Subgroups — C₂₉×#24903 #20319803

Order 7424.

986 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#452	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×SD₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#2421	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2339	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#2097	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2077	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2036	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1933	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1923	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1877	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1862	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1804	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1788	C₂	1	1	yes	maximal, characteristic
16	C₂²×#41×C₂₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
23	C₂₉×#452	—	2	4	no	—
24	C₄×SD₁₆×C₂₉	—	2	4	no	—
25	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
34	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
35	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
36	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
39	C₂₉×#400	—	2	1	no	—
40	C₂₉×#397	—	2	1	no	—
41	C₂₉×#391	C₂²	1	1	yes	characteristic
42	C₂₉×#391	C₂²	1	1	yes	characteristic
43	C₂₉×#391	C₂²	1	1	yes	characteristic
44	C₂₉×#389	C₂²	1	1	yes	characteristic
45	C₂₉×#388	—	2	1	no	—
46	C₂₉×#387	—	2	1	no	—
47	C₂₉×#386	—	2	1	no	—
48	C₂₉×#386	—	2	1	no	—
49	C₂₉×#382	C₂²	1	1	yes	characteristic
50	C₂₉×#381	—	2	1	no	—
51	C₂₉×#380	C₂²	1	1	yes	characteristic
52	C₂₉×#380	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
54	C₂×C₂₉×#95	—	2	1	no	—
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	C₂×#41×C₂₉	—	2	2	no	—
62	C₂×#41×C₂₉	—	2	2	no	—
63	C₂×#41×C₂₉	—	2	2	no	—
64	C₂×#41×C₂₉	—	2	2	no	—
65	C₂×#41×C₂₉	—	4	1	no	—
66	C₂×#41×C₂₉	—	4	1	no	—
67	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₂₉	—	2	1	no	—
70	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₂₉	—	2	1	no	—
72	C₂³×C₄×C₂₉	—	2	1	no	—
73	C₂³×C₄×C₂₉	—	2	1	no	—
74	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
75	C₂×Q₁₆×C₂₉	—	2	2	no	—
76	C₂×Q₁₆×C₂₉	—	2	2	no	—
77	C₂×Q₁₆×C₂₉	—	4	1	no	—
78	C₂×SD₁₆×C₂₉	—	2	2	no	—
79	C₂×SD₁₆×C₂₉	—	2	2	no	—
80	C₂×SD₁₆×C₂₉	D₄	1	4	yes	—
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×C₂²⋊Q₈	—	2	2	no	—
86	C₂₉×C₂²⋊Q₈	—	4	1	no	—
87	C₄×Q₈×C₂₉	—	2	2	no	—
88	C₄×Q₈×C₂₉	—	4	1	no	—
89	C₄×D₄×C₂₉	—	2	2	no	—
90	C₄×D₄×C₂₉	—	2	2	no	—
91	C₄×D₄×C₂₉	—	4	1	no	—
92	C₄×D₄×C₂₉	—	4	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	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₂₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
111	C₂₉×#107	—	4	1	no	—
112	C₂₉×#106	—	2	2	no	—
113	C₂₉×C₄⋊C₈	—	4	1	no	—
114	C₂₉×#103	—	2	2	no	—
115	C₂₉×#103	—	2	2	no	—
116	C₂₉×#103	—	2	2	no	—
117	C₂₉×#103	—	4	1	no	—
118	C₂₉×#103	—	4	1	no	—
119	C₂₉×#102	—	2	2	no	—
120	C₂₉×#102	—	2	2	no	—
121	C₂₉×#102	—	2	2	no	—
122	C₂₉×C₂²⋊C₈	—	2	2	no	—
123	C₂₉×C₂²⋊C₈	—	4	1	no	—
124	C₄×C₈×C₂₉	—	2	2	no	—
125	C₂₉×#95	—	2	1	no	—
126	C₂₉×#95	—	2	1	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	—	2	1	no	—
136	C₂₉×#95	D₄	1	1	yes	characteristic
137	C₂₉×#95	D₄	1	1	yes	characteristic
138	C₂⁴×C₂₉	—	2	1	no	—
139	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
140	#41×C₂₉	—	4	4	no	—
141	#41×C₂₉	—	4	4	no	—
142	#41×C₂₉	—	4	4	no	—
143	#41×C₂₉	—	4	4	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	—	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	C₂×D₄	1	2	yes	—
155	C₂×Q₈×C₂₉	#41	1	2	yes	—
156	C₂×D₄×C₂₉	—	2	4	no	—
157	C₂×D₄×C₂₉	—	2	1	no	—
158	C₂×D₄×C₂₉	—	2	1	no	—
159	C₂×D₄×C₂₉	—	2	1	no	—
160	C₂×D₄×C₂₉	—	4	2	no	—
161	C₂×D₄×C₂₉	—	4	2	no	—
162	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
163	C₂×D₄×C₂₉	#41	1	2	yes	—
164	C₂×D₄×C₂₉	#41	1	2	yes	—
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	—	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	—	2	1	no	—
179	C₂²×C₄×C₂₉	—	4	2	no	—
180	C₂²×C₄×C₂₉	—	4	2	no	—
181	C₂²×C₄×C₂₉	—	4	2	no	—
182	C₂²×C₄×C₂₉	—	4	2	no	—
183	C₂²×C₄×C₂₉	—	4	2	no	—
184	C₂²×C₄×C₂₉	—	4	2	no	—
185	C₂²×C₄×C₂₉	—	8	1	no	—
186	C₂²×C₄×C₂₉	—	8	1	no	—
187	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
193	Q₁₆×C₂₉	—	4	4	no	—
194	SD₁₆×C₂₉	—	2	8	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	—	2	1	no	—
203	C₂×C₈×C₂₉	—	2	1	no	—
204	C₂×C₈×C₂₉	—	2	1	no	—
205	C₂×C₈×C₂₉	—	2	1	no	—
206	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
217	C₄⋊C₄×C₂₉	—	4	2	no	—
218	C₄⋊C₄×C₂₉	—	4	2	no	—
219	C₄⋊C₄×C₂₉	—	4	2	no	—
220	C₂²⋊C₄×C₂₉	—	2	2	no	—
221	C₂²⋊C₄×C₂₉	—	4	1	no	—
222	C₂²⋊C₄×C₂₉	—	4	2	no	—
223	C₂²⋊C₄×C₂₉	—	4	2	no	—
224	C₂²⋊C₄×C₂₉	—	4	2	no	—
225	C₂²⋊C₄×C₂₉	—	4	2	no	—
226	C₂²⋊C₄×C₂₉	—	8	1	no	—
227	C₄²×C₂₉	—	2	1	no	—
228	C₄²×C₂₉	—	2	1	no	—
229	C₄²×C₂₉	—	2	1	no	—
230	C₄²×C₂₉	—	2	1	no	—
231	C₄²×C₂₉	—	4	2	no	—
232	#24903	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂³×C₂₉	—	2	2	no	—
234	C₂³×C₂₉	—	2	2	no	—
235	C₂³×C₂₉	—	2	2	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	—	4	1	no	—
244	C₂³×C₂₉	—	4	1	no	—
245	C₂³×C₂₉	—	4	1	no	—
246	C₂³×C₂₉	—	4	1	no	—
247	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
248	Q₈×C₂₉	—	2	2	no	—
249	Q₈×C₂₉	—	2	2	no	—
250	Q₈×C₂₉	—	2	2	no	—
251	Q₈×C₂₉	—	2	2	no	—
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	D₄×C₂₉	—	2	2	no	—
257	D₄×C₂₉	—	2	2	no	—
258	D₄×C₂₉	—	2	2	no	—
259	D₄×C₂₉	—	4	8	no	—
260	D₄×C₂₉	#123	1	4	yes	—
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	2	no	—
265	C₂×C₄×C₂₉	—	2	1	no	—
266	C₂×C₄×C₂₉	—	2	2	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	1	no	—
272	C₂×C₄×C₂₉	—	2	1	no	—
273	C₂×C₄×C₂₉	—	2	1	no	—
274	C₂×C₄×C₂₉	—	2	1	no	—
275	C₂×C₄×C₂₉	—	2	1	no	—
276	C₂×C₄×C₂₉	—	2	1	no	—
277	C₂×C₄×C₂₉	—	4	8	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	—	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	—	8	4	no	—
302	C₂×C₄×C₂₉	—	8	4	no	—
303	C₂×C₄×C₂₉	#135	1	2	yes	—
304	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
306	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
307	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
308	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
309	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
310	C₈×C₂₉	—	2	2	no	—
311	C₈×C₂₉	—	4	1	no	—
312	C₈×C₂₉	—	4	1	no	—
313	C₈×C₂₉	—	4	1	no	—
314	C₂×#452	C₂×C₂₉	1	1	yes	characteristic
315	C₂×C₄×SD₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
316	#2421	C₂×C₂₉	1	1	yes	characteristic, complemented
317	#2339	C₂×C₂₉	1	1	yes	characteristic
318	#2097	C₂×C₂₉	1	1	yes	characteristic, complemented
319	#2077	C₂×C₂₉	1	1	yes	characteristic, complemented
320	#2056	C₂×C₂₉	1	1	yes	characteristic, complemented
321	#2036	C₂×C₂₉	1	1	yes	characteristic, complemented
322	#1933	C₂×C₂₉	1	1	yes	characteristic, complemented
323	#1923	C₂×C₂₉	1	1	yes	characteristic, complemented
324	#1878	C₂×C₂₉	1	1	yes	characteristic, complemented
325	#1877	C₂×C₂₉	1	1	yes	characteristic, complemented
326	#1862	C₂×C₂₉	1	1	yes	characteristic, complemented
327	#1804	C₂×C₂₉	1	1	yes	characteristic, complemented
328	#1788	C₂×C₂₉	1	1	yes	characteristic
329	C₂²×C₂₉	—	2	4	no	—
330	C₂²×C₂₉	—	4	2	no	—
331	C₂²×C₂₉	—	4	2	no	—
332	C₂²×C₂₉	—	4	2	no	—
333	C₂²×C₂₉	—	4	2	no	—
334	C₂²×C₂₉	—	4	2	no	—
335	C₂²×C₂₉	—	4	2	no	—
336	C₂²×C₂₉	—	4	1	no	—
337	C₂²×C₂₉	—	4	1	no	—
338	C₂²×C₂₉	—	4	1	no	—
339	C₂²×C₂₉	—	4	1	no	—
340	C₂²×C₂₉	—	4	1	no	—
341	C₂²×C₂₉	—	4	1	no	—
342	C₂²×C₂₉	—	4	1	no	—
343	C₂²×C₂₉	#525	1	1	yes	characteristic
344	C₂²×C₂₉	D₄²	1	1	yes	characteristic
345	C₂²×C₂₉	#546	1	1	yes	characteristic
346	C₂²×C₂₉	C₂×#135	1	1	yes	characteristic
347	C₂²×C₂₉	#575	1	1	yes	characteristic
348	C₂²×C₂₉	#577	1	1	yes	characteristic
349	C₂²×C₂₉	#578	1	1	yes	characteristic
350	C₄×C₂₉	—	2	2	no	—
351	C₄×C₂₉	—	4	1	no	—
352	C₄×C₂₉	—	4	2	no	—
353	C₄×C₂₉	—	4	2	no	—
354	C₄×C₂₉	—	4	1	no	—
355	C₄×C₂₉	—	4	1	no	—
356	C₄×C₂₉	—	4	1	no	—
357	C₄×C₂₉	—	8	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	C₂×#123	1	1	yes	characteristic
363	C₄×C₂₉	#538	1	1	yes	characteristic
364	C₄×C₂₉	#546	1	1	yes	characteristic
365	C₄×C₂₉	#551	1	1	yes	characteristic
366	C₂²×#41	C₂²×C₂₉	1	1	yes	characteristic
367	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
368	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
369	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
370	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
371	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
372	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
373	#452	—	2	4	no	—
374	C₄×SD₁₆	—	2	4	no	—
375	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
376	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
377	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
378	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
379	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
380	C₂×#103	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×#102	C₂²×C₂₉	1	1	yes	characteristic
384	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
385	C₂×#102	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×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
389	#400	—	2	1	no	—
390	#397	—	2	1	no	—
391	#391	C₂²×C₂₉	1	1	yes	characteristic
392	#391	C₂²×C₂₉	1	1	yes	characteristic
393	#391	C₂²×C₂₉	1	1	yes	characteristic
394	#389	C₂²×C₂₉	1	1	yes	characteristic
395	#388	—	2	1	no	—
396	#387	—	2	1	no	—
397	#386	—	2	1	no	—
398	#386	—	2	1	no	—
399	#382	C₂²×C₂₉	1	1	yes	characteristic
400	#381	—	2	1	no	—
401	#380	C₂²×C₂₉	1	1	yes	characteristic
402	#380	C₂²×C₂₉	1	1	yes	characteristic
403	C₄×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
404	C₂×#95	—	2	1	no	—
405	#340	C₂²×C₂₉	1	1	yes	characteristic
406	#340	C₂²×C₂₉	1	1	yes	characteristic
407	#340	C₂²×C₂₉	1	1	yes	characteristic
408	#340	C₂²×C₂₉	1	1	yes	characteristic
409	#336	C₂²×C₂₉	1	1	yes	characteristic
410	#336	C₂²×C₂₉	1	1	yes	characteristic
411	C₂×C₂₉	—	4	4	no	—
412	C₂×C₂₉	—	8	1	no	—
413	C₂×C₂₉	#2418	1	1	yes	characteristic
414	C₂×C₂₉	#3102	1	1	yes	characteristic
415	C₂×C₂₉	#3120	1	1	yes	characteristic
416	C₂×C₂₉	#3269	1	1	yes	characteristic
417	C₂×C₂₉	#3282	1	1	yes	characteristic
418	C₂×C₂₉	#3302	1	1	yes	characteristic
419	C₂×C₂₉	#3323	1	1	yes	characteristic
420	C₂×#41	—	2	2	no	—
421	C₂×#41	—	2	2	no	—
422	C₂×#41	—	2	2	no	—
423	C₂×#41	—	2	2	no	—
424	C₂×#41	—	4	1	no	—
425	C₂×#41	—	4	1	no	—
426	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
427	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
428	C₂²×D₄	—	2	1	no	—
429	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
430	C₂³×C₄	—	2	1	no	—
431	C₂³×C₄	—	2	1	no	—
432	C₂³×C₄	—	2	1	no	—
433	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
434	C₂×Q₁₆	—	2	2	no	—
435	C₂×Q₁₆	—	2	2	no	—
436	C₂×Q₁₆	—	4	1	no	—
437	C₂×SD₁₆	—	2	2	no	—
438	C₂×SD₁₆	—	2	2	no	—
439	C₂×SD₁₆	D₄×C₂₉	1	4	yes	—
440	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
441	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
442	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
443	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
444	C₂²⋊Q₈	—	2	2	no	—
445	C₂²⋊Q₈	—	4	1	no	—
446	C₄×Q₈	—	2	2	no	—
447	C₄×Q₈	—	4	1	no	—
448	C₄×D₄	—	2	2	no	—
449	C₄×D₄	—	2	2	no	—
450	C₄×D₄	—	4	1	no	—
451	C₄×D₄	—	4	1	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	—	2	1	no	—
454	C₂×C₄⋊C₄	—	2	1	no	—
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×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
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	D₄×C₂₉	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
467	C₂×C₄²	—	2	1	no	—
468	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
469	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
470	#107	—	4	1	no	—
471	#106	—	2	2	no	—
472	C₄⋊C₈	—	4	1	no	—
473	#103	—	2	2	no	—
474	#103	—	2	2	no	—
475	#103	—	2	2	no	—
476	#103	—	4	1	no	—
477	#103	—	4	1	no	—
478	#102	—	2	2	no	—
479	#102	—	2	2	no	—
480	#102	—	2	2	no	—
481	C₂²⋊C₈	—	2	2	no	—
482	C₂²⋊C₈	—	4	1	no	—
483	C₄×C₈	—	2	2	no	—
484	#95	—	2	1	no	—
485	#95	—	2	1	no	—
486	#95	—	2	1	no	—
487	#95	—	2	1	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	#95	—	2	1	no	—
494	#95	—	2	1	no	—
495	#95	D₄×C₂₉	1	1	yes	characteristic
496	#95	D₄×C₂₉	1	1	yes	characteristic
497	C₂₉	#24903	1	1	yes	characteristic, direct product factor, Sylow
498	C₂⁴	—	2	1	no	—
499	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
500	#41	—	4	4	no	—
501	#41	—	4	4	no	—
502	#41	—	4	4	no	—
503	#41	—	4	4	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
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	C₂×D₄×C₂₉	1	2	yes	—
515	C₂×Q₈	#41×C₂₉	1	2	yes	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	4	2	no	—
521	C₂×D₄	—	4	2	no	—
522	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
523	C₂×D₄	#41×C₂₉	1	2	yes	—
524	C₂×D₄	#41×C₂₉	1	2	yes	—
525	C₂²×C₄	—	2	4	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
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	—	4	2	no	—
540	C₂²×C₄	—	4	2	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	4	2	no	—
544	C₂²×C₄	—	4	2	no	—
545	C₂²×C₄	—	8	1	no	—
546	C₂²×C₄	—	8	1	no	—
547	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
548	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
549	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
550	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
551	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
553	Q₁₆	—	4	4	no	—
554	SD₁₆	—	2	8	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	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	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	—	4	2	no	—
578	C₄⋊C₄	—	4	2	no	—
579	C₄⋊C₄	—	4	2	no	—
580	C₂²⋊C₄	—	2	2	no	—
581	C₂²⋊C₄	—	4	1	no	—
582	C₂²⋊C₄	—	4	2	no	—
583	C₂²⋊C₄	—	4	2	no	—
584	C₂²⋊C₄	—	4	2	no	—
585	C₂²⋊C₄	—	4	2	no	—
586	C₂²⋊C₄	—	8	1	no	—
587	C₄²	—	2	1	no	—
588	C₄²	—	2	1	no	—
589	C₄²	—	2	1	no	—
590	C₄²	—	2	1	no	—
591	C₄²	—	4	2	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
607	Q₈	—	2	2	no	—
608	Q₈	—	2	2	no	—
609	Q₈	—	2	2	no	—
610	Q₈	—	2	2	no	—
611	Q₈	—	4	1	no	—
612	Q₈	—	4	1	no	—
613	Q₈	—	4	1	no	—
614	Q₈	—	4	1	no	—
615	D₄	—	2	2	no	—
616	D₄	—	2	2	no	—
617	D₄	—	2	2	no	—
618	D₄	—	4	8	no	—
619	D₄	C₂₉×#123	1	4	yes	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	2	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	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	4	8	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	—	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	—	8	4	no	—
661	C₂×C₄	—	8	4	no	—
662	C₂×C₄	C₂₉×#135	1	2	yes	—
663	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
664	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
665	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
666	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
667	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
668	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
669	C₈	—	2	2	no	—
670	C₈	—	4	1	no	—
671	C₈	—	4	1	no	—
672	C₈	—	4	1	no	—
673	C₂²	—	2	4	no	—
674	C₂²	—	4	2	no	—
675	C₂²	—	4	2	no	—
676	C₂²	—	4	2	no	—
677	C₂²	—	4	2	no	—
678	C₂²	—	4	2	no	—
679	C₂²	—	4	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	1	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	C₂₉×#525	1	1	yes	characteristic
688	C₂²	D₄²×C₂₉	1	1	yes	characteristic
689	C₂²	C₂₉×#546	1	1	yes	characteristic
690	C₂²	C₂×C₂₉×#135	1	1	yes	characteristic
691	C₂²	C₂₉×#575	1	1	yes	characteristic
692	C₂²	C₂₉×#577	1	1	yes	characteristic
693	C₂²	C₂₉×#578	1	1	yes	characteristic
694	C₄	—	2	2	no	—
695	C₄	—	4	1	no	—
696	C₄	—	4	2	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	1	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	1	no	—
701	C₄	—	8	1	no	—
702	C₄	—	8	1	no	—
703	C₄	—	8	1	no	—
704	C₄	—	8	1	no	—
705	C₄	—	8	1	no	—
706	C₄	C₂×C₂₉×#123	1	1	yes	characteristic
707	C₄	C₂₉×#538	1	1	yes	characteristic
708	C₄	C₂₉×#546	1	1	yes	characteristic
709	C₄	C₂₉×#551	1	1	yes	characteristic
710	C₂	—	4	4	no	—
711	C₂	—	8	1	no	—
712	C₂	C₂₉×#2418	1	1	yes	characteristic
713	C₂	C₂₉×#3102	1	1	yes	characteristic
714	C₂	C₂₉×#3120	1	1	yes	characteristic
715	C₂	C₂₉×#3269	1	1	yes	characteristic
716	C₂	C₂₉×#3282	1	1	yes	characteristic
717	C₂	C₂₉×#3302	1	1	yes	characteristic
718	C₂	C₂₉×#3323	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂²×#41×C₂₉	C₂²
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
2. C₂×C₄×SD₁₆×C₂₉	C₂	semidirect
3. C₂₉×#2421	C₂	semidirect
5. C₂₉×#2097	C₂	semidirect
6. C₂₉×#2077	C₂	semidirect
7. C₂₉×#2056	C₂	semidirect
8. C₂₉×#2036	C₂	semidirect
9. C₂₉×#1933	C₂	semidirect
10. C₂₉×#1923	C₂	semidirect
11. C₂₉×#1878	C₂	semidirect
12. C₂₉×#1877	C₂	semidirect
13. C₂₉×#1862	C₂	semidirect
14. C₂₉×#1804	C₂	semidirect
232. #24903	C₂₉	direct (N × H)
315. C₂×C₄×SD₁₆	C₂×C₂₉	semidirect
316. #2421	C₂×C₂₉	semidirect
318. #2097	C₂×C₂₉	semidirect
319. #2077	C₂×C₂₉	semidirect
320. #2056	C₂×C₂₉	semidirect
321. #2036	C₂×C₂₉	semidirect
322. #1933	C₂×C₂₉	semidirect
323. #1923	C₂×C₂₉	semidirect
324. #1878	C₂×C₂₉	semidirect
325. #1877	C₂×C₂₉	semidirect
326. #1862	C₂×C₂₉	semidirect
327. #1804	C₂×C₂₉	semidirect
497. C₂₉	#24903	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×#452	2
C₂×C₄×SD₁₆×C₂₉	2
C₂₉×#2421	2
C₂₉×#2339	2
C₂₉×#2097	2
C₂₉×#2077	2
C₂₉×#2056	2
C₂₉×#2036	2
C₂₉×#1933	2
C₂₉×#1923	2
C₂₉×#1878	2
C₂₉×#1877	2
C₂₉×#1862	2
C₂₉×#1804	2
C₂₉×#1788	2
#24903	29

Subgroups — C29×#24903 #20319803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#24903 #20319803