Subgroups — C₂₉×#19165 #20314065

Order 7424.

674 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3101	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×#476	C₂	1	1	yes	maximal, characteristic
4	D₄×M₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#1695	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1691	C₂	1	2	yes	maximal, complemented
7	C₂₉×#1675	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1671	C₂	1	2	yes	maximal, complemented
9	C₂₉×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1550	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1548	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×M₁₆×C₂₉	—	2	1	no	—
13	C₂₉×#533	C₂²	1	1	yes	characteristic
14	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
16	C₂₉×#501	—	2	2	no	—
17	C₂₉×#500	C₂²	1	2	yes	complemented
18	C₂₉×#498	C₂²	1	2	yes	complemented
19	C₂₉×#483	—	2	1	no	—
20	C₂₉×#476	—	2	1	no	—
21	C₂₉×#476	—	2	1	no	—
22	C₂₉×#476	C₂²	1	2	yes	—
23	C₂₉×#476	C₂²	1	1	yes	characteristic
24	C₂₉×#476	C₂²	1	2	yes	—
25	C₂₉×#476	C₂²	1	1	yes	characteristic
26	C₂₉×#461	C₂²	1	1	yes	characteristic
27	C₂₉×#461	C₂²	1	1	yes	characteristic
28	C₂₉×#450	—	2	1	no	—
29	C₄×SD₁₆×C₂₉	—	2	1	no	—
30	C₄×SD₁₆×C₂₉	—	2	1	no	—
31	C₂₉×#436	C₂²	1	2	yes	—
32	C₂₉×#435	—	2	2	no	—
33	C₈×D₄×C₂₉	C₂²	1	2	yes	—
34	C₂₉×#431	C₂²	1	1	yes	characteristic
35	C₂₉×#428	—	2	1	no	—
36	C₂₉×#428	—	2	1	no	—
37	C₂×C₂₉×#106	—	2	1	no	—
38	C₂₉×#423	C₂²	1	1	yes	characteristic
39	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₉×#102	—	2	1	no	—
41	C₂₉×#407	—	2	1	no	—
42	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
43	C₂₉×#335	C₂²	1	2	yes	complemented
44	C₂₉×#334	C₂²	1	2	yes	complemented
45	C₂₉×#333	C₂²	1	2	yes	complemented
46	C₂₉×#333	C₂²	1	2	yes	complemented
47	C₂₉×#333	C₂²	1	2	yes	complemented
48	C₂₉×#332	C₂²	1	2	yes	complemented
49	C₂²×Q₈×C₂₉	—	2	1	no	—
50	C₂²×D₄×C₂₉	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₂₉	—	2	1	no	—
52	C₂×SD₁₆×C₂₉	—	2	1	no	—
53	C₂×SD₁₆×C₂₉	—	2	1	no	—
54	C₂×M₁₆×C₂₉	—	2	1	no	—
55	C₂×M₁₆×C₂₉	—	2	2	no	—
56	C₂×M₁₆×C₂₉	—	4	4	no	—
57	C₂×M₁₆×C₂₉	D₄	1	1	yes	characteristic
58	C₂×M₁₆×C₂₉	D₄	1	1	yes	characteristic
59	C₂²×C₈×C₂₉	—	2	1	no	—
60	C₂²×C₈×C₂₉	—	2	2	no	—
61	C₂₉×C₄⋊Q₈	—	2	1	no	—
62	C₂₉×C₄⋊Q₈	—	2	1	no	—
63	C₂₉×C₄⋊Q₈	—	2	1	no	—
64	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₂₉×#125	—	2	1	no	—
68	C₂₉×C₂²⋊Q₈	—	2	1	no	—
69	C₂₉×C₂²⋊Q₈	—	2	1	no	—
70	C₄×Q₈×C₂₉	—	2	1	no	—
71	C₄×Q₈×C₂₉	—	2	1	no	—
72	C₄×D₄×C₂₉	—	2	1	no	—
73	C₄×D₄×C₂₉	—	2	1	no	—
74	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
75	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
76	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
77	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
78	C₂₉×#117	—	2	1	no	—
79	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
83	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
84	C₂₉×#107	—	2	2	no	—
85	C₂₉×#107	—	2	2	no	—
86	C₂₉×#106	—	2	2	no	—
87	C₂₉×#106	—	2	2	no	—
88	C₂₉×#106	—	2	2	no	—
89	C₂₉×#106	—	2	2	no	—
90	C₂₉×#106	—	2	1	no	—
91	C₂₉×#106	—	2	1	no	—
92	C₂₉×C₄⋊C₈	—	2	1	no	—
93	C₂₉×C₄⋊C₈	—	2	1	no	—
94	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
95	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
96	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
97	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
98	C₂₉×#103	—	2	1	no	—
99	C₂₉×#103	—	2	1	no	—
100	C₂₉×#102	—	2	1	no	—
101	C₂₉×#102	—	2	1	no	—
102	C₂₉×#102	—	2	2	no	—
103	C₂₉×#102	—	2	2	no	—
104	C₂₉×C₂²⋊C₈	—	2	1	no	—
105	C₂₉×C₂²⋊C₈	—	2	2	no	—
106	C₂₉×C₂²⋊C₈	—	2	2	no	—
107	C₂₉×#97	D₄	1	2	yes	—
108	C₄×C₈×C₂₉	—	2	1	no	—
109	C₄×C₈×C₂₉	C₂³	1	2	yes	—
110	C₂⁴×C₂₉	—	2	1	no	—
111	C₂×Q₈×C₂₉	—	2	1	no	—
112	C₂×Q₈×C₂₉	—	2	1	no	—
113	C₂×Q₈×C₂₉	—	2	2	no	—
114	C₂×Q₈×C₂₉	—	4	1	no	—
115	C₂×Q₈×C₂₉	—	8	2	no	—
116	C₂×D₄×C₂₉	—	2	2	no	—
117	C₂×D₄×C₂₉	—	2	1	no	—
118	C₂×D₄×C₂₉	—	4	1	no	—
119	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
120	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₂₉	—	2	1	no	—
122	C₂²×C₄×C₂₉	—	2	1	no	—
123	C₂²×C₄×C₂₉	—	2	1	no	—
124	C₂²×C₄×C₂₉	—	2	1	no	—
125	C₂²×C₄×C₂₉	—	2	1	no	—
126	C₂²×C₄×C₂₉	—	4	2	no	—
127	C₂²×C₄×C₂₉	—	4	2	no	—
128	C₂²×C₄×C₂₉	—	4	1	no	—
129	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
132	SD₁₆×C₂₉	—	4	2	no	—
133	SD₁₆×C₂₉	—	4	2	no	—
134	M₁₆×C₂₉	—	2	2	no	—
135	M₁₆×C₂₉	—	4	2	no	—
136	M₁₆×C₂₉	—	4	4	no	—
137	M₁₆×C₂₉	SD₁₆	1	4	yes	complemented
138	C₂×C₈×C₂₉	—	2	2	no	—
139	C₂×C₈×C₂₉	—	2	2	no	—
140	C₂×C₈×C₂₉	—	2	1	no	—
141	C₂×C₈×C₂₉	—	2	1	no	—
142	C₂×C₈×C₂₉	—	4	2	no	—
143	C₂×C₈×C₂₉	—	4	4	no	—
144	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
146	C₄⋊C₄×C₂₉	—	2	1	no	—
147	C₄⋊C₄×C₂₉	—	2	2	no	—
148	C₄⋊C₄×C₂₉	—	2	2	no	—
149	C₄⋊C₄×C₂₉	—	2	1	no	—
150	C₄⋊C₄×C₂₉	—	2	1	no	—
151	C₄⋊C₄×C₂₉	—	2	1	no	—
152	C₄⋊C₄×C₂₉	—	2	1	no	—
153	C₄⋊C₄×C₂₉	—	4	1	no	—
154	C₄⋊C₄×C₂₉	—	4	1	no	—
155	C₄⋊C₄×C₂₉	—	4	1	no	—
156	C₄⋊C₄×C₂₉	—	4	1	no	—
157	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
158	C₄⋊C₄×C₂₉	C₂×D₄	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	—	4	1	no	—
164	C₄²×C₂₉	—	4	1	no	—
165	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₂₉	#41	1	1	yes	characteristic
168	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
169	#19165	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂³×C₂₉	—	2	1	no	—
171	C₂³×C₂₉	—	2	1	no	—
172	C₂³×C₂₉	—	4	2	no	—
173	C₂³×C₂₉	—	4	2	no	—
174	C₂³×C₂₉	—	8	1	no	—
175	C₂³×C₂₉	#121	1	1	yes	characteristic
176	Q₈×C₂₉	—	4	1	no	—
177	Q₈×C₂₉	—	4	1	no	—
178	Q₈×C₂₉	—	8	1	no	—
179	Q₈×C₂₉	—	8	2	no	—
180	Q₈×C₂₉	—	8	2	no	—
181	D₄×C₂₉	—	2	1	no	—
182	D₄×C₂₉	—	2	1	no	—
183	D₄×C₂₉	—	2	1	no	—
184	D₄×C₂₉	—	4	2	no	—
185	D₄×C₂₉	#137	1	2	yes	—
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	—	4	1	no	—
191	C₂×C₄×C₂₉	—	4	2	no	—
192	C₂×C₄×C₂₉	—	4	1	no	—
193	C₂×C₄×C₂₉	—	4	1	no	—
194	C₂×C₄×C₂₉	—	4	1	no	—
195	C₂×C₄×C₂₉	—	4	1	no	—
196	C₂×C₄×C₂₉	—	4	2	no	—
197	C₂×C₄×C₂₉	—	4	2	no	—
198	C₂×C₄×C₂₉	—	4	1	no	—
199	C₂×C₄×C₂₉	—	4	1	no	—
200	C₂×C₄×C₂₉	—	4	2	no	—
201	C₂×C₄×C₂₉	—	8	2	no	—
202	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
203	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
204	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
205	C₂×C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
206	C₂×C₄×C₂₉	#137	1	2	yes	—
207	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
210	C₈×C₂₉	—	2	2	no	—
211	C₈×C₂₉	—	4	2	no	—
212	C₈×C₂₉	—	4	1	no	—
213	C₈×C₂₉	—	4	2	no	—
214	C₈×C₂₉	—	4	1	no	—
215	C₈×C₂₉	C₂×SD₁₆	1	4	yes	—
216	#3165	C₂×C₂₉	1	1	yes	characteristic, complemented
217	#3101	C₂×C₂₉	1	1	yes	characteristic
218	C₂×#476	C₂×C₂₉	1	1	yes	characteristic
219	D₄×M₁₆	C₂×C₂₉	1	1	yes	characteristic
220	#1695	C₂×C₂₉	1	2	yes	complemented
221	#1691	C₂×C₂₉	1	2	yes	complemented
222	#1675	C₂×C₂₉	1	2	yes	complemented
223	#1671	C₂×C₂₉	1	2	yes	complemented
224	#1565	C₂×C₂₉	1	1	yes	characteristic, complemented
225	#1550	C₂×C₂₉	1	1	yes	characteristic, complemented
226	#1548	C₂×C₂₉	1	1	yes	characteristic, complemented
227	C₂²×C₂₉	—	2	1	no	—
228	C₂²×C₂₉	—	2	1	no	—
229	C₂²×C₂₉	—	2	2	no	—
230	C₂²×C₂₉	—	4	1	no	—
231	C₂²×C₂₉	—	4	1	no	—
232	C₂²×C₂₉	—	4	1	no	—
233	C₂²×C₂₉	—	4	1	no	—
234	C₂²×C₂₉	—	4	1	no	—
235	C₂²×C₂₉	—	8	4	no	—
236	C₂²×C₂₉	#461	1	2	yes	—
237	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
238	C₄×C₂₉	—	2	1	no	—
239	C₄×C₂₉	—	2	1	no	—
240	C₄×C₂₉	—	2	1	no	—
241	C₄×C₂₉	—	4	1	no	—
242	C₄×C₂₉	—	4	1	no	—
243	C₄×C₂₉	—	8	1	no	—
244	C₄×C₂₉	—	8	2	no	—
245	C₄×C₂₉	—	8	1	no	—
246	C₄×C₂₉	#461	1	2	yes	—
247	C₄×C₂₉	C₂²×SD₁₆	1	1	yes	characteristic
248	C₄×C₂₉	C₂×#137	1	1	yes	characteristic
249	C₄×C₂₉	C₂×#137	1	1	yes	characteristic
250	C₄×C₂₉	#575	1	1	yes	characteristic
251	C₂²×M₁₆	—	2	1	no	—
252	#533	C₂²×C₂₉	1	1	yes	characteristic
253	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
255	#501	—	2	2	no	—
256	#500	C₂²×C₂₉	1	2	yes	complemented
257	#498	C₂²×C₂₉	1	2	yes	complemented
258	#483	—	2	1	no	—
259	#476	—	2	1	no	—
260	#476	—	2	1	no	—
261	#476	C₂²×C₂₉	1	1	yes	characteristic
262	#476	C₂²×C₂₉	1	1	yes	characteristic
263	#476	C₂²×C₂₉	1	2	yes	—
264	#476	C₂²×C₂₉	1	2	yes	—
265	#461	C₂²×C₂₉	1	1	yes	characteristic
266	#461	C₂²×C₂₉	1	1	yes	characteristic
267	#450	—	2	1	no	—
268	C₄×SD₁₆	—	2	1	no	—
269	C₄×SD₁₆	—	2	1	no	—
270	#436	C₂²×C₂₉	1	2	yes	—
271	#435	—	2	2	no	—
272	C₈×D₄	C₂²×C₂₉	1	2	yes	—
273	#431	C₂²×C₂₉	1	1	yes	characteristic
274	#428	—	2	1	no	—
275	#428	—	2	1	no	—
276	C₂×#106	—	2	1	no	—
277	#423	C₂²×C₂₉	1	1	yes	characteristic
278	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
279	C₂×#102	—	2	1	no	—
280	#407	—	2	1	no	—
281	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
282	#335	C₂²×C₂₉	1	2	yes	complemented
283	#334	C₂²×C₂₉	1	2	yes	complemented
284	#333	C₂²×C₂₉	1	2	yes	complemented
285	#333	C₂²×C₂₉	1	2	yes	complemented
286	#333	C₂²×C₂₉	1	2	yes	complemented
287	#332	C₂²×C₂₉	1	2	yes	complemented
288	C₂×C₂₉	—	2	2	no	—
289	C₂×C₂₉	—	4	2	no	—
290	C₂×C₂₉	—	8	1	no	—
291	C₂×C₂₉	C₂×#461	1	1	yes	characteristic
292	C₂×C₂₉	#3056	1	1	yes	characteristic
293	C₂×C₂₉	#3068	1	1	yes	characteristic
294	C₂²×Q₈	—	2	1	no	—
295	C₂²×D₄	D₄×C₂₉	1	1	yes	characteristic
296	C₂³×C₄	—	2	1	no	—
297	C₂×SD₁₆	—	2	1	no	—
298	C₂×SD₁₆	—	2	1	no	—
299	C₂×M₁₆	—	2	1	no	—
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	—	4	4	no	—
302	C₂×M₁₆	D₄×C₂₉	1	1	yes	characteristic
303	C₂×M₁₆	D₄×C₂₉	1	1	yes	characteristic
304	C₂²×C₈	—	2	1	no	—
305	C₂²×C₈	—	2	2	no	—
306	C₄⋊Q₈	—	2	1	no	—
307	C₄⋊Q₈	—	2	1	no	—
308	C₄⋊Q₈	—	2	1	no	—
309	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
310	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
311	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
312	#125	—	2	1	no	—
313	C₂²⋊Q₈	—	2	1	no	—
314	C₂²⋊Q₈	—	2	1	no	—
315	C₄×Q₈	—	2	1	no	—
316	C₄×Q₈	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	—	2	1	no	—
319	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
320	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
321	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
322	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
323	#117	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
329	#107	—	2	2	no	—
330	#107	—	2	2	no	—
331	#106	—	2	2	no	—
332	#106	—	2	2	no	—
333	#106	—	2	2	no	—
334	#106	—	2	2	no	—
335	#106	—	2	1	no	—
336	#106	—	2	1	no	—
337	C₄⋊C₈	—	2	1	no	—
338	C₄⋊C₈	—	2	1	no	—
339	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
340	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
341	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
342	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
343	#103	—	2	1	no	—
344	#103	—	2	1	no	—
345	#102	—	2	2	no	—
346	#102	—	2	2	no	—
347	#102	—	2	1	no	—
348	#102	—	2	1	no	—
349	C₂²⋊C₈	—	2	1	no	—
350	C₂²⋊C₈	—	2	2	no	—
351	C₂²⋊C₈	—	2	2	no	—
352	#97	D₄×C₂₉	1	2	yes	—
353	C₄×C₈	—	2	1	no	—
354	C₄×C₈	C₂³×C₂₉	1	2	yes	—
355	C₂₉	#19165	1	1	yes	characteristic, direct product factor, Sylow
356	C₂⁴	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	4	1	no	—
361	C₂×Q₈	—	8	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	4	1	no	—
365	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
366	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
377	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
378	SD₁₆	—	4	2	no	—
379	SD₁₆	—	4	2	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	4	2	no	—
382	M₁₆	—	4	4	no	—
383	M₁₆	SD₁₆×C₂₉	1	4	yes	complemented
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	4	2	no	—
389	C₂×C₈	—	4	4	no	—
390	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
391	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	4	1	no	—
400	C₄⋊C₄	—	4	1	no	—
401	C₄⋊C₄	—	4	1	no	—
402	C₄⋊C₄	—	4	1	no	—
403	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
404	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	—	2	1	no	—
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	4	1	no	—
410	C₄²	—	4	1	no	—
411	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
412	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
413	C₄²	#41×C₂₉	1	1	yes	characteristic
414	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
415	C₂³	—	2	1	no	—
416	C₂³	—	2	1	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	8	1	no	—
420	C₂³	C₂₉×#121	1	1	yes	characteristic
421	Q₈	—	4	1	no	—
422	Q₈	—	4	1	no	—
423	Q₈	—	8	2	no	—
424	Q₈	—	8	1	no	—
425	Q₈	—	8	2	no	—
426	D₄	—	2	1	no	—
427	D₄	—	2	1	no	—
428	D₄	—	2	1	no	—
429	D₄	—	4	2	no	—
430	D₄	C₂₉×#137	1	2	yes	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	8	2	no	—
447	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
448	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
449	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
450	C₂×C₄	C₂×SD₁₆×C₂₉	1	2	yes	—
451	C₂×C₄	C₂₉×#137	1	2	yes	—
452	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
454	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
455	C₈	—	2	2	no	—
456	C₈	—	4	2	no	—
457	C₈	—	4	1	no	—
458	C₈	—	4	2	no	—
459	C₈	—	4	1	no	—
460	C₈	C₂×SD₁₆×C₂₉	1	4	yes	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	4	1	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	8	4	no	—
470	C₂²	C₂₉×#461	1	2	yes	—
471	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	2	1	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	1	no	—
477	C₄	—	8	1	no	—
478	C₄	—	8	2	no	—
479	C₄	—	8	1	no	—
480	C₄	C₂₉×#461	1	2	yes	—
481	C₄	C₂²×SD₁₆×C₂₉	1	1	yes	characteristic
482	C₄	C₂×C₂₉×#137	1	1	yes	characteristic
483	C₄	C₂×C₂₉×#137	1	1	yes	characteristic
484	C₄	C₂₉×#575	1	1	yes	characteristic
485	C₂	—	2	2	no	—
486	C₂	—	4	2	no	—
487	C₂	—	8	1	no	—
488	C₂	C₂×C₂₉×#461	1	1	yes	characteristic
489	C₂	C₂₉×#3056	1	1	yes	characteristic
490	C₂	C₂₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂²×D₄×C₂₉	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3165	C₂	semidirect
5. C₂₉×#1695	C₂	semidirect
6. C₂₉×#1691	C₂	semidirect
7. C₂₉×#1675	C₂	semidirect
8. C₂₉×#1671	C₂	semidirect
9. C₂₉×#1565	C₂	semidirect
10. C₂₉×#1550	C₂	semidirect
11. C₂₉×#1548	C₂	semidirect
17. C₂₉×#500	C₂²	semidirect
18. C₂₉×#498	C₂²	semidirect
43. C₂₉×#335	C₂²	semidirect
44. C₂₉×#334	C₂²	semidirect
45. C₂₉×#333	C₂²	semidirect
46. C₂₉×#333	C₂²	semidirect
47. C₂₉×#333	C₂²	semidirect
48. C₂₉×#332	C₂²	semidirect
137. M₁₆×C₂₉	SD₁₆	semidirect
169. #19165	C₂₉	direct (N × H)
216. #3165	C₂×C₂₉	semidirect
220. #1695	C₂×C₂₉	semidirect
221. #1691	C₂×C₂₉	semidirect
222. #1675	C₂×C₂₉	semidirect
223. #1671	C₂×C₂₉	semidirect
224. #1565	C₂×C₂₉	semidirect
225. #1550	C₂×C₂₉	semidirect
226. #1548	C₂×C₂₉	semidirect
256. #500	C₂²×C₂₉	semidirect
257. #498	C₂²×C₂₉	semidirect
282. #335	C₂²×C₂₉	semidirect
283. #334	C₂²×C₂₉	semidirect
284. #333	C₂²×C₂₉	semidirect
285. #333	C₂²×C₂₉	semidirect
286. #333	C₂²×C₂₉	semidirect
287. #332	C₂²×C₂₉	semidirect
355. C₂₉	#19165	direct (N × H)
383. M₁₆	SD₁₆×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#3165	2
C₂₉×#3101	2
C₂×C₂₉×#476	2
D₄×M₁₆×C₂₉	2
C₂₉×#1695	2
C₂₉×#1691	2
C₂₉×#1675	2
C₂₉×#1671	2
C₂₉×#1565	2
C₂₉×#1550	2
C₂₉×#1548	2
#19165	29

Subgroups — C29×#19165 #20314065

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19165 #20314065