Subgroups — C₂₉×#28776 #20323676

Order 7424.

774 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#2442	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2440	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×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1992	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1944	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1943	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1853	C₂	1	1	yes	maximal, characteristic
12	C₂₉×#1852	C₂	1	1	yes	maximal, characteristic
13	C₂₉×#1807	C₂	1	1	yes	maximal, characteristic
14	C₂₉×#1752	C₂	1	1	yes	maximal, characteristic
15	C₂×C₂₉×#340	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×C₂²⋊Q₈	—	2	1	no	—
20	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×#107	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×#106	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
31	C₂₉×#400	—	2	1	no	—
32	C₂₉×#398	—	2	1	no	—
33	C₂₉×#398	—	2	1	no	—
34	C₂₉×#395	—	2	1	no	—
35	C₂₉×#389	C₂²	1	1	yes	characteristic
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×#385	—	2	1	no	—
40	C₂₉×#385	—	2	1	no	—
41	C₂₉×#384	C₂²	1	1	yes	characteristic
42	C₂₉×#382	C₂²	1	1	yes	characteristic
43	C₂₉×#380	—	2	1	no	—
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	—	2	1	no	—
61	C₂³×C₄×C₂₉	—	2	1	no	—
62	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₂₉	—	4	1	no	—
64	C₂²×C₈×C₂₉	—	4	1	no	—
65	C₂²×C₈×C₂₉	Q₈	1	4	yes	complemented
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	C₂₉×C₂²⋊Q₈	—	4	4	no	—
75	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₂₉	—	2	2	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	—	2	1	no	—
86	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
89	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
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×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₂₉	D₄	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	—	4	1	no	—
106	C₂₉×#106	—	2	2	no	—
107	C₂₉×#106	—	4	1	no	—
108	C₂₉×#106	—	4	1	no	—
109	C₂₉×#106	—	4	1	no	—
110	C₂₉×C₂²⋊C₈	Q₈	1	4	yes	complemented
111	C₂₉×#97	—	4	1	no	—
112	C₂₉×#97	—	4	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	—	2	1	no	—
121	C₂₉×#95	D₄	1	1	yes	characteristic
122	C₂₉×#95	D₄	1	1	yes	characteristic
123	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
124	C₂×Q₈×C₂₉	—	4	2	no	—
125	C₂×Q₈×C₂₉	—	4	2	no	—
126	C₂×Q₈×C₂₉	—	8	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	—	2	1	no	—
139	C₂²×C₄×C₂₉	—	4	2	no	—
140	C₂²×C₄×C₂₉	—	4	2	no	—
141	C₂²×C₄×C₂₉	—	4	2	no	—
142	C₂²×C₄×C₂₉	—	4	2	no	—
143	C₂²×C₄×C₂₉	—	8	1	no	—
144	C₂²×C₄×C₂₉	—	8	1	no	—
145	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₂₉	C₂×Q₈	1	2	yes	—
151	C₂²×C₄×C₂₉	C₂×Q₈	1	2	yes	—
152	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
153	C₂×C₈×C₂₉	—	2	1	no	—
154	C₂×C₈×C₂₉	—	2	1	no	—
155	C₂×C₈×C₂₉	—	2	1	no	—
156	C₂×C₈×C₂₉	—	2	1	no	—
157	C₂×C₈×C₂₉	—	2	1	no	—
158	C₂×C₈×C₂₉	—	2	1	no	—
159	C₂×C₈×C₂₉	—	2	1	no	—
160	C₂×C₈×C₂₉	—	2	1	no	—
161	C₂×C₈×C₂₉	—	4	4	no	—
162	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
163	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
164	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
165	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
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	—	2	1	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	—	4	2	no	—
181	C₄⋊C₄×C₂₉	—	4	2	no	—
182	C₄⋊C₄×C₂₉	—	4	2	no	—
183	C₄⋊C₄×C₂₉	—	4	2	no	—
184	C₄⋊C₄×C₂₉	—	4	2	no	—
185	C₄⋊C₄×C₂₉	—	4	2	no	—
186	C₄⋊C₄×C₂₉	—	4	2	no	—
187	C₄⋊C₄×C₂₉	—	4	2	no	—
188	C₄⋊C₄×C₂₉	—	8	1	no	—
189	C₄⋊C₄×C₂₉	—	8	1	no	—
190	C₄⋊C₄×C₂₉	—	8	1	no	—
191	C₄⋊C₄×C₂₉	#41	1	2	yes	—
192	C₄⋊C₄×C₂₉	#41	1	2	yes	—
193	C₂²⋊C₄×C₂₉	—	2	2	no	—
194	C₂²⋊C₄×C₂₉	—	2	2	no	—
195	C₂²⋊C₄×C₂₉	—	4	2	no	—
196	C₂²⋊C₄×C₂₉	—	4	2	no	—
197	C₄²×C₂₉	—	2	1	no	—
198	C₄²×C₂₉	—	2	1	no	—
199	C₄²×C₂₉	—	2	1	no	—
200	C₄²×C₂₉	—	2	1	no	—
201	#28776	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂³×C₂₉	—	2	1	no	—
203	C₂³×C₂₉	—	2	1	no	—
204	C₂³×C₂₉	—	2	1	no	—
205	C₂³×C₂₉	—	2	1	no	—
206	C₂³×C₂₉	C₄⋊Q₈	1	2	yes	—
207	C₂³×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
208	C₂³×C₂₉	#137	1	2	yes	—
209	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
210	Q₈×C₂₉	—	8	4	no	—
211	C₂×C₄×C₂₉	—	2	1	no	—
212	C₂×C₄×C₂₉	—	2	1	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	2	no	—
217	C₂×C₄×C₂₉	—	2	1	no	—
218	C₂×C₄×C₂₉	—	2	1	no	—
219	C₂×C₄×C₂₉	—	2	1	no	—
220	C₂×C₄×C₂₉	—	2	1	no	—
221	C₂×C₄×C₂₉	—	2	2	no	—
222	C₂×C₄×C₂₉	—	2	2	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	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	—	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	—	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	—	8	4	no	—
254	C₂×C₄×C₂₉	—	8	4	no	—
255	C₂×C₄×C₂₉	C₄⋊Q₈	1	2	yes	—
256	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
257	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
258	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
260	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
261	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
262	C₈×C₂₉	—	2	2	no	—
263	C₈×C₂₉	—	2	2	no	—
264	C₈×C₂₉	—	2	2	no	—
265	C₈×C₂₉	—	2	2	no	—
266	#2442	C₂×C₂₉	1	1	yes	characteristic
267	#2440	C₂×C₂₉	1	1	yes	characteristic
268	#2085	C₂×C₂₉	1	1	yes	characteristic, complemented
269	#2084	C₂×C₂₉	1	1	yes	characteristic, complemented
270	#2059	C₂×C₂₉	1	1	yes	characteristic, complemented
271	#2058	C₂×C₂₉	1	1	yes	characteristic, complemented
272	#1993	C₂×C₂₉	1	1	yes	characteristic, complemented
273	#1992	C₂×C₂₉	1	1	yes	characteristic, complemented
274	#1944	C₂×C₂₉	1	1	yes	characteristic, complemented
275	#1943	C₂×C₂₉	1	1	yes	characteristic, complemented
276	#1853	C₂×C₂₉	1	1	yes	characteristic
277	#1852	C₂×C₂₉	1	1	yes	characteristic
278	#1807	C₂×C₂₉	1	1	yes	characteristic
279	#1752	C₂×C₂₉	1	1	yes	characteristic
280	C₂×#340	C₂×C₂₉	1	1	yes	characteristic
281	C₂²×C₂₉	—	2	2	no	—
282	C₂²×C₂₉	—	2	2	no	—
283	C₂²×C₂₉	—	2	2	no	—
284	C₂²×C₂₉	—	2	2	no	—
285	C₂²×C₂₉	—	2	2	no	—
286	C₂²×C₂₉	—	2	2	no	—
287	C₂²×C₂₉	#501	1	4	yes	—
288	C₂²×C₂₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
289	C₂²×C₂₉	#546	1	1	yes	characteristic
290	C₂²×C₂₉	#546	1	1	yes	characteristic
291	C₂²×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
292	C₂²×C₂₉	C₂×#137	1	1	yes	characteristic
293	C₂²×C₂₉	#577	1	1	yes	characteristic
294	C₂²×C₂₉	#577	1	1	yes	characteristic
295	C₄×C₂₉	—	2	2	no	—
296	C₄×C₂₉	—	4	1	no	—
297	C₄×C₂₉	—	4	2	no	—
298	C₄×C₂₉	—	4	1	no	—
299	C₄×C₂₉	—	4	2	no	—
300	C₄×C₂₉	—	4	1	no	—
301	C₄×C₂₉	—	4	1	no	—
302	C₄×C₂₉	—	8	1	no	—
303	C₄×C₂₉	—	8	1	no	—
304	C₄×C₂₉	—	8	1	no	—
305	C₄×C₂₉	—	8	1	no	—
306	C₄×C₂₉	—	8	1	no	—
307	C₄×C₂₉	—	8	1	no	—
308	C₄×C₂₉	#533	1	1	yes	characteristic
309	C₄×C₂₉	#543	1	1	yes	characteristic
310	C₄×C₂₉	#554	1	1	yes	characteristic
311	C₄×C₂₉	#554	1	1	yes	characteristic
312	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic
313	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
314	C₂×#125	C₂²×C₂₉	1	1	yes	characteristic
315	C₂×C₂²⋊Q₈	—	2	1	no	—
316	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
317	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
318	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
319	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
320	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
321	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
322	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
323	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
324	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
325	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
326	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
327	#400	—	2	1	no	—
328	#398	—	2	1	no	—
329	#398	—	2	1	no	—
330	#395	—	2	1	no	—
331	#389	C₂²×C₂₉	1	1	yes	characteristic
332	#389	C₂²×C₂₉	1	1	yes	characteristic
333	#389	C₂²×C₂₉	1	1	yes	characteristic
334	#389	C₂²×C₂₉	1	1	yes	characteristic
335	#385	—	2	1	no	—
336	#385	—	2	1	no	—
337	#384	C₂²×C₂₉	1	1	yes	characteristic
338	#382	C₂²×C₂₉	1	1	yes	characteristic
339	#380	—	2	1	no	—
340	#380	C₂²×C₂₉	1	1	yes	characteristic
341	#380	C₂²×C₂₉	1	1	yes	characteristic
342	C₄×C₂²⋊C₄	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	#340	C₂²×C₂₉	1	1	yes	characteristic
347	#340	C₂²×C₂₉	1	1	yes	characteristic
348	#340	C₂²×C₂₉	1	1	yes	characteristic
349	#340	C₂²×C₂₉	1	1	yes	characteristic
350	#340	C₂²×C₂₉	1	1	yes	characteristic
351	#340	C₂²×C₂₉	1	1	yes	characteristic
352	#340	C₂²×C₂₉	1	1	yes	characteristic
353	#336	C₂²×C₂₉	1	1	yes	characteristic
354	#336	C₂²×C₂₉	1	1	yes	characteristic
355	C₂×C₂₉	—	2	4	no	—
356	C₂×C₂₉	#2549	1	1	yes	characteristic
357	C₂×C₂₉	C₂×#501	1	1	yes	characteristic
358	C₂×C₂₉	#3163	1	1	yes	characteristic
359	C₂×C₂₉	#3306	1	1	yes	characteristic
360	C₂×C₂₉	#3310	1	1	yes	characteristic
361	C₂×C₂₉	#3316	1	1	yes	characteristic
362	C₂×C₂₉	#3320	1	1	yes	characteristic
363	C₂²×Q₈	—	2	1	no	—
364	C₂³×C₄	—	2	1	no	—
365	C₂³×C₄	—	2	1	no	—
366	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
367	C₂²×C₈	—	4	1	no	—
368	C₂²×C₈	—	4	1	no	—
369	C₂²×C₈	Q₈×C₂₉	1	4	yes	complemented
370	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
373	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
374	C₄⋊Q₈	—	2	2	no	—
375	C₄⋊Q₈	—	4	1	no	—
376	#125	—	2	2	no	—
377	#125	—	4	1	no	—
378	C₂²⋊Q₈	—	4	4	no	—
379	C₂×C₄⋊C₄	—	2	2	no	—
380	C₂×C₄⋊C₄	—	2	2	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	4	1	no	—
393	C₂×C₄⋊C₄	—	4	1	no	—
394	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×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×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
405	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
407	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
408	#107	—	2	2	no	—
409	#107	—	4	1	no	—
410	#106	—	2	2	no	—
411	#106	—	4	1	no	—
412	#106	—	4	1	no	—
413	#106	—	4	1	no	—
414	C₂²⋊C₈	Q₈×C₂₉	1	4	yes	complemented
415	#97	—	4	1	no	—
416	#97	—	4	1	no	—
417	#95	—	2	1	no	—
418	#95	—	2	1	no	—
419	#95	—	2	1	no	—
420	#95	—	2	1	no	—
421	#95	—	2	1	no	—
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	#95	—	2	1	no	—
425	#95	D₄×C₂₉	1	1	yes	characteristic
426	#95	D₄×C₂₉	1	1	yes	characteristic
427	C₂₉	#28776	1	1	yes	characteristic, direct product factor, Sylow
428	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
429	C₂×Q₈	—	4	2	no	—
430	C₂×Q₈	—	4	2	no	—
431	C₂×Q₈	—	8	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	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	4	2	no	—
445	C₂²×C₄	—	4	2	no	—
446	C₂²×C₄	—	4	2	no	—
447	C₂²×C₄	—	4	2	no	—
448	C₂²×C₄	—	8	1	no	—
449	C₂²×C₄	—	8	1	no	—
450	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
455	C₂²×C₄	C₂×Q₈×C₂₉	1	2	yes	—
456	C₂²×C₄	C₂×Q₈×C₂₉	1	2	yes	—
457	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	4	4	no	—
467	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
468	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
469	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
470	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	4	2	no	—
486	C₄⋊C₄	—	4	2	no	—
487	C₄⋊C₄	—	4	2	no	—
488	C₄⋊C₄	—	4	2	no	—
489	C₄⋊C₄	—	4	2	no	—
490	C₄⋊C₄	—	4	2	no	—
491	C₄⋊C₄	—	4	2	no	—
492	C₄⋊C₄	—	4	2	no	—
493	C₄⋊C₄	—	8	1	no	—
494	C₄⋊C₄	—	8	1	no	—
495	C₄⋊C₄	—	8	1	no	—
496	C₄⋊C₄	#41×C₂₉	1	2	yes	—
497	C₄⋊C₄	#41×C₂₉	1	2	yes	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	4	2	no	—
501	C₂²⋊C₄	—	4	2	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₂³	—	2	1	no	—
507	C₂³	—	2	1	no	—
508	C₂³	—	2	1	no	—
509	C₂³	—	2	1	no	—
510	C₂³	C₂₉×C₄⋊Q₈	1	2	yes	—
511	C₂³	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
512	C₂³	C₂₉×#137	1	2	yes	—
513	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
514	Q₈	—	8	4	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
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	—	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	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	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	—	8	4	no	—
558	C₂×C₄	—	8	4	no	—
559	C₂×C₄	C₂₉×C₄⋊Q₈	1	2	yes	—
560	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
561	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
562	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
563	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
564	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
565	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
566	C₈	—	2	2	no	—
567	C₈	—	2	2	no	—
568	C₈	—	2	2	no	—
569	C₈	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	C₂₉×#501	1	4	yes	—
577	C₂²	C₂×C₂₉×C₄⋊Q₈	1	1	yes	characteristic
578	C₂²	C₂₉×#546	1	1	yes	characteristic
579	C₂²	C₂₉×#546	1	1	yes	characteristic
580	C₂²	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
581	C₂²	C₂×C₂₉×#137	1	1	yes	characteristic
582	C₂²	C₂₉×#577	1	1	yes	characteristic
583	C₂²	C₂₉×#577	1	1	yes	characteristic
584	C₄	—	2	2	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	2	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	8	1	no	—
592	C₄	—	8	1	no	—
593	C₄	—	8	1	no	—
594	C₄	—	8	1	no	—
595	C₄	—	8	1	no	—
596	C₄	—	8	1	no	—
597	C₄	C₂₉×#533	1	1	yes	characteristic
598	C₄	C₂₉×#543	1	1	yes	characteristic
599	C₄	C₂₉×#554	1	1	yes	characteristic
600	C₄	C₂₉×#554	1	1	yes	characteristic
601	C₂	—	2	4	no	—
602	C₂	C₂₉×#2549	1	1	yes	characteristic
603	C₂	C₂×C₂₉×#501	1	1	yes	characteristic
604	C₂	C₂₉×#3163	1	1	yes	characteristic
605	C₂	C₂₉×#3306	1	1	yes	characteristic
606	C₂	C₂₉×#3310	1	1	yes	characteristic
607	C₂	C₂₉×#3316	1	1	yes	characteristic
608	C₂	C₂₉×#3320	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×#1993	C₂	semidirect
8. C₂₉×#1992	C₂	semidirect
9. C₂₉×#1944	C₂	semidirect
10. C₂₉×#1943	C₂	semidirect
65. C₂²×C₈×C₂₉	Q₈	semidirect
110. C₂₉×C₂²⋊C₈	Q₈	semidirect
201. #28776	C₂₉	direct (N × H)
268. #2085	C₂×C₂₉	semidirect
269. #2084	C₂×C₂₉	semidirect
270. #2059	C₂×C₂₉	semidirect
271. #2058	C₂×C₂₉	semidirect
272. #1993	C₂×C₂₉	semidirect
273. #1992	C₂×C₂₉	semidirect
274. #1944	C₂×C₂₉	semidirect
275. #1943	C₂×C₂₉	semidirect
369. C₂²×C₈	Q₈×C₂₉	semidirect
414. C₂²⋊C₈	Q₈×C₂₉	semidirect
427. C₂₉	#28776	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×#2442	2
C₂₉×#2440	2
C₂₉×#2085	2
C₂₉×#2084	2
C₂₉×#2059	2
C₂₉×#2058	2
C₂₉×#1993	2
C₂₉×#1992	2
C₂₉×#1944	2
C₂₉×#1943	2
C₂₉×#1853	2
C₂₉×#1852	2
C₂₉×#1807	2
C₂₉×#1752	2
C₂×C₂₉×#340	2
#28776	29

Subgroups — C29×#28776 #20323676

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#28776 #20323676