Subgroups — C₂₉×#19570 #20314470

Order 7424.

584 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3254	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#3227	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2986	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1702	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1692	C₂	1	2	yes	maximal, complemented
7	C₂₉×#1682	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1672	C₂	1	2	yes	maximal, complemented
9	C₂₉×#1574	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1546	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1543	C₂	1	1	yes	maximal, characteristic
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	C₂₉×#498	C₂²	1	2	yes	—
16	C₂₉×#494	—	2	1	no	—
17	C₂₉×#487	—	2	1	no	—
18	C₂₉×#486	C₂²	1	2	yes	—
19	C₂₉×#481	—	2	2	no	—
20	C₂₉×#477	C₂²	1	2	yes	—
21	C₂₉×#476	—	2	1	no	—
22	C₂₉×#476	—	2	1	no	—
23	C₂₉×#474	—	2	1	no	—
24	C₂₉×#468	—	2	2	no	—
25	C₂₉×#462	C₂²	1	2	yes	—
26	C₂₉×#462	C₂²	1	2	yes	—
27	C₂₉×#461	—	2	1	no	—
28	C₂₉×#460	C₂²	1	2	yes	—
29	C₂₉×#451	—	2	2	no	—
30	C₂₉×#446	—	2	1	no	—
31	C₂₉×#446	C₂²	1	2	yes	—
32	C₈×Q₈×C₂₉	—	2	1	no	—
33	C₈×Q₈×C₂₉	C₂²	1	2	yes	—
34	C₂₉×#433	—	2	2	no	—
35	C₂₉×#431	C₂²	1	1	yes	characteristic
36	C₂₉×#431	C₂²	1	1	yes	characteristic
37	C₂₉×#431	C₂²	1	1	yes	characteristic
38	C₂₉×#423	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	2	yes	—
45	C₂₉×#331	C₂²	1	1	yes	characteristic
46	C₂₉×#331	C₂²	1	1	yes	characteristic
47	C₂×#41×C₂₉	—	2	1	no	—
48	C₂²×Q₈×C₂₉	—	2	1	no	—
49	C₂×Q₁₆×C₂₉	—	2	2	no	—
50	C₂×Q₁₆×C₂₉	—	2	2	no	—
51	C₂×SD₁₆×C₂₉	—	2	2	no	—
52	C₂×M₁₆×C₂₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
57	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
58	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₂₉×#127	C₂³	1	1	yes	characteristic
61	C₂₉×#125	—	2	1	no	—
62	C₂₉×#124	—	2	1	no	—
63	C₂₉×C₂²⋊Q₈	—	2	1	no	—
64	C₂₉×C₂²⋊Q₈	D₄	1	2	yes	—
65	C₂₉×#121	—	2	1	no	—
66	C₂₉×#121	—	2	1	no	—
67	C₄×Q₈×C₂₉	—	2	1	no	—
68	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
69	C₄×D₄×C₂₉	—	2	1	no	—
70	C₄×D₄×C₂₉	—	2	1	no	—
71	C₂₉×#117	—	2	1	no	—
72	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
74	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
75	C₂₉×#107	—	2	2	no	—
76	C₂₉×#106	—	2	2	no	—
77	C₂₉×#106	—	2	2	no	—
78	C₂₉×C₄⋊C₈	—	2	2	no	—
79	C₂₉×C₄⋊C₈	—	2	2	no	—
80	C₂₉×C₄⋊C₈	—	2	1	no	—
81	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
82	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
83	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
84	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
88	C₂₉×#103	—	2	2	no	—
89	C₂₉×#103	—	2	2	no	—
90	C₂₉×#103	—	2	2	no	—
91	C₂₉×#102	—	2	2	no	—
92	C₂₉×#102	—	2	2	no	—
93	C₂₉×#102	—	2	2	no	—
94	C₂₉×C₂²⋊C₈	—	2	1	no	—
95	C₂₉×C₂²⋊C₈	—	2	1	no	—
96	C₂₉×C₂²⋊C₈	D₄	1	2	yes	—
97	C₂₉×#97	—	2	2	no	—
98	C₄×C₈×C₂₉	—	2	2	no	—
99	C₄×C₈×C₂₉	—	2	1	no	—
100	C₄×C₈×C₂₉	—	2	1	no	—
101	C₄×C₈×C₂₉	C₂³	1	2	yes	—
102	#41×C₂₉	—	8	2	no	—
103	C₂×Q₈×C₂₉	—	2	1	no	—
104	C₂×Q₈×C₂₉	—	2	2	no	—
105	C₂×Q₈×C₂₉	—	2	1	no	—
106	C₂×Q₈×C₂₉	—	4	1	no	—
107	C₂×Q₈×C₂₉	—	8	1	no	—
108	C₂×Q₈×C₂₉	—	8	1	no	—
109	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
110	C₂×D₄×C₂₉	—	2	1	no	—
111	C₂×D₄×C₂₉	—	2	1	no	—
112	C₂×D₄×C₂₉	—	2	1	no	—
113	C₂×D₄×C₂₉	—	4	1	no	—
114	C₂²×C₄×C₂₉	—	4	1	no	—
115	C₂²×C₄×C₂₉	—	4	1	no	—
116	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
119	Q₁₆×C₂₉	—	8	2	no	—
120	Q₁₆×C₂₉	—	8	2	no	—
121	SD₁₆×C₂₉	—	8	2	no	—
122	M₁₆×C₂₉	—	8	1	no	—
123	C₂×C₈×C₂₉	—	2	2	no	—
124	C₂×C₈×C₂₉	—	2	1	no	—
125	C₂×C₈×C₂₉	—	2	1	no	—
126	C₂×C₈×C₂₉	—	2	1	no	—
127	C₂×C₈×C₂₉	—	2	1	no	—
128	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
130	C₄⋊C₄×C₂₉	—	2	1	no	—
131	C₄⋊C₄×C₂₉	—	2	1	no	—
132	C₄⋊C₄×C₂₉	—	2	1	no	—
133	C₄⋊C₄×C₂₉	—	2	2	no	—
134	C₄⋊C₄×C₂₉	—	2	2	no	—
135	C₄⋊C₄×C₂₉	—	2	2	no	—
136	C₄⋊C₄×C₂₉	—	2	1	no	—
137	C₄⋊C₄×C₂₉	—	2	1	no	—
138	C₄⋊C₄×C₂₉	—	2	2	no	—
139	C₄⋊C₄×C₂₉	—	4	1	no	—
140	C₄⋊C₄×C₂₉	—	4	1	no	—
141	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
142	C₂²⋊C₄×C₂₉	—	2	2	no	—
143	C₂²⋊C₄×C₂₉	—	4	1	no	—
144	C₂²⋊C₄×C₂₉	—	4	1	no	—
145	C₄²×C₂₉	—	2	2	no	—
146	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₂₉	#41	1	1	yes	characteristic
149	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
150	#19570	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂³×C₂₉	—	4	1	no	—
152	C₂³×C₂₉	#121	1	1	yes	characteristic
153	Q₈×C₂₉	—	2	2	no	—
154	Q₈×C₂₉	—	2	2	no	—
155	Q₈×C₂₉	—	4	2	no	—
156	Q₈×C₂₉	—	4	2	no	—
157	Q₈×C₂₉	—	4	2	no	—
158	Q₈×C₂₉	—	8	1	no	—
159	Q₈×C₂₉	—	8	2	no	—
160	D₄×C₂₉	—	4	1	no	—
161	D₄×C₂₉	—	4	1	no	—
162	D₄×C₂₉	—	4	1	no	—
163	D₄×C₂₉	—	4	1	no	—
164	D₄×C₂₉	—	8	1	no	—
165	D₄×C₂₉	—	8	2	no	—
166	C₂×C₄×C₂₉	—	2	1	no	—
167	C₂×C₄×C₂₉	—	2	1	no	—
168	C₂×C₄×C₂₉	—	2	1	no	—
169	C₂×C₄×C₂₉	—	2	1	no	—
170	C₂×C₄×C₂₉	—	2	2	no	—
171	C₂×C₄×C₂₉	—	2	2	no	—
172	C₂×C₄×C₂₉	—	2	2	no	—
173	C₂×C₄×C₂₉	—	4	1	no	—
174	C₂×C₄×C₂₉	—	4	2	no	—
175	C₂×C₄×C₂₉	—	8	2	no	—
176	C₂×C₄×C₂₉	—	8	2	no	—
177	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
178	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
179	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
180	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
183	C₈×C₂₉	—	2	2	no	—
184	C₈×C₂₉	—	2	2	no	—
185	C₈×C₂₉	—	4	2	no	—
186	C₈×C₂₉	—	4	1	no	—
187	C₈×C₂₉	—	4	1	no	—
188	C₈×C₂₉	—	4	1	no	—
189	C₈×C₂₉	—	4	1	no	—
190	#3254	C₂×C₂₉	1	1	yes	characteristic
191	#3227	C₂×C₂₉	1	1	yes	characteristic
192	#3209	C₂×C₂₉	1	1	yes	characteristic, complemented
193	#2986	C₂×C₂₉	1	1	yes	characteristic, complemented
194	#1702	C₂×C₂₉	1	2	yes	complemented
195	#1692	C₂×C₂₉	1	2	yes	complemented
196	#1682	C₂×C₂₉	1	2	yes	complemented
197	#1672	C₂×C₂₉	1	2	yes	complemented
198	#1574	C₂×C₂₉	1	1	yes	characteristic, complemented
199	#1546	C₂×C₂₉	1	1	yes	characteristic, complemented
200	#1543	C₂×C₂₉	1	1	yes	characteristic
201	C₂²×C₂₉	—	2	1	no	—
202	C₂²×C₂₉	—	2	1	no	—
203	C₂²×C₂₉	—	2	1	no	—
204	C₂²×C₂₉	—	8	1	no	—
205	C₂²×C₂₉	—	8	1	no	—
206	C₂²×C₂₉	—	8	1	no	—
207	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
208	C₄×C₂₉	—	2	1	no	—
209	C₄×C₂₉	—	2	1	no	—
210	C₄×C₂₉	—	2	1	no	—
211	C₄×C₂₉	—	4	2	no	—
212	C₄×C₂₉	—	4	2	no	—
213	C₄×C₂₉	—	8	2	no	—
214	C₄×C₂₉	—	8	1	no	—
215	C₄×C₂₉	#471	1	2	yes	—
216	C₄×C₂₉	#576	1	1	yes	characteristic
217	C₄×C₂₉	#577	1	1	yes	characteristic
218	C₄×C₂₉	#578	1	1	yes	characteristic
219	C₄×C₂₉	#578	1	1	yes	characteristic
220	#533	C₂²×C₂₉	1	1	yes	characteristic
221	#532	C₂²×C₂₉	1	1	yes	characteristic
222	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
223	#498	C₂²×C₂₉	1	2	yes	—
224	#494	—	2	1	no	—
225	#487	—	2	1	no	—
226	#486	C₂²×C₂₉	1	2	yes	—
227	#481	—	2	2	no	—
228	#477	C₂²×C₂₉	1	2	yes	—
229	#476	—	2	1	no	—
230	#476	—	2	1	no	—
231	#474	—	2	1	no	—
232	#468	—	2	2	no	—
233	#462	C₂²×C₂₉	1	2	yes	—
234	#462	C₂²×C₂₉	1	2	yes	—
235	#461	—	2	1	no	—
236	#460	C₂²×C₂₉	1	2	yes	—
237	#451	—	2	2	no	—
238	#446	—	2	1	no	—
239	#446	C₂²×C₂₉	1	2	yes	—
240	C₈×Q₈	—	2	1	no	—
241	C₈×Q₈	C₂²×C₂₉	1	2	yes	—
242	#433	—	2	2	no	—
243	#431	C₂²×C₂₉	1	1	yes	characteristic
244	#431	C₂²×C₂₉	1	1	yes	characteristic
245	#431	C₂²×C₂₉	1	1	yes	characteristic
246	#423	C₂²×C₂₉	1	1	yes	characteristic
247	#335	C₂²×C₂₉	1	2	yes	—
248	#334	C₂²×C₂₉	1	2	yes	—
249	#333	C₂²×C₂₉	1	1	yes	characteristic
250	#333	C₂²×C₂₉	1	1	yes	characteristic
251	#332	C₂²×C₂₉	1	2	yes	—
252	#332	C₂²×C₂₉	1	2	yes	—
253	#331	C₂²×C₂₉	1	1	yes	characteristic
254	#331	C₂²×C₂₉	1	1	yes	characteristic
255	C₂×C₂₉	—	4	1	no	—
256	C₂×C₂₉	—	16	1	no	—
257	C₂×C₂₉	#3044	1	1	yes	characteristic
258	C₂×C₂₉	#3062	1	1	yes	characteristic
259	C₂×C₂₉	C₂×#471	1	1	yes	characteristic
260	C₂×#41	—	2	1	no	—
261	C₂²×Q₈	—	2	1	no	—
262	C₂×Q₁₆	—	2	2	no	—
263	C₂×Q₁₆	—	2	2	no	—
264	C₂×SD₁₆	—	2	2	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	—	2	1	no	—
269	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
270	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
271	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
272	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
273	#127	C₂³×C₂₉	1	1	yes	characteristic
274	#125	—	2	1	no	—
275	#124	—	2	1	no	—
276	C₂²⋊Q₈	—	2	1	no	—
277	C₂²⋊Q₈	D₄×C₂₉	1	2	yes	—
278	#121	—	2	1	no	—
279	#121	—	2	1	no	—
280	C₄×Q₈	—	2	1	no	—
281	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
282	C₄×D₄	—	2	1	no	—
283	C₄×D₄	—	2	1	no	—
284	#117	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
288	#107	—	2	2	no	—
289	#106	—	2	2	no	—
290	#106	—	2	2	no	—
291	C₄⋊C₈	—	2	2	no	—
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	D₄×C₂₉	1	1	yes	characteristic
295	C₄⋊C₈	D₄×C₂₉	1	1	yes	characteristic
296	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
297	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
298	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
299	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
300	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
301	#103	—	2	2	no	—
302	#103	—	2	2	no	—
303	#103	—	2	2	no	—
304	#102	—	2	2	no	—
305	#102	—	2	2	no	—
306	#102	—	2	2	no	—
307	C₂²⋊C₈	—	2	1	no	—
308	C₂²⋊C₈	—	2	1	no	—
309	C₂²⋊C₈	D₄×C₂₉	1	2	yes	—
310	#97	—	2	2	no	—
311	C₄×C₈	—	2	2	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	—	2	1	no	—
314	C₄×C₈	C₂³×C₂₉	1	2	yes	—
315	C₂₉	#19570	1	1	yes	characteristic, direct product factor, Sylow
316	#41	—	8	2	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	4	1	no	—
321	C₂×Q₈	—	8	1	no	—
322	C₂×Q₈	—	8	1	no	—
323	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	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	#41×C₂₉	1	1	yes	characteristic
333	Q₁₆	—	8	2	no	—
334	Q₁₆	—	8	2	no	—
335	SD₁₆	—	8	2	no	—
336	M₁₆	—	8	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
343	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₂²⋊C₄	—	4	1	no	—
358	C₂²⋊C₄	—	4	1	no	—
359	C₄²	—	2	2	no	—
360	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
361	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
362	C₄²	#41×C₂₉	1	1	yes	characteristic
363	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
364	C₂³	—	4	1	no	—
365	C₂³	C₂₉×#121	1	1	yes	characteristic
366	Q₈	—	2	2	no	—
367	Q₈	—	2	2	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	8	1	no	—
372	Q₈	—	8	2	no	—
373	D₄	—	4	1	no	—
374	D₄	—	4	1	no	—
375	D₄	—	4	1	no	—
376	D₄	—	4	1	no	—
377	D₄	—	8	1	no	—
378	D₄	—	8	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	8	2	no	—
389	C₂×C₄	—	8	2	no	—
390	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
391	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
392	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
395	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
396	C₈	—	2	2	no	—
397	C₈	—	2	2	no	—
398	C₈	—	4	2	no	—
399	C₈	—	4	1	no	—
400	C₈	—	4	1	no	—
401	C₈	—	4	1	no	—
402	C₈	—	4	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	8	2	no	—
416	C₄	—	8	1	no	—
417	C₄	C₂₉×#471	1	2	yes	—
418	C₄	C₂₉×#576	1	1	yes	characteristic
419	C₄	C₂₉×#577	1	1	yes	characteristic
420	C₄	C₂₉×#578	1	1	yes	characteristic
421	C₄	C₂₉×#578	1	1	yes	characteristic
422	C₂	—	4	1	no	—
423	C₂	—	16	1	no	—
424	C₂	C₂₉×#3044	1	1	yes	characteristic
425	C₂	C₂₉×#3062	1	1	yes	characteristic
426	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×#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×#3209	C₂	semidirect
4. C₂₉×#2986	C₂	semidirect
5. C₂₉×#1702	C₂	semidirect
6. C₂₉×#1692	C₂	semidirect
7. C₂₉×#1682	C₂	semidirect
8. C₂₉×#1672	C₂	semidirect
9. C₂₉×#1574	C₂	semidirect
10. C₂₉×#1546	C₂	semidirect
150. #19570	C₂₉	direct (N × H)
192. #3209	C₂×C₂₉	semidirect
193. #2986	C₂×C₂₉	semidirect
194. #1702	C₂×C₂₉	semidirect
195. #1692	C₂×C₂₉	semidirect
196. #1682	C₂×C₂₉	semidirect
197. #1672	C₂×C₂₉	semidirect
198. #1574	C₂×C₂₉	semidirect
199. #1546	C₂×C₂₉	semidirect
315. C₂₉	#19570	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×#3254	2
C₂₉×#3227	2
C₂₉×#3209	2
C₂₉×#2986	2
C₂₉×#1702	2
C₂₉×#1692	2
C₂₉×#1682	2
C₂₉×#1672	2
C₂₉×#1574	2
C₂₉×#1546	2
C₂₉×#1543	2
#19570	29

Subgroups — C29×#19570 #20314470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19570 #20314470