Subgroups — C₂₉×#18037 #20312937

Order 7424.

654 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#2971	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#2970	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₂₉×#135	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1590	C₂	1	2	yes	maximal, complemented
5	C₂₉×#1584	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1581	C₂	1	2	yes	maximal, complemented
7	C₈×SD₁₆×C₂₉	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1568	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1488	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1488	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₉×#135	C₄	1	1	yes	characteristic
13	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
14	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
15	C₂₉×#446	C₂²	1	2	yes	—
16	C₈×Q₈×C₂₉	C₂²	1	2	yes	—
17	C₄×Q₁₆×C₂₉	C₄	1	1	yes	characteristic
18	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
19	C₄×SD₁₆×C₂₉	C₄	1	1	yes	characteristic
20	C₄×SD₁₆×C₂₉	C₄	1	1	yes	characteristic
21	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
22	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
23	C₄×D₈×C₂₉	C₄	1	1	yes	characteristic
24	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
25	C₂₉×#436	—	2	2	no	—
26	C₂₉×#436	C₂²	1	2	yes	—
27	C₂₉×#435	—	2	2	no	—
28	C₈×D₄×C₂₉	C₂²	1	2	yes	—
29	C₂₉×#432	—	2	1	no	—
30	C₂₉×#432	—	2	1	no	—
31	C₂₉×#432	C₂²	1	1	yes	characteristic
32	C₂₉×#432	C₂²	1	1	yes	characteristic
33	C₂₉×#431	C₂²	1	1	yes	characteristic
34	C₂₉×#427	C₄	1	1	yes	characteristic
35	C₂₉×#416	C₄	1	1	yes	characteristic
36	C₂₉×#416	C₄	1	1	yes	characteristic
37	C₄×M₁₆×C₂₉	—	2	1	no	—
38	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
39	C₂×C₂₉×#97	—	2	1	no	—
40	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
41	C₂₉×#335	C₂²	1	2	yes	—
42	C₂₉×#334	C₂²	1	2	yes	—
43	C₂₉×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₂₉×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₂₉×D₄⋊C₈	C₂²	1	2	yes	—
46	C₂₉×D₄⋊C₈	C₂²	1	2	yes	—
47	C₂₉×#322	C₂²	1	2	yes	—
48	C₈²×C₂₉	C₂²	1	2	yes	—
49	C₂×#41×C₂₉	C₂×C₄	1	1	yes	characteristic
50	C₂×#41×C₂₉	C₂×C₄	1	1	yes	characteristic
51	C₂₉×#135	—	2	4	no	—
52	C₂×Q₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
53	C₂×SD₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
54	C₂×SD₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
55	C₂×D₈×C₂₉	C₂×C₄	1	1	yes	characteristic
56	C₂×M₁₆×C₂₉	—	2	2	no	—
57	C₂×M₁₆×C₂₉	D₄	1	2	yes	—
58	C₂²×C₈×C₂₉	—	2	2	no	—
59	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
61	C₄×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
62	C₄×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
63	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
64	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
65	C₄×D₄×C₂₉	—	2	1	no	—
66	C₄×D₄×C₂₉	—	2	1	no	—
67	C₄×D₄×C₂₉	—	2	1	no	—
68	C₄×D₄×C₂₉	—	2	1	no	—
69	C₄×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
70	C₄×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
71	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
72	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
73	C₂₉×#117	—	2	1	no	—
74	C₂₉×#117	—	2	1	no	—
75	C₂₉×#117	C₂×C₄	1	1	yes	characteristic
76	C₂₉×#117	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₂₉	—	2	1	no	—
78	C₂×C₄²×C₂₉	—	2	1	no	—
79	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
80	C₂₉×#107	C₂×C₄	1	1	yes	characteristic
81	C₂₉×#107	C₂×C₄	1	1	yes	characteristic
82	C₂₉×#106	C₂×C₄	1	1	yes	characteristic
83	C₂₉×#106	C₂×C₄	1	1	yes	characteristic
84	C₂₉×C₄⋊C₈	—	2	2	no	—
85	C₂₉×C₄⋊C₈	—	2	2	no	—
86	C₂₉×C₄⋊C₈	—	2	1	no	—
87	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
88	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
89	C₂₉×#103	C₂×C₄	1	1	yes	characteristic
90	C₂₉×#103	C₂×C₄	1	1	yes	characteristic
91	C₂₉×#103	C₂×C₄	1	1	yes	characteristic
92	C₂₉×#103	C₂×C₄	1	1	yes	characteristic
93	C₂₉×#102	C₂×C₄	1	1	yes	characteristic
94	C₂₉×#102	C₂×C₄	1	1	yes	characteristic
95	C₂₉×#102	C₂×C₄	1	1	yes	characteristic
96	C₂₉×#102	C₂×C₄	1	1	yes	characteristic
97	C₂₉×C₂²⋊C₈	—	2	1	no	—
98	C₂₉×C₂²⋊C₈	—	2	1	no	—
99	C₂₉×C₂²⋊C₈	—	2	1	no	—
100	C₂₉×C₂²⋊C₈	—	2	2	no	—
101	C₂₉×C₂²⋊C₈	—	2	2	no	—
102	C₂₉×#97	—	2	2	no	—
103	C₂₉×#97	—	2	1	no	—
104	C₂₉×#97	—	2	1	no	—
105	C₂₉×#97	D₄	1	1	yes	characteristic
106	C₂₉×#97	D₄	1	1	yes	characteristic
107	C₄×C₈×C₂₉	—	2	2	no	—
108	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
109	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
110	C₄×C₈×C₂₉	C₂³	1	2	yes	—
111	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
112	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
113	C₄×C₈×C₂₉	C₂³	1	2	yes	—
114	#41×C₂₉	—	2	2	no	—
115	#41×C₂₉	—	2	2	no	—
116	#41×C₂₉	—	4	1	no	—
117	#41×C₂₉	—	4	1	no	—
118	C₂×Q₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
119	C₂×Q₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
120	C₂×D₄×C₂₉	—	2	1	no	—
121	C₂×D₄×C₂₉	—	2	1	no	—
122	C₂×D₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
123	C₂×D₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₂₉	—	2	1	no	—
125	C₂²×C₄×C₂₉	—	2	1	no	—
126	C₂²×C₄×C₂₉	—	2	1	no	—
127	C₂²×C₄×C₂₉	—	2	1	no	—
128	C₂²×C₄×C₂₉	—	2	1	no	—
129	C₂²×C₄×C₂₉	—	2	1	no	—
130	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
133	Q₁₆×C₂₉	—	2	2	no	—
134	SD₁₆×C₂₉	—	2	2	no	—
135	SD₁₆×C₂₉	M₁₆	1	4	yes	complemented
136	D₈×C₂₉	—	2	2	no	—
137	M₁₆×C₂₉	—	2	4	no	—
138	M₁₆×C₂₉	—	4	4	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	—	4	1	no	—
144	C₂×C₈×C₂₉	—	4	4	no	—
145	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
151	C₄⋊C₄×C₂₉	—	2	1	no	—
152	C₄⋊C₄×C₂₉	—	2	1	no	—
153	C₄⋊C₄×C₂₉	—	2	1	no	—
154	C₄⋊C₄×C₂₉	—	2	1	no	—
155	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
156	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
157	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
158	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
159	C₂²⋊C₄×C₂₉	—	2	1	no	—
160	C₂²⋊C₄×C₂₉	—	2	1	no	—
161	C₂²⋊C₄×C₂₉	—	2	1	no	—
162	C₂²⋊C₄×C₂₉	—	2	1	no	—
163	C₂²⋊C₄×C₂₉	—	2	1	no	—
164	C₂²⋊C₄×C₂₉	—	2	1	no	—
165	C₄²×C₂₉	—	2	1	no	—
166	C₄²×C₂₉	—	2	1	no	—
167	C₄²×C₂₉	—	2	1	no	—
168	C₄²×C₂₉	—	2	1	no	—
169	C₄²×C₂₉	—	2	1	no	—
170	C₄²×C₂₉	—	2	1	no	—
171	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₂₉	#41	1	1	yes	characteristic
174	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
175	#18037	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂³×C₂₉	—	2	1	no	—
177	C₂³×C₂₉	—	2	1	no	—
178	C₂³×C₂₉	C₄×D₄	1	1	yes	characteristic
179	Q₈×C₂₉	—	2	1	no	—
180	Q₈×C₂₉	—	2	1	no	—
181	Q₈×C₂₉	—	2	1	no	—
182	Q₈×C₂₉	C₂×M₁₆	1	2	yes	—
183	D₄×C₂₉	—	2	1	no	—
184	D₄×C₂₉	—	2	1	no	—
185	D₄×C₂₉	—	2	1	no	—
186	D₄×C₂₉	—	4	2	no	—
187	D₄×C₂₉	—	4	2	no	—
188	D₄×C₂₉	C₂×M₁₆	1	2	yes	—
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	2	no	—
193	C₂×C₄×C₂₉	—	2	1	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	—	4	1	no	—
199	C₂×C₄×C₂₉	—	4	2	no	—
200	C₂×C₄×C₂₉	—	4	2	no	—
201	C₂×C₄×C₂₉	—	4	2	no	—
202	C₂×C₄×C₂₉	—	4	2	no	—
203	C₂×C₄×C₂₉	—	8	1	no	—
204	C₂×C₄×C₂₉	—	8	1	no	—
205	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
206	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
211	C₈×C₂₉	—	2	1	no	—
212	C₈×C₂₉	—	2	1	no	—
213	C₈×C₂₉	—	2	1	no	—
214	C₈×C₂₉	—	2	2	no	—
215	C₈×C₂₉	—	4	2	no	—
216	C₈×C₂₉	—	4	2	no	—
217	C₈×C₂₉	—	4	2	no	—
218	C₈×C₂₉	C₂×M₁₆	1	2	yes	—
219	C₈×C₂₉	#135	1	4	yes	complemented
220	#2971	C₂×C₂₉	1	1	yes	characteristic, complemented
221	#2970	C₂×C₂₉	1	1	yes	characteristic, complemented
222	C₄×#135	C₂×C₂₉	1	1	yes	characteristic
223	#1590	C₂×C₂₉	1	2	yes	complemented
224	#1584	C₂×C₂₉	1	2	yes	complemented
225	#1581	C₂×C₂₉	1	2	yes	complemented
226	C₈×SD₁₆	C₂×C₂₉	1	2	yes	complemented
227	#1568	C₂×C₂₉	1	1	yes	characteristic, complemented
228	#1488	C₂×C₂₉	1	1	yes	characteristic, complemented
229	#1488	C₂×C₂₉	1	1	yes	characteristic, complemented
230	C₈×M₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
231	C₂²×C₂₉	—	2	1	no	—
232	C₂²×C₂₉	—	2	2	no	—
233	C₂²×C₂₉	—	2	1	no	—
234	C₂²×C₂₉	—	2	1	no	—
235	C₂²×C₂₉	—	4	1	no	—
236	C₂²×C₂₉	—	4	1	no	—
237	C₂²×C₂₉	—	4	1	no	—
238	C₂²×C₂₉	—	4	1	no	—
239	C₂²×C₂₉	—	4	1	no	—
240	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
241	C₄×C₂₉	—	2	1	no	—
242	C₄×C₂₉	—	2	2	no	—
243	C₄×C₂₉	—	2	1	no	—
244	C₄×C₂₉	—	2	1	no	—
245	C₄×C₂₉	—	2	1	no	—
246	C₄×C₂₉	—	4	1	no	—
247	C₄×C₂₉	—	4	1	no	—
248	C₄×C₂₉	—	4	1	no	—
249	C₄×C₂₉	—	4	1	no	—
250	C₄×C₂₉	—	4	1	no	—
251	C₄×C₂₉	C₂²×M₁₆	1	1	yes	characteristic
252	C₄×C₂₉	#568	1	1	yes	characteristic
253	C₄×C₂₉	C₂×#135	1	2	yes	—
254	C₂×#135	C₄×C₂₉	1	1	yes	characteristic
255	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
256	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
257	#446	C₂²×C₂₉	1	2	yes	—
258	C₈×Q₈	C₂²×C₂₉	1	2	yes	—
259	C₄×Q₁₆	C₄×C₂₉	1	1	yes	characteristic
260	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
261	C₄×SD₁₆	C₄×C₂₉	1	1	yes	characteristic
262	C₄×SD₁₆	C₄×C₂₉	1	1	yes	characteristic
263	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
264	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
265	C₄×D₈	C₄×C₂₉	1	1	yes	characteristic
266	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
267	#436	—	2	2	no	—
268	#436	C₂²×C₂₉	1	2	yes	—
269	#435	—	2	2	no	—
270	C₈×D₄	C₂²×C₂₉	1	2	yes	—
271	#432	—	2	1	no	—
272	#432	—	2	1	no	—
273	#432	C₂²×C₂₉	1	1	yes	characteristic
274	#432	C₂²×C₂₉	1	1	yes	characteristic
275	#431	C₂²×C₂₉	1	1	yes	characteristic
276	#427	C₄×C₂₉	1	1	yes	characteristic
277	#416	C₄×C₂₉	1	1	yes	characteristic
278	#416	C₄×C₂₉	1	1	yes	characteristic
279	C₄×M₁₆	—	2	1	no	—
280	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
281	C₂×#97	—	2	1	no	—
282	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
283	#335	C₂²×C₂₉	1	2	yes	—
284	#334	C₂²×C₂₉	1	2	yes	—
285	Q₈⋊C₈	C₂²×C₂₉	1	2	yes	—
286	Q₈⋊C₈	C₂²×C₂₉	1	2	yes	—
287	D₄⋊C₈	C₂²×C₂₉	1	2	yes	—
288	D₄⋊C₈	C₂²×C₂₉	1	2	yes	—
289	#322	C₂²×C₂₉	1	2	yes	—
290	C₈²	C₂²×C₂₉	1	2	yes	—
291	C₂×C₂₉	—	4	1	no	—
292	C₂×C₂₉	—	4	2	no	—
293	C₂×C₂₉	—	8	1	no	—
294	C₂×C₂₉	D₄×M₁₆	1	1	yes	characteristic
295	C₂×C₂₉	C₄×#135	1	1	yes	characteristic
296	C₂×C₂₉	#2957	1	1	yes	characteristic
297	C₂×#41	C₂×C₄×C₂₉	1	1	yes	characteristic
298	C₂×#41	C₂×C₄×C₂₉	1	1	yes	characteristic
299	#135	—	2	4	no	—
300	C₂×Q₁₆	C₂×C₄×C₂₉	1	1	yes	characteristic
301	C₂×SD₁₆	C₂×C₄×C₂₉	1	1	yes	characteristic
302	C₂×SD₁₆	C₂×C₄×C₂₉	1	1	yes	characteristic
303	C₂×D₈	C₂×C₄×C₂₉	1	1	yes	characteristic
304	C₂×M₁₆	—	2	2	no	—
305	C₂×M₁₆	D₄×C₂₉	1	2	yes	—
306	C₂²×C₈	—	2	2	no	—
307	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
308	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
309	C₄×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
310	C₄×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
311	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
312	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
318	C₄×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
319	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
320	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
321	#117	—	2	1	no	—
322	#117	—	2	1	no	—
323	#117	C₂×C₄×C₂₉	1	1	yes	characteristic
324	#117	C₂×C₄×C₂₉	1	1	yes	characteristic
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
328	#107	C₂×C₄×C₂₉	1	1	yes	characteristic
329	#107	C₂×C₄×C₂₉	1	1	yes	characteristic
330	#106	C₂×C₄×C₂₉	1	1	yes	characteristic
331	#106	C₂×C₄×C₂₉	1	1	yes	characteristic
332	C₄⋊C₈	—	2	2	no	—
333	C₄⋊C₈	—	2	2	no	—
334	C₄⋊C₈	—	2	1	no	—
335	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
336	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
337	#103	C₂×C₄×C₂₉	1	1	yes	characteristic
338	#103	C₂×C₄×C₂₉	1	1	yes	characteristic
339	#103	C₂×C₄×C₂₉	1	1	yes	characteristic
340	#103	C₂×C₄×C₂₉	1	1	yes	characteristic
341	#102	C₂×C₄×C₂₉	1	1	yes	characteristic
342	#102	C₂×C₄×C₂₉	1	1	yes	characteristic
343	#102	C₂×C₄×C₂₉	1	1	yes	characteristic
344	#102	C₂×C₄×C₂₉	1	1	yes	characteristic
345	C₂²⋊C₈	—	2	1	no	—
346	C₂²⋊C₈	—	2	1	no	—
347	C₂²⋊C₈	—	2	1	no	—
348	C₂²⋊C₈	—	2	2	no	—
349	C₂²⋊C₈	—	2	2	no	—
350	#97	—	2	2	no	—
351	#97	—	2	1	no	—
352	#97	—	2	1	no	—
353	#97	D₄×C₂₉	1	1	yes	characteristic
354	#97	D₄×C₂₉	1	1	yes	characteristic
355	C₄×C₈	—	2	2	no	—
356	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
357	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
358	C₄×C₈	C₂³×C₂₉	1	2	yes	—
359	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
360	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
361	C₄×C₈	C₂³×C₂₉	1	2	yes	—
362	C₂₉	#18037	1	1	yes	characteristic, direct product factor, Sylow
363	#41	—	2	2	no	—
364	#41	—	2	2	no	—
365	#41	—	4	1	no	—
366	#41	—	4	1	no	—
367	C₂×Q₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
368	C₂×Q₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
372	C₂×D₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
381	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
382	Q₁₆	—	2	2	no	—
383	SD₁₆	—	2	2	no	—
384	SD₁₆	M₁₆×C₂₉	1	4	yes	complemented
385	D₈	—	2	2	no	—
386	M₁₆	—	2	4	no	—
387	M₁₆	—	4	4	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	4	1	no	—
393	C₂×C₈	—	4	4	no	—
394	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
395	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
396	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
397	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
398	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
399	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
405	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
406	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
407	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	1	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	2	1	no	—
420	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
421	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
422	C₄²	#41×C₂₉	1	1	yes	characteristic
423	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
424	C₂³	—	2	1	no	—
425	C₂³	—	2	1	no	—
426	C₂³	C₄×D₄×C₂₉	1	1	yes	characteristic
427	Q₈	—	2	1	no	—
428	Q₈	—	2	1	no	—
429	Q₈	—	2	1	no	—
430	Q₈	C₂×M₁₆×C₂₉	1	2	yes	—
431	D₄	—	2	1	no	—
432	D₄	—	2	1	no	—
433	D₄	—	2	1	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	D₄	C₂×M₁₆×C₂₉	1	2	yes	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	1	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	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	8	1	no	—
452	C₂×C₄	—	8	1	no	—
453	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
454	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
455	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
456	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
458	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
459	C₈	—	2	1	no	—
460	C₈	—	2	1	no	—
461	C₈	—	2	1	no	—
462	C₈	—	2	2	no	—
463	C₈	—	4	2	no	—
464	C₈	—	4	2	no	—
465	C₈	—	4	2	no	—
466	C₈	C₂×M₁₆×C₂₉	1	2	yes	—
467	C₈	C₂₉×#135	1	4	yes	complemented
468	C₂²	—	2	1	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
478	C₄	—	2	1	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	2	1	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	1	no	—
487	C₄	—	4	1	no	—
488	C₄	C₂²×M₁₆×C₂₉	1	1	yes	characteristic
489	C₄	C₂₉×#568	1	1	yes	characteristic
490	C₄	C₂×C₂₉×#135	1	2	yes	—
491	C₂	—	4	1	no	—
492	C₂	—	4	2	no	—
493	C₂	—	8	1	no	—
494	C₂	D₄×M₁₆×C₂₉	1	1	yes	characteristic
495	C₂	C₄×C₂₉×#135	1	1	yes	characteristic
496	C₂	C₂₉×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₄²	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂×C₄×D₄
prime radical	C₂×C₂₉×#135	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₄×M₁₆×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#2971	C₂	semidirect
2. C₂₉×#2970	C₂	semidirect
4. C₂₉×#1590	C₂	semidirect
5. C₂₉×#1584	C₂	semidirect
6. C₂₉×#1581	C₂	semidirect
7. C₈×SD₁₆×C₂₉	C₂	semidirect
8. C₂₉×#1568	C₂	semidirect
9. C₂₉×#1488	C₂	semidirect
10. C₂₉×#1488	C₂	semidirect
11. C₈×M₁₆×C₂₉	C₂	semidirect
135. SD₁₆×C₂₉	M₁₆	semidirect
175. #18037	C₂₉	direct (N × H)
219. C₈×C₂₉	#135	semidirect
220. #2971	C₂×C₂₉	semidirect
221. #2970	C₂×C₂₉	semidirect
223. #1590	C₂×C₂₉	semidirect
224. #1584	C₂×C₂₉	semidirect
225. #1581	C₂×C₂₉	semidirect
226. C₈×SD₁₆	C₂×C₂₉	semidirect
227. #1568	C₂×C₂₉	semidirect
228. #1488	C₂×C₂₉	semidirect
229. #1488	C₂×C₂₉	semidirect
230. C₈×M₁₆	C₂×C₂₉	semidirect
362. C₂₉	#18037	direct (N × H)
384. SD₁₆	M₁₆×C₂₉	semidirect
467. C₈	C₂₉×#135	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#2971	2
C₂₉×#2970	2
C₄×C₂₉×#135	2
C₂₉×#1590	2
C₂₉×#1584	2
C₂₉×#1581	2
C₈×SD₁₆×C₂₉	2
C₂₉×#1568	2
C₂₉×#1488	2
C₈×M₁₆×C₂₉	2
#18037	29

Subgroups — C29×#18037 #20312937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18037 #20312937