Subgroups — C₂₉×#28774 #20323674

Order 7424.

722 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#2441	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2439	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2085	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2084	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2058	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1991	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1990	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1942	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1941	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1854	C₂	1	1	yes	maximal, characteristic
12	C₂₉×#1854	C₂	1	1	yes	maximal, characteristic
13	C₂₉×#1807	C₂	1	1	yes	maximal, characteristic
14	C₈×C₂²⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic
15	C₂₉×#1735	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₈×C₂₉	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×#125	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
20	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
24	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
25	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
30	C₂₉×#399	—	2	1	no	—
31	C₂₉×#396	—	2	1	no	—
32	C₂₉×#396	—	2	1	no	—
33	C₂₉×#393	—	2	1	no	—
34	C₂₉×#391	—	2	1	no	—
35	C₂₉×#389	—	2	1	no	—
36	C₂₉×#389	C₂²	1	1	yes	characteristic
37	C₂₉×#389	C₂²	1	1	yes	characteristic
38	C₂₉×#389	C₂²	1	1	yes	characteristic
39	C₂₉×#389	C₂²	1	1	yes	characteristic
40	C₂₉×#387	—	2	1	no	—
41	C₂₉×#387	—	2	1	no	—
42	C₂₉×#384	C₂²	1	1	yes	characteristic
43	C₂₉×#382	C₂²	1	1	yes	characteristic
44	C₂₉×#380	C₂²	1	1	yes	characteristic
45	C₂₉×#380	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
47	C₂₉×#340	C₂²	1	1	yes	characteristic
48	C₂₉×#340	C₂²	1	1	yes	characteristic
49	C₂₉×#340	C₂²	1	1	yes	characteristic
50	C₂₉×#340	C₂²	1	1	yes	characteristic
51	C₂₉×#340	C₂²	1	1	yes	characteristic
52	C₂₉×#340	C₂²	1	1	yes	characteristic
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×#336	C₂²	1	1	yes	characteristic
58	C₂₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₂₉	—	2	1	no	—
60	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₂₉	—	4	1	no	—
62	C₂²×C₈×C₂₉	—	4	1	no	—
63	C₂²×C₈×C₂₉	Q₈	1	4	yes	complemented
64	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
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	C₂₉×C₄⋊Q₈	—	2	2	no	—
69	C₂₉×C₄⋊Q₈	—	4	1	no	—
70	C₂₉×#125	—	2	2	no	—
71	C₂₉×#125	—	4	1	no	—
72	C₂₉×#117	—	2	2	no	—
73	C₂₉×#117	—	2	2	no	—
74	C₂₉×#117	—	4	1	no	—
75	C₂₉×#117	—	4	1	no	—
76	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₂₉	—	2	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	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₂₉	C₂³	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	D₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
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	C₂₉×#107	—	2	2	no	—
104	C₂₉×#107	—	4	1	no	—
105	C₂₉×#106	—	2	2	no	—
106	C₂₉×#106	—	4	1	no	—
107	C₂₉×#106	—	4	1	no	—
108	C₂₉×#106	—	4	1	no	—
109	C₂₉×C₂²⋊C₈	Q₈	1	4	yes	complemented
110	C₄×C₈×C₂₉	—	4	1	no	—
111	C₄×C₈×C₂₉	—	4	1	no	—
112	C₂₉×#95	—	2	1	no	—
113	C₂₉×#95	—	2	1	no	—
114	C₂₉×#95	—	2	1	no	—
115	C₂₉×#95	—	2	1	no	—
116	C₂₉×#95	—	2	1	no	—
117	C₂₉×#95	—	2	1	no	—
118	C₂₉×#95	—	2	1	no	—
119	C₂₉×#95	—	2	1	no	—
120	C₂₉×#95	D₄	1	1	yes	characteristic
121	C₂₉×#95	D₄	1	1	yes	characteristic
122	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
123	C₂×Q₈×C₂₉	—	4	2	no	—
124	C₂×Q₈×C₂₉	—	4	2	no	—
125	C₂×Q₈×C₂₉	—	8	1	no	—
126	C₂²×C₄×C₂₉	—	2	1	no	—
127	C₂²×C₄×C₂₉	—	2	1	no	—
128	C₂²×C₄×C₂₉	—	2	1	no	—
129	C₂²×C₄×C₂₉	—	2	1	no	—
130	C₂²×C₄×C₂₉	—	2	1	no	—
131	C₂²×C₄×C₂₉	—	2	1	no	—
132	C₂²×C₄×C₂₉	—	2	1	no	—
133	C₂²×C₄×C₂₉	—	2	1	no	—
134	C₂²×C₄×C₂₉	—	2	1	no	—
135	C₂²×C₄×C₂₉	—	2	1	no	—
136	C₂²×C₄×C₂₉	—	2	1	no	—
137	C₂²×C₄×C₂₉	—	2	1	no	—
138	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₂₉	C₂×Q₈	1	2	yes	—
144	C₂²×C₄×C₂₉	C₂×Q₈	1	2	yes	—
145	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
146	C₂×C₈×C₂₉	—	2	1	no	—
147	C₂×C₈×C₂₉	—	2	1	no	—
148	C₂×C₈×C₂₉	—	2	1	no	—
149	C₂×C₈×C₂₉	—	2	1	no	—
150	C₂×C₈×C₂₉	—	2	1	no	—
151	C₂×C₈×C₂₉	—	2	1	no	—
152	C₂×C₈×C₂₉	—	2	1	no	—
153	C₂×C₈×C₂₉	—	2	1	no	—
154	C₂×C₈×C₂₉	—	4	4	no	—
155	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
156	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
157	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
158	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
159	C₄⋊C₄×C₂₉	—	2	1	no	—
160	C₄⋊C₄×C₂₉	—	2	1	no	—
161	C₄⋊C₄×C₂₉	—	2	1	no	—
162	C₄⋊C₄×C₂₉	—	2	1	no	—
163	C₄⋊C₄×C₂₉	—	2	1	no	—
164	C₄⋊C₄×C₂₉	—	2	1	no	—
165	C₄⋊C₄×C₂₉	—	2	1	no	—
166	C₄⋊C₄×C₂₉	—	2	1	no	—
167	C₄⋊C₄×C₂₉	—	2	1	no	—
168	C₄⋊C₄×C₂₉	—	2	1	no	—
169	C₄⋊C₄×C₂₉	—	2	1	no	—
170	C₄⋊C₄×C₂₉	—	2	1	no	—
171	C₄⋊C₄×C₂₉	—	2	1	no	—
172	C₄⋊C₄×C₂₉	—	2	1	no	—
173	C₄⋊C₄×C₂₉	—	4	2	no	—
174	C₄⋊C₄×C₂₉	—	4	2	no	—
175	C₄⋊C₄×C₂₉	—	4	2	no	—
176	C₄⋊C₄×C₂₉	—	4	2	no	—
177	C₄⋊C₄×C₂₉	—	4	2	no	—
178	C₄⋊C₄×C₂₉	—	4	2	no	—
179	C₄⋊C₄×C₂₉	—	8	1	no	—
180	C₄⋊C₄×C₂₉	—	8	1	no	—
181	C₄⋊C₄×C₂₉	—	8	1	no	—
182	C₄⋊C₄×C₂₉	#41	1	2	yes	—
183	C₄⋊C₄×C₂₉	#41	1	2	yes	—
184	C₂²⋊C₄×C₂₉	—	2	2	no	—
185	C₂²⋊C₄×C₂₉	—	2	2	no	—
186	C₂²⋊C₄×C₂₉	—	4	2	no	—
187	C₂²⋊C₄×C₂₉	—	4	2	no	—
188	C₂²⋊C₄×C₂₉	—	8	1	no	—
189	C₂²⋊C₄×C₂₉	—	8	1	no	—
190	C₄²×C₂₉	—	2	1	no	—
191	C₄²×C₂₉	—	2	1	no	—
192	C₄²×C₂₉	—	2	1	no	—
193	C₄²×C₂₉	—	2	1	no	—
194	C₄²×C₂₉	—	4	2	no	—
195	C₄²×C₂₉	—	4	2	no	—
196	#28774	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂³×C₂₉	—	2	1	no	—
198	C₂³×C₂₉	—	2	1	no	—
199	C₂³×C₂₉	—	2	1	no	—
200	C₂³×C₂₉	—	2	1	no	—
201	C₂³×C₂₉	—	2	1	no	—
202	C₂³×C₂₉	—	2	1	no	—
203	C₂³×C₂₉	C₄⋊Q₈	1	2	yes	—
204	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
205	Q₈×C₂₉	—	8	4	no	—
206	C₂×C₄×C₂₉	—	2	1	no	—
207	C₂×C₄×C₂₉	—	2	1	no	—
208	C₂×C₄×C₂₉	—	2	1	no	—
209	C₂×C₄×C₂₉	—	2	1	no	—
210	C₂×C₄×C₂₉	—	2	1	no	—
211	C₂×C₄×C₂₉	—	2	1	no	—
212	C₂×C₄×C₂₉	—	2	2	no	—
213	C₂×C₄×C₂₉	—	2	2	no	—
214	C₂×C₄×C₂₉	—	2	2	no	—
215	C₂×C₄×C₂₉	—	2	2	no	—
216	C₂×C₄×C₂₉	—	2	1	no	—
217	C₂×C₄×C₂₉	—	2	1	no	—
218	C₂×C₄×C₂₉	—	2	2	no	—
219	C₂×C₄×C₂₉	—	2	2	no	—
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	—	4	1	no	—
225	C₂×C₄×C₂₉	—	4	1	no	—
226	C₂×C₄×C₂₉	—	4	1	no	—
227	C₂×C₄×C₂₉	—	4	1	no	—
228	C₂×C₄×C₂₉	—	4	1	no	—
229	C₂×C₄×C₂₉	—	4	1	no	—
230	C₂×C₄×C₂₉	—	4	1	no	—
231	C₂×C₄×C₂₉	—	4	1	no	—
232	C₂×C₄×C₂₉	—	4	1	no	—
233	C₂×C₄×C₂₉	—	4	1	no	—
234	C₂×C₄×C₂₉	—	4	1	no	—
235	C₂×C₄×C₂₉	—	4	1	no	—
236	C₂×C₄×C₂₉	—	4	1	no	—
237	C₂×C₄×C₂₉	—	4	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	C₄⋊Q₈	1	2	yes	—
247	C₂×C₄×C₂₉	#135	1	2	yes	—
248	C₂×C₄×C₂₉	#135	1	2	yes	—
249	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
250	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
251	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
252	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
253	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
254	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
255	C₈×C₂₉	—	2	2	no	—
256	C₈×C₂₉	—	2	2	no	—
257	C₈×C₂₉	—	2	2	no	—
258	C₈×C₂₉	—	2	2	no	—
259	#2441	C₂×C₂₉	1	1	yes	characteristic
260	#2439	C₂×C₂₉	1	1	yes	characteristic
261	#2085	C₂×C₂₉	1	1	yes	characteristic, complemented
262	#2084	C₂×C₂₉	1	1	yes	characteristic, complemented
263	#2059	C₂×C₂₉	1	1	yes	characteristic, complemented
264	#2058	C₂×C₂₉	1	1	yes	characteristic, complemented
265	#1991	C₂×C₂₉	1	1	yes	characteristic, complemented
266	#1990	C₂×C₂₉	1	1	yes	characteristic, complemented
267	#1942	C₂×C₂₉	1	1	yes	characteristic, complemented
268	#1941	C₂×C₂₉	1	1	yes	characteristic, complemented
269	#1854	C₂×C₂₉	1	1	yes	characteristic
270	#1854	C₂×C₂₉	1	1	yes	characteristic
271	#1807	C₂×C₂₉	1	1	yes	characteristic
272	C₈×C₂²⋊C₄	C₂×C₂₉	1	1	yes	characteristic
273	#1735	C₂×C₂₉	1	1	yes	characteristic
274	C₂²×C₂₉	—	2	2	no	—
275	C₂²×C₂₉	—	2	2	no	—
276	C₂²×C₂₉	—	2	2	no	—
277	C₂²×C₂₉	—	4	1	no	—
278	C₂²×C₂₉	—	4	1	no	—
279	C₂²×C₂₉	—	4	1	no	—
280	C₂²×C₂₉	—	4	1	no	—
281	C₂²×C₂₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
282	C₂²×C₂₉	#546	1	1	yes	characteristic
283	C₂²×C₂₉	#546	1	1	yes	characteristic
284	C₂²×C₂₉	C₂×#135	1	1	yes	characteristic
285	C₂²×C₂₉	C₂×#135	1	1	yes	characteristic
286	C₂²×C₂₉	#577	1	1	yes	characteristic
287	C₂²×C₂₉	#577	1	1	yes	characteristic
288	C₄×C₂₉	—	2	2	no	—
289	C₄×C₂₉	—	2	2	no	—
290	C₄×C₂₉	—	2	2	no	—
291	C₄×C₂₉	—	4	2	no	—
292	C₄×C₂₉	—	4	1	no	—
293	C₄×C₂₉	—	4	2	no	—
294	C₄×C₂₉	—	4	1	no	—
295	C₄×C₂₉	—	8	1	no	—
296	C₄×C₂₉	—	8	1	no	—
297	C₄×C₂₉	—	8	1	no	—
298	C₄×C₂₉	—	8	1	no	—
299	C₄×C₂₉	—	8	1	no	—
300	C₄×C₂₉	—	8	1	no	—
301	C₄×C₂₉	#533	1	1	yes	characteristic
302	C₄×C₂₉	#543	1	1	yes	characteristic
303	C₄×C₂₉	#554	1	1	yes	characteristic
304	C₄×C₂₉	#554	1	1	yes	characteristic
305	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic
306	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
307	C₂×#125	C₂²×C₂₉	1	1	yes	characteristic
308	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
309	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
310	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
311	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
312	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
313	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
314	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
315	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
316	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
317	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
318	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
319	#399	—	2	1	no	—
320	#396	—	2	1	no	—
321	#396	—	2	1	no	—
322	#393	—	2	1	no	—
323	#391	—	2	1	no	—
324	#389	—	2	1	no	—
325	#389	C₂²×C₂₉	1	1	yes	characteristic
326	#389	C₂²×C₂₉	1	1	yes	characteristic
327	#389	C₂²×C₂₉	1	1	yes	characteristic
328	#389	C₂²×C₂₉	1	1	yes	characteristic
329	#387	—	2	1	no	—
330	#387	—	2	1	no	—
331	#384	C₂²×C₂₉	1	1	yes	characteristic
332	#382	C₂²×C₂₉	1	1	yes	characteristic
333	#380	C₂²×C₂₉	1	1	yes	characteristic
334	#380	C₂²×C₂₉	1	1	yes	characteristic
335	C₄×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
336	#340	C₂²×C₂₉	1	1	yes	characteristic
337	#340	C₂²×C₂₉	1	1	yes	characteristic
338	#340	C₂²×C₂₉	1	1	yes	characteristic
339	#340	C₂²×C₂₉	1	1	yes	characteristic
340	#340	C₂²×C₂₉	1	1	yes	characteristic
341	#340	C₂²×C₂₉	1	1	yes	characteristic
342	#340	C₂²×C₂₉	1	1	yes	characteristic
343	#340	C₂²×C₂₉	1	1	yes	characteristic
344	#340	C₂²×C₂₉	1	1	yes	characteristic
345	#340	C₂²×C₂₉	1	1	yes	characteristic
346	#336	C₂²×C₂₉	1	1	yes	characteristic
347	#336	C₂²×C₂₉	1	1	yes	characteristic
348	C₂×C₂₉	—	4	2	no	—
349	C₂×C₂₉	#2549	1	1	yes	characteristic
350	C₂×C₂₉	#3160	1	1	yes	characteristic
351	C₂×C₂₉	#3163	1	1	yes	characteristic
352	C₂×C₂₉	#3296	1	1	yes	characteristic
353	C₂×C₂₉	#3301	1	1	yes	characteristic
354	C₂×C₂₉	#3303	1	1	yes	characteristic
355	C₂×C₂₉	#3304	1	1	yes	characteristic
356	C₂²×Q₈	—	2	1	no	—
357	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
358	C₂²×C₈	—	4	1	no	—
359	C₂²×C₈	—	4	1	no	—
360	C₂²×C₈	Q₈×C₂₉	1	4	yes	complemented
361	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
362	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
363	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
365	C₄⋊Q₈	—	2	2	no	—
366	C₄⋊Q₈	—	4	1	no	—
367	#125	—	2	2	no	—
368	#125	—	4	1	no	—
369	#117	—	2	2	no	—
370	#117	—	2	2	no	—
371	#117	—	4	1	no	—
372	#117	—	4	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
395	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	—	2	1	no	—
398	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
399	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
400	#107	—	2	2	no	—
401	#107	—	4	1	no	—
402	#106	—	2	2	no	—
403	#106	—	4	1	no	—
404	#106	—	4	1	no	—
405	#106	—	4	1	no	—
406	C₂²⋊C₈	Q₈×C₂₉	1	4	yes	complemented
407	C₄×C₈	—	4	1	no	—
408	C₄×C₈	—	4	1	no	—
409	#95	—	2	1	no	—
410	#95	—	2	1	no	—
411	#95	—	2	1	no	—
412	#95	—	2	1	no	—
413	#95	—	2	1	no	—
414	#95	—	2	1	no	—
415	#95	—	2	1	no	—
416	#95	—	2	1	no	—
417	#95	D₄×C₂₉	1	1	yes	characteristic
418	#95	D₄×C₂₉	1	1	yes	characteristic
419	C₂₉	#28774	1	1	yes	characteristic, direct product factor, Sylow
420	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
421	C₂×Q₈	—	4	2	no	—
422	C₂×Q₈	—	4	2	no	—
423	C₂×Q₈	—	8	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
441	C₂²×C₄	C₂×Q₈×C₂₉	1	2	yes	—
442	C₂²×C₄	C₂×Q₈×C₂₉	1	2	yes	—
443	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	4	4	no	—
453	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
454	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
455	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
456	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	4	2	no	—
472	C₄⋊C₄	—	4	2	no	—
473	C₄⋊C₄	—	4	2	no	—
474	C₄⋊C₄	—	4	2	no	—
475	C₄⋊C₄	—	4	2	no	—
476	C₄⋊C₄	—	4	2	no	—
477	C₄⋊C₄	—	8	1	no	—
478	C₄⋊C₄	—	8	1	no	—
479	C₄⋊C₄	—	8	1	no	—
480	C₄⋊C₄	#41×C₂₉	1	2	yes	—
481	C₄⋊C₄	#41×C₂₉	1	2	yes	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	4	2	no	—
485	C₂²⋊C₄	—	4	2	no	—
486	C₂²⋊C₄	—	8	1	no	—
487	C₂²⋊C₄	—	8	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	4	2	no	—
493	C₄²	—	4	2	no	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	2	1	no	—
500	C₂³	C₂₉×C₄⋊Q₈	1	2	yes	—
501	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
502	Q₈	—	8	4	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	C₂₉×C₄⋊Q₈	1	2	yes	—
544	C₂×C₄	C₂₉×#135	1	2	yes	—
545	C₂×C₄	C₂₉×#135	1	2	yes	—
546	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
547	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
548	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
549	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
550	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
551	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
552	C₈	—	2	2	no	—
553	C₈	—	2	2	no	—
554	C₈	—	2	2	no	—
555	C₈	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	C₂×C₂₉×C₄⋊Q₈	1	1	yes	characteristic
564	C₂²	C₂₉×#546	1	1	yes	characteristic
565	C₂²	C₂₉×#546	1	1	yes	characteristic
566	C₂²	C₂×C₂₉×#135	1	1	yes	characteristic
567	C₂²	C₂×C₂₉×#135	1	1	yes	characteristic
568	C₂²	C₂₉×#577	1	1	yes	characteristic
569	C₂²	C₂₉×#577	1	1	yes	characteristic
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	4	2	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	1	no	—
577	C₄	—	8	1	no	—
578	C₄	—	8	1	no	—
579	C₄	—	8	1	no	—
580	C₄	—	8	1	no	—
581	C₄	—	8	1	no	—
582	C₄	—	8	1	no	—
583	C₄	C₂₉×#533	1	1	yes	characteristic
584	C₄	C₂₉×#543	1	1	yes	characteristic
585	C₄	C₂₉×#554	1	1	yes	characteristic
586	C₄	C₂₉×#554	1	1	yes	characteristic
587	C₂	—	4	2	no	—
588	C₂	C₂₉×#2549	1	1	yes	characteristic
589	C₂	C₂₉×#3160	1	1	yes	characteristic
590	C₂	C₂₉×#3163	1	1	yes	characteristic
591	C₂	C₂₉×#3296	1	1	yes	characteristic
592	C₂	C₂₉×#3301	1	1	yes	characteristic
593	C₂	C₂₉×#3303	1	1	yes	characteristic
594	C₂	C₂₉×#3304	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₂₉×#2085	C₂	semidirect
4. C₂₉×#2084	C₂	semidirect
5. C₂₉×#2059	C₂	semidirect
6. C₂₉×#2058	C₂	semidirect
7. C₂₉×#1991	C₂	semidirect
8. C₂₉×#1990	C₂	semidirect
9. C₂₉×#1942	C₂	semidirect
10. C₂₉×#1941	C₂	semidirect
63. C₂²×C₈×C₂₉	Q₈	semidirect
109. C₂₉×C₂²⋊C₈	Q₈	semidirect
196. #28774	C₂₉	direct (N × H)
261. #2085	C₂×C₂₉	semidirect
262. #2084	C₂×C₂₉	semidirect
263. #2059	C₂×C₂₉	semidirect
264. #2058	C₂×C₂₉	semidirect
265. #1991	C₂×C₂₉	semidirect
266. #1990	C₂×C₂₉	semidirect
267. #1942	C₂×C₂₉	semidirect
268. #1941	C₂×C₂₉	semidirect
360. C₂²×C₈	Q₈×C₂₉	semidirect
406. C₂²⋊C₈	Q₈×C₂₉	semidirect
419. C₂₉	#28774	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×#2441	2
C₂₉×#2439	2
C₂₉×#2085	2
C₂₉×#2084	2
C₂₉×#2059	2
C₂₉×#2058	2
C₂₉×#1991	2
C₂₉×#1990	2
C₂₉×#1942	2
C₂₉×#1941	2
C₂₉×#1854	2
C₂₉×#1807	2
C₈×C₂²⋊C₄×C₂₉	2
C₂₉×#1735	2
#28774	29

Subgroups — C29×#28774 #20323674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#28774 #20323674