Subgroups — C₂₉×#22923 #20317823

Order 7424.

870 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#482	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2363	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2347	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#1941	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1934	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1926	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1921	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1919	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1893	C₂	1	1	yes	maximal, characteristic
10	C₂₉×#1862	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₂₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₂₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×C₂²⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1735	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₈×C₂₉	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
20	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
21	C₂₉×#482	C₄	1	8	yes	complemented
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×#102	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
33	C₂₉×#390	—	2	1	no	—
34	C₂₉×#390	C₂²	1	1	yes	characteristic
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×#388	—	2	1	no	—
39	C₂₉×#388	—	2	1	no	—
40	C₂₉×#388	—	2	1	no	—
41	C₂₉×#386	—	2	1	no	—
42	C₂₉×#383	—	2	1	no	—
43	C₂₉×#380	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₂₉	—	2	1	no	—
45	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊C₄×C₂₉	—	2	1	no	—
49	C₄×C₂²⋊C₄×C₂₉	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×#340	C₂²	1	1	yes	characteristic
58	C₂₉×#336	C₂²	1	1	yes	characteristic
59	C₂₉×#336	C₂²	1	1	yes	characteristic
60	C₂²×D₄×C₂₉	—	2	1	no	—
61	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₂₉	—	2	1	no	—
63	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₂₉	—	2	2	no	—
65	C₂²×C₈×C₂₉	—	2	2	no	—
66	C₂²×C₈×C₂₉	—	4	1	no	—
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	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
71	C₂₉×#121	—	2	2	no	—
72	C₂₉×#121	C₂×C₄	1	4	yes	—
73	C₄×D₄×C₂₉	—	2	2	no	—
74	C₄×D₄×C₂₉	—	4	1	no	—
75	C₂₉×#117	—	2	2	no	—
76	C₂₉×#117	—	2	2	no	—
77	C₂₉×#117	—	4	1	no	—
78	C₂₉×#117	C₂×C₄	1	4	yes	complemented
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	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₂₉	—	2	1	no	—
99	C₂×C₄²×C₂₉	—	2	1	no	—
100	C₂×C₄²×C₂₉	—	2	1	no	—
101	C₂×C₄²×C₂₉	—	2	1	no	—
102	C₂×C₄²×C₂₉	—	2	1	no	—
103	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
105	C₂₉×#107	—	2	2	no	—
106	C₂₉×#107	C₂×C₄	1	4	yes	complemented
107	C₂₉×#106	—	4	1	no	—
108	C₂₉×#106	C₂×C₄	1	4	yes	complemented
109	C₂₉×#102	—	2	2	no	—
110	C₂₉×#102	—	4	1	no	—
111	C₂₉×#102	C₂×C₄	1	4	yes	—
112	C₂₉×#102	C₂×C₄	1	4	yes	—
113	C₂₉×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
114	C₄×C₈×C₂₉	—	2	2	no	—
115	C₄×C₈×C₂₉	—	4	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	—	2	1	no	—
122	C₂₉×#95	—	2	1	no	—
123	C₂₉×#95	D₄	1	1	yes	characteristic
124	C₂₉×#95	D₄	1	1	yes	characteristic
125	C₂⁴×C₂₉	—	2	1	no	—
126	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
127	C₂×D₄×C₂₉	—	2	4	no	—
128	C₂×D₄×C₂₉	—	2	1	no	—
129	C₂×D₄×C₂₉	—	2	1	no	—
130	C₂×D₄×C₂₉	—	2	1	no	—
131	C₂×D₄×C₂₉	—	2	1	no	—
132	C₂×D₄×C₂₉	—	2	1	no	—
133	C₂×D₄×C₂₉	—	8	1	no	—
134	C₂×D₄×C₂₉	—	8	1	no	—
135	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
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	—	2	1	no	—
140	C₂²×C₄×C₂₉	—	2	1	no	—
141	C₂²×C₄×C₂₉	—	2	1	no	—
142	C₂²×C₄×C₂₉	—	2	1	no	—
143	C₂²×C₄×C₂₉	—	2	1	no	—
144	C₂²×C₄×C₂₉	—	2	1	no	—
145	C₂²×C₄×C₂₉	—	2	1	no	—
146	C₂²×C₄×C₂₉	—	2	1	no	—
147	C₂²×C₄×C₂₉	—	4	2	no	—
148	C₂²×C₄×C₂₉	—	4	2	no	—
149	C₂²×C₄×C₂₉	—	8	1	no	—
150	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
151	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₂₉	#41	1	2	yes	—
157	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
162	C₂×C₈×C₂₉	—	2	1	no	—
163	C₂×C₈×C₂₉	—	2	1	no	—
164	C₂×C₈×C₂₉	—	2	1	no	—
165	C₂×C₈×C₂₉	—	2	1	no	—
166	C₂×C₈×C₂₉	—	2	1	no	—
167	C₂×C₈×C₂₉	—	4	4	no	—
168	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
169	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
170	C₂×C₈×C₂₉	#41	1	2	yes	—
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	—	2	1	no	—
181	C₄⋊C₄×C₂₉	—	4	2	no	—
182	C₄⋊C₄×C₂₉	—	4	2	no	—
183	C₄⋊C₄×C₂₉	—	8	1	no	—
184	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
185	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
186	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
187	C₄⋊C₄×C₂₉	#41	1	2	yes	—
188	C₂²⋊C₄×C₂₉	—	2	4	no	—
189	C₂²⋊C₄×C₂₉	—	2	4	no	—
190	C₂²⋊C₄×C₂₉	—	2	2	no	—
191	C₂²⋊C₄×C₂₉	—	2	2	no	—
192	C₂²⋊C₄×C₂₉	—	4	2	no	—
193	C₂²⋊C₄×C₂₉	—	4	2	no	—
194	C₂²⋊C₄×C₂₉	—	4	2	no	—
195	C₂²⋊C₄×C₂₉	—	8	1	no	—
196	C₂²⋊C₄×C₂₉	—	8	1	no	—
197	C₄²×C₂₉	—	2	4	no	—
198	C₄²×C₂₉	—	2	1	no	—
199	C₄²×C₂₉	—	2	1	no	—
200	C₄²×C₂₉	—	2	1	no	—
201	C₄²×C₂₉	—	2	1	no	—
202	C₄²×C₂₉	—	4	2	no	—
203	C₄²×C₂₉	—	8	1	no	—
204	C₄²×C₂₉	—	8	1	no	—
205	C₄²×C₂₉	—	8	1	no	—
206	#22923	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂³×C₂₉	—	2	1	no	—
208	C₂³×C₂₉	—	2	1	no	—
209	C₂³×C₂₉	—	2	1	no	—
210	C₂³×C₂₉	—	2	1	no	—
211	C₂³×C₂₉	—	2	1	no	—
212	C₂³×C₂₉	—	2	1	no	—
213	C₂³×C₂₉	—	2	2	no	—
214	C₂³×C₂₉	—	4	1	no	—
215	C₂³×C₂₉	—	4	1	no	—
216	C₂³×C₂₉	—	4	1	no	—
217	C₂³×C₂₉	—	4	1	no	—
218	C₂³×C₂₉	—	4	1	no	—
219	C₂³×C₂₉	—	4	1	no	—
220	C₂³×C₂₉	C₄×D₄	1	2	yes	—
221	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
222	D₄×C₂₉	—	2	2	no	—
223	D₄×C₂₉	—	2	2	no	—
224	D₄×C₂₉	—	4	1	no	—
225	D₄×C₂₉	—	4	1	no	—
226	D₄×C₂₉	—	8	4	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	—	2	1	no	—
232	C₂×C₄×C₂₉	—	2	1	no	—
233	C₂×C₄×C₂₉	—	2	2	no	—
234	C₂×C₄×C₂₉	—	2	2	no	—
235	C₂×C₄×C₂₉	—	2	2	no	—
236	C₂×C₄×C₂₉	—	2	2	no	—
237	C₂×C₄×C₂₉	—	2	2	no	—
238	C₂×C₄×C₂₉	—	2	2	no	—
239	C₂×C₄×C₂₉	—	2	2	no	—
240	C₂×C₄×C₂₉	—	2	1	no	—
241	C₂×C₄×C₂₉	—	2	2	no	—
242	C₂×C₄×C₂₉	—	2	1	no	—
243	C₂×C₄×C₂₉	—	2	1	no	—
244	C₂×C₄×C₂₉	—	2	1	no	—
245	C₂×C₄×C₂₉	—	2	1	no	—
246	C₂×C₄×C₂₉	—	2	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	—	4	1	no	—
254	C₂×C₄×C₂₉	—	4	1	no	—
255	C₂×C₄×C₂₉	—	4	1	no	—
256	C₂×C₄×C₂₉	—	4	1	no	—
257	C₂×C₄×C₂₉	—	4	1	no	—
258	C₂×C₄×C₂₉	—	4	1	no	—
259	C₂×C₄×C₂₉	—	4	1	no	—
260	C₂×C₄×C₂₉	—	4	1	no	—
261	C₂×C₄×C₂₉	—	4	1	no	—
262	C₂×C₄×C₂₉	—	4	1	no	—
263	C₂×C₄×C₂₉	—	4	1	no	—
264	C₂×C₄×C₂₉	—	8	4	no	—
265	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
266	C₂×C₄×C₂₉	#135	1	2	yes	—
267	C₂×C₄×C₂₉	#135	1	2	yes	—
268	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
269	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
270	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
272	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
273	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
274	C₈×C₂₉	—	2	2	no	—
275	C₈×C₂₉	—	2	2	no	—
276	C₈×C₂₉	—	2	2	no	—
277	C₈×C₂₉	—	4	1	no	—
278	C₂×#482	C₂×C₂₉	1	1	yes	characteristic
279	#2363	C₂×C₂₉	1	1	yes	characteristic
280	#2347	C₂×C₂₉	1	1	yes	characteristic, complemented
281	#1941	C₂×C₂₉	1	1	yes	characteristic, complemented
282	#1934	C₂×C₂₉	1	1	yes	characteristic, complemented
283	#1926	C₂×C₂₉	1	1	yes	characteristic, complemented
284	#1921	C₂×C₂₉	1	1	yes	characteristic, complemented
285	#1919	C₂×C₂₉	1	1	yes	characteristic, complemented
286	#1893	C₂×C₂₉	1	1	yes	characteristic
287	#1862	C₂×C₂₉	1	1	yes	characteristic, complemented
288	#1854	C₂×C₂₉	1	1	yes	characteristic, complemented
289	C₄×#107	C₂×C₂₉	1	1	yes	characteristic, complemented
290	C₄×#102	C₂×C₂₉	1	1	yes	characteristic, complemented
291	C₈×C₂²⋊C₄	C₂×C₂₉	1	1	yes	characteristic, complemented
292	#1735	C₂×C₂₉	1	1	yes	characteristic, complemented
293	C₂²×C₂₉	—	2	2	no	—
294	C₂²×C₂₉	—	2	2	no	—
295	C₂²×C₂₉	—	2	2	no	—
296	C₂²×C₂₉	—	4	1	no	—
297	C₂²×C₂₉	—	4	1	no	—
298	C₂²×C₂₉	—	4	1	no	—
299	C₂²×C₂₉	—	4	1	no	—
300	C₂²×C₂₉	—	4	2	no	—
301	C₂²×C₂₉	—	4	2	no	—
302	C₂²×C₂₉	—	4	2	no	—
303	C₂²×C₂₉	—	8	1	no	—
304	C₂²×C₂₉	—	8	1	no	—
305	C₂²×C₂₉	—	8	1	no	—
306	C₂²×C₂₉	—	8	1	no	—
307	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
308	C₂²×C₂₉	#546	1	1	yes	characteristic
309	C₂²×C₂₉	#547	1	1	yes	characteristic
310	C₂²×C₂₉	C₂×#135	1	1	yes	characteristic
311	C₂²×C₂₉	C₂×#135	1	1	yes	characteristic
312	C₂²×C₂₉	#576	1	1	yes	characteristic
313	C₂²×C₂₉	#577	1	1	yes	characteristic
314	C₄×C₂₉	—	2	2	no	—
315	C₄×C₂₉	—	2	2	no	—
316	C₄×C₂₉	—	2	2	no	—
317	C₄×C₂₉	—	4	1	no	—
318	C₄×C₂₉	—	4	2	no	—
319	C₄×C₂₉	—	4	2	no	—
320	C₄×C₂₉	—	4	2	no	—
321	C₄×C₂₉	—	4	2	no	—
322	C₄×C₂₉	—	4	1	no	—
323	C₄×C₂₉	—	8	1	no	—
324	C₄×C₂₉	—	8	1	no	—
325	C₄×C₂₉	—	8	1	no	—
326	C₄×C₂₉	C₄×#41	1	1	yes	characteristic
327	C₄×C₂₉	#520	1	1	yes	characteristic
328	C₄×C₂₉	#551	1	1	yes	characteristic
329	C₄×C₂₉	#552	1	1	yes	characteristic
330	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic
331	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic
332	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
333	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
334	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
335	#482	C₄×C₂₉	1	8	yes	complemented
336	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
337	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
338	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
339	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
340	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
341	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
342	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
343	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
344	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
345	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
346	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
347	#390	—	2	1	no	—
348	#390	C₂²×C₂₉	1	1	yes	characteristic
349	#389	C₂²×C₂₉	1	1	yes	characteristic
350	#389	C₂²×C₂₉	1	1	yes	characteristic
351	#389	C₂²×C₂₉	1	1	yes	characteristic
352	#388	—	2	1	no	—
353	#388	—	2	1	no	—
354	#388	—	2	1	no	—
355	#386	—	2	1	no	—
356	#383	—	2	1	no	—
357	#380	C₂²×C₂₉	1	1	yes	characteristic
358	C₄×C₄⋊C₄	—	2	1	no	—
359	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
360	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
361	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
362	C₄×C₂²⋊C₄	—	2	1	no	—
363	C₄×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
364	#340	C₂²×C₂₉	1	1	yes	characteristic
365	#340	C₂²×C₂₉	1	1	yes	characteristic
366	#340	C₂²×C₂₉	1	1	yes	characteristic
367	#340	C₂²×C₂₉	1	1	yes	characteristic
368	#340	C₂²×C₂₉	1	1	yes	characteristic
369	#340	C₂²×C₂₉	1	1	yes	characteristic
370	#340	C₂²×C₂₉	1	1	yes	characteristic
371	#340	C₂²×C₂₉	1	1	yes	characteristic
372	#336	C₂²×C₂₉	1	1	yes	characteristic
373	#336	C₂²×C₂₉	1	1	yes	characteristic
374	C₂×C₂₉	—	4	2	no	—
375	C₂×C₂₉	—	8	2	no	—
376	C₂×C₂₉	#2359	1	1	yes	characteristic
377	C₂×C₂₉	C₄×#135	1	1	yes	characteristic
378	C₂×C₂₉	#2946	1	1	yes	characteristic
379	C₂×C₂₉	#3297	1	1	yes	characteristic
380	C₂×C₂₉	#3304	1	1	yes	characteristic
381	C₂×C₂₉	#3339	1	1	yes	characteristic
382	C₂×C₂₉	#3340	1	1	yes	characteristic
383	C₂²×D₄	—	2	1	no	—
384	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
385	C₂³×C₄	—	2	1	no	—
386	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
387	C₂²×C₈	—	2	2	no	—
388	C₂²×C₈	—	2	2	no	—
389	C₂²×C₈	—	4	1	no	—
390	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
391	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
392	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
394	#121	—	2	2	no	—
395	#121	C₂×C₄×C₂₉	1	4	yes	—
396	C₄×D₄	—	2	2	no	—
397	C₄×D₄	—	4	1	no	—
398	#117	—	2	2	no	—
399	#117	—	2	2	no	—
400	#117	—	4	1	no	—
401	#117	C₂×C₄×C₂₉	1	4	yes	complemented
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	1	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
421	C₂×C₄²	—	2	1	no	—
422	C₂×C₄²	—	2	1	no	—
423	C₂×C₄²	—	2	1	no	—
424	C₂×C₄²	—	2	1	no	—
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
427	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
428	#107	—	2	2	no	—
429	#107	C₂×C₄×C₂₉	1	4	yes	complemented
430	#106	—	4	1	no	—
431	#106	C₂×C₄×C₂₉	1	4	yes	complemented
432	#102	—	2	2	no	—
433	#102	—	4	1	no	—
434	#102	C₂×C₄×C₂₉	1	4	yes	—
435	#102	C₂×C₄×C₂₉	1	4	yes	—
436	C₂²⋊C₈	C₂×C₄×C₂₉	1	4	yes	complemented
437	C₄×C₈	—	2	2	no	—
438	C₄×C₈	—	4	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	D₄×C₂₉	1	1	yes	characteristic
447	#95	D₄×C₂₉	1	1	yes	characteristic
448	C₂₉	#22923	1	1	yes	characteristic, direct product factor, Sylow
449	C₂⁴	—	2	1	no	—
450	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
451	C₂×D₄	—	2	4	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	8	1	no	—
458	C₂×D₄	—	8	1	no	—
459	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	4	2	no	—
473	C₂²×C₄	—	8	1	no	—
474	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
475	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
480	C₂²×C₄	#41×C₂₉	1	2	yes	—
481	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	4	4	no	—
492	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
493	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
494	C₂×C₈	#41×C₂₉	1	2	yes	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	4	2	no	—
506	C₄⋊C₄	—	4	2	no	—
507	C₄⋊C₄	—	8	1	no	—
508	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
509	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
510	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
511	C₄⋊C₄	#41×C₂₉	1	2	yes	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	2	4	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	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	—	8	1	no	—
521	C₄²	—	2	4	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	4	2	no	—
527	C₄²	—	8	1	no	—
528	C₄²	—	8	1	no	—
529	C₄²	—	8	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	4	1	no	—
538	C₂³	—	4	1	no	—
539	C₂³	—	4	1	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	4	1	no	—
542	C₂³	—	4	1	no	—
543	C₂³	C₄×D₄×C₂₉	1	2	yes	—
544	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
545	D₄	—	2	2	no	—
546	D₄	—	2	2	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	8	4	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	8	4	no	—
588	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
589	C₂×C₄	C₂₉×#135	1	2	yes	—
590	C₂×C₄	C₂₉×#135	1	2	yes	—
591	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
592	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
593	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
594	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
595	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
596	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
597	C₈	—	2	2	no	—
598	C₈	—	2	2	no	—
599	C₈	—	2	2	no	—
600	C₈	—	4	1	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	8	1	no	—
612	C₂²	—	8	1	no	—
613	C₂²	—	8	1	no	—
614	C₂²	—	8	1	no	—
615	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
616	C₂²	C₂₉×#546	1	1	yes	characteristic
617	C₂²	C₂₉×#547	1	1	yes	characteristic
618	C₂²	C₂×C₂₉×#135	1	1	yes	characteristic
619	C₂²	C₂×C₂₉×#135	1	1	yes	characteristic
620	C₂²	C₂₉×#576	1	1	yes	characteristic
621	C₂²	C₂₉×#577	1	1	yes	characteristic
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	2	no	—
625	C₄	—	4	2	no	—
626	C₄	—	4	2	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	—	8	1	no	—
632	C₄	—	8	1	no	—
633	C₄	—	8	1	no	—
634	C₄	C₄×#41×C₂₉	1	1	yes	characteristic
635	C₄	C₂₉×#520	1	1	yes	characteristic
636	C₄	C₂₉×#551	1	1	yes	characteristic
637	C₄	C₂₉×#552	1	1	yes	characteristic
638	C₂	—	4	2	no	—
639	C₂	—	8	2	no	—
640	C₂	C₂₉×#2359	1	1	yes	characteristic
641	C₂	C₄×C₂₉×#135	1	1	yes	characteristic
642	C₂	C₂₉×#2946	1	1	yes	characteristic
643	C₂	C₂₉×#3297	1	1	yes	characteristic
644	C₂	C₂₉×#3304	1	1	yes	characteristic
645	C₂	C₂₉×#3339	1	1	yes	characteristic
646	C₂	C₂₉×#3340	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#121	C₂²
LCS	G ▷ C₂×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×#2347	C₂	semidirect
4. C₂₉×#1941	C₂	semidirect
5. C₂₉×#1934	C₂	semidirect
6. C₂₉×#1926	C₂	semidirect
7. C₂₉×#1921	C₂	semidirect
8. C₂₉×#1919	C₂	semidirect
10. C₂₉×#1862	C₂	semidirect
11. C₂₉×#1854	C₂	semidirect
12. C₄×C₂₉×#107	C₂	semidirect
13. C₄×C₂₉×#102	C₂	semidirect
14. C₈×C₂²⋊C₄×C₂₉	C₂	semidirect
15. C₂₉×#1735	C₂	semidirect
21. C₂₉×#482	C₄	semidirect
78. C₂₉×#117	C₂×C₄	semidirect
106. C₂₉×#107	C₂×C₄	semidirect
108. C₂₉×#106	C₂×C₄	semidirect
113. C₂₉×C₂²⋊C₈	C₂×C₄	semidirect
206. #22923	C₂₉	direct (N × H)
280. #2347	C₂×C₂₉	semidirect
281. #1941	C₂×C₂₉	semidirect
282. #1934	C₂×C₂₉	semidirect
283. #1926	C₂×C₂₉	semidirect
284. #1921	C₂×C₂₉	semidirect
285. #1919	C₂×C₂₉	semidirect
287. #1862	C₂×C₂₉	semidirect
288. #1854	C₂×C₂₉	semidirect
289. C₄×#107	C₂×C₂₉	semidirect
290. C₄×#102	C₂×C₂₉	semidirect
291. C₈×C₂²⋊C₄	C₂×C₂₉	semidirect
292. #1735	C₂×C₂₉	semidirect
335. #482	C₄×C₂₉	semidirect
401. #117	C₂×C₄×C₂₉	semidirect
429. #107	C₂×C₄×C₂₉	semidirect
431. #106	C₂×C₄×C₂₉	semidirect
436. C₂²⋊C₈	C₂×C₄×C₂₉	semidirect
448. C₂₉	#22923	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×#482	2
C₂₉×#2363	2
C₂₉×#2347	2
C₂₉×#1941	2
C₂₉×#1934	2
C₂₉×#1926	2
C₂₉×#1921	2
C₂₉×#1919	2
C₂₉×#1893	2
C₂₉×#1862	2
C₂₉×#1854	2
C₄×C₂₉×#107	2
C₄×C₂₉×#102	2
C₈×C₂²⋊C₄×C₂₉	2
C₂₉×#1735	2
#22923	29

Subgroups — C29×#22923 #20317823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#22923 #20317823