Subgroups — C₂₉×#22627 #20317527

Order 7424.

868 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#1940	C₂	1	2	yes	maximal, complemented
3	C₂₉×#1917	C₂	1	2	yes	maximal, complemented
4	C₂₉×#1916	C₂	1	2	yes	maximal, complemented
5	C₂₉×#1797	C₂	1	1	yes	maximal, characteristic
6	C₂₉×#1797	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#1797	C₂	1	1	yes	maximal, characteristic
8	C₂₉×#1771	C₂	1	2	yes	maximal, complemented
9	C₂₉×#1749	C₂	1	1	yes	maximal, characteristic
10	C₂₉×#1749	C₂	1	1	yes	maximal, characteristic
11	C₄×C₂₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₄⋊C₄×C₂₉	C₄	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₂₉	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₉×#97	C₂²	1	2	yes	—
25	C₂×C₂₉×#97	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₂₉	C₂²	1	2	yes	—
27	C₄×C₄⋊C₄×C₂₉	C₄	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₂₉	C₄	1	1	yes	characteristic
29	C₄×C₄⋊C₄×C₂₉	C₄	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₂₉	C₄	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
35	C₂×C₂₉×#95	C₄	1	1	yes	characteristic
36	C₂×C₂₉×#95	C₄	1	1	yes	characteristic
37	C₂₉×#336	C₂²	1	2	yes	—
38	C₂₉×#336	C₂²	1	2	yes	—
39	C₂₉×#336	C₂²	1	2	yes	—
40	C₂₉×#336	C₂²	1	2	yes	—
41	C₂₉×#336	C₂²	1	2	yes	—
42	C₂₉×#336	C₂²	1	2	yes	—
43	C₂³×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
52	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
53	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
55	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
56	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₂₉	—	2	4	no	—
65	C₂×C₄²×C₂₉	—	4	2	no	—
66	C₂×C₄²×C₂₉	—	4	2	no	—
67	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
79	C₂₉×C₄⋊C₈	—	2	4	no	—
80	C₂₉×C₄⋊C₈	—	4	2	no	—
81	C₂₉×C₄⋊C₈	—	4	2	no	—
82	C₂₉×C₂²⋊C₈	—	2	2	no	—
83	C₂₉×C₂²⋊C₈	—	2	2	no	—
84	C₂₉×C₂²⋊C₈	—	2	2	no	—
85	C₂₉×C₂²⋊C₈	Q₈	1	4	yes	—
86	C₂₉×#97	—	2	4	no	—
87	C₂₉×#97	—	4	2	no	—
88	C₄×C₈×C₂₉	—	4	2	no	—
89	C₂₉×#95	C₂×C₄	1	1	yes	characteristic
90	C₂₉×#95	C₂×C₄	1	1	yes	characteristic
91	C₂₉×#95	C₂×C₄	1	1	yes	characteristic
92	C₂₉×#95	C₂×C₄	1	1	yes	characteristic
93	C₂₉×#95	C₂×C₄	1	1	yes	characteristic
94	C₂₉×#95	C₂×C₄	1	1	yes	characteristic
95	C₂₉×#95	C₂×C₄	1	1	yes	characteristic
96	C₂₉×#95	C₂×C₄	1	1	yes	characteristic
97	C₂⁴×C₂₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₂₉	—	2	2	no	—
99	C₂²×C₄×C₂₉	—	2	2	no	—
100	C₂²×C₄×C₂₉	—	2	2	no	—
101	C₂²×C₄×C₂₉	—	2	2	no	—
102	C₂²×C₄×C₂₉	—	2	2	no	—
103	C₂²×C₄×C₂₉	—	2	2	no	—
104	C₂²×C₄×C₂₉	—	2	2	no	—
105	C₂²×C₄×C₂₉	—	2	2	no	—
106	C₂²×C₄×C₂₉	—	2	2	no	—
107	C₂²×C₄×C₂₉	—	2	2	no	—
108	C₂²×C₄×C₂₉	—	2	2	no	—
109	C₂²×C₄×C₂₉	—	2	2	no	—
110	C₂²×C₄×C₂₉	—	4	1	no	—
111	C₂²×C₄×C₂₉	—	4	1	no	—
112	C₂²×C₄×C₂₉	—	4	1	no	—
113	C₂²×C₄×C₂₉	—	4	1	no	—
114	C₂²×C₄×C₂₉	—	4	1	no	—
115	C₂²×C₄×C₂₉	—	4	1	no	—
116	C₂²×C₄×C₂₉	—	4	1	no	—
117	C₂²×C₄×C₂₉	M₁₆	1	4	yes	—
118	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₂₉	C₂×Q₈	1	2	yes	—
132	C₂²×C₄×C₂₉	#41	1	2	yes	—
133	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
134	C₂×C₈×C₂₉	—	2	2	no	—
135	C₂×C₈×C₂₉	—	2	2	no	—
136	C₂×C₈×C₂₉	—	2	2	no	—
137	C₂×C₈×C₂₉	—	2	2	no	—
138	C₂×C₈×C₂₉	—	2	2	no	—
139	C₂×C₈×C₂₉	—	2	2	no	—
140	C₂×C₈×C₂₉	—	2	2	no	—
141	C₂×C₈×C₂₉	—	2	2	no	—
142	C₂×C₈×C₂₉	—	2	2	no	—
143	C₂×C₈×C₂₉	—	2	2	no	—
144	C₂×C₈×C₂₉	—	2	2	no	—
145	C₂×C₈×C₂₉	C₂×Q₈	1	4	yes	—
146	C₄⋊C₄×C₂₉	—	2	2	no	—
147	C₄⋊C₄×C₂₉	—	2	2	no	—
148	C₄⋊C₄×C₂₉	—	2	2	no	—
149	C₄⋊C₄×C₂₉	—	2	2	no	—
150	C₄⋊C₄×C₂₉	—	2	2	no	—
151	C₄⋊C₄×C₂₉	—	2	2	no	—
152	C₄⋊C₄×C₂₉	—	2	2	no	—
153	C₄⋊C₄×C₂₉	M₁₆	1	4	yes	—
154	C₄²×C₂₉	—	2	2	no	—
155	C₄²×C₂₉	—	2	2	no	—
156	C₄²×C₂₉	—	2	2	no	—
157	C₄²×C₂₉	—	2	2	no	—
158	C₄²×C₂₉	—	2	2	no	—
159	C₄²×C₂₉	—	2	2	no	—
160	C₄²×C₂₉	—	2	2	no	—
161	C₄²×C₂₉	—	4	1	no	—
162	C₄²×C₂₉	—	4	1	no	—
163	C₄²×C₂₉	—	4	1	no	—
164	C₄²×C₂₉	—	4	1	no	—
165	C₄²×C₂₉	#41	1	4	yes	—
166	#22627	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂³×C₂₉	—	2	1	no	—
168	C₂³×C₂₉	—	2	1	no	—
169	C₂³×C₂₉	—	2	1	no	—
170	C₂³×C₂₉	—	2	1	no	—
171	C₂³×C₂₉	C₄×Q₈	1	2	yes	—
172	C₂³×C₂₉	C₂×M₁₆	1	2	yes	—
173	C₂³×C₂₉	#131	1	2	yes	—
174	C₂³×C₂₉	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₂₉	—	2	8	no	—
176	C₂×C₄×C₂₉	—	2	1	no	—
177	C₂×C₄×C₂₉	—	2	1	no	—
178	C₂×C₄×C₂₉	—	2	1	no	—
179	C₂×C₄×C₂₉	—	2	1	no	—
180	C₂×C₄×C₂₉	—	2	1	no	—
181	C₂×C₄×C₂₉	—	2	1	no	—
182	C₂×C₄×C₂₉	—	2	1	no	—
183	C₂×C₄×C₂₉	—	2	1	no	—
184	C₂×C₄×C₂₉	—	2	1	no	—
185	C₂×C₄×C₂₉	—	2	1	no	—
186	C₂×C₄×C₂₉	—	2	1	no	—
187	C₂×C₄×C₂₉	—	2	1	no	—
188	C₂×C₄×C₂₉	—	2	1	no	—
189	C₂×C₄×C₂₉	—	2	1	no	—
190	C₂×C₄×C₂₉	—	2	1	no	—
191	C₂×C₄×C₂₉	—	2	1	no	—
192	C₂×C₄×C₂₉	—	2	4	no	—
193	C₂×C₄×C₂₉	—	2	4	no	—
194	C₂×C₄×C₂₉	—	2	1	no	—
195	C₂×C₄×C₂₉	—	2	1	no	—
196	C₂×C₄×C₂₉	—	2	1	no	—
197	C₂×C₄×C₂₉	—	2	1	no	—
198	C₂×C₄×C₂₉	—	2	1	no	—
199	C₂×C₄×C₂₉	—	2	1	no	—
200	C₂×C₄×C₂₉	—	2	1	no	—
201	C₂×C₄×C₂₉	—	2	1	no	—
202	C₂×C₄×C₂₉	—	2	1	no	—
203	C₂×C₄×C₂₉	—	2	1	no	—
204	C₂×C₄×C₂₉	—	2	1	no	—
205	C₂×C₄×C₂₉	—	2	1	no	—
206	C₂×C₄×C₂₉	—	2	1	no	—
207	C₂×C₄×C₂₉	—	2	1	no	—
208	C₂×C₄×C₂₉	—	2	1	no	—
209	C₂×C₄×C₂₉	—	4	4	no	—
210	C₂×C₄×C₂₉	—	4	4	no	—
211	C₂×C₄×C₂₉	—	4	4	no	—
212	C₂×C₄×C₂₉	—	4	4	no	—
213	C₂×C₄×C₂₉	—	4	4	no	—
214	C₂×C₄×C₂₉	#117	1	2	yes	—
215	C₂×C₄×C₂₉	#117	1	2	yes	—
216	C₂×C₄×C₂₉	C₄×Q₈	1	2	yes	—
217	C₂×C₄×C₂₉	C₂×M₁₆	1	2	yes	—
218	C₂×C₄×C₂₉	C₂×M₁₆	1	2	yes	—
219	C₂×C₄×C₂₉	C₂×M₁₆	1	2	yes	—
220	C₂×C₄×C₂₉	C₂×M₁₆	1	2	yes	—
221	C₂×C₄×C₂₉	C₂×M₁₆	1	2	yes	—
222	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
223	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
225	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
226	C₈×C₂₉	—	2	4	no	—
227	C₈×C₂₉	—	4	2	no	—
228	C₈×C₂₉	—	4	2	no	—
229	C₈×C₂₉	—	4	2	no	—
230	C₂×C₄×C₄⋊C₄	C₂×C₂₉	1	1	yes	characteristic
231	#1940	C₂×C₂₉	1	2	yes	complemented
232	#1917	C₂×C₂₉	1	2	yes	complemented
233	#1916	C₂×C₂₉	1	2	yes	complemented
234	#1797	C₂×C₂₉	1	1	yes	characteristic
235	#1797	C₂×C₂₉	1	1	yes	characteristic
236	#1797	C₂×C₂₉	1	1	yes	characteristic
237	#1771	C₂×C₂₉	1	2	yes	complemented
238	#1749	C₂×C₂₉	1	1	yes	characteristic
239	#1749	C₂×C₂₉	1	1	yes	characteristic
240	C₄×C₂²⋊C₈	C₂×C₂₉	1	1	yes	characteristic
241	C₂²×C₂₉	—	2	2	no	—
242	C₂²×C₂₉	—	2	2	no	—
243	C₂²×C₂₉	—	2	2	no	—
244	C₂²×C₂₉	—	2	2	no	—
245	C₂²×C₂₉	—	2	2	no	—
246	C₂²×C₂₉	—	2	2	no	—
247	C₂²×C₂₉	#446	1	4	yes	—
248	C₂²×C₂₉	C₂×#117	1	1	yes	characteristic
249	C₂²×C₂₉	C₂×C₄×Q₈	1	1	yes	characteristic
250	C₂²×C₂₉	#518	1	1	yes	characteristic
251	C₂²×C₂₉	C₂²×M₁₆	1	1	yes	characteristic
252	C₂²×C₂₉	C₂²×M₁₆	1	1	yes	characteristic
253	C₂²×C₂₉	C₂×#131	1	1	yes	characteristic
254	C₂²×C₂₉	#568	1	1	yes	characteristic
255	C₄×C₂₉	—	2	2	no	—
256	C₄×C₂₉	—	2	2	no	—
257	C₄×C₂₉	—	2	2	no	—
258	C₄×C₂₉	—	2	2	no	—
259	C₄×C₂₉	—	2	2	no	—
260	C₄×C₂₉	—	2	2	no	—
261	C₄×C₂₉	—	2	2	no	—
262	C₄×C₂₉	—	2	2	no	—
263	C₄×C₂₉	—	4	1	no	—
264	C₄×C₂₉	—	4	1	no	—
265	C₄×C₂₉	—	4	1	no	—
266	C₄×C₂₉	—	4	1	no	—
267	C₄×C₂₉	—	4	1	no	—
268	C₄×C₂₉	#553	1	2	yes	—
269	C₄×C₂₉	#554	1	2	yes	—
270	C₂²×C₄⋊C₄	C₄×C₂₉	1	1	yes	characteristic
271	C₂²×C₄⋊C₄	C₄×C₂₉	1	1	yes	characteristic
272	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
273	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
274	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
275	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
276	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
277	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
278	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
279	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
280	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
281	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
282	C₂×#97	C₂²×C₂₉	1	2	yes	—
283	C₂×#97	C₂²×C₂₉	1	2	yes	—
284	C₂×C₄×C₈	C₂²×C₂₉	1	2	yes	—
285	C₄×C₄⋊C₄	C₄×C₂₉	1	1	yes	characteristic
286	C₄×C₄⋊C₄	C₄×C₂₉	1	1	yes	characteristic
287	C₄×C₄⋊C₄	C₄×C₂₉	1	1	yes	characteristic
288	C₄×C₄⋊C₄	C₄×C₂₉	1	1	yes	characteristic
289	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
290	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
291	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
292	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
293	C₂×#95	C₄×C₂₉	1	1	yes	characteristic
294	C₂×#95	C₄×C₂₉	1	1	yes	characteristic
295	#336	C₂²×C₂₉	1	2	yes	—
296	#336	C₂²×C₂₉	1	2	yes	—
297	#336	C₂²×C₂₉	1	2	yes	—
298	#336	C₂²×C₂₉	1	2	yes	—
299	#336	C₂²×C₂₉	1	2	yes	—
300	#336	C₂²×C₂₉	1	2	yes	—
301	C₂×C₂₉	—	2	4	no	—
302	C₂×C₂₉	#2345	1	1	yes	characteristic
303	C₂×C₂₉	#2920	1	1	yes	characteristic
304	C₂×C₂₉	#2924	1	1	yes	characteristic
305	C₂×C₂₉	C₂×#446	1	1	yes	characteristic
306	C₂×C₂₉	Q₈×M₁₆	1	1	yes	characteristic
307	C₂×C₂₉	#2973	1	1	yes	characteristic
308	C₂×C₂₉	#2974	1	1	yes	characteristic
309	C₂³×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
310	C₂³×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
311	C₂³×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
312	C₂³×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
313	C₂³×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
314	C₂³×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
315	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
316	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
317	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
318	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
319	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
320	C₂×C₄⋊C₄	—	2	4	no	—
321	C₂×C₄⋊C₄	—	2	4	no	—
322	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
330	C₂×C₄²	—	2	4	no	—
331	C₂×C₄²	—	4	2	no	—
332	C₂×C₄²	—	4	2	no	—
333	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
334	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
335	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
336	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
337	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
338	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
339	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
342	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
345	C₄⋊C₈	—	2	4	no	—
346	C₄⋊C₈	—	4	2	no	—
347	C₄⋊C₈	—	4	2	no	—
348	C₂²⋊C₈	—	2	2	no	—
349	C₂²⋊C₈	—	2	2	no	—
350	C₂²⋊C₈	—	2	2	no	—
351	C₂²⋊C₈	Q₈×C₂₉	1	4	yes	—
352	#97	—	2	4	no	—
353	#97	—	4	2	no	—
354	C₄×C₈	—	4	2	no	—
355	#95	C₂×C₄×C₂₉	1	1	yes	characteristic
356	#95	C₂×C₄×C₂₉	1	1	yes	characteristic
357	#95	C₂×C₄×C₂₉	1	1	yes	characteristic
358	#95	C₂×C₄×C₂₉	1	1	yes	characteristic
359	#95	C₂×C₄×C₂₉	1	1	yes	characteristic
360	#95	C₂×C₄×C₂₉	1	1	yes	characteristic
361	#95	C₂×C₄×C₂₉	1	1	yes	characteristic
362	#95	C₂×C₄×C₂₉	1	1	yes	characteristic
363	C₂₉	#22627	1	1	yes	characteristic, direct product factor, Sylow
364	C₂⁴	C₂²×C₄×C₂₉	1	1	yes	characteristic
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	4	1	no	—
378	C₂²×C₄	—	4	1	no	—
379	C₂²×C₄	—	4	1	no	—
380	C₂²×C₄	—	4	1	no	—
381	C₂²×C₄	—	4	1	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	—	4	1	no	—
384	C₂²×C₄	M₁₆×C₂₉	1	4	yes	—
385	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
386	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
387	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
388	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
389	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
390	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
391	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
392	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
393	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
394	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
395	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
396	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
397	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
398	C₂²×C₄	C₂×Q₈×C₂₉	1	2	yes	—
399	C₂²×C₄	#41×C₂₉	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	C₂×Q₈×C₂₉	1	4	yes	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	M₁₆×C₂₉	1	4	yes	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	4	1	no	—
429	C₄²	—	4	1	no	—
430	C₄²	—	4	1	no	—
431	C₄²	—	4	1	no	—
432	C₄²	#41×C₂₉	1	4	yes	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	C₄×Q₈×C₂₉	1	2	yes	—
438	C₂³	C₂×M₁₆×C₂₉	1	2	yes	—
439	C₂³	C₂₉×#131	1	2	yes	—
440	C₂³	C₂³×C₄×C₂₉	1	1	yes	characteristic
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	C₂₉×#117	1	2	yes	—
481	C₂×C₄	C₂₉×#117	1	2	yes	—
482	C₂×C₄	C₄×Q₈×C₂₉	1	2	yes	—
483	C₂×C₄	C₂×M₁₆×C₂₉	1	2	yes	—
484	C₂×C₄	C₂×M₁₆×C₂₉	1	2	yes	—
485	C₂×C₄	C₂×M₁₆×C₂₉	1	2	yes	—
486	C₂×C₄	C₂×M₁₆×C₂₉	1	2	yes	—
487	C₂×C₄	C₂×M₁₆×C₂₉	1	2	yes	—
488	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
489	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
490	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
491	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
492	C₈	—	2	4	no	—
493	C₈	—	4	2	no	—
494	C₈	—	4	2	no	—
495	C₈	—	4	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	C₂₉×#446	1	4	yes	—
503	C₂²	C₂×C₂₉×#117	1	1	yes	characteristic
504	C₂²	C₂×C₄×Q₈×C₂₉	1	1	yes	characteristic
505	C₂²	C₂₉×#518	1	1	yes	characteristic
506	C₂²	C₂²×M₁₆×C₂₉	1	1	yes	characteristic
507	C₂²	C₂²×M₁₆×C₂₉	1	1	yes	characteristic
508	C₂²	C₂×C₂₉×#131	1	1	yes	characteristic
509	C₂²	C₂₉×#568	1	1	yes	characteristic
510	C₄	—	2	2	no	—
511	C₄	—	2	2	no	—
512	C₄	—	2	2	no	—
513	C₄	—	2	2	no	—
514	C₄	—	2	2	no	—
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	1	no	—
523	C₄	C₂₉×#553	1	2	yes	—
524	C₄	C₂₉×#554	1	2	yes	—
525	C₂	—	2	4	no	—
526	C₂	C₂₉×#2345	1	1	yes	characteristic
527	C₂	C₂₉×#2920	1	1	yes	characteristic
528	C₂	C₂₉×#2924	1	1	yes	characteristic
529	C₂	C₂×C₂₉×#446	1	1	yes	characteristic
530	C₂	Q₈×M₁₆×C₂₉	1	1	yes	characteristic
531	C₂	C₂₉×#2973	1	1	yes	characteristic
532	C₂	C₂₉×#2974	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
socle	C₂³×C₂₉	C₂³×C₄
prime radical	C₂⁴×C₂₉	C₂²×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
2. C₂₉×#1940	C₂	semidirect
3. C₂₉×#1917	C₂	semidirect
4. C₂₉×#1916	C₂	semidirect
8. C₂₉×#1771	C₂	semidirect
166. #22627	C₂₉	direct (N × H)
231. #1940	C₂×C₂₉	semidirect
232. #1917	C₂×C₂₉	semidirect
233. #1916	C₂×C₂₉	semidirect
237. #1771	C₂×C₂₉	semidirect
363. C₂₉	#22627	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×C₄×C₄⋊C₄×C₂₉	2
C₂₉×#1940	2
C₂₉×#1917	2
C₂₉×#1916	2
C₂₉×#1797	2
C₂₉×#1771	2
C₂₉×#1749	2
C₄×C₂₉×C₂²⋊C₈	2
#22627	29

Subgroups — C29×#22627 #20317527

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#22627 #20317527