Subgroups — C₂₉×#9233 #20304133

Order 7424.

724 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×#3100	C₂	1	1	yes	maximal, characteristic
2	C₄²×D₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#1962	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#1502	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1486	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1303	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1276	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#532	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₄×C₂₉	—	2	1	no	—
10	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₂₉	—	2	1	no	—
12	C₂₉×#480	—	2	1	no	—
13	C₂₉×#474	C₄	1	2	yes	complemented
14	C₂₉×#459	C₄	1	2	yes	complemented
15	C₂₉×#447	—	2	1	no	—
16	C₄×D₈×C₂₉	—	2	2	no	—
17	C₂₉×#431	C₂²	1	1	yes	characteristic
18	C₂₉×#431	C₂²	1	1	yes	characteristic
19	C₂₉×#423	C₂²	1	1	yes	characteristic
20	C₂×C₂₉×#104	—	2	1	no	—
21	C₂×C₂₉×#104	—	2	1	no	—
22	C₄×C₄⋊C₄×C₂₉	—	2	1	no	—
23	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊C₄×C₂₉	—	2	2	no	—
25	C₄×C₂²⋊C₄×C₂₉	—	2	1	no	—
26	C₄³×C₂₉	C₂²	1	1	yes	characteristic
27	C₂₉×#327	—	2	2	no	—
28	C₂₉×D₄⋊C₈	—	2	2	no	—
29	C₂×#41×C₂₉	—	2	1	no	—
30	C₂²×D₄×C₂₉	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₂₉	—	2	2	no	—
32	C₂³×C₄×C₂₉	—	2	1	no	—
33	C₂×D₈×C₂₉	—	2	2	no	—
34	C₂×M₁₆×C₂₉	—	2	1	no	—
35	C₂₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
36	C₂₉×#127	C₂×C₄	1	1	yes	characteristic, complemented
37	C₂₉×#124	—	2	1	no	—
38	C₂₉×#121	—	2	1	no	—
39	C₂₉×#121	—	2	1	no	—
40	C₄×D₄×C₂₉	—	2	8	no	—
41	C₄×D₄×C₂₉	—	2	1	no	—
42	C₄×D₄×C₂₉	—	2	1	no	—
43	C₄×D₄×C₂₉	—	2	1	no	—
44	C₄×D₄×C₂₉	—	2	1	no	—
45	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
46	C₄×D₄×C₂₉	D₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
51	C₂×C₄²×C₂₉	—	2	1	no	—
52	C₂×C₄²×C₂₉	—	2	2	no	—
53	C₂×C₄²×C₂₉	—	2	1	no	—
54	C₂×C₄²×C₂₉	—	2	1	no	—
55	C₂×C₄²×C₂₉	—	4	2	no	—
56	C₂×C₄²×C₂₉	—	4	2	no	—
57	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
60	C₂₉×#107	—	2	2	no	—
61	C₂₉×C₄⋊C₈	—	2	1	no	—
62	C₂₉×C₄⋊C₈	—	2	1	no	—
63	C₂₉×C₄⋊C₈	—	2	1	no	—
64	C₂₉×C₄⋊C₈	C₂×C₄	1	2	yes	complemented
65	C₂₉×#104	—	4	2	no	—
66	C₂₉×#104	—	4	2	no	—
67	C₂₉×#102	—	2	2	no	—
68	C₂₉×#102	—	2	2	no	—
69	C₂₉×C₂²⋊C₈	—	2	1	no	—
70	C₂₉×C₂²⋊C₈	—	2	1	no	—
71	C₄×C₈×C₂₉	—	2	1	no	—
72	C₄×C₈×C₂₉	—	2	1	no	—
73	C₂₉×#95	—	2	2	no	—
74	C₂₉×#95	D₄	1	2	yes	—
75	C₂⁴×C₂₉	—	2	1	no	—
76	#41×C₂₉	—	4	1	no	—
77	#41×C₂₉	—	4	1	no	—
78	#41×C₂₉	—	4	1	no	—
79	#41×C₂₉	—	4	1	no	—
80	C₂×Q₈×C₂₉	—	2	1	no	—
81	C₂×D₄×C₂₉	—	2	4	no	—
82	C₂×D₄×C₂₉	—	2	1	no	—
83	C₂×D₄×C₂₉	—	2	1	no	—
84	C₂×D₄×C₂₉	—	2	1	no	—
85	C₂×D₄×C₂₉	—	2	1	no	—
86	C₂×D₄×C₂₉	—	4	1	no	—
87	C₂×D₄×C₂₉	C₂²⋊C₄	1	2	yes	—
88	C₂²×C₄×C₂₉	—	2	1	no	—
89	C₂²×C₄×C₂₉	—	2	8	no	—
90	C₂²×C₄×C₂₉	—	2	1	no	—
91	C₂²×C₄×C₂₉	—	2	2	no	—
92	C₂²×C₄×C₂₉	—	2	1	no	—
93	C₂²×C₄×C₂₉	—	2	2	no	—
94	C₂²×C₄×C₂₉	—	2	2	no	—
95	C₂²×C₄×C₂₉	—	4	4	no	—
96	C₂²×C₄×C₂₉	—	4	4	no	—
97	C₂²×C₄×C₂₉	—	4	1	no	—
98	C₂²×C₄×C₂₉	—	4	1	no	—
99	C₂²×C₄×C₂₉	—	4	1	no	—
100	C₂²×C₄×C₂₉	—	4	1	no	—
101	C₂²×C₄×C₂₉	—	4	1	no	—
102	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
105	D₈×C₂₉	—	4	4	no	—
106	M₁₆×C₂₉	—	4	1	no	—
107	M₁₆×C₂₉	—	4	1	no	—
108	C₂×C₈×C₂₉	—	2	2	no	—
109	C₂×C₈×C₂₉	—	4	1	no	—
110	C₂×C₈×C₂₉	—	4	1	no	—
111	C₄⋊C₄×C₂₉	—	2	4	no	—
112	C₄⋊C₄×C₂₉	—	2	1	no	—
113	C₄⋊C₄×C₂₉	—	2	1	no	—
114	C₄⋊C₄×C₂₉	—	2	1	no	—
115	C₄⋊C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
116	C₂²⋊C₄×C₂₉	—	2	8	no	—
117	C₂²⋊C₄×C₂₉	—	2	2	no	—
118	C₂²⋊C₄×C₂₉	—	2	2	no	—
119	C₂²⋊C₄×C₂₉	—	4	1	no	—
120	C₂²⋊C₄×C₂₉	—	4	1	no	—
121	C₄²×C₂₉	—	2	4	no	—
122	C₄²×C₂₉	—	2	1	no	—
123	C₄²×C₂₉	—	2	1	no	—
124	C₄²×C₂₉	—	2	1	no	—
125	C₄²×C₂₉	—	4	2	no	—
126	C₄²×C₂₉	—	4	4	no	—
127	C₄²×C₂₉	—	4	1	no	—
128	C₄²×C₂₉	—	4	1	no	—
129	C₄²×C₂₉	D₈	1	2	yes	complemented
130	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₂₉	#41	1	1	yes	characteristic
133	C₄²×C₂₉	#41	1	1	yes	characteristic
134	#9233	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂³×C₂₉	—	2	4	no	—
136	C₂³×C₂₉	—	2	2	no	—
137	C₂³×C₂₉	—	4	2	no	—
138	C₂³×C₂₉	—	4	1	no	—
139	C₂³×C₂₉	—	4	1	no	—
140	C₂³×C₂₉	—	4	1	no	—
141	C₂³×C₂₉	#120	1	1	yes	characteristic
142	Q₈×C₂₉	—	4	1	no	—
143	Q₈×C₂₉	—	4	1	no	—
144	D₄×C₂₉	—	2	4	no	—
145	D₄×C₂₉	—	2	2	no	—
146	D₄×C₂₉	—	4	2	no	—
147	D₄×C₂₉	—	4	1	no	—
148	D₄×C₂₉	—	4	1	no	—
149	D₄×C₂₉	—	8	1	no	—
150	D₄×C₂₉	—	8	1	no	—
151	D₄×C₂₉	—	8	1	no	—
152	D₄×C₂₉	#104	1	4	yes	complemented
153	C₂×C₄×C₂₉	—	2	2	no	—
154	C₂×C₄×C₂₉	—	2	2	no	—
155	C₂×C₄×C₂₉	—	2	2	no	—
156	C₂×C₄×C₂₉	—	2	2	no	—
157	C₂×C₄×C₂₉	—	2	2	no	—
158	C₂×C₄×C₂₉	—	2	4	no	—
159	C₂×C₄×C₂₉	—	2	2	no	—
160	C₂×C₄×C₂₉	—	4	1	no	—
161	C₂×C₄×C₂₉	—	4	16	no	—
162	C₂×C₄×C₂₉	—	4	1	no	—
163	C₂×C₄×C₂₉	—	4	2	no	—
164	C₂×C₄×C₂₉	—	4	2	no	—
165	C₂×C₄×C₂₉	—	4	1	no	—
166	C₂×C₄×C₂₉	—	4	1	no	—
167	C₂×C₄×C₂₉	—	4	1	no	—
168	C₂×C₄×C₂₉	—	4	2	no	—
169	C₂×C₄×C₂₉	—	4	2	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	—	8	1	no	—
174	C₂×C₄×C₂₉	—	8	1	no	—
175	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₂₉	C₄×D₄	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	#123	1	1	yes	characteristic
181	C₂×C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
182	C₂×C₄×C₂₉	#135	1	1	yes	characteristic
183	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₈×C₂₉	—	4	2	no	—
186	C₈×C₂₉	—	8	1	no	—
187	C₈×C₂₉	—	8	1	no	—
188	#3100	C₂×C₂₉	1	1	yes	characteristic
189	C₄²×D₄	C₂×C₂₉	1	1	yes	characteristic, complemented
190	#1962	C₂×C₂₉	1	1	yes	characteristic, complemented
191	#1502	C₂×C₂₉	1	1	yes	characteristic, complemented
192	#1486	C₂×C₂₉	1	1	yes	characteristic, complemented
193	#1303	C₂×C₂₉	1	1	yes	characteristic, complemented
194	#1276	C₂×C₂₉	1	1	yes	characteristic, complemented
195	C₂²×C₂₉	—	2	1	no	—
196	C₂²×C₂₉	—	2	1	no	—
197	C₂²×C₂₉	—	2	4	no	—
198	C₂²×C₂₉	—	4	4	no	—
199	C₂²×C₂₉	—	4	4	no	—
200	C₂²×C₂₉	—	4	2	no	—
201	C₂²×C₂₉	—	4	2	no	—
202	C₂²×C₂₉	—	8	1	no	—
203	C₂²×C₂₉	—	8	1	no	—
204	C₂²×C₂₉	—	8	1	no	—
205	C₂²×C₂₉	#386	1	1	yes	characteristic
206	C₂²×C₂₉	#447	1	1	yes	characteristic
207	C₂²×C₂₉	#449	1	1	yes	characteristic
208	C₄×C₂₉	—	2	4	no	—
209	C₄×C₂₉	—	2	1	no	—
210	C₄×C₂₉	—	2	1	no	—
211	C₄×C₂₉	—	2	1	no	—
212	C₄×C₂₉	—	4	2	no	—
213	C₄×C₂₉	—	4	4	no	—
214	C₄×C₂₉	—	4	2	no	—
215	C₄×C₂₉	—	8	1	no	—
216	C₄×C₂₉	C₂×#104	1	2	yes	—
217	C₄×C₂₉	C₄×D₈	1	1	yes	characteristic
218	C₄×C₂₉	#442	1	1	yes	characteristic
219	C₄×C₂₉	#459	1	1	yes	characteristic
220	C₄×C₂₉	#463	1	1	yes	characteristic
221	#532	C₂²×C₂₉	1	1	yes	characteristic
222	C₂×C₄×D₄	—	2	1	no	—
223	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
224	C₂²×C₄²	—	2	1	no	—
225	#480	—	2	1	no	—
226	#474	C₄×C₂₉	1	2	yes	complemented
227	#459	C₄×C₂₉	1	2	yes	complemented
228	#447	—	2	1	no	—
229	C₄×D₈	—	2	2	no	—
230	#431	C₂²×C₂₉	1	1	yes	characteristic
231	#431	C₂²×C₂₉	1	1	yes	characteristic
232	#423	C₂²×C₂₉	1	1	yes	characteristic
233	C₂×#104	—	2	1	no	—
234	C₂×#104	—	2	1	no	—
235	C₄×C₄⋊C₄	—	2	1	no	—
236	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
237	C₄×C₂²⋊C₄	—	2	1	no	—
238	C₄×C₂²⋊C₄	—	2	2	no	—
239	C₄³	C₂²×C₂₉	1	1	yes	characteristic
240	#327	—	2	2	no	—
241	D₄⋊C₈	—	2	2	no	—
242	C₂×C₂₉	—	2	1	no	—
243	C₂×C₂₉	—	2	1	no	—
244	C₂×C₂₉	—	4	4	no	—
245	C₂×C₂₉	—	16	1	no	—
246	C₂×C₂₉	#1879	1	1	yes	characteristic
247	C₂×C₂₉	#1896	1	1	yes	characteristic
248	C₂×C₂₉	#1906	1	1	yes	characteristic
249	C₂×#41	—	2	1	no	—
250	C₂²×D₄	D₄×C₂₉	1	1	yes	characteristic
251	C₂³×C₄	—	2	2	no	—
252	C₂³×C₄	—	2	1	no	—
253	C₂×D₈	—	2	2	no	—
254	C₂×M₁₆	—	2	1	no	—
255	C₄⋊Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic, complemented
256	#127	C₂×C₄×C₂₉	1	1	yes	characteristic, complemented
257	#124	—	2	1	no	—
258	#121	—	2	1	no	—
259	#121	—	2	1	no	—
260	C₄×D₄	—	2	8	no	—
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
266	C₄×D₄	D₄×C₂₉	1	2	yes	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	—	4	2	no	—
276	C₂×C₄²	—	4	2	no	—
277	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
278	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
279	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
280	#107	—	2	2	no	—
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	—	2	1	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	C₂×C₄×C₂₉	1	2	yes	complemented
285	#104	—	4	2	no	—
286	#104	—	4	2	no	—
287	#102	—	2	2	no	—
288	#102	—	2	2	no	—
289	C₂²⋊C₈	—	2	1	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	—	2	1	no	—
293	#95	—	2	2	no	—
294	#95	D₄×C₂₉	1	2	yes	—
295	C₂₉	#9233	1	1	yes	characteristic, direct product factor, Sylow
296	C₂⁴	—	2	1	no	—
297	#41	—	4	1	no	—
298	#41	—	4	1	no	—
299	#41	—	4	1	no	—
300	#41	—	4	1	no	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	C₂²⋊C₄×C₂₉	1	2	yes	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	8	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	4	4	no	—
317	C₂²×C₄	—	4	4	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
326	D₈	—	4	4	no	—
327	M₁₆	—	4	1	no	—
328	M₁₆	—	4	1	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	C₂²⋊C₄×C₂₉	1	2	yes	—
337	C₂²⋊C₄	—	2	8	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	4	1	no	—
341	C₂²⋊C₄	—	4	1	no	—
342	C₄²	—	2	4	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	4	4	no	—
347	C₄²	—	4	2	no	—
348	C₄²	—	4	1	no	—
349	C₄²	—	4	1	no	—
350	C₄²	D₈×C₂₉	1	2	yes	complemented
351	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
352	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
353	C₄²	#41×C₂₉	1	1	yes	characteristic
354	C₄²	#41×C₂₉	1	1	yes	characteristic
355	C₂³	—	2	4	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	1	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	1	no	—
361	C₂³	C₂₉×#120	1	1	yes	characteristic
362	Q₈	—	4	1	no	—
363	Q₈	—	4	1	no	—
364	D₄	—	2	4	no	—
365	D₄	—	2	2	no	—
366	D₄	—	4	1	no	—
367	D₄	—	4	1	no	—
368	D₄	—	4	2	no	—
369	D₄	—	8	1	no	—
370	D₄	—	8	1	no	—
371	D₄	—	8	1	no	—
372	D₄	C₂₉×#104	1	4	yes	complemented
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	16	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	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	8	1	no	—
394	C₂×C₄	—	8	1	no	—
395	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
396	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
397	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
398	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
399	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
400	C₂×C₄	C₂₉×#123	1	1	yes	characteristic
401	C₂×C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
402	C₂×C₄	C₂₉×#135	1	1	yes	characteristic
403	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
404	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
405	C₈	—	4	2	no	—
406	C₈	—	8	1	no	—
407	C₈	—	8	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	4	4	no	—
412	C₂²	—	4	4	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	1	no	—
417	C₂²	—	8	1	no	—
418	C₂²	C₂₉×#386	1	1	yes	characteristic
419	C₂²	C₂₉×#447	1	1	yes	characteristic
420	C₂²	C₂₉×#449	1	1	yes	characteristic
421	C₄	—	2	4	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	1	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	8	1	no	—
429	C₄	C₂×C₂₉×#104	1	2	yes	—
430	C₄	C₄×D₈×C₂₉	1	1	yes	characteristic
431	C₄	C₂₉×#442	1	1	yes	characteristic
432	C₄	C₂₉×#459	1	1	yes	characteristic
433	C₄	C₂₉×#463	1	1	yes	characteristic
434	C₂	—	2	1	no	—
435	C₂	—	2	1	no	—
436	C₂	—	4	4	no	—
437	C₂	—	16	1	no	—
438	C₂	C₂₉×#1879	1	1	yes	characteristic
439	C₂	C₂₉×#1896	1	1	yes	characteristic
440	C₂	C₂₉×#1906	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	#121
commutator	C₄²	C₂²×C₄×C₂₉
Frattini, cosocle	C₂×C₄²	C₂³×C₂₉
socle	C₂²×C₂₉	#386
prime radical	C₂₉×#3100	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₄²×D₄×C₂₉	C₂	semidirect
3. C₂₉×#1962	C₂	semidirect
4. C₂₉×#1502	C₂	semidirect
5. C₂₉×#1486	C₂	semidirect
6. C₂₉×#1303	C₂	semidirect
7. C₂₉×#1276	C₂	semidirect
13. C₂₉×#474	C₄	semidirect
14. C₂₉×#459	C₄	semidirect
35. C₂₉×C₄⋊Q₈	C₂×C₄	semidirect
36. C₂₉×#127	C₂×C₄	semidirect
64. C₂₉×C₄⋊C₈	C₂×C₄	semidirect
129. C₄²×C₂₉	D₈	semidirect
134. #9233	C₂₉	direct (N × H)
152. D₄×C₂₉	#104	semidirect
189. C₄²×D₄	C₂×C₂₉	semidirect
190. #1962	C₂×C₂₉	semidirect
191. #1502	C₂×C₂₉	semidirect
192. #1486	C₂×C₂₉	semidirect
193. #1303	C₂×C₂₉	semidirect
194. #1276	C₂×C₂₉	semidirect
226. #474	C₄×C₂₉	semidirect
227. #459	C₄×C₂₉	semidirect
255. C₄⋊Q₈	C₂×C₄×C₂₉	semidirect
256. #127	C₂×C₄×C₂₉	semidirect
284. C₄⋊C₈	C₂×C₄×C₂₉	semidirect
295. C₂₉	#9233	direct (N × H)
350. C₄²	D₈×C₂₉	semidirect
372. D₄	C₂₉×#104	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₉×#3100	2
C₄²×D₄×C₂₉	2
C₂₉×#1962	2
C₂₉×#1502	2
C₂₉×#1486	2
C₂₉×#1303	2
C₂₉×#1276	2
#9233	29

Subgroups — C29×#9233 #20304133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#9233 #20304133