Subgroups — C₂₉×#19704 #20314604

Order 7424.

704 conjugacy classes of subgroups.

The subgroup lattice has 422 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×#3227	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3206	C₂	1	1	yes	maximal, characteristic
5	C₂×C₂₉×#500	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#3131	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#1723	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1722	C₂	1	2	yes	maximal, complemented
9	C₂₉×#1719	C₂	1	2	yes	maximal, complemented
10	C₂₉×#1718	C₂	1	2	yes	maximal, complemented
11	C₂₉×#1452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#533	C₂²	1	1	yes	characteristic
13	C₂₉×#532	C₂²	1	1	yes	characteristic
14	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂₉×#500	—	2	2	no	—
17	C₂₉×#500	C₂²	1	2	yes	—
18	C₂₉×#500	C₂²	1	2	yes	—
19	C₂₉×#500	C₂²	1	2	yes	—
20	C₂₉×#498	C₂²	1	2	yes	—
21	C₂₉×#494	C₂²	1	2	yes	—
22	C₂₉×#492	C₂²	1	2	yes	—
23	C₂₉×#488	—	2	2	no	—
24	C₂₉×#487	C₂²	1	2	yes	—
25	C₂₉×#487	C₂²	1	2	yes	—
26	C₂₉×#487	C₂²	1	2	yes	—
27	C₂₉×#487	C₂²	1	1	yes	characteristic
28	C₂₉×#487	C₂²	1	1	yes	characteristic
29	C₂₉×#486	C₂²	1	2	yes	—
30	C₂₉×#486	C₂²	1	1	yes	characteristic
31	C₂₉×#486	C₂²	1	1	yes	characteristic
32	C₂₉×#484	—	2	2	no	—
33	C₂₉×#481	—	2	2	no	—
34	C₂₉×#477	—	2	2	no	—
35	C₂₉×#476	—	2	2	no	—
36	C₂₉×#462	—	2	2	no	—
37	C₂₉×#461	—	2	2	no	—
38	C₂₉×#451	—	2	2	no	—
39	C₂₉×#448	—	2	2	no	—
40	C₂₉×#431	C₂²	1	1	yes	characteristic
41	C₂₉×#431	C₂²	1	1	yes	characteristic
42	C₂×C₂₉×#107	—	2	2	no	—
43	C₂₉×#416	—	2	2	no	—
44	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
45	C₂₉×#322	C₂²	1	2	yes	—
46	C₂₉×#322	C₂²	1	2	yes	—
47	C₂×#41×C₂₉	—	2	1	no	—
48	C₂²×Q₈×C₂₉	—	2	1	no	—
49	C₂²×Q₈×C₂₉	—	2	1	no	—
50	C₂×Q₁₆×C₂₉	—	2	4	no	—
51	C₂×SD₁₆×C₂₉	—	2	4	no	—
52	C₂²×C₈×C₂₉	D₄	1	2	yes	—
53	C₂₉×C₄⋊Q₈	—	2	1	no	—
54	C₂₉×C₄⋊Q₈	—	2	1	no	—
55	C₂₉×C₄⋊Q₈	—	2	1	no	—
56	C₂₉×C₄⋊Q₈	—	2	1	no	—
57	C₂₉×C₄⋊Q₈	—	2	1	no	—
58	C₂₉×C₄⋊Q₈	—	2	1	no	—
59	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
62	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₂₉×#127	C₂³	1	1	yes	characteristic
65	C₂₉×#125	—	2	1	no	—
66	C₂₉×#124	—	2	1	no	—
67	C₂₉×C₂²⋊Q₈	—	2	1	no	—
68	C₂₉×C₂²⋊Q₈	—	2	1	no	—
69	C₂₉×#121	—	2	1	no	—
70	C₂₉×#121	—	2	1	no	—
71	C₄×Q₈×C₂₉	—	2	1	no	—
72	C₄×Q₈×C₂₉	—	2	1	no	—
73	C₄×D₄×C₂₉	—	2	1	no	—
74	C₄×D₄×C₂₉	—	2	1	no	—
75	C₂₉×#117	—	2	1	no	—
76	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
80	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
81	C₂₉×#107	—	2	4	no	—
82	C₂₉×#107	—	2	4	no	—
83	C₂₉×#107	—	2	4	no	—
84	C₂₉×#106	—	2	4	no	—
85	C₂₉×C₄⋊C₈	D₄	1	2	yes	—
86	C₂₉×C₄⋊C₈	D₄	1	2	yes	—
87	C₂₉×#103	—	2	4	no	—
88	C₂₉×#103	—	2	4	no	—
89	C₂₉×#103	—	2	4	no	—
90	C₂₉×#103	—	2	2	no	—
91	C₂₉×#103	—	2	2	no	—
92	C₂₉×#102	—	2	4	no	—
93	C₂₉×#102	—	2	2	no	—
94	C₂₉×#102	—	2	2	no	—
95	C₂₉×C₂²⋊C₈	D₄	1	2	yes	—
96	C₂₉×C₂²⋊C₈	D₄	1	2	yes	—
97	C₄×C₈×C₂₉	D₄	1	2	yes	—
98	C₄×C₈×C₂₉	C₂³	1	2	yes	—
99	C₄×C₈×C₂₉	C₂³	1	2	yes	—
100	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
102	#41×C₂₉	—	4	4	no	—
103	C₂×Q₈×C₂₉	—	2	1	no	—
104	C₂×Q₈×C₂₉	—	2	1	no	—
105	C₂×Q₈×C₂₉	—	2	1	no	—
106	C₂×Q₈×C₂₉	—	2	2	no	—
107	C₂×Q₈×C₂₉	—	2	2	no	—
108	C₂×Q₈×C₂₉	—	4	1	no	—
109	C₂×Q₈×C₂₉	—	4	1	no	—
110	C₂×Q₈×C₂₉	—	8	2	no	—
111	C₂×Q₈×C₂₉	—	8	2	no	—
112	C₂×D₄×C₂₉	—	2	1	no	—
113	C₂×D₄×C₂₉	—	2	1	no	—
114	C₂×D₄×C₂₉	—	2	1	no	—
115	C₂×D₄×C₂₉	—	4	1	no	—
116	C₂²×C₄×C₂₉	—	4	1	no	—
117	C₂²×C₄×C₂₉	—	4	1	no	—
118	C₂²×C₄×C₂₉	—	4	1	no	—
119	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
122	Q₁₆×C₂₉	—	8	4	no	—
123	SD₁₆×C₂₉	—	8	4	no	—
124	C₂×C₈×C₂₉	—	2	4	no	—
125	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₂₉	C₂×D₄	1	4	yes	—
128	C₂×C₈×C₂₉	C₂×D₄	1	4	yes	—
129	C₄⋊C₄×C₂₉	—	2	2	no	—
130	C₄⋊C₄×C₂₉	—	2	2	no	—
131	C₄⋊C₄×C₂₉	—	2	2	no	—
132	C₄⋊C₄×C₂₉	—	2	2	no	—
133	C₄⋊C₄×C₂₉	—	2	1	no	—
134	C₄⋊C₄×C₂₉	—	2	1	no	—
135	C₄⋊C₄×C₂₉	—	2	1	no	—
136	C₄⋊C₄×C₂₉	—	2	1	no	—
137	C₄⋊C₄×C₂₉	—	2	1	no	—
138	C₄⋊C₄×C₂₉	—	2	1	no	—
139	C₄⋊C₄×C₂₉	—	4	1	no	—
140	C₄⋊C₄×C₂₉	—	4	1	no	—
141	C₄⋊C₄×C₂₉	—	4	1	no	—
142	C₄⋊C₄×C₂₉	—	4	1	no	—
143	C₄⋊C₄×C₂₉	—	4	1	no	—
144	C₄⋊C₄×C₂₉	—	4	1	no	—
145	C₂²⋊C₄×C₂₉	—	4	1	no	—
146	C₂²⋊C₄×C₂₉	—	4	1	no	—
147	C₂²⋊C₄×C₂₉	—	4	1	no	—
148	C₄²×C₂₉	—	4	1	no	—
149	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
153	#19704	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂³×C₂₉	—	4	1	no	—
155	C₂³×C₂₉	#127	1	1	yes	characteristic
156	Q₈×C₂₉	—	4	2	no	—
157	Q₈×C₂₉	—	4	4	no	—
158	Q₈×C₂₉	—	4	2	no	—
159	Q₈×C₂₉	—	4	4	no	—
160	Q₈×C₂₉	—	4	2	no	—
161	Q₈×C₂₉	—	8	2	no	—
162	Q₈×C₂₉	—	8	2	no	—
163	D₄×C₂₉	—	4	2	no	—
164	D₄×C₂₉	—	4	2	no	—
165	D₄×C₂₉	—	4	2	no	—
166	D₄×C₂₉	—	8	2	no	—
167	C₂×C₄×C₂₉	—	2	2	no	—
168	C₂×C₄×C₂₉	—	2	2	no	—
169	C₂×C₄×C₂₉	—	4	1	no	—
170	C₂×C₄×C₂₉	—	4	1	no	—
171	C₂×C₄×C₂₉	—	4	1	no	—
172	C₂×C₄×C₂₉	—	4	2	no	—
173	C₂×C₄×C₂₉	—	4	2	no	—
174	C₂×C₄×C₂₉	—	8	2	no	—
175	C₂×C₄×C₂₉	—	8	2	no	—
176	C₂×C₄×C₂₉	—	8	2	no	—
177	C₂×C₄×C₂₉	#127	1	1	yes	characteristic
178	C₂×C₄×C₂₉	#127	1	1	yes	characteristic
179	C₂×C₄×C₂₉	#127	1	1	yes	characteristic
180	C₂×C₄×C₂₉	#137	1	4	yes	—
181	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
184	C₈×C₂₉	—	2	2	no	—
185	C₈×C₂₉	—	2	2	no	—
186	C₈×C₂₉	—	2	4	no	—
187	C₈×C₂₉	—	2	4	no	—
188	#3230	C₂×C₂₉	1	1	yes	characteristic, complemented
189	#3227	C₂×C₂₉	1	1	yes	characteristic
190	#3209	C₂×C₂₉	1	1	yes	characteristic, complemented
191	#3206	C₂×C₂₉	1	1	yes	characteristic
192	C₂×#500	C₂×C₂₉	1	1	yes	characteristic, complemented
193	#3131	C₂×C₂₉	1	1	yes	characteristic
194	#1723	C₂×C₂₉	1	2	yes	complemented
195	#1722	C₂×C₂₉	1	2	yes	complemented
196	#1719	C₂×C₂₉	1	2	yes	complemented
197	#1718	C₂×C₂₉	1	2	yes	complemented
198	#1452	C₂×C₂₉	1	1	yes	characteristic, complemented
199	C₂²×C₂₉	—	2	1	no	—
200	C₂²×C₂₉	—	2	1	no	—
201	C₂²×C₂₉	—	8	1	no	—
202	C₂²×C₂₉	—	8	1	no	—
203	C₂²×C₂₉	—	8	1	no	—
204	C₂²×C₂₉	#497	1	2	yes	—
205	C₂²×C₂₉	C₂×#127	1	1	yes	characteristic
206	C₄×C₂₉	—	2	1	no	—
207	C₄×C₂₉	—	2	1	no	—
208	C₄×C₂₉	—	8	1	no	—
209	C₄×C₂₉	—	8	2	no	—
210	C₄×C₂₉	—	8	2	no	—
211	C₄×C₂₉	—	8	1	no	—
212	C₄×C₂₉	—	8	1	no	—
213	C₄×C₂₉	#497	1	2	yes	—
214	C₄×C₂₉	C₂×#137	1	2	yes	—
215	C₄×C₂₉	#576	1	2	yes	—
216	C₄×C₂₉	#578	1	2	yes	—
217	#533	C₂²×C₂₉	1	1	yes	characteristic
218	#532	C₂²×C₂₉	1	1	yes	characteristic
219	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
220	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
221	#500	—	2	2	no	—
222	#500	C₂²×C₂₉	1	2	yes	—
223	#500	C₂²×C₂₉	1	2	yes	—
224	#500	C₂²×C₂₉	1	2	yes	—
225	#498	C₂²×C₂₉	1	2	yes	—
226	#494	C₂²×C₂₉	1	2	yes	—
227	#492	C₂²×C₂₉	1	2	yes	—
228	#488	—	2	2	no	—
229	#487	C₂²×C₂₉	1	1	yes	characteristic
230	#487	C₂²×C₂₉	1	1	yes	characteristic
231	#487	C₂²×C₂₉	1	2	yes	—
232	#487	C₂²×C₂₉	1	2	yes	—
233	#487	C₂²×C₂₉	1	2	yes	—
234	#486	C₂²×C₂₉	1	1	yes	characteristic
235	#486	C₂²×C₂₉	1	1	yes	characteristic
236	#486	C₂²×C₂₉	1	2	yes	—
237	#484	—	2	2	no	—
238	#481	—	2	2	no	—
239	#477	—	2	2	no	—
240	#476	—	2	2	no	—
241	#462	—	2	2	no	—
242	#461	—	2	2	no	—
243	#451	—	2	2	no	—
244	#448	—	2	2	no	—
245	#431	C₂²×C₂₉	1	1	yes	characteristic
246	#431	C₂²×C₂₉	1	1	yes	characteristic
247	C₂×#107	—	2	2	no	—
248	#416	—	2	2	no	—
249	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
250	#322	C₂²×C₂₉	1	2	yes	—
251	#322	C₂²×C₂₉	1	2	yes	—
252	C₂×C₂₉	—	2	2	no	—
253	C₂×C₂₉	—	16	1	no	—
254	C₂×C₂₉	C₂×#497	1	1	yes	characteristic
255	C₂×C₂₉	#3155	1	1	yes	characteristic
256	C₂×C₂₉	#3156	1	1	yes	characteristic
257	C₂×#41	—	2	1	no	—
258	C₂²×Q₈	—	2	1	no	—
259	C₂²×Q₈	—	2	1	no	—
260	C₂×Q₁₆	—	2	4	no	—
261	C₂×SD₁₆	—	2	4	no	—
262	C₂²×C₈	D₄×C₂₉	1	2	yes	—
263	C₄⋊Q₈	—	2	1	no	—
264	C₄⋊Q₈	—	2	1	no	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	—	2	1	no	—
269	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
270	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
271	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
272	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
273	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
274	#127	C₂³×C₂₉	1	1	yes	characteristic
275	#125	—	2	1	no	—
276	#124	—	2	1	no	—
277	C₂²⋊Q₈	—	2	1	no	—
278	C₂²⋊Q₈	—	2	1	no	—
279	#121	—	2	1	no	—
280	#121	—	2	1	no	—
281	C₄×Q₈	—	2	1	no	—
282	C₄×Q₈	—	2	1	no	—
283	C₄×D₄	—	2	1	no	—
284	C₄×D₄	—	2	1	no	—
285	#117	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
291	#107	—	2	4	no	—
292	#107	—	2	4	no	—
293	#107	—	2	4	no	—
294	#106	—	2	4	no	—
295	C₄⋊C₈	D₄×C₂₉	1	2	yes	—
296	C₄⋊C₈	D₄×C₂₉	1	2	yes	—
297	#103	—	2	2	no	—
298	#103	—	2	2	no	—
299	#103	—	2	4	no	—
300	#103	—	2	4	no	—
301	#103	—	2	4	no	—
302	#102	—	2	2	no	—
303	#102	—	2	2	no	—
304	#102	—	2	4	no	—
305	C₂²⋊C₈	D₄×C₂₉	1	2	yes	—
306	C₂²⋊C₈	D₄×C₂₉	1	2	yes	—
307	C₄×C₈	D₄×C₂₉	1	2	yes	—
308	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
309	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
310	C₄×C₈	C₂³×C₂₉	1	2	yes	—
311	C₄×C₈	C₂³×C₂₉	1	2	yes	—
312	C₂₉	#19704	1	1	yes	characteristic, direct product factor, Sylow
313	#41	—	4	4	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	4	1	no	—
320	C₂×Q₈	—	4	1	no	—
321	C₂×Q₈	—	8	2	no	—
322	C₂×Q₈	—	8	2	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
333	Q₁₆	—	8	4	no	—
334	SD₁₆	—	8	4	no	—
335	C₂×C₈	—	2	4	no	—
336	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
337	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
338	C₂×C₈	C₂×D₄×C₂₉	1	4	yes	—
339	C₂×C₈	C₂×D₄×C₂₉	1	4	yes	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	4	1	no	—
351	C₄⋊C₄	—	4	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₂²⋊C₄	—	4	1	no	—
357	C₂²⋊C₄	—	4	1	no	—
358	C₂²⋊C₄	—	4	1	no	—
359	C₄²	—	4	1	no	—
360	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
361	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
362	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
363	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
364	C₂³	—	4	1	no	—
365	C₂³	C₂₉×#127	1	1	yes	characteristic
366	Q₈	—	4	2	no	—
367	Q₈	—	4	4	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	4	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	8	2	no	—
372	Q₈	—	8	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	8	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	8	2	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	—	8	2	no	—
387	C₂×C₄	C₂₉×#127	1	1	yes	characteristic
388	C₂×C₄	C₂₉×#127	1	1	yes	characteristic
389	C₂×C₄	C₂₉×#127	1	1	yes	characteristic
390	C₂×C₄	C₂₉×#137	1	4	yes	—
391	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
392	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	2	2	no	—
396	C₈	—	2	4	no	—
397	C₈	—	2	4	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	8	1	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	C₂₉×#497	1	2	yes	—
404	C₂²	C₂×C₂₉×#127	1	1	yes	characteristic
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	8	1	no	—
408	C₄	—	8	2	no	—
409	C₄	—	8	2	no	—
410	C₄	—	8	1	no	—
411	C₄	—	8	1	no	—
412	C₄	C₂₉×#497	1	2	yes	—
413	C₄	C₂×C₂₉×#137	1	2	yes	—
414	C₄	C₂₉×#576	1	2	yes	—
415	C₄	C₂₉×#578	1	2	yes	—
416	C₂	—	2	2	no	—
417	C₂	—	16	1	no	—
418	C₂	C₂×C₂₉×#497	1	1	yes	characteristic
419	C₂	C₂₉×#3155	1	1	yes	characteristic
420	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×#532	C₂²
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
3. C₂₉×#3209	C₂	semidirect
5. C₂×C₂₉×#500	C₂	semidirect
7. C₂₉×#1723	C₂	semidirect
8. C₂₉×#1722	C₂	semidirect
9. C₂₉×#1719	C₂	semidirect
10. C₂₉×#1718	C₂	semidirect
11. C₂₉×#1452	C₂	semidirect
153. #19704	C₂₉	direct (N × H)
188. #3230	C₂×C₂₉	semidirect
190. #3209	C₂×C₂₉	semidirect
192. C₂×#500	C₂×C₂₉	semidirect
194. #1723	C₂×C₂₉	semidirect
195. #1722	C₂×C₂₉	semidirect
196. #1719	C₂×C₂₉	semidirect
197. #1718	C₂×C₂₉	semidirect
198. #1452	C₂×C₂₉	semidirect
312. C₂₉	#19704	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×#3227	2
C₂₉×#3209	2
C₂₉×#3206	2
C₂×C₂₉×#500	2
C₂₉×#3131	2
C₂₉×#1723	2
C₂₉×#1722	2
C₂₉×#1719	2
C₂₉×#1718	2
C₂₉×#1452	2
#19704	29

Subgroups — C29×#19704 #20314604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19704 #20314604