Subgroups — C₂₉×#22008 #20316908

Order 7424.

894 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×D₄×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#1954	C₂	1	2	yes	maximal
3	C₂₉×#1939	C₂	1	2	yes	maximal, complemented
4	C₂₉×#1923	C₂	1	4	yes	maximal, complemented
5	C₂₉×#1817	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1797	C₂	1	2	yes	maximal, complemented
7	C₄×C₂₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1744	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×D₄×C₂₉	C₄	1	1	yes	characteristic
10	C₂×C₄×D₄×C₂₉	C₄	1	1	yes	characteristic
11	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₂₉	C₂²	1	2	yes	—
13	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₂₉×C₄⋊C₈	C₂²	1	4	yes	—
15	C₂×C₂₉×C₂²⋊C₈	C₂²	1	4	yes	—
16	C₂×C₂₉×C₂²⋊C₈	C₂²	1	4	yes	—
17	C₂×C₄×C₈×C₂₉	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₂₉	C₂²	1	2	yes	—
19	C₄×C₄⋊C₄×C₂₉	C₄	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₂₉	C₄	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
22	C₄×C₂²⋊C₄×C₂₉	C₄	1	2	yes	—
23	C₄×C₂²⋊C₄×C₂₉	C₄	1	2	yes	—
24	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
25	C₄³×C₂₉	C₂²	1	1	yes	characteristic
26	C₂₉×#336	C₂²	1	2	yes	—
27	C₂₉×#336	C₂²	1	4	yes	—
28	C₂₉×#336	C₂²	1	1	yes	characteristic
29	C₂₉×#336	C₂²	1	1	yes	characteristic
30	C₂₉×#336	C₂²	1	2	yes	—
31	C₂²×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₂₉	C₂×C₄	1	2	yes	—
33	C₂³×C₄×C₂₉	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
35	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
36	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
37	C₂²×C₈×C₂₉	C₂³	1	4	yes	—
38	C₄×D₄×C₂₉	—	2	4	no	—
39	C₄×D₄×C₂₉	—	2	4	no	—
40	C₄×D₄×C₂₉	C₈	1	8	yes	complemented
41	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
45	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
46	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₂₉	—	4	4	no	—
48	C₂×C₄²×C₂₉	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₂₉	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
56	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
58	C₂₉×C₄⋊C₈	—	2	4	no	—
59	C₂₉×C₄⋊C₈	—	4	4	no	—
60	C₂₉×C₂²⋊C₈	—	4	4	no	—
61	C₂₉×C₂²⋊C₈	—	4	4	no	—
62	C₄×C₈×C₂₉	—	2	4	no	—
63	C₄×C₈×C₂₉	—	4	2	no	—
64	C₂₉×#95	C₂×C₄	1	2	yes	—
65	C₂₉×#95	C₂×C₄	1	2	yes	—
66	C₂₉×#95	C₂×C₄	1	2	yes	—
67	C₂⁴×C₂₉	C₂²×C₄	1	2	yes	—
68	C₂×D₄×C₂₉	—	2	2	no	—
69	C₂×D₄×C₂₉	—	2	2	no	—
70	C₂×D₄×C₂₉	C₂×C₈	1	4	yes	—
71	C₂²×C₄×C₂₉	—	2	4	no	—
72	C₂²×C₄×C₂₉	—	2	4	no	—
73	C₂²×C₄×C₂₉	—	2	4	no	—
74	C₂²×C₄×C₂₉	—	2	2	no	—
75	C₂²×C₄×C₂₉	—	2	2	no	—
76	C₂²×C₄×C₂₉	—	4	2	no	—
77	C₂²×C₄×C₂₉	—	4	2	no	—
78	C₂²×C₄×C₂₉	—	4	2	no	—
79	C₂²×C₄×C₂₉	—	4	2	no	—
80	C₂²×C₄×C₂₉	C₂×C₈	1	8	yes	—
81	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
86	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
91	C₂×C₈×C₂₉	—	2	2	no	—
92	C₂×C₈×C₂₉	—	2	2	no	—
93	C₂×C₈×C₂₉	—	2	4	no	—
94	C₂×C₈×C₂₉	—	2	4	no	—
95	C₂×C₈×C₂₉	—	2	2	no	—
96	C₂×C₈×C₂₉	—	2	2	no	—
97	C₂×C₈×C₂₉	—	2	4	no	—
98	C₂×C₈×C₂₉	—	2	2	no	—
99	C₂×C₈×C₂₉	—	2	2	no	—
100	C₄⋊C₄×C₂₉	—	2	2	no	—
101	C₄⋊C₄×C₂₉	—	2	2	no	—
102	C₄⋊C₄×C₂₉	C₂×C₈	1	4	yes	—
103	C₂²⋊C₄×C₂₉	—	2	4	no	—
104	C₂²⋊C₄×C₂₉	—	2	4	no	—
105	C₂²⋊C₄×C₂₉	C₂×C₈	1	8	yes	—
106	C₄²×C₂₉	—	2	2	no	—
107	C₄²×C₂₉	—	2	4	no	—
108	C₄²×C₂₉	—	2	1	no	—
109	C₄²×C₂₉	—	2	1	no	—
110	C₄²×C₂₉	—	4	2	no	—
111	C₄²×C₂₉	—	4	2	no	—
112	C₄²×C₂₉	—	4	1	no	—
113	C₄²×C₂₉	—	4	1	no	—
114	C₄²×C₂₉	C₂×C₈	1	4	yes	—
115	C₄²×C₂₉	M₁₆	1	4	yes	—
116	C₄²×C₂₉	#41	1	4	yes	—
117	#22008	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂³×C₂₉	—	2	2	no	—
119	C₂³×C₂₉	—	2	2	no	—
120	C₂³×C₂₉	—	2	2	no	—
121	C₂³×C₂₉	—	2	2	no	—
122	C₂³×C₂₉	—	2	2	no	—
123	C₂³×C₂₉	—	2	2	no	—
124	C₂³×C₂₉	C₂²×C₈	1	4	yes	—
125	C₂³×C₂₉	C₂³×C₄	1	1	yes	characteristic
126	D₄×C₂₉	—	2	8	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	1	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	1	no	—
136	C₂×C₄×C₂₉	—	2	1	no	—
137	C₂×C₄×C₂₉	—	2	1	no	—
138	C₂×C₄×C₂₉	—	2	2	no	—
139	C₂×C₄×C₂₉	—	2	2	no	—
140	C₂×C₄×C₂₉	—	2	2	no	—
141	C₂×C₄×C₂₉	—	2	2	no	—
142	C₂×C₄×C₂₉	—	2	2	no	—
143	C₂×C₄×C₂₉	—	2	2	no	—
144	C₂×C₄×C₂₉	—	2	2	no	—
145	C₂×C₄×C₂₉	—	4	8	no	—
146	C₂×C₄×C₂₉	—	4	8	no	—
147	C₂×C₄×C₂₉	—	4	4	no	—
148	C₂×C₄×C₂₉	—	4	4	no	—
149	C₂×C₄×C₂₉	#117	1	2	yes	—
150	C₂×C₄×C₂₉	#117	1	2	yes	—
151	C₂×C₄×C₂₉	C₂²×C₈	1	2	yes	—
152	C₂×C₄×C₂₉	C₂²×C₈	1	2	yes	—
153	C₂×C₄×C₂₉	C₂²×C₈	1	4	yes	—
154	C₂×C₄×C₂₉	C₂²×C₈	1	2	yes	—
155	C₂×C₄×C₂₉	C₂×M₁₆	1	2	yes	—
156	C₂×C₄×C₂₉	C₂×M₁₆	1	2	yes	—
157	C₂×C₄×C₂₉	C₂×M₁₆	1	2	yes	—
158	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
159	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
160	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
161	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
162	C₈×C₂₉	—	4	2	no	—
163	C₈×C₂₉	—	4	4	no	—
164	C₈×C₂₉	—	4	2	no	—
165	C₄²×D₄	C₂×C₂₉	1	1	yes	characteristic
166	#1954	C₂×C₂₉	1	2	yes	—
167	#1939	C₂×C₂₉	1	2	yes	complemented
168	#1923	C₂×C₂₉	1	4	yes	complemented
169	#1817	C₂×C₂₉	1	2	yes	complemented
170	#1797	C₂×C₂₉	1	2	yes	complemented
171	C₄×C₄⋊C₈	C₂×C₂₉	1	1	yes	characteristic, complemented
172	#1744	C₂×C₂₉	1	1	yes	characteristic, complemented
173	C₂²×C₂₉	—	2	4	no	—
174	C₂²×C₂₉	—	2	4	no	—
175	C₂²×C₂₉	—	2	4	no	—
176	C₂²×C₂₉	—	4	2	no	—
177	C₂²×C₂₉	—	4	2	no	—
178	C₂²×C₂₉	—	4	2	no	—
179	C₂²×C₂₉	—	4	2	no	—
180	C₂²×C₂₉	C₂×#117	1	1	yes	characteristic
181	C₂²×C₂₉	#518	1	1	yes	characteristic
182	C₂²×C₂₉	#520	1	1	yes	characteristic
183	C₂²×C₂₉	C₂³×C₈	1	1	yes	characteristic
184	C₂²×C₂₉	C₂²×M₁₆	1	1	yes	characteristic
185	C₂²×C₂₉	#568	1	1	yes	characteristic
186	C₂²×C₂₉	#568	1	1	yes	characteristic
187	C₄×C₂₉	—	2	2	no	—
188	C₄×C₂₉	—	2	2	no	—
189	C₄×C₂₉	—	2	4	no	—
190	C₄×C₂₉	—	2	2	no	—
191	C₄×C₂₉	—	2	2	no	—
192	C₄×C₂₉	—	2	2	no	—
193	C₄×C₂₉	—	4	2	no	—
194	C₄×C₂₉	—	4	2	no	—
195	C₄×C₂₉	#431	1	4	yes	—
196	C₄×C₂₉	#540	1	2	yes	—
197	C₄×C₂₉	#542	1	2	yes	—
198	C₂×C₄×D₄	C₄×C₂₉	1	1	yes	characteristic
199	C₂×C₄×D₄	C₄×C₂₉	1	1	yes	characteristic
200	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
201	C₂²×C₄²	C₂²×C₂₉	1	2	yes	—
202	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
203	C₂×C₄⋊C₈	C₂²×C₂₉	1	4	yes	—
204	C₂×C₂²⋊C₈	C₂²×C₂₉	1	4	yes	—
205	C₂×C₂²⋊C₈	C₂²×C₂₉	1	4	yes	—
206	C₂×C₄×C₈	C₂²×C₂₉	1	2	yes	—
207	C₂×C₄×C₈	C₂²×C₂₉	1	2	yes	—
208	C₄×C₄⋊C₄	C₄×C₂₉	1	1	yes	characteristic
209	C₄×C₄⋊C₄	C₄×C₂₉	1	1	yes	characteristic
210	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
211	C₄×C₂²⋊C₄	C₄×C₂₉	1	2	yes	—
212	C₄×C₂²⋊C₄	C₄×C₂₉	1	2	yes	—
213	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
214	C₄³	C₂²×C₂₉	1	1	yes	characteristic
215	#336	C₂²×C₂₉	1	1	yes	characteristic
216	#336	C₂²×C₂₉	1	2	yes	—
217	#336	C₂²×C₂₉	1	1	yes	characteristic
218	#336	C₂²×C₂₉	1	4	yes	—
219	#336	C₂²×C₂₉	1	2	yes	—
220	C₂×C₂₉	—	4	4	no	—
221	C₂×C₂₉	#2319	1	1	yes	characteristic
222	C₂×C₂₉	C₂×#431	1	1	yes	characteristic
223	C₂×C₂₉	#2923	1	1	yes	characteristic
224	C₂×C₂₉	#2972	1	1	yes	characteristic
225	C₂×C₂₉	#2975	1	1	yes	characteristic
226	C₂×C₂₉	#2988	1	1	yes	characteristic
227	C₂×C₂₉	#2989	1	1	yes	characteristic
228	C₂²×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
229	C₂³×C₄	C₂×C₄×C₂₉	1	2	yes	—
230	C₂³×C₄	C₂×C₄×C₂₉	1	2	yes	—
231	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
232	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
233	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
234	C₂²×C₈	C₂³×C₂₉	1	4	yes	—
235	C₄×D₄	—	2	4	no	—
236	C₄×D₄	—	2	4	no	—
237	C₄×D₄	C₈×C₂₉	1	8	yes	complemented
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×C₂²⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
242	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
243	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
244	C₂×C₄²	—	4	4	no	—
245	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
246	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
247	C₂×C₄²	C₂×C₄×C₂₉	1	2	yes	—
248	C₂×C₄²	C₂×C₄×C₂₉	1	2	yes	—
249	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
250	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
253	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
254	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
255	C₄⋊C₈	—	2	4	no	—
256	C₄⋊C₈	—	4	4	no	—
257	C₂²⋊C₈	—	4	4	no	—
258	C₂²⋊C₈	—	4	4	no	—
259	C₄×C₈	—	2	4	no	—
260	C₄×C₈	—	4	2	no	—
261	#95	C₂×C₄×C₂₉	1	2	yes	—
262	#95	C₂×C₄×C₂₉	1	2	yes	—
263	#95	C₂×C₄×C₂₉	1	2	yes	—
264	C₂₉	#22008	1	1	yes	characteristic, direct product factor, Sylow
265	C₂⁴	C₂²×C₄×C₂₉	1	2	yes	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	C₂×C₈×C₂₉	1	4	yes	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	C₂×C₈×C₂₉	1	8	yes	—
279	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
280	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
281	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
282	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
283	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
284	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
285	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
286	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
287	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
288	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	4	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	C₂×C₈×C₂₉	1	4	yes	—
301	C₂²⋊C₄	—	2	4	no	—
302	C₂²⋊C₄	—	2	4	no	—
303	C₂²⋊C₄	C₂×C₈×C₂₉	1	8	yes	—
304	C₄²	—	2	1	no	—
305	C₄²	—	2	4	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	1	no	—
308	C₄²	—	4	2	no	—
309	C₄²	—	4	2	no	—
310	C₄²	—	4	1	no	—
311	C₄²	—	4	1	no	—
312	C₄²	C₂×C₈×C₂₉	1	4	yes	—
313	C₄²	M₁₆×C₂₉	1	4	yes	—
314	C₄²	#41×C₂₉	1	4	yes	—
315	C₂³	—	2	2	no	—
316	C₂³	—	2	2	no	—
317	C₂³	—	2	2	no	—
318	C₂³	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	C₂²×C₈×C₂₉	1	4	yes	—
322	C₂³	C₂³×C₄×C₂₉	1	1	yes	characteristic
323	D₄	—	2	8	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	8	no	—
343	C₂×C₄	—	4	8	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	C₂₉×#117	1	2	yes	—
347	C₂×C₄	C₂₉×#117	1	2	yes	—
348	C₂×C₄	C₂²×C₈×C₂₉	1	2	yes	—
349	C₂×C₄	C₂²×C₈×C₂₉	1	2	yes	—
350	C₂×C₄	C₂²×C₈×C₂₉	1	4	yes	—
351	C₂×C₄	C₂²×C₈×C₂₉	1	2	yes	—
352	C₂×C₄	C₂×M₁₆×C₂₉	1	2	yes	—
353	C₂×C₄	C₂×M₁₆×C₂₉	1	2	yes	—
354	C₂×C₄	C₂×M₁₆×C₂₉	1	2	yes	—
355	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
356	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
357	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
358	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
359	C₈	—	4	2	no	—
360	C₈	—	4	4	no	—
361	C₈	—	4	2	no	—
362	C₂²	—	2	4	no	—
363	C₂²	—	2	4	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	C₂×C₂₉×#117	1	1	yes	characteristic
370	C₂²	C₂₉×#518	1	1	yes	characteristic
371	C₂²	C₂₉×#520	1	1	yes	characteristic
372	C₂²	C₂³×C₈×C₂₉	1	1	yes	characteristic
373	C₂²	C₂²×M₁₆×C₂₉	1	1	yes	characteristic
374	C₂²	C₂₉×#568	1	1	yes	characteristic
375	C₂²	C₂₉×#568	1	1	yes	characteristic
376	C₄	—	2	2	no	—
377	C₄	—	2	4	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	C₂₉×#431	1	4	yes	—
385	C₄	C₂₉×#540	1	2	yes	—
386	C₄	C₂₉×#542	1	2	yes	—
387	C₂	—	4	4	no	—
388	C₂	C₂₉×#2319	1	1	yes	characteristic
389	C₂	C₂×C₂₉×#431	1	1	yes	characteristic
390	C₂	C₂₉×#2923	1	1	yes	characteristic
391	C₂	C₂₉×#2972	1	1	yes	characteristic
392	C₂	C₂₉×#2975	1	1	yes	characteristic
393	C₂	C₂₉×#2988	1	1	yes	characteristic
394	C₂	C₂₉×#2989	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₉	C₂⁴
commutator	C₂²	C₂³×C₈×C₂₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
socle	C₂³×C₂₉	C₂³×C₄
prime radical	C₂²×D₄×C₂₉	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₉×#1939	C₂	semidirect
4. C₂₉×#1923	C₂	semidirect
5. C₂₉×#1817	C₂	semidirect
6. C₂₉×#1797	C₂	semidirect
7. C₄×C₂₉×C₄⋊C₈	C₂	semidirect
8. C₂₉×#1744	C₂	semidirect
40. C₄×D₄×C₂₉	C₈	semidirect
117. #22008	C₂₉	direct (N × H)
167. #1939	C₂×C₂₉	semidirect
168. #1923	C₂×C₂₉	semidirect
169. #1817	C₂×C₂₉	semidirect
170. #1797	C₂×C₂₉	semidirect
171. C₄×C₄⋊C₈	C₂×C₂₉	semidirect
172. #1744	C₂×C₂₉	semidirect
237. C₄×D₄	C₈×C₂₉	semidirect
264. C₂₉	#22008	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄²×D₄×C₂₉	2
C₂₉×#1954	2
C₂₉×#1939	2
C₂₉×#1923	2
C₂₉×#1817	2
C₂₉×#1797	2
C₄×C₂₉×C₄⋊C₈	2
C₂₉×#1744	2
#22008	29

Subgroups — C29×#22008 #20316908

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#22008 #20316908