Subgroups — C₂₉×#33090 #20327990

Order 7424.

770 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#2645	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#2275	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#1928	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#1928	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1927	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1921	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1920	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1918	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1877	C₂	1	1	yes	maximal, characteristic
10	C₂₉×#1877	C₂	1	1	yes	maximal, characteristic
11	C₂₉×#1877	C₂	1	1	yes	maximal, characteristic
12	C₂₉×#1864	C₂	1	1	yes	maximal, characteristic
13	C₂₉×#1862	C₂	1	1	yes	maximal, characteristic
14	C₂₉×#1862	C₂	1	1	yes	maximal, characteristic
15	C₂₉×#1840	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
20	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
24	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
25	C₂×C₂₉×#103	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	C₂₉×#401	—	2	1	no	—
30	C₂₉×#400	—	2	1	no	—
31	C₂₉×#400	—	2	1	no	—
32	C₂₉×#400	—	2	1	no	—
33	C₂₉×#391	C₂²	1	1	yes	characteristic
34	C₂₉×#391	C₂²	1	1	yes	characteristic
35	C₂₉×#391	C₂²	1	1	yes	characteristic
36	C₂₉×#389	C₂²	1	1	yes	characteristic
37	C₂₉×#389	C₂²	1	1	yes	characteristic
38	C₂₉×#389	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
42	C₄×C₂²⋊C₄×C₂₉	—	2	1	no	—
43	C₄×C₂²⋊C₄×C₂₉	—	2	1	no	—
44	C₄×C₂²⋊C₄×C₂₉	—	2	1	no	—
45	C₂₉×#376	C₂²	1	1	yes	characteristic
46	C₂×C₂₉×#95	—	2	1	no	—
47	C₂₉×#340	C₂²	1	1	yes	characteristic
48	C₂₉×#340	C₂²	1	1	yes	characteristic
49	C₂₉×#340	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×#336	C₂²	1	1	yes	characteristic
54	C₂₉×#336	C₂²	1	1	yes	characteristic
55	C₂₉×#336	C₂²	1	1	yes	characteristic
56	C₂₉×#336	C₂²	1	1	yes	characteristic
57	C₂₉×#336	C₂²	1	1	yes	characteristic
58	C₂₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₂₉	—	2	1	no	—
62	C₂³×C₄×C₂₉	—	2	1	no	—
63	C₂³×C₄×C₂₉	—	2	1	no	—
64	C₂×SD₁₆×C₂₉	—	2	2	no	—
65	C₂×SD₁₆×C₂₉	—	2	2	no	—
66	C₂×SD₁₆×C₂₉	—	2	2	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	C₄×D₄×C₂₉	—	2	2	no	—
72	C₄×D₄×C₂₉	—	2	2	no	—
73	C₄×D₄×C₂₉	—	2	2	no	—
74	C₄×D₄×C₂₉	—	2	2	no	—
75	C₄×D₄×C₂₉	—	2	2	no	—
76	C₄×D₄×C₂₉	—	2	2	no	—
77	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₂₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
89	C₂×C₄²×C₂₉	—	2	1	no	—
90	C₂×C₄²×C₂₉	—	2	1	no	—
91	C₂×C₄²×C₂₉	—	2	1	no	—
92	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
95	C₂₉×#107	—	2	2	no	—
96	C₂₉×#107	—	2	2	no	—
97	C₂₉×#106	—	2	2	no	—
98	C₂₉×#103	—	2	2	no	—
99	C₂₉×#103	—	2	2	no	—
100	C₂₉×#103	—	2	2	no	—
101	C₂₉×#102	—	2	2	no	—
102	C₂₉×#102	—	2	2	no	—
103	C₂₉×#102	—	2	2	no	—
104	C₂₉×#95	—	2	1	no	—
105	C₂₉×#95	—	2	1	no	—
106	C₂₉×#95	—	2	1	no	—
107	C₂₉×#95	—	2	1	no	—
108	C₂₉×#95	—	2	1	no	—
109	C₂₉×#95	—	2	1	no	—
110	C₂₉×#95	—	2	1	no	—
111	C₂₉×#95	—	2	1	no	—
112	C₂₉×#95	—	2	1	no	—
113	C₂₉×#95	—	2	1	no	—
114	C₂₉×#95	—	2	1	no	—
115	C₂₉×#95	—	2	1	no	—
116	C₂₉×#95	D₄	1	1	yes	characteristic
117	C₂₉×#95	D₄	1	1	yes	characteristic
118	C₂₉×#95	D₄	1	1	yes	characteristic
119	C₂₉×#95	D₄	1	1	yes	characteristic
120	C₂⁴×C₂₉	—	2	1	no	—
121	C₂×Q₈×C₂₉	—	2	1	no	—
122	C₂×Q₈×C₂₉	—	2	1	no	—
123	C₂×Q₈×C₂₉	—	2	1	no	—
124	C₂×Q₈×C₂₉	—	2	1	no	—
125	C₂×Q₈×C₂₉	—	2	1	no	—
126	C₂×Q₈×C₂₉	—	2	1	no	—
127	C₂×D₄×C₂₉	—	2	1	no	—
128	C₂×D₄×C₂₉	—	2	1	no	—
129	C₂×D₄×C₂₉	—	2	1	no	—
130	C₂×D₄×C₂₉	#41	1	2	yes	—
131	C₂×D₄×C₂₉	#41	1	2	yes	—
132	C₂×D₄×C₂₉	#41	1	2	yes	—
133	C₂²×C₄×C₂₉	—	2	1	no	—
134	C₂²×C₄×C₂₉	—	2	1	no	—
135	C₂²×C₄×C₂₉	—	2	1	no	—
136	C₂²×C₄×C₂₉	—	2	4	no	—
137	C₂²×C₄×C₂₉	—	2	4	no	—
138	C₂²×C₄×C₂₉	—	2	4	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	—	8	1	no	—
144	C₂²×C₄×C₂₉	—	8	1	no	—
145	C₂²×C₄×C₂₉	—	8	1	no	—
146	C₂²×C₄×C₂₉	—	8	1	no	—
147	C₂²×C₄×C₂₉	—	8	1	no	—
148	C₂²×C₄×C₂₉	—	8	1	no	—
149	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
156	SD₁₆×C₂₉	—	4	4	no	—
157	C₂×C₈×C₂₉	—	2	1	no	—
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	—	2	1	no	—
168	C₂×C₈×C₂₉	—	2	1	no	—
169	C₄⋊C₄×C₂₉	—	2	1	no	—
170	C₄⋊C₄×C₂₉	—	2	1	no	—
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	—	8	1	no	—
179	C₄⋊C₄×C₂₉	—	8	1	no	—
180	C₄⋊C₄×C₂₉	—	8	1	no	—
181	C₄⋊C₄×C₂₉	#41	1	2	yes	—
182	C₄⋊C₄×C₂₉	#41	1	2	yes	—
183	C₄⋊C₄×C₂₉	#41	1	2	yes	—
184	C₂²⋊C₄×C₂₉	—	2	4	no	—
185	C₂²⋊C₄×C₂₉	—	2	4	no	—
186	C₂²⋊C₄×C₂₉	—	2	4	no	—
187	C₄²×C₂₉	—	2	1	no	—
188	C₄²×C₂₉	—	2	1	no	—
189	C₄²×C₂₉	—	2	1	no	—
190	C₄²×C₂₉	—	2	1	no	—
191	C₄²×C₂₉	—	2	1	no	—
192	C₄²×C₂₉	—	2	1	no	—
193	C₄²×C₂₉	—	8	1	no	—
194	C₄²×C₂₉	—	8	1	no	—
195	C₄²×C₂₉	—	8	1	no	—
196	#33090	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂³×C₂₉	—	2	2	no	—
198	C₂³×C₂₉	—	2	2	no	—
199	C₂³×C₂₉	—	2	2	no	—
200	C₂³×C₂₉	—	4	1	no	—
201	C₂³×C₂₉	—	4	1	no	—
202	C₂³×C₂₉	—	4	1	no	—
203	C₂³×C₂₉	—	4	1	no	—
204	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
205	Q₈×C₂₉	—	4	1	no	—
206	Q₈×C₂₉	—	4	1	no	—
207	Q₈×C₂₉	—	4	1	no	—
208	Q₈×C₂₉	—	4	1	no	—
209	D₄×C₂₉	—	2	2	no	—
210	D₄×C₂₉	—	2	2	no	—
211	D₄×C₂₉	—	2	2	no	—
212	D₄×C₂₉	#126	1	4	yes	—
213	C₂×C₄×C₂₉	—	2	1	no	—
214	C₂×C₄×C₂₉	—	2	1	no	—
215	C₂×C₄×C₂₉	—	2	1	no	—
216	C₂×C₄×C₂₉	—	2	1	no	—
217	C₂×C₄×C₂₉	—	2	1	no	—
218	C₂×C₄×C₂₉	—	2	1	no	—
219	C₂×C₄×C₂₉	—	2	2	no	—
220	C₂×C₄×C₂₉	—	2	2	no	—
221	C₂×C₄×C₂₉	—	2	2	no	—
222	C₂×C₄×C₂₉	—	2	1	no	—
223	C₂×C₄×C₂₉	—	2	1	no	—
224	C₂×C₄×C₂₉	—	2	1	no	—
225	C₂×C₄×C₂₉	—	2	1	no	—
226	C₂×C₄×C₂₉	—	2	1	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	1	no	—
234	C₂×C₄×C₂₉	—	4	1	no	—
235	C₂×C₄×C₂₉	—	4	1	no	—
236	C₂×C₄×C₂₉	—	4	1	no	—
237	C₂×C₄×C₂₉	—	4	1	no	—
238	C₂×C₄×C₂₉	—	4	1	no	—
239	C₂×C₄×C₂₉	—	4	1	no	—
240	C₂×C₄×C₂₉	—	4	1	no	—
241	C₂×C₄×C₂₉	—	4	1	no	—
242	C₂×C₄×C₂₉	—	4	1	no	—
243	C₂×C₄×C₂₉	—	4	1	no	—
244	C₂×C₄×C₂₉	—	4	1	no	—
245	C₂×C₄×C₂₉	—	4	1	no	—
246	C₂×C₄×C₂₉	—	4	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	—	8	4	no	—
253	C₂×C₄×C₂₉	—	8	4	no	—
254	C₂×C₄×C₂₉	—	8	4	no	—
255	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
256	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
257	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
260	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
261	C₈×C₂₉	—	4	1	no	—
262	C₈×C₂₉	—	4	1	no	—
263	C₈×C₂₉	—	4	1	no	—
264	C₈×C₂₉	—	4	1	no	—
265	#2645	C₂×C₂₉	1	1	yes	characteristic, complemented
266	#2275	C₂×C₂₉	1	1	yes	characteristic
267	#1928	C₂×C₂₉	1	1	yes	characteristic, complemented
268	#1928	C₂×C₂₉	1	1	yes	characteristic, complemented
269	#1927	C₂×C₂₉	1	1	yes	characteristic, complemented
270	#1921	C₂×C₂₉	1	1	yes	characteristic, complemented
271	#1920	C₂×C₂₉	1	1	yes	characteristic, complemented
272	#1918	C₂×C₂₉	1	1	yes	characteristic, complemented
273	#1877	C₂×C₂₉	1	1	yes	characteristic
274	#1877	C₂×C₂₉	1	1	yes	characteristic
275	#1877	C₂×C₂₉	1	1	yes	characteristic
276	#1864	C₂×C₂₉	1	1	yes	characteristic
277	#1862	C₂×C₂₉	1	1	yes	characteristic
278	#1862	C₂×C₂₉	1	1	yes	characteristic
279	#1840	C₂×C₂₉	1	1	yes	characteristic, complemented
280	C₂²×C₂₉	—	2	4	no	—
281	C₂²×C₂₉	—	4	2	no	—
282	C₂²×C₂₉	—	4	2	no	—
283	C₂²×C₂₉	—	4	2	no	—
284	C₂²×C₂₉	—	4	2	no	—
285	C₂²×C₂₉	—	4	2	no	—
286	C₂²×C₂₉	—	4	2	no	—
287	C₂²×C₂₉	#525	1	1	yes	characteristic
288	C₂²×C₂₉	#525	1	1	yes	characteristic
289	C₂²×C₂₉	#525	1	1	yes	characteristic
290	C₂²×C₂₉	#576	1	1	yes	characteristic
291	C₂²×C₂₉	#577	1	1	yes	characteristic
292	C₂²×C₂₉	#577	1	1	yes	characteristic
293	C₂²×C₂₉	#578	1	1	yes	characteristic
294	C₄×C₂₉	—	4	1	no	—
295	C₄×C₂₉	—	4	1	no	—
296	C₄×C₂₉	—	4	2	no	—
297	C₄×C₂₉	—	4	2	no	—
298	C₄×C₂₉	—	4	1	no	—
299	C₄×C₂₉	—	4	1	no	—
300	C₄×C₂₉	—	4	1	no	—
301	C₄×C₂₉	—	4	2	no	—
302	C₄×C₂₉	—	4	1	no	—
303	C₄×C₂₉	—	8	1	no	—
304	C₄×C₂₉	—	8	1	no	—
305	C₄×C₂₉	—	8	1	no	—
306	C₄×C₂₉	—	8	1	no	—
307	C₄×C₂₉	C₂×#126	1	1	yes	characteristic
308	C₄×C₂₉	#529	1	1	yes	characteristic
309	C₄×C₂₉	#529	1	1	yes	characteristic
310	C₄×C₂₉	#529	1	1	yes	characteristic
311	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
312	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
313	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
314	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
315	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
316	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
317	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
318	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
319	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
320	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
321	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
322	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
323	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
324	#401	—	2	1	no	—
325	#400	—	2	1	no	—
326	#400	—	2	1	no	—
327	#400	—	2	1	no	—
328	#391	C₂²×C₂₉	1	1	yes	characteristic
329	#391	C₂²×C₂₉	1	1	yes	characteristic
330	#391	C₂²×C₂₉	1	1	yes	characteristic
331	#389	C₂²×C₂₉	1	1	yes	characteristic
332	#389	C₂²×C₂₉	1	1	yes	characteristic
333	#389	C₂²×C₂₉	1	1	yes	characteristic
334	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
335	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
336	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
337	C₄×C₂²⋊C₄	—	2	1	no	—
338	C₄×C₂²⋊C₄	—	2	1	no	—
339	C₄×C₂²⋊C₄	—	2	1	no	—
340	#376	C₂²×C₂₉	1	1	yes	characteristic
341	C₂×#95	—	2	1	no	—
342	#340	C₂²×C₂₉	1	1	yes	characteristic
343	#340	C₂²×C₂₉	1	1	yes	characteristic
344	#340	C₂²×C₂₉	1	1	yes	characteristic
345	#340	C₂²×C₂₉	1	1	yes	characteristic
346	#340	C₂²×C₂₉	1	1	yes	characteristic
347	#340	C₂²×C₂₉	1	1	yes	characteristic
348	#336	C₂²×C₂₉	1	1	yes	characteristic
349	#336	C₂²×C₂₉	1	1	yes	characteristic
350	#336	C₂²×C₂₉	1	1	yes	characteristic
351	#336	C₂²×C₂₉	1	1	yes	characteristic
352	#336	C₂²×C₂₉	1	1	yes	characteristic
353	#336	C₂²×C₂₉	1	1	yes	characteristic
354	C₂×C₂₉	—	4	4	no	—
355	C₂×C₂₉	#2852	1	1	yes	characteristic
356	C₂×C₂₉	#3118	1	1	yes	characteristic
357	C₂×C₂₉	#3118	1	1	yes	characteristic
358	C₂×C₂₉	#3120	1	1	yes	characteristic
359	C₂×C₂₉	#3120	1	1	yes	characteristic
360	C₂×C₂₉	#3123	1	1	yes	characteristic
361	C₂×C₂₉	#3124	1	1	yes	characteristic
362	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
363	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
364	C₂³×C₄	—	2	1	no	—
365	C₂³×C₄	—	2	1	no	—
366	C₂³×C₄	—	2	1	no	—
367	C₂×SD₁₆	—	2	2	no	—
368	C₂×SD₁₆	—	2	2	no	—
369	C₂×SD₁₆	—	2	2	no	—
370	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
373	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
374	C₄×D₄	—	2	2	no	—
375	C₄×D₄	—	2	2	no	—
376	C₄×D₄	—	2	2	no	—
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	—	2	2	no	—
379	C₄×D₄	—	2	2	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₄²	—	2	1	no	—
393	C₂×C₄²	—	2	1	no	—
394	C₂×C₄²	—	2	1	no	—
395	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
396	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
397	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
398	#107	—	2	2	no	—
399	#107	—	2	2	no	—
400	#106	—	2	2	no	—
401	#103	—	2	2	no	—
402	#103	—	2	2	no	—
403	#103	—	2	2	no	—
404	#102	—	2	2	no	—
405	#102	—	2	2	no	—
406	#102	—	2	2	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	#95	—	2	1	no	—
410	#95	—	2	1	no	—
411	#95	—	2	1	no	—
412	#95	—	2	1	no	—
413	#95	—	2	1	no	—
414	#95	—	2	1	no	—
415	#95	—	2	1	no	—
416	#95	—	2	1	no	—
417	#95	—	2	1	no	—
418	#95	—	2	1	no	—
419	#95	D₄×C₂₉	1	1	yes	characteristic
420	#95	D₄×C₂₉	1	1	yes	characteristic
421	#95	D₄×C₂₉	1	1	yes	characteristic
422	#95	D₄×C₂₉	1	1	yes	characteristic
423	C₂₉	#33090	1	1	yes	characteristic, direct product factor, Sylow
424	C₂⁴	—	2	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	#41×C₂₉	1	2	yes	—
435	C₂×D₄	#41×C₂₉	1	2	yes	—
436	C₂×D₄	#41×C₂₉	1	2	yes	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	8	1	no	—
448	C₂²×C₄	—	8	1	no	—
449	C₂²×C₄	—	8	1	no	—
450	C₂²×C₄	—	8	1	no	—
451	C₂²×C₄	—	8	1	no	—
452	C₂²×C₄	—	8	1	no	—
453	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
459	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
460	SD₁₆	—	4	4	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	8	1	no	—
483	C₄⋊C₄	—	8	1	no	—
484	C₄⋊C₄	—	8	1	no	—
485	C₄⋊C₄	#41×C₂₉	1	2	yes	—
486	C₄⋊C₄	#41×C₂₉	1	2	yes	—
487	C₄⋊C₄	#41×C₂₉	1	2	yes	—
488	C₂²⋊C₄	—	2	4	no	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	8	1	no	—
498	C₄²	—	8	1	no	—
499	C₄²	—	8	1	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	4	1	no	—
504	C₂³	—	4	1	no	—
505	C₂³	—	4	1	no	—
506	C₂³	—	4	1	no	—
507	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
508	Q₈	—	4	1	no	—
509	Q₈	—	4	1	no	—
510	Q₈	—	4	1	no	—
511	Q₈	—	4	1	no	—
512	D₄	—	2	2	no	—
513	D₄	—	2	2	no	—
514	D₄	—	2	2	no	—
515	D₄	C₂₉×#126	1	4	yes	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	8	4	no	—
556	C₂×C₄	—	8	4	no	—
557	C₂×C₄	—	8	4	no	—
558	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
559	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
560	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
561	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
562	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
563	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
564	C₈	—	4	1	no	—
565	C₈	—	4	1	no	—
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₂²	—	2	4	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	4	2	no	—
575	C₂²	C₂₉×#525	1	1	yes	characteristic
576	C₂²	C₂₉×#525	1	1	yes	characteristic
577	C₂²	C₂₉×#525	1	1	yes	characteristic
578	C₂²	C₂₉×#576	1	1	yes	characteristic
579	C₂²	C₂₉×#577	1	1	yes	characteristic
580	C₂²	C₂₉×#577	1	1	yes	characteristic
581	C₂²	C₂₉×#578	1	1	yes	characteristic
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	2	no	—
585	C₄	—	4	2	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	2	no	—
590	C₄	—	4	1	no	—
591	C₄	—	8	1	no	—
592	C₄	—	8	1	no	—
593	C₄	—	8	1	no	—
594	C₄	—	8	1	no	—
595	C₄	C₂×C₂₉×#126	1	1	yes	characteristic
596	C₄	C₂₉×#529	1	1	yes	characteristic
597	C₄	C₂₉×#529	1	1	yes	characteristic
598	C₄	C₂₉×#529	1	1	yes	characteristic
599	C₂	—	4	4	no	—
600	C₂	C₂₉×#2852	1	1	yes	characteristic
601	C₂	C₂₉×#3118	1	1	yes	characteristic
602	C₂	C₂₉×#3118	1	1	yes	characteristic
603	C₂	C₂₉×#3120	1	1	yes	characteristic
604	C₂	C₂₉×#3120	1	1	yes	characteristic
605	C₂	C₂₉×#3123	1	1	yes	characteristic
606	C₂	C₂₉×#3124	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	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂₉×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#2645	C₂	semidirect
3. C₂₉×#1928	C₂	semidirect
4. C₂₉×#1928	C₂	semidirect
5. C₂₉×#1927	C₂	semidirect
6. C₂₉×#1921	C₂	semidirect
7. C₂₉×#1920	C₂	semidirect
8. C₂₉×#1918	C₂	semidirect
15. C₂₉×#1840	C₂	semidirect
196. #33090	C₂₉	direct (N × H)
265. #2645	C₂×C₂₉	semidirect
267. #1928	C₂×C₂₉	semidirect
268. #1928	C₂×C₂₉	semidirect
269. #1927	C₂×C₂₉	semidirect
270. #1921	C₂×C₂₉	semidirect
271. #1920	C₂×C₂₉	semidirect
272. #1918	C₂×C₂₉	semidirect
279. #1840	C₂×C₂₉	semidirect
423. C₂₉	#33090	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×#2645	2
C₂₉×#2275	2
C₂₉×#1928	2
C₂₉×#1927	2
C₂₉×#1921	2
C₂₉×#1920	2
C₂₉×#1918	2
C₂₉×#1877	2
C₂₉×#1864	2
C₂₉×#1862	2
C₂₉×#1840	2
#33090	29

Subgroups — C29×#33090 #20327990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#33090 #20327990