Subgroups — C₂₉×#19232 #20314132

Order 7424.

652 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3246	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#3206	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2935	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#1693	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1691	C₂	1	2	yes	maximal, complemented
7	C₂₉×#1673	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×#1542	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₉×#332	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₉×#131	—	2	1	no	—
13	C₂₉×#533	C₂²	1	1	yes	characteristic
14	C₂₉×#532	C₂²	1	1	yes	characteristic
15	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂₉×#501	—	2	2	no	—
17	C₂₉×#500	C₂²	1	2	yes	—
18	C₂₉×#498	C₂²	1	2	yes	—
19	C₂₉×#492	—	2	1	no	—
20	C₂₉×#487	—	2	1	no	—
21	C₂₉×#476	C₂²	1	2	yes	—
22	C₂₉×#475	—	2	1	no	—
23	C₂₉×#465	—	2	2	no	—
24	C₂₉×#461	C₂²	1	2	yes	—
25	C₂₉×#461	C₂²	1	2	yes	—
26	C₂₉×#461	C₂²	1	2	yes	—
27	C₂₉×#460	—	2	1	no	—
28	C₂₉×#448	—	2	2	no	—
29	C₂₉×#436	C₂²	1	2	yes	—
30	C₂₉×#435	—	2	2	no	—
31	C₈×D₄×C₂₉	C₂²	1	2	yes	—
32	C₂₉×#431	C₂²	1	1	yes	characteristic
33	C₂₉×#428	—	2	1	no	—
34	C₂₉×#428	—	2	1	no	—
35	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₂₉×#408	—	2	1	no	—
38	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
39	C₂₉×#335	C₂²	1	2	yes	—
40	C₂₉×#334	C₂²	1	2	yes	—
41	C₂₉×#333	C₂²	1	1	yes	characteristic
42	C₂₉×#333	C₂²	1	1	yes	characteristic
43	C₂₉×#332	C₂²	1	2	yes	—
44	C₂₉×#332	C₂²	1	1	yes	characteristic
45	C₂₉×#332	C₂²	1	2	yes	—
46	C₂₉×#332	C₂²	1	1	yes	characteristic
47	C₂×#41×C₂₉	—	2	1	no	—
48	C₂²×Q₈×C₂₉	—	2	1	no	—
49	C₂×SD₁₆×C₂₉	—	2	2	no	—
50	C₂×SD₁₆×C₂₉	—	2	2	no	—
51	C₂×SD₁₆×C₂₉	—	2	2	no	—
52	C₂₉×#131	—	4	4	no	—
53	C₂×M₁₆×C₂₉	—	2	2	no	—
54	C₂×M₁₆×C₂₉	D₄	1	1	yes	characteristic
55	C₂×M₁₆×C₂₉	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₂₉	—	2	1	no	—
57	C₂²×C₈×C₂₉	—	2	1	no	—
58	C₂²×C₈×C₂₉	—	2	2	no	—
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	D₄	1	1	yes	characteristic
63	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₂₉×#127	D₄	1	1	yes	characteristic
67	C₂₉×#125	—	2	1	no	—
68	C₂₉×#124	—	2	1	no	—
69	C₂₉×C₂²⋊Q₈	—	2	1	no	—
70	C₂₉×C₂²⋊Q₈	—	2	1	no	—
71	C₂₉×#121	—	2	1	no	—
72	C₂₉×#121	D₄	1	2	yes	—
73	C₄×Q₈×C₂₉	—	2	1	no	—
74	C₄×Q₈×C₂₉	—	2	1	no	—
75	C₄×D₄×C₂₉	—	2	1	no	—
76	C₄×D₄×C₂₉	C₂³	1	2	yes	—
77	C₂₉×#117	—	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	2	no	—
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×C₄⋊C₈	—	2	1	no	—
87	C₂₉×C₄⋊C₈	—	2	1	no	—
88	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
89	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#103	—	2	2	no	—
94	C₂₉×#103	—	2	2	no	—
95	C₂₉×#103	—	2	2	no	—
96	C₂₉×#102	—	2	2	no	—
97	C₂₉×C₂²⋊C₈	—	2	1	no	—
98	C₂₉×C₂²⋊C₈	—	2	2	no	—
99	C₂₉×C₂²⋊C₈	—	2	2	no	—
100	C₂₉×#97	D₄	1	2	yes	—
101	C₄×C₈×C₂₉	—	2	1	no	—
102	C₄×C₈×C₂₉	C₂³	1	2	yes	—
103	#41×C₂₉	—	4	2	no	—
104	#41×C₂₉	—	4	2	no	—
105	C₂×Q₈×C₂₉	—	2	1	no	—
106	C₂×Q₈×C₂₉	—	2	1	no	—
107	C₂×Q₈×C₂₉	—	2	2	no	—
108	C₂×Q₈×C₂₉	—	2	1	no	—
109	C₂×Q₈×C₂₉	—	4	1	no	—
110	C₂×Q₈×C₂₉	—	8	1	no	—
111	C₂×Q₈×C₂₉	—	8	1	no	—
112	C₂×D₄×C₂₉	—	2	2	no	—
113	C₂×D₄×C₂₉	—	2	1	no	—
114	C₂×D₄×C₂₉	—	2	1	no	—
115	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₂₉	—	2	2	no	—
117	C₂²×C₄×C₂₉	—	4	1	no	—
118	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
121	SD₁₆×C₂₉	—	8	2	no	—
122	SD₁₆×C₂₉	—	8	2	no	—
123	SD₁₆×C₂₉	—	8	2	no	—
124	M₁₆×C₂₉	—	2	2	no	—
125	M₁₆×C₂₉	—	4	4	no	—
126	M₁₆×C₂₉	SD₁₆	1	4	yes	complemented
127	C₂×C₈×C₂₉	—	2	1	no	—
128	C₂×C₈×C₂₉	—	2	1	no	—
129	C₂×C₈×C₂₉	—	2	2	no	—
130	C₂×C₈×C₂₉	—	2	1	no	—
131	C₂×C₈×C₂₉	—	2	1	no	—
132	C₂×C₈×C₂₉	—	4	2	no	—
133	C₂×C₈×C₂₉	—	4	4	no	—
134	C₂×C₈×C₂₉	—	8	1	no	—
135	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
137	C₄⋊C₄×C₂₉	—	2	1	no	—
138	C₄⋊C₄×C₂₉	—	2	2	no	—
139	C₄⋊C₄×C₂₉	—	2	1	no	—
140	C₄⋊C₄×C₂₉	—	2	1	no	—
141	C₄⋊C₄×C₂₉	—	2	1	no	—
142	C₄⋊C₄×C₂₉	—	2	2	no	—
143	C₄⋊C₄×C₂₉	—	2	1	no	—
144	C₄⋊C₄×C₂₉	—	4	1	no	—
145	C₄⋊C₄×C₂₉	—	4	1	no	—
146	C₄⋊C₄×C₂₉	—	4	1	no	—
147	C₄⋊C₄×C₂₉	—	4	1	no	—
148	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
149	C₂²⋊C₄×C₂₉	—	2	2	no	—
150	C₂²⋊C₄×C₂₉	—	2	2	no	—
151	C₂²⋊C₄×C₂₉	—	4	1	no	—
152	C₄²×C₂₉	—	4	1	no	—
153	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₂₉	#41	1	1	yes	characteristic
156	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
157	#19232	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂³×C₂₉	—	2	2	no	—
159	C₂³×C₂₉	#121	1	1	yes	characteristic
160	Q₈×C₂₉	—	4	2	no	—
161	Q₈×C₂₉	—	4	1	no	—
162	Q₈×C₂₉	—	4	2	no	—
163	Q₈×C₂₉	—	4	2	no	—
164	Q₈×C₂₉	—	4	1	no	—
165	Q₈×C₂₉	—	8	1	no	—
166	Q₈×C₂₉	—	8	2	no	—
167	D₄×C₂₉	—	2	2	no	—
168	D₄×C₂₉	—	2	2	no	—
169	D₄×C₂₉	—	4	4	no	—
170	D₄×C₂₉	—	4	2	no	—
171	D₄×C₂₉	—	8	1	no	—
172	C₂×C₄×C₂₉	—	2	1	no	—
173	C₂×C₄×C₂₉	—	2	1	no	—
174	C₂×C₄×C₂₉	—	2	2	no	—
175	C₂×C₄×C₂₉	—	4	1	no	—
176	C₂×C₄×C₂₉	—	4	2	no	—
177	C₂×C₄×C₂₉	—	4	2	no	—
178	C₂×C₄×C₂₉	—	4	1	no	—
179	C₂×C₄×C₂₉	—	4	1	no	—
180	C₂×C₄×C₂₉	—	4	2	no	—
181	C₂×C₄×C₂₉	—	8	2	no	—
182	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
183	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
184	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
185	C₂×C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
186	C₂×C₄×C₂₉	#137	1	2	yes	—
187	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
190	C₈×C₂₉	—	2	2	no	—
191	C₈×C₂₉	—	4	1	no	—
192	C₈×C₂₉	—	4	1	no	—
193	C₈×C₂₉	—	4	2	no	—
194	C₈×C₂₉	—	4	1	no	—
195	C₈×C₂₉	—	4	1	no	—
196	C₈×C₂₉	C₂×SD₁₆	1	4	yes	—
197	#3246	C₂×C₂₉	1	1	yes	characteristic
198	#3206	C₂×C₂₉	1	1	yes	characteristic
199	#3165	C₂×C₂₉	1	1	yes	characteristic, complemented
200	#2935	C₂×C₂₉	1	1	yes	characteristic
201	#1693	C₂×C₂₉	1	2	yes	complemented
202	#1691	C₂×C₂₉	1	2	yes	complemented
203	#1673	C₂×C₂₉	1	2	yes	complemented
204	#1671	C₂×C₂₉	1	2	yes	complemented
205	#1565	C₂×C₂₉	1	1	yes	characteristic, complemented
206	#1542	C₂×C₂₉	1	1	yes	characteristic, complemented
207	C₂×#332	C₂×C₂₉	1	1	yes	characteristic, complemented
208	C₂²×C₂₉	—	2	1	no	—
209	C₂²×C₂₉	—	2	1	no	—
210	C₂²×C₂₉	—	4	2	no	—
211	C₂²×C₂₉	—	4	2	no	—
212	C₂²×C₂₉	—	4	2	no	—
213	C₂²×C₂₉	#461	1	2	yes	—
214	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
215	C₄×C₂₉	—	2	1	no	—
216	C₄×C₂₉	—	2	1	no	—
217	C₄×C₂₉	—	2	1	no	—
218	C₄×C₂₉	—	4	2	no	—
219	C₄×C₂₉	—	8	2	no	—
220	C₄×C₂₉	—	8	1	no	—
221	C₄×C₂₉	—	8	1	no	—
222	C₄×C₂₉	#461	1	2	yes	—
223	C₄×C₂₉	C₂²×SD₁₆	1	1	yes	characteristic
224	C₄×C₂₉	C₂×#137	1	1	yes	characteristic
225	C₄×C₂₉	#576	1	1	yes	characteristic
226	C₄×C₂₉	#577	1	1	yes	characteristic
227	C₂×#131	—	2	1	no	—
228	#533	C₂²×C₂₉	1	1	yes	characteristic
229	#532	C₂²×C₂₉	1	1	yes	characteristic
230	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
231	#501	—	2	2	no	—
232	#500	C₂²×C₂₉	1	2	yes	—
233	#498	C₂²×C₂₉	1	2	yes	—
234	#492	—	2	1	no	—
235	#487	—	2	1	no	—
236	#476	C₂²×C₂₉	1	2	yes	—
237	#475	—	2	1	no	—
238	#465	—	2	2	no	—
239	#461	C₂²×C₂₉	1	2	yes	—
240	#461	C₂²×C₂₉	1	2	yes	—
241	#461	C₂²×C₂₉	1	2	yes	—
242	#460	—	2	1	no	—
243	#448	—	2	2	no	—
244	#436	C₂²×C₂₉	1	2	yes	—
245	#435	—	2	2	no	—
246	C₈×D₄	C₂²×C₂₉	1	2	yes	—
247	#431	C₂²×C₂₉	1	1	yes	characteristic
248	#428	—	2	1	no	—
249	#428	—	2	1	no	—
250	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
252	#408	—	2	1	no	—
253	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
254	#335	C₂²×C₂₉	1	2	yes	—
255	#334	C₂²×C₂₉	1	2	yes	—
256	#333	C₂²×C₂₉	1	1	yes	characteristic
257	#333	C₂²×C₂₉	1	1	yes	characteristic
258	#332	C₂²×C₂₉	1	2	yes	—
259	#332	C₂²×C₂₉	1	2	yes	—
260	#332	C₂²×C₂₉	1	1	yes	characteristic
261	#332	C₂²×C₂₉	1	1	yes	characteristic
262	C₂×C₂₉	—	2	2	no	—
263	C₂×C₂₉	—	8	2	no	—
264	C₂×C₂₉	C₂×#461	1	1	yes	characteristic
265	C₂×C₂₉	#3062	1	1	yes	characteristic
266	C₂×C₂₉	#3069	1	1	yes	characteristic
267	C₂×#41	—	2	1	no	—
268	C₂²×Q₈	—	2	1	no	—
269	C₂×SD₁₆	—	2	2	no	—
270	C₂×SD₁₆	—	2	2	no	—
271	C₂×SD₁₆	—	2	2	no	—
272	#131	—	4	4	no	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	D₄×C₂₉	1	1	yes	characteristic
275	C₂×M₁₆	D₄×C₂₉	1	1	yes	characteristic
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	2	no	—
279	C₄⋊Q₈	—	2	1	no	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
283	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
284	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
285	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
286	#127	D₄×C₂₉	1	1	yes	characteristic
287	#125	—	2	1	no	—
288	#124	—	2	1	no	—
289	C₂²⋊Q₈	—	2	1	no	—
290	C₂²⋊Q₈	—	2	1	no	—
291	#121	—	2	1	no	—
292	#121	D₄×C₂₉	1	2	yes	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	C₂³×C₂₉	1	2	yes	—
297	#117	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
301	#107	—	2	2	no	—
302	#107	—	2	2	no	—
303	#106	—	2	2	no	—
304	#106	—	2	2	no	—
305	#106	—	2	2	no	—
306	C₄⋊C₈	—	2	1	no	—
307	C₄⋊C₈	—	2	1	no	—
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	1	yes	characteristic
312	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
313	#103	—	2	2	no	—
314	#103	—	2	2	no	—
315	#103	—	2	2	no	—
316	#102	—	2	2	no	—
317	C₂²⋊C₈	—	2	1	no	—
318	C₂²⋊C₈	—	2	2	no	—
319	C₂²⋊C₈	—	2	2	no	—
320	#97	D₄×C₂₉	1	2	yes	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	C₂³×C₂₉	1	2	yes	—
323	C₂₉	#19232	1	1	yes	characteristic, direct product factor, Sylow
324	#41	—	4	2	no	—
325	#41	—	4	2	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	4	1	no	—
331	C₂×Q₈	—	8	1	no	—
332	C₂×Q₈	—	8	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
341	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
342	SD₁₆	—	8	2	no	—
343	SD₁₆	—	8	2	no	—
344	SD₁₆	—	8	2	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	4	4	no	—
347	M₁₆	SD₁₆×C₂₉	1	4	yes	complemented
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	4	2	no	—
354	C₂×C₈	—	4	4	no	—
355	C₂×C₈	—	8	1	no	—
356	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
357	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	4	1	no	—
366	C₄⋊C₄	—	4	1	no	—
367	C₄⋊C₄	—	4	1	no	—
368	C₄⋊C₄	—	4	1	no	—
369	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	4	1	no	—
373	C₄²	—	4	1	no	—
374	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
375	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
376	C₄²	#41×C₂₉	1	1	yes	characteristic
377	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
378	C₂³	—	2	2	no	—
379	C₂³	C₂₉×#121	1	1	yes	characteristic
380	Q₈	—	4	2	no	—
381	Q₈	—	4	1	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	4	2	no	—
384	Q₈	—	4	1	no	—
385	Q₈	—	8	1	no	—
386	Q₈	—	8	2	no	—
387	D₄	—	2	2	no	—
388	D₄	—	2	2	no	—
389	D₄	—	4	4	no	—
390	D₄	—	4	2	no	—
391	D₄	—	8	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	8	2	no	—
402	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
403	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
404	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
405	C₂×C₄	C₂×SD₁₆×C₂₉	1	2	yes	—
406	C₂×C₄	C₂₉×#137	1	2	yes	—
407	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
408	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
409	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
410	C₈	—	2	2	no	—
411	C₈	—	4	1	no	—
412	C₈	—	4	1	no	—
413	C₈	—	4	2	no	—
414	C₈	—	4	1	no	—
415	C₈	—	4	1	no	—
416	C₈	C₂×SD₁₆×C₂₉	1	4	yes	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	C₂₉×#461	1	2	yes	—
423	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	4	2	no	—
428	C₄	—	8	2	no	—
429	C₄	—	8	1	no	—
430	C₄	—	8	1	no	—
431	C₄	C₂₉×#461	1	2	yes	—
432	C₄	C₂²×SD₁₆×C₂₉	1	1	yes	characteristic
433	C₄	C₂×C₂₉×#137	1	1	yes	characteristic
434	C₄	C₂₉×#576	1	1	yes	characteristic
435	C₄	C₂₉×#577	1	1	yes	characteristic
436	C₂	—	2	2	no	—
437	C₂	—	8	2	no	—
438	C₂	C₂×C₂₉×#461	1	1	yes	characteristic
439	C₂	C₂₉×#3062	1	1	yes	characteristic
440	C₂	C₂₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#121
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
3. C₂₉×#3165	C₂	semidirect
5. C₂₉×#1693	C₂	semidirect
6. C₂₉×#1691	C₂	semidirect
7. C₂₉×#1673	C₂	semidirect
8. C₂₉×#1671	C₂	semidirect
9. C₂₉×#1565	C₂	semidirect
10. C₂₉×#1542	C₂	semidirect
11. C₂×C₂₉×#332	C₂	semidirect
126. M₁₆×C₂₉	SD₁₆	semidirect
157. #19232	C₂₉	direct (N × H)
199. #3165	C₂×C₂₉	semidirect
201. #1693	C₂×C₂₉	semidirect
202. #1691	C₂×C₂₉	semidirect
203. #1673	C₂×C₂₉	semidirect
204. #1671	C₂×C₂₉	semidirect
205. #1565	C₂×C₂₉	semidirect
206. #1542	C₂×C₂₉	semidirect
207. C₂×#332	C₂×C₂₉	semidirect
323. C₂₉	#19232	direct (N × H)
347. 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×#3246	2
C₂₉×#3206	2
C₂₉×#3165	2
C₂₉×#2935	2
C₂₉×#1693	2
C₂₉×#1691	2
C₂₉×#1673	2
C₂₉×#1671	2
C₂₉×#1565	2
C₂₉×#1542	2
C₂×C₂₉×#332	2
#19232	29

Subgroups — C29×#19232 #20314132

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19232 #20314132