Subgroups — C₂₉×#26049 #20320949

Order 7424.

834 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#478	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#474	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2550	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2349	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#2087	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2086	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2059	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2058	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1949	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1939	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1864	C₂	1	1	yes	maximal, characteristic
12	C₂₉×#1864	C₂	1	1	yes	maximal, characteristic
13	C₂₉×#1846	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1804	C₂	1	1	yes	maximal, characteristic
15	C₄×C₂₉×#102	C₂	1	1	yes	maximal, characteristic
16	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×#125	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
21	C₂₉×#478	—	2	4	no	—
22	C₂₉×#474	—	2	4	no	—
23	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
24	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
25	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
34	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
35	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
37	C₂₉×#398	—	2	1	no	—
38	C₂₉×#395	—	2	1	no	—
39	C₂₉×#391	—	2	1	no	—
40	C₂₉×#389	—	2	1	no	—
41	C₂₉×#389	C₂²	1	1	yes	characteristic
42	C₂₉×#389	C₂²	1	1	yes	characteristic
43	C₂₉×#389	C₂²	1	1	yes	characteristic
44	C₂₉×#389	C₂²	1	1	yes	characteristic
45	C₂₉×#385	—	2	1	no	—
46	C₂₉×#385	—	2	1	no	—
47	C₂₉×#382	C₂²	1	1	yes	characteristic
48	C₂₉×#382	C₂²	1	1	yes	characteristic
49	C₂₉×#380	—	2	1	no	—
50	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
52	C₂×C₂₉×#95	—	2	1	no	—
53	C₂₉×#340	C₂²	1	1	yes	characteristic
54	C₂₉×#340	C₂²	1	1	yes	characteristic
55	C₂₉×#340	C₂²	1	1	yes	characteristic
56	C₂₉×#340	C₂²	1	1	yes	characteristic
57	C₂₉×#340	C₂²	1	1	yes	characteristic
58	C₂₉×#340	C₂²	1	1	yes	characteristic
59	C₂₉×#336	C₂²	1	1	yes	characteristic
60	C₂₉×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₂₉	—	2	1	no	—
62	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₂₉	—	2	1	no	—
64	C₂³×C₄×C₂₉	—	2	1	no	—
65	C₂³×C₄×C₂₉	—	2	1	no	—
66	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
70	C₂₉×C₄⋊Q₈	—	2	2	no	—
71	C₂₉×C₄⋊Q₈	—	4	1	no	—
72	C₂₉×#125	—	2	2	no	—
73	C₂₉×#125	—	4	1	no	—
74	C₄×D₄×C₂₉	—	2	2	no	—
75	C₄×D₄×C₂₉	—	2	2	no	—
76	C₄×D₄×C₂₉	—	2	2	no	—
77	C₄×D₄×C₂₉	—	4	1	no	—
78	C₄×D₄×C₂₉	—	4	1	no	—
79	C₄×D₄×C₂₉	Q₈	1	4	yes	complemented
80	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
99	C₂×C₄²×C₂₉	—	2	1	no	—
100	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
103	C₂₉×#107	—	2	2	no	—
104	C₂₉×#107	—	2	2	no	—
105	C₂₉×#107	—	2	2	no	—
106	C₂₉×#106	—	2	2	no	—
107	C₂₉×#106	—	4	1	no	—
108	C₂₉×#106	—	4	1	no	—
109	C₂₉×C₄⋊C₈	—	2	2	no	—
110	C₂₉×C₄⋊C₈	—	2	2	no	—
111	C₂₉×C₄⋊C₈	—	2	2	no	—
112	C₂₉×#102	—	2	2	no	—
113	C₂₉×#102	—	2	2	no	—
114	C₂₉×#102	D₄	1	4	yes	—
115	C₂₉×#102	Q₈	1	4	yes	complemented
116	C₄×C₈×C₂₉	—	2	2	no	—
117	C₂₉×#95	—	2	1	no	—
118	C₂₉×#95	—	2	1	no	—
119	C₂₉×#95	—	2	1	no	—
120	C₂₉×#95	—	2	1	no	—
121	C₂₉×#95	—	2	1	no	—
122	C₂₉×#95	—	2	1	no	—
123	C₂₉×#95	—	2	1	no	—
124	C₂₉×#95	—	2	1	no	—
125	C₂₉×#95	—	2	1	no	—
126	C₂₉×#95	D₄	1	1	yes	characteristic
127	C₂₉×#95	D₄	1	1	yes	characteristic
128	C₂⁴×C₂₉	—	2	1	no	—
129	C₂×Q₈×C₂₉	—	4	2	no	—
130	C₂×Q₈×C₂₉	—	4	2	no	—
131	C₂×Q₈×C₂₉	—	8	1	no	—
132	C₂×D₄×C₂₉	—	2	1	no	—
133	C₂×D₄×C₂₉	—	2	1	no	—
134	C₂×D₄×C₂₉	—	2	1	no	—
135	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
136	C₂×D₄×C₂₉	C₂×Q₈	1	2	yes	—
137	C₂×D₄×C₂₉	C₂×Q₈	1	2	yes	—
138	C₂²×C₄×C₂₉	—	2	1	no	—
139	C₂²×C₄×C₂₉	—	2	1	no	—
140	C₂²×C₄×C₂₉	—	2	1	no	—
141	C₂²×C₄×C₂₉	—	2	4	no	—
142	C₂²×C₄×C₂₉	—	2	1	no	—
143	C₂²×C₄×C₂₉	—	2	1	no	—
144	C₂²×C₄×C₂₉	—	2	1	no	—
145	C₂²×C₄×C₂₉	—	2	1	no	—
146	C₂²×C₄×C₂₉	—	4	2	no	—
147	C₂²×C₄×C₂₉	—	4	2	no	—
148	C₂²×C₄×C₂₉	—	4	2	no	—
149	C₂²×C₄×C₂₉	—	4	2	no	—
150	C₂²×C₄×C₂₉	—	8	1	no	—
151	C₂²×C₄×C₂₉	—	8	1	no	—
152	C₂²×C₄×C₂₉	—	8	1	no	—
153	C₂²×C₄×C₂₉	—	8	1	no	—
154	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
161	C₂×C₈×C₂₉	—	2	1	no	—
162	C₂×C₈×C₂₉	—	2	1	no	—
163	C₂×C₈×C₂₉	—	2	1	no	—
164	C₂×C₈×C₂₉	—	2	1	no	—
165	C₂×C₈×C₂₉	—	2	1	no	—
166	C₂×C₈×C₂₉	—	2	1	no	—
167	C₂×C₈×C₂₉	—	2	1	no	—
168	C₂×C₈×C₂₉	—	2	1	no	—
169	C₂×C₈×C₂₉	—	2	1	no	—
170	C₂×C₈×C₂₉	—	2	1	no	—
171	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
172	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
173	C₄⋊C₄×C₂₉	—	2	2	no	—
174	C₄⋊C₄×C₂₉	—	2	1	no	—
175	C₄⋊C₄×C₂₉	—	2	1	no	—
176	C₄⋊C₄×C₂₉	—	2	1	no	—
177	C₄⋊C₄×C₂₉	—	2	1	no	—
178	C₄⋊C₄×C₂₉	—	2	1	no	—
179	C₄⋊C₄×C₂₉	—	2	1	no	—
180	C₄⋊C₄×C₂₉	—	2	1	no	—
181	C₄⋊C₄×C₂₉	—	2	1	no	—
182	C₄⋊C₄×C₂₉	—	2	1	no	—
183	C₄⋊C₄×C₂₉	—	2	1	no	—
184	C₄⋊C₄×C₂₉	—	2	1	no	—
185	C₄⋊C₄×C₂₉	—	4	1	no	—
186	C₄⋊C₄×C₂₉	—	4	2	no	—
187	C₄⋊C₄×C₂₉	—	4	2	no	—
188	C₄⋊C₄×C₂₉	—	4	2	no	—
189	C₄⋊C₄×C₂₉	—	4	2	no	—
190	C₄⋊C₄×C₂₉	—	8	1	no	—
191	C₄⋊C₄×C₂₉	—	8	1	no	—
192	C₄⋊C₄×C₂₉	—	8	1	no	—
193	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
194	C₄⋊C₄×C₂₉	C₂×Q₈	1	2	yes	—
195	C₄⋊C₄×C₂₉	C₂×Q₈	1	2	yes	—
196	C₂²⋊C₄×C₂₉	—	2	4	no	—
197	C₂²⋊C₄×C₂₉	—	4	2	no	—
198	C₂²⋊C₄×C₂₉	—	4	2	no	—
199	C₄²×C₂₉	—	2	1	no	—
200	C₄²×C₂₉	—	2	1	no	—
201	C₄²×C₂₉	—	2	1	no	—
202	C₄²×C₂₉	—	2	1	no	—
203	C₄²×C₂₉	—	8	1	no	—
204	C₄²×C₂₉	C₂×Q₈	1	2	yes	—
205	C₄²×C₂₉	#41	1	2	yes	—
206	#26049	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂³×C₂₉	—	2	2	no	—
208	C₂³×C₂₉	—	2	2	no	—
209	C₂³×C₂₉	—	2	2	no	—
210	C₂³×C₂₉	—	4	1	no	—
211	C₂³×C₂₉	—	4	1	no	—
212	C₂³×C₂₉	—	4	1	no	—
213	C₂³×C₂₉	—	4	1	no	—
214	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
215	Q₈×C₂₉	—	8	4	no	—
216	D₄×C₂₉	—	2	2	no	—
217	D₄×C₂₉	—	2	2	no	—
218	D₄×C₂₉	—	2	2	no	—
219	D₄×C₂₉	C₄⋊Q₈	1	4	yes	—
220	C₂×C₄×C₂₉	—	2	1	no	—
221	C₂×C₄×C₂₉	—	2	1	no	—
222	C₂×C₄×C₂₉	—	2	1	no	—
223	C₂×C₄×C₂₉	—	2	1	no	—
224	C₂×C₄×C₂₉	—	2	1	no	—
225	C₂×C₄×C₂₉	—	2	1	no	—
226	C₂×C₄×C₂₉	—	2	2	no	—
227	C₂×C₄×C₂₉	—	2	1	no	—
228	C₂×C₄×C₂₉	—	2	1	no	—
229	C₂×C₄×C₂₉	—	2	1	no	—
230	C₂×C₄×C₂₉	—	2	2	no	—
231	C₂×C₄×C₂₉	—	2	2	no	—
232	C₂×C₄×C₂₉	—	2	1	no	—
233	C₂×C₄×C₂₉	—	2	1	no	—
234	C₂×C₄×C₂₉	—	2	1	no	—
235	C₂×C₄×C₂₉	—	2	1	no	—
236	C₂×C₄×C₂₉	—	2	1	no	—
237	C₂×C₄×C₂₉	—	2	1	no	—
238	C₂×C₄×C₂₉	—	4	1	no	—
239	C₂×C₄×C₂₉	—	4	1	no	—
240	C₂×C₄×C₂₉	—	4	1	no	—
241	C₂×C₄×C₂₉	—	4	1	no	—
242	C₂×C₄×C₂₉	—	4	1	no	—
243	C₂×C₄×C₂₉	—	4	1	no	—
244	C₂×C₄×C₂₉	—	4	1	no	—
245	C₂×C₄×C₂₉	—	4	1	no	—
246	C₂×C₄×C₂₉	—	4	1	no	—
247	C₂×C₄×C₂₉	—	4	1	no	—
248	C₂×C₄×C₂₉	—	4	1	no	—
249	C₂×C₄×C₂₉	—	4	1	no	—
250	C₂×C₄×C₂₉	—	4	1	no	—
251	C₂×C₄×C₂₉	—	4	1	no	—
252	C₂×C₄×C₂₉	—	4	1	no	—
253	C₂×C₄×C₂₉	—	4	1	no	—
254	C₂×C₄×C₂₉	—	4	1	no	—
255	C₂×C₄×C₂₉	—	4	1	no	—
256	C₂×C₄×C₂₉	—	8	4	no	—
257	C₂×C₄×C₂₉	—	8	4	no	—
258	C₂×C₄×C₂₉	—	8	4	no	—
259	C₂×C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
260	C₂×C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
261	C₂×C₄×C₂₉	#135	1	2	yes	—
262	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
264	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
265	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
266	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
267	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
268	C₈×C₂₉	—	2	2	no	—
269	C₈×C₂₉	—	2	2	no	—
270	C₈×C₂₉	—	4	1	no	—
271	C₈×C₂₉	—	4	1	no	—
272	C₂×#478	C₂×C₂₉	1	1	yes	characteristic
273	C₂×#474	C₂×C₂₉	1	1	yes	characteristic
274	#2550	C₂×C₂₉	1	1	yes	characteristic, complemented
275	#2349	C₂×C₂₉	1	1	yes	characteristic
276	#2087	C₂×C₂₉	1	1	yes	characteristic, complemented
277	#2086	C₂×C₂₉	1	1	yes	characteristic, complemented
278	#2059	C₂×C₂₉	1	1	yes	characteristic, complemented
279	#2058	C₂×C₂₉	1	1	yes	characteristic, complemented
280	#1949	C₂×C₂₉	1	1	yes	characteristic, complemented
281	#1939	C₂×C₂₉	1	1	yes	characteristic, complemented
282	#1864	C₂×C₂₉	1	1	yes	characteristic
283	#1864	C₂×C₂₉	1	1	yes	characteristic
284	#1846	C₂×C₂₉	1	1	yes	characteristic, complemented
285	#1804	C₂×C₂₉	1	1	yes	characteristic
286	C₄×#102	C₂×C₂₉	1	1	yes	characteristic
287	C₂²×C₂₉	—	2	4	no	—
288	C₂²×C₂₉	—	4	2	no	—
289	C₂²×C₂₉	—	4	2	no	—
290	C₂²×C₂₉	—	4	2	no	—
291	C₂²×C₂₉	—	4	2	no	—
292	C₂²×C₂₉	—	4	2	no	—
293	C₂²×C₂₉	—	4	2	no	—
294	C₂²×C₂₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
295	C₂²×C₂₉	D₄²	1	1	yes	characteristic
296	C₂²×C₂₉	D₄×Q₈	1	1	yes	characteristic
297	C₂²×C₂₉	C₂×#135	1	1	yes	characteristic
298	C₂²×C₂₉	#575	1	1	yes	characteristic
299	C₂²×C₂₉	#576	1	1	yes	characteristic
300	C₂²×C₂₉	#577	1	1	yes	characteristic
301	C₄×C₂₉	—	2	2	no	—
302	C₄×C₂₉	—	2	2	no	—
303	C₄×C₂₉	—	2	2	no	—
304	C₄×C₂₉	—	4	2	no	—
305	C₄×C₂₉	—	4	2	no	—
306	C₄×C₂₉	—	4	1	no	—
307	C₄×C₂₉	—	4	1	no	—
308	C₄×C₂₉	—	4	1	no	—
309	C₄×C₂₉	—	4	2	no	—
310	C₄×C₂₉	—	8	1	no	—
311	C₄×C₂₉	—	8	1	no	—
312	C₄×C₂₉	—	8	1	no	—
313	C₄×C₂₉	—	8	1	no	—
314	C₄×C₂₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
315	C₄×C₂₉	#544	1	1	yes	characteristic
316	C₄×C₂₉	#547	1	1	yes	characteristic
317	C₄×C₂₉	#554	1	1	yes	characteristic
318	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
319	C₂×#125	C₂²×C₂₉	1	1	yes	characteristic
320	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
321	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
322	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
323	#478	—	2	4	no	—
324	#474	—	2	4	no	—
325	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
326	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
327	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
328	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
329	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
330	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
331	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
332	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
333	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
334	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
335	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
336	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
337	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
338	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
339	#398	—	2	1	no	—
340	#395	—	2	1	no	—
341	#391	—	2	1	no	—
342	#389	—	2	1	no	—
343	#389	C₂²×C₂₉	1	1	yes	characteristic
344	#389	C₂²×C₂₉	1	1	yes	characteristic
345	#389	C₂²×C₂₉	1	1	yes	characteristic
346	#389	C₂²×C₂₉	1	1	yes	characteristic
347	#385	—	2	1	no	—
348	#385	—	2	1	no	—
349	#382	C₂²×C₂₉	1	1	yes	characteristic
350	#382	C₂²×C₂₉	1	1	yes	characteristic
351	#380	—	2	1	no	—
352	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
353	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
354	C₂×#95	—	2	1	no	—
355	#340	C₂²×C₂₉	1	1	yes	characteristic
356	#340	C₂²×C₂₉	1	1	yes	characteristic
357	#340	C₂²×C₂₉	1	1	yes	characteristic
358	#340	C₂²×C₂₉	1	1	yes	characteristic
359	#340	C₂²×C₂₉	1	1	yes	characteristic
360	#340	C₂²×C₂₉	1	1	yes	characteristic
361	#336	C₂²×C₂₉	1	1	yes	characteristic
362	#336	C₂²×C₂₉	1	1	yes	characteristic
363	C₂×C₂₉	—	4	4	no	—
364	C₂×C₂₉	#2440	1	1	yes	characteristic
365	C₂×C₂₉	#3076	1	1	yes	characteristic
366	C₂×C₂₉	#3081	1	1	yes	characteristic
367	C₂×C₂₉	#3275	1	1	yes	characteristic
368	C₂×C₂₉	#3280	1	1	yes	characteristic
369	C₂×C₂₉	#3381	1	1	yes	characteristic
370	C₂×C₂₉	#3389	1	1	yes	characteristic
371	C₂²×Q₈	—	2	1	no	—
372	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
373	C₂³×C₄	—	2	1	no	—
374	C₂³×C₄	—	2	1	no	—
375	C₂³×C₄	—	2	1	no	—
376	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
377	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
378	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
379	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
380	C₄⋊Q₈	—	2	2	no	—
381	C₄⋊Q₈	—	4	1	no	—
382	#125	—	2	2	no	—
383	#125	—	4	1	no	—
384	C₄×D₄	—	2	2	no	—
385	C₄×D₄	—	2	2	no	—
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	—	4	1	no	—
388	C₄×D₄	—	4	1	no	—
389	C₄×D₄	Q₈×C₂₉	1	4	yes	complemented
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
398	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₄²	—	2	1	no	—
410	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
411	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
412	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
413	#107	—	2	2	no	—
414	#107	—	2	2	no	—
415	#107	—	2	2	no	—
416	#106	—	2	2	no	—
417	#106	—	4	1	no	—
418	#106	—	4	1	no	—
419	C₄⋊C₈	—	2	2	no	—
420	C₄⋊C₈	—	2	2	no	—
421	C₄⋊C₈	—	2	2	no	—
422	#102	—	2	2	no	—
423	#102	—	2	2	no	—
424	#102	D₄×C₂₉	1	4	yes	—
425	#102	Q₈×C₂₉	1	4	yes	complemented
426	C₄×C₈	—	2	2	no	—
427	#95	—	2	1	no	—
428	#95	—	2	1	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	—	2	1	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	#95	D₄×C₂₉	1	1	yes	characteristic
437	#95	D₄×C₂₉	1	1	yes	characteristic
438	C₂₉	#26049	1	1	yes	characteristic, direct product factor, Sylow
439	C₂⁴	—	2	1	no	—
440	C₂×Q₈	—	4	2	no	—
441	C₂×Q₈	—	4	2	no	—
442	C₂×Q₈	—	8	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
447	C₂×D₄	C₂×Q₈×C₂₉	1	2	yes	—
448	C₂×D₄	C₂×Q₈×C₂₉	1	2	yes	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	4	2	no	—
458	C₂²×C₄	—	4	2	no	—
459	C₂²×C₄	—	4	2	no	—
460	C₂²×C₄	—	4	2	no	—
461	C₂²×C₄	—	8	1	no	—
462	C₂²×C₄	—	8	1	no	—
463	C₂²×C₄	—	8	1	no	—
464	C₂²×C₄	—	8	1	no	—
465	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
471	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
483	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	4	1	no	—
497	C₄⋊C₄	—	4	2	no	—
498	C₄⋊C₄	—	4	2	no	—
499	C₄⋊C₄	—	4	2	no	—
500	C₄⋊C₄	—	4	2	no	—
501	C₄⋊C₄	—	8	1	no	—
502	C₄⋊C₄	—	8	1	no	—
503	C₄⋊C₄	—	8	1	no	—
504	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
505	C₄⋊C₄	C₂×Q₈×C₂₉	1	2	yes	—
506	C₄⋊C₄	C₂×Q₈×C₂₉	1	2	yes	—
507	C₂²⋊C₄	—	2	4	no	—
508	C₂²⋊C₄	—	4	2	no	—
509	C₂²⋊C₄	—	4	2	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	8	1	no	—
515	C₄²	C₂×Q₈×C₂₉	1	2	yes	—
516	C₄²	#41×C₂₉	1	2	yes	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	2	no	—
519	C₂³	—	2	2	no	—
520	C₂³	—	4	1	no	—
521	C₂³	—	4	1	no	—
522	C₂³	—	4	1	no	—
523	C₂³	—	4	1	no	—
524	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
525	Q₈	—	8	4	no	—
526	D₄	—	2	2	no	—
527	D₄	—	2	2	no	—
528	D₄	—	2	2	no	—
529	D₄	C₂₉×C₄⋊Q₈	1	4	yes	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	8	4	no	—
567	C₂×C₄	—	8	4	no	—
568	C₂×C₄	—	8	4	no	—
569	C₂×C₄	C₂₉×C₂²⋊Q₈	1	2	yes	—
570	C₂×C₄	C₂₉×C₂²⋊Q₈	1	2	yes	—
571	C₂×C₄	C₂₉×#135	1	2	yes	—
572	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
573	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
574	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
575	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
576	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
577	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
578	C₈	—	2	2	no	—
579	C₈	—	2	2	no	—
580	C₈	—	4	1	no	—
581	C₈	—	4	1	no	—
582	C₂²	—	2	4	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	2	no	—
589	C₂²	C₂×C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
590	C₂²	D₄²×C₂₉	1	1	yes	characteristic
591	C₂²	D₄×Q₈×C₂₉	1	1	yes	characteristic
592	C₂²	C₂×C₂₉×#135	1	1	yes	characteristic
593	C₂²	C₂₉×#575	1	1	yes	characteristic
594	C₂²	C₂₉×#576	1	1	yes	characteristic
595	C₂²	C₂₉×#577	1	1	yes	characteristic
596	C₄	—	2	2	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	2	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	2	no	—
603	C₄	—	4	2	no	—
604	C₄	—	4	2	no	—
605	C₄	—	8	1	no	—
606	C₄	—	8	1	no	—
607	C₄	—	8	1	no	—
608	C₄	—	8	1	no	—
609	C₄	C₂×C₂₉×C₄⋊Q₈	1	1	yes	characteristic
610	C₄	C₂₉×#544	1	1	yes	characteristic
611	C₄	C₂₉×#547	1	1	yes	characteristic
612	C₄	C₂₉×#554	1	1	yes	characteristic
613	C₂	—	4	4	no	—
614	C₂	C₂₉×#2440	1	1	yes	characteristic
615	C₂	C₂₉×#3076	1	1	yes	characteristic
616	C₂	C₂₉×#3081	1	1	yes	characteristic
617	C₂	C₂₉×#3275	1	1	yes	characteristic
618	C₂	C₂₉×#3280	1	1	yes	characteristic
619	C₂	C₂₉×#3381	1	1	yes	characteristic
620	C₂	C₂₉×#3389	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂²×D₄×C₂₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₄×C₄⋊C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₉×#2550	C₂	semidirect
5. C₂₉×#2087	C₂	semidirect
6. C₂₉×#2086	C₂	semidirect
7. C₂₉×#2059	C₂	semidirect
8. C₂₉×#2058	C₂	semidirect
9. C₂₉×#1949	C₂	semidirect
10. C₂₉×#1939	C₂	semidirect
13. C₂₉×#1846	C₂	semidirect
79. C₄×D₄×C₂₉	Q₈	semidirect
115. C₂₉×#102	Q₈	semidirect
206. #26049	C₂₉	direct (N × H)
274. #2550	C₂×C₂₉	semidirect
276. #2087	C₂×C₂₉	semidirect
277. #2086	C₂×C₂₉	semidirect
278. #2059	C₂×C₂₉	semidirect
279. #2058	C₂×C₂₉	semidirect
280. #1949	C₂×C₂₉	semidirect
281. #1939	C₂×C₂₉	semidirect
284. #1846	C₂×C₂₉	semidirect
389. C₄×D₄	Q₈×C₂₉	semidirect
425. #102	Q₈×C₂₉	semidirect
438. C₂₉	#26049	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#478	2
C₂×C₂₉×#474	2
C₂₉×#2550	2
C₂₉×#2349	2
C₂₉×#2087	2
C₂₉×#2086	2
C₂₉×#2059	2
C₂₉×#2058	2
C₂₉×#1949	2
C₂₉×#1939	2
C₂₉×#1864	2
C₂₉×#1846	2
C₂₉×#1804	2
C₄×C₂₉×#102	2
#26049	29

Subgroups — C29×#26049 #20320949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#26049 #20320949