Subgroups — C₂₉×#24766 #20319666

Order 7424.

960 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#468	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#465	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×#461	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₉×#424	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2621	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2324	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2066	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#2055	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#2055	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1981	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1949	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1894	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1892	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1804	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₂₉	C₂²	1	1	yes	characteristic
20	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
25	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
26	C₂₉×#468	—	2	4	no	—
27	C₂₉×#465	—	2	4	no	—
28	C₂₉×#461	—	2	4	no	—
29	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
31	C₂₉×#424	—	2	4	no	—
32	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₂₉×C₄⋊C₈	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×#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×#102	C₂²	1	1	yes	characteristic
43	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
44	C₂₉×#398	—	2	1	no	—
45	C₂₉×#398	—	2	1	no	—
46	C₂₉×#397	—	2	1	no	—
47	C₂₉×#397	—	2	1	no	—
48	C₂₉×#391	C₂²	1	1	yes	characteristic
49	C₂₉×#391	C₂²	1	1	yes	characteristic
50	C₂₉×#390	—	2	1	no	—
51	C₂₉×#390	C₂²	1	1	yes	characteristic
52	C₂₉×#389	C₂²	1	1	yes	characteristic
53	C₂₉×#388	—	2	1	no	—
54	C₂₉×#386	—	2	1	no	—
55	C₂₉×#385	—	2	1	no	—
56	C₂₉×#382	C₂²	1	1	yes	characteristic
57	C₂₉×#380	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₂₉	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×Q₈×C₂₉	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₂₉	—	2	1	no	—
66	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₂₉	—	2	1	no	—
68	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
69	C₂×SD₁₆×C₂₉	—	2	2	no	—
70	C₂×SD₁₆×C₂₉	—	2	2	no	—
71	C₂×SD₁₆×C₂₉	—	2	2	no	—
72	C₂×SD₁₆×C₂₉	—	2	2	no	—
73	C₂×SD₁₆×C₂₉	—	4	1	no	—
74	C₂×SD₁₆×C₂₉	—	4	1	no	—
75	C₂×M₁₆×C₂₉	—	2	2	no	—
76	C₂×M₁₆×C₂₉	—	2	2	no	—
77	C₂×M₁₆×C₂₉	—	4	1	no	—
78	C₂²×C₈×C₂₉	—	2	2	no	—
79	C₂²×C₈×C₂₉	—	2	2	no	—
80	C₂²×C₈×C₂₉	—	4	1	no	—
81	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
85	C₂₉×C₄⋊Q₈	—	2	2	no	—
86	C₂₉×C₄⋊Q₈	—	2	2	no	—
87	C₂₉×C₂²⋊Q₈	—	2	2	no	—
88	C₂₉×C₂²⋊Q₈	—	2	2	no	—
89	C₂₉×C₂²⋊Q₈	—	2	2	no	—
90	C₂₉×C₂²⋊Q₈	—	2	2	no	—
91	C₂₉×#121	—	2	2	no	—
92	C₂₉×#121	D₄	1	4	yes	—
93	C₄×D₄×C₂₉	—	2	2	no	—
94	C₄×D₄×C₂₉	—	2	2	no	—
95	C₂₉×#117	—	2	2	no	—
96	C₂₉×#117	—	2	2	no	—
97	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₂₉	D₄	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×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₂₉	—	2	1	no	—
119	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
121	C₂₉×#107	—	2	2	no	—
122	C₂₉×#106	—	2	2	no	—
123	C₂₉×C₄⋊C₈	—	2	2	no	—
124	C₂₉×C₄⋊C₈	—	2	2	no	—
125	C₂₉×C₄⋊C₈	—	2	2	no	—
126	C₂₉×C₄⋊C₈	D₄	1	4	yes	complemented
127	C₂₉×#103	—	2	2	no	—
128	C₂₉×#103	—	2	2	no	—
129	C₂₉×#103	—	2	2	no	—
130	C₂₉×#103	—	2	2	no	—
131	C₂₉×#103	—	4	1	no	—
132	C₂₉×#103	—	4	1	no	—
133	C₂₉×#102	—	2	2	no	—
134	C₂₉×#102	—	2	2	no	—
135	C₂₉×#95	—	2	1	no	—
136	C₂₉×#95	—	2	1	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	C₂₉×#95	—	2	1	no	—
143	C₂₉×#95	—	2	1	no	—
144	C₂⁴×C₂₉	—	2	1	no	—
145	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
150	C₂×Q₈×C₂₉	—	2	1	no	—
151	C₂×Q₈×C₂₉	—	2	1	no	—
152	C₂×Q₈×C₂₉	—	2	1	no	—
153	C₂×Q₈×C₂₉	—	2	1	no	—
154	C₂×Q₈×C₂₉	—	2	1	no	—
155	C₂×Q₈×C₂₉	—	2	1	no	—
156	C₂×Q₈×C₂₉	—	2	1	no	—
157	C₂×Q₈×C₂₉	—	2	1	no	—
158	C₂×D₄×C₂₉	—	2	4	no	—
159	C₂×D₄×C₂₉	—	2	1	no	—
160	C₂×D₄×C₂₉	—	2	1	no	—
161	C₂×D₄×C₂₉	—	2	1	no	—
162	C₂×D₄×C₂₉	—	2	1	no	—
163	C₂×D₄×C₂₉	—	2	1	no	—
164	C₂×D₄×C₂₉	—	8	1	no	—
165	C₂×D₄×C₂₉	—	8	1	no	—
166	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
175	C₂²×C₄×C₂₉	—	2	1	no	—
176	C₂²×C₄×C₂₉	—	2	1	no	—
177	C₂²×C₄×C₂₉	—	2	1	no	—
178	C₂²×C₄×C₂₉	—	4	2	no	—
179	C₂²×C₄×C₂₉	—	8	1	no	—
180	C₂²×C₄×C₂₉	—	8	1	no	—
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×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₂₉	#41	1	2	yes	—
188	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
189	SD₁₆×C₂₉	—	4	4	no	—
190	SD₁₆×C₂₉	—	4	4	no	—
191	M₁₆×C₂₉	—	4	4	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	—	2	1	no	—
198	C₂×C₈×C₂₉	—	2	1	no	—
199	C₂×C₈×C₂₉	—	2	1	no	—
200	C₂×C₈×C₂₉	—	2	1	no	—
201	C₂×C₈×C₂₉	—	2	1	no	—
202	C₂×C₈×C₂₉	—	4	4	no	—
203	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
204	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
205	C₄⋊C₄×C₂₉	—	2	2	no	—
206	C₄⋊C₄×C₂₉	—	2	2	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	—	2	1	no	—
212	C₄⋊C₄×C₂₉	—	2	1	no	—
213	C₄⋊C₄×C₂₉	—	2	1	no	—
214	C₄⋊C₄×C₂₉	—	2	1	no	—
215	C₄⋊C₄×C₂₉	—	2	1	no	—
216	C₄⋊C₄×C₂₉	—	4	2	no	—
217	C₄⋊C₄×C₂₉	—	4	2	no	—
218	C₄⋊C₄×C₂₉	—	4	2	no	—
219	C₄⋊C₄×C₂₉	—	4	2	no	—
220	C₄⋊C₄×C₂₉	—	8	1	no	—
221	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
222	C₂²⋊C₄×C₂₉	—	2	4	no	—
223	C₂²⋊C₄×C₂₉	—	2	2	no	—
224	C₂²⋊C₄×C₂₉	—	2	2	no	—
225	C₂²⋊C₄×C₂₉	—	4	2	no	—
226	C₂²⋊C₄×C₂₉	—	4	2	no	—
227	C₂²⋊C₄×C₂₉	—	4	2	no	—
228	C₂²⋊C₄×C₂₉	—	8	1	no	—
229	C₂²⋊C₄×C₂₉	—	8	1	no	—
230	C₂²⋊C₄×C₂₉	—	8	1	no	—
231	C₄²×C₂₉	—	2	1	no	—
232	C₄²×C₂₉	—	2	1	no	—
233	C₄²×C₂₉	—	8	1	no	—
234	C₄²×C₂₉	C₂×D₄	1	2	yes	—
235	C₄²×C₂₉	#41	1	2	yes	—
236	#24766	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	2	no	—
244	C₂³×C₂₉	—	4	1	no	—
245	C₂³×C₂₉	—	4	1	no	—
246	C₂³×C₂₉	—	4	1	no	—
247	C₂³×C₂₉	—	4	1	no	—
248	C₂³×C₂₉	—	4	1	no	—
249	C₂³×C₂₉	—	4	1	no	—
250	C₂³×C₂₉	#121	1	2	yes	—
251	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
252	Q₈×C₂₉	—	4	1	no	—
253	Q₈×C₂₉	—	4	1	no	—
254	Q₈×C₂₉	—	4	1	no	—
255	Q₈×C₂₉	—	4	1	no	—
256	Q₈×C₂₉	—	4	1	no	—
257	Q₈×C₂₉	—	4	1	no	—
258	Q₈×C₂₉	—	4	1	no	—
259	Q₈×C₂₉	—	4	1	no	—
260	D₄×C₂₉	—	2	2	no	—
261	D₄×C₂₉	—	2	2	no	—
262	D₄×C₂₉	—	4	1	no	—
263	D₄×C₂₉	—	4	1	no	—
264	D₄×C₂₉	—	8	4	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	—	2	1	no	—
270	C₂×C₄×C₂₉	—	2	1	no	—
271	C₂×C₄×C₂₉	—	2	2	no	—
272	C₂×C₄×C₂₉	—	2	2	no	—
273	C₂×C₄×C₂₉	—	2	2	no	—
274	C₂×C₄×C₂₉	—	2	2	no	—
275	C₂×C₄×C₂₉	—	2	1	no	—
276	C₂×C₄×C₂₉	—	2	1	no	—
277	C₂×C₄×C₂₉	—	2	2	no	—
278	C₂×C₄×C₂₉	—	2	1	no	—
279	C₂×C₄×C₂₉	—	2	1	no	—
280	C₂×C₄×C₂₉	—	2	1	no	—
281	C₂×C₄×C₂₉	—	2	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	—	4	1	no	—
295	C₂×C₄×C₂₉	—	4	1	no	—
296	C₂×C₄×C₂₉	—	4	1	no	—
297	C₂×C₄×C₂₉	—	4	1	no	—
298	C₂×C₄×C₂₉	—	4	1	no	—
299	C₂×C₄×C₂₉	—	4	1	no	—
300	C₂×C₄×C₂₉	—	4	1	no	—
301	C₂×C₄×C₂₉	—	4	1	no	—
302	C₂×C₄×C₂₉	—	8	4	no	—
303	C₂×C₄×C₂₉	#121	1	2	yes	—
304	C₂×C₄×C₂₉	#121	1	2	yes	—
305	C₂×C₄×C₂₉	#121	1	2	yes	—
306	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
310	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
311	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
312	C₈×C₂₉	—	2	2	no	—
313	C₈×C₂₉	—	2	2	no	—
314	C₈×C₂₉	—	4	1	no	—
315	C₈×C₂₉	—	4	1	no	—
316	C₂×#468	C₂×C₂₉	1	1	yes	characteristic
317	C₂×#465	C₂×C₂₉	1	1	yes	characteristic
318	C₂×#461	C₂×C₂₉	1	1	yes	characteristic, complemented
319	C₂×#424	C₂×C₂₉	1	1	yes	characteristic, complemented
320	#2621	C₂×C₂₉	1	1	yes	characteristic, complemented
321	#2324	C₂×C₂₉	1	1	yes	characteristic
322	#2068	C₂×C₂₉	1	1	yes	characteristic, complemented
323	#2066	C₂×C₂₉	1	1	yes	characteristic, complemented
324	#2055	C₂×C₂₉	1	1	yes	characteristic, complemented
325	#2055	C₂×C₂₉	1	1	yes	characteristic, complemented
326	#1981	C₂×C₂₉	1	1	yes	characteristic, complemented
327	#1949	C₂×C₂₉	1	1	yes	characteristic, complemented
328	#1894	C₂×C₂₉	1	1	yes	characteristic, complemented
329	#1892	C₂×C₂₉	1	1	yes	characteristic, complemented
330	#1804	C₂×C₂₉	1	1	yes	characteristic, complemented
331	C₂²×C₂₉	—	2	2	no	—
332	C₂²×C₂₉	—	2	2	no	—
333	C₂²×C₂₉	—	2	2	no	—
334	C₂²×C₂₉	—	4	1	no	—
335	C₂²×C₂₉	—	4	1	no	—
336	C₂²×C₂₉	—	4	1	no	—
337	C₂²×C₂₉	—	4	1	no	—
338	C₂²×C₂₉	—	4	2	no	—
339	C₂²×C₂₉	—	4	2	no	—
340	C₂²×C₂₉	—	4	2	no	—
341	C₂²×C₂₉	—	8	1	no	—
342	C₂²×C₂₉	—	8	1	no	—
343	C₂²×C₂₉	—	8	1	no	—
344	C₂²×C₂₉	—	8	1	no	—
345	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
346	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
347	C₂²×C₂₉	#537	1	1	yes	characteristic
348	C₂²×C₂₉	#577	1	1	yes	characteristic
349	C₂²×C₂₉	#577	1	1	yes	characteristic
350	C₂²×C₂₉	#577	1	1	yes	characteristic
351	C₂²×C₂₉	#578	1	1	yes	characteristic
352	C₄×C₂₉	—	2	2	no	—
353	C₄×C₂₉	—	2	2	no	—
354	C₄×C₂₉	—	2	2	no	—
355	C₄×C₂₉	—	4	2	no	—
356	C₄×C₂₉	—	4	1	no	—
357	C₄×C₂₉	—	4	1	no	—
358	C₄×C₂₉	—	8	1	no	—
359	C₄×C₂₉	—	8	1	no	—
360	C₄×C₂₉	—	8	1	no	—
361	C₄×C₂₉	—	8	1	no	—
362	C₄×C₂₉	—	8	1	no	—
363	C₄×C₂₉	—	8	1	no	—
364	C₄×C₂₉	D₄²	1	1	yes	characteristic
365	C₄×C₂₉	#547	1	1	yes	characteristic
366	C₄×C₂₉	#548	1	1	yes	characteristic
367	C₄×C₂₉	#553	1	1	yes	characteristic
368	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
369	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
370	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
371	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic
372	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
373	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
374	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
375	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic
376	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
377	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
378	#468	—	2	4	no	—
379	#465	—	2	4	no	—
380	#461	—	2	4	no	—
381	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
382	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
383	#424	—	2	4	no	—
384	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
385	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
386	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
387	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
388	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
389	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
390	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
391	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
392	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
393	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
394	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
395	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
396	#398	—	2	1	no	—
397	#398	—	2	1	no	—
398	#397	—	2	1	no	—
399	#397	—	2	1	no	—
400	#391	C₂²×C₂₉	1	1	yes	characteristic
401	#391	C₂²×C₂₉	1	1	yes	characteristic
402	#390	—	2	1	no	—
403	#390	C₂²×C₂₉	1	1	yes	characteristic
404	#389	C₂²×C₂₉	1	1	yes	characteristic
405	#388	—	2	1	no	—
406	#386	—	2	1	no	—
407	#385	—	2	1	no	—
408	#382	C₂²×C₂₉	1	1	yes	characteristic
409	#380	C₂²×C₂₉	1	1	yes	characteristic
410	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
411	#340	C₂²×C₂₉	1	1	yes	characteristic
412	#340	C₂²×C₂₉	1	1	yes	characteristic
413	#340	C₂²×C₂₉	1	1	yes	characteristic
414	#340	C₂²×C₂₉	1	1	yes	characteristic
415	C₂×C₂₉	—	4	2	no	—
416	C₂×C₂₉	—	8	2	no	—
417	C₂×C₂₉	#2416	1	1	yes	characteristic
418	C₂×C₂₉	#3042	1	1	yes	characteristic
419	C₂×C₂₉	#3046	1	1	yes	characteristic
420	C₂×C₂₉	#3057	1	1	yes	characteristic
421	C₂×C₂₉	#3063	1	1	yes	characteristic
422	C₂×C₂₉	#3258	1	1	yes	characteristic
423	C₂×C₂₉	#3260	1	1	yes	characteristic
424	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
425	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
426	C₂²×D₄	—	2	1	no	—
427	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
428	C₂³×C₄	—	2	1	no	—
429	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
430	C₂×SD₁₆	—	2	2	no	—
431	C₂×SD₁₆	—	2	2	no	—
432	C₂×SD₁₆	—	2	2	no	—
433	C₂×SD₁₆	—	2	2	no	—
434	C₂×SD₁₆	—	4	1	no	—
435	C₂×SD₁₆	—	4	1	no	—
436	C₂×M₁₆	—	2	2	no	—
437	C₂×M₁₆	—	2	2	no	—
438	C₂×M₁₆	—	4	1	no	—
439	C₂²×C₈	—	2	2	no	—
440	C₂²×C₈	—	2	2	no	—
441	C₂²×C₈	—	4	1	no	—
442	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
443	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
444	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
445	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
446	C₄⋊Q₈	—	2	2	no	—
447	C₄⋊Q₈	—	2	2	no	—
448	C₂²⋊Q₈	—	2	2	no	—
449	C₂²⋊Q₈	—	2	2	no	—
450	C₂²⋊Q₈	—	2	2	no	—
451	C₂²⋊Q₈	—	2	2	no	—
452	#121	—	2	2	no	—
453	#121	D₄×C₂₉	1	4	yes	—
454	C₄×D₄	—	2	2	no	—
455	C₄×D₄	—	2	2	no	—
456	#117	—	2	2	no	—
457	#117	—	2	2	no	—
458	C₂×C₄⋊C₄	—	2	1	no	—
459	C₂×C₄⋊C₄	—	2	1	no	—
460	C₂×C₄⋊C₄	—	2	1	no	—
461	C₂×C₄⋊C₄	—	2	1	no	—
462	C₂×C₄⋊C₄	—	2	1	no	—
463	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
464	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
466	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
467	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
470	C₂×C₂²⋊C₄	—	2	1	no	—
471	C₂×C₂²⋊C₄	—	2	1	no	—
472	C₂×C₂²⋊C₄	—	2	1	no	—
473	C₂×C₂²⋊C₄	—	2	1	no	—
474	C₂×C₂²⋊C₄	—	2	1	no	—
475	C₂×C₂²⋊C₄	—	2	1	no	—
476	C₂×C₂²⋊C₄	—	2	1	no	—
477	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
478	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
479	C₂×C₄²	—	2	1	no	—
480	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
481	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
482	#107	—	2	2	no	—
483	#106	—	2	2	no	—
484	C₄⋊C₈	—	2	2	no	—
485	C₄⋊C₈	—	2	2	no	—
486	C₄⋊C₈	—	2	2	no	—
487	C₄⋊C₈	D₄×C₂₉	1	4	yes	complemented
488	#103	—	2	2	no	—
489	#103	—	2	2	no	—
490	#103	—	2	2	no	—
491	#103	—	2	2	no	—
492	#103	—	4	1	no	—
493	#103	—	4	1	no	—
494	#102	—	2	2	no	—
495	#102	—	2	2	no	—
496	#95	—	2	1	no	—
497	#95	—	2	1	no	—
498	#95	—	2	1	no	—
499	#95	—	2	1	no	—
500	#95	—	2	1	no	—
501	#95	—	2	1	no	—
502	#95	—	2	1	no	—
503	#95	—	2	1	no	—
504	#95	—	2	1	no	—
505	C₂₉	#24766	1	1	yes	characteristic, direct product factor, Sylow
506	C₂⁴	—	2	1	no	—
507	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	1	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	1	no	—
520	C₂×D₄	—	2	4	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	8	1	no	—
527	C₂×D₄	—	8	1	no	—
528	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	4	2	no	—
541	C₂²×C₄	—	8	1	no	—
542	C₂²×C₄	—	8	1	no	—
543	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
544	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
545	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
546	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
547	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
548	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
549	C₂²×C₄	#41×C₂₉	1	2	yes	—
550	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
551	SD₁₆	—	4	4	no	—
552	SD₁₆	—	4	4	no	—
553	M₁₆	—	4	4	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	4	4	no	—
565	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
566	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	4	2	no	—
579	C₄⋊C₄	—	4	2	no	—
580	C₄⋊C₄	—	4	2	no	—
581	C₄⋊C₄	—	4	2	no	—
582	C₄⋊C₄	—	8	1	no	—
583	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	2	2	no	—
587	C₂²⋊C₄	—	4	2	no	—
588	C₂²⋊C₄	—	4	2	no	—
589	C₂²⋊C₄	—	4	2	no	—
590	C₂²⋊C₄	—	8	1	no	—
591	C₂²⋊C₄	—	8	1	no	—
592	C₂²⋊C₄	—	8	1	no	—
593	C₄²	—	2	1	no	—
594	C₄²	—	2	1	no	—
595	C₄²	—	8	1	no	—
596	C₄²	C₂×D₄×C₂₉	1	2	yes	—
597	C₄²	#41×C₂₉	1	2	yes	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	1	no	—
604	C₂³	—	2	2	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	1	no	—
609	C₂³	—	4	1	no	—
610	C₂³	—	4	1	no	—
611	C₂³	C₂₉×#121	1	2	yes	—
612	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
613	Q₈	—	4	1	no	—
614	Q₈	—	4	1	no	—
615	Q₈	—	4	1	no	—
616	Q₈	—	4	1	no	—
617	Q₈	—	4	1	no	—
618	Q₈	—	4	1	no	—
619	Q₈	—	4	1	no	—
620	Q₈	—	4	1	no	—
621	D₄	—	2	2	no	—
622	D₄	—	2	2	no	—
623	D₄	—	4	1	no	—
624	D₄	—	4	1	no	—
625	D₄	—	8	4	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	8	4	no	—
664	C₂×C₄	C₂₉×#121	1	2	yes	—
665	C₂×C₄	C₂₉×#121	1	2	yes	—
666	C₂×C₄	C₂₉×#121	1	2	yes	—
667	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
668	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
669	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
670	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
671	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
672	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
673	C₈	—	2	2	no	—
674	C₈	—	2	2	no	—
675	C₈	—	4	1	no	—
676	C₈	—	4	1	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	4	2	no	—
687	C₂²	—	8	1	no	—
688	C₂²	—	8	1	no	—
689	C₂²	—	8	1	no	—
690	C₂²	—	8	1	no	—
691	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
692	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
693	C₂²	C₂₉×#537	1	1	yes	characteristic
694	C₂²	C₂₉×#577	1	1	yes	characteristic
695	C₂²	C₂₉×#577	1	1	yes	characteristic
696	C₂²	C₂₉×#577	1	1	yes	characteristic
697	C₂²	C₂₉×#578	1	1	yes	characteristic
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	2	2	no	—
701	C₄	—	4	2	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	1	no	—
704	C₄	—	8	1	no	—
705	C₄	—	8	1	no	—
706	C₄	—	8	1	no	—
707	C₄	—	8	1	no	—
708	C₄	—	8	1	no	—
709	C₄	—	8	1	no	—
710	C₄	D₄²×C₂₉	1	1	yes	characteristic
711	C₄	C₂₉×#547	1	1	yes	characteristic
712	C₄	C₂₉×#548	1	1	yes	characteristic
713	C₄	C₂₉×#553	1	1	yes	characteristic
714	C₂	—	4	2	no	—
715	C₂	—	8	2	no	—
716	C₂	C₂₉×#2416	1	1	yes	characteristic
717	C₂	C₂₉×#3042	1	1	yes	characteristic
718	C₂	C₂₉×#3046	1	1	yes	characteristic
719	C₂	C₂₉×#3057	1	1	yes	characteristic
720	C₂	C₂₉×#3063	1	1	yes	characteristic
721	C₂	C₂₉×#3258	1	1	yes	characteristic
722	C₂	C₂₉×#3260	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₂₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₂₉×#461	C₂	semidirect
4. C₂×C₂₉×#424	C₂	semidirect
5. C₂₉×#2621	C₂	semidirect
7. C₂₉×#2068	C₂	semidirect
8. C₂₉×#2066	C₂	semidirect
9. C₂₉×#2055	C₂	semidirect
10. C₂₉×#2055	C₂	semidirect
11. C₂₉×#1981	C₂	semidirect
12. C₂₉×#1949	C₂	semidirect
13. C₂₉×#1894	C₂	semidirect
14. C₂₉×#1892	C₂	semidirect
15. C₂₉×#1804	C₂	semidirect
126. C₂₉×C₄⋊C₈	D₄	semidirect
236. #24766	C₂₉	direct (N × H)
318. C₂×#461	C₂×C₂₉	semidirect
319. C₂×#424	C₂×C₂₉	semidirect
320. #2621	C₂×C₂₉	semidirect
322. #2068	C₂×C₂₉	semidirect
323. #2066	C₂×C₂₉	semidirect
324. #2055	C₂×C₂₉	semidirect
325. #2055	C₂×C₂₉	semidirect
326. #1981	C₂×C₂₉	semidirect
327. #1949	C₂×C₂₉	semidirect
328. #1894	C₂×C₂₉	semidirect
329. #1892	C₂×C₂₉	semidirect
330. #1804	C₂×C₂₉	semidirect
487. C₄⋊C₈	D₄×C₂₉	semidirect
505. C₂₉	#24766	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×#468	2
C₂×C₂₉×#465	2
C₂×C₂₉×#461	2
C₂×C₂₉×#424	2
C₂₉×#2621	2
C₂₉×#2324	2
C₂₉×#2068	2
C₂₉×#2066	2
C₂₉×#2055	2
C₂₉×#1981	2
C₂₉×#1949	2
C₂₉×#1894	2
C₂₉×#1892	2
C₂₉×#1804	2
#24766	29

Subgroups — C29×#24766 #20319666

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#24766 #20319666