Subgroups — C₂₉×#7952 #20302852

Order 7424.

610 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#432	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#432	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2285	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1285	C₂	1	4	yes	maximal, complemented
5	C₂×C₂₉×#117	C₄	1	2	yes	—
6	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
7	C₂₉×#432	—	2	1	no	—
8	C₂₉×#432	—	2	1	no	—
9	C₂₉×#432	—	2	1	no	—
10	C₂₉×#432	—	2	1	no	—
11	C₂₉×#432	C₄	1	2	yes	complemented
12	C₂₉×#432	C₄	1	2	yes	complemented
13	C₂₉×#432	C₂²	1	2	yes	—
14	C₂₉×#432	C₂²	1	2	yes	—
15	C₂×C₂₉×C₄⋊C₈	—	2	1	no	—
16	C₂×C₂₉×C₄⋊C₈	C₄	1	2	yes	complemented
17	C₂×C₂₉×C₂²⋊C₈	—	2	1	no	—
18	C₂×C₂₉×C₂²⋊C₈	—	2	1	no	—
19	C₂×C₂₉×#97	—	2	1	no	—
20	C₂×C₂₉×#97	C₄	1	2	yes	complemented
21	C₂₉×#384	—	2	1	no	—
22	C₂₉×#382	—	2	1	no	—
23	C₂₉×#380	—	2	1	no	—
24	C₂₉×#380	—	2	1	no	—
25	C₄×C₄⋊C₄×C₂₉	C₄	1	2	yes	—
26	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
27	C₂³×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₂₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₂₉	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₂₉	—	2	2	no	—
31	C₂²×C₈×C₂₉	—	2	2	no	—
32	C₂₉×#117	—	4	4	no	—
33	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
34	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
35	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
36	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
37	C₂×C₄²×C₂₉	C₂×C₄	1	4	yes	—
38	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₂₉	Q₈	1	1	yes	characteristic
48	C₂×C₄²×C₂₉	Q₈	1	1	yes	characteristic
49	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
50	C₂₉×C₄⋊C₈	—	2	2	no	—
51	C₂₉×C₄⋊C₈	—	2	2	no	—
52	C₂₉×C₄⋊C₈	—	2	2	no	—
53	C₂₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
54	C₂₉×C₂²⋊C₈	—	2	2	no	—
55	C₂₉×C₂²⋊C₈	—	2	2	no	—
56	C₂₉×C₂²⋊C₈	—	2	2	no	—
57	C₂₉×C₂²⋊C₈	—	2	2	no	—
58	C₂₉×#97	—	2	2	no	—
59	C₂₉×#97	—	2	2	no	—
60	C₂₉×#97	—	2	2	no	—
61	C₂₉×#97	C₂×C₄	1	4	yes	—
62	C₂₉×#95	—	2	2	no	—
63	C₂₉×#95	—	2	2	no	—
64	C₂⁴×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₂₉	—	2	2	no	—
66	C₂²×C₄×C₂₉	—	2	2	no	—
67	C₂²×C₄×C₂₉	—	2	4	no	—
68	C₂²×C₄×C₂₉	—	4	2	no	—
69	C₂²×C₄×C₂₉	—	4	2	no	—
70	C₂²×C₄×C₂₉	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₂₉	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
88	C₂×C₈×C₂₉	—	2	4	no	—
89	C₂×C₈×C₂₉	—	2	4	no	—
90	C₂×C₈×C₂₉	—	4	4	no	—
91	C₂×C₈×C₂₉	—	4	4	no	—
92	C₄⋊C₄×C₂₉	—	4	4	no	—
93	C₄⋊C₄×C₂₉	—	4	4	no	—
94	C₄⋊C₄×C₂₉	—	4	4	no	—
95	C₂²⋊C₄×C₂₉	—	4	4	no	—
96	C₄²×C₂₉	—	4	4	no	—
97	C₄²×C₂₉	C₄²	1	1	yes	characteristic
98	C₄²×C₂₉	C₄²	1	1	yes	characteristic
99	C₄²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₂₉	C₂×Q₈	1	1	yes	characteristic
113	#7952	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂³×C₂₉	—	4	1	no	—
115	C₂³×C₂₉	—	4	1	no	—
116	C₂³×C₂₉	#95	1	1	yes	characteristic
117	C₂³×C₂₉	#95	1	1	yes	characteristic
118	C₂³×C₂₉	#100	1	2	yes	—
119	C₂³×C₂₉	#101	1	2	yes	—
120	C₂³×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₂₉	—	2	2	no	—
122	C₂×C₄×C₂₉	—	2	2	no	—
123	C₂×C₄×C₂₉	—	2	2	no	—
124	C₂×C₄×C₂₉	—	2	2	no	—
125	C₂×C₄×C₂₉	—	2	1	no	—
126	C₂×C₄×C₂₉	—	2	1	no	—
127	C₂×C₄×C₂₉	—	2	1	no	—
128	C₂×C₄×C₂₉	—	2	1	no	—
129	C₂×C₄×C₂₉	—	2	2	no	—
130	C₂×C₄×C₂₉	—	2	2	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	—	4	1	no	—
136	C₂×C₄×C₂₉	—	4	1	no	—
137	C₂×C₄×C₂₉	—	4	1	no	—
138	C₂×C₄×C₂₉	—	4	1	no	—
139	C₂×C₄×C₂₉	—	4	1	no	—
140	C₂×C₄×C₂₉	—	4	1	no	—
141	C₂×C₄×C₂₉	—	4	4	no	—
142	C₂×C₄×C₂₉	—	4	4	no	—
143	C₂×C₄×C₂₉	—	4	4	no	—
144	C₂×C₄×C₂₉	#95	1	1	yes	characteristic
145	C₂×C₄×C₂₉	#95	1	1	yes	characteristic
146	C₂×C₄×C₂₉	#95	1	1	yes	characteristic
147	C₂×C₄×C₂₉	#95	1	1	yes	characteristic
148	C₂×C₄×C₂₉	#95	1	1	yes	characteristic
149	C₂×C₄×C₂₉	#95	1	1	yes	characteristic
150	C₂×C₄×C₂₉	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₈×C₂₉	—	4	4	no	—
157	C₈×C₂₉	—	4	4	no	—
158	C₂×#432	C₂×C₂₉	1	1	yes	characteristic
159	C₂×#432	C₂×C₂₉	1	1	yes	characteristic
160	#2285	C₂×C₂₉	1	1	yes	characteristic
161	#1285	C₂×C₂₉	1	4	yes	complemented
162	C₂²×C₂₉	—	2	1	no	—
163	C₂²×C₂₉	—	2	1	no	—
164	C₂²×C₂₉	—	2	1	no	—
165	C₂²×C₂₉	—	2	1	no	—
166	C₂²×C₂₉	—	2	1	no	—
167	C₂²×C₂₉	—	2	1	no	—
168	C₂²×C₂₉	—	4	2	no	—
169	C₂²×C₂₉	—	4	2	no	—
170	C₂²×C₂₉	#343	1	2	yes	—
171	C₂²×C₂₉	#343	1	2	yes	—
172	C₂²×C₂₉	C₂×#95	1	1	yes	characteristic
173	C₂²×C₂₉	C₂×#100	1	1	yes	characteristic
174	C₂²×C₂₉	C₂×#101	1	1	yes	characteristic
175	C₄×C₂₉	—	2	1	no	—
176	C₄×C₂₉	—	2	1	no	—
177	C₄×C₂₉	—	2	1	no	—
178	C₄×C₂₉	—	2	1	no	—
179	C₄×C₂₉	—	2	1	no	—
180	C₄×C₂₉	—	2	1	no	—
181	C₄×C₂₉	—	2	1	no	—
182	C₄×C₂₉	—	2	1	no	—
183	C₄×C₂₉	—	2	1	no	—
184	C₄×C₂₉	—	2	1	no	—
185	C₄×C₂₉	—	8	4	no	—
186	C₄×C₂₉	H(3,ℤ/4)	1	2	yes	—
187	C₄×C₂₉	#421	1	2	yes	—
188	C₂×#117	C₄×C₂₉	1	2	yes	—
189	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
190	#432	—	2	1	no	—
191	#432	—	2	1	no	—
192	#432	—	2	1	no	—
193	#432	—	2	1	no	—
194	#432	C₄×C₂₉	1	2	yes	complemented
195	#432	C₄×C₂₉	1	2	yes	complemented
196	#432	C₂²×C₂₉	1	2	yes	—
197	#432	C₂²×C₂₉	1	2	yes	—
198	C₂×C₄⋊C₈	—	2	1	no	—
199	C₂×C₄⋊C₈	C₄×C₂₉	1	2	yes	complemented
200	C₂×C₂²⋊C₈	—	2	1	no	—
201	C₂×C₂²⋊C₈	—	2	1	no	—
202	C₂×#97	—	2	1	no	—
203	C₂×#97	C₄×C₂₉	1	2	yes	complemented
204	#384	—	2	1	no	—
205	#382	—	2	1	no	—
206	#380	—	2	1	no	—
207	#380	—	2	1	no	—
208	C₄×C₄⋊C₄	C₄×C₂₉	1	2	yes	—
209	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
210	C₂×C₂₉	—	2	1	no	—
211	C₂×C₂₉	—	2	2	no	—
212	C₂×C₂₉	—	2	2	no	—
213	C₂×C₂₉	—	2	1	no	—
214	C₂×C₂₉	C₂×H(3,ℤ/4)	1	1	yes	characteristic
215	C₂×C₂₉	#1733	1	1	yes	characteristic
216	C₂×C₂₉	C₂×#343	1	1	yes	characteristic
217	C₂³×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
218	C₂³×C₄	D₄×C₂₉	1	1	yes	characteristic
219	C₂³×C₄	D₄×C₂₉	1	1	yes	characteristic
220	C₂²×C₈	—	2	2	no	—
221	C₂²×C₈	—	2	2	no	—
222	#117	—	4	4	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	—	2	2	no	—
226	C₂×C₂²⋊C₄	—	2	2	no	—
227	C₂×C₄²	C₂×C₄×C₂₉	1	4	yes	—
228	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
229	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
230	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
231	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
232	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
233	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
234	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
235	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
236	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
237	C₂×C₄²	Q₈×C₂₉	1	1	yes	characteristic
238	C₂×C₄²	Q₈×C₂₉	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
240	C₄⋊C₈	—	2	2	no	—
241	C₄⋊C₈	—	2	2	no	—
242	C₄⋊C₈	—	2	2	no	—
243	C₄⋊C₈	C₂×C₄×C₂₉	1	4	yes	—
244	C₂²⋊C₈	—	2	2	no	—
245	C₂²⋊C₈	—	2	2	no	—
246	C₂²⋊C₈	—	2	2	no	—
247	C₂²⋊C₈	—	2	2	no	—
248	#97	—	2	2	no	—
249	#97	—	2	2	no	—
250	#97	—	2	2	no	—
251	#97	C₂×C₄×C₂₉	1	4	yes	—
252	#95	—	2	2	no	—
253	#95	—	2	2	no	—
254	C₂₉	#7952	1	1	yes	characteristic, direct product factor, Sylow
255	C₂⁴	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	C₄²×C₂₉	1	1	yes	characteristic
262	C₂²×C₄	C₄²×C₂₉	1	1	yes	characteristic
263	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
264	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
265	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
266	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
267	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
268	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
269	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
270	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
271	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
272	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
273	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
274	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
275	C₂²×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
276	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	4	4	no	—
282	C₂×C₈	—	4	4	no	—
283	C₄⋊C₄	—	4	4	no	—
284	C₄⋊C₄	—	4	4	no	—
285	C₄⋊C₄	—	4	4	no	—
286	C₂²⋊C₄	—	4	4	no	—
287	C₄²	—	4	4	no	—
288	C₄²	C₄²×C₂₉	1	1	yes	characteristic
289	C₄²	C₄²×C₂₉	1	1	yes	characteristic
290	C₄²	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
291	C₄²	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
292	C₄²	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
293	C₄²	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
294	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
295	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
296	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
297	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
298	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
299	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
300	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
301	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
302	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
303	C₄²	C₂×Q₈×C₂₉	1	1	yes	characteristic
304	C₂³	—	4	1	no	—
305	C₂³	—	4	1	no	—
306	C₂³	C₂₉×#95	1	1	yes	characteristic
307	C₂³	C₂₉×#95	1	1	yes	characteristic
308	C₂³	C₂₉×#100	1	2	yes	—
309	C₂³	C₂₉×#101	1	2	yes	—
310	C₂³	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
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	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	C₂₉×#95	1	1	yes	characteristic
335	C₂×C₄	C₂₉×#95	1	1	yes	characteristic
336	C₂×C₄	C₂₉×#95	1	1	yes	characteristic
337	C₂×C₄	C₂₉×#95	1	1	yes	characteristic
338	C₂×C₄	C₂₉×#95	1	1	yes	characteristic
339	C₂×C₄	C₂₉×#95	1	1	yes	characteristic
340	C₂×C₄	C₂×C₄²×C₂₉	1	1	yes	characteristic
341	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
342	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
343	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
344	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
345	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
346	C₈	—	4	4	no	—
347	C₈	—	4	4	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	2	no	—
356	C₂²	C₂₉×#343	1	2	yes	—
357	C₂²	C₂₉×#343	1	2	yes	—
358	C₂²	C₂×C₂₉×#95	1	1	yes	characteristic
359	C₂²	C₂×C₂₉×#100	1	1	yes	characteristic
360	C₂²	C₂×C₂₉×#101	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	8	4	no	—
372	C₄	C₂₉×H(3,ℤ/4)	1	2	yes	—
373	C₄	C₂₉×#421	1	2	yes	—
374	C₂	—	2	1	no	—
375	C₂	—	2	2	no	—
376	C₂	—	2	2	no	—
377	C₂	—	2	1	no	—
378	C₂	C₂×C₂₉×H(3,ℤ/4)	1	1	yes	characteristic
379	C₂	C₂₉×#1733	1	1	yes	characteristic
380	C₂	C₂×C₂₉×#343	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#95
commutator	C₂×C₄	C₂×C₄²×C₂₉
Frattini, cosocle	C₂×C₄²	C₂³×C₂₉
prime radical	C₂⁴×C₂₉	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂₉×#1285	C₂	semidirect
11. C₂₉×#432	C₄	semidirect
12. C₂₉×#432	C₄	semidirect
16. C₂×C₂₉×C₄⋊C₈	C₄	semidirect
20. C₂×C₂₉×#97	C₄	semidirect
113. #7952	C₂₉	direct (N × H)
161. #1285	C₂×C₂₉	semidirect
194. #432	C₄×C₂₉	semidirect
195. #432	C₄×C₂₉	semidirect
199. C₂×C₄⋊C₈	C₄×C₂₉	semidirect
203. C₂×#97	C₄×C₂₉	semidirect
254. C₂₉	#7952	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×#432	2
C₂₉×#2285	2
C₂₉×#1285	2
#7952	29

Subgroups — C29×#7952 #20302852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#7952 #20302852