂₉	1	2	yes	—
286	#336	C₂²×C₂₉	1	2	yes	—
287	C₂×C₂₉	C₄×#121	1	1	yes	characteristic
288	C₂×C₂₉	C₂×#441	1	1	yes	characteristic
289	C₂×C₂₉	C₄×#137	1	1	yes	characteristic
290	C₂×C₂₉	#3037	1	1	yes	characteristic
291	C₂×C₂₉	#3039	1	1	yes	characteristic
292	C₂×C₂₉	#3113	1	1	yes	characteristic
293	C₂×C₂₉	#3116	1	1	yes	characteristic
294	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
295	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
296	C₂×Q₁₆	—	2	4	no	—
297	C₂×Q₁₆	—	2	4	no	—
298	C₂×Q₁₆	C₂×C₄×C₂₉	1	8	yes	—
299	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
300	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
301	C₄⋊Q₈	—	2	2	no	—
302	C₄⋊Q₈	C₂×C₄×C₂₉	1	4	yes	—
303	C₄×Q₈	—	2	2	no	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×Q₈	—	2	2	no	—
306	C₄×Q₈	—	2	2	no	—
307	C₄×Q₈	—	2	4	no	—
308	C₄×Q₈	—	2	4	no	—
309	C₄×Q₈	C₂×C₄×C₂₉	1	4	yes	—
310	C₄×Q₈	D₄×C₂₉	1	4	yes	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	—	2	2	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
331	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
332	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
333	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
336	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
337	#106	—	2	4	no	—
338	C₄⋊C₈	—	2	2	no	—
339	C₄⋊C₈	C₂×C₄×C₂₉	1	4	yes	—
340	#103	—	2	4	no	—
341	#103	—	2	4	no	—
342	#103	—	2	4	no	—
343	#103	C₂×C₄×C₂₉	1	8	yes	—
344	#97	—	2	4	no	—
345	#95	—	2	1	no	—
346	#95	—	2	1	no	—
347	#95	—	2	1	no	—
348	#95	—	2	2	no	—
349	#95	—	2	2	no	—
350	C₂₉	#21506	1	1	yes	characteristic, direct product factor, Sylow
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	C₂²×C₄×C₂₉	1	4	yes	—
360	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
361	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
362	C₂×Q₈	#41×C₂₉	1	2	yes	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
375	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
376	Q₁₆	—	2	16	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	C₂²×C₄×C₂₉	1	4	yes	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₄⋊C₄	—	4	4	no	—
395	C₄⋊C₄	—	4	2	no	—
396	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
397	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
398	C₄⋊C₄	#41×C₂₉	1	2	yes	—
399	C₄²	—	2	4	no	—
400	C₄²	—	2	4	no	—
401	C₄²	—	2	4	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	2	1	no	—
407	C₄²	—	4	1	no	—
408	C₄²	—	4	2	no	—
409	C₄²	—	4	4	no	—
410	C₄²	—	4	2	no	—
411	C₄²	—	4	2	no	—
412	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
413	C₄²	C₂×D₄×C₂₉	1	2	yes	—
414	C₄²	#41×C₂₉	1	2	yes	—
415	C₄²	#41×C₂₉	1	2	yes	—
416	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
417	Q₈	—	2	2	no	—
418	Q₈	—	2	2	no	—
419	Q₈	—	2	2	no	—
420	Q₈	—	2	4	no	—
421	Q₈	—	2	4	no	—
422	Q₈	—	4	2	no	—
423	Q₈	—	4	2	no	—
424	Q₈	C₄×D₄×C₂₉	1	4	yes	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
455	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
456	C₂×C₄	C₂₉×#121	1	2	yes	—
457	C₂×C₄	C₂₉×#121	1	2	yes	—
458	C₂×C₄	C₂₉×#137	1	2	yes	—
459	C₂×C₄	C₂₉×#137	1	2	yes	—
460	C₂×C₄	C₂₉×#137	1	2	yes	—
461	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
463	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
464	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
465	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
466	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
467	C₈	—	2	4	no	—
468	C₈	—	4	2	no	—
469	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
470	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
471	C₂²	C₂₉×#525	1	1	yes	characteristic
472	C₂²	C₂×C₂₉×#137	1	1	yes	characteristic
473	C₂²	C₂×C₂₉×#137	1	1	yes	characteristic
474	C₂²	C₂×C₂₉×#137	1	1	yes	characteristic
475	C₂²	C₂₉×#575	1	1	yes	characteristic
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	2	2	no	—
479	C₄	—	2	4	no	—
480	C₄	—	2	2	no	—
481	C₄	—	4	2	no	—
482	C₄	—	4	2	no	—
483	C₄	—	4	4	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	2	no	—
486	C₄	—	8	2	no	—
487	C₄	C₂₉×#441	1	4	yes	complemented
488	C₄	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
489	C₄	C₄×#41×C₂₉	1	1	yes	characteristic
490	C₄	C₂₉×#529	1	1	yes	characteristic
491	C₄	C₂₉×#532	1	1	yes	characteristic
492	C₂	C₄×C₂₉×#121	1	1	yes	characteristic
493	C₂	C₂×C₂₉×#441	1	1	yes	characteristic
494	C₂	C₄×C₂₉×#137	1	1	yes	characteristic
495	C₂	C₂₉×#3037	1	1	yes	characteristic
496	C₂	C₂₉×#3039	1	1	yes	characteristic
497	C₂	C₂₉×#3113	1	1	yes	characteristic
498	C₂	C₂₉×#3116	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
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
18. C₂₉×#462	C₄	semidirect
166. #21506	C₂₉	direct (N × H)
249. C₄×C₂₉	#441	semidirect
260. #462	C₄×C₂₉	semidirect
350. C₂₉	#21506	direct (N × H)
487. C₄	C₂₉×#441	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#462	2
C₂×C₂₉×#441	2
C₄×C₂₉×C₄⋊Q₈	2
C₄²×Q₈×C₂₉	2
C₂₉×#1981	2
C₂₉×#1948	2
C₂₉×#1927	2
C₂₉×#1878	2
C₂₉×#1803	2
C₂₉×#1767	2
C₂₉×#1763	2
#21506	29

Subgroups — C29×#21506 #20316406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#21506 #20316406