Subgroups — C₂₉×#26468 #20321368

Order 7424.

806 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#477	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#478	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2550	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2367	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#2068	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2067	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#2026	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2023	C₂	1	1	yes	maximal, characteristic
9	C₂₉×#1983	C₂	1	1	yes	maximal, characteristic
10	C₂₉×#1958	C₂	1	1	yes	maximal, characteristic
11	C₂₉×#1949	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1939	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1865	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1862	C₂	1	1	yes	maximal, characteristic
15	C₄×C₂₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×#125	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
21	C₂₉×#478	—	2	4	no	—
22	C₂₉×#477	—	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×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×#103	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×C₂₉×#102	C₂²	1	1	yes	characteristic
37	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
39	C₂₉×#398	—	2	1	no	—
40	C₂₉×#395	—	2	1	no	—
41	C₂₉×#391	—	2	1	no	—
42	C₂₉×#391	C₂²	1	1	yes	characteristic
43	C₂₉×#390	C₂²	1	1	yes	characteristic
44	C₂₉×#389	—	2	1	no	—
45	C₂₉×#389	C₂²	1	1	yes	characteristic
46	C₂₉×#389	C₂²	1	1	yes	characteristic
47	C₂₉×#388	—	2	1	no	—
48	C₂₉×#388	—	2	1	no	—
49	C₂₉×#385	—	2	1	no	—
50	C₂₉×#382	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₂₉	—	2	1	no	—
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×Q₈×C₂₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₂₉	—	2	1	no	—
65	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
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	C₂₉×C₄⋊Q₈	—	2	2	no	—
70	C₂₉×C₄⋊Q₈	—	4	1	no	—
71	C₂₉×#125	—	2	2	no	—
72	C₂₉×#125	—	4	1	no	—
73	C₂₉×#124	—	2	2	no	—
74	C₂₉×#124	Q₈	1	4	yes	complemented
75	C₄×Q₈×C₂₉	—	2	2	no	—
76	C₄×Q₈×C₂₉	—	4	1	no	—
77	C₄×D₄×C₂₉	—	2	2	no	—
78	C₄×D₄×C₂₉	—	4	1	no	—
79	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₂₉	C₂³	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×C₂²⋊C₄×C₂₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
98	C₂×C₄²×C₂₉	—	2	1	no	—
99	C₂×C₄²×C₂₉	—	2	1	no	—
100	C₂×C₄²×C₂₉	—	2	1	no	—
101	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
104	C₂₉×#107	—	2	2	no	—
105	C₂₉×#107	—	2	2	no	—
106	C₂₉×#107	D₄	1	4	yes	—
107	C₂₉×#106	—	2	2	no	—
108	C₂₉×C₄⋊C₈	—	2	2	no	—
109	C₂₉×C₄⋊C₈	—	2	2	no	—
110	C₂₉×C₄⋊C₈	—	2	2	no	—
111	C₂₉×#103	—	2	2	no	—
112	C₂₉×#103	—	2	2	no	—
113	C₂₉×#103	—	2	2	no	—
114	C₂₉×#103	—	4	1	no	—
115	C₂₉×#102	—	2	2	no	—
116	C₂₉×#102	—	2	2	no	—
117	C₂₉×#102	—	2	2	no	—
118	C₂₉×#102	—	4	1	no	—
119	C₄×C₈×C₂₉	—	2	2	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	—	2	1	no	—
127	C₂₉×#95	—	2	1	no	—
128	C₂₉×#95	D₄	1	1	yes	characteristic
129	C₂₉×#95	D₄	1	1	yes	characteristic
130	C₂⁴×C₂₉	—	2	1	no	—
131	C₂×Q₈×C₂₉	—	2	1	no	—
132	C₂×Q₈×C₂₉	—	2	1	no	—
133	C₂×Q₈×C₂₉	—	2	1	no	—
134	C₂×Q₈×C₂₉	—	2	1	no	—
135	C₂×Q₈×C₂₉	—	2	1	no	—
136	C₂×Q₈×C₂₉	—	4	2	no	—
137	C₂×Q₈×C₂₉	—	4	2	no	—
138	C₂×Q₈×C₂₉	—	8	1	no	—
139	C₂×Q₈×C₂₉	C₂×Q₈	1	2	yes	—
140	C₂×D₄×C₂₉	—	2	1	no	—
141	C₂×D₄×C₂₉	—	2	1	no	—
142	C₂×D₄×C₂₉	—	2	1	no	—
143	C₂×D₄×C₂₉	—	2	1	no	—
144	C₂×D₄×C₂₉	—	2	1	no	—
145	C₂×D₄×C₂₉	C₂×Q₈	1	2	yes	—
146	C₂²×C₄×C₂₉	—	2	1	no	—
147	C₂²×C₄×C₂₉	—	2	1	no	—
148	C₂²×C₄×C₂₉	—	2	1	no	—
149	C₂²×C₄×C₂₉	—	2	1	no	—
150	C₂²×C₄×C₂₉	—	2	1	no	—
151	C₂²×C₄×C₂₉	—	2	1	no	—
152	C₂²×C₄×C₂₉	—	2	1	no	—
153	C₂²×C₄×C₂₉	—	4	2	no	—
154	C₂²×C₄×C₂₉	—	4	2	no	—
155	C₂²×C₄×C₂₉	—	8	1	no	—
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	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
172	C₂×C₈×C₂₉	—	2	1	no	—
173	C₂×C₈×C₂₉	—	2	1	no	—
174	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
175	C₄⋊C₄×C₂₉	—	2	2	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	—	4	2	no	—
191	C₄⋊C₄×C₂₉	—	8	1	no	—
192	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
193	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
194	C₄⋊C₄×C₂₉	#41	1	2	yes	—
195	C₂²⋊C₄×C₂₉	—	2	4	no	—
196	C₂²⋊C₄×C₂₉	—	2	4	no	—
197	C₂²⋊C₄×C₂₉	—	4	2	no	—
198	C₂²⋊C₄×C₂₉	—	4	2	no	—
199	C₂²⋊C₄×C₂₉	—	8	1	no	—
200	C₄²×C₂₉	—	2	1	no	—
201	C₄²×C₂₉	—	2	1	no	—
202	C₄²×C₂₉	—	2	1	no	—
203	C₄²×C₂₉	—	2	1	no	—
204	C₄²×C₂₉	—	4	2	no	—
205	C₄²×C₂₉	—	8	1	no	—
206	C₄²×C₂₉	—	8	1	no	—
207	C₄²×C₂₉	C₂×Q₈	1	2	yes	—
208	C₄²×C₂₉	#41	1	2	yes	—
209	#26468	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂³×C₂₉	—	2	2	no	—
211	C₂³×C₂₉	—	4	1	no	—
212	C₂³×C₂₉	—	4	1	no	—
213	C₂³×C₂₉	—	4	1	no	—
214	C₂³×C₂₉	—	4	1	no	—
215	C₂³×C₂₉	—	4	1	no	—
216	C₂³×C₂₉	—	4	1	no	—
217	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
218	Q₈×C₂₉	—	2	2	no	—
219	Q₈×C₂₉	—	2	2	no	—
220	Q₈×C₂₉	—	4	1	no	—
221	Q₈×C₂₉	—	4	1	no	—
222	Q₈×C₂₉	—	8	4	no	—
223	D₄×C₂₉	—	2	2	no	—
224	D₄×C₂₉	—	2	2	no	—
225	D₄×C₂₉	—	4	1	no	—
226	D₄×C₂₉	—	4	1	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	1	no	—
231	C₂×C₄×C₂₉	—	2	1	no	—
232	C₂×C₄×C₂₉	—	2	1	no	—
233	C₂×C₄×C₂₉	—	2	2	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	2	no	—
238	C₂×C₄×C₂₉	—	2	2	no	—
239	C₂×C₄×C₂₉	—	2	2	no	—
240	C₂×C₄×C₂₉	—	2	1	no	—
241	C₂×C₄×C₂₉	—	2	1	no	—
242	C₂×C₄×C₂₉	—	2	1	no	—
243	C₂×C₄×C₂₉	—	2	1	no	—
244	C₂×C₄×C₂₉	—	2	1	no	—
245	C₂×C₄×C₂₉	—	2	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	—	4	1	no	—
257	C₂×C₄×C₂₉	—	4	1	no	—
258	C₂×C₄×C₂₉	—	4	1	no	—
259	C₂×C₄×C₂₉	—	4	1	no	—
260	C₂×C₄×C₂₉	—	4	1	no	—
261	C₂×C₄×C₂₉	—	4	1	no	—
262	C₂×C₄×C₂₉	—	4	1	no	—
263	C₂×C₄×C₂₉	—	8	4	no	—
264	C₂×C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
265	C₂×C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
266	C₂×C₄×C₂₉	#135	1	2	yes	—
267	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
269	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
270	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
272	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
273	C₈×C₂₉	—	2	2	no	—
274	C₈×C₂₉	—	4	1	no	—
275	C₈×C₂₉	—	4	1	no	—
276	C₈×C₂₉	—	4	1	no	—
277	C₂×#477	C₂×C₂₉	1	1	yes	characteristic, complemented
278	C₂×#478	C₂×C₂₉	1	1	yes	characteristic
279	#2550	C₂×C₂₉	1	1	yes	characteristic, complemented
280	#2367	C₂×C₂₉	1	1	yes	characteristic
281	#2068	C₂×C₂₉	1	1	yes	characteristic, complemented
282	#2067	C₂×C₂₉	1	1	yes	characteristic
283	#2026	C₂×C₂₉	1	1	yes	characteristic, complemented
284	#2023	C₂×C₂₉	1	1	yes	characteristic
285	#1983	C₂×C₂₉	1	1	yes	characteristic
286	#1958	C₂×C₂₉	1	1	yes	characteristic
287	#1949	C₂×C₂₉	1	1	yes	characteristic, complemented
288	#1939	C₂×C₂₉	1	1	yes	characteristic, complemented
289	#1865	C₂×C₂₉	1	1	yes	characteristic, complemented
290	#1862	C₂×C₂₉	1	1	yes	characteristic
291	C₄×#107	C₂×C₂₉	1	1	yes	characteristic, complemented
292	C₂²×C₂₉	—	4	2	no	—
293	C₂²×C₂₉	—	4	2	no	—
294	C₂²×C₂₉	—	4	2	no	—
295	C₂²×C₂₉	—	8	1	no	—
296	C₂²×C₂₉	—	8	1	no	—
297	C₂²×C₂₉	—	8	1	no	—
298	C₂²×C₂₉	—	8	1	no	—
299	C₂²×C₂₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
300	C₂²×C₂₉	D₄²	1	1	yes	characteristic
301	C₂²×C₂₉	#548	1	1	yes	characteristic
302	C₂²×C₂₉	C₂×#135	1	1	yes	characteristic
303	C₂²×C₂₉	#575	1	1	yes	characteristic
304	C₂²×C₂₉	#576	1	1	yes	characteristic
305	C₂²×C₂₉	#578	1	1	yes	characteristic
306	C₄×C₂₉	—	2	2	no	—
307	C₄×C₂₉	—	2	2	no	—
308	C₄×C₂₉	—	2	2	no	—
309	C₄×C₂₉	—	4	2	no	—
310	C₄×C₂₉	—	4	2	no	—
311	C₄×C₂₉	—	4	1	no	—
312	C₄×C₂₉	—	4	1	no	—
313	C₄×C₂₉	—	4	2	no	—
314	C₄×C₂₉	—	4	2	no	—
315	C₄×C₂₉	—	4	1	no	—
316	C₄×C₂₉	—	8	1	no	—
317	C₄×C₂₉	—	8	1	no	—
318	C₄×C₂₉	—	8	1	no	—
319	C₄×C₂₉	#532	1	1	yes	characteristic
320	C₄×C₂₉	#542	1	1	yes	characteristic
321	C₄×C₂₉	D₄×Q₈	1	1	yes	characteristic
322	C₄×C₂₉	#554	1	1	yes	characteristic
323	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
324	C₂×#125	C₂²×C₂₉	1	1	yes	characteristic
325	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
326	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
327	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
328	#478	—	2	4	no	—
329	#477	—	2	4	no	—
330	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
331	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
332	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
333	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
334	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
335	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
336	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
337	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
338	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
339	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
340	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
341	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
342	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
343	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
344	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
345	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
346	#398	—	2	1	no	—
347	#395	—	2	1	no	—
348	#391	—	2	1	no	—
349	#391	C₂²×C₂₉	1	1	yes	characteristic
350	#390	C₂²×C₂₉	1	1	yes	characteristic
351	#389	—	2	1	no	—
352	#389	C₂²×C₂₉	1	1	yes	characteristic
353	#389	C₂²×C₂₉	1	1	yes	characteristic
354	#388	—	2	1	no	—
355	#388	—	2	1	no	—
356	#385	—	2	1	no	—
357	#382	C₂²×C₂₉	1	1	yes	characteristic
358	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
359	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
360	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
361	C₄×C₂²⋊C₄	—	2	1	no	—
362	#340	C₂²×C₂₉	1	1	yes	characteristic
363	#340	C₂²×C₂₉	1	1	yes	characteristic
364	#340	C₂²×C₂₉	1	1	yes	characteristic
365	#340	C₂²×C₂₉	1	1	yes	characteristic
366	#336	C₂²×C₂₉	1	1	yes	characteristic
367	#336	C₂²×C₂₉	1	1	yes	characteristic
368	C₂×C₂₉	—	8	2	no	—
369	C₂×C₂₉	#2452	1	1	yes	characteristic
370	C₂×C₂₉	#3076	1	1	yes	characteristic
371	C₂×C₂₉	#3083	1	1	yes	characteristic
372	C₂×C₂₉	#3273	1	1	yes	characteristic
373	C₂×C₂₉	#3285	1	1	yes	characteristic
374	C₂×C₂₉	#3361	1	1	yes	characteristic
375	C₂×C₂₉	#3377	1	1	yes	characteristic
376	C₂²×Q₈	—	2	1	no	—
377	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
378	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
379	C₂³×C₄	—	2	1	no	—
380	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
381	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
382	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
383	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
384	C₄⋊Q₈	—	2	2	no	—
385	C₄⋊Q₈	—	4	1	no	—
386	#125	—	2	2	no	—
387	#125	—	4	1	no	—
388	#124	—	2	2	no	—
389	#124	Q₈×C₂₉	1	4	yes	complemented
390	C₄×Q₈	—	2	2	no	—
391	C₄×Q₈	—	4	1	no	—
392	C₄×D₄	—	2	2	no	—
393	C₄×D₄	—	4	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	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
401	C₂×C₄⋊C₄	D₄×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×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	—	2	1	no	—
415	C₂×C₄²	—	2	1	no	—
416	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
417	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
418	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
419	#107	—	2	2	no	—
420	#107	—	2	2	no	—
421	#107	D₄×C₂₉	1	4	yes	—
422	#106	—	2	2	no	—
423	C₄⋊C₈	—	2	2	no	—
424	C₄⋊C₈	—	2	2	no	—
425	C₄⋊C₈	—	2	2	no	—
426	#103	—	2	2	no	—
427	#103	—	2	2	no	—
428	#103	—	2	2	no	—
429	#103	—	4	1	no	—
430	#102	—	2	2	no	—
431	#102	—	2	2	no	—
432	#102	—	2	2	no	—
433	#102	—	4	1	no	—
434	C₄×C₈	—	2	2	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	D₄×C₂₉	1	1	yes	characteristic
444	#95	D₄×C₂₉	1	1	yes	characteristic
445	C₂₉	#26468	1	1	yes	characteristic, direct product factor, Sylow
446	C₂⁴	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	4	2	no	—
453	C₂×Q₈	—	4	2	no	—
454	C₂×Q₈	—	8	1	no	—
455	C₂×Q₈	C₂×Q₈×C₂₉	1	2	yes	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	C₂×Q₈×C₂₉	1	2	yes	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	4	2	no	—
470	C₂²×C₄	—	4	2	no	—
471	C₂²×C₄	—	8	1	no	—
472	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
473	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
478	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
491	C₄⋊C₄	—	2	2	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	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	4	1	no	—
502	C₄⋊C₄	—	4	2	no	—
503	C₄⋊C₄	—	4	2	no	—
504	C₄⋊C₄	—	4	2	no	—
505	C₄⋊C₄	—	4	2	no	—
506	C₄⋊C₄	—	4	2	no	—
507	C₄⋊C₄	—	8	1	no	—
508	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
509	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
510	C₄⋊C₄	#41×C₂₉	1	2	yes	—
511	C₂²⋊C₄	—	2	4	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	4	2	no	—
514	C₂²⋊C₄	—	4	2	no	—
515	C₂²⋊C₄	—	8	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	4	2	no	—
521	C₄²	—	8	1	no	—
522	C₄²	—	8	1	no	—
523	C₄²	C₂×Q₈×C₂₉	1	2	yes	—
524	C₄²	#41×C₂₉	1	2	yes	—
525	C₂³	—	2	2	no	—
526	C₂³	—	4	1	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	4	1	no	—
530	C₂³	—	4	1	no	—
531	C₂³	—	4	1	no	—
532	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
533	Q₈	—	2	2	no	—
534	Q₈	—	2	2	no	—
535	Q₈	—	4	1	no	—
536	Q₈	—	4	1	no	—
537	Q₈	—	8	4	no	—
538	D₄	—	2	2	no	—
539	D₄	—	2	2	no	—
540	D₄	—	4	1	no	—
541	D₄	—	4	1	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	—	2	2	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	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	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	8	4	no	—
579	C₂×C₄	C₂₉×C₂²⋊Q₈	1	2	yes	—
580	C₂×C₄	C₂₉×C₂²⋊Q₈	1	2	yes	—
581	C₂×C₄	C₂₉×#135	1	2	yes	—
582	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
583	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
584	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
585	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
586	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
587	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
588	C₈	—	2	2	no	—
589	C₈	—	4	1	no	—
590	C₈	—	4	1	no	—
591	C₈	—	4	1	no	—
592	C₂²	—	4	2	no	—
593	C₂²	—	4	2	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	8	1	no	—
596	C₂²	—	8	1	no	—
597	C₂²	—	8	1	no	—
598	C₂²	—	8	1	no	—
599	C₂²	C₂×C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
600	C₂²	D₄²×C₂₉	1	1	yes	characteristic
601	C₂²	C₂₉×#548	1	1	yes	characteristic
602	C₂²	C₂×C₂₉×#135	1	1	yes	characteristic
603	C₂²	C₂₉×#575	1	1	yes	characteristic
604	C₂²	C₂₉×#576	1	1	yes	characteristic
605	C₂²	C₂₉×#578	1	1	yes	characteristic
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	2	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	2	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	2	no	—
616	C₄	—	8	1	no	—
617	C₄	—	8	1	no	—
618	C₄	—	8	1	no	—
619	C₄	C₂₉×#532	1	1	yes	characteristic
620	C₄	C₂₉×#542	1	1	yes	characteristic
621	C₄	D₄×Q₈×C₂₉	1	1	yes	characteristic
622	C₄	C₂₉×#554	1	1	yes	characteristic
623	C₂	—	8	2	no	—
624	C₂	C₂₉×#2452	1	1	yes	characteristic
625	C₂	C₂₉×#3076	1	1	yes	characteristic
626	C₂	C₂₉×#3083	1	1	yes	characteristic
627	C₂	C₂₉×#3273	1	1	yes	characteristic
628	C₂	C₂₉×#3285	1	1	yes	characteristic
629	C₂	C₂₉×#3361	1	1	yes	characteristic
630	C₂	C₂₉×#3377	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
1. C₂×C₂₉×#477	C₂	semidirect
3. C₂₉×#2550	C₂	semidirect
5. C₂₉×#2068	C₂	semidirect
7. C₂₉×#2026	C₂	semidirect
11. C₂₉×#1949	C₂	semidirect
12. C₂₉×#1939	C₂	semidirect
13. C₂₉×#1865	C₂	semidirect
15. C₄×C₂₉×#107	C₂	semidirect
74. C₂₉×#124	Q₈	semidirect
209. #26468	C₂₉	direct (N × H)
277. C₂×#477	C₂×C₂₉	semidirect
279. #2550	C₂×C₂₉	semidirect
281. #2068	C₂×C₂₉	semidirect
283. #2026	C₂×C₂₉	semidirect
287. #1949	C₂×C₂₉	semidirect
288. #1939	C₂×C₂₉	semidirect
289. #1865	C₂×C₂₉	semidirect
291. C₄×#107	C₂×C₂₉	semidirect
389. #124	Q₈×C₂₉	semidirect
445. C₂₉	#26468	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×#477	2
C₂×C₂₉×#478	2
C₂₉×#2550	2
C₂₉×#2367	2
C₂₉×#2068	2
C₂₉×#2067	2
C₂₉×#2026	2
C₂₉×#2023	2
C₂₉×#1983	2
C₂₉×#1958	2
C₂₉×#1949	2
C₂₉×#1939	2
C₂₉×#1865	2
C₂₉×#1862	2
C₄×C₂₉×#107	2
#26468	29

Subgroups — C29×#26468 #20321368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#26468 #20321368