Subgroups — C₂₉×#21463 #20316363

Order 7424.

1344 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#519	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#451	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×#441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×Q₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2323	C₂	1	1	yes	maximal, characteristic
6	C₂₉×#1878	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1878	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1873	C₂	1	1	yes	maximal, characteristic
9	C₂₉×#1865	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1854	C₂	1	1	yes	maximal, characteristic
12	C₂₉×#1787	C₂	1	1	yes	maximal, characteristic
13	C₂₉×#1763	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1750	C₂	1	1	yes	maximal, characteristic
16	C₂³×Q₈×C₂₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂₉×#519	—	2	4	no	—
21	C₂₉×#519	—	2	4	no	—
22	C₂×C₄×Q₈×C₂₉	—	2	1	no	—
23	C₂×C₄×Q₈×C₂₉	—	2	1	no	—
24	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#117	—	2	1	no	—
30	C₂×C₂₉×#117	—	2	1	no	—
31	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
33	C₂₉×#451	C₄	1	8	yes	complemented
34	C₂₉×#441	—	2	4	no	—
35	C₄×Q₁₆×C₂₉	—	2	4	no	—
36	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
37	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
38	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
39	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
40	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
41	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
42	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
43	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
44	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
45	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
46	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
50	C₂₉×#391	C₂²	1	1	yes	characteristic
51	C₂₉×#389	—	2	1	no	—
52	C₂₉×#389	C₂²	1	1	yes	characteristic
53	C₂₉×#388	—	2	1	no	—
54	C₂₉×#388	—	2	1	no	—
55	C₂₉×#387	—	2	1	no	—
56	C₂₉×#380	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
58	C₂₉×#340	C₂²	1	1	yes	characteristic
59	C₂₉×#340	C₂²	1	1	yes	characteristic
60	C₂₉×#340	C₂²	1	1	yes	characteristic
61	C₂₉×#340	C₂²	1	1	yes	characteristic
62	C₂₉×#336	C₂²	1	1	yes	characteristic
63	C₂₉×#336	C₂²	1	1	yes	characteristic
64	C₂²×Q₈×C₂₉	—	2	2	no	—
65	C₂²×Q₈×C₂₉	—	2	2	no	—
66	C₂²×Q₈×C₂₉	—	2	2	no	—
67	C₂²×Q₈×C₂₉	—	2	2	no	—
68	C₂²×Q₈×C₂₉	—	2	1	no	—
69	C₂²×Q₈×C₂₉	—	2	2	no	—
70	C₂²×Q₈×C₂₉	C₂×C₄	1	4	yes	—
71	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
73	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₂₉	—	2	1	no	—
75	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
76	C₂×Q₁₆×C₂₉	—	2	2	no	—
77	C₂×Q₁₆×C₂₉	—	2	2	no	—
78	C₂×Q₁₆×C₂₉	—	2	2	no	—
79	C₂×Q₁₆×C₂₉	—	2	2	no	—
80	C₂×Q₁₆×C₂₉	C₂×C₄	1	4	yes	—
81	C₂×Q₁₆×C₂₉	C₂×C₄	1	4	yes	—
82	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
86	C₂₉×C₂²⋊Q₈	—	2	2	no	—
87	C₂₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
88	C₄×Q₈×C₂₉	—	2	8	no	—
89	C₄×Q₈×C₂₉	—	2	8	no	—
90	C₄×Q₈×C₂₉	—	2	2	no	—
91	C₄×Q₈×C₂₉	—	2	2	no	—
92	C₄×Q₈×C₂₉	—	2	2	no	—
93	C₄×Q₈×C₂₉	—	2	2	no	—
94	C₄×Q₈×C₂₉	—	2	2	no	—
95	C₄×Q₈×C₂₉	—	2	2	no	—
96	C₄×Q₈×C₂₉	—	2	2	no	—
97	C₄×Q₈×C₂₉	—	2	2	no	—
98	C₄×Q₈×C₂₉	D₄	1	4	yes	—
99	C₄×Q₈×C₂₉	D₄	1	4	yes	—
100	C₂₉×#117	—	2	8	no	—
101	C₂₉×#117	—	2	8	no	—
102	C₂₉×#117	—	2	2	no	—
103	C₂₉×#117	—	2	2	no	—
104	C₂₉×#117	—	2	2	no	—
105	C₂₉×#117	—	2	2	no	—
106	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
113	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
124	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
125	C₂×C₄²×C₂₉	—	2	1	no	—
126	C₂×C₄²×C₂₉	—	2	1	no	—
127	C₂×C₄²×C₂₉	—	2	1	no	—
128	C₂×C₄²×C₂₉	—	2	1	no	—
129	C₂×C₄²×C₂₉	—	2	1	no	—
130	C₂×C₄²×C₂₉	—	2	1	no	—
131	C₂×C₄²×C₂₉	—	2	1	no	—
132	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
134	C₂₉×#107	—	2	2	no	—
135	C₂₉×#106	—	2	2	no	—
136	C₂₉×#103	—	2	2	no	—
137	C₂₉×#103	—	2	2	no	—
138	C₂₉×#103	—	2	2	no	—
139	C₂₉×#103	—	2	2	no	—
140	C₂₉×#103	—	2	2	no	—
141	C₂₉×#103	—	2	2	no	—
142	C₂₉×#103	C₂×C₄	1	4	yes	—
143	C₂₉×#103	C₂×C₄	1	4	yes	—
144	C₂₉×C₂²⋊C₈	—	2	2	no	—
145	C₂₉×C₂²⋊C₈	C₂×C₄	1	4	yes	—
146	C₂₉×#97	—	2	2	no	—
147	C₄×C₈×C₂₉	—	2	2	no	—
148	C₂₉×#95	—	2	1	no	—
149	C₂₉×#95	—	2	1	no	—
150	C₂₉×#95	—	2	1	no	—
151	C₂₉×#95	—	2	1	no	—
152	C₂₉×#95	—	2	1	no	—
153	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₂₉	—	2	4	no	—
155	C₂×Q₈×C₂₉	—	2	8	no	—
156	C₂×Q₈×C₂₉	—	2	8	no	—
157	C₂×Q₈×C₂₉	—	2	4	no	—
158	C₂×Q₈×C₂₉	—	2	8	no	—
159	C₂×Q₈×C₂₉	—	2	8	no	—
160	C₂×Q₈×C₂₉	—	2	4	no	—
161	C₂×Q₈×C₂₉	—	2	1	no	—
162	C₂×Q₈×C₂₉	—	2	1	no	—
163	C₂×Q₈×C₂₉	—	2	1	no	—
164	C₂×Q₈×C₂₉	—	2	1	no	—
165	C₂×Q₈×C₂₉	—	2	1	no	—
166	C₂×Q₈×C₂₉	—	2	1	no	—
167	C₂×Q₈×C₂₉	—	2	1	no	—
168	C₂×Q₈×C₂₉	—	2	1	no	—
169	C₂×Q₈×C₂₉	—	2	1	no	—
170	C₂×Q₈×C₂₉	—	2	1	no	—
171	C₂×Q₈×C₂₉	—	2	1	no	—
172	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
173	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
174	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
175	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
176	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
177	C₂×Q₈×C₂₉	#41	1	2	yes	—
178	C₂×Q₈×C₂₉	#41	1	2	yes	—
179	C₂²×C₄×C₂₉	—	2	4	no	—
180	C₂²×C₄×C₂₉	—	2	4	no	—
181	C₂²×C₄×C₂₉	—	2	4	no	—
182	C₂²×C₄×C₂₉	—	2	1	no	—
183	C₂²×C₄×C₂₉	—	2	1	no	—
184	C₂²×C₄×C₂₉	—	2	1	no	—
185	C₂²×C₄×C₂₉	—	2	1	no	—
186	C₂²×C₄×C₂₉	—	2	1	no	—
187	C₂²×C₄×C₂₉	—	2	1	no	—
188	C₂²×C₄×C₂₉	—	2	1	no	—
189	C₂²×C₄×C₂₉	—	2	1	no	—
190	C₂²×C₄×C₂₉	—	2	1	no	—
191	C₂²×C₄×C₂₉	—	2	1	no	—
192	C₂²×C₄×C₂₉	—	2	1	no	—
193	C₂²×C₄×C₂₉	—	2	1	no	—
194	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
195	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₂₉	#41	1	2	yes	—
201	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
202	Q₁₆×C₂₉	—	2	8	no	—
203	Q₁₆×C₂₉	—	2	8	no	—
204	C₂×C₈×C₂₉	—	2	1	no	—
205	C₂×C₈×C₂₉	—	2	1	no	—
206	C₂×C₈×C₂₉	—	2	1	no	—
207	C₂×C₈×C₂₉	—	2	1	no	—
208	C₂×C₈×C₂₉	—	2	1	no	—
209	C₂×C₈×C₂₉	—	2	1	no	—
210	C₂×C₈×C₂₉	—	2	1	no	—
211	C₂×C₈×C₂₉	—	2	1	no	—
212	C₂×C₈×C₂₉	—	2	1	no	—
213	C₂×C₈×C₂₉	—	2	1	no	—
214	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
215	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
216	C₄⋊C₄×C₂₉	—	2	4	no	—
217	C₄⋊C₄×C₂₉	—	2	4	no	—
218	C₄⋊C₄×C₂₉	—	2	4	no	—
219	C₄⋊C₄×C₂₉	—	2	4	no	—
220	C₄⋊C₄×C₂₉	—	2	4	no	—
221	C₄⋊C₄×C₂₉	—	2	2	no	—
222	C₄⋊C₄×C₂₉	—	2	2	no	—
223	C₄⋊C₄×C₂₉	—	2	1	no	—
224	C₄⋊C₄×C₂₉	—	2	1	no	—
225	C₄⋊C₄×C₂₉	—	2	1	no	—
226	C₄⋊C₄×C₂₉	—	2	1	no	—
227	C₄⋊C₄×C₂₉	—	2	1	no	—
228	C₄⋊C₄×C₂₉	—	2	1	no	—
229	C₄⋊C₄×C₂₉	—	2	1	no	—
230	C₄⋊C₄×C₂₉	—	4	2	no	—
231	C₄⋊C₄×C₂₉	—	8	1	no	—
232	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
233	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
234	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
235	C₂²⋊C₄×C₂₉	—	2	4	no	—
236	C₂²⋊C₄×C₂₉	—	2	4	no	—
237	C₂²⋊C₄×C₂₉	—	2	2	no	—
238	C₂²⋊C₄×C₂₉	—	2	2	no	—
239	C₂²⋊C₄×C₂₉	—	8	1	no	—
240	C₄²×C₂₉	—	2	4	no	—
241	C₄²×C₂₉	—	2	4	no	—
242	C₄²×C₂₉	—	2	4	no	—
243	C₄²×C₂₉	—	2	4	no	—
244	C₄²×C₂₉	—	2	4	no	—
245	C₄²×C₂₉	—	2	1	no	—
246	C₄²×C₂₉	—	2	1	no	—
247	C₄²×C₂₉	—	4	2	no	—
248	C₄²×C₂₉	—	8	1	no	—
249	C₄²×C₂₉	C₂×D₄	1	2	yes	—
250	C₄²×C₂₉	C₂×D₄	1	2	yes	—
251	#21463	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
252	C₂³×C₂₉	—	2	1	no	—
253	C₂³×C₂₉	—	2	1	no	—
254	C₂³×C₂₉	—	2	1	no	—
255	C₂³×C₂₉	—	2	1	no	—
256	C₂³×C₂₉	—	2	1	no	—
257	C₂³×C₂₉	—	2	1	no	—
258	C₂³×C₂₉	C₄×D₄	1	2	yes	—
259	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
260	Q₈×C₂₉	—	2	16	no	—
261	Q₈×C₂₉	—	2	2	no	—
262	Q₈×C₂₉	—	2	2	no	—
263	Q₈×C₂₉	—	2	2	no	—
264	Q₈×C₂₉	—	2	2	no	—
265	Q₈×C₂₉	—	2	2	no	—
266	Q₈×C₂₉	—	2	2	no	—
267	Q₈×C₂₉	—	2	2	no	—
268	Q₈×C₂₉	—	2	2	no	—
269	Q₈×C₂₉	—	4	1	no	—
270	Q₈×C₂₉	—	4	1	no	—
271	Q₈×C₂₉	C₄×D₄	1	4	yes	—
272	Q₈×C₂₉	C₄×D₄	1	4	yes	—
273	C₂×C₄×C₂₉	—	2	16	no	—
274	C₂×C₄×C₂₉	—	2	2	no	—
275	C₂×C₄×C₂₉	—	2	2	no	—
276	C₂×C₄×C₂₉	—	2	2	no	—
277	C₂×C₄×C₂₉	—	2	2	no	—
278	C₂×C₄×C₂₉	—	2	1	no	—
279	C₂×C₄×C₂₉	—	2	2	no	—
280	C₂×C₄×C₂₉	—	2	2	no	—
281	C₂×C₄×C₂₉	—	2	1	no	—
282	C₂×C₄×C₂₉	—	2	1	no	—
283	C₂×C₄×C₂₉	—	2	1	no	—
284	C₂×C₄×C₂₉	—	2	1	no	—
285	C₂×C₄×C₂₉	—	2	1	no	—
286	C₂×C₄×C₂₉	—	2	2	no	—
287	C₂×C₄×C₂₉	—	2	2	no	—
288	C₂×C₄×C₂₉	—	2	2	no	—
289	C₂×C₄×C₂₉	—	2	2	no	—
290	C₂×C₄×C₂₉	—	2	2	no	—
291	C₂×C₄×C₂₉	—	2	2	no	—
292	C₂×C₄×C₂₉	—	2	1	no	—
293	C₂×C₄×C₂₉	—	2	1	no	—
294	C₂×C₄×C₂₉	—	2	2	no	—
295	C₂×C₄×C₂₉	—	2	2	no	—
296	C₂×C₄×C₂₉	—	2	1	no	—
297	C₂×C₄×C₂₉	—	2	1	no	—
298	C₂×C₄×C₂₉	—	2	1	no	—
299	C₂×C₄×C₂₉	—	2	1	no	—
300	C₂×C₄×C₂₉	—	4	1	no	—
301	C₂×C₄×C₂₉	—	4	1	no	—
302	C₂×C₄×C₂₉	—	4	1	no	—
303	C₂×C₄×C₂₉	—	4	1	no	—
304	C₂×C₄×C₂₉	—	4	1	no	—
305	C₂×C₄×C₂₉	—	4	1	no	—
306	C₂×C₄×C₂₉	—	4	1	no	—
307	C₂×C₄×C₂₉	—	4	1	no	—
308	C₂×C₄×C₂₉	—	4	1	no	—
309	C₂×C₄×C₂₉	—	4	1	no	—
310	C₂×C₄×C₂₉	—	4	1	no	—
311	C₂×C₄×C₂₉	—	4	1	no	—
312	C₂×C₄×C₂₉	—	4	1	no	—
313	C₂×C₄×C₂₉	—	4	1	no	—
314	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
315	C₂×C₄×C₂₉	#120	1	2	yes	—
316	C₂×C₄×C₂₉	#120	1	2	yes	—
317	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
318	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
321	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
322	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
323	C₈×C₂₉	—	2	2	no	—
324	C₈×C₂₉	—	2	2	no	—
325	C₈×C₂₉	—	4	1	no	—
326	C₈×C₂₉	—	4	1	no	—
327	C₂×#519	C₂×C₂₉	1	1	yes	characteristic
328	C₂×#451	C₂×C₂₉	1	1	yes	characteristic
329	C₂×#441	C₂×C₂₉	1	1	yes	characteristic, complemented
330	C₂×C₄×Q₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
331	#2323	C₂×C₂₉	1	1	yes	characteristic
332	#1878	C₂×C₂₉	1	1	yes	characteristic, complemented
333	#1878	C₂×C₂₉	1	1	yes	characteristic, complemented
334	#1873	C₂×C₂₉	1	1	yes	characteristic
335	#1865	C₂×C₂₉	1	1	yes	characteristic, complemented
336	#1863	C₂×C₂₉	1	1	yes	characteristic, complemented
337	#1854	C₂×C₂₉	1	1	yes	characteristic
338	#1787	C₂×C₂₉	1	1	yes	characteristic
339	#1763	C₂×C₂₉	1	1	yes	characteristic, complemented
340	C₄×#103	C₂×C₂₉	1	1	yes	characteristic, complemented
341	#1750	C₂×C₂₉	1	1	yes	characteristic
342	C₂²×C₂₉	—	2	2	no	—
343	C₂²×C₂₉	—	2	2	no	—
344	C₂²×C₂₉	—	2	2	no	—
345	C₂²×C₂₉	—	4	1	no	—
346	C₂²×C₂₉	—	4	1	no	—
347	C₂²×C₂₉	—	4	1	no	—
348	C₂²×C₂₉	—	4	1	no	—
349	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
350	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
351	C₂²×C₂₉	#525	1	1	yes	characteristic
352	C₂²×C₂₉	#577	1	1	yes	characteristic
353	C₂²×C₂₉	#578	1	1	yes	characteristic
354	C₂²×C₂₉	#578	1	1	yes	characteristic
355	C₂²×C₂₉	#578	1	1	yes	characteristic
356	C₄×C₂₉	—	2	2	no	—
357	C₄×C₂₉	—	2	2	no	—
358	C₄×C₂₉	—	2	4	no	—
359	C₄×C₂₉	—	2	4	no	—
360	C₄×C₂₉	—	2	2	no	—
361	C₄×C₂₉	—	4	2	no	—
362	C₄×C₂₉	—	4	1	no	—
363	C₄×C₂₉	—	4	2	no	—
364	C₄×C₂₉	—	4	1	no	—
365	C₄×C₂₉	—	4	2	no	—
366	C₄×C₂₉	—	4	2	no	—
367	C₄×C₂₉	—	8	1	no	—
368	C₄×C₂₉	—	8	1	no	—
369	C₄×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
370	C₄×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
371	C₄×C₂₉	#525	1	1	yes	characteristic
372	C₄×C₂₉	#525	1	1	yes	characteristic
373	C₂³×Q₈	C₂²×C₂₉	1	1	yes	characteristic
374	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
375	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
376	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
377	#519	—	2	4	no	—
378	#519	—	2	4	no	—
379	C₂×C₄×Q₈	—	2	1	no	—
380	C₂×C₄×Q₈	—	2	1	no	—
381	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
382	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
383	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
384	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
385	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
386	C₂×#117	—	2	1	no	—
387	C₂×#117	—	2	1	no	—
388	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
389	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
390	#451	C₄×C₂₉	1	8	yes	complemented
391	#441	—	2	4	no	—
392	C₄×Q₁₆	—	2	4	no	—
393	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
394	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
395	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
396	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
397	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
398	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
399	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
400	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
401	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
402	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
403	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
404	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
405	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
406	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
407	#391	C₂²×C₂₉	1	1	yes	characteristic
408	#389	—	2	1	no	—
409	#389	C₂²×C₂₉	1	1	yes	characteristic
410	#388	—	2	1	no	—
411	#388	—	2	1	no	—
412	#387	—	2	1	no	—
413	#380	C₂²×C₂₉	1	1	yes	characteristic
414	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
415	#340	C₂²×C₂₉	1	1	yes	characteristic
416	#340	C₂²×C₂₉	1	1	yes	characteristic
417	#340	C₂²×C₂₉	1	1	yes	characteristic
418	#340	C₂²×C₂₉	1	1	yes	characteristic
419	#336	C₂²×C₂₉	1	1	yes	characteristic
420	#336	C₂²×C₂₉	1	1	yes	characteristic
421	C₂×C₂₉	—	4	2	no	—
422	C₂×C₂₉	C₄×#120	1	1	yes	characteristic
423	C₂×C₂₉	#2947	1	1	yes	characteristic
424	C₂×C₂₉	#2950	1	1	yes	characteristic
425	C₂×C₂₉	#3011	1	1	yes	characteristic
426	C₂×C₂₉	#3013	1	1	yes	characteristic
427	C₂×C₂₉	#3121	1	1	yes	characteristic
428	C₂×C₂₉	#3127	1	1	yes	characteristic
429	C₂²×Q₈	—	2	2	no	—
430	C₂²×Q₈	—	2	2	no	—
431	C₂²×Q₈	—	2	2	no	—
432	C₂²×Q₈	—	2	2	no	—
433	C₂²×Q₈	—	2	1	no	—
434	C₂²×Q₈	—	2	2	no	—
435	C₂²×Q₈	C₂×C₄×C₂₉	1	4	yes	—
436	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
437	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
438	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
439	C₂³×C₄	—	2	1	no	—
440	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
441	C₂×Q₁₆	—	2	2	no	—
442	C₂×Q₁₆	—	2	2	no	—
443	C₂×Q₁₆	—	2	2	no	—
444	C₂×Q₁₆	—	2	2	no	—
445	C₂×Q₁₆	C₂×C₄×C₂₉	1	4	yes	—
446	C₂×Q₁₆	C₂×C₄×C₂₉	1	4	yes	—
447	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
448	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
449	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
450	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
451	C₂²⋊Q₈	—	2	2	no	—
452	C₂²⋊Q₈	C₂×C₄×C₂₉	1	4	yes	—
453	C₄×Q₈	—	2	8	no	—
454	C₄×Q₈	—	2	8	no	—
455	C₄×Q₈	—	2	2	no	—
456	C₄×Q₈	—	2	2	no	—
457	C₄×Q₈	—	2	2	no	—
458	C₄×Q₈	—	2	2	no	—
459	C₄×Q₈	—	2	2	no	—
460	C₄×Q₈	—	2	2	no	—
461	C₄×Q₈	—	2	2	no	—
462	C₄×Q₈	—	2	2	no	—
463	C₄×Q₈	D₄×C₂₉	1	4	yes	—
464	C₄×Q₈	D₄×C₂₉	1	4	yes	—
465	#117	—	2	8	no	—
466	#117	—	2	8	no	—
467	#117	—	2	2	no	—
468	#117	—	2	2	no	—
469	#117	—	2	2	no	—
470	#117	—	2	2	no	—
471	C₂×C₄⋊C₄	—	2	1	no	—
472	C₂×C₄⋊C₄	—	2	1	no	—
473	C₂×C₄⋊C₄	—	2	1	no	—
474	C₂×C₄⋊C₄	—	2	1	no	—
475	C₂×C₄⋊C₄	—	2	1	no	—
476	C₂×C₄⋊C₄	—	2	1	no	—
477	C₂×C₄⋊C₄	—	2	1	no	—
478	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
479	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
480	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
481	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	—	2	1	no	—
486	C₂×C₂²⋊C₄	—	2	1	no	—
487	C₂×C₂²⋊C₄	—	2	1	no	—
488	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
489	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
490	C₂×C₄²	—	2	1	no	—
491	C₂×C₄²	—	2	1	no	—
492	C₂×C₄²	—	2	1	no	—
493	C₂×C₄²	—	2	1	no	—
494	C₂×C₄²	—	2	1	no	—
495	C₂×C₄²	—	2	1	no	—
496	C₂×C₄²	—	2	1	no	—
497	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
499	#107	—	2	2	no	—
500	#106	—	2	2	no	—
501	#103	—	2	2	no	—
502	#103	—	2	2	no	—
503	#103	—	2	2	no	—
504	#103	—	2	2	no	—
505	#103	—	2	2	no	—
506	#103	—	2	2	no	—
507	#103	C₂×C₄×C₂₉	1	4	yes	—
508	#103	C₂×C₄×C₂₉	1	4	yes	—
509	C₂²⋊C₈	—	2	2	no	—
510	C₂²⋊C₈	C₂×C₄×C₂₉	1	4	yes	—
511	#97	—	2	2	no	—
512	C₄×C₈	—	2	2	no	—
513	#95	—	2	1	no	—
514	#95	—	2	1	no	—
515	#95	—	2	1	no	—
516	#95	—	2	1	no	—
517	#95	—	2	1	no	—
518	C₂₉	#21463	1	1	yes	characteristic, direct product factor, Sylow
519	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
520	C₂×Q₈	—	2	4	no	—
521	C₂×Q₈	—	2	8	no	—
522	C₂×Q₈	—	2	8	no	—
523	C₂×Q₈	—	2	4	no	—
524	C₂×Q₈	—	2	8	no	—
525	C₂×Q₈	—	2	8	no	—
526	C₂×Q₈	—	2	4	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	—	2	1	no	—
534	C₂×Q₈	—	2	1	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
539	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
540	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
541	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
542	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
543	C₂×Q₈	#41×C₂₉	1	2	yes	—
544	C₂×Q₈	#41×C₂₉	1	2	yes	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	2	4	no	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
561	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
562	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
564	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
565	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
566	C₂²×C₄	#41×C₂₉	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
568	Q₁₆	—	2	8	no	—
569	Q₁₆	—	2	8	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
581	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	2	no	—
588	C₄⋊C₄	—	2	2	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	4	2	no	—
597	C₄⋊C₄	—	8	1	no	—
598	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
599	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
600	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	8	1	no	—
606	C₄²	—	2	4	no	—
607	C₄²	—	2	4	no	—
608	C₄²	—	2	4	no	—
609	C₄²	—	2	4	no	—
610	C₄²	—	2	4	no	—
611	C₄²	—	2	1	no	—
612	C₄²	—	2	1	no	—
613	C₄²	—	4	2	no	—
614	C₄²	—	8	1	no	—
615	C₄²	C₂×D₄×C₂₉	1	2	yes	—
616	C₄²	C₂×D₄×C₂₉	1	2	yes	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	C₄×D₄×C₂₉	1	2	yes	—
624	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
625	Q₈	—	2	16	no	—
626	Q₈	—	2	2	no	—
627	Q₈	—	2	2	no	—
628	Q₈	—	2	2	no	—
629	Q₈	—	2	2	no	—
630	Q₈	—	2	2	no	—
631	Q₈	—	2	2	no	—
632	Q₈	—	2	2	no	—
633	Q₈	—	2	2	no	—
634	Q₈	—	4	1	no	—
635	Q₈	—	4	1	no	—
636	Q₈	C₄×D₄×C₂₉	1	4	yes	—
637	Q₈	C₄×D₄×C₂₉	1	4	yes	—
638	C₂×C₄	—	2	16	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
680	C₂×C₄	C₂₉×#120	1	2	yes	—
681	C₂×C₄	C₂₉×#120	1	2	yes	—
682	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
683	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
684	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
685	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
686	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
687	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
688	C₈	—	2	2	no	—
689	C₈	—	2	2	no	—
690	C₈	—	4	1	no	—
691	C₈	—	4	1	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
700	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
701	C₂²	C₂₉×#525	1	1	yes	characteristic
702	C₂²	C₂₉×#577	1	1	yes	characteristic
703	C₂²	C₂₉×#578	1	1	yes	characteristic
704	C₂²	C₂₉×#578	1	1	yes	characteristic
705	C₂²	C₂₉×#578	1	1	yes	characteristic
706	C₄	—	2	2	no	—
707	C₄	—	2	2	no	—
708	C₄	—	2	4	no	—
709	C₄	—	2	4	no	—
710	C₄	—	2	2	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	1	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	1	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	2	no	—
717	C₄	—	8	1	no	—
718	C₄	—	8	1	no	—
719	C₄	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
720	C₄	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
721	C₄	C₂₉×#525	1	1	yes	characteristic
722	C₄	C₂₉×#525	1	1	yes	characteristic
723	C₂	—	4	2	no	—
724	C₂	C₄×C₂₉×#120	1	1	yes	characteristic
725	C₂	C₂₉×#2947	1	1	yes	characteristic
726	C₂	C₂₉×#2950	1	1	yes	characteristic
727	C₂	C₂₉×#3011	1	1	yes	characteristic
728	C₂	C₂₉×#3013	1	1	yes	characteristic
729	C₂	C₂₉×#3121	1	1	yes	characteristic
730	C₂	C₂₉×#3127	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	C₂⁴×C₂₉	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₂₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₂₉×#441	C₂	semidirect
4. C₂×C₄×Q₁₆×C₂₉	C₂	semidirect
6. C₂₉×#1878	C₂	semidirect
7. C₂₉×#1878	C₂	semidirect
9. C₂₉×#1865	C₂	semidirect
10. C₂₉×#1863	C₂	semidirect
13. C₂₉×#1763	C₂	semidirect
14. C₄×C₂₉×#103	C₂	semidirect
33. C₂₉×#451	C₄	semidirect
251. #21463	C₂₉	direct (N × H)
329. C₂×#441	C₂×C₂₉	semidirect
330. C₂×C₄×Q₁₆	C₂×C₂₉	semidirect
332. #1878	C₂×C₂₉	semidirect
333. #1878	C₂×C₂₉	semidirect
335. #1865	C₂×C₂₉	semidirect
336. #1863	C₂×C₂₉	semidirect
339. #1763	C₂×C₂₉	semidirect
340. C₄×#103	C₂×C₂₉	semidirect
390. #451	C₄×C₂₉	semidirect
518. C₂₉	#21463	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×#519	2
C₂×C₂₉×#451	2
C₂×C₂₉×#441	2
C₂×C₄×Q₁₆×C₂₉	2
C₂₉×#2323	2
C₂₉×#1878	2
C₂₉×#1873	2
C₂₉×#1865	2
C₂₉×#1863	2
C₂₉×#1854	2
C₂₉×#1787	2
C₂₉×#1763	2
C₄×C₂₉×#103	2
C₂₉×#1750	2
#21463	29

Subgroups — C29×#21463 #20316363

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#21463 #20316363