Subgroups — C₂₉×#19505 #20314405

Order 7424.

622 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3226	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3214	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#3206	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2981	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1699	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1685	C₂	1	2	yes	maximal, complemented
7	C₂₉×#1679	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1665	C₂	1	2	yes	maximal, complemented
9	C₂₉×#1572	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1556	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1553	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#532	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×#500	—	2	1	no	—
16	C₂₉×#496	—	2	1	no	—
17	C₂₉×#492	C₂²	1	1	yes	characteristic
18	C₂₉×#492	C₂²	1	1	yes	characteristic
19	C₂₉×#489	—	2	1	no	—
20	C₂₉×#487	C₂²	1	1	yes	characteristic
21	C₂₉×#487	C₂²	1	1	yes	characteristic
22	C₂₉×#486	—	2	1	no	—
23	C₂₉×#480	—	2	2	no	—
24	C₂₉×#474	C₂²	1	2	yes	—
25	C₂₉×#474	C₂²	1	2	yes	—
26	C₂₉×#461	—	2	2	no	—
27	C₂₉×#461	C₂²	1	2	yes	—
28	C₂₉×#459	C₂²	1	2	yes	—
29	C₂₉×#449	—	2	2	no	—
30	C₂₉×#448	—	2	2	no	—
31	C₂₉×#436	C₂²	1	2	yes	—
32	C₂₉×#435	—	2	2	no	—
33	C₈×D₄×C₂₉	C₂²	1	2	yes	—
34	C₂₉×#432	C₂²	1	1	yes	characteristic
35	C₂₉×#432	C₂²	1	1	yes	characteristic
36	C₂₉×#431	C₂²	1	1	yes	characteristic
37	C₂₉×#431	C₂²	1	1	yes	characteristic
38	C₂₉×#408	—	2	2	no	—
39	C₂₉×#335	C₂²	1	2	yes	—
40	C₂₉×#334	C₂²	1	2	yes	—
41	C₂₉×#332	C₂²	1	2	yes	—
42	C₂₉×#332	C₂²	1	2	yes	—
43	C₂₉×#332	C₂²	1	2	yes	—
44	C₂₉×#331	C₂²	1	2	yes	—
45	C₂×#41×C₂₉	—	2	1	no	—
46	C₂×#41×C₂₉	—	2	1	no	—
47	C₂²×Q₈×C₂₉	—	2	1	no	—
48	C₂×SD₁₆×C₂₉	—	2	2	no	—
49	C₂×SD₁₆×C₂₉	—	2	2	no	—
50	C₂×SD₁₆×C₂₉	—	2	2	no	—
51	C₂×D₈×C₂₉	—	2	2	no	—
52	C₂×M₁₆×C₂₉	—	2	2	no	—
53	C₂²×C₈×C₂₉	—	2	2	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	D₄	1	1	yes	characteristic
58	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
59	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
60	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₂₉×#127	D₄	1	1	yes	characteristic
62	C₂₉×#127	C₂³	1	1	yes	characteristic
63	C₂₉×#124	—	2	1	no	—
64	C₂₉×#124	—	2	1	no	—
65	C₂₉×#121	—	2	1	no	—
66	C₂₉×#121	—	2	1	no	—
67	C₂₉×#121	—	2	1	no	—
68	C₂₉×#121	D₄	1	2	yes	—
69	C₄×D₄×C₂₉	—	2	1	no	—
70	C₄×D₄×C₂₉	—	2	1	no	—
71	C₄×D₄×C₂₉	—	2	1	no	—
72	C₄×D₄×C₂₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
75	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
76	C₂₉×#107	—	2	2	no	—
77	C₂₉×#107	—	2	2	no	—
78	C₂₉×C₄⋊C₈	D₄	1	2	yes	—
79	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
80	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
81	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
82	C₂₉×#103	—	2	2	no	—
83	C₂₉×#103	—	2	2	no	—
84	C₂₉×#103	—	2	2	no	—
85	C₂₉×#102	—	2	2	no	—
86	C₂₉×#102	—	2	2	no	—
87	C₂₉×#102	—	2	2	no	—
88	C₂₉×C₂²⋊C₈	—	2	1	no	—
89	C₂₉×C₂²⋊C₈	—	2	1	no	—
90	C₂₉×C₂²⋊C₈	—	2	1	no	—
91	C₂₉×C₂²⋊C₈	—	2	2	no	—
92	C₂₉×C₂²⋊C₈	—	2	2	no	—
93	C₂₉×C₂²⋊C₈	D₄	1	2	yes	—
94	C₂₉×#97	—	2	1	no	—
95	C₂₉×#97	—	2	1	no	—
96	C₄×C₈×C₂₉	—	2	1	no	—
97	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
99	#41×C₂₉	—	8	2	no	—
100	#41×C₂₉	—	8	2	no	—
101	C₂×Q₈×C₂₉	—	2	1	no	—
102	C₂×Q₈×C₂₉	—	2	1	no	—
103	C₂×Q₈×C₂₉	—	2	1	no	—
104	C₂×Q₈×C₂₉	—	2	1	no	—
105	C₂×Q₈×C₂₉	—	4	1	no	—
106	C₂×Q₈×C₂₉	—	8	2	no	—
107	C₂×D₄×C₂₉	—	2	2	no	—
108	C₂×D₄×C₂₉	—	2	1	no	—
109	C₂×D₄×C₂₉	—	2	1	no	—
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	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₂₉	—	2	2	no	—
116	C₂²×C₄×C₂₉	—	4	1	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	D₈×C₂₉	—	8	2	no	—
125	M₁₆×C₂₉	—	8	2	no	—
126	C₂×C₈×C₂₉	—	2	2	no	—
127	C₂×C₈×C₂₉	—	2	2	no	—
128	C₂×C₈×C₂₉	—	2	2	no	—
129	C₂×C₈×C₂₉	—	8	2	no	—
130	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
132	C₄⋊C₄×C₂₉	—	2	1	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	C₂×D₄	1	2	yes	—
142	C₂²⋊C₄×C₂₉	—	2	2	no	—
143	C₂²⋊C₄×C₂₉	—	2	2	no	—
144	C₂²⋊C₄×C₂₉	—	4	1	no	—
145	C₂²⋊C₄×C₂₉	—	4	1	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	#19505	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂³×C₂₉	—	2	2	no	—
152	C₂³×C₂₉	—	4	1	no	—
153	C₂³×C₂₉	#121	1	1	yes	characteristic
154	Q₈×C₂₉	—	4	2	no	—
155	Q₈×C₂₉	—	4	2	no	—
156	Q₈×C₂₉	—	4	2	no	—
157	Q₈×C₂₉	—	8	1	no	—
158	Q₈×C₂₉	—	8	2	no	—
159	D₄×C₂₉	—	2	2	no	—
160	D₄×C₂₉	—	2	2	no	—
161	D₄×C₂₉	—	4	2	no	—
162	D₄×C₂₉	—	4	2	no	—
163	D₄×C₂₉	—	8	1	no	—
164	D₄×C₂₉	—	8	1	no	—
165	D₄×C₂₉	—	8	1	no	—
166	D₄×C₂₉	—	8	2	no	—
167	D₄×C₂₉	—	8	2	no	—
168	C₂×C₄×C₂₉	—	2	2	no	—
169	C₂×C₄×C₂₉	—	2	2	no	—
170	C₂×C₄×C₂₉	—	2	2	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	—	4	1	no	—
175	C₂×C₄×C₂₉	—	4	1	no	—
176	C₂×C₄×C₂₉	—	4	1	no	—
177	C₂×C₄×C₂₉	—	8	2	no	—
178	C₂×C₄×C₂₉	—	8	2	no	—
179	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
180	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
181	C₂×C₄×C₂₉	#121	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	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
185	C₈×C₂₉	—	2	2	no	—
186	C₈×C₂₉	—	2	2	no	—
187	C₈×C₂₉	—	4	2	no	—
188	C₈×C₂₉	—	4	2	no	—
189	C₈×C₂₉	—	4	2	no	—
190	#3226	C₂×C₂₉	1	1	yes	characteristic, complemented
191	#3214	C₂×C₂₉	1	1	yes	characteristic
192	#3206	C₂×C₂₉	1	1	yes	characteristic, complemented
193	#2981	C₂×C₂₉	1	1	yes	characteristic, complemented
194	#1699	C₂×C₂₉	1	2	yes	complemented
195	#1685	C₂×C₂₉	1	2	yes	complemented
196	#1679	C₂×C₂₉	1	2	yes	complemented
197	#1665	C₂×C₂₉	1	2	yes	complemented
198	#1572	C₂×C₂₉	1	1	yes	characteristic, complemented
199	#1556	C₂×C₂₉	1	1	yes	characteristic, complemented
200	#1553	C₂×C₂₉	1	1	yes	characteristic, complemented
201	C₂²×C₂₉	—	2	1	no	—
202	C₂²×C₂₉	—	2	1	no	—
203	C₂²×C₂₉	—	2	1	no	—
204	C₂²×C₂₉	—	4	2	no	—
205	C₂²×C₂₉	—	4	2	no	—
206	C₂²×C₂₉	—	4	2	no	—
207	C₂²×C₂₉	—	8	1	no	—
208	C₂²×C₂₉	—	8	1	no	—
209	C₂²×C₂₉	—	8	1	no	—
210	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
211	C₄×C₂₉	—	2	1	no	—
212	C₄×C₂₉	—	2	1	no	—
213	C₄×C₂₉	—	2	1	no	—
214	C₄×C₂₉	—	2	1	no	—
215	C₄×C₂₉	—	4	2	no	—
216	C₄×C₂₉	—	8	1	no	—
217	C₄×C₂₉	—	8	1	no	—
218	C₄×C₂₉	—	8	1	no	—
219	C₄×C₂₉	#576	1	2	yes	—
220	C₄×C₂₉	#577	1	2	yes	—
221	#532	C₂²×C₂₉	1	1	yes	characteristic
222	#532	C₂²×C₂₉	1	1	yes	characteristic
223	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
224	#500	—	2	1	no	—
225	#496	—	2	1	no	—
226	#492	C₂²×C₂₉	1	1	yes	characteristic
227	#492	C₂²×C₂₉	1	1	yes	characteristic
228	#489	—	2	1	no	—
229	#487	C₂²×C₂₉	1	1	yes	characteristic
230	#487	C₂²×C₂₉	1	1	yes	characteristic
231	#486	—	2	1	no	—
232	#480	—	2	2	no	—
233	#474	C₂²×C₂₉	1	2	yes	—
234	#474	C₂²×C₂₉	1	2	yes	—
235	#461	—	2	2	no	—
236	#461	C₂²×C₂₉	1	2	yes	—
237	#459	C₂²×C₂₉	1	2	yes	—
238	#449	—	2	2	no	—
239	#448	—	2	2	no	—
240	#436	C₂²×C₂₉	1	2	yes	—
241	#435	—	2	2	no	—
242	C₈×D₄	C₂²×C₂₉	1	2	yes	—
243	#432	C₂²×C₂₉	1	1	yes	characteristic
244	#432	C₂²×C₂₉	1	1	yes	characteristic
245	#431	C₂²×C₂₉	1	1	yes	characteristic
246	#431	C₂²×C₂₉	1	1	yes	characteristic
247	#408	—	2	2	no	—
248	#335	C₂²×C₂₉	1	2	yes	—
249	#334	C₂²×C₂₉	1	2	yes	—
250	#332	C₂²×C₂₉	1	2	yes	—
251	#332	C₂²×C₂₉	1	2	yes	—
252	#332	C₂²×C₂₉	1	2	yes	—
253	#331	C₂²×C₂₉	1	2	yes	—
254	C₂×C₂₉	—	4	1	no	—
255	C₂×C₂₉	—	8	2	no	—
256	C₂×C₂₉	—	16	1	no	—
257	C₂×C₂₉	#3041	1	1	yes	characteristic
258	C₂×C₂₉	#3057	1	1	yes	characteristic
259	C₂×C₂₉	#3069	1	1	yes	characteristic
260	C₂×#41	—	2	1	no	—
261	C₂×#41	—	2	1	no	—
262	C₂²×Q₈	—	2	1	no	—
263	C₂×SD₁₆	—	2	2	no	—
264	C₂×SD₁₆	—	2	2	no	—
265	C₂×SD₁₆	—	2	2	no	—
266	C₂×D₈	—	2	2	no	—
267	C₂×M₁₆	—	2	2	no	—
268	C₂²×C₈	—	2	2	no	—
269	C₄⋊Q₈	—	2	1	no	—
270	C₄⋊Q₈	—	2	1	no	—
271	C₄⋊Q₈	—	2	1	no	—
272	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
273	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
274	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
275	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
276	#127	D₄×C₂₉	1	1	yes	characteristic
277	#127	C₂³×C₂₉	1	1	yes	characteristic
278	#124	—	2	1	no	—
279	#124	—	2	1	no	—
280	#121	—	2	1	no	—
281	#121	—	2	1	no	—
282	#121	—	2	1	no	—
283	#121	D₄×C₂₉	1	2	yes	—
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	C₂³×C₂₉	1	2	yes	—
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	2	no	—
292	#107	—	2	2	no	—
293	C₄⋊C₈	D₄×C₂₉	1	2	yes	—
294	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
295	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
296	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
297	#103	—	2	2	no	—
298	#103	—	2	2	no	—
299	#103	—	2	2	no	—
300	#102	—	2	2	no	—
301	#102	—	2	2	no	—
302	#102	—	2	2	no	—
303	C₂²⋊C₈	—	2	1	no	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₂²⋊C₈	—	2	1	no	—
306	C₂²⋊C₈	—	2	2	no	—
307	C₂²⋊C₈	—	2	2	no	—
308	C₂²⋊C₈	D₄×C₂₉	1	2	yes	—
309	#97	—	2	1	no	—
310	#97	—	2	1	no	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
313	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
314	C₂₉	#19505	1	1	yes	characteristic, direct product factor, Sylow
315	#41	—	8	2	no	—
316	#41	—	8	2	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	4	1	no	—
322	C₂×Q₈	—	8	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	—	4	1	no	—
334	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
336	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
337	SD₁₆	—	8	2	no	—
338	SD₁₆	—	8	2	no	—
339	SD₁₆	—	8	2	no	—
340	D₈	—	8	2	no	—
341	M₁₆	—	8	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	8	2	no	—
346	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
347	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	4	1	no	—
361	C₂²⋊C₄	—	4	1	no	—
362	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
363	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
364	C₄²	#41×C₂₉	1	1	yes	characteristic
365	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
366	C₂³	—	2	2	no	—
367	C₂³	—	4	1	no	—
368	C₂³	C₂₉×#121	1	1	yes	characteristic
369	Q₈	—	4	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	8	1	no	—
373	Q₈	—	8	2	no	—
374	D₄	—	2	2	no	—
375	D₄	—	2	2	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	8	1	no	—
379	D₄	—	8	1	no	—
380	D₄	—	8	1	no	—
381	D₄	—	8	2	no	—
382	D₄	—	8	2	no	—
383	C₂×C₄	—	2	2	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	—	4	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	8	2	no	—
393	C₂×C₄	—	8	2	no	—
394	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
395	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
396	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
397	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
399	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
400	C₈	—	2	2	no	—
401	C₈	—	2	2	no	—
402	C₈	—	4	2	no	—
403	C₈	—	4	2	no	—
404	C₈	—	4	2	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	1	no	—
414	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	4	2	no	—
420	C₄	—	8	1	no	—
421	C₄	—	8	1	no	—
422	C₄	—	8	1	no	—
423	C₄	C₂₉×#576	1	2	yes	—
424	C₄	C₂₉×#577	1	2	yes	—
425	C₂	—	4	1	no	—
426	C₂	—	8	2	no	—
427	C₂	—	16	1	no	—
428	C₂	C₂₉×#3041	1	1	yes	characteristic
429	C₂	C₂₉×#3057	1	1	yes	characteristic
430	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×#3214	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×#3226	C₂	semidirect
3. C₂₉×#3206	C₂	semidirect
4. C₂₉×#2981	C₂	semidirect
5. C₂₉×#1699	C₂	semidirect
6. C₂₉×#1685	C₂	semidirect
7. C₂₉×#1679	C₂	semidirect
8. C₂₉×#1665	C₂	semidirect
9. C₂₉×#1572	C₂	semidirect
10. C₂₉×#1556	C₂	semidirect
11. C₂₉×#1553	C₂	semidirect
150. #19505	C₂₉	direct (N × H)
190. #3226	C₂×C₂₉	semidirect
192. #3206	C₂×C₂₉	semidirect
193. #2981	C₂×C₂₉	semidirect
194. #1699	C₂×C₂₉	semidirect
195. #1685	C₂×C₂₉	semidirect
196. #1679	C₂×C₂₉	semidirect
197. #1665	C₂×C₂₉	semidirect
198. #1572	C₂×C₂₉	semidirect
199. #1556	C₂×C₂₉	semidirect
200. #1553	C₂×C₂₉	semidirect
314. C₂₉	#19505	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×#3226	2
C₂₉×#3214	2
C₂₉×#3206	2
C₂₉×#2981	2
C₂₉×#1699	2
C₂₉×#1685	2
C₂₉×#1679	2
C₂₉×#1665	2
C₂₉×#1572	2
C₂₉×#1556	2
C₂₉×#1553	2
#19505	29

Subgroups — C29×#19505 #20314405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19505 #20314405