Subgroups — C₂₉×#28872 #20323772

Order 7424.

660 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#2494	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2421	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2097	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2085	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2076	C₂	1	1	yes	maximal, characteristic
6	C₂₉×#2035	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#1943	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1933	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1920	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1894	C₂	1	1	yes	maximal, characteristic
11	C₂₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1835	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1809	C₂	1	1	yes	maximal, characteristic
14	C₂₉×#1763	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1753	C₂	1	1	yes	maximal, characteristic
16	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
20	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#106	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×#103	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
30	C₂₉×#401	—	2	1	no	—
31	C₂₉×#400	—	2	1	no	—
32	C₂₉×#397	—	2	1	no	—
33	C₂₉×#397	—	2	1	no	—
34	C₂₉×#391	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×#387	—	2	1	no	—
41	C₂₉×#387	—	2	1	no	—
42	C₂₉×#382	C₂²	1	1	yes	characteristic
43	C₂₉×#382	C₂²	1	1	yes	characteristic
44	C₂₉×#380	C₂²	1	1	yes	characteristic
45	C₂₉×#380	C₂²	1	1	yes	characteristic
46	C₂₉×#380	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊C₄×C₂₉	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×#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×#336	C₂²	1	1	yes	characteristic
58	C₂₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
61	C₂×M₁₆×C₂₉	—	2	2	no	—
62	C₂×M₁₆×C₂₉	—	2	2	no	—
63	C₂×M₁₆×C₂₉	—	4	1	no	—
64	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
68	C₂₉×C₂²⋊Q₈	—	2	2	no	—
69	C₂₉×C₂²⋊Q₈	—	4	1	no	—
70	C₄×Q₈×C₂₉	—	2	2	no	—
71	C₄×Q₈×C₂₉	—	4	1	no	—
72	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₂₉	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
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	C₂₉×#107	—	2	2	no	—
95	C₂₉×#107	—	4	1	no	—
96	C₂₉×#106	—	2	2	no	—
97	C₂₉×#106	—	4	1	no	—
98	C₂₉×#103	—	2	2	no	—
99	C₂₉×#103	—	2	2	no	—
100	C₂₉×#103	—	2	2	no	—
101	C₂₉×#103	—	2	2	no	—
102	C₂₉×C₂²⋊C₈	—	2	2	no	—
103	C₂₉×#97	—	4	1	no	—
104	C₄×C₈×C₂₉	—	2	2	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	—	2	1	no	—
117	C₂₉×#95	—	2	1	no	—
118	C₂₉×#95	D₄	1	1	yes	characteristic
119	C₂₉×#95	D₄	1	1	yes	characteristic
120	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
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	#41	1	2	yes	—
127	C₂²×C₄×C₂₉	—	2	1	no	—
128	C₂²×C₄×C₂₉	—	2	1	no	—
129	C₂²×C₄×C₂₉	—	2	1	no	—
130	C₂²×C₄×C₂₉	—	2	1	no	—
131	C₂²×C₄×C₂₉	—	2	1	no	—
132	C₂²×C₄×C₂₉	—	2	1	no	—
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	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	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
147	M₁₆×C₂₉	—	4	4	no	—
148	C₂×C₈×C₂₉	—	2	1	no	—
149	C₂×C₈×C₂₉	—	2	1	no	—
150	C₂×C₈×C₂₉	—	2	1	no	—
151	C₂×C₈×C₂₉	—	2	1	no	—
152	C₂×C₈×C₂₉	—	2	1	no	—
153	C₂×C₈×C₂₉	—	2	1	no	—
154	C₂×C₈×C₂₉	—	2	1	no	—
155	C₂×C₈×C₂₉	—	2	1	no	—
156	C₂×C₈×C₂₉	—	2	1	no	—
157	C₂×C₈×C₂₉	#41	1	2	yes	—
158	C₂×C₈×C₂₉	#41	1	2	yes	—
159	C₂×C₈×C₂₉	#41	1	2	yes	—
160	C₄⋊C₄×C₂₉	—	2	1	no	—
161	C₄⋊C₄×C₂₉	—	2	1	no	—
162	C₄⋊C₄×C₂₉	—	2	1	no	—
163	C₄⋊C₄×C₂₉	—	2	1	no	—
164	C₄⋊C₄×C₂₉	—	2	1	no	—
165	C₄⋊C₄×C₂₉	—	2	1	no	—
166	C₄⋊C₄×C₂₉	—	2	1	no	—
167	C₄⋊C₄×C₂₉	—	2	1	no	—
168	C₄⋊C₄×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	—	4	2	no	—
175	C₄⋊C₄×C₂₉	—	4	2	no	—
176	C₄⋊C₄×C₂₉	—	4	2	no	—
177	C₄⋊C₄×C₂₉	—	4	2	no	—
178	C₄⋊C₄×C₂₉	—	8	1	no	—
179	C₂²⋊C₄×C₂₉	—	4	1	no	—
180	C₂²⋊C₄×C₂₉	—	4	1	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	—	8	1	no	—
185	C₄²×C₂₉	—	2	1	no	—
186	C₄²×C₂₉	—	2	1	no	—
187	C₄²×C₂₉	—	2	1	no	—
188	C₄²×C₂₉	—	2	1	no	—
189	C₄²×C₂₉	—	4	2	no	—
190	C₄²×C₂₉	—	8	1	no	—
191	#28872	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂³×C₂₉	—	2	1	no	—
193	C₂³×C₂₉	—	2	1	no	—
194	C₂³×C₂₉	—	2	1	no	—
195	C₂³×C₂₉	—	2	1	no	—
196	C₂³×C₂₉	—	2	1	no	—
197	C₂³×C₂₉	—	2	1	no	—
198	C₂³×C₂₉	—	2	1	no	—
199	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
200	Q₈×C₂₉	—	2	2	no	—
201	Q₈×C₂₉	—	2	2	no	—
202	Q₈×C₂₉	—	4	1	no	—
203	Q₈×C₂₉	—	4	1	no	—
204	C₂×C₄×C₂₉	—	2	1	no	—
205	C₂×C₄×C₂₉	—	2	1	no	—
206	C₂×C₄×C₂₉	—	2	1	no	—
207	C₂×C₄×C₂₉	—	2	2	no	—
208	C₂×C₄×C₂₉	—	2	1	no	—
209	C₂×C₄×C₂₉	—	2	1	no	—
210	C₂×C₄×C₂₉	—	2	1	no	—
211	C₂×C₄×C₂₉	—	2	1	no	—
212	C₂×C₄×C₂₉	—	2	1	no	—
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	1	no	—
220	C₂×C₄×C₂₉	—	4	1	no	—
221	C₂×C₄×C₂₉	—	4	1	no	—
222	C₂×C₄×C₂₉	—	4	1	no	—
223	C₂×C₄×C₂₉	—	4	1	no	—
224	C₂×C₄×C₂₉	—	4	1	no	—
225	C₂×C₄×C₂₉	—	4	1	no	—
226	C₂×C₄×C₂₉	—	4	1	no	—
227	C₂×C₄×C₂₉	—	4	1	no	—
228	C₂×C₄×C₂₉	—	4	1	no	—
229	C₂×C₄×C₂₉	—	4	1	no	—
230	C₂×C₄×C₂₉	—	4	1	no	—
231	C₂×C₄×C₂₉	—	4	1	no	—
232	C₂×C₄×C₂₉	—	4	1	no	—
233	C₂×C₄×C₂₉	—	4	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	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
252	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
253	C₈×C₂₉	—	2	2	no	—
254	C₈×C₂₉	—	2	2	no	—
255	C₈×C₂₉	—	2	2	no	—
256	C₈×C₂₉	—	4	1	no	—
257	#2494	C₂×C₂₉	1	1	yes	characteristic
258	#2421	C₂×C₂₉	1	1	yes	characteristic
259	#2097	C₂×C₂₉	1	1	yes	characteristic, complemented
260	#2085	C₂×C₂₉	1	1	yes	characteristic, complemented
261	#2076	C₂×C₂₉	1	1	yes	characteristic
262	#2035	C₂×C₂₉	1	1	yes	characteristic
263	#1943	C₂×C₂₉	1	1	yes	characteristic, complemented
264	#1933	C₂×C₂₉	1	1	yes	characteristic, complemented
265	#1920	C₂×C₂₉	1	1	yes	characteristic, complemented
266	#1894	C₂×C₂₉	1	1	yes	characteristic
267	#1863	C₂×C₂₉	1	1	yes	characteristic, complemented
268	#1835	C₂×C₂₉	1	1	yes	characteristic, complemented
269	#1809	C₂×C₂₉	1	1	yes	characteristic
270	#1763	C₂×C₂₉	1	1	yes	characteristic, complemented
271	#1753	C₂×C₂₉	1	1	yes	characteristic
272	C₂²×C₂₉	—	4	1	no	—
273	C₂²×C₂₉	—	4	1	no	—
274	C₂²×C₂₉	—	4	1	no	—
275	C₂²×C₂₉	—	4	1	no	—
276	C₂²×C₂₉	—	4	1	no	—
277	C₂²×C₂₉	—	4	1	no	—
278	C₂²×C₂₉	—	4	1	no	—
279	C₂²×C₂₉	#532	1	1	yes	characteristic
280	C₂²×C₂₉	#546	1	1	yes	characteristic
281	C₂²×C₂₉	#547	1	1	yes	characteristic
282	C₂²×C₂₉	#575	1	1	yes	characteristic
283	C₂²×C₂₉	#575	1	1	yes	characteristic
284	C₂²×C₂₉	#577	1	1	yes	characteristic
285	C₂²×C₂₉	#578	1	1	yes	characteristic
286	C₄×C₂₉	—	4	1	no	—
287	C₄×C₂₉	—	4	1	no	—
288	C₄×C₂₉	—	4	1	no	—
289	C₄×C₂₉	—	4	2	no	—
290	C₄×C₂₉	—	4	1	no	—
291	C₄×C₂₉	—	4	1	no	—
292	C₄×C₂₉	—	8	1	no	—
293	C₄×C₂₉	—	8	1	no	—
294	C₄×C₂₉	—	8	1	no	—
295	C₄×C₂₉	—	8	1	no	—
296	C₄×C₂₉	—	8	1	no	—
297	C₄×C₂₉	—	8	1	no	—
298	C₄×C₂₉	—	8	1	no	—
299	C₄×C₂₉	#529	1	1	yes	characteristic
300	C₄×C₂₉	#539	1	1	yes	characteristic
301	C₄×C₂₉	#551	1	1	yes	characteristic
302	C₄×C₂₉	#552	1	1	yes	characteristic
303	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
304	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
305	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
306	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
307	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
308	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
309	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
310	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
311	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
312	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
313	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
314	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
315	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
316	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
317	#401	—	2	1	no	—
318	#400	—	2	1	no	—
319	#397	—	2	1	no	—
320	#397	—	2	1	no	—
321	#391	C₂²×C₂₉	1	1	yes	characteristic
322	#389	C₂²×C₂₉	1	1	yes	characteristic
323	#389	C₂²×C₂₉	1	1	yes	characteristic
324	#389	C₂²×C₂₉	1	1	yes	characteristic
325	#388	—	2	1	no	—
326	#388	—	2	1	no	—
327	#387	—	2	1	no	—
328	#387	—	2	1	no	—
329	#382	C₂²×C₂₉	1	1	yes	characteristic
330	#382	C₂²×C₂₉	1	1	yes	characteristic
331	#380	C₂²×C₂₉	1	1	yes	characteristic
332	#380	C₂²×C₂₉	1	1	yes	characteristic
333	#380	C₂²×C₂₉	1	1	yes	characteristic
334	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
335	C₄×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
336	#340	C₂²×C₂₉	1	1	yes	characteristic
337	#340	C₂²×C₂₉	1	1	yes	characteristic
338	#340	C₂²×C₂₉	1	1	yes	characteristic
339	#340	C₂²×C₂₉	1	1	yes	characteristic
340	#340	C₂²×C₂₉	1	1	yes	characteristic
341	#340	C₂²×C₂₉	1	1	yes	characteristic
342	#340	C₂²×C₂₉	1	1	yes	characteristic
343	#340	C₂²×C₂₉	1	1	yes	characteristic
344	#336	C₂²×C₂₉	1	1	yes	characteristic
345	#336	C₂²×C₂₉	1	1	yes	characteristic
346	C₂×C₂₉	—	8	1	no	—
347	C₂×C₂₉	#2553	1	1	yes	characteristic
348	C₂×C₂₉	#3178	1	1	yes	characteristic
349	C₂×C₂₉	#3183	1	1	yes	characteristic
350	C₂×C₂₉	#3326	1	1	yes	characteristic
351	C₂×C₂₉	#3327	1	1	yes	characteristic
352	C₂×C₂₉	#3349	1	1	yes	characteristic
353	C₂×C₂₉	#3350	1	1	yes	characteristic
354	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
355	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
356	C₂×M₁₆	—	2	2	no	—
357	C₂×M₁₆	—	2	2	no	—
358	C₂×M₁₆	—	4	1	no	—
359	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
360	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
361	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
362	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
363	C₂²⋊Q₈	—	2	2	no	—
364	C₂²⋊Q₈	—	4	1	no	—
365	C₄×Q₈	—	2	2	no	—
366	C₄×Q₈	—	4	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
379	C₂×C₂²⋊C₄	—	2	1	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
384	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
388	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
389	#107	—	2	2	no	—
390	#107	—	4	1	no	—
391	#106	—	2	2	no	—
392	#106	—	4	1	no	—
393	#103	—	2	2	no	—
394	#103	—	2	2	no	—
395	#103	—	2	2	no	—
396	#103	—	2	2	no	—
397	C₂²⋊C₈	—	2	2	no	—
398	#97	—	4	1	no	—
399	C₄×C₈	—	2	2	no	—
400	#95	—	2	1	no	—
401	#95	—	2	1	no	—
402	#95	—	2	1	no	—
403	#95	—	2	1	no	—
404	#95	—	2	1	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	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	D₄×C₂₉	1	1	yes	characteristic
414	#95	D₄×C₂₉	1	1	yes	characteristic
415	C₂₉	#28872	1	1	yes	characteristic, direct product factor, Sylow
416	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	2	1	no	—
421	C₂×Q₈	—	2	1	no	—
422	C₂×Q₈	#41×C₂₉	1	2	yes	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
442	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
443	M₁₆	—	4	4	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	#41×C₂₉	1	2	yes	—
454	C₂×C₈	#41×C₂₉	1	2	yes	—
455	C₂×C₈	#41×C₂₉	1	2	yes	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	4	2	no	—
471	C₄⋊C₄	—	4	2	no	—
472	C₄⋊C₄	—	4	2	no	—
473	C₄⋊C₄	—	4	2	no	—
474	C₄⋊C₄	—	8	1	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₂²⋊C₄	—	4	1	no	—
477	C₂²⋊C₄	—	4	2	no	—
478	C₂²⋊C₄	—	4	2	no	—
479	C₂²⋊C₄	—	4	2	no	—
480	C₂²⋊C₄	—	8	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	4	2	no	—
486	C₄²	—	8	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	—	2	1	no	—
489	C₂³	—	2	1	no	—
490	C₂³	—	2	1	no	—
491	C₂³	—	2	1	no	—
492	C₂³	—	2	1	no	—
493	C₂³	—	2	1	no	—
494	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
495	Q₈	—	2	2	no	—
496	Q₈	—	2	2	no	—
497	Q₈	—	4	1	no	—
498	Q₈	—	4	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	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	C₂×#41×C₂₉	1	1	yes	characteristic
543	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
544	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
545	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
546	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
547	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
548	C₈	—	2	2	no	—
549	C₈	—	2	2	no	—
550	C₈	—	2	2	no	—
551	C₈	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	C₂₉×#532	1	1	yes	characteristic
560	C₂²	C₂₉×#546	1	1	yes	characteristic
561	C₂²	C₂₉×#547	1	1	yes	characteristic
562	C₂²	C₂₉×#575	1	1	yes	characteristic
563	C₂²	C₂₉×#575	1	1	yes	characteristic
564	C₂²	C₂₉×#577	1	1	yes	characteristic
565	C₂²	C₂₉×#578	1	1	yes	characteristic
566	C₄	—	4	1	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	8	1	no	—
573	C₄	—	8	1	no	—
574	C₄	—	8	1	no	—
575	C₄	—	8	1	no	—
576	C₄	—	8	1	no	—
577	C₄	—	8	1	no	—
578	C₄	—	8	1	no	—
579	C₄	C₂₉×#529	1	1	yes	characteristic
580	C₄	C₂₉×#539	1	1	yes	characteristic
581	C₄	C₂₉×#551	1	1	yes	characteristic
582	C₄	C₂₉×#552	1	1	yes	characteristic
583	C₂	—	8	1	no	—
584	C₂	C₂₉×#2553	1	1	yes	characteristic
585	C₂	C₂₉×#3178	1	1	yes	characteristic
586	C₂	C₂₉×#3183	1	1	yes	characteristic
587	C₂	C₂₉×#3326	1	1	yes	characteristic
588	C₂	C₂₉×#3327	1	1	yes	characteristic
589	C₂	C₂₉×#3349	1	1	yes	characteristic
590	C₂	C₂₉×#3350	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂⁴×C₂₉	C₂×D₄
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
3. C₂₉×#2097	C₂	semidirect
4. C₂₉×#2085	C₂	semidirect
7. C₂₉×#1943	C₂	semidirect
8. C₂₉×#1933	C₂	semidirect
9. C₂₉×#1920	C₂	semidirect
11. C₂₉×#1863	C₂	semidirect
12. C₂₉×#1835	C₂	semidirect
14. C₂₉×#1763	C₂	semidirect
191. #28872	C₂₉	direct (N × H)
259. #2097	C₂×C₂₉	semidirect
260. #2085	C₂×C₂₉	semidirect
263. #1943	C₂×C₂₉	semidirect
264. #1933	C₂×C₂₉	semidirect
265. #1920	C₂×C₂₉	semidirect
267. #1863	C₂×C₂₉	semidirect
268. #1835	C₂×C₂₉	semidirect
270. #1763	C₂×C₂₉	semidirect
415. C₂₉	#28872	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×#2494	2
C₂₉×#2421	2
C₂₉×#2097	2
C₂₉×#2085	2
C₂₉×#2076	2
C₂₉×#2035	2
C₂₉×#1943	2
C₂₉×#1933	2
C₂₉×#1920	2
C₂₉×#1894	2
C₂₉×#1863	2
C₂₉×#1835	2
C₂₉×#1809	2
C₂₉×#1763	2
C₂₉×#1753	2
#28872	29

Subgroups — C29×#28872 #20323772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#28872 #20323772