Subgroups — C₂₉×#34946 #20329846

Order 7424.

2834 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2563	C₂	1	2	yes	maximal, complemented
4	C₂₉×#2562	C₂	1	4	yes	maximal, complemented
5	C₂₉×#2561	C₂	1	4	yes	maximal, complemented
6	C₂₉×#2547	C₂	1	2	yes	maximal, complemented
7	C₂₉×#2503	C₂	1	2	yes	maximal, complemented
8	C₂₉×#2435	C₂	1	2	yes	maximal
9	C₂₉×#2398	C₂	1	4	yes	maximal, complemented
10	C₄×C₂₉×#124	C₂	1	4	yes	maximal, complemented
11	C₂₉×#2280	C₂	1	4	yes	maximal, complemented
12	C₄×C₂₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₂₉	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₂₉	C₂²	1	2	yes	—
15	C₂₉×#533	—	2	8	no	—
16	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₂₉×#125	C₂²	1	2	yes	complemented
19	C₂×C₂₉×#124	C₂²	1	4	yes	—
20	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	complemented
23	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	complemented
24	C₂×C₄×D₄×C₂₉	—	2	8	no	—
25	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
29	C₂×C₂₉×#117	C₂²	1	2	yes	—
30	C₂×C₂₉×#117	C₂²	1	2	yes	—
31	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
33	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
34	C₂₉×#400	C₂²	1	8	yes	complemented
35	C₂₉×#397	C₂²	1	8	yes	complemented
36	C₂₉×#394	C₂²	1	8	yes	—
37	C₂₉×#393	C₂²	1	8	yes	complemented
38	C₂₉×#391	C₂²	1	4	yes	complemented
39	C₂₉×#390	C₂²	1	4	yes	—
40	C₂₉×#388	C₂²	1	16	yes	complemented
41	C₂₉×#382	C₂²	1	4	yes	complemented
42	C₂₉×#381	C₂²	1	8	yes	—
43	C₂₉×#380	C₂²	1	8	yes	complemented
44	C₂₉×#380	C₂²	1	8	yes	complemented
45	C₂₉×#379	C₂²	1	8	yes	—
46	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	complemented
47	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	complemented
48	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
49	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
50	C₄×C₂²⋊C₄×C₂₉	C₂²	1	16	yes	complemented
51	C₂₉×#376	C₂²	1	2	yes	complemented
52	C₄³×C₂₉	C₂²	1	2	yes	complemented
53	C₂⁵×C₂₉	C₂³	1	2	yes	—
54	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
55	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
56	C₂²×D₄×C₂₉	—	2	8	no	—
57	C₂²×D₄×C₂₉	—	2	4	no	—
58	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
59	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
60	C₂³×C₄×C₂₉	—	2	8	no	—
61	C₂³×C₄×C₂₉	—	2	16	no	—
62	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
63	C₂³×C₄×C₂₉	C₂³	1	4	yes	—
64	C₂³×C₄×C₂₉	C₂³	1	4	yes	—
65	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
68	C₂₉×C₄⋊Q₈	—	2	4	no	—
69	C₂₉×C₄⋊Q₈	—	2	4	no	—
70	C₂₉×#125	—	2	8	no	—
71	C₂₉×#124	—	2	16	no	—
72	C₂₉×C₂²⋊Q₈	—	2	8	no	—
73	C₂₉×C₂²⋊Q₈	—	2	8	no	—
74	C₄×Q₈×C₂₉	—	2	8	no	—
75	C₄×Q₈×C₂₉	—	2	8	no	—
76	C₄×D₄×C₂₉	—	2	8	no	—
77	C₄×D₄×C₂₉	—	2	8	no	—
78	C₄×D₄×C₂₉	—	2	8	no	—
79	C₄×D₄×C₂₉	—	2	8	no	—
80	C₂₉×#117	—	2	8	no	—
81	C₂₉×#117	—	2	8	no	—
82	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
83	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
92	C₂×C₂²⋊C₄×C₂₉	—	2	8	no	—
93	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₂₉	C₂³	1	16	yes	—
98	C₂×C₂²⋊C₄×C₂₉	C₂³	1	16	yes	—
99	C₂×C₄²×C₂₉	D₄	1	8	yes	—
100	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
101	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
102	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
103	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
104	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
108	C₂₉×#95	C₂³	1	4	yes	—
109	C₂₉×#95	C₂³	1	4	yes	—
110	C₂₉×#95	C₂³	1	16	yes	—
111	C₂₉×#95	C₂³	1	16	yes	—
112	C₂⁴×C₂₉	—	2	4	no	—
113	C₂⁴×C₂₉	—	2	8	no	—
114	C₂⁴×C₂₉	—	2	8	no	—
115	C₂⁴×C₂₉	—	4	4	no	—
116	C₂⁴×C₂₉	C₂⁴	1	4	yes	—
117	C₂⁴×C₂₉	C₂⁴	1	1	yes	characteristic
118	C₂×Q₈×C₂₉	—	2	4	no	—
119	C₂×Q₈×C₂₉	—	2	4	no	—
120	C₂×Q₈×C₂₉	—	2	8	no	—
121	C₂×Q₈×C₂₉	—	4	4	no	—
122	C₂×D₄×C₂₉	—	2	32	no	—
123	C₂×D₄×C₂₉	—	2	8	no	—
124	C₂×D₄×C₂₉	—	2	4	no	—
125	C₂×D₄×C₂₉	—	2	4	no	—
126	C₂×D₄×C₂₉	—	2	4	no	—
127	C₂×D₄×C₂₉	#41	1	8	yes	—
128	C₂²×C₄×C₂₉	—	2	4	no	—
129	C₂²×C₄×C₂₉	—	2	4	no	—
130	C₂²×C₄×C₂₉	—	2	8	no	—
131	C₂²×C₄×C₂₉	—	2	8	no	—
132	C₂²×C₄×C₂₉	—	2	8	no	—
133	C₂²×C₄×C₂₉	—	2	16	no	—
134	C₂²×C₄×C₂₉	—	2	16	no	—
135	C₂²×C₄×C₂₉	—	4	2	no	—
136	C₂²×C₄×C₂₉	—	4	32	no	—
137	C₂²×C₄×C₂₉	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₂₉	C₂×D₄	1	4	yes	—
139	C₂²×C₄×C₂₉	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₂₉	#41	1	8	yes	—
141	C₂²×C₄×C₂₉	C₂⁴	1	8	yes	—
142	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
146	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
147	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
148	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
149	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
150	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
151	C₄⋊C₄×C₂₉	—	2	4	no	—
152	C₄⋊C₄×C₂₉	—	2	4	no	—
153	C₄⋊C₄×C₂₉	—	2	4	no	—
154	C₄⋊C₄×C₂₉	—	2	4	no	—
155	C₄⋊C₄×C₂₉	—	2	8	no	—
156	C₄⋊C₄×C₂₉	—	2	8	no	—
157	C₄⋊C₄×C₂₉	—	2	4	no	—
158	C₄⋊C₄×C₂₉	—	2	4	no	—
159	C₄⋊C₄×C₂₉	—	2	8	no	—
160	C₂²⋊C₄×C₂₉	—	2	8	no	—
161	C₂²⋊C₄×C₂₉	—	2	8	no	—
162	C₂²⋊C₄×C₂₉	—	2	32	no	—
163	C₂²⋊C₄×C₂₉	—	2	8	no	—
164	C₂²⋊C₄×C₂₉	—	2	8	no	—
165	C₂²⋊C₄×C₂₉	—	4	16	no	—
166	C₄²×C₂₉	—	2	8	no	—
167	C₄²×C₂₉	—	2	8	no	—
168	C₄²×C₂₉	—	2	8	no	—
169	C₄²×C₂₉	—	4	4	no	—
170	C₄²×C₂₉	C₂×D₄	1	4	yes	—
171	C₄²×C₂₉	C₂×D₄	1	4	yes	—
172	C₄²×C₂₉	C₂×D₄	1	4	yes	—
173	C₄²×C₂₉	C₂×D₄	1	4	yes	—
174	#34946	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂³×C₂₉	—	2	2	no	—
176	C₂³×C₂₉	—	2	2	no	—
177	C₂³×C₂₉	—	2	16	no	—
178	C₂³×C₂₉	—	2	4	no	—
179	C₂³×C₂₉	—	2	8	no	—
180	C₂³×C₂₉	—	2	4	no	—
181	C₂³×C₂₉	—	2	8	no	—
182	C₂³×C₂₉	—	4	32	no	—
183	C₂³×C₂₉	—	4	8	no	—
184	C₂³×C₂₉	—	4	8	no	—
185	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
186	C₂³×C₂₉	C₂×#41	1	8	yes	—
187	C₂³×C₂₉	C₂×#41	1	4	yes	—
188	C₂³×C₂₉	C₂⁵	1	1	yes	characteristic
189	Q₈×C₂₉	—	4	8	no	—
190	Q₈×C₂₉	—	4	8	no	—
191	D₄×C₂₉	—	2	16	no	—
192	D₄×C₂₉	—	2	16	no	—
193	C₂×C₄×C₂₉	—	2	2	no	—
194	C₂×C₄×C₂₉	—	2	2	no	—
195	C₂×C₄×C₂₉	—	2	2	no	—
196	C₂×C₄×C₂₉	—	2	8	no	—
197	C₂×C₄×C₂₉	—	2	4	no	—
198	C₂×C₄×C₂₉	—	2	4	no	—
199	C₂×C₄×C₂₉	—	2	4	no	—
200	C₂×C₄×C₂₉	—	2	8	no	—
201	C₂×C₄×C₂₉	—	2	8	no	—
202	C₂×C₄×C₂₉	—	2	8	no	—
203	C₂×C₄×C₂₉	—	2	8	no	—
204	C₂×C₄×C₂₉	—	2	8	no	—
205	C₂×C₄×C₂₉	—	2	8	no	—
206	C₂×C₄×C₂₉	—	4	4	no	—
207	C₂×C₄×C₂₉	—	4	8	no	—
208	C₂×C₄×C₂₉	—	4	16	no	—
209	C₂×C₄×C₂₉	—	4	16	no	—
210	C₂×C₄×C₂₉	#124	1	16	yes	complemented
211	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
212	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
213	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
217	C₂×C₄×C₂₉	C₂×#41	1	4	yes	—
218	C₂×C₄×C₂₉	C₂×#41	1	4	yes	—
219	C₂×C₄×C₂₉	C₂×#41	1	4	yes	—
220	C₂×#533	C₂×C₂₉	1	1	yes	characteristic, complemented
221	C₂²×C₄×D₄	C₂×C₂₉	1	1	yes	characteristic
222	#2563	C₂×C₂₉	1	2	yes	complemented
223	#2562	C₂×C₂₉	1	4	yes	complemented
224	#2561	C₂×C₂₉	1	4	yes	complemented
225	#2547	C₂×C₂₉	1	2	yes	complemented
226	#2503	C₂×C₂₉	1	2	yes	complemented
227	#2435	C₂×C₂₉	1	2	yes	—
228	#2398	C₂×C₂₉	1	4	yes	complemented
229	C₄×#124	C₂×C₂₉	1	4	yes	complemented
230	#2280	C₂×C₂₉	1	4	yes	complemented
231	C₄×#117	C₂×C₂₉	1	1	yes	characteristic, complemented
232	C₂²×C₂₉	—	2	2	no	—
233	C₂²×C₂₉	—	2	2	no	—
234	C₂²×C₂₉	—	2	8	no	—
235	C₂²×C₂₉	—	2	8	no	—
236	C₂²×C₂₉	—	2	16	no	—
237	C₂²×C₂₉	—	4	32	no	—
238	C₂²×C₂₉	—	4	4	no	—
239	C₂²×C₂₉	—	4	4	no	—
240	C₂²×C₂₉	—	4	8	no	—
241	C₂²×C₂₉	C₂×#124	1	4	yes	—
242	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
243	C₂²×C₂₉	C₂²×#41	1	2	yes	—
244	C₂²×C₂₉	C₂²×#41	1	2	yes	—
245	C₂²×C₂₉	#585	1	2	yes	—
246	C₄×C₂₉	—	2	2	no	—
247	C₄×C₂₉	—	2	2	no	—
248	C₄×C₂₉	—	2	2	no	—
249	C₄×C₂₉	—	4	4	no	—
250	C₄×C₂₉	—	4	4	no	—
251	C₄×C₂₉	—	4	4	no	—
252	C₄×C₂₉	—	4	8	no	—
253	C₄×C₂₉	#525	1	4	yes	—
254	C₄×C₂₉	C₂×#124	1	4	yes	—
255	C₄×C₂₉	C₂×#124	1	4	yes	—
256	C₂³×D₄	C₂²×C₂₉	1	1	yes	characteristic
257	C₂⁴×C₄	C₂²×C₂₉	1	2	yes	—
258	#533	—	2	8	no	—
259	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
260	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
261	C₂×#125	C₂²×C₂₉	1	2	yes	complemented
262	C₂×#124	C₂²×C₂₉	1	4	yes	—
263	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	2	yes	—
264	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	2	yes	—
265	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	complemented
266	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	complemented
267	C₂×C₄×D₄	—	2	8	no	—
268	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
269	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
270	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
271	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
272	C₂×#117	C₂²×C₂₉	1	2	yes	—
273	C₂×#117	C₂²×C₂₉	1	2	yes	—
274	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
275	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
276	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
277	#400	C₂²×C₂₉	1	8	yes	complemented
278	#397	C₂²×C₂₉	1	8	yes	complemented
279	#394	C₂²×C₂₉	1	8	yes	—
280	#393	C₂²×C₂₉	1	8	yes	complemented
281	#391	C₂²×C₂₉	1	4	yes	complemented
282	#390	C₂²×C₂₉	1	4	yes	—
283	#388	C₂²×C₂₉	1	16	yes	complemented
284	#382	C₂²×C₂₉	1	4	yes	complemented
285	#381	C₂²×C₂₉	1	8	yes	—
286	#380	C₂²×C₂₉	1	8	yes	complemented
287	#380	C₂²×C₂₉	1	8	yes	complemented
288	#379	C₂²×C₂₉	1	8	yes	—
289	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	complemented
290	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	complemented
291	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
292	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
293	C₄×C₂²⋊C₄	C₂²×C₂₉	1	16	yes	complemented
294	#376	C₂²×C₂₉	1	2	yes	complemented
295	C₄³	C₂²×C₂₉	1	2	yes	complemented
296	C₂×C₂₉	—	2	4	no	—
297	C₂×C₂₉	—	4	8	no	—
298	C₂×C₂₉	C₂×#525	1	1	yes	characteristic
299	C₂×C₂₉	C₂²×#124	1	1	yes	characteristic
300	C₂×C₂₉	#3449	1	1	yes	characteristic
301	C₂×C₂₉	#3475	1	4	yes	—
302	C₂⁵	C₂³×C₂₉	1	2	yes	—
303	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
304	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
305	C₂²×D₄	—	2	8	no	—
306	C₂²×D₄	—	2	4	no	—
307	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
308	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
309	C₂³×C₄	—	2	8	no	—
310	C₂³×C₄	—	2	16	no	—
311	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
312	C₂³×C₄	C₂³×C₂₉	1	4	yes	—
313	C₂³×C₄	C₂³×C₂₉	1	4	yes	—
314	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
315	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
316	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
317	C₄⋊Q₈	—	2	4	no	—
318	C₄⋊Q₈	—	2	4	no	—
319	#125	—	2	8	no	—
320	#124	—	2	16	no	—
321	C₂²⋊Q₈	—	2	8	no	—
322	C₂²⋊Q₈	—	2	8	no	—
323	C₄×Q₈	—	2	8	no	—
324	C₄×Q₈	—	2	8	no	—
325	C₄×D₄	—	2	8	no	—
326	C₄×D₄	—	2	8	no	—
327	C₄×D₄	—	2	8	no	—
328	C₄×D₄	—	2	8	no	—
329	#117	—	2	8	no	—
330	#117	—	2	8	no	—
331	C₂×C₄⋊C₄	—	2	4	no	—
332	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
336	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
337	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
338	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
339	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
340	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
341	C₂×C₂²⋊C₄	—	2	8	no	—
342	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
343	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₂₉	1	16	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₂₉	1	16	yes	—
348	C₂×C₄²	D₄×C₂₉	1	8	yes	—
349	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
350	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
351	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
352	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
353	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
354	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
355	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
356	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
357	#95	C₂³×C₂₉	1	4	yes	—
358	#95	C₂³×C₂₉	1	4	yes	—
359	#95	C₂³×C₂₉	1	16	yes	—
360	#95	C₂³×C₂₉	1	16	yes	—
361	C₂₉	#34946	1	1	yes	characteristic, direct product factor, Sylow
362	C₂⁴	—	2	4	no	—
363	C₂⁴	—	2	8	no	—
364	C₂⁴	—	2	8	no	—
365	C₂⁴	—	4	4	no	—
366	C₂⁴	C₂⁴×C₂₉	1	4	yes	—
367	C₂⁴	C₂⁴×C₂₉	1	1	yes	characteristic
368	C₂×Q₈	—	2	4	no	—
369	C₂×Q₈	—	2	4	no	—
370	C₂×Q₈	—	2	8	no	—
371	C₂×Q₈	—	4	4	no	—
372	C₂×D₄	—	2	32	no	—
373	C₂×D₄	—	2	8	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	#41×C₂₉	1	8	yes	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	8	no	—
381	C₂²×C₄	—	2	8	no	—
382	C₂²×C₄	—	2	8	no	—
383	C₂²×C₄	—	2	16	no	—
384	C₂²×C₄	—	2	16	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	—	4	32	no	—
387	C₂²×C₄	C₂×D₄×C₂₉	1	4	yes	—
388	C₂²×C₄	C₂×D₄×C₂₉	1	4	yes	—
389	C₂²×C₄	C₂×D₄×C₂₉	1	4	yes	—
390	C₂²×C₄	#41×C₂₉	1	8	yes	—
391	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
392	C₂²×C₄	C₂⁴×C₂₉	1	8	yes	—
393	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
394	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
395	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
396	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
397	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
398	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
399	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
400	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	8	no	—
406	C₄⋊C₄	—	2	8	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	8	no	—
410	C₂²⋊C₄	—	2	8	no	—
411	C₂²⋊C₄	—	2	8	no	—
412	C₂²⋊C₄	—	2	32	no	—
413	C₂²⋊C₄	—	2	8	no	—
414	C₂²⋊C₄	—	2	8	no	—
415	C₂²⋊C₄	—	4	16	no	—
416	C₄²	—	2	8	no	—
417	C₄²	—	2	8	no	—
418	C₄²	—	2	8	no	—
419	C₄²	—	4	4	no	—
420	C₄²	C₂×D₄×C₂₉	1	4	yes	—
421	C₄²	C₂×D₄×C₂₉	1	4	yes	—
422	C₄²	C₂×D₄×C₂₉	1	4	yes	—
423	C₄²	C₂×D₄×C₂₉	1	4	yes	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	16	no	—
427	C₂³	—	2	4	no	—
428	C₂³	—	2	8	no	—
429	C₂³	—	2	4	no	—
430	C₂³	—	2	8	no	—
431	C₂³	—	4	32	no	—
432	C₂³	—	4	8	no	—
433	C₂³	—	4	8	no	—
434	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
435	C₂³	C₂×#41×C₂₉	1	8	yes	—
436	C₂³	C₂×#41×C₂₉	1	4	yes	—
437	C₂³	C₂⁵×C₂₉	1	1	yes	characteristic
438	Q₈	—	4	8	no	—
439	Q₈	—	4	8	no	—
440	D₄	—	2	16	no	—
441	D₄	—	2	16	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	8	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	2	8	no	—
453	C₂×C₄	—	2	8	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	8	no	—
457	C₂×C₄	—	4	16	no	—
458	C₂×C₄	—	4	16	no	—
459	C₂×C₄	C₂₉×#124	1	16	yes	complemented
460	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
461	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
462	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
463	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
464	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
465	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
466	C₂×C₄	C₂×#41×C₂₉	1	4	yes	—
467	C₂×C₄	C₂×#41×C₂₉	1	4	yes	—
468	C₂×C₄	C₂×#41×C₂₉	1	4	yes	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	8	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	16	no	—
473	C₂²	—	2	8	no	—
474	C₂²	—	4	32	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	8	no	—
477	C₂²	—	4	4	no	—
478	C₂²	C₂×C₂₉×#124	1	4	yes	—
479	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
480	C₂²	C₂²×#41×C₂₉	1	2	yes	—
481	C₂²	C₂²×#41×C₂₉	1	2	yes	—
482	C₂²	C₂₉×#585	1	2	yes	—
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	4	4	no	—
487	C₄	—	4	8	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	4	no	—
490	C₄	C₂₉×#525	1	4	yes	—
491	C₄	C₂×C₂₉×#124	1	4	yes	—
492	C₄	C₂×C₂₉×#124	1	4	yes	—
493	C₂	—	2	4	no	—
494	C₂	—	4	8	no	—
495	C₂	C₂×C₂₉×#525	1	1	yes	characteristic
496	C₂	C₂²×C₂₉×#124	1	1	yes	characteristic
497	C₂	C₂₉×#3449	1	1	yes	characteristic
498	C₂	C₂₉×#3475	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₉
socle	C₂³×C₂₉	C₂⁵
prime radical	C₂³×D₄×C₂₉	C₂²
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
1. C₂×C₂₉×#533	C₂	semidirect
3. C₂₉×#2563	C₂	semidirect
4. C₂₉×#2562	C₂	semidirect
5. C₂₉×#2561	C₂	semidirect
6. C₂₉×#2547	C₂	semidirect
7. C₂₉×#2503	C₂	semidirect
9. C₂₉×#2398	C₂	semidirect
10. C₄×C₂₉×#124	C₂	semidirect
11. C₂₉×#2280	C₂	semidirect
12. C₄×C₂₉×#117	C₂	semidirect
16. C₂×C₂₉×C₄⋊Q₈	C₂²	semidirect
17. C₂×C₂₉×C₄⋊Q₈	C₂²	semidirect
18. C₂×C₂₉×#125	C₂²	semidirect
22. C₂×C₄×Q₈×C₂₉	C₂²	semidirect
23. C₂×C₄×Q₈×C₂₉	C₂²	semidirect
34. C₂₉×#400	C₂²	semidirect
35. C₂₉×#397	C₂²	semidirect
37. C₂₉×#393	C₂²	semidirect
38. C₂₉×#391	C₂²	semidirect
40. C₂₉×#388	C₂²	semidirect
41. C₂₉×#382	C₂²	semidirect
43. C₂₉×#380	C₂²	semidirect
44. C₂₉×#380	C₂²	semidirect
46. C₄×C₄⋊C₄×C₂₉	C₂²	semidirect
47. C₄×C₄⋊C₄×C₂₉	C₂²	semidirect
50. C₄×C₂²⋊C₄×C₂₉	C₂²	semidirect
51. C₂₉×#376	C₂²	semidirect
52. C₄³×C₂₉	C₂²	semidirect
174. #34946	C₂₉	direct (N × H)
210. C₂×C₄×C₂₉	#124	semidirect
220. C₂×#533	C₂×C₂₉	semidirect
222. #2563	C₂×C₂₉	semidirect
223. #2562	C₂×C₂₉	semidirect
224. #2561	C₂×C₂₉	semidirect
225. #2547	C₂×C₂₉	semidirect
226. #2503	C₂×C₂₉	semidirect
228. #2398	C₂×C₂₉	semidirect
229. C₄×#124	C₂×C₂₉	semidirect
230. #2280	C₂×C₂₉	semidirect
231. C₄×#117	C₂×C₂₉	semidirect
259. C₂×C₄⋊Q₈	C₂²×C₂₉	semidirect
260. C₂×C₄⋊Q₈	C₂²×C₂₉	semidirect
261. C₂×#125	C₂²×C₂₉	semidirect
265. C₂×C₄×Q₈	C₂²×C₂₉	semidirect
266. C₂×C₄×Q₈	C₂²×C₂₉	semidirect
277. #400	C₂²×C₂₉	semidirect
278. #397	C₂²×C₂₉	semidirect
280. #393	C₂²×C₂₉	semidirect
281. #391	C₂²×C₂₉	semidirect
283. #388	C₂²×C₂₉	semidirect
284. #382	C₂²×C₂₉	semidirect
286. #380	C₂²×C₂₉	semidirect
287. #380	C₂²×C₂₉	semidirect
289. C₄×C₄⋊C₄	C₂²×C₂₉	semidirect
290. C₄×C₄⋊C₄	C₂²×C₂₉	semidirect
293. C₄×C₂²⋊C₄	C₂²×C₂₉	semidirect
294. #376	C₂²×C₂₉	semidirect
295. C₄³	C₂²×C₂₉	semidirect
361. C₂₉	#34946	direct (N × H)
459. C₂×C₄	C₂₉×#124	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#533	2
C₂²×C₄×D₄×C₂₉	2
C₂₉×#2563	2
C₂₉×#2562	2
C₂₉×#2561	2
C₂₉×#2547	2
C₂₉×#2503	2
C₂₉×#2435	2
C₂₉×#2398	2
C₄×C₂₉×#124	2
C₂₉×#2280	2
C₄×C₂₉×#117	2
#34946	29

Subgroups — C29×#34946 #20329846

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#34946 #20329846