Subgroups — C₂₉×#25955 #20320855

Order 7424.

990 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₉×#103	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2440	C₂	1	1	yes	maximal, characteristic
4	Q₈×C₂²⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#2096	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2066	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2066	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2024	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1865	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1865	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1853	C₂	1	1	yes	maximal, characteristic
12	C₂₉×#1850	C₂	1	1	yes	maximal, characteristic
13	C₂₉×#1807	C₂	1	1	yes	maximal, characteristic
14	C₂₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1787	C₂	1	1	yes	maximal, characteristic
16	C₂³×Q₈×C₂₉	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₂₉	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
23	C₂₉×#475	—	2	4	no	—
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×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×#103	—	2	4	no	—
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×#103	C₂²	1	1	yes	characteristic
35	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
36	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
37	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
38	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
39	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂₉×#398	—	2	1	no	—
41	C₂₉×#395	—	2	1	no	—
42	C₂₉×#391	—	2	1	no	—
43	C₂₉×#391	—	2	1	no	—
44	C₂₉×#391	C₂²	1	1	yes	characteristic
45	C₂₉×#391	C₂²	1	1	yes	characteristic
46	C₂₉×#389	C₂²	1	1	yes	characteristic
47	C₂₉×#389	C₂²	1	1	yes	characteristic
48	C₂₉×#385	—	2	1	no	—
49	C₂₉×#384	C₂²	1	1	yes	characteristic
50	C₂₉×#380	—	2	1	no	—
51	C₂₉×#380	C₂²	1	1	yes	characteristic
52	C₂₉×#380	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊C₄×C₂₉	—	2	1	no	—
54	C₄×C₂²⋊C₄×C₂₉	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×Q₈×C₂₉	—	2	1	no	—
63	C₂²×Q₈×C₂₉	—	2	2	no	—
64	C₂²×Q₈×C₂₉	—	2	2	no	—
65	C₂²×Q₈×C₂₉	—	2	2	no	—
66	C₂²×Q₈×C₂₉	—	4	1	no	—
67	C₂²×Q₈×C₂₉	—	4	1	no	—
68	C₂²×Q₈×C₂₉	Q₈	1	4	yes	complemented
69	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₂₉	—	2	1	no	—
72	C₂³×C₄×C₂₉	—	2	1	no	—
73	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₂₉	—	2	2	no	—
75	C₂²×C₈×C₂₉	—	2	2	no	—
76	C₂²×C₈×C₂₉	—	4	1	no	—
77	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
81	C₂₉×C₄⋊Q₈	—	2	2	no	—
82	C₂₉×C₄⋊Q₈	—	4	1	no	—
83	C₂₉×C₂²⋊Q₈	—	4	4	no	—
84	C₄×Q₈×C₂₉	—	2	2	no	—
85	C₄×Q₈×C₂₉	—	2	2	no	—
86	C₄×Q₈×C₂₉	—	4	1	no	—
87	C₄×Q₈×C₂₉	—	4	1	no	—
88	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
89	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
98	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₂₉	—	2	1	no	—
109	C₂×C₄²×C₂₉	—	2	1	no	—
110	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
112	C₂₉×#106	—	2	2	no	—
113	C₂₉×#106	—	2	2	no	—
114	C₂₉×#106	—	4	1	no	—
115	C₂₉×#106	—	4	1	no	—
116	C₂₉×C₄⋊C₈	—	2	2	no	—
117	C₂₉×C₄⋊C₈	—	4	1	no	—
118	C₂₉×#103	—	2	2	no	—
119	C₂₉×#103	—	2	2	no	—
120	C₂₉×#103	—	2	2	no	—
121	C₂₉×#103	—	2	2	no	—
122	C₂₉×#103	—	2	2	no	—
123	C₂₉×#103	—	4	1	no	—
124	C₂₉×#103	—	4	1	no	—
125	C₂₉×#103	D₄	1	4	yes	—
126	C₂₉×C₂²⋊C₈	—	2	2	no	—
127	C₂₉×#95	—	2	1	no	—
128	C₂₉×#95	—	2	1	no	—
129	C₂₉×#95	—	2	1	no	—
130	C₂₉×#95	—	2	1	no	—
131	C₂₉×#95	—	2	1	no	—
132	C₂₉×#95	—	2	1	no	—
133	C₂₉×#95	—	2	1	no	—
134	C₂₉×#95	—	2	1	no	—
135	C₂₉×#95	D₄	1	1	yes	characteristic
136	C₂₉×#95	D₄	1	1	yes	characteristic
137	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
138	C₂×Q₈×C₂₉	—	2	4	no	—
139	C₂×Q₈×C₂₉	—	2	1	no	—
140	C₂×Q₈×C₂₉	—	2	1	no	—
141	C₂×Q₈×C₂₉	—	2	1	no	—
142	C₂×Q₈×C₂₉	—	2	1	no	—
143	C₂×Q₈×C₂₉	—	2	8	no	—
144	C₂×Q₈×C₂₉	—	2	1	no	—
145	C₂×Q₈×C₂₉	—	2	1	no	—
146	C₂×Q₈×C₂₉	—	2	1	no	—
147	C₂×Q₈×C₂₉	—	2	1	no	—
148	C₂×Q₈×C₂₉	—	4	2	no	—
149	C₂×Q₈×C₂₉	—	4	2	no	—
150	C₂×Q₈×C₂₉	—	4	2	no	—
151	C₂×Q₈×C₂₉	—	4	4	no	—
152	C₂×Q₈×C₂₉	—	4	4	no	—
153	C₂×Q₈×C₂₉	—	4	4	no	—
154	C₂×Q₈×C₂₉	—	4	2	no	—
155	C₂×Q₈×C₂₉	—	8	1	no	—
156	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
157	C₂×Q₈×C₂₉	C₂×Q₈	1	2	yes	—
158	C₂×Q₈×C₂₉	C₂×Q₈	1	2	yes	—
159	C₂×Q₈×C₂₉	#41	1	2	yes	—
160	C₂²×C₄×C₂₉	—	2	1	no	—
161	C₂²×C₄×C₂₉	—	2	1	no	—
162	C₂²×C₄×C₂₉	—	2	1	no	—
163	C₂²×C₄×C₂₉	—	2	1	no	—
164	C₂²×C₄×C₂₉	—	2	1	no	—
165	C₂²×C₄×C₂₉	—	2	4	no	—
166	C₂²×C₄×C₂₉	—	2	1	no	—
167	C₂²×C₄×C₂₉	—	2	1	no	—
168	C₂²×C₄×C₂₉	—	2	1	no	—
169	C₂²×C₄×C₂₉	—	2	1	no	—
170	C₂²×C₄×C₂₉	—	2	1	no	—
171	C₂²×C₄×C₂₉	—	2	1	no	—
172	C₂²×C₄×C₂₉	—	2	1	no	—
173	C₂²×C₄×C₂₉	—	4	2	no	—
174	C₂²×C₄×C₂₉	—	4	2	no	—
175	C₂²×C₄×C₂₉	—	4	2	no	—
176	C₂²×C₄×C₂₉	—	4	2	no	—
177	C₂²×C₄×C₂₉	—	8	1	no	—
178	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₂₉	C₂×Q₈	1	2	yes	—
184	C₂²×C₄×C₂₉	#41	1	2	yes	—
185	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
186	C₂×C₈×C₂₉	—	2	1	no	—
187	C₂×C₈×C₂₉	—	2	1	no	—
188	C₂×C₈×C₂₉	—	2	1	no	—
189	C₂×C₈×C₂₉	—	2	1	no	—
190	C₂×C₈×C₂₉	—	2	1	no	—
191	C₂×C₈×C₂₉	—	2	1	no	—
192	C₂×C₈×C₂₉	—	2	1	no	—
193	C₂×C₈×C₂₉	—	2	1	no	—
194	C₂×C₈×C₂₉	—	2	1	no	—
195	C₂×C₈×C₂₉	—	2	1	no	—
196	C₂×C₈×C₂₉	—	2	1	no	—
197	C₂×C₈×C₂₉	—	4	4	no	—
198	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
199	C₄⋊C₄×C₂₉	—	2	1	no	—
200	C₄⋊C₄×C₂₉	—	2	1	no	—
201	C₄⋊C₄×C₂₉	—	2	1	no	—
202	C₄⋊C₄×C₂₉	—	2	1	no	—
203	C₄⋊C₄×C₂₉	—	2	1	no	—
204	C₄⋊C₄×C₂₉	—	2	1	no	—
205	C₄⋊C₄×C₂₉	—	2	1	no	—
206	C₄⋊C₄×C₂₉	—	2	1	no	—
207	C₄⋊C₄×C₂₉	—	2	1	no	—
208	C₄⋊C₄×C₂₉	—	2	1	no	—
209	C₄⋊C₄×C₂₉	—	2	1	no	—
210	C₄⋊C₄×C₂₉	—	4	2	no	—
211	C₄⋊C₄×C₂₉	—	4	2	no	—
212	C₄⋊C₄×C₂₉	—	4	2	no	—
213	C₄⋊C₄×C₂₉	—	4	2	no	—
214	C₄⋊C₄×C₂₉	—	4	2	no	—
215	C₄⋊C₄×C₂₉	—	4	2	no	—
216	C₄⋊C₄×C₂₉	—	4	2	no	—
217	C₄⋊C₄×C₂₉	—	8	1	no	—
218	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
219	C₂²⋊C₄×C₂₉	—	2	2	no	—
220	C₂²⋊C₄×C₂₉	—	4	2	no	—
221	C₂²⋊C₄×C₂₉	—	4	2	no	—
222	C₂²⋊C₄×C₂₉	SD₁₆	1	4	yes	—
223	C₄²×C₂₉	—	2	1	no	—
224	C₄²×C₂₉	—	2	1	no	—
225	C₄²×C₂₉	—	2	1	no	—
226	C₄²×C₂₉	—	2	1	no	—
227	C₄²×C₂₉	—	4	2	no	—
228	C₄²×C₂₉	—	4	2	no	—
229	#25955	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂³×C₂₉	—	2	1	no	—
231	C₂³×C₂₉	—	2	1	no	—
232	C₂³×C₂₉	—	2	1	no	—
233	C₂³×C₂₉	—	2	1	no	—
234	C₂³×C₂₉	C₂²⋊Q₈	1	2	yes	—
235	C₂³×C₂₉	C₂×SD₁₆	1	2	yes	—
236	C₂³×C₂₉	#137	1	2	yes	—
237	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
238	Q₈×C₂₉	—	2	2	no	—
239	Q₈×C₂₉	—	2	2	no	—
240	Q₈×C₂₉	—	2	2	no	—
241	Q₈×C₂₉	—	2	2	no	—
242	Q₈×C₂₉	—	2	2	no	—
243	Q₈×C₂₉	—	4	8	no	—
244	Q₈×C₂₉	—	4	1	no	—
245	Q₈×C₂₉	—	4	1	no	—
246	Q₈×C₂₉	—	8	4	no	—
247	Q₈×C₂₉	C₂²⋊Q₈	1	4	yes	complemented
248	C₂×C₄×C₂₉	—	2	2	no	—
249	C₂×C₄×C₂₉	—	2	1	no	—
250	C₂×C₄×C₂₉	—	2	2	no	—
251	C₂×C₄×C₂₉	—	2	1	no	—
252	C₂×C₄×C₂₉	—	2	1	no	—
253	C₂×C₄×C₂₉	—	2	2	no	—
254	C₂×C₄×C₂₉	—	2	1	no	—
255	C₂×C₄×C₂₉	—	2	1	no	—
256	C₂×C₄×C₂₉	—	2	1	no	—
257	C₂×C₄×C₂₉	—	2	2	no	—
258	C₂×C₄×C₂₉	—	2	2	no	—
259	C₂×C₄×C₂₉	—	2	2	no	—
260	C₂×C₄×C₂₉	—	2	2	no	—
261	C₂×C₄×C₂₉	—	2	2	no	—
262	C₂×C₄×C₂₉	—	2	1	no	—
263	C₂×C₄×C₂₉	—	2	2	no	—
264	C₂×C₄×C₂₉	—	2	1	no	—
265	C₂×C₄×C₂₉	—	2	1	no	—
266	C₂×C₄×C₂₉	—	2	1	no	—
267	C₂×C₄×C₂₉	—	2	1	no	—
268	C₂×C₄×C₂₉	—	2	1	no	—
269	C₂×C₄×C₂₉	—	4	8	no	—
270	C₂×C₄×C₂₉	—	4	1	no	—
271	C₂×C₄×C₂₉	—	4	1	no	—
272	C₂×C₄×C₂₉	—	4	1	no	—
273	C₂×C₄×C₂₉	—	4	1	no	—
274	C₂×C₄×C₂₉	—	4	1	no	—
275	C₂×C₄×C₂₉	—	4	1	no	—
276	C₂×C₄×C₂₉	—	4	1	no	—
277	C₂×C₄×C₂₉	—	4	1	no	—
278	C₂×C₄×C₂₉	—	4	1	no	—
279	C₂×C₄×C₂₉	—	4	1	no	—
280	C₂×C₄×C₂₉	—	4	1	no	—
281	C₂×C₄×C₂₉	—	4	1	no	—
282	C₂×C₄×C₂₉	—	4	1	no	—
283	C₂×C₄×C₂₉	—	4	1	no	—
284	C₂×C₄×C₂₉	—	4	1	no	—
285	C₂×C₄×C₂₉	—	4	1	no	—
286	C₂×C₄×C₂₉	—	4	1	no	—
287	C₂×C₄×C₂₉	—	4	1	no	—
288	C₂×C₄×C₂₉	—	4	1	no	—
289	C₂×C₄×C₂₉	—	8	4	no	—
290	C₂×C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
291	C₂×C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
292	C₂×C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
293	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
295	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
296	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
297	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
298	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
299	C₈×C₂₉	—	2	2	no	—
300	C₈×C₂₉	—	4	1	no	—
301	C₈×C₂₉	—	4	1	no	—
302	C₈×C₂₉	—	4	1	no	—
303	C₂×#475	C₂×C₂₉	1	1	yes	characteristic, complemented
304	C₂²×#103	C₂×C₂₉	1	1	yes	characteristic
305	#2440	C₂×C₂₉	1	1	yes	characteristic
306	Q₈×C₂²⋊C₄	C₂×C₂₉	1	1	yes	characteristic
307	#2096	C₂×C₂₉	1	1	yes	characteristic, complemented
308	#2066	C₂×C₂₉	1	1	yes	characteristic, complemented
309	#2066	C₂×C₂₉	1	1	yes	characteristic, complemented
310	#2024	C₂×C₂₉	1	1	yes	characteristic, complemented
311	#1865	C₂×C₂₉	1	1	yes	characteristic, complemented
312	#1865	C₂×C₂₉	1	1	yes	characteristic, complemented
313	#1853	C₂×C₂₉	1	1	yes	characteristic
314	#1850	C₂×C₂₉	1	1	yes	characteristic
315	#1807	C₂×C₂₉	1	1	yes	characteristic
316	#1803	C₂×C₂₉	1	1	yes	characteristic, complemented
317	#1787	C₂×C₂₉	1	1	yes	characteristic
318	C₂²×C₂₉	—	2	2	no	—
319	C₂²×C₂₉	—	2	2	no	—
320	C₂²×C₂₉	—	2	2	no	—
321	C₂²×C₂₉	—	2	2	no	—
322	C₂²×C₂₉	—	2	2	no	—
323	C₂²×C₂₉	—	2	2	no	—
324	C₂²×C₂₉	#475	1	4	yes	complemented
325	C₂²×C₂₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
326	C₂²×C₂₉	D₄²	1	1	yes	characteristic
327	C₂²×C₂₉	#546	1	1	yes	characteristic
328	C₂²×C₂₉	C₂²×SD₁₆	1	1	yes	characteristic
329	C₂²×C₂₉	C₂×#137	1	1	yes	characteristic
330	C₂²×C₂₉	#577	1	1	yes	characteristic
331	C₂²×C₂₉	#578	1	1	yes	characteristic
332	C₄×C₂₉	—	2	2	no	—
333	C₄×C₂₉	—	2	4	no	—
334	C₄×C₂₉	—	2	2	no	—
335	C₄×C₂₉	—	2	2	no	—
336	C₄×C₂₉	—	4	2	no	—
337	C₄×C₂₉	—	4	1	no	—
338	C₄×C₂₉	—	4	2	no	—
339	C₄×C₂₉	—	4	1	no	—
340	C₄×C₂₉	—	8	1	no	—
341	C₄×C₂₉	—	8	1	no	—
342	C₄×C₂₉	—	8	1	no	—
343	C₄×C₂₉	—	8	1	no	—
344	C₄×C₂₉	—	8	1	no	—
345	C₄×C₂₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
346	C₄×C₂₉	#543	1	1	yes	characteristic
347	C₄×C₂₉	#546	1	1	yes	characteristic
348	C₄×C₂₉	#551	1	1	yes	characteristic
349	C₂³×Q₈	C₂²×C₂₉	1	1	yes	characteristic
350	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic
351	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
352	C₂×C₂²⋊Q₈	—	2	1	no	—
353	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
354	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
355	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
356	#475	—	2	4	no	—
357	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
358	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
359	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
360	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
361	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
362	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
363	C₂×#103	—	2	4	no	—
364	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
365	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
366	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
367	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
368	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
369	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
370	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
371	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
372	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
373	#398	—	2	1	no	—
374	#395	—	2	1	no	—
375	#391	—	2	1	no	—
376	#391	—	2	1	no	—
377	#391	C₂²×C₂₉	1	1	yes	characteristic
378	#391	C₂²×C₂₉	1	1	yes	characteristic
379	#389	C₂²×C₂₉	1	1	yes	characteristic
380	#389	C₂²×C₂₉	1	1	yes	characteristic
381	#385	—	2	1	no	—
382	#384	C₂²×C₂₉	1	1	yes	characteristic
383	#380	—	2	1	no	—
384	#380	C₂²×C₂₉	1	1	yes	characteristic
385	#380	C₂²×C₂₉	1	1	yes	characteristic
386	C₄×C₂²⋊C₄	—	2	1	no	—
387	C₄×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
388	#340	C₂²×C₂₉	1	1	yes	characteristic
389	#340	C₂²×C₂₉	1	1	yes	characteristic
390	#340	C₂²×C₂₉	1	1	yes	characteristic
391	#340	C₂²×C₂₉	1	1	yes	characteristic
392	#336	C₂²×C₂₉	1	1	yes	characteristic
393	#336	C₂²×C₂₉	1	1	yes	characteristic
394	C₂×C₂₉	—	2	4	no	—
395	C₂×C₂₉	#2437	1	1	yes	characteristic
396	C₂×C₂₉	C₂×#475	1	1	yes	characteristic
397	C₂×C₂₉	#3082	1	1	yes	characteristic
398	C₂×C₂₉	#3270	1	1	yes	characteristic
399	C₂×C₂₉	D₄×SD₁₆	1	1	yes	characteristic
400	C₂×C₂₉	#3298	1	1	yes	characteristic
401	C₂×C₂₉	#3316	1	1	yes	characteristic
402	C₂²×Q₈	—	2	1	no	—
403	C₂²×Q₈	—	2	1	no	—
404	C₂²×Q₈	—	2	2	no	—
405	C₂²×Q₈	—	2	2	no	—
406	C₂²×Q₈	—	2	2	no	—
407	C₂²×Q₈	—	4	1	no	—
408	C₂²×Q₈	—	4	1	no	—
409	C₂²×Q₈	Q₈×C₂₉	1	4	yes	complemented
410	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
411	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
412	C₂³×C₄	—	2	1	no	—
413	C₂³×C₄	—	2	1	no	—
414	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
415	C₂²×C₈	—	2	2	no	—
416	C₂²×C₈	—	2	2	no	—
417	C₂²×C₈	—	4	1	no	—
418	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
419	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
420	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
421	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
422	C₄⋊Q₈	—	2	2	no	—
423	C₄⋊Q₈	—	4	1	no	—
424	C₂²⋊Q₈	—	4	4	no	—
425	C₄×Q₈	—	2	2	no	—
426	C₄×Q₈	—	2	2	no	—
427	C₄×Q₈	—	4	1	no	—
428	C₄×Q₈	—	4	1	no	—
429	C₂×C₄⋊C₄	—	2	2	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	—	2	1	no	—
438	C₂×C₄⋊C₄	—	4	1	no	—
439	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
448	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
449	C₂×C₄²	—	2	1	no	—
450	C₂×C₄²	—	2	1	no	—
451	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
452	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
453	#106	—	2	2	no	—
454	#106	—	2	2	no	—
455	#106	—	4	1	no	—
456	#106	—	4	1	no	—
457	C₄⋊C₈	—	2	2	no	—
458	C₄⋊C₈	—	4	1	no	—
459	#103	—	2	2	no	—
460	#103	—	2	2	no	—
461	#103	—	2	2	no	—
462	#103	—	2	2	no	—
463	#103	—	2	2	no	—
464	#103	—	4	1	no	—
465	#103	—	4	1	no	—
466	#103	D₄×C₂₉	1	4	yes	—
467	C₂²⋊C₈	—	2	2	no	—
468	#95	—	2	1	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	#95	—	2	1	no	—
472	#95	—	2	1	no	—
473	#95	—	2	1	no	—
474	#95	—	2	1	no	—
475	#95	—	2	1	no	—
476	#95	D₄×C₂₉	1	1	yes	characteristic
477	#95	D₄×C₂₉	1	1	yes	characteristic
478	C₂₉	#25955	1	1	yes	characteristic, direct product factor, Sylow
479	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
480	C₂×Q₈	—	2	4	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	8	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	4	2	no	—
491	C₂×Q₈	—	4	2	no	—
492	C₂×Q₈	—	4	2	no	—
493	C₂×Q₈	—	4	4	no	—
494	C₂×Q₈	—	4	4	no	—
495	C₂×Q₈	—	4	4	no	—
496	C₂×Q₈	—	4	2	no	—
497	C₂×Q₈	—	8	1	no	—
498	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
499	C₂×Q₈	C₂×Q₈×C₂₉	1	2	yes	—
500	C₂×Q₈	C₂×Q₈×C₂₉	1	2	yes	—
501	C₂×Q₈	#41×C₂₉	1	2	yes	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	4	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	4	2	no	—
516	C₂²×C₄	—	4	2	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	—	4	2	no	—
519	C₂²×C₄	—	8	1	no	—
520	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
521	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
522	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
523	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
525	C₂²×C₄	C₂×Q₈×C₂₉	1	2	yes	—
526	C₂²×C₄	#41×C₂₉	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	4	4	no	—
540	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	4	2	no	—
553	C₄⋊C₄	—	4	2	no	—
554	C₄⋊C₄	—	4	2	no	—
555	C₄⋊C₄	—	4	2	no	—
556	C₄⋊C₄	—	4	2	no	—
557	C₄⋊C₄	—	4	2	no	—
558	C₄⋊C₄	—	4	2	no	—
559	C₄⋊C₄	—	8	1	no	—
560	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	4	2	no	—
563	C₂²⋊C₄	—	4	2	no	—
564	C₂²⋊C₄	SD₁₆×C₂₉	1	4	yes	—
565	C₄²	—	2	1	no	—
566	C₄²	—	2	1	no	—
567	C₄²	—	2	1	no	—
568	C₄²	—	2	1	no	—
569	C₄²	—	4	2	no	—
570	C₄²	—	4	2	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	C₂₉×C₂²⋊Q₈	1	2	yes	—
576	C₂³	C₂×SD₁₆×C₂₉	1	2	yes	—
577	C₂³	C₂₉×#137	1	2	yes	—
578	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
579	Q₈	—	2	2	no	—
580	Q₈	—	2	2	no	—
581	Q₈	—	2	2	no	—
582	Q₈	—	2	2	no	—
583	Q₈	—	2	2	no	—
584	Q₈	—	4	8	no	—
585	Q₈	—	4	1	no	—
586	Q₈	—	4	1	no	—
587	Q₈	—	8	4	no	—
588	Q₈	C₂₉×C₂²⋊Q₈	1	4	yes	complemented
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	4	8	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	8	4	no	—
631	C₂×C₄	C₂₉×C₂²⋊Q₈	1	2	yes	—
632	C₂×C₄	C₂×SD₁₆×C₂₉	1	2	yes	—
633	C₂×C₄	C₂×SD₁₆×C₂₉	1	2	yes	—
634	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
635	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
636	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
637	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
638	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
639	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
640	C₈	—	2	2	no	—
641	C₈	—	4	1	no	—
642	C₈	—	4	1	no	—
643	C₈	—	4	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	2	no	—
650	C₂²	C₂₉×#475	1	4	yes	complemented
651	C₂²	C₂×C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
652	C₂²	D₄²×C₂₉	1	1	yes	characteristic
653	C₂²	C₂₉×#546	1	1	yes	characteristic
654	C₂²	C₂²×SD₁₆×C₂₉	1	1	yes	characteristic
655	C₂²	C₂×C₂₉×#137	1	1	yes	characteristic
656	C₂²	C₂₉×#577	1	1	yes	characteristic
657	C₂²	C₂₉×#578	1	1	yes	characteristic
658	C₄	—	2	2	no	—
659	C₄	—	2	4	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	2	no	—
662	C₄	—	4	2	no	—
663	C₄	—	4	1	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	1	no	—
666	C₄	—	8	1	no	—
667	C₄	—	8	1	no	—
668	C₄	—	8	1	no	—
669	C₄	—	8	1	no	—
670	C₄	—	8	1	no	—
671	C₄	C₂×C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
672	C₄	C₂₉×#543	1	1	yes	characteristic
673	C₄	C₂₉×#546	1	1	yes	characteristic
674	C₄	C₂₉×#551	1	1	yes	characteristic
675	C₂	—	2	4	no	—
676	C₂	C₂₉×#2437	1	1	yes	characteristic
677	C₂	C₂×C₂₉×#475	1	1	yes	characteristic
678	C₂	C₂₉×#3082	1	1	yes	characteristic
679	C₂	C₂₉×#3270	1	1	yes	characteristic
680	C₂	D₄×SD₁₆×C₂₉	1	1	yes	characteristic
681	C₂	C₂₉×#3298	1	1	yes	characteristic
682	C₂	C₂₉×#3316	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
1. C₂×C₂₉×#475	C₂	semidirect
5. C₂₉×#2096	C₂	semidirect
6. C₂₉×#2066	C₂	semidirect
7. C₂₉×#2066	C₂	semidirect
8. C₂₉×#2024	C₂	semidirect
9. C₂₉×#1865	C₂	semidirect
10. C₂₉×#1865	C₂	semidirect
14. C₂₉×#1803	C₂	semidirect
68. C₂²×Q₈×C₂₉	Q₈	semidirect
229. #25955	C₂₉	direct (N × H)
247. Q₈×C₂₉	C₂²⋊Q₈	semidirect
303. C₂×#475	C₂×C₂₉	semidirect
307. #2096	C₂×C₂₉	semidirect
308. #2066	C₂×C₂₉	semidirect
309. #2066	C₂×C₂₉	semidirect
310. #2024	C₂×C₂₉	semidirect
311. #1865	C₂×C₂₉	semidirect
312. #1865	C₂×C₂₉	semidirect
316. #1803	C₂×C₂₉	semidirect
324. C₂²×C₂₉	#475	semidirect
409. C₂²×Q₈	Q₈×C₂₉	semidirect
478. C₂₉	#25955	direct (N × H)
588. Q₈	C₂₉×C₂²⋊Q₈	semidirect
650. C₂²	C₂₉×#475	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#475	2
C₂²×C₂₉×#103	2
C₂₉×#2440	2
Q₈×C₂²⋊C₄×C₂₉	2
C₂₉×#2096	2
C₂₉×#2066	2
C₂₉×#2024	2
C₂₉×#1865	2
C₂₉×#1853	2
C₂₉×#1850	2
C₂₉×#1807	2
C₂₉×#1803	2
C₂₉×#1787	2
#25955	29

Subgroups — C29×#25955 #20320855

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#25955 #20320855