Subgroups — C₂₉×#28818 #20323718

Order 7424.

722 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#501	C₂	1	2	yes	maximal
2	C₂₉×#2550	C₂	1	2	yes	maximal
3	C₂₉×#2059	C₂	1	2	yes	maximal
4	C₂₉×#2057	C₂	1	2	yes	maximal
5	C₂₉×#1949	C₂	1	2	yes	maximal
6	C₂₉×#1943	C₂	1	2	yes	maximal
7	C₂₉×#1846	C₂	1	1	yes	maximal, characteristic
8	C₄×C₂₉×#107	C₂	1	1	yes	maximal, characteristic
9	C₂₉×#1770	C₂	1	1	yes	maximal, characteristic
10	C₂×C₂₉×C₄⋊Q₈	C₂²	1	2	yes	—
11	C₂×C₂₉×#125	C₂²	1	2	yes	—
12	C₂₉×#501	—	2	8	no	—
13	C₂×C₂₉×#107	C₂²	1	2	yes	—
14	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
15	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
16	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×#106	C₂²	1	2	yes	—
19	C₂×C₂₉×#106	C₂²	1	2	yes	—
20	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#97	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
23	C₂₉×#398	—	2	2	no	—
24	C₂₉×#395	—	2	2	no	—
25	C₂₉×#391	—	2	2	no	—
26	C₂₉×#389	—	2	2	no	—
27	C₂₉×#389	C₂²	1	2	yes	—
28	C₂₉×#389	C₂²	1	2	yes	—
29	C₂₉×#382	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
31	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
32	C₂₉×#340	C₂²	1	2	yes	—
33	C₂₉×#340	C₂²	1	2	yes	—
34	C₂₉×#340	C₂²	1	2	yes	—
35	C₂₉×#336	C₂²	1	2	yes	—
36	C₂²×Q₈×C₂₉	—	2	2	no	—
37	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
38	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
40	C₂₉×C₄⋊Q₈	—	2	4	no	—
41	C₂₉×C₄⋊Q₈	—	4	2	no	—
42	C₂₉×#125	—	2	4	no	—
43	C₂₉×#125	—	4	2	no	—
44	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
45	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
55	C₂×C₄²×C₂₉	—	2	2	no	—
56	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
57	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
58	C₂₉×#107	—	2	4	no	—
59	C₂₉×#107	—	4	1	no	—
60	C₂₉×#107	—	4	1	no	—
61	C₂₉×#107	D₄	1	4	yes	—
62	C₂₉×#107	Q₈	1	4	yes	complemented
63	C₂₉×#106	—	2	4	no	—
64	C₂₉×#106	—	2	4	no	—
65	C₂₉×C₄⋊C₈	Q₈	1	4	yes	complemented
66	C₂₉×#97	—	2	4	no	—
67	C₄×C₈×C₂₉	Q₈	1	4	yes	complemented
68	C₂₉×#95	—	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	D₄	1	2	yes	—
74	C₂×Q₈×C₂₉	—	4	4	no	—
75	C₂×Q₈×C₂₉	—	4	4	no	—
76	C₂×Q₈×C₂₉	—	8	2	no	—
77	C₂²×C₄×C₂₉	—	2	2	no	—
78	C₂²×C₄×C₂₉	—	2	2	no	—
79	C₂²×C₄×C₂₉	—	2	2	no	—
80	C₂²×C₄×C₂₉	—	2	2	no	—
81	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
82	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
86	C₂×C₈×C₂₉	—	2	2	no	—
87	C₂×C₈×C₂₉	—	2	1	no	—
88	C₂×C₈×C₂₉	—	2	1	no	—
89	C₂×C₈×C₂₉	—	2	2	no	—
90	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
91	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
92	C₂×C₈×C₂₉	C₂×Q₈	1	4	yes	—
93	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
94	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
95	C₄⋊C₄×C₂₉	—	2	2	no	—
96	C₄⋊C₄×C₂₉	—	2	2	no	—
97	C₄⋊C₄×C₂₉	—	2	2	no	—
98	C₄⋊C₄×C₂₉	—	2	2	no	—
99	C₄⋊C₄×C₂₉	—	2	2	no	—
100	C₄⋊C₄×C₂₉	—	2	2	no	—
101	C₄⋊C₄×C₂₉	—	4	1	no	—
102	C₄⋊C₄×C₂₉	—	4	1	no	—
103	C₄⋊C₄×C₂₉	—	4	4	no	—
104	C₄⋊C₄×C₂₉	—	4	4	no	—
105	C₄⋊C₄×C₂₉	—	4	4	no	—
106	C₄⋊C₄×C₂₉	—	4	4	no	—
107	C₄⋊C₄×C₂₉	—	8	2	no	—
108	C₄⋊C₄×C₂₉	C₂×D₄	1	4	yes	—
109	C₄⋊C₄×C₂₉	C₂×Q₈	1	4	yes	—
110	C₄²×C₂₉	—	2	2	no	—
111	C₄²×C₂₉	—	2	2	no	—
112	C₄²×C₂₉	—	8	2	no	—
113	C₄²×C₂₉	C₂×Q₈	1	2	yes	—
114	C₄²×C₂₉	C₂×Q₈	1	2	yes	—
115	#28818	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
117	Q₈×C₂₉	—	8	8	no	—
118	C₂×C₄×C₂₉	—	2	1	no	—
119	C₂×C₄×C₂₉	—	2	1	no	—
120	C₂×C₄×C₂₉	—	2	1	no	—
121	C₂×C₄×C₂₉	—	2	1	no	—
122	C₂×C₄×C₂₉	—	2	2	no	—
123	C₂×C₄×C₂₉	—	2	2	no	—
124	C₂×C₄×C₂₉	—	2	4	no	—
125	C₂×C₄×C₂₉	—	2	4	no	—
126	C₂×C₄×C₂₉	—	2	2	no	—
127	C₂×C₄×C₂₉	—	2	2	no	—
128	C₂×C₄×C₂₉	—	2	2	no	—
129	C₂×C₄×C₂₉	—	2	2	no	—
130	C₂×C₄×C₂₉	—	4	2	no	—
131	C₂×C₄×C₂₉	—	4	2	no	—
132	C₂×C₄×C₂₉	—	4	2	no	—
133	C₂×C₄×C₂₉	—	4	2	no	—
134	C₂×C₄×C₂₉	—	4	2	no	—
135	C₂×C₄×C₂₉	—	4	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	C₄⋊Q₈	1	2	yes	—
141	C₂×C₄×C₂₉	C₄⋊Q₈	1	2	yes	—
142	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
143	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
144	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
145	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
146	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
147	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
148	C₈×C₂₉	—	2	2	no	—
149	C₈×C₂₉	—	2	4	no	—
150	C₈×C₂₉	C₄⋊Q₈	1	4	yes	—
151	C₂×#501	C₂×C₂₉	1	2	yes	—
152	#2550	C₂×C₂₉	1	2	yes	—
153	#2059	C₂×C₂₉	1	2	yes	—
154	#2057	C₂×C₂₉	1	2	yes	—
155	#1949	C₂×C₂₉	1	2	yes	—
156	#1943	C₂×C₂₉	1	2	yes	—
157	#1846	C₂×C₂₉	1	1	yes	characteristic
158	C₄×#107	C₂×C₂₉	1	1	yes	characteristic
159	#1770	C₂×C₂₉	1	1	yes	characteristic
160	C₂²×C₂₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
161	C₂²×C₂₉	D₄²	1	1	yes	characteristic
162	C₂²×C₂₉	D₄×Q₈	1	1	yes	characteristic
163	C₂²×C₂₉	#575	1	1	yes	characteristic
164	C₂²×C₂₉	#575	1	1	yes	characteristic
165	C₂²×C₂₉	#576	1	1	yes	characteristic
166	C₂²×C₂₉	#578	1	1	yes	characteristic
167	C₄×C₂₉	—	2	2	no	—
168	C₄×C₂₉	—	2	2	no	—
169	C₄×C₂₉	—	4	4	no	—
170	C₄×C₂₉	—	4	2	no	—
171	C₄×C₂₉	—	4	4	no	—
172	C₄×C₂₉	—	4	2	no	—
173	C₄×C₂₉	—	8	2	no	—
174	C₄×C₂₉	—	8	2	no	—
175	C₄×C₂₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
176	C₄×C₂₉	#544	1	1	yes	characteristic
177	C₄×C₂₉	D₄×Q₈	1	1	yes	characteristic
178	C₄×C₂₉	Q₈²	1	1	yes	characteristic
179	C₂×C₄⋊Q₈	C₂²×C₂₉	1	2	yes	—
180	C₂×#125	C₂²×C₂₉	1	2	yes	—
181	#501	—	2	8	no	—
182	C₂×#107	C₂²×C₂₉	1	2	yes	—
183	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
184	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
185	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
186	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
187	C₂×#106	C₂²×C₂₉	1	2	yes	—
188	C₂×#106	C₂²×C₂₉	1	2	yes	—
189	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
190	C₂×#97	C₂²×C₂₉	1	2	yes	—
191	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
192	#398	—	2	2	no	—
193	#395	—	2	2	no	—
194	#391	—	2	2	no	—
195	#389	—	2	2	no	—
196	#389	C₂²×C₂₉	1	2	yes	—
197	#389	C₂²×C₂₉	1	2	yes	—
198	#382	C₂²×C₂₉	1	2	yes	—
199	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
200	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
201	#340	C₂²×C₂₉	1	2	yes	—
202	#340	C₂²×C₂₉	1	2	yes	—
203	#340	C₂²×C₂₉	1	2	yes	—
204	#336	C₂²×C₂₉	1	2	yes	—
205	C₂×C₂₉	#2551	1	1	yes	characteristic
206	C₂×C₂₉	#3162	1	1	yes	characteristic
207	C₂×C₂₉	#3164	1	1	yes	characteristic
208	C₂×C₂₉	#3273	1	1	yes	characteristic
209	C₂×C₂₉	#3277	1	1	yes	characteristic
210	C₂×C₂₉	#3389	1	1	yes	characteristic
211	C₂×C₂₉	#3390	1	1	yes	characteristic
212	C₂²×Q₈	—	2	2	no	—
213	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
214	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
215	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
216	C₄⋊Q₈	—	2	4	no	—
217	C₄⋊Q₈	—	4	2	no	—
218	#125	—	2	4	no	—
219	#125	—	4	2	no	—
220	C₂×C₄⋊C₄	—	2	2	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
226	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
228	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
229	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
230	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
231	C₂×C₄²	—	2	2	no	—
232	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
233	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
234	#107	—	2	4	no	—
235	#107	—	4	1	no	—
236	#107	—	4	1	no	—
237	#107	D₄×C₂₉	1	4	yes	—
238	#107	Q₈×C₂₉	1	4	yes	complemented
239	#106	—	2	4	no	—
240	#106	—	2	4	no	—
241	C₄⋊C₈	Q₈×C₂₉	1	4	yes	complemented
242	#97	—	2	4	no	—
243	C₄×C₈	Q₈×C₂₉	1	4	yes	complemented
244	#95	—	2	2	no	—
245	#95	—	2	2	no	—
246	#95	—	2	2	no	—
247	#95	—	2	2	no	—
248	#95	—	2	2	no	—
249	#95	D₄×C₂₉	1	2	yes	—
250	C₂₉	#28818	1	1	yes	characteristic, direct product factor, Sylow
251	C₂×Q₈	—	4	4	no	—
252	C₂×Q₈	—	4	4	no	—
253	C₂×Q₈	—	8	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
259	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
260	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
261	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
262	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	1	no	—
265	C₂×C₈	—	2	1	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
268	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
269	C₂×C₈	C₂×Q₈×C₂₉	1	4	yes	—
270	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
271	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
272	C₄⋊C₄	—	2	2	no	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	2	2	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	—	4	1	no	—
279	C₄⋊C₄	—	4	1	no	—
280	C₄⋊C₄	—	4	4	no	—
281	C₄⋊C₄	—	4	4	no	—
282	C₄⋊C₄	—	4	4	no	—
283	C₄⋊C₄	—	4	4	no	—
284	C₄⋊C₄	—	8	2	no	—
285	C₄⋊C₄	C₂×D₄×C₂₉	1	4	yes	—
286	C₄⋊C₄	C₂×Q₈×C₂₉	1	4	yes	—
287	C₄²	—	2	2	no	—
288	C₄²	—	2	2	no	—
289	C₄²	—	8	2	no	—
290	C₄²	C₂×Q₈×C₂₉	1	2	yes	—
291	C₄²	C₂×Q₈×C₂₉	1	2	yes	—
292	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
293	Q₈	—	8	8	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	C₂₉×C₄⋊Q₈	1	2	yes	—
317	C₂×C₄	C₂₉×C₄⋊Q₈	1	2	yes	—
318	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
319	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
320	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
321	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
322	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
323	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
324	C₈	—	2	2	no	—
325	C₈	—	2	4	no	—
326	C₈	C₂₉×C₄⋊Q₈	1	4	yes	—
327	C₂²	C₂×C₂₉×C₄⋊Q₈	1	1	yes	characteristic
328	C₂²	D₄²×C₂₉	1	1	yes	characteristic
329	C₂²	D₄×Q₈×C₂₉	1	1	yes	characteristic
330	C₂²	C₂₉×#575	1	1	yes	characteristic
331	C₂²	C₂₉×#575	1	1	yes	characteristic
332	C₂²	C₂₉×#576	1	1	yes	characteristic
333	C₂²	C₂₉×#578	1	1	yes	characteristic
334	C₄	—	2	2	no	—
335	C₄	—	2	2	no	—
336	C₄	—	4	2	no	—
337	C₄	—	4	4	no	—
338	C₄	—	4	2	no	—
339	C₄	—	4	4	no	—
340	C₄	—	8	2	no	—
341	C₄	—	8	2	no	—
342	C₄	C₂×C₂₉×C₄⋊Q₈	1	1	yes	characteristic
343	C₄	C₂₉×#544	1	1	yes	characteristic
344	C₄	D₄×Q₈×C₂₉	1	1	yes	characteristic
345	C₄	Q₈²×C₂₉	1	1	yes	characteristic
346	C₂	C₂₉×#2551	1	1	yes	characteristic
347	C₂	C₂₉×#3162	1	1	yes	characteristic
348	C₂	C₂₉×#3164	1	1	yes	characteristic
349	C₂	C₂₉×#3273	1	1	yes	characteristic
350	C₂	C₂₉×#3277	1	1	yes	characteristic
351	C₂	C₂₉×#3389	1	1	yes	characteristic
352	C₂	C₂₉×#3390	1	1	yes	characteristic

	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 ◁ C₄×C₄⋊C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
62. C₂₉×#107	Q₈	semidirect
65. C₂₉×C₄⋊C₈	Q₈	semidirect
67. C₄×C₈×C₂₉	Q₈	semidirect
115. #28818	C₂₉	direct (N × H)
238. #107	Q₈×C₂₉	semidirect
241. C₄⋊C₈	Q₈×C₂₉	semidirect
243. C₄×C₈	Q₈×C₂₉	semidirect
250. C₂₉	#28818	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×#501	2
C₂₉×#2550	2
C₂₉×#2059	2
C₂₉×#2057	2
C₂₉×#1949	2
C₂₉×#1943	2
C₂₉×#1846	2
C₄×C₂₉×#107	2
C₂₉×#1770	2
#28818	29

Subgroups — C29×#28818 #20323718

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#28818 #20323718