Subgroups — C₂₉×#19740 #20314640

Order 7424.

704 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3230	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3228	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3226	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3210	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#3207	C₂	1	1	yes	maximal, characteristic
6	C₂₉×#3206	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1723	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1722	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1719	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1719	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1717	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1714	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1710	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1706	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1454	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#533	C₂²	1	1	yes	characteristic
17	C₂₉×#532	C₂²	1	1	yes	characteristic
18	C₂₉×#532	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂₉×#500	C₂²	1	1	yes	characteristic
21	C₂₉×#500	C₂²	1	1	yes	characteristic
22	C₂₉×#500	C₂²	1	1	yes	characteristic
23	C₂₉×#500	C₂²	1	1	yes	characteristic
24	C₂₉×#500	C₂²	1	1	yes	characteristic
25	C₂₉×#498	C₂²	1	1	yes	characteristic
26	C₂₉×#494	C₂²	1	1	yes	characteristic
27	C₂₉×#493	C₂²	1	1	yes	characteristic
28	C₂₉×#492	C₂²	1	1	yes	characteristic
29	C₂₉×#492	C₂²	1	1	yes	characteristic
30	C₂₉×#492	C₂²	1	1	yes	characteristic
31	C₂₉×#492	C₂²	1	1	yes	characteristic
32	C₂₉×#487	C₂²	1	1	yes	characteristic
33	C₂₉×#487	C₂²	1	1	yes	characteristic
34	C₂₉×#487	C₂²	1	1	yes	characteristic
35	C₂₉×#487	C₂²	1	1	yes	characteristic
36	C₂₉×#487	C₂²	1	1	yes	characteristic
37	C₂₉×#487	C₂²	1	1	yes	characteristic
38	C₂₉×#486	C₂²	1	1	yes	characteristic
39	C₂₉×#486	C₂²	1	1	yes	characteristic
40	C₂₉×#486	C₂²	1	1	yes	characteristic
41	C₂₉×#486	C₂²	1	1	yes	characteristic
42	C₂₉×#486	C₂²	1	1	yes	characteristic
43	C₂₉×#486	C₂²	1	1	yes	characteristic
44	C₂₉×#484	—	2	2	no	—
45	C₂₉×#482	—	2	2	no	—
46	C₂₉×#480	—	2	2	no	—
47	C₂₉×#478	—	2	2	no	—
48	C₂₉×#477	—	2	2	no	—
49	C₂₉×#474	—	2	2	no	—
50	C₂₉×#464	—	2	2	no	—
51	C₂₉×#463	—	2	2	no	—
52	C₂₉×#461	—	2	2	no	—
53	C₂₉×#452	—	2	2	no	—
54	C₂₉×#449	—	2	2	no	—
55	C₂₉×#448	—	2	2	no	—
56	C₂₉×#431	C₂²	1	1	yes	characteristic
57	C₂₉×#431	C₂²	1	1	yes	characteristic
58	C₂₉×#431	C₂²	1	1	yes	characteristic
59	C₂₉×#322	C₂²	1	1	yes	characteristic
60	C₂₉×#322	C₂²	1	1	yes	characteristic
61	C₂₉×#322	C₂²	1	1	yes	characteristic
62	C₈²×C₂₉	C₂²	1	1	yes	characteristic
63	C₂×#41×C₂₉	—	2	1	no	—
64	C₂×#41×C₂₉	—	2	1	no	—
65	C₂²×Q₈×C₂₉	—	2	1	no	—
66	C₂×Q₁₆×C₂₉	—	2	2	no	—
67	C₂×SD₁₆×C₂₉	—	2	2	no	—
68	C₂×SD₁₆×C₂₉	—	2	2	no	—
69	C₂×SD₁₆×C₂₉	—	2	2	no	—
70	C₂×SD₁₆×C₂₉	—	2	2	no	—
71	C₂×D₈×C₂₉	—	2	2	no	—
72	C₂₉×C₄⋊Q₈	—	2	1	no	—
73	C₂₉×C₄⋊Q₈	—	2	1	no	—
74	C₂₉×C₄⋊Q₈	—	2	1	no	—
75	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
76	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
77	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
78	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₂₉×#127	C₂³	1	1	yes	characteristic
82	C₂₉×#127	C₂³	1	1	yes	characteristic
83	C₂₉×#125	—	2	1	no	—
84	C₂₉×#124	—	2	1	no	—
85	C₂₉×#124	—	2	1	no	—
86	C₂₉×C₂²⋊Q₈	—	2	1	no	—
87	C₂₉×C₂²⋊Q₈	—	2	1	no	—
88	C₂₉×#121	—	2	1	no	—
89	C₂₉×#121	—	2	1	no	—
90	C₂₉×#121	—	2	1	no	—
91	C₂₉×#121	—	2	1	no	—
92	C₄×Q₈×C₂₉	—	2	1	no	—
93	C₄×Q₈×C₂₉	—	2	1	no	—
94	C₄×D₄×C₂₉	—	2	1	no	—
95	C₄×D₄×C₂₉	—	2	1	no	—
96	C₄×D₄×C₂₉	—	2	1	no	—
97	C₄×D₄×C₂₉	—	2	1	no	—
98	C₂₉×#117	—	2	1	no	—
99	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
101	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
102	C₂₉×#107	—	2	2	no	—
103	C₂₉×#107	—	2	2	no	—
104	C₂₉×#107	—	2	2	no	—
105	C₂₉×#107	—	2	2	no	—
106	C₂₉×#107	—	2	2	no	—
107	C₂₉×#106	—	2	2	no	—
108	C₂₉×C₄⋊C₈	D₄	1	2	yes	—
109	C₂₉×C₄⋊C₈	D₄	1	2	yes	—
110	C₂₉×C₄⋊C₈	D₄	1	2	yes	—
111	C₂₉×#103	—	2	2	no	—
112	C₂₉×#103	—	2	2	no	—
113	C₂₉×#103	—	2	2	no	—
114	C₂₉×#103	—	2	2	no	—
115	C₂₉×#103	—	2	2	no	—
116	C₂₉×#103	—	2	2	no	—
117	C₂₉×#102	—	2	2	no	—
118	C₂₉×#102	—	2	2	no	—
119	C₂₉×#102	—	2	2	no	—
120	C₂₉×#102	—	2	2	no	—
121	C₂₉×#102	—	2	2	no	—
122	C₂₉×#102	—	2	2	no	—
123	C₂₉×C₂²⋊C₈	D₄	1	2	yes	—
124	C₂₉×C₂²⋊C₈	D₄	1	2	yes	—
125	C₂₉×C₂²⋊C₈	D₄	1	2	yes	—
126	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
127	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
128	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
129	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
130	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
131	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
132	#41×C₂₉	—	8	2	no	—
133	#41×C₂₉	—	8	2	no	—
134	C₂×Q₈×C₂₉	—	2	1	no	—
135	C₂×Q₈×C₂₉	—	2	1	no	—
136	C₂×Q₈×C₂₉	—	2	1	no	—
137	C₂×Q₈×C₂₉	—	2	1	no	—
138	C₂×Q₈×C₂₉	—	2	1	no	—
139	C₂×Q₈×C₂₉	—	2	1	no	—
140	C₂×Q₈×C₂₉	—	4	1	no	—
141	C₂×Q₈×C₂₉	—	8	2	no	—
142	C₂×D₄×C₂₉	—	2	1	no	—
143	C₂×D₄×C₂₉	—	2	1	no	—
144	C₂×D₄×C₂₉	—	2	1	no	—
145	C₂×D₄×C₂₉	—	2	1	no	—
146	C₂×D₄×C₂₉	—	2	1	no	—
147	C₂×D₄×C₂₉	—	2	1	no	—
148	C₂×D₄×C₂₉	—	4	1	no	—
149	C₂×D₄×C₂₉	—	4	1	no	—
150	C₂²×C₄×C₂₉	—	4	1	no	—
151	C₂²×C₄×C₂₉	—	4	1	no	—
152	C₂²×C₄×C₂₉	—	4	1	no	—
153	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
156	Q₁₆×C₂₉	—	8	2	no	—
157	SD₁₆×C₂₉	—	8	2	no	—
158	SD₁₆×C₂₉	—	8	2	no	—
159	SD₁₆×C₂₉	—	8	2	no	—
160	SD₁₆×C₂₉	—	8	2	no	—
161	D₈×C₂₉	—	8	2	no	—
162	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
163	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
164	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
165	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
166	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
167	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
168	C₄⋊C₄×C₂₉	—	2	1	no	—
169	C₄⋊C₄×C₂₉	—	2	1	no	—
170	C₄⋊C₄×C₂₉	—	2	1	no	—
171	C₄⋊C₄×C₂₉	—	2	1	no	—
172	C₄⋊C₄×C₂₉	—	2	1	no	—
173	C₄⋊C₄×C₂₉	—	2	1	no	—
174	C₄⋊C₄×C₂₉	—	2	1	no	—
175	C₄⋊C₄×C₂₉	—	2	1	no	—
176	C₄⋊C₄×C₂₉	—	2	1	no	—
177	C₄⋊C₄×C₂₉	—	2	1	no	—
178	C₄⋊C₄×C₂₉	—	2	1	no	—
179	C₄⋊C₄×C₂₉	—	2	1	no	—
180	C₄⋊C₄×C₂₉	—	4	1	no	—
181	C₄⋊C₄×C₂₉	—	4	1	no	—
182	C₄⋊C₄×C₂₉	—	4	1	no	—
183	C₄⋊C₄×C₂₉	—	4	1	no	—
184	C₂²⋊C₄×C₂₉	—	4	1	no	—
185	C₂²⋊C₄×C₂₉	—	4	1	no	—
186	C₂²⋊C₄×C₂₉	—	4	1	no	—
187	C₂²⋊C₄×C₂₉	—	4	1	no	—
188	C₂²⋊C₄×C₂₉	—	4	1	no	—
189	C₄²×C₂₉	—	4	1	no	—
190	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
194	#19740	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂³×C₂₉	—	4	1	no	—
196	C₂³×C₂₉	—	4	1	no	—
197	C₂³×C₂₉	#127	1	1	yes	characteristic
198	Q₈×C₂₉	—	4	2	no	—
199	Q₈×C₂₉	—	4	2	no	—
200	Q₈×C₂₉	—	4	2	no	—
201	Q₈×C₂₉	—	4	2	no	—
202	Q₈×C₂₉	—	4	2	no	—
203	Q₈×C₂₉	—	4	2	no	—
204	Q₈×C₂₉	—	8	2	no	—
205	D₄×C₂₉	—	4	2	no	—
206	D₄×C₂₉	—	4	2	no	—
207	D₄×C₂₉	—	4	2	no	—
208	D₄×C₂₉	—	4	2	no	—
209	D₄×C₂₉	—	4	2	no	—
210	D₄×C₂₉	—	4	2	no	—
211	D₄×C₂₉	—	8	2	no	—
212	D₄×C₂₉	—	8	2	no	—
213	C₂×C₄×C₂₉	—	2	2	no	—
214	C₂×C₄×C₂₉	—	2	2	no	—
215	C₂×C₄×C₂₉	—	2	2	no	—
216	C₂×C₄×C₂₉	—	4	1	no	—
217	C₂×C₄×C₂₉	—	4	1	no	—
218	C₂×C₄×C₂₉	—	4	1	no	—
219	C₂×C₄×C₂₉	—	4	1	no	—
220	C₂×C₄×C₂₉	—	4	1	no	—
221	C₂×C₄×C₂₉	—	4	1	no	—
222	C₂×C₄×C₂₉	—	8	2	no	—
223	C₂×C₄×C₂₉	—	8	2	no	—
224	C₂×C₄×C₂₉	—	8	2	no	—
225	C₂×C₄×C₂₉	#127	1	1	yes	characteristic
226	C₂×C₄×C₂₉	#127	1	1	yes	characteristic
227	C₂×C₄×C₂₉	#127	1	1	yes	characteristic
228	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
231	C₈×C₂₉	—	2	2	no	—
232	C₈×C₂₉	—	2	2	no	—
233	C₈×C₂₉	—	2	2	no	—
234	C₈×C₂₉	—	2	2	no	—
235	C₈×C₂₉	—	2	2	no	—
236	C₈×C₂₉	—	2	2	no	—
237	#3230	C₂×C₂₉	1	1	yes	characteristic, complemented
238	#3228	C₂×C₂₉	1	1	yes	characteristic, complemented
239	#3226	C₂×C₂₉	1	1	yes	characteristic, complemented
240	#3210	C₂×C₂₉	1	1	yes	characteristic, complemented
241	#3207	C₂×C₂₉	1	1	yes	characteristic
242	#3206	C₂×C₂₉	1	1	yes	characteristic, complemented
243	#1723	C₂×C₂₉	1	1	yes	characteristic, complemented
244	#1722	C₂×C₂₉	1	1	yes	characteristic, complemented
245	#1719	C₂×C₂₉	1	1	yes	characteristic, complemented
246	#1719	C₂×C₂₉	1	1	yes	characteristic, complemented
247	#1717	C₂×C₂₉	1	1	yes	characteristic, complemented
248	#1714	C₂×C₂₉	1	1	yes	characteristic, complemented
249	#1710	C₂×C₂₉	1	1	yes	characteristic, complemented
250	#1706	C₂×C₂₉	1	1	yes	characteristic, complemented
251	#1454	C₂×C₂₉	1	1	yes	characteristic, complemented
252	C₂²×C₂₉	—	2	1	no	—
253	C₂²×C₂₉	—	2	1	no	—
254	C₂²×C₂₉	—	2	1	no	—
255	C₂²×C₂₉	—	8	1	no	—
256	C₂²×C₂₉	—	8	1	no	—
257	C₂²×C₂₉	—	8	1	no	—
258	C₂²×C₂₉	—	8	1	no	—
259	C₂²×C₂₉	—	8	1	no	—
260	C₂²×C₂₉	—	8	1	no	—
261	C₂²×C₂₉	C₂×#127	1	1	yes	characteristic
262	C₄×C₂₉	—	2	1	no	—
263	C₄×C₂₉	—	2	1	no	—
264	C₄×C₂₉	—	2	1	no	—
265	C₄×C₂₉	—	8	1	no	—
266	C₄×C₂₉	—	8	1	no	—
267	C₄×C₂₉	—	8	1	no	—
268	C₄×C₂₉	—	8	1	no	—
269	C₄×C₂₉	—	8	1	no	—
270	C₄×C₂₉	—	8	1	no	—
271	C₄×C₂₉	#576	1	2	yes	—
272	C₄×C₂₉	#577	1	2	yes	—
273	C₄×C₂₉	#578	1	2	yes	—
274	#533	C₂²×C₂₉	1	1	yes	characteristic
275	#532	C₂²×C₂₉	1	1	yes	characteristic
276	#532	C₂²×C₂₉	1	1	yes	characteristic
277	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
278	#500	C₂²×C₂₉	1	1	yes	characteristic
279	#500	C₂²×C₂₉	1	1	yes	characteristic
280	#500	C₂²×C₂₉	1	1	yes	characteristic
281	#500	C₂²×C₂₉	1	1	yes	characteristic
282	#500	C₂²×C₂₉	1	1	yes	characteristic
283	#498	C₂²×C₂₉	1	1	yes	characteristic
284	#494	C₂²×C₂₉	1	1	yes	characteristic
285	#493	C₂²×C₂₉	1	1	yes	characteristic
286	#492	C₂²×C₂₉	1	1	yes	characteristic
287	#492	C₂²×C₂₉	1	1	yes	characteristic
288	#492	C₂²×C₂₉	1	1	yes	characteristic
289	#492	C₂²×C₂₉	1	1	yes	characteristic
290	#487	C₂²×C₂₉	1	1	yes	characteristic
291	#487	C₂²×C₂₉	1	1	yes	characteristic
292	#487	C₂²×C₂₉	1	1	yes	characteristic
293	#487	C₂²×C₂₉	1	1	yes	characteristic
294	#487	C₂²×C₂₉	1	1	yes	characteristic
295	#487	C₂²×C₂₉	1	1	yes	characteristic
296	#486	C₂²×C₂₉	1	1	yes	characteristic
297	#486	C₂²×C₂₉	1	1	yes	characteristic
298	#486	C₂²×C₂₉	1	1	yes	characteristic
299	#486	C₂²×C₂₉	1	1	yes	characteristic
300	#486	C₂²×C₂₉	1	1	yes	characteristic
301	#486	C₂²×C₂₉	1	1	yes	characteristic
302	#484	—	2	2	no	—
303	#482	—	2	2	no	—
304	#480	—	2	2	no	—
305	#478	—	2	2	no	—
306	#477	—	2	2	no	—
307	#474	—	2	2	no	—
308	#464	—	2	2	no	—
309	#463	—	2	2	no	—
310	#461	—	2	2	no	—
311	#452	—	2	2	no	—
312	#449	—	2	2	no	—
313	#448	—	2	2	no	—
314	#431	C₂²×C₂₉	1	1	yes	characteristic
315	#431	C₂²×C₂₉	1	1	yes	characteristic
316	#431	C₂²×C₂₉	1	1	yes	characteristic
317	#322	C₂²×C₂₉	1	1	yes	characteristic
318	#322	C₂²×C₂₉	1	1	yes	characteristic
319	#322	C₂²×C₂₉	1	1	yes	characteristic
320	C₈²	C₂²×C₂₉	1	1	yes	characteristic
321	C₂×C₂₉	—	4	1	no	—
322	C₂×C₂₉	—	16	1	no	—
323	C₂×C₂₉	—	16	1	no	—
324	C₂×C₂₉	#3154	1	1	yes	characteristic
325	C₂×C₂₉	#3155	1	1	yes	characteristic
326	C₂×C₂₉	#3156	1	1	yes	characteristic
327	C₂×#41	—	2	1	no	—
328	C₂×#41	—	2	1	no	—
329	C₂²×Q₈	—	2	1	no	—
330	C₂×Q₁₆	—	2	2	no	—
331	C₂×SD₁₆	—	2	2	no	—
332	C₂×SD₁₆	—	2	2	no	—
333	C₂×SD₁₆	—	2	2	no	—
334	C₂×SD₁₆	—	2	2	no	—
335	C₂×D₈	—	2	2	no	—
336	C₄⋊Q₈	—	2	1	no	—
337	C₄⋊Q₈	—	2	1	no	—
338	C₄⋊Q₈	—	2	1	no	—
339	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
340	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
341	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
342	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
343	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
344	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
345	#127	C₂³×C₂₉	1	1	yes	characteristic
346	#127	C₂³×C₂₉	1	1	yes	characteristic
347	#125	—	2	1	no	—
348	#124	—	2	1	no	—
349	#124	—	2	1	no	—
350	C₂²⋊Q₈	—	2	1	no	—
351	C₂²⋊Q₈	—	2	1	no	—
352	#121	—	2	1	no	—
353	#121	—	2	1	no	—
354	#121	—	2	1	no	—
355	#121	—	2	1	no	—
356	C₄×Q₈	—	2	1	no	—
357	C₄×Q₈	—	2	1	no	—
358	C₄×D₄	—	2	1	no	—
359	C₄×D₄	—	2	1	no	—
360	C₄×D₄	—	2	1	no	—
361	C₄×D₄	—	2	1	no	—
362	#117	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
366	#107	—	2	2	no	—
367	#107	—	2	2	no	—
368	#107	—	2	2	no	—
369	#107	—	2	2	no	—
370	#107	—	2	2	no	—
371	#106	—	2	2	no	—
372	C₄⋊C₈	D₄×C₂₉	1	2	yes	—
373	C₄⋊C₈	D₄×C₂₉	1	2	yes	—
374	C₄⋊C₈	D₄×C₂₉	1	2	yes	—
375	#103	—	2	2	no	—
376	#103	—	2	2	no	—
377	#103	—	2	2	no	—
378	#103	—	2	2	no	—
379	#103	—	2	2	no	—
380	#103	—	2	2	no	—
381	#102	—	2	2	no	—
382	#102	—	2	2	no	—
383	#102	—	2	2	no	—
384	#102	—	2	2	no	—
385	#102	—	2	2	no	—
386	#102	—	2	2	no	—
387	C₂²⋊C₈	D₄×C₂₉	1	2	yes	—
388	C₂²⋊C₈	D₄×C₂₉	1	2	yes	—
389	C₂²⋊C₈	D₄×C₂₉	1	2	yes	—
390	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
391	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
392	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
393	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
394	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
395	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
396	C₂₉	#19740	1	1	yes	characteristic, direct product factor, Sylow
397	#41	—	8	2	no	—
398	#41	—	8	2	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	—	2	1	no	—
404	C₂×Q₈	—	2	1	no	—
405	C₂×Q₈	—	4	1	no	—
406	C₂×Q₈	—	8	2	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	4	1	no	—
414	C₂×D₄	—	4	1	no	—
415	C₂²×C₄	—	4	1	no	—
416	C₂²×C₄	—	4	1	no	—
417	C₂²×C₄	—	4	1	no	—
418	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
421	Q₁₆	—	8	2	no	—
422	SD₁₆	—	8	2	no	—
423	SD₁₆	—	8	2	no	—
424	SD₁₆	—	8	2	no	—
425	SD₁₆	—	8	2	no	—
426	D₈	—	8	2	no	—
427	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
428	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
429	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
430	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
431	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
432	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	4	1	no	—
446	C₄⋊C₄	—	4	1	no	—
447	C₄⋊C₄	—	4	1	no	—
448	C₄⋊C₄	—	4	1	no	—
449	C₂²⋊C₄	—	4	1	no	—
450	C₂²⋊C₄	—	4	1	no	—
451	C₂²⋊C₄	—	4	1	no	—
452	C₂²⋊C₄	—	4	1	no	—
453	C₂²⋊C₄	—	4	1	no	—
454	C₄²	—	4	1	no	—
455	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
456	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
457	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
458	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
459	C₂³	—	4	1	no	—
460	C₂³	—	4	1	no	—
461	C₂³	C₂₉×#127	1	1	yes	characteristic
462	Q₈	—	4	2	no	—
463	Q₈	—	4	2	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	4	2	no	—
466	Q₈	—	4	2	no	—
467	Q₈	—	4	2	no	—
468	Q₈	—	8	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	8	2	no	—
476	D₄	—	8	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	8	2	no	—
487	C₂×C₄	—	8	2	no	—
488	C₂×C₄	—	8	2	no	—
489	C₂×C₄	C₂₉×#127	1	1	yes	characteristic
490	C₂×C₄	C₂₉×#127	1	1	yes	characteristic
491	C₂×C₄	C₂₉×#127	1	1	yes	characteristic
492	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
493	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
494	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
495	C₈	—	2	2	no	—
496	C₈	—	2	2	no	—
497	C₈	—	2	2	no	—
498	C₈	—	2	2	no	—
499	C₈	—	2	2	no	—
500	C₈	—	2	2	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	8	1	no	—
505	C₂²	—	8	1	no	—
506	C₂²	—	8	1	no	—
507	C₂²	—	8	1	no	—
508	C₂²	—	8	1	no	—
509	C₂²	—	8	1	no	—
510	C₂²	C₂×C₂₉×#127	1	1	yes	characteristic
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	8	1	no	—
515	C₄	—	8	1	no	—
516	C₄	—	8	1	no	—
517	C₄	—	8	1	no	—
518	C₄	—	8	1	no	—
519	C₄	—	8	1	no	—
520	C₄	C₂₉×#576	1	2	yes	—
521	C₄	C₂₉×#577	1	2	yes	—
522	C₄	C₂₉×#578	1	2	yes	—
523	C₂	—	4	1	no	—
524	C₂	—	16	1	no	—
525	C₂	—	16	1	no	—
526	C₂	C₂₉×#3154	1	1	yes	characteristic
527	C₂	C₂₉×#3155	1	1	yes	characteristic
528	C₂	C₂₉×#3156	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂₉×#3207	C₂
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×#3230	C₂	semidirect
2. C₂₉×#3228	C₂	semidirect
3. C₂₉×#3226	C₂	semidirect
4. C₂₉×#3210	C₂	semidirect
6. C₂₉×#3206	C₂	semidirect
7. C₂₉×#1723	C₂	semidirect
8. C₂₉×#1722	C₂	semidirect
9. C₂₉×#1719	C₂	semidirect
10. C₂₉×#1719	C₂	semidirect
11. C₂₉×#1717	C₂	semidirect
12. C₂₉×#1714	C₂	semidirect
13. C₂₉×#1710	C₂	semidirect
14. C₂₉×#1706	C₂	semidirect
15. C₂₉×#1454	C₂	semidirect
194. #19740	C₂₉	direct (N × H)
237. #3230	C₂×C₂₉	semidirect
238. #3228	C₂×C₂₉	semidirect
239. #3226	C₂×C₂₉	semidirect
240. #3210	C₂×C₂₉	semidirect
242. #3206	C₂×C₂₉	semidirect
243. #1723	C₂×C₂₉	semidirect
244. #1722	C₂×C₂₉	semidirect
245. #1719	C₂×C₂₉	semidirect
246. #1719	C₂×C₂₉	semidirect
247. #1717	C₂×C₂₉	semidirect
248. #1714	C₂×C₂₉	semidirect
249. #1710	C₂×C₂₉	semidirect
250. #1706	C₂×C₂₉	semidirect
251. #1454	C₂×C₂₉	semidirect
396. C₂₉	#19740	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×#3230	2
C₂₉×#3228	2
C₂₉×#3226	2
C₂₉×#3210	2
C₂₉×#3207	2
C₂₉×#3206	2
C₂₉×#1723	2
C₂₉×#1722	2
C₂₉×#1719	2
C₂₉×#1717	2
C₂₉×#1714	2
C₂₉×#1710	2
C₂₉×#1706	2
C₂₉×#1454	2
#19740	29

Subgroups — C29×#19740 #20314640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19740 #20314640