Subgroups — C₂₉×#23143 #20318043

Order 7424.

1010 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#469	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2363	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#2361	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#1936	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1934	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1920	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1920	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1879	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1875	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1874	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1762	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₂₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1753	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₂₉	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₂₉	—	2	1	no	—
21	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
25	C₂₉×#469	C₄	1	8	yes	complemented
26	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
36	C₂₉×#390	—	2	1	no	—
37	C₂₉×#390	C₂²	1	1	yes	characteristic
38	C₂₉×#390	C₂²	1	1	yes	characteristic
39	C₂₉×#389	C₂²	1	1	yes	characteristic
40	C₂₉×#389	C₂²	1	1	yes	characteristic
41	C₂₉×#388	—	2	1	no	—
42	C₂₉×#388	—	2	1	no	—
43	C₂₉×#386	—	2	1	no	—
44	C₂₉×#386	—	2	1	no	—
45	C₂₉×#385	—	2	1	no	—
46	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊C₄×C₂₉	—	2	1	no	—
49	C₄×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
50	C₂₉×#340	C₂²	1	1	yes	characteristic
51	C₂₉×#340	C₂²	1	1	yes	characteristic
52	C₂₉×#340	C₂²	1	1	yes	characteristic
53	C₂₉×#340	C₂²	1	1	yes	characteristic
54	C₂₉×#340	C₂²	1	1	yes	characteristic
55	C₂₉×#340	C₂²	1	1	yes	characteristic
56	C₂₉×#340	C₂²	1	1	yes	characteristic
57	C₂₉×#340	C₂²	1	1	yes	characteristic
58	C₂₉×#336	C₂²	1	1	yes	characteristic
59	C₂₉×#336	C₂²	1	1	yes	characteristic
60	C₂²×D₄×C₂₉	—	2	1	no	—
61	C₂²×D₄×C₂₉	—	2	1	no	—
62	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₂₉	—	2	1	no	—
65	C₂³×C₄×C₂₉	—	2	1	no	—
66	C₂³×C₄×C₂₉	—	2	1	no	—
67	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
68	C₂×D₈×C₂₉	—	4	1	no	—
69	C₂×D₈×C₂₉	—	4	1	no	—
70	C₂×D₈×C₂₉	C₂×C₄	1	4	yes	complemented
71	C₂×M₁₆×C₂₉	—	4	1	no	—
72	C₂×M₁₆×C₂₉	—	4	1	no	—
73	C₂×M₁₆×C₂₉	C₂×C₄	1	4	yes	complemented
74	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
78	C₂₉×#121	—	2	2	no	—
79	C₂₉×#121	—	2	2	no	—
80	C₂₉×#121	C₂×C₄	1	4	yes	complemented
81	C₂₉×#121	C₂×C₄	1	4	yes	complemented
82	C₄×D₄×C₂₉	—	2	2	no	—
83	C₄×D₄×C₂₉	—	2	2	no	—
84	C₄×D₄×C₂₉	—	4	1	no	—
85	C₄×D₄×C₂₉	—	4	1	no	—
86	C₄×D₄×C₂₉	—	4	4	no	—
87	C₂₉×#117	—	2	2	no	—
88	C₂₉×#117	—	4	1	no	—
89	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
90	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
94	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₂₉	—	2	1	no	—
112	C₂×C₄²×C₂₉	—	2	1	no	—
113	C₂×C₄²×C₂₉	—	2	1	no	—
114	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
116	C₂₉×#106	C₂×C₄	1	4	yes	complemented
117	C₂₉×#102	—	2	2	no	—
118	C₂₉×#102	—	2	2	no	—
119	C₂₉×#102	—	4	1	no	—
120	C₂₉×#102	—	4	1	no	—
121	C₂₉×#102	C₂×C₄	1	4	yes	complemented
122	C₂₉×#102	C₂×C₄	1	4	yes	complemented
123	C₂₉×C₂²⋊C₈	—	2	2	no	—
124	C₂₉×#97	—	4	1	no	—
125	C₄×C₈×C₂₉	—	4	1	no	—
126	C₂₉×#95	—	2	1	no	—
127	C₂₉×#95	—	2	1	no	—
128	C₂₉×#95	—	2	1	no	—
129	C₂₉×#95	—	2	1	no	—
130	C₂₉×#95	D₄	1	1	yes	characteristic
131	C₂₉×#95	D₄	1	1	yes	characteristic
132	C₂⁴×C₂₉	—	2	1	no	—
133	C₂⁴×C₂₉	—	2	1	no	—
134	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
135	C₂×D₄×C₂₉	—	2	4	no	—
136	C₂×D₄×C₂₉	—	2	4	no	—
137	C₂×D₄×C₂₉	—	2	1	no	—
138	C₂×D₄×C₂₉	—	2	1	no	—
139	C₂×D₄×C₂₉	—	2	1	no	—
140	C₂×D₄×C₂₉	—	2	1	no	—
141	C₂×D₄×C₂₉	—	2	1	no	—
142	C₂×D₄×C₂₉	—	2	1	no	—
143	C₂×D₄×C₂₉	—	2	1	no	—
144	C₂×D₄×C₂₉	—	2	1	no	—
145	C₂×D₄×C₂₉	—	2	1	no	—
146	C₂×D₄×C₂₉	—	2	1	no	—
147	C₂×D₄×C₂₉	—	4	2	no	—
148	C₂×D₄×C₂₉	—	4	2	no	—
149	C₂×D₄×C₂₉	—	8	1	no	—
150	C₂×D₄×C₂₉	—	8	1	no	—
151	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
152	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
153	C₂²×C₄×C₂₉	—	2	1	no	—
154	C₂²×C₄×C₂₉	—	2	1	no	—
155	C₂²×C₄×C₂₉	—	2	1	no	—
156	C₂²×C₄×C₂₉	—	2	1	no	—
157	C₂²×C₄×C₂₉	—	2	1	no	—
158	C₂²×C₄×C₂₉	—	2	1	no	—
159	C₂²×C₄×C₂₉	—	2	1	no	—
160	C₂²×C₄×C₂₉	—	2	1	no	—
161	C₂²×C₄×C₂₉	—	2	1	no	—
162	C₂²×C₄×C₂₉	—	2	1	no	—
163	C₂²×C₄×C₂₉	—	4	2	no	—
164	C₂²×C₄×C₂₉	—	4	2	no	—
165	C₂²×C₄×C₂₉	—	4	2	no	—
166	C₂²×C₄×C₂₉	—	4	2	no	—
167	C₂²×C₄×C₂₉	—	4	2	no	—
168	C₂²×C₄×C₂₉	—	4	2	no	—
169	C₂²×C₄×C₂₉	—	8	1	no	—
170	C₂²×C₄×C₂₉	—	8	1	no	—
171	C₂²×C₄×C₂₉	—	8	1	no	—
172	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
173	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₂₉	#41	1	2	yes	—
179	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
180	D₈×C₂₉	—	4	4	no	—
181	M₁₆×C₂₉	—	4	4	no	—
182	C₂×C₈×C₂₉	—	2	1	no	—
183	C₂×C₈×C₂₉	—	2	1	no	—
184	C₂×C₈×C₂₉	—	2	1	no	—
185	C₂×C₈×C₂₉	—	2	1	no	—
186	C₂×C₈×C₂₉	—	2	1	no	—
187	C₂×C₈×C₂₉	—	2	1	no	—
188	C₂×C₈×C₂₉	—	2	1	no	—
189	C₂×C₈×C₂₉	—	2	1	no	—
190	C₂×C₈×C₂₉	—	2	1	no	—
191	C₂×C₈×C₂₉	—	2	1	no	—
192	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
193	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
194	C₄⋊C₄×C₂₉	—	2	1	no	—
195	C₄⋊C₄×C₂₉	—	2	1	no	—
196	C₄⋊C₄×C₂₉	—	2	1	no	—
197	C₄⋊C₄×C₂₉	—	2	1	no	—
198	C₄⋊C₄×C₂₉	—	2	1	no	—
199	C₄⋊C₄×C₂₉	—	2	1	no	—
200	C₄⋊C₄×C₂₉	—	2	1	no	—
201	C₄⋊C₄×C₂₉	—	2	1	no	—
202	C₄⋊C₄×C₂₉	—	4	2	no	—
203	C₄⋊C₄×C₂₉	—	4	2	no	—
204	C₄⋊C₄×C₂₉	—	8	1	no	—
205	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
206	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
207	C₄⋊C₄×C₂₉	#41	1	2	yes	—
208	C₄⋊C₄×C₂₉	#41	1	2	yes	—
209	C₂²⋊C₄×C₂₉	—	2	4	no	—
210	C₂²⋊C₄×C₂₉	—	2	4	no	—
211	C₂²⋊C₄×C₂₉	—	2	2	no	—
212	C₂²⋊C₄×C₂₉	—	4	1	no	—
213	C₂²⋊C₄×C₂₉	—	4	2	no	—
214	C₂²⋊C₄×C₂₉	—	4	2	no	—
215	C₂²⋊C₄×C₂₉	—	4	2	no	—
216	C₂²⋊C₄×C₂₉	—	4	2	no	—
217	C₂²⋊C₄×C₂₉	—	4	2	no	—
218	C₂²⋊C₄×C₂₉	—	8	1	no	—
219	C₂²⋊C₄×C₂₉	—	8	1	no	—
220	C₄²×C₂₉	—	2	1	no	—
221	C₄²×C₂₉	—	2	1	no	—
222	C₄²×C₂₉	—	2	1	no	—
223	C₄²×C₂₉	—	2	1	no	—
224	C₄²×C₂₉	—	4	2	no	—
225	C₄²×C₂₉	—	4	2	no	—
226	C₄²×C₂₉	—	8	1	no	—
227	#23143	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂³×C₂₉	—	2	1	no	—
229	C₂³×C₂₉	—	2	1	no	—
230	C₂³×C₂₉	—	2	1	no	—
231	C₂³×C₂₉	—	2	1	no	—
232	C₂³×C₂₉	—	2	1	no	—
233	C₂³×C₂₉	—	2	1	no	—
234	C₂³×C₂₉	—	2	2	no	—
235	C₂³×C₂₉	—	2	2	no	—
236	C₂³×C₂₉	—	4	1	no	—
237	C₂³×C₂₉	—	4	1	no	—
238	C₂³×C₂₉	—	4	1	no	—
239	C₂³×C₂₉	—	4	1	no	—
240	C₂³×C₂₉	—	4	1	no	—
241	C₂³×C₂₉	—	4	1	no	—
242	C₂³×C₂₉	—	4	1	no	—
243	C₂³×C₂₉	—	4	1	no	—
244	C₂³×C₂₉	—	4	1	no	—
245	C₂³×C₂₉	—	4	1	no	—
246	C₂³×C₂₉	—	4	1	no	—
247	C₂³×C₂₉	—	4	1	no	—
248	C₂³×C₂₉	C₄×D₄	1	2	yes	—
249	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
250	D₄×C₂₉	—	2	2	no	—
251	D₄×C₂₉	—	2	2	no	—
252	D₄×C₂₉	—	2	2	no	—
253	D₄×C₂₉	—	2	2	no	—
254	D₄×C₂₉	—	4	8	no	—
255	D₄×C₂₉	—	4	1	no	—
256	D₄×C₂₉	—	4	1	no	—
257	D₄×C₂₉	—	4	1	no	—
258	D₄×C₂₉	—	4	1	no	—
259	D₄×C₂₉	—	8	4	no	—
260	C₂×C₄×C₂₉	—	2	1	no	—
261	C₂×C₄×C₂₉	—	2	1	no	—
262	C₂×C₄×C₂₉	—	2	1	no	—
263	C₂×C₄×C₂₉	—	2	1	no	—
264	C₂×C₄×C₂₉	—	2	2	no	—
265	C₂×C₄×C₂₉	—	2	2	no	—
266	C₂×C₄×C₂₉	—	2	2	no	—
267	C₂×C₄×C₂₉	—	2	2	no	—
268	C₂×C₄×C₂₉	—	2	2	no	—
269	C₂×C₄×C₂₉	—	2	2	no	—
270	C₂×C₄×C₂₉	—	2	1	no	—
271	C₂×C₄×C₂₉	—	2	1	no	—
272	C₂×C₄×C₂₉	—	2	1	no	—
273	C₂×C₄×C₂₉	—	2	2	no	—
274	C₂×C₄×C₂₉	—	2	2	no	—
275	C₂×C₄×C₂₉	—	2	1	no	—
276	C₂×C₄×C₂₉	—	2	1	no	—
277	C₂×C₄×C₂₉	—	2	1	no	—
278	C₂×C₄×C₂₉	—	2	1	no	—
279	C₂×C₄×C₂₉	—	2	1	no	—
280	C₂×C₄×C₂₉	—	2	1	no	—
281	C₂×C₄×C₂₉	—	4	1	no	—
282	C₂×C₄×C₂₉	—	4	1	no	—
283	C₂×C₄×C₂₉	—	4	1	no	—
284	C₂×C₄×C₂₉	—	4	1	no	—
285	C₂×C₄×C₂₉	—	4	1	no	—
286	C₂×C₄×C₂₉	—	4	1	no	—
287	C₂×C₄×C₂₉	—	4	1	no	—
288	C₂×C₄×C₂₉	—	4	1	no	—
289	C₂×C₄×C₂₉	—	4	1	no	—
290	C₂×C₄×C₂₉	—	4	1	no	—
291	C₂×C₄×C₂₉	—	4	1	no	—
292	C₂×C₄×C₂₉	—	4	1	no	—
293	C₂×C₄×C₂₉	—	4	1	no	—
294	C₂×C₄×C₂₉	—	4	1	no	—
295	C₂×C₄×C₂₉	—	8	4	no	—
296	C₂×C₄×C₂₉	—	8	4	no	—
297	C₂×C₄×C₂₉	—	8	4	no	—
298	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
299	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
300	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
301	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
302	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
303	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
304	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
305	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
306	C₈×C₂₉	—	2	2	no	—
307	C₈×C₂₉	—	2	2	no	—
308	C₈×C₂₉	—	4	1	no	—
309	C₈×C₂₉	—	4	1	no	—
310	C₂×#469	C₂×C₂₉	1	1	yes	characteristic
311	#2363	C₂×C₂₉	1	1	yes	characteristic, complemented
312	#2361	C₂×C₂₉	1	1	yes	characteristic, complemented
313	#1936	C₂×C₂₉	1	1	yes	characteristic, complemented
314	#1934	C₂×C₂₉	1	1	yes	characteristic, complemented
315	#1920	C₂×C₂₉	1	1	yes	characteristic, complemented
316	#1920	C₂×C₂₉	1	1	yes	characteristic, complemented
317	#1879	C₂×C₂₉	1	1	yes	characteristic, complemented
318	#1879	C₂×C₂₉	1	1	yes	characteristic, complemented
319	#1875	C₂×C₂₉	1	1	yes	characteristic, complemented
320	#1874	C₂×C₂₉	1	1	yes	characteristic, complemented
321	#1762	C₂×C₂₉	1	1	yes	characteristic, complemented
322	C₄×#102	C₂×C₂₉	1	1	yes	characteristic, complemented
323	#1753	C₂×C₂₉	1	1	yes	characteristic, complemented
324	#1736	C₂×C₂₉	1	1	yes	characteristic, complemented
325	C₂²×C₂₉	—	2	2	no	—
326	C₂²×C₂₉	—	2	2	no	—
327	C₂²×C₂₉	—	2	2	no	—
328	C₂²×C₂₉	—	4	1	no	—
329	C₂²×C₂₉	—	4	1	no	—
330	C₂²×C₂₉	—	4	1	no	—
331	C₂²×C₂₉	—	4	1	no	—
332	C₂²×C₂₉	—	4	2	no	—
333	C₂²×C₂₉	—	4	2	no	—
334	C₂²×C₂₉	—	4	2	no	—
335	C₂²×C₂₉	—	4	2	no	—
336	C₂²×C₂₉	—	4	2	no	—
337	C₂²×C₂₉	—	4	2	no	—
338	C₂²×C₂₉	—	8	1	no	—
339	C₂²×C₂₉	—	8	1	no	—
340	C₂²×C₂₉	—	8	1	no	—
341	C₂²×C₂₉	—	8	1	no	—
342	C₂²×C₂₉	—	8	1	no	—
343	C₂²×C₂₉	—	8	1	no	—
344	C₂²×C₂₉	—	8	1	no	—
345	C₂²×C₂₉	—	8	1	no	—
346	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
347	C₂²×C₂₉	#546	1	1	yes	characteristic
348	C₂²×C₂₉	#546	1	1	yes	characteristic
349	C₂²×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
350	C₂²×C₂₉	#575	1	1	yes	characteristic
351	C₂²×C₂₉	#576	1	1	yes	characteristic
352	C₂²×C₂₉	#577	1	1	yes	characteristic
353	C₄×C₂₉	—	2	2	no	—
354	C₄×C₂₉	—	2	2	no	—
355	C₄×C₂₉	—	4	2	no	—
356	C₄×C₂₉	—	4	2	no	—
357	C₄×C₂₉	—	4	2	no	—
358	C₄×C₂₉	—	4	1	no	—
359	C₄×C₂₉	—	4	1	no	—
360	C₄×C₂₉	—	4	2	no	—
361	C₄×C₂₉	—	4	1	no	—
362	C₄×C₂₉	—	8	1	no	—
363	C₄×C₂₉	—	8	1	no	—
364	C₄×C₂₉	C₄×#41	1	1	yes	characteristic
365	C₄×C₂₉	#518	1	1	yes	characteristic
366	C₄×C₂₉	#553	1	1	yes	characteristic
367	C₄×C₂₉	#553	1	1	yes	characteristic
368	C₂²×D₈	C₂²×C₂₉	1	1	yes	characteristic
369	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
370	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic
371	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic
372	C₂×C₄×D₄	—	2	1	no	—
373	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
374	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
375	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
376	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
377	#469	C₄×C₂₉	1	8	yes	complemented
378	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
379	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
380	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
381	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
382	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
383	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
384	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
385	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
386	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
387	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
388	#390	—	2	1	no	—
389	#390	C₂²×C₂₉	1	1	yes	characteristic
390	#390	C₂²×C₂₉	1	1	yes	characteristic
391	#389	C₂²×C₂₉	1	1	yes	characteristic
392	#389	C₂²×C₂₉	1	1	yes	characteristic
393	#388	—	2	1	no	—
394	#388	—	2	1	no	—
395	#386	—	2	1	no	—
396	#386	—	2	1	no	—
397	#385	—	2	1	no	—
398	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
399	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
400	C₄×C₂²⋊C₄	—	2	1	no	—
401	C₄×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
402	#340	C₂²×C₂₉	1	1	yes	characteristic
403	#340	C₂²×C₂₉	1	1	yes	characteristic
404	#340	C₂²×C₂₉	1	1	yes	characteristic
405	#340	C₂²×C₂₉	1	1	yes	characteristic
406	#340	C₂²×C₂₉	1	1	yes	characteristic
407	#340	C₂²×C₂₉	1	1	yes	characteristic
408	#340	C₂²×C₂₉	1	1	yes	characteristic
409	#340	C₂²×C₂₉	1	1	yes	characteristic
410	#336	C₂²×C₂₉	1	1	yes	characteristic
411	#336	C₂²×C₂₉	1	1	yes	characteristic
412	C₂×C₂₉	—	4	2	no	—
413	C₂×C₂₉	—	8	2	no	—
414	C₂×C₂₉	—	8	2	no	—
415	C₂×C₂₉	#2364	1	1	yes	characteristic
416	C₂×C₂₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
417	C₂×C₂₉	#2946	1	1	yes	characteristic
418	C₂×C₂₉	#3306	1	1	yes	characteristic
419	C₂×C₂₉	#3309	1	1	yes	characteristic
420	C₂×C₂₉	#3325	1	1	yes	characteristic
421	C₂×C₂₉	#3326	1	1	yes	characteristic
422	C₂²×D₄	—	2	1	no	—
423	C₂²×D₄	—	2	1	no	—
424	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
425	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
426	C₂³×C₄	—	2	1	no	—
427	C₂³×C₄	—	2	1	no	—
428	C₂³×C₄	—	2	1	no	—
429	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
430	C₂×D₈	—	4	1	no	—
431	C₂×D₈	—	4	1	no	—
432	C₂×D₈	C₂×C₄×C₂₉	1	4	yes	complemented
433	C₂×M₁₆	—	4	1	no	—
434	C₂×M₁₆	—	4	1	no	—
435	C₂×M₁₆	C₂×C₄×C₂₉	1	4	yes	complemented
436	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
437	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
438	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
439	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
440	#121	—	2	2	no	—
441	#121	—	2	2	no	—
442	#121	C₂×C₄×C₂₉	1	4	yes	complemented
443	#121	C₂×C₄×C₂₉	1	4	yes	complemented
444	C₄×D₄	—	2	2	no	—
445	C₄×D₄	—	2	2	no	—
446	C₄×D₄	—	4	1	no	—
447	C₄×D₄	—	4	1	no	—
448	C₄×D₄	—	4	4	no	—
449	#117	—	2	2	no	—
450	#117	—	4	1	no	—
451	C₂×C₄⋊C₄	—	2	2	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	—	2	1	no	—
454	C₂×C₄⋊C₄	—	2	1	no	—
455	C₂×C₄⋊C₄	—	4	1	no	—
456	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	—	2	1	no	—
467	C₂×C₂²⋊C₄	—	2	1	no	—
468	C₂×C₂²⋊C₄	—	2	1	no	—
469	C₂×C₂²⋊C₄	—	2	1	no	—
470	C₂×C₂²⋊C₄	—	2	1	no	—
471	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
472	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
473	C₂×C₄²	—	2	1	no	—
474	C₂×C₄²	—	2	1	no	—
475	C₂×C₄²	—	2	1	no	—
476	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
477	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
478	#106	C₂×C₄×C₂₉	1	4	yes	complemented
479	#102	—	2	2	no	—
480	#102	—	2	2	no	—
481	#102	—	4	1	no	—
482	#102	—	4	1	no	—
483	#102	C₂×C₄×C₂₉	1	4	yes	complemented
484	#102	C₂×C₄×C₂₉	1	4	yes	complemented
485	C₂²⋊C₈	—	2	2	no	—
486	#97	—	4	1	no	—
487	C₄×C₈	—	4	1	no	—
488	#95	—	2	1	no	—
489	#95	—	2	1	no	—
490	#95	—	2	1	no	—
491	#95	—	2	1	no	—
492	#95	D₄×C₂₉	1	1	yes	characteristic
493	#95	D₄×C₂₉	1	1	yes	characteristic
494	C₂₉	#23143	1	1	yes	characteristic, direct product factor, Sylow
495	C₂⁴	—	2	1	no	—
496	C₂⁴	—	2	1	no	—
497	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
498	C₂×D₄	—	2	4	no	—
499	C₂×D₄	—	2	4	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	4	2	no	—
511	C₂×D₄	—	4	2	no	—
512	C₂×D₄	—	8	1	no	—
513	C₂×D₄	—	8	1	no	—
514	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
515	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	4	2	no	—
527	C₂²×C₄	—	4	2	no	—
528	C₂²×C₄	—	4	2	no	—
529	C₂²×C₄	—	4	2	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	4	2	no	—
532	C₂²×C₄	—	8	1	no	—
533	C₂²×C₄	—	8	1	no	—
534	C₂²×C₄	—	8	1	no	—
535	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
536	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
537	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
538	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
539	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
540	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
541	C₂²×C₄	#41×C₂₉	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
543	D₈	—	4	4	no	—
544	M₁₆	—	4	4	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
556	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	4	2	no	—
566	C₄⋊C₄	—	4	2	no	—
567	C₄⋊C₄	—	8	1	no	—
568	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
569	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
570	C₄⋊C₄	#41×C₂₉	1	2	yes	—
571	C₄⋊C₄	#41×C₂₉	1	2	yes	—
572	C₂²⋊C₄	—	2	4	no	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	2	no	—
575	C₂²⋊C₄	—	4	1	no	—
576	C₂²⋊C₄	—	4	2	no	—
577	C₂²⋊C₄	—	4	2	no	—
578	C₂²⋊C₄	—	4	2	no	—
579	C₂²⋊C₄	—	4	2	no	—
580	C₂²⋊C₄	—	4	2	no	—
581	C₂²⋊C₄	—	8	1	no	—
582	C₂²⋊C₄	—	8	1	no	—
583	C₄²	—	2	1	no	—
584	C₄²	—	2	1	no	—
585	C₄²	—	2	1	no	—
586	C₄²	—	2	1	no	—
587	C₄²	—	4	2	no	—
588	C₄²	—	4	2	no	—
589	C₄²	—	8	1	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	2	no	—
597	C₂³	—	2	2	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	1	no	—
600	C₂³	—	4	1	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	1	no	—
609	C₂³	—	4	1	no	—
610	C₂³	C₄×D₄×C₂₉	1	2	yes	—
611	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
612	D₄	—	2	2	no	—
613	D₄	—	2	2	no	—
614	D₄	—	2	2	no	—
615	D₄	—	2	2	no	—
616	D₄	—	4	8	no	—
617	D₄	—	4	1	no	—
618	D₄	—	4	1	no	—
619	D₄	—	4	1	no	—
620	D₄	—	4	1	no	—
621	D₄	—	8	4	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	8	4	no	—
658	C₂×C₄	—	8	4	no	—
659	C₂×C₄	—	8	4	no	—
660	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
661	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
662	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
663	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
664	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
665	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
666	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
667	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
668	C₈	—	2	2	no	—
669	C₈	—	2	2	no	—
670	C₈	—	4	1	no	—
671	C₈	—	4	1	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	4	1	no	—
676	C₂²	—	4	1	no	—
677	C₂²	—	4	1	no	—
678	C₂²	—	4	1	no	—
679	C₂²	—	4	2	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	4	2	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	8	1	no	—
686	C₂²	—	8	1	no	—
687	C₂²	—	8	1	no	—
688	C₂²	—	8	1	no	—
689	C₂²	—	8	1	no	—
690	C₂²	—	8	1	no	—
691	C₂²	—	8	1	no	—
692	C₂²	—	8	1	no	—
693	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
694	C₂²	C₂₉×#546	1	1	yes	characteristic
695	C₂²	C₂₉×#546	1	1	yes	characteristic
696	C₂²	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
697	C₂²	C₂₉×#575	1	1	yes	characteristic
698	C₂²	C₂₉×#576	1	1	yes	characteristic
699	C₂²	C₂₉×#577	1	1	yes	characteristic
700	C₄	—	2	2	no	—
701	C₄	—	2	2	no	—
702	C₄	—	4	2	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	2	no	—
705	C₄	—	4	1	no	—
706	C₄	—	4	1	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	1	no	—
709	C₄	—	8	1	no	—
710	C₄	—	8	1	no	—
711	C₄	C₄×#41×C₂₉	1	1	yes	characteristic
712	C₄	C₂₉×#518	1	1	yes	characteristic
713	C₄	C₂₉×#553	1	1	yes	characteristic
714	C₄	C₂₉×#553	1	1	yes	characteristic
715	C₂	—	4	2	no	—
716	C₂	—	8	2	no	—
717	C₂	—	8	2	no	—
718	C₂	C₂₉×#2364	1	1	yes	characteristic
719	C₂	C₄×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
720	C₂	C₂₉×#2946	1	1	yes	characteristic
721	C₂	C₂₉×#3306	1	1	yes	characteristic
722	C₂	C₂₉×#3309	1	1	yes	characteristic
723	C₂	C₂₉×#3325	1	1	yes	characteristic
724	C₂	C₂₉×#3326	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	C₂×C₂₉×#469	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₄×C₂²⋊C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#2363	C₂	semidirect
3. C₂₉×#2361	C₂	semidirect
4. C₂₉×#1936	C₂	semidirect
5. C₂₉×#1934	C₂	semidirect
6. C₂₉×#1920	C₂	semidirect
7. C₂₉×#1920	C₂	semidirect
8. C₂₉×#1879	C₂	semidirect
9. C₂₉×#1879	C₂	semidirect
10. C₂₉×#1875	C₂	semidirect
11. C₂₉×#1874	C₂	semidirect
12. C₂₉×#1762	C₂	semidirect
13. C₄×C₂₉×#102	C₂	semidirect
14. C₂₉×#1753	C₂	semidirect
15. C₂₉×#1736	C₂	semidirect
25. C₂₉×#469	C₄	semidirect
70. C₂×D₈×C₂₉	C₂×C₄	semidirect
73. C₂×M₁₆×C₂₉	C₂×C₄	semidirect
80. C₂₉×#121	C₂×C₄	semidirect
81. C₂₉×#121	C₂×C₄	semidirect
116. C₂₉×#106	C₂×C₄	semidirect
121. C₂₉×#102	C₂×C₄	semidirect
122. C₂₉×#102	C₂×C₄	semidirect
227. #23143	C₂₉	direct (N × H)
311. #2363	C₂×C₂₉	semidirect
312. #2361	C₂×C₂₉	semidirect
313. #1936	C₂×C₂₉	semidirect
314. #1934	C₂×C₂₉	semidirect
315. #1920	C₂×C₂₉	semidirect
316. #1920	C₂×C₂₉	semidirect
317. #1879	C₂×C₂₉	semidirect
318. #1879	C₂×C₂₉	semidirect
319. #1875	C₂×C₂₉	semidirect
320. #1874	C₂×C₂₉	semidirect
321. #1762	C₂×C₂₉	semidirect
322. C₄×#102	C₂×C₂₉	semidirect
323. #1753	C₂×C₂₉	semidirect
324. #1736	C₂×C₂₉	semidirect
377. #469	C₄×C₂₉	semidirect
432. C₂×D₈	C₂×C₄×C₂₉	semidirect
435. C₂×M₁₆	C₂×C₄×C₂₉	semidirect
442. #121	C₂×C₄×C₂₉	semidirect
443. #121	C₂×C₄×C₂₉	semidirect
478. #106	C₂×C₄×C₂₉	semidirect
483. #102	C₂×C₄×C₂₉	semidirect
484. #102	C₂×C₄×C₂₉	semidirect
494. C₂₉	#23143	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×#469	2
C₂₉×#2363	2
C₂₉×#2361	2
C₂₉×#1936	2
C₂₉×#1934	2
C₂₉×#1920	2
C₂₉×#1879	2
C₂₉×#1875	2
C₂₉×#1874	2
C₂₉×#1762	2
C₄×C₂₉×#102	2
C₂₉×#1753	2
C₂₉×#1736	2
#23143	29

Subgroups — C29×#23143 #20318043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#23143 #20318043