Subgroups — C₂₉×#33285 #20328185

Order 7424.

634 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#2647	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2642	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#1992	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1991	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#1960	C₂	1	1	yes	maximal, characteristic
6	C₂₉×#1956	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#1935	C₂	1	2	yes	maximal
8	C₂₉×#1935	C₂	1	2	yes	maximal
9	C₂₉×#1933	C₂	1	2	yes	maximal
10	C₂₉×#1933	C₂	1	2	yes	maximal
11	C₂₉×#1726	C₂	1	1	yes	maximal, characteristic
12	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₂₉×#125	C₂²	1	1	yes	characteristic
14	C₂×C₂₉×#103	C₂²	1	2	yes	—
15	C₂×C₂₉×#103	C₂²	1	2	yes	—
16	C₂×C₂₉×#103	C₂²	1	2	yes	—
17	C₂×C₂₉×#103	C₂²	1	2	yes	—
18	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
20	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
24	C₂₉×#400	—	2	2	no	—
25	C₂₉×#400	—	2	2	no	—
26	C₂₉×#400	—	2	2	no	—
27	C₂₉×#398	—	2	2	no	—
28	C₂₉×#391	C₂²	1	2	yes	—
29	C₂₉×#391	C₂²	1	2	yes	—
30	C₂₉×#389	C₂²	1	2	yes	—
31	C₂₉×#389	C₂²	1	2	yes	—
32	C₂₉×#384	C₂²	1	1	yes	characteristic
33	C₂₉×#382	C₂²	1	1	yes	characteristic
34	C₂₉×#376	C₂²	1	1	yes	characteristic
35	C₂₉×#340	C₂²	1	2	yes	—
36	C₂₉×#340	C₂²	1	2	yes	—
37	C₂₉×#340	C₂²	1	2	yes	—
38	C₂₉×#340	C₂²	1	2	yes	—
39	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
40	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
44	C₂₉×C₄⋊Q₈	—	2	2	no	—
45	C₂₉×C₄⋊Q₈	—	2	2	no	—
46	C₂₉×#125	—	2	2	no	—
47	C₂₉×#125	—	2	2	no	—
48	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
56	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
59	C₂₉×#103	—	2	4	no	—
60	C₂₉×#103	—	2	4	no	—
61	C₂₉×#103	—	2	4	no	—
62	C₂₉×#103	—	2	4	no	—
63	C₂₉×#97	—	2	2	no	—
64	C₂₉×#97	—	2	2	no	—
65	C₂₉×#97	—	2	2	no	—
66	C₄×C₈×C₂₉	—	2	2	no	—
67	C₄×C₈×C₂₉	—	2	2	no	—
68	C₄×C₈×C₂₉	—	2	2	no	—
69	C₂₉×#95	—	2	2	no	—
70	C₂₉×#95	—	2	2	no	—
71	C₂₉×#95	—	2	2	no	—
72	C₂₉×#95	—	2	2	no	—
73	C₂₉×#95	—	2	4	no	—
74	C₂₉×#95	—	2	2	no	—
75	C₂₉×#95	D₄	1	2	yes	—
76	C₂₉×#95	D₄	1	2	yes	—
77	C₂×Q₈×C₂₉	—	2	2	no	—
78	C₂×Q₈×C₂₉	—	2	2	no	—
79	C₂×Q₈×C₂₉	—	2	2	no	—
80	C₂×Q₈×C₂₉	—	2	2	no	—
81	C₂×Q₈×C₂₉	—	2	2	no	—
82	C₂×Q₈×C₂₉	—	2	2	no	—
83	C₂²×C₄×C₂₉	—	2	2	no	—
84	C₂²×C₄×C₂₉	—	2	2	no	—
85	C₂²×C₄×C₂₉	—	2	2	no	—
86	C₂²×C₄×C₂₉	—	2	2	no	—
87	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
92	C₂×C₈×C₂₉	—	2	1	no	—
93	C₂×C₈×C₂₉	—	2	1	no	—
94	C₂×C₈×C₂₉	—	2	1	no	—
95	C₂×C₈×C₂₉	—	2	1	no	—
96	C₂×C₈×C₂₉	—	2	1	no	—
97	C₂×C₈×C₂₉	—	2	1	no	—
98	C₂×C₈×C₂₉	—	2	1	no	—
99	C₂×C₈×C₂₉	—	2	1	no	—
100	C₂×C₈×C₂₉	#41	1	2	yes	—
101	C₂×C₈×C₂₉	#41	1	2	yes	—
102	C₂×C₈×C₂₉	#41	1	2	yes	—
103	C₂×C₈×C₂₉	#41	1	2	yes	—
104	C₄⋊C₄×C₂₉	—	2	2	no	—
105	C₄⋊C₄×C₂₉	—	2	2	no	—
106	C₄⋊C₄×C₂₉	—	2	2	no	—
107	C₄⋊C₄×C₂₉	—	2	2	no	—
108	C₄⋊C₄×C₂₉	—	2	2	no	—
109	C₄⋊C₄×C₂₉	—	2	2	no	—
110	C₄⋊C₄×C₂₉	—	4	4	no	—
111	C₄⋊C₄×C₂₉	—	4	4	no	—
112	C₄⋊C₄×C₂₉	—	8	2	no	—
113	C₄⋊C₄×C₂₉	—	8	2	no	—
114	C₄⋊C₄×C₂₉	—	8	2	no	—
115	C₄²×C₂₉	—	2	1	no	—
116	C₄²×C₂₉	—	2	1	no	—
117	C₄²×C₂₉	—	2	1	no	—
118	C₄²×C₂₉	—	2	1	no	—
119	C₄²×C₂₉	#41	1	2	yes	—
120	C₄²×C₂₉	#41	1	2	yes	—
121	#33285	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
123	Q₈×C₂₉	—	4	2	no	—
124	Q₈×C₂₉	—	4	2	no	—
125	Q₈×C₂₉	—	4	2	no	—
126	Q₈×C₂₉	—	4	2	no	—
127	C₂×C₄×C₂₉	—	2	2	no	—
128	C₂×C₄×C₂₉	—	2	2	no	—
129	C₂×C₄×C₂₉	—	2	1	no	—
130	C₂×C₄×C₂₉	—	2	1	no	—
131	C₂×C₄×C₂₉	—	2	2	no	—
132	C₂×C₄×C₂₉	—	2	2	no	—
133	C₂×C₄×C₂₉	—	2	2	no	—
134	C₂×C₄×C₂₉	—	2	2	no	—
135	C₂×C₄×C₂₉	—	2	2	no	—
136	C₂×C₄×C₂₉	—	4	2	no	—
137	C₂×C₄×C₂₉	—	4	2	no	—
138	C₂×C₄×C₂₉	—	4	2	no	—
139	C₂×C₄×C₂₉	—	4	2	no	—
140	C₂×C₄×C₂₉	—	4	2	no	—
141	C₂×C₄×C₂₉	—	4	2	no	—
142	C₂×C₄×C₂₉	—	4	2	no	—
143	C₂×C₄×C₂₉	—	4	2	no	—
144	C₂×C₄×C₂₉	—	4	2	no	—
145	C₂×C₄×C₂₉	—	4	2	no	—
146	C₂×C₄×C₂₉	—	4	2	no	—
147	C₂×C₄×C₂₉	—	4	2	no	—
148	C₂×C₄×C₂₉	#124	1	4	yes	—
149	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
155	C₈×C₂₉	—	2	2	no	—
156	C₈×C₂₉	—	2	2	no	—
157	C₈×C₂₉	—	2	2	no	—
158	C₈×C₂₉	—	2	2	no	—
159	#2647	C₂×C₂₉	1	1	yes	characteristic
160	#2642	C₂×C₂₉	1	1	yes	characteristic
161	#1992	C₂×C₂₉	1	1	yes	characteristic
162	#1991	C₂×C₂₉	1	1	yes	characteristic
163	#1960	C₂×C₂₉	1	1	yes	characteristic
164	#1956	C₂×C₂₉	1	1	yes	characteristic
165	#1935	C₂×C₂₉	1	2	yes	—
166	#1935	C₂×C₂₉	1	2	yes	—
167	#1933	C₂×C₂₉	1	2	yes	—
168	#1933	C₂×C₂₉	1	2	yes	—
169	#1726	C₂×C₂₉	1	1	yes	characteristic
170	C₂²×C₂₉	C₂×#124	1	1	yes	characteristic
171	C₂²×C₂₉	#532	1	1	yes	characteristic
172	C₂²×C₂₉	#532	1	1	yes	characteristic
173	C₂²×C₂₉	#577	1	2	yes	—
174	C₂²×C₂₉	#578	1	2	yes	—
175	C₄×C₂₉	—	2	4	no	—
176	C₄×C₂₉	—	4	1	no	—
177	C₄×C₂₉	—	4	1	no	—
178	C₄×C₂₉	—	4	2	no	—
179	C₄×C₂₉	—	8	2	no	—
180	C₄×C₂₉	—	8	2	no	—
181	C₄×C₂₉	—	8	2	no	—
182	C₄×C₂₉	—	8	2	no	—
183	C₄×C₂₉	#529	1	1	yes	characteristic
184	C₄×C₂₉	#529	1	1	yes	characteristic
185	C₄×C₂₉	#529	1	1	yes	characteristic
186	C₄×C₂₉	#529	1	1	yes	characteristic
187	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
188	C₂×#125	C₂²×C₂₉	1	1	yes	characteristic
189	C₂×#103	C₂²×C₂₉	1	2	yes	—
190	C₂×#103	C₂²×C₂₉	1	2	yes	—
191	C₂×#103	C₂²×C₂₉	1	2	yes	—
192	C₂×#103	C₂²×C₂₉	1	2	yes	—
193	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
194	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
195	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
196	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
197	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
198	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
199	#400	—	2	2	no	—
200	#400	—	2	2	no	—
201	#400	—	2	2	no	—
202	#398	—	2	2	no	—
203	#391	C₂²×C₂₉	1	2	yes	—
204	#391	C₂²×C₂₉	1	2	yes	—
205	#389	C₂²×C₂₉	1	2	yes	—
206	#389	C₂²×C₂₉	1	2	yes	—
207	#384	C₂²×C₂₉	1	1	yes	characteristic
208	#382	C₂²×C₂₉	1	1	yes	characteristic
209	#376	C₂²×C₂₉	1	1	yes	characteristic
210	#340	C₂²×C₂₉	1	2	yes	—
211	#340	C₂²×C₂₉	1	2	yes	—
212	#340	C₂²×C₂₉	1	2	yes	—
213	#340	C₂²×C₂₉	1	2	yes	—
214	C₂×C₂₉	#2861	1	1	yes	characteristic
215	C₂×C₂₉	#3137	1	2	yes	—
216	C₂×C₂₉	#3174	1	1	yes	characteristic
217	C₂×C₂₉	#3177	1	1	yes	characteristic
218	C₂×C₂₉	#3178	1	2	yes	—
219	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
220	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
221	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
222	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
223	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
224	C₄⋊Q₈	—	2	2	no	—
225	C₄⋊Q₈	—	2	2	no	—
226	#125	—	2	2	no	—
227	#125	—	2	2	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
234	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
235	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
236	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
237	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
238	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
239	#103	—	2	4	no	—
240	#103	—	2	4	no	—
241	#103	—	2	4	no	—
242	#103	—	2	4	no	—
243	#97	—	2	2	no	—
244	#97	—	2	2	no	—
245	#97	—	2	2	no	—
246	C₄×C₈	—	2	2	no	—
247	C₄×C₈	—	2	2	no	—
248	C₄×C₈	—	2	2	no	—
249	#95	—	2	2	no	—
250	#95	—	2	2	no	—
251	#95	—	2	2	no	—
252	#95	—	2	2	no	—
253	#95	—	2	4	no	—
254	#95	—	2	2	no	—
255	#95	D₄×C₂₉	1	2	yes	—
256	#95	D₄×C₂₉	1	2	yes	—
257	C₂₉	#33285	1	1	yes	characteristic, direct product factor, Sylow
258	C₂×Q₈	—	2	2	no	—
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	—	2	2	no	—
261	C₂×Q₈	—	2	2	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
270	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
271	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
272	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
273	C₂×C₈	—	2	1	no	—
274	C₂×C₈	—	2	1	no	—
275	C₂×C₈	—	2	1	no	—
276	C₂×C₈	—	2	1	no	—
277	C₂×C₈	—	2	1	no	—
278	C₂×C₈	—	2	1	no	—
279	C₂×C₈	—	2	1	no	—
280	C₂×C₈	—	2	1	no	—
281	C₂×C₈	#41×C₂₉	1	2	yes	—
282	C₂×C₈	#41×C₂₉	1	2	yes	—
283	C₂×C₈	#41×C₂₉	1	2	yes	—
284	C₂×C₈	#41×C₂₉	1	2	yes	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	4	4	no	—
292	C₄⋊C₄	—	4	4	no	—
293	C₄⋊C₄	—	8	2	no	—
294	C₄⋊C₄	—	8	2	no	—
295	C₄⋊C₄	—	8	2	no	—
296	C₄²	—	2	1	no	—
297	C₄²	—	2	1	no	—
298	C₄²	—	2	1	no	—
299	C₄²	—	2	1	no	—
300	C₄²	#41×C₂₉	1	2	yes	—
301	C₄²	#41×C₂₉	1	2	yes	—
302	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
303	Q₈	—	4	2	no	—
304	Q₈	—	4	2	no	—
305	Q₈	—	4	2	no	—
306	Q₈	—	4	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	C₂₉×#124	1	4	yes	—
329	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
330	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
331	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
332	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
333	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
334	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
335	C₈	—	2	2	no	—
336	C₈	—	2	2	no	—
337	C₈	—	2	2	no	—
338	C₈	—	2	2	no	—
339	C₂²	C₂×C₂₉×#124	1	1	yes	characteristic
340	C₂²	C₂₉×#532	1	1	yes	characteristic
341	C₂²	C₂₉×#532	1	1	yes	characteristic
342	C₂²	C₂₉×#577	1	2	yes	—
343	C₂²	C₂₉×#578	1	2	yes	—
344	C₄	—	2	4	no	—
345	C₄	—	4	1	no	—
346	C₄	—	4	1	no	—
347	C₄	—	4	2	no	—
348	C₄	—	8	2	no	—
349	C₄	—	8	2	no	—
350	C₄	—	8	2	no	—
351	C₄	—	8	2	no	—
352	C₄	C₂₉×#529	1	1	yes	characteristic
353	C₄	C₂₉×#529	1	1	yes	characteristic
354	C₄	C₂₉×#529	1	1	yes	characteristic
355	C₄	C₂₉×#529	1	1	yes	characteristic
356	C₂	C₂₉×#2861	1	1	yes	characteristic
357	C₂	C₂₉×#3137	1	2	yes	—
358	C₂	C₂₉×#3174	1	1	yes	characteristic
359	C₂	C₂₉×#3177	1	1	yes	characteristic
360	C₂	C₂₉×#3178	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂₉×#376 ◁ G

Complements

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

N	H ≅ G/N	type
121. #33285	C₂₉	direct (N × H)
257. C₂₉	#33285	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×#2647	2
C₂₉×#2642	2
C₂₉×#1992	2
C₂₉×#1991	2
C₂₉×#1960	2
C₂₉×#1956	2
C₂₉×#1935	2
C₂₉×#1933	2
C₂₉×#1726	2
#33285	29

Subgroups — C29×#33285 #20328185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#33285 #20328185