Subgroups — C₂₉×#19513 #20314413

Order 7424.

610 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×#3227	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3227	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3214	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2981	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1697	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1691	C₂	1	2	yes	maximal, complemented
7	C₂₉×#1677	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1671	C₂	1	2	yes	maximal, complemented
9	C₂₉×#1572	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1558	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×#498	—	2	1	no	—
16	C₂₉×#498	C₂²	1	1	yes	characteristic
17	C₂₉×#498	C₂²	1	1	yes	characteristic
18	C₂₉×#496	—	2	1	no	—
19	C₂₉×#489	—	2	1	no	—
20	C₂₉×#486	—	2	1	no	—
21	C₂₉×#486	C₂²	1	1	yes	characteristic
22	C₂₉×#486	C₂²	1	1	yes	characteristic
23	C₂₉×#481	—	2	2	no	—
24	C₂₉×#481	—	2	2	no	—
25	C₂₉×#476	—	2	2	no	—
26	C₂₉×#476	C₂²	1	2	yes	—
27	C₂₉×#476	C₂²	1	2	yes	—
28	C₂₉×#461	C₂²	1	2	yes	—
29	C₂₉×#459	C₂²	1	2	yes	—
30	C₂₉×#449	—	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×#333	C₂²	1	2	yes	—
42	C₂₉×#333	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×D₈×C₂₉	—	2	2	no	—
50	C₂×M₁₆×C₂₉	—	2	2	no	—
51	C₂²×C₈×C₂₉	—	2	2	no	—
52	C₂₉×C₄⋊Q₈	—	2	1	no	—
53	C₂₉×C₄⋊Q₈	—	2	1	no	—
54	C₂₉×C₄⋊Q₈	—	2	1	no	—
55	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
56	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
57	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
58	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
59	C₂₉×#127	D₄	1	1	yes	characteristic
60	C₂₉×#127	C₂³	1	1	yes	characteristic
61	C₂₉×#124	—	2	1	no	—
62	C₂₉×#124	—	2	1	no	—
63	C₂₉×#121	—	2	1	no	—
64	C₂₉×#121	—	2	1	no	—
65	C₂₉×#121	—	2	1	no	—
66	C₂₉×#121	D₄	1	2	yes	—
67	C₄×D₄×C₂₉	—	2	1	no	—
68	C₄×D₄×C₂₉	—	2	1	no	—
69	C₄×D₄×C₂₉	—	2	1	no	—
70	C₄×D₄×C₂₉	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
73	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
74	C₂₉×#106	—	2	2	no	—
75	C₂₉×#106	—	2	2	no	—
76	C₂₉×#106	—	2	2	no	—
77	C₂₉×#106	—	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×#102	—	2	2	no	—
84	C₂₉×#102	—	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	D₈×C₂₉	—	8	2	no	—
123	M₁₆×C₂₉	—	8	2	no	—
124	C₂×C₈×C₂₉	—	2	2	no	—
125	C₂×C₈×C₂₉	—	2	2	no	—
126	C₂×C₈×C₂₉	—	2	2	no	—
127	C₂×C₈×C₂₉	—	8	2	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	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	—	4	1	no	—
138	C₄⋊C₄×C₂₉	—	4	1	no	—
139	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
140	C₂²⋊C₄×C₂₉	—	2	2	no	—
141	C₂²⋊C₄×C₂₉	—	2	2	no	—
142	C₂²⋊C₄×C₂₉	—	4	1	no	—
143	C₂²⋊C₄×C₂₉	—	4	1	no	—
144	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₂₉	#41	1	1	yes	characteristic
147	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
148	#19513	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂³×C₂₉	—	2	2	no	—
150	C₂³×C₂₉	—	4	1	no	—
151	C₂³×C₂₉	#121	1	1	yes	characteristic
152	Q₈×C₂₉	—	4	2	no	—
153	Q₈×C₂₉	—	8	1	no	—
154	Q₈×C₂₉	—	8	1	no	—
155	Q₈×C₂₉	—	8	1	no	—
156	Q₈×C₂₉	—	8	2	no	—
157	D₄×C₂₉	—	2	2	no	—
158	D₄×C₂₉	—	2	2	no	—
159	D₄×C₂₉	—	4	2	no	—
160	D₄×C₂₉	—	4	2	no	—
161	D₄×C₂₉	—	8	1	no	—
162	D₄×C₂₉	—	8	1	no	—
163	D₄×C₂₉	—	8	1	no	—
164	D₄×C₂₉	—	8	2	no	—
165	D₄×C₂₉	—	8	2	no	—
166	C₂×C₄×C₂₉	—	2	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	2	no	—
171	C₂×C₄×C₂₉	—	4	2	no	—
172	C₂×C₄×C₂₉	—	4	1	no	—
173	C₂×C₄×C₂₉	—	4	1	no	—
174	C₂×C₄×C₂₉	—	4	1	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	2	no	—
187	C₈×C₂₉	—	4	2	no	—
188	#3227	C₂×C₂₉	1	1	yes	characteristic, complemented
189	#3227	C₂×C₂₉	1	1	yes	characteristic, complemented
190	#3214	C₂×C₂₉	1	1	yes	characteristic
191	#2981	C₂×C₂₉	1	1	yes	characteristic, complemented
192	#1697	C₂×C₂₉	1	2	yes	complemented
193	#1691	C₂×C₂₉	1	2	yes	complemented
194	#1677	C₂×C₂₉	1	2	yes	complemented
195	#1671	C₂×C₂₉	1	2	yes	complemented
196	#1572	C₂×C₂₉	1	1	yes	characteristic, complemented
197	#1558	C₂×C₂₉	1	1	yes	characteristic, complemented
198	#1553	C₂×C₂₉	1	1	yes	characteristic, complemented
199	C₂²×C₂₉	—	2	1	no	—
200	C₂²×C₂₉	—	2	1	no	—
201	C₂²×C₂₉	—	2	1	no	—
202	C₂²×C₂₉	—	4	2	no	—
203	C₂²×C₂₉	—	4	2	no	—
204	C₂²×C₂₉	—	4	2	no	—
205	C₂²×C₂₉	—	8	1	no	—
206	C₂²×C₂₉	—	8	1	no	—
207	C₂²×C₂₉	—	8	1	no	—
208	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
209	C₄×C₂₉	—	2	1	no	—
210	C₄×C₂₉	—	2	1	no	—
211	C₄×C₂₉	—	2	1	no	—
212	C₄×C₂₉	—	2	1	no	—
213	C₄×C₂₉	—	4	2	no	—
214	C₄×C₂₉	—	8	1	no	—
215	C₄×C₂₉	—	8	1	no	—
216	C₄×C₂₉	—	8	1	no	—
217	C₄×C₂₉	#577	1	2	yes	—
218	C₄×C₂₉	#577	1	2	yes	—
219	#532	C₂²×C₂₉	1	1	yes	characteristic
220	#532	C₂²×C₂₉	1	1	yes	characteristic
221	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
222	#498	—	2	1	no	—
223	#498	C₂²×C₂₉	1	1	yes	characteristic
224	#498	C₂²×C₂₉	1	1	yes	characteristic
225	#496	—	2	1	no	—
226	#489	—	2	1	no	—
227	#486	—	2	1	no	—
228	#486	C₂²×C₂₉	1	1	yes	characteristic
229	#486	C₂²×C₂₉	1	1	yes	characteristic
230	#481	—	2	2	no	—
231	#481	—	2	2	no	—
232	#476	—	2	2	no	—
233	#476	C₂²×C₂₉	1	2	yes	—
234	#476	C₂²×C₂₉	1	2	yes	—
235	#461	C₂²×C₂₉	1	2	yes	—
236	#459	C₂²×C₂₉	1	2	yes	—
237	#449	—	2	2	no	—
238	#436	C₂²×C₂₉	1	2	yes	—
239	#435	—	2	2	no	—
240	C₈×D₄	C₂²×C₂₉	1	2	yes	—
241	#432	C₂²×C₂₉	1	1	yes	characteristic
242	#432	C₂²×C₂₉	1	1	yes	characteristic
243	#431	C₂²×C₂₉	1	1	yes	characteristic
244	#431	C₂²×C₂₉	1	1	yes	characteristic
245	#408	—	2	2	no	—
246	#335	C₂²×C₂₉	1	2	yes	—
247	#334	C₂²×C₂₉	1	2	yes	—
248	#333	C₂²×C₂₉	1	2	yes	—
249	#333	C₂²×C₂₉	1	2	yes	—
250	#332	C₂²×C₂₉	1	2	yes	—
251	#331	C₂²×C₂₉	1	2	yes	—
252	C₂×C₂₉	—	4	1	no	—
253	C₂×C₂₉	—	8	2	no	—
254	C₂×C₂₉	—	16	1	no	—
255	C₂×C₂₉	#3042	1	1	yes	characteristic
256	C₂×C₂₉	#3057	1	1	yes	characteristic
257	C₂×C₂₉	#3068	1	1	yes	characteristic
258	C₂×#41	—	2	1	no	—
259	C₂×#41	—	2	1	no	—
260	C₂²×Q₈	—	2	1	no	—
261	C₂×SD₁₆	—	2	2	no	—
262	C₂×D₈	—	2	2	no	—
263	C₂×M₁₆	—	2	2	no	—
264	C₂²×C₈	—	2	2	no	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
269	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
270	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
271	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
272	#127	D₄×C₂₉	1	1	yes	characteristic
273	#127	C₂³×C₂₉	1	1	yes	characteristic
274	#124	—	2	1	no	—
275	#124	—	2	1	no	—
276	#121	—	2	1	no	—
277	#121	—	2	1	no	—
278	#121	—	2	1	no	—
279	#121	D₄×C₂₉	1	2	yes	—
280	C₄×D₄	—	2	1	no	—
281	C₄×D₄	—	2	1	no	—
282	C₄×D₄	—	2	1	no	—
283	C₄×D₄	C₂³×C₂₉	1	2	yes	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
287	#106	—	2	2	no	—
288	#106	—	2	2	no	—
289	#106	—	2	2	no	—
290	#106	—	2	2	no	—
291	C₄⋊C₈	D₄×C₂₉	1	2	yes	—
292	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
293	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
294	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
295	#103	—	2	2	no	—
296	#102	—	2	2	no	—
297	#102	—	2	2	no	—
298	#102	—	2	2	no	—
299	#102	—	2	2	no	—
300	#102	—	2	2	no	—
301	C₂²⋊C₈	—	2	1	no	—
302	C₂²⋊C₈	—	2	1	no	—
303	C₂²⋊C₈	—	2	1	no	—
304	C₂²⋊C₈	—	2	2	no	—
305	C₂²⋊C₈	—	2	2	no	—
306	C₂²⋊C₈	D₄×C₂₉	1	2	yes	—
307	#97	—	2	1	no	—
308	#97	—	2	1	no	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
311	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
312	C₂₉	#19513	1	1	yes	characteristic, direct product factor, Sylow
313	#41	—	8	2	no	—
314	#41	—	8	2	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	4	1	no	—
320	C₂×Q₈	—	8	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
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	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
334	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
335	SD₁₆	—	8	2	no	—
336	D₈	—	8	2	no	—
337	M₁₆	—	8	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	8	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	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	4	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₂²⋊C₄	—	2	2	no	—
356	C₂²⋊C₄	—	4	1	no	—
357	C₂²⋊C₄	—	4	1	no	—
358	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
359	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
360	C₄²	#41×C₂₉	1	1	yes	characteristic
361	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
362	C₂³	—	2	2	no	—
363	C₂³	—	4	1	no	—
364	C₂³	C₂₉×#121	1	1	yes	characteristic
365	Q₈	—	4	2	no	—
366	Q₈	—	8	1	no	—
367	Q₈	—	8	1	no	—
368	Q₈	—	8	1	no	—
369	Q₈	—	8	2	no	—
370	D₄	—	2	2	no	—
371	D₄	—	2	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	8	1	no	—
375	D₄	—	8	1	no	—
376	D₄	—	8	1	no	—
377	D₄	—	8	2	no	—
378	D₄	—	8	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	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	2	no	—
400	C₈	—	4	2	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	—	8	1	no	—
410	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	8	1	no	—
417	C₄	—	8	1	no	—
418	C₄	—	8	1	no	—
419	C₄	C₂₉×#577	1	2	yes	—
420	C₄	C₂₉×#577	1	2	yes	—
421	C₂	—	4	1	no	—
422	C₂	—	8	2	no	—
423	C₂	—	16	1	no	—
424	C₂	C₂₉×#3042	1	1	yes	characteristic
425	C₂	C₂₉×#3057	1	1	yes	characteristic
426	C₂	C₂₉×#3068	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×#3227	C₂	semidirect
2. C₂₉×#3227	C₂	semidirect
4. C₂₉×#2981	C₂	semidirect
5. C₂₉×#1697	C₂	semidirect
6. C₂₉×#1691	C₂	semidirect
7. C₂₉×#1677	C₂	semidirect
8. C₂₉×#1671	C₂	semidirect
9. C₂₉×#1572	C₂	semidirect
10. C₂₉×#1558	C₂	semidirect
11. C₂₉×#1553	C₂	semidirect
148. #19513	C₂₉	direct (N × H)
188. #3227	C₂×C₂₉	semidirect
189. #3227	C₂×C₂₉	semidirect
191. #2981	C₂×C₂₉	semidirect
192. #1697	C₂×C₂₉	semidirect
193. #1691	C₂×C₂₉	semidirect
194. #1677	C₂×C₂₉	semidirect
195. #1671	C₂×C₂₉	semidirect
196. #1572	C₂×C₂₉	semidirect
197. #1558	C₂×C₂₉	semidirect
198. #1553	C₂×C₂₉	semidirect
312. C₂₉	#19513	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×#3227	2
C₂₉×#3214	2
C₂₉×#2981	2
C₂₉×#1697	2
C₂₉×#1691	2
C₂₉×#1677	2
C₂₉×#1671	2
C₂₉×#1572	2
C₂₉×#1558	2
C₂₉×#1553	2
#19513	29

Subgroups — C29×#19513 #20314413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19513 #20314413