Subgroups — C₂₉×#25708 #20320608

Order 7424.

1028 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#552	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×#479	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2562	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#2036	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2036	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1989	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1954	C₂	1	1	yes	maximal, characteristic
11	C₂₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1853	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1852	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#552	—	2	4	no	—
17	C₂₉×#552	—	2	4	no	—
18	C₂×C₂₉×#126	—	2	1	no	—
19	C₂×C₂₉×#125	—	2	1	no	—
20	C₂×C₂₉×#125	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#125	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×#123	—	2	1	no	—
23	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×#117	—	2	1	no	—
28	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
30	C₂₉×#499	—	2	4	no	—
31	C₂₉×#479	—	2	4	no	—
32	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
34	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
35	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
36	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
37	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
38	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
40	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
41	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
42	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
43	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
48	C₂₉×#400	—	2	1	no	—
49	C₂₉×#394	—	2	1	no	—
50	C₂₉×#388	—	2	1	no	—
51	C₂₉×#388	—	2	1	no	—
52	C₂₉×#380	C₂²	1	1	yes	characteristic
53	C₂₉×#380	C₂²	1	1	yes	characteristic
54	C₂₉×#380	C₂²	1	1	yes	characteristic
55	C₂₉×#380	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
57	C₂₉×#340	C₂²	1	1	yes	characteristic
58	C₂₉×#340	C₂²	1	1	yes	characteristic
59	C₂₉×#340	C₂²	1	1	yes	characteristic
60	C₂₉×#340	C₂²	1	1	yes	characteristic
61	C₂₉×#340	C₂²	1	1	yes	characteristic
62	C₂₉×#340	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₂₉	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₂₉	—	2	1	no	—
66	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×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	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
72	C₂₉×#126	—	2	8	no	—
73	C₂₉×#125	—	2	8	no	—
74	C₂₉×#125	—	2	2	no	—
75	C₂₉×#125	—	2	2	no	—
76	C₂₉×#125	—	2	2	no	—
77	C₂₉×#125	D₄	1	4	yes	—
78	C₂₉×#123	—	2	8	no	—
79	C₂₉×C₂²⋊Q₈	—	2	2	no	—
80	C₂₉×C₂²⋊Q₈	—	2	2	no	—
81	C₂₉×C₂²⋊Q₈	—	2	2	no	—
82	C₂₉×C₂²⋊Q₈	—	2	2	no	—
83	C₄×Q₈×C₂₉	—	2	2	no	—
84	C₄×Q₈×C₂₉	D₄	1	4	yes	—
85	C₄×D₄×C₂₉	—	2	2	no	—
86	C₄×D₄×C₂₉	—	2	2	no	—
87	C₂₉×#117	—	2	8	no	—
88	C₂₉×#117	—	2	2	no	—
89	C₂₉×#117	—	2	2	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	2	no	—
97	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
98	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₂₉	D₄	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×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₂₉	—	2	1	no	—
118	C₂×C₄²×C₂₉	—	2	1	no	—
119	C₂×C₄²×C₂₉	—	2	1	no	—
120	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
121	C₂₉×#107	—	2	2	no	—
122	C₂₉×#107	—	2	2	no	—
123	C₂₉×#107	—	2	2	no	—
124	C₂₉×#106	—	2	2	no	—
125	C₂₉×#106	—	2	2	no	—
126	C₂₉×#106	—	2	2	no	—
127	C₂₉×C₄⋊C₈	—	2	2	no	—
128	C₂₉×#103	—	2	2	no	—
129	C₂₉×#103	—	2	2	no	—
130	C₂₉×#103	—	2	2	no	—
131	C₂₉×#103	—	2	2	no	—
132	C₂₉×C₂²⋊C₈	—	2	2	no	—
133	C₂₉×C₂²⋊C₈	—	2	2	no	—
134	C₂₉×C₂²⋊C₈	—	2	2	no	—
135	C₂₉×C₂²⋊C₈	—	2	2	no	—
136	C₄×C₈×C₂₉	—	2	2	no	—
137	C₂₉×#95	—	2	1	no	—
138	C₂₉×#95	—	2	1	no	—
139	C₂₉×#95	—	2	1	no	—
140	C₂₉×#95	—	2	1	no	—
141	C₂₉×#95	—	2	1	no	—
142	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
143	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
149	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
150	C₂×D₄×C₂₉	—	2	2	no	—
151	C₂×D₄×C₂₉	—	2	2	no	—
152	C₂×D₄×C₂₉	—	4	1	no	—
153	C₂²×C₄×C₂₉	—	2	4	no	—
154	C₂²×C₄×C₂₉	—	2	1	no	—
155	C₂²×C₄×C₂₉	—	2	1	no	—
156	C₂²×C₄×C₂₉	—	2	1	no	—
157	C₂²×C₄×C₂₉	—	2	1	no	—
158	C₂²×C₄×C₂₉	—	2	1	no	—
159	C₂²×C₄×C₂₉	—	2	1	no	—
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	1	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	—	2	1	no	—
174	C₂²×C₄×C₂₉	—	4	2	no	—
175	C₂²×C₄×C₂₉	—	4	2	no	—
176	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
181	C₂×C₈×C₂₉	—	2	1	no	—
182	C₂×C₈×C₂₉	—	2	1	no	—
183	C₂×C₈×C₂₉	—	2	1	no	—
184	C₂×C₈×C₂₉	—	2	1	no	—
185	C₂×C₈×C₂₉	—	2	1	no	—
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	#41	1	2	yes	—
192	C₂×C₈×C₂₉	#41	1	2	yes	—
193	C₄⋊C₄×C₂₉	—	2	4	no	—
194	C₄⋊C₄×C₂₉	—	2	4	no	—
195	C₄⋊C₄×C₂₉	—	2	4	no	—
196	C₄⋊C₄×C₂₉	—	2	4	no	—
197	C₄⋊C₄×C₂₉	—	2	4	no	—
198	C₄⋊C₄×C₂₉	—	2	4	no	—
199	C₄⋊C₄×C₂₉	—	2	2	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	—	2	1	no	—
211	C₄⋊C₄×C₂₉	—	4	2	no	—
212	C₄⋊C₄×C₂₉	—	4	2	no	—
213	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
214	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
215	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
216	C₂²⋊C₄×C₂₉	—	2	4	no	—
217	C₂²⋊C₄×C₂₉	—	2	4	no	—
218	C₂²⋊C₄×C₂₉	—	2	4	no	—
219	C₂²⋊C₄×C₂₉	—	2	2	no	—
220	C₂²⋊C₄×C₂₉	—	2	2	no	—
221	C₂²⋊C₄×C₂₉	—	4	2	no	—
222	C₂²⋊C₄×C₂₉	—	4	2	no	—
223	C₂²⋊C₄×C₂₉	—	8	1	no	—
224	C₂²⋊C₄×C₂₉	—	8	1	no	—
225	C₄²×C₂₉	—	2	4	no	—
226	C₄²×C₂₉	—	2	4	no	—
227	C₄²×C₂₉	—	8	1	no	—
228	C₄²×C₂₉	C₂×D₄	1	2	yes	—
229	C₄²×C₂₉	C₂×D₄	1	2	yes	—
230	#25708	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂³×C₂₉	—	2	1	no	—
232	C₂³×C₂₉	—	2	1	no	—
233	C₂³×C₂₉	—	2	1	no	—
234	C₂³×C₂₉	—	2	1	no	—
235	C₂³×C₂₉	—	2	1	no	—
236	C₂³×C₂₉	—	2	1	no	—
237	C₂³×C₂₉	—	2	1	no	—
238	C₂³×C₂₉	—	2	1	no	—
239	C₂³×C₂₉	—	2	1	no	—
240	C₂³×C₂₉	—	2	1	no	—
241	C₂³×C₂₉	—	2	1	no	—
242	C₂³×C₂₉	—	2	1	no	—
243	C₂³×C₂₉	—	2	1	no	—
244	C₂³×C₂₉	#135	1	2	yes	—
245	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
246	Q₈×C₂₉	—	2	2	no	—
247	Q₈×C₂₉	—	2	2	no	—
248	Q₈×C₂₉	—	4	1	no	—
249	Q₈×C₂₉	—	4	1	no	—
250	D₄×C₂₉	—	4	4	no	—
251	C₂×C₄×C₂₉	—	2	1	no	—
252	C₂×C₄×C₂₉	—	2	1	no	—
253	C₂×C₄×C₂₉	—	2	1	no	—
254	C₂×C₄×C₂₉	—	2	1	no	—
255	C₂×C₄×C₂₉	—	2	1	no	—
256	C₂×C₄×C₂₉	—	2	2	no	—
257	C₂×C₄×C₂₉	—	2	2	no	—
258	C₂×C₄×C₂₉	—	2	2	no	—
259	C₂×C₄×C₂₉	—	2	1	no	—
260	C₂×C₄×C₂₉	—	2	2	no	—
261	C₂×C₄×C₂₉	—	2	1	no	—
262	C₂×C₄×C₂₉	—	2	1	no	—
263	C₂×C₄×C₂₉	—	2	1	no	—
264	C₂×C₄×C₂₉	—	2	1	no	—
265	C₂×C₄×C₂₉	—	4	8	no	—
266	C₂×C₄×C₂₉	—	4	1	no	—
267	C₂×C₄×C₂₉	—	4	1	no	—
268	C₂×C₄×C₂₉	—	4	1	no	—
269	C₂×C₄×C₂₉	—	4	1	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	—	4	1	no	—
290	C₂×C₄×C₂₉	—	4	1	no	—
291	C₂×C₄×C₂₉	—	4	1	no	—
292	C₂×C₄×C₂₉	—	4	1	no	—
293	C₂×C₄×C₂₉	—	4	1	no	—
294	C₂×C₄×C₂₉	#120	1	2	yes	—
295	C₂×C₄×C₂₉	#120	1	2	yes	—
296	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
298	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
299	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
300	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
301	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
302	C₈×C₂₉	—	2	2	no	—
303	C₈×C₂₉	—	2	2	no	—
304	C₈×C₂₉	—	4	1	no	—
305	C₈×C₂₉	—	4	1	no	—
306	C₂×#552	C₂×C₂₉	1	1	yes	characteristic
307	C₂×#499	C₂×C₂₉	1	1	yes	characteristic, complemented
308	C₂×#479	C₂×C₂₉	1	1	yes	characteristic, complemented
309	#2562	C₂×C₂₉	1	1	yes	characteristic
310	#2036	C₂×C₂₉	1	1	yes	characteristic, complemented
311	#2036	C₂×C₂₉	1	1	yes	characteristic, complemented
312	#2035	C₂×C₂₉	1	1	yes	characteristic, complemented
313	#2035	C₂×C₂₉	1	1	yes	characteristic, complemented
314	#1989	C₂×C₂₉	1	1	yes	characteristic, complemented
315	#1954	C₂×C₂₉	1	1	yes	characteristic
316	#1854	C₂×C₂₉	1	1	yes	characteristic, complemented
317	#1854	C₂×C₂₉	1	1	yes	characteristic, complemented
318	#1853	C₂×C₂₉	1	1	yes	characteristic, complemented
319	#1852	C₂×C₂₉	1	1	yes	characteristic, complemented
320	C₄×#103	C₂×C₂₉	1	1	yes	characteristic, complemented
321	C₂²×C₂₉	—	2	2	no	—
322	C₂²×C₂₉	—	2	2	no	—
323	C₂²×C₂₉	—	2	2	no	—
324	C₂²×C₂₉	—	4	1	no	—
325	C₂²×C₂₉	—	4	1	no	—
326	C₂²×C₂₉	—	4	1	no	—
327	C₂²×C₂₉	—	4	1	no	—
328	C₂²×C₂₉	—	4	1	no	—
329	C₂²×C₂₉	—	4	1	no	—
330	C₂²×C₂₉	—	4	1	no	—
331	C₂²×C₂₉	—	4	1	no	—
332	C₂²×C₂₉	—	4	1	no	—
333	C₂²×C₂₉	—	4	1	no	—
334	C₂²×C₂₉	—	4	1	no	—
335	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
336	C₂²×C₂₉	#547	1	1	yes	characteristic
337	C₂²×C₂₉	#547	1	1	yes	characteristic
338	C₂²×C₂₉	C₂×#135	1	1	yes	characteristic
339	C₂²×C₂₉	#575	1	1	yes	characteristic
340	C₂²×C₂₉	#577	1	1	yes	characteristic
341	C₂²×C₂₉	#578	1	1	yes	characteristic
342	C₄×C₂₉	—	2	2	no	—
343	C₄×C₂₉	—	2	2	no	—
344	C₄×C₂₉	—	4	1	no	—
345	C₄×C₂₉	—	4	1	no	—
346	C₄×C₂₉	—	4	2	no	—
347	C₄×C₂₉	—	4	2	no	—
348	C₄×C₂₉	—	4	2	no	—
349	C₄×C₂₉	—	4	2	no	—
350	C₄×C₂₉	—	8	1	no	—
351	C₄×C₂₉	—	8	1	no	—
352	C₄×C₂₉	—	8	1	no	—
353	C₄×C₂₉	—	8	1	no	—
354	C₄×C₂₉	#532	1	1	yes	characteristic
355	C₄×C₂₉	#536	1	1	yes	characteristic
356	C₄×C₂₉	#548	1	1	yes	characteristic
357	C₄×C₂₉	#548	1	1	yes	characteristic
358	#552	—	2	4	no	—
359	#552	—	2	4	no	—
360	C₂×#126	—	2	1	no	—
361	C₂×#125	—	2	1	no	—
362	C₂×#125	C₂²×C₂₉	1	1	yes	characteristic
363	C₂×#125	C₂²×C₂₉	1	1	yes	characteristic
364	C₂×#123	—	2	1	no	—
365	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
366	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
367	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
368	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
369	C₂×#117	—	2	1	no	—
370	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
371	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
372	#499	—	2	4	no	—
373	#479	—	2	4	no	—
374	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
375	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
376	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
377	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
378	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
379	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
380	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
381	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
382	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
383	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
384	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
385	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
386	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
387	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
388	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
389	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
390	#400	—	2	1	no	—
391	#394	—	2	1	no	—
392	#388	—	2	1	no	—
393	#388	—	2	1	no	—
394	#380	C₂²×C₂₉	1	1	yes	characteristic
395	#380	C₂²×C₂₉	1	1	yes	characteristic
396	#380	C₂²×C₂₉	1	1	yes	characteristic
397	#380	C₂²×C₂₉	1	1	yes	characteristic
398	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
399	#340	C₂²×C₂₉	1	1	yes	characteristic
400	#340	C₂²×C₂₉	1	1	yes	characteristic
401	#340	C₂²×C₂₉	1	1	yes	characteristic
402	#340	C₂²×C₂₉	1	1	yes	characteristic
403	#340	C₂²×C₂₉	1	1	yes	characteristic
404	#340	C₂²×C₂₉	1	1	yes	characteristic
405	C₂×C₂₉	—	4	2	no	—
406	C₂×C₂₉	—	8	1	no	—
407	C₂×C₂₉	#2432	1	1	yes	characteristic
408	C₂×C₂₉	#3002	1	1	yes	characteristic
409	C₂×C₂₉	#3013	1	1	yes	characteristic
410	C₂×C₂₉	#3336	1	1	yes	characteristic
411	C₂×C₂₉	#3337	1	1	yes	characteristic
412	C₂×C₂₉	#3351	1	1	yes	characteristic
413	C₂×C₂₉	#3352	1	1	yes	characteristic
414	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
415	C₂²×D₄	D₄×C₂₉	1	1	yes	characteristic
416	C₂³×C₄	—	2	1	no	—
417	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
418	C₂³×C₄	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	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
423	#126	—	2	8	no	—
424	#125	—	2	8	no	—
425	#125	—	2	2	no	—
426	#125	—	2	2	no	—
427	#125	—	2	2	no	—
428	#125	D₄×C₂₉	1	4	yes	—
429	#123	—	2	8	no	—
430	C₂²⋊Q₈	—	2	2	no	—
431	C₂²⋊Q₈	—	2	2	no	—
432	C₂²⋊Q₈	—	2	2	no	—
433	C₂²⋊Q₈	—	2	2	no	—
434	C₄×Q₈	—	2	2	no	—
435	C₄×Q₈	D₄×C₂₉	1	4	yes	—
436	C₄×D₄	—	2	2	no	—
437	C₄×D₄	—	2	2	no	—
438	#117	—	2	8	no	—
439	#117	—	2	2	no	—
440	#117	—	2	2	no	—
441	C₂×C₄⋊C₄	—	2	1	no	—
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	—	2	1	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄⋊C₄	—	2	2	no	—
448	C₂×C₄⋊C₄	—	2	2	no	—
449	C₂×C₄⋊C₄	—	2	1	no	—
450	C₂×C₄⋊C₄	—	2	1	no	—
451	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
459	C₂×C₂²⋊C₄	—	2	1	no	—
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₂²⋊C₄	—	2	1	no	—
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
467	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
468	C₂×C₄²	—	2	1	no	—
469	C₂×C₄²	—	2	1	no	—
470	C₂×C₄²	—	2	1	no	—
471	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
472	#107	—	2	2	no	—
473	#107	—	2	2	no	—
474	#107	—	2	2	no	—
475	#106	—	2	2	no	—
476	#106	—	2	2	no	—
477	#106	—	2	2	no	—
478	C₄⋊C₈	—	2	2	no	—
479	#103	—	2	2	no	—
480	#103	—	2	2	no	—
481	#103	—	2	2	no	—
482	#103	—	2	2	no	—
483	C₂²⋊C₈	—	2	2	no	—
484	C₂²⋊C₈	—	2	2	no	—
485	C₂²⋊C₈	—	2	2	no	—
486	C₂²⋊C₈	—	2	2	no	—
487	C₄×C₈	—	2	2	no	—
488	#95	—	2	1	no	—
489	#95	—	2	1	no	—
490	#95	—	2	1	no	—
491	#95	—	2	1	no	—
492	#95	—	2	1	no	—
493	C₂₉	#25708	1	1	yes	characteristic, direct product factor, Sylow
494	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
495	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	—	2	2	no	—
504	C₂×D₄	—	4	1	no	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	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	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	4	2	no	—
527	C₂²×C₄	—	4	2	no	—
528	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
529	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
530	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
531	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
532	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
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	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	#41×C₂₉	1	2	yes	—
544	C₂×C₈	#41×C₂₉	1	2	yes	—
545	C₄⋊C₄	—	2	4	no	—
546	C₄⋊C₄	—	2	4	no	—
547	C₄⋊C₄	—	2	4	no	—
548	C₄⋊C₄	—	2	4	no	—
549	C₄⋊C₄	—	2	4	no	—
550	C₄⋊C₄	—	2	4	no	—
551	C₄⋊C₄	—	2	2	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	4	2	no	—
564	C₄⋊C₄	—	4	2	no	—
565	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
566	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
567	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
568	C₂²⋊C₄	—	2	4	no	—
569	C₂²⋊C₄	—	2	4	no	—
570	C₂²⋊C₄	—	2	4	no	—
571	C₂²⋊C₄	—	2	2	no	—
572	C₂²⋊C₄	—	2	2	no	—
573	C₂²⋊C₄	—	4	2	no	—
574	C₂²⋊C₄	—	4	2	no	—
575	C₂²⋊C₄	—	8	1	no	—
576	C₂²⋊C₄	—	8	1	no	—
577	C₄²	—	2	4	no	—
578	C₄²	—	2	4	no	—
579	C₄²	—	8	1	no	—
580	C₄²	C₂×D₄×C₂₉	1	2	yes	—
581	C₄²	C₂×D₄×C₂₉	1	2	yes	—
582	C₂³	—	2	1	no	—
583	C₂³	—	2	1	no	—
584	C₂³	—	2	1	no	—
585	C₂³	—	2	1	no	—
586	C₂³	—	2	1	no	—
587	C₂³	—	2	1	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	C₂₉×#135	1	2	yes	—
596	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
597	Q₈	—	2	2	no	—
598	Q₈	—	2	2	no	—
599	Q₈	—	4	1	no	—
600	Q₈	—	4	1	no	—
601	D₄	—	4	4	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	4	8	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	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	C₂₉×#120	1	2	yes	—
646	C₂×C₄	C₂₉×#120	1	2	yes	—
647	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
648	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
649	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
650	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
651	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
652	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
653	C₈	—	2	2	no	—
654	C₈	—	2	2	no	—
655	C₈	—	4	1	no	—
656	C₈	—	4	1	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	1	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	4	1	no	—
664	C₂²	—	4	1	no	—
665	C₂²	—	4	1	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	1	no	—
670	C₂²	—	4	1	no	—
671	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
672	C₂²	C₂₉×#547	1	1	yes	characteristic
673	C₂²	C₂₉×#547	1	1	yes	characteristic
674	C₂²	C₂×C₂₉×#135	1	1	yes	characteristic
675	C₂²	C₂₉×#575	1	1	yes	characteristic
676	C₂²	C₂₉×#577	1	1	yes	characteristic
677	C₂²	C₂₉×#578	1	1	yes	characteristic
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	4	1	no	—
681	C₄	—	4	1	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	2	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	2	no	—
686	C₄	—	8	1	no	—
687	C₄	—	8	1	no	—
688	C₄	—	8	1	no	—
689	C₄	—	8	1	no	—
690	C₄	C₂₉×#532	1	1	yes	characteristic
691	C₄	C₂₉×#536	1	1	yes	characteristic
692	C₄	C₂₉×#548	1	1	yes	characteristic
693	C₄	C₂₉×#548	1	1	yes	characteristic
694	C₂	—	4	2	no	—
695	C₂	—	8	1	no	—
696	C₂	C₂₉×#2432	1	1	yes	characteristic
697	C₂	C₂₉×#3002	1	1	yes	characteristic
698	C₂	C₂₉×#3013	1	1	yes	characteristic
699	C₂	C₂₉×#3336	1	1	yes	characteristic
700	C₂	C₂₉×#3337	1	1	yes	characteristic
701	C₂	C₂₉×#3351	1	1	yes	characteristic
702	C₂	C₂₉×#3352	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	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₄×D₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₉×#499	C₂	semidirect
3. C₂×C₂₉×#479	C₂	semidirect
5. C₂₉×#2036	C₂	semidirect
6. C₂₉×#2036	C₂	semidirect
7. C₂₉×#2035	C₂	semidirect
8. C₂₉×#2035	C₂	semidirect
9. C₂₉×#1989	C₂	semidirect
11. C₂₉×#1854	C₂	semidirect
12. C₂₉×#1854	C₂	semidirect
13. C₂₉×#1853	C₂	semidirect
14. C₂₉×#1852	C₂	semidirect
15. C₄×C₂₉×#103	C₂	semidirect
230. #25708	C₂₉	direct (N × H)
307. C₂×#499	C₂×C₂₉	semidirect
308. C₂×#479	C₂×C₂₉	semidirect
310. #2036	C₂×C₂₉	semidirect
311. #2036	C₂×C₂₉	semidirect
312. #2035	C₂×C₂₉	semidirect
313. #2035	C₂×C₂₉	semidirect
314. #1989	C₂×C₂₉	semidirect
316. #1854	C₂×C₂₉	semidirect
317. #1854	C₂×C₂₉	semidirect
318. #1853	C₂×C₂₉	semidirect
319. #1852	C₂×C₂₉	semidirect
320. C₄×#103	C₂×C₂₉	semidirect
493. C₂₉	#25708	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×#552	2
C₂×C₂₉×#499	2
C₂×C₂₉×#479	2
C₂₉×#2562	2
C₂₉×#2036	2
C₂₉×#2035	2
C₂₉×#1989	2
C₂₉×#1954	2
C₂₉×#1854	2
C₂₉×#1853	2
C₂₉×#1852	2
C₄×C₂₉×#103	2
#25708	29

Subgroups — C29×#25708 #20320608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#25708 #20320608