Subgroups — C₂₉×#19357 #20314257

Order 7424.

596 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3238	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#3218	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×#498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2966	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#1692	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1691	C₂	1	2	yes	maximal, complemented
7	C₂₉×#1672	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1671	C₂	1	2	yes	maximal, complemented
9	C₂₉×#1568	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1558	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1556	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂₉×#529	C₂²	1	1	yes	characteristic
15	C₂₉×#501	—	2	1	no	—
16	C₂₉×#498	—	2	1	no	—
17	C₂₉×#498	—	2	1	no	—
18	C₂₉×#498	C₂²	1	2	yes	—
19	C₂₉×#498	C₂²	1	2	yes	—
20	C₂₉×#497	—	2	1	no	—
21	C₂₉×#491	—	2	1	no	—
22	C₂₉×#489	—	2	1	no	—
23	C₂₉×#483	—	2	1	no	—
24	C₂₉×#480	—	2	1	no	—
25	C₂₉×#477	C₂²	1	2	yes	—
26	C₂₉×#476	C₂²	1	2	yes	—
27	C₂₉×#462	C₂²	1	2	yes	—
28	C₂₉×#461	C₂²	1	2	yes	—
29	C₂₉×#451	—	2	1	no	—
30	C₂₉×#448	—	2	1	no	—
31	C₂₉×#446	C₂²	1	1	yes	characteristic
32	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
33	C₂₉×#436	C₂²	1	1	yes	characteristic
34	C₂₉×#435	—	2	1	no	—
35	C₈×D₄×C₂₉	—	2	1	no	—
36	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
37	C₂₉×#433	—	2	1	no	—
38	C₂₉×#432	C₂²	1	1	yes	characteristic
39	C₂₉×#432	C₂²	1	1	yes	characteristic
40	C₂₉×#432	C₂²	1	1	yes	characteristic
41	C₂×C₂₉×#106	—	2	1	no	—
42	C₂×C₂₉×#106	—	2	1	no	—
43	C₂₉×#405	—	2	1	no	—
44	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
45	C₂₉×#335	C₂²	1	2	yes	—
46	C₂₉×#334	C₂²	1	2	yes	—
47	C₂₉×#333	C₂²	1	2	yes	—
48	C₂₉×#333	C₂²	1	2	yes	—
49	C₂₉×#332	C₂²	1	2	yes	—
50	C₂₉×#332	C₂²	1	2	yes	—
51	C₂²×Q₈×C₂₉	—	2	1	no	—
52	C₂²×Q₈×C₂₉	—	2	1	no	—
53	C₂×Q₁₆×C₂₉	—	2	2	no	—
54	C₂×SD₁₆×C₂₉	—	2	2	no	—
55	C₂×M₁₆×C₂₉	—	2	1	no	—
56	C₂²×C₈×C₂₉	—	2	1	no	—
57	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
58	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
59	C₂₉×C₄⋊Q₈	—	2	1	no	—
60	C₂₉×C₄⋊Q₈	—	2	1	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	—	2	1	no	—
65	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
67	C₂₉×#126	—	2	1	no	—
68	C₂₉×#125	D₄	1	1	yes	characteristic
69	C₂₉×#124	D₄	1	1	yes	characteristic
70	C₂₉×#123	—	2	1	no	—
71	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
72	C₂₉×#121	D₄	1	1	yes	characteristic
73	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
74	C₄×D₄×C₂₉	—	2	1	no	—
75	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
76	C₂₉×#117	—	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×C₄⋊C₄×C₂₉	—	2	1	no	—
81	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
82	C₂₉×#107	—	2	2	no	—
83	C₂₉×#106	—	2	2	no	—
84	C₂₉×#106	—	2	2	no	—
85	C₂₉×#106	—	2	2	no	—
86	C₂₉×#106	—	2	2	no	—
87	C₂₉×#106	—	2	2	no	—
88	C₂₉×C₄⋊C₈	—	2	1	no	—
89	C₂₉×C₄⋊C₈	—	2	1	no	—
90	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
91	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
92	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
93	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
94	C₂₉×#103	—	2	2	no	—
95	C₂₉×#103	—	2	2	no	—
96	C₂₉×#103	—	2	2	no	—
97	C₂₉×#102	—	2	2	no	—
98	C₂₉×C₂²⋊C₈	—	2	1	no	—
99	C₂₉×C₂²⋊C₈	—	2	1	no	—
100	C₂₉×C₂²⋊C₈	—	2	1	no	—
101	C₂₉×C₂²⋊C₈	—	2	1	no	—
102	C₂₉×C₂²⋊C₈	—	2	1	no	—
103	C₂₉×#97	—	2	1	no	—
104	C₂₉×#97	—	2	1	no	—
105	C₂₉×#97	—	2	1	no	—
106	C₂₉×#97	—	2	1	no	—
107	C₄×C₈×C₂₉	—	2	1	no	—
108	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
109	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
110	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
112	C₂×Q₈×C₂₉	—	2	2	no	—
113	C₂×Q₈×C₂₉	—	2	2	no	—
114	C₂×Q₈×C₂₉	—	4	1	no	—
115	C₂×Q₈×C₂₉	—	4	1	no	—
116	C₂×Q₈×C₂₉	—	8	2	no	—
117	C₂×Q₈×C₂₉	—	8	2	no	—
118	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
119	C₂×D₄×C₂₉	—	2	1	no	—
120	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₂₉	—	2	1	no	—
122	C₂²×C₄×C₂₉	—	4	1	no	—
123	C₂²×C₄×C₂₉	—	4	1	no	—
124	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
127	Q₁₆×C₂₉	—	8	2	no	—
128	SD₁₆×C₂₉	—	8	2	no	—
129	M₁₆×C₂₉	—	4	2	no	—
130	C₂×C₈×C₂₉	—	2	2	no	—
131	C₂×C₈×C₂₉	—	2	2	no	—
132	C₂×C₈×C₂₉	—	2	1	no	—
133	C₂×C₈×C₂₉	—	2	1	no	—
134	C₂×C₈×C₂₉	—	2	2	no	—
135	C₂×C₈×C₂₉	—	2	2	no	—
136	C₂×C₈×C₂₉	—	4	2	no	—
137	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
141	C₄⋊C₄×C₂₉	—	2	1	no	—
142	C₄⋊C₄×C₂₉	—	2	1	no	—
143	C₄⋊C₄×C₂₉	—	2	1	no	—
144	C₄⋊C₄×C₂₉	—	2	1	no	—
145	C₄⋊C₄×C₂₉	—	2	2	no	—
146	C₄⋊C₄×C₂₉	—	2	2	no	—
147	C₄⋊C₄×C₂₉	—	2	2	no	—
148	C₄⋊C₄×C₂₉	—	2	2	no	—
149	C₄⋊C₄×C₂₉	—	4	1	no	—
150	C₄⋊C₄×C₂₉	—	4	1	no	—
151	C₄⋊C₄×C₂₉	—	4	1	no	—
152	C₄⋊C₄×C₂₉	—	4	1	no	—
153	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
154	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
155	C₂²⋊C₄×C₂₉	—	2	1	no	—
156	C₂²⋊C₄×C₂₉	—	2	1	no	—
157	C₂²⋊C₄×C₂₉	—	2	1	no	—
158	C₂²⋊C₄×C₂₉	—	2	1	no	—
159	C₂²⋊C₄×C₂₉	—	2	1	no	—
160	C₄²×C₂₉	—	2	1	no	—
161	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₂₉	#41	1	1	yes	characteristic
164	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
165	#19357	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂³×C₂₉	—	2	1	no	—
167	C₂³×C₂₉	#121	1	1	yes	characteristic
168	Q₈×C₂₉	—	2	2	no	—
169	Q₈×C₂₉	—	4	2	no	—
170	Q₈×C₂₉	—	4	2	no	—
171	Q₈×C₂₉	—	8	2	no	—
172	Q₈×C₂₉	—	8	2	no	—
173	Q₈×C₂₉	—	8	2	no	—
174	D₄×C₂₉	—	2	2	no	—
175	D₄×C₂₉	—	4	2	no	—
176	C₂×C₄×C₂₉	—	2	2	no	—
177	C₂×C₄×C₂₉	—	2	1	no	—
178	C₂×C₄×C₂₉	—	2	1	no	—
179	C₂×C₄×C₂₉	—	2	2	no	—
180	C₂×C₄×C₂₉	—	2	1	no	—
181	C₂×C₄×C₂₉	—	2	1	no	—
182	C₂×C₄×C₂₉	—	2	1	no	—
183	C₂×C₄×C₂₉	—	4	1	no	—
184	C₂×C₄×C₂₉	—	4	1	no	—
185	C₂×C₄×C₂₉	—	4	2	no	—
186	C₂×C₄×C₂₉	—	4	2	no	—
187	C₂×C₄×C₂₉	—	8	2	no	—
188	C₂×C₄×C₂₉	—	8	2	no	—
189	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
190	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
191	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
192	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
195	C₈×C₂₉	—	2	1	no	—
196	C₈×C₂₉	—	2	1	no	—
197	C₈×C₂₉	—	4	1	no	—
198	C₈×C₂₉	—	4	1	no	—
199	C₈×C₂₉	—	4	2	no	—
200	C₈×C₂₉	—	4	2	no	—
201	C₈×C₂₉	#137	1	2	yes	—
202	C₈×C₂₉	#137	1	2	yes	—
203	#3238	C₂×C₂₉	1	1	yes	characteristic
204	#3218	C₂×C₂₉	1	1	yes	characteristic
205	C₂×#498	C₂×C₂₉	1	1	yes	characteristic, complemented
206	#2966	C₂×C₂₉	1	1	yes	characteristic
207	#1692	C₂×C₂₉	1	2	yes	complemented
208	#1691	C₂×C₂₉	1	2	yes	complemented
209	#1672	C₂×C₂₉	1	2	yes	complemented
210	#1671	C₂×C₂₉	1	2	yes	complemented
211	#1568	C₂×C₂₉	1	1	yes	characteristic, complemented
212	#1558	C₂×C₂₉	1	1	yes	characteristic, complemented
213	#1556	C₂×C₂₉	1	1	yes	characteristic, complemented
214	C₂²×C₂₉	—	2	1	no	—
215	C₂²×C₂₉	—	2	1	no	—
216	C₂²×C₂₉	—	4	1	no	—
217	C₂²×C₂₉	—	4	1	no	—
218	C₂²×C₂₉	—	4	1	no	—
219	C₂²×C₂₉	#471	1	2	yes	—
220	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
221	C₄×C₂₉	—	2	1	no	—
222	C₄×C₂₉	—	2	1	no	—
223	C₄×C₂₉	—	2	1	no	—
224	C₄×C₂₉	—	2	1	no	—
225	C₄×C₂₉	—	4	1	no	—
226	C₄×C₂₉	—	4	1	no	—
227	C₄×C₂₉	—	4	1	no	—
228	C₄×C₂₉	—	8	2	no	—
229	C₄×C₂₉	—	8	2	no	—
230	C₄×C₂₉	C₂×#137	1	1	yes	characteristic
231	C₄×C₂₉	C₂×#137	1	1	yes	characteristic
232	C₄×C₂₉	#577	1	2	yes	—
233	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
234	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
235	#529	C₂²×C₂₉	1	1	yes	characteristic
236	#501	—	2	1	no	—
237	#498	—	2	1	no	—
238	#498	—	2	1	no	—
239	#498	C₂²×C₂₉	1	2	yes	—
240	#498	C₂²×C₂₉	1	2	yes	—
241	#497	—	2	1	no	—
242	#491	—	2	1	no	—
243	#489	—	2	1	no	—
244	#483	—	2	1	no	—
245	#480	—	2	1	no	—
246	#477	C₂²×C₂₉	1	2	yes	—
247	#476	C₂²×C₂₉	1	2	yes	—
248	#462	C₂²×C₂₉	1	2	yes	—
249	#461	C₂²×C₂₉	1	2	yes	—
250	#451	—	2	1	no	—
251	#448	—	2	1	no	—
252	#446	C₂²×C₂₉	1	1	yes	characteristic
253	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
254	#436	C₂²×C₂₉	1	1	yes	characteristic
255	#435	—	2	1	no	—
256	C₈×D₄	—	2	1	no	—
257	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
258	#433	—	2	1	no	—
259	#432	C₂²×C₂₉	1	1	yes	characteristic
260	#432	C₂²×C₂₉	1	1	yes	characteristic
261	#432	C₂²×C₂₉	1	1	yes	characteristic
262	C₂×#106	—	2	1	no	—
263	C₂×#106	—	2	1	no	—
264	#405	—	2	1	no	—
265	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
266	#335	C₂²×C₂₉	1	2	yes	—
267	#334	C₂²×C₂₉	1	2	yes	—
268	#333	C₂²×C₂₉	1	2	yes	—
269	#333	C₂²×C₂₉	1	2	yes	—
270	#332	C₂²×C₂₉	1	2	yes	—
271	#332	C₂²×C₂₉	1	2	yes	—
272	C₂×C₂₉	—	2	2	no	—
273	C₂×C₂₉	—	8	1	no	—
274	C₂×C₂₉	#3039	1	1	yes	characteristic
275	C₂×C₂₉	#3057	1	1	yes	characteristic
276	C₂×C₂₉	C₂×#471	1	1	yes	characteristic
277	C₂²×Q₈	—	2	1	no	—
278	C₂²×Q₈	—	2	1	no	—
279	C₂×Q₁₆	—	2	2	no	—
280	C₂×SD₁₆	—	2	2	no	—
281	C₂×M₁₆	—	2	1	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
284	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	—	2	1	no	—
287	C₄⋊Q₈	—	2	1	no	—
288	C₄⋊Q₈	—	2	1	no	—
289	C₄⋊Q₈	—	2	1	no	—
290	C₄⋊Q₈	—	2	1	no	—
291	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
292	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
293	#126	—	2	1	no	—
294	#125	D₄×C₂₉	1	1	yes	characteristic
295	#124	D₄×C₂₉	1	1	yes	characteristic
296	#123	—	2	1	no	—
297	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
298	#121	D₄×C₂₉	1	1	yes	characteristic
299	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
302	#117	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
308	#107	—	2	2	no	—
309	#106	—	2	2	no	—
310	#106	—	2	2	no	—
311	#106	—	2	2	no	—
312	#106	—	2	2	no	—
313	#106	—	2	2	no	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	—	2	1	no	—
316	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
317	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
318	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
319	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
320	#103	—	2	2	no	—
321	#103	—	2	2	no	—
322	#103	—	2	2	no	—
323	#102	—	2	2	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₂²⋊C₈	—	2	1	no	—
326	C₂²⋊C₈	—	2	1	no	—
327	C₂²⋊C₈	—	2	1	no	—
328	C₂²⋊C₈	—	2	1	no	—
329	#97	—	2	1	no	—
330	#97	—	2	1	no	—
331	#97	—	2	1	no	—
332	#97	—	2	1	no	—
333	C₄×C₈	—	2	1	no	—
334	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
335	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
336	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
337	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
338	C₂₉	#19357	1	1	yes	characteristic, direct product factor, Sylow
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	4	1	no	—
342	C₂×Q₈	—	4	1	no	—
343	C₂×Q₈	—	8	2	no	—
344	C₂×Q₈	—	8	2	no	—
345	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	4	1	no	—
350	C₂²×C₄	—	4	1	no	—
351	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
353	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
354	Q₁₆	—	8	2	no	—
355	SD₁₆	—	8	2	no	—
356	M₁₆	—	4	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	4	2	no	—
364	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
365	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
366	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
367	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₄⋊C₄	—	4	1	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₄⋊C₄	—	4	1	no	—
380	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
381	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	2	1	no	—
386	C₂²⋊C₄	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
389	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
390	C₄²	#41×C₂₉	1	1	yes	characteristic
391	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
392	C₂³	—	2	1	no	—
393	C₂³	C₂₉×#121	1	1	yes	characteristic
394	Q₈	—	2	2	no	—
395	Q₈	—	4	2	no	—
396	Q₈	—	4	2	no	—
397	Q₈	—	8	2	no	—
398	Q₈	—	8	2	no	—
399	Q₈	—	8	2	no	—
400	D₄	—	2	2	no	—
401	D₄	—	4	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	8	2	no	—
414	C₂×C₄	—	8	2	no	—
415	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
416	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
417	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
418	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
419	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
420	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
421	C₈	—	2	1	no	—
422	C₈	—	2	1	no	—
423	C₈	—	4	1	no	—
424	C₈	—	4	1	no	—
425	C₈	—	4	2	no	—
426	C₈	—	4	2	no	—
427	C₈	C₂₉×#137	1	2	yes	—
428	C₈	C₂₉×#137	1	2	yes	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	4	1	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	C₂₉×#471	1	2	yes	—
435	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	—	4	1	no	—
443	C₄	—	8	2	no	—
444	C₄	—	8	2	no	—
445	C₄	C₂×C₂₉×#137	1	1	yes	characteristic
446	C₄	C₂×C₂₉×#137	1	1	yes	characteristic
447	C₄	C₂₉×#577	1	2	yes	—
448	C₂	—	2	2	no	—
449	C₂	—	8	1	no	—
450	C₂	C₂₉×#3039	1	1	yes	characteristic
451	C₂	C₂₉×#3057	1	1	yes	characteristic
452	C₂	C₂×C₂₉×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂₉×#121	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
3. C₂×C₂₉×#498	C₂	semidirect
5. C₂₉×#1692	C₂	semidirect
6. C₂₉×#1691	C₂	semidirect
7. C₂₉×#1672	C₂	semidirect
8. C₂₉×#1671	C₂	semidirect
9. C₂₉×#1568	C₂	semidirect
10. C₂₉×#1558	C₂	semidirect
11. C₂₉×#1556	C₂	semidirect
165. #19357	C₂₉	direct (N × H)
205. C₂×#498	C₂×C₂₉	semidirect
207. #1692	C₂×C₂₉	semidirect
208. #1691	C₂×C₂₉	semidirect
209. #1672	C₂×C₂₉	semidirect
210. #1671	C₂×C₂₉	semidirect
211. #1568	C₂×C₂₉	semidirect
212. #1558	C₂×C₂₉	semidirect
213. #1556	C₂×C₂₉	semidirect
338. C₂₉	#19357	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×#3238	2
C₂₉×#3218	2
C₂×C₂₉×#498	2
C₂₉×#2966	2
C₂₉×#1692	2
C₂₉×#1691	2
C₂₉×#1672	2
C₂₉×#1671	2
C₂₉×#1568	2
C₂₉×#1558	2
C₂₉×#1556	2
#19357	29

Subgroups — C29×#19357 #20314257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19357 #20314257