Subgroups — C₂₉×#22313 #20317213

Order 7424.

666 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#1985	C₂	1	2	yes	maximal
3	C₂₉×#1984	C₂	1	2	yes	maximal
4	C₂₉×#1940	C₂	1	2	yes	maximal
5	C₂₉×#1917	C₂	1	2	yes	maximal
6	C₂₉×#1916	C₂	1	2	yes	maximal
7	C₂₉×#1831	C₂	1	1	yes	maximal, characteristic
8	C₂₉×#1771	C₂	1	2	yes	maximal
9	C₂₉×#1745	C₂	1	1	yes	maximal, characteristic
10	C₂×C₂₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	—
12	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
13	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
16	C₂×C₂₉×#97	C₂²	1	2	yes	—
17	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₂₉	C₂²	1	2	yes	—
19	C₂₉×#391	C₄	1	2	yes	—
20	C₂₉×#389	C₄	1	2	yes	—
21	C₂₉×#389	C₄	1	1	yes	characteristic
22	C₂₉×#389	C₄	1	1	yes	characteristic
23	C₂₉×#384	C₄	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
27	C₄³×C₂₉	C₂²	1	1	yes	characteristic
28	C₂₉×#336	C₂²	1	2	yes	—
29	C₂₉×#336	C₂²	1	2	yes	—
30	C₂₉×#336	C₂²	1	2	yes	—
31	C₂₉×#336	C₂²	1	2	yes	—
32	C₂₉×#336	C₂²	1	2	yes	—
33	C₂₉×#336	C₂²	1	2	yes	—
34	C₂₉×#336	C₂²	1	1	yes	characteristic
35	C₂₉×#336	C₂²	1	2	yes	—
36	C₂₉×#336	C₂²	1	1	yes	characteristic
37	C₂²×Q₈×C₂₉	C₂×C₄	1	2	yes	—
38	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
39	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
40	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
41	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
42	C₂₉×C₄⋊Q₈	—	2	4	no	—
43	C₄×Q₈×C₂₉	—	4	2	no	—
44	C₄×Q₈×C₂₉	—	4	2	no	—
45	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
60	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
61	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
63	C₂₉×C₄⋊C₈	—	2	4	no	—
64	C₂₉×C₄⋊C₈	—	4	2	no	—
65	C₂₉×C₄⋊C₈	—	4	2	no	—
66	C₂₉×#97	—	2	2	no	—
67	C₂₉×#97	—	4	2	no	—
68	C₂₉×#97	Q₈	1	4	yes	complemented
69	C₄×C₈×C₂₉	—	4	2	no	—
70	C₂₉×#95	C₂×C₄	1	2	yes	—
71	C₂₉×#95	C₂×C₄	1	2	yes	—
72	C₂₉×#95	C₂×C₄	1	2	yes	—
73	C₂₉×#95	C₂×C₄	1	2	yes	—
74	C₂×Q₈×C₂₉	—	2	4	no	—
75	C₂×Q₈×C₂₉	—	2	4	no	—
76	C₂×Q₈×C₂₉	—	4	2	no	—
77	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
88	C₂×C₈×C₂₉	—	2	2	no	—
89	C₂×C₈×C₂₉	—	2	2	no	—
90	C₂×C₈×C₂₉	—	2	2	no	—
91	C₂×C₈×C₂₉	—	2	2	no	—
92	C₂×C₈×C₂₉	—	2	2	no	—
93	C₂×C₈×C₂₉	—	2	2	no	—
94	C₂×C₈×C₂₉	—	2	2	no	—
95	C₂×C₈×C₂₉	—	2	2	no	—
96	C₂×C₈×C₂₉	—	2	2	no	—
97	C₂×C₈×C₂₉	—	2	2	no	—
98	C₂×C₈×C₂₉	—	2	2	no	—
99	C₂×C₈×C₂₉	C₂×Q₈	1	4	yes	—
100	C₄⋊C₄×C₂₉	—	2	4	no	—
101	C₄⋊C₄×C₂₉	—	2	2	no	—
102	C₄⋊C₄×C₂₉	—	4	2	no	—
103	C₄⋊C₄×C₂₉	—	4	1	no	—
104	C₄⋊C₄×C₂₉	—	4	1	no	—
105	C₄⋊C₄×C₂₉	—	4	2	no	—
106	C₄⋊C₄×C₂₉	—	4	2	no	—
107	C₄⋊C₄×C₂₉	—	4	2	no	—
108	C₄⋊C₄×C₂₉	M₁₆	1	4	yes	—
109	C₄²×C₂₉	—	2	2	no	—
110	C₄²×C₂₉	—	2	2	no	—
111	C₄²×C₂₉	—	2	2	no	—
112	C₄²×C₂₉	—	2	2	no	—
113	C₄²×C₂₉	—	2	2	no	—
114	C₄²×C₂₉	—	2	2	no	—
115	C₄²×C₂₉	—	2	2	no	—
116	C₄²×C₂₉	—	2	2	no	—
117	C₄²×C₂₉	—	4	1	no	—
118	C₄²×C₂₉	—	4	1	no	—
119	C₄²×C₂₉	C₂×Q₈	1	2	yes	—
120	C₄²×C₂₉	#41	1	2	yes	—
121	#22313	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂³×C₂₉	C₂³×C₄	1	1	yes	characteristic
123	Q₈×C₂₉	—	4	8	no	—
124	C₂×C₄×C₂₉	—	2	1	no	—
125	C₂×C₄×C₂₉	—	2	2	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	1	no	—
130	C₂×C₄×C₂₉	—	2	2	no	—
131	C₂×C₄×C₂₉	—	2	1	no	—
132	C₂×C₄×C₂₉	—	2	1	no	—
133	C₂×C₄×C₂₉	—	2	1	no	—
134	C₂×C₄×C₂₉	—	2	1	no	—
135	C₂×C₄×C₂₉	—	2	2	no	—
136	C₂×C₄×C₂₉	—	2	2	no	—
137	C₂×C₄×C₂₉	—	2	2	no	—
138	C₂×C₄×C₂₉	—	2	1	no	—
139	C₂×C₄×C₂₉	—	2	2	no	—
140	C₂×C₄×C₂₉	—	2	1	no	—
141	C₂×C₄×C₂₉	—	2	2	no	—
142	C₂×C₄×C₂₉	—	2	1	no	—
143	C₂×C₄×C₂₉	—	2	1	no	—
144	C₂×C₄×C₂₉	—	2	1	no	—
145	C₂×C₄×C₂₉	—	2	2	no	—
146	C₂×C₄×C₂₉	—	2	2	no	—
147	C₂×C₄×C₂₉	—	2	2	no	—
148	C₂×C₄×C₂₉	—	2	2	no	—
149	C₂×C₄×C₂₉	C₄×Q₈	1	2	yes	—
150	C₂×C₄×C₂₉	C₄×Q₈	1	2	yes	—
151	C₂×C₄×C₂₉	C₂×M₁₆	1	2	yes	—
152	C₂×C₄×C₂₉	C₂×M₁₆	1	4	yes	—
153	C₂×C₄×C₂₉	#131	1	2	yes	—
154	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
157	C₂×C₄×C₂₉	2₋¹⁺⁴	1	2	yes	—
158	C₈×C₂₉	—	2	4	no	—
159	C₈×C₂₉	—	4	2	no	—
160	C₈×C₂₉	—	4	2	no	—
161	C₈×C₂₉	—	4	2	no	—
162	C₄×C₄⋊Q₈	C₂×C₂₉	1	1	yes	characteristic
163	#1985	C₂×C₂₉	1	2	yes	—
164	#1984	C₂×C₂₉	1	2	yes	—
165	#1940	C₂×C₂₉	1	2	yes	—
166	#1917	C₂×C₂₉	1	2	yes	—
167	#1916	C₂×C₂₉	1	2	yes	—
168	#1831	C₂×C₂₉	1	1	yes	characteristic
169	#1771	C₂×C₂₉	1	2	yes	—
170	#1745	C₂×C₂₉	1	1	yes	characteristic
171	C₂²×C₂₉	C₂×C₄×Q₈	1	1	yes	characteristic
172	C₂²×C₂₉	#518	1	1	yes	characteristic
173	C₂²×C₂₉	#519	1	1	yes	characteristic
174	C₂²×C₂₉	C₂²×M₁₆	1	1	yes	characteristic
175	C₂²×C₂₉	C₂×#131	1	1	yes	characteristic
176	C₂²×C₂₉	#568	1	1	yes	characteristic
177	C₂²×C₂₉	#568	1	1	yes	characteristic
178	C₄×C₂₉	—	2	2	no	—
179	C₄×C₂₉	—	2	2	no	—
180	C₄×C₂₉	—	2	4	no	—
181	C₄×C₂₉	—	2	2	no	—
182	C₄×C₂₉	—	2	2	no	—
183	C₄×C₂₉	—	4	2	no	—
184	C₄×C₂₉	—	4	1	no	—
185	C₄×C₂₉	—	4	2	no	—
186	C₄×C₂₉	—	4	2	no	—
187	C₄×C₂₉	—	4	1	no	—
188	C₄×C₂₉	#542	1	2	yes	—
189	C₄×C₂₉	#544	1	2	yes	—
190	C₂×C₄⋊Q₈	C₄×C₂₉	1	1	yes	characteristic
191	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	—
192	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
193	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
194	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
195	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
196	C₂×#97	C₂²×C₂₉	1	2	yes	—
197	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
198	C₂×C₄×C₈	C₂²×C₂₉	1	2	yes	—
199	#391	C₄×C₂₉	1	2	yes	—
200	#389	C₄×C₂₉	1	2	yes	—
201	#389	C₄×C₂₉	1	1	yes	characteristic
202	#389	C₄×C₂₉	1	1	yes	characteristic
203	#384	C₄×C₂₉	1	1	yes	characteristic
204	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
205	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
206	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
207	C₄³	C₂²×C₂₉	1	1	yes	characteristic
208	#336	C₂²×C₂₉	1	2	yes	—
209	#336	C₂²×C₂₉	1	1	yes	characteristic
210	#336	C₂²×C₂₉	1	1	yes	characteristic
211	#336	C₂²×C₂₉	1	2	yes	—
212	#336	C₂²×C₂₉	1	2	yes	—
213	#336	C₂²×C₂₉	1	2	yes	—
214	#336	C₂²×C₂₉	1	2	yes	—
215	#336	C₂²×C₂₉	1	2	yes	—
216	#336	C₂²×C₂₉	1	2	yes	—
217	C₂×C₂₉	#2331	1	1	yes	characteristic
218	C₂×C₂₉	#2962	1	1	yes	characteristic
219	C₂×C₂₉	Q₈×M₁₆	1	1	yes	characteristic
220	C₂×C₂₉	#2974	1	1	yes	characteristic
221	C₂×C₂₉	#2980	1	1	yes	characteristic
222	C₂×C₂₉	#2983	1	1	yes	characteristic
223	C₂×C₂₉	#2985	1	1	yes	characteristic
224	C₂²×Q₈	C₂×C₄×C₂₉	1	2	yes	—
225	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
226	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
227	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
228	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
229	C₄⋊Q₈	—	2	4	no	—
230	C₄×Q₈	—	4	2	no	—
231	C₄×Q₈	—	4	2	no	—
232	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
234	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
235	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
236	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
237	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
238	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
241	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
242	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
243	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
244	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
245	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
246	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
247	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
248	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
250	C₄⋊C₈	—	2	4	no	—
251	C₄⋊C₈	—	4	2	no	—
252	C₄⋊C₈	—	4	2	no	—
253	#97	—	2	2	no	—
254	#97	—	4	2	no	—
255	#97	Q₈×C₂₉	1	4	yes	complemented
256	C₄×C₈	—	4	2	no	—
257	#95	C₂×C₄×C₂₉	1	2	yes	—
258	#95	C₂×C₄×C₂₉	1	2	yes	—
259	#95	C₂×C₄×C₂₉	1	2	yes	—
260	#95	C₂×C₄×C₂₉	1	2	yes	—
261	C₂₉	#22313	1	1	yes	characteristic, direct product factor, Sylow
262	C₂×Q₈	—	2	4	no	—
263	C₂×Q₈	—	2	4	no	—
264	C₂×Q₈	—	4	2	no	—
265	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
266	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
267	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
268	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
269	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
270	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
271	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
272	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
273	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
275	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	C₂×Q₈×C₂₉	1	4	yes	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	4	2	no	—
291	C₄⋊C₄	—	4	2	no	—
292	C₄⋊C₄	—	4	2	no	—
293	C₄⋊C₄	—	4	2	no	—
294	C₄⋊C₄	—	4	1	no	—
295	C₄⋊C₄	—	4	1	no	—
296	C₄⋊C₄	M₁₆×C₂₉	1	4	yes	—
297	C₄²	—	2	2	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	4	1	no	—
306	C₄²	—	4	1	no	—
307	C₄²	C₂×Q₈×C₂₉	1	2	yes	—
308	C₄²	#41×C₂₉	1	2	yes	—
309	C₂³	C₂³×C₄×C₂₉	1	1	yes	characteristic
310	Q₈	—	4	8	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	C₄×Q₈×C₂₉	1	2	yes	—
337	C₂×C₄	C₄×Q₈×C₂₉	1	2	yes	—
338	C₂×C₄	C₂×M₁₆×C₂₉	1	2	yes	—
339	C₂×C₄	C₂×M₁₆×C₂₉	1	4	yes	—
340	C₂×C₄	C₂₉×#131	1	2	yes	—
341	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
342	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
343	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
344	C₂×C₄	C₂₉×2₋¹⁺⁴	1	2	yes	—
345	C₈	—	2	4	no	—
346	C₈	—	4	2	no	—
347	C₈	—	4	2	no	—
348	C₈	—	4	2	no	—
349	C₂²	C₂×C₄×Q₈×C₂₉	1	1	yes	characteristic
350	C₂²	C₂₉×#518	1	1	yes	characteristic
351	C₂²	C₂₉×#519	1	1	yes	characteristic
352	C₂²	C₂²×M₁₆×C₂₉	1	1	yes	characteristic
353	C₂²	C₂×C₂₉×#131	1	1	yes	characteristic
354	C₂²	C₂₉×#568	1	1	yes	characteristic
355	C₂²	C₂₉×#568	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	2	4	no	—
359	C₄	—	2	2	no	—
360	C₄	—	2	2	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	1	no	—
363	C₄	—	4	2	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	1	no	—
366	C₄	C₂₉×#542	1	2	yes	—
367	C₄	C₂₉×#544	1	2	yes	—
368	C₂	C₂₉×#2331	1	1	yes	characteristic
369	C₂	C₂₉×#2962	1	1	yes	characteristic
370	C₂	Q₈×M₁₆×C₂₉	1	1	yes	characteristic
371	C₂	C₂₉×#2974	1	1	yes	characteristic
372	C₂	C₂₉×#2980	1	1	yes	characteristic
373	C₂	C₂₉×#2983	1	1	yes	characteristic
374	C₂	C₂₉×#2985	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
68. C₂₉×#97	Q₈	semidirect
121. #22313	C₂₉	direct (N × H)
255. #97	Q₈×C₂₉	semidirect
261. C₂₉	#22313	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₂₉×C₄⋊Q₈	2
C₂₉×#1985	2
C₂₉×#1984	2
C₂₉×#1940	2
C₂₉×#1917	2
C₂₉×#1916	2
C₂₉×#1831	2
C₂₉×#1771	2
C₂₉×#1745	2
#22313	29

Subgroups — C29×#22313 #20317213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#22313 #20317213