Subgroups — C₂₉×#22222 #20317122

Order 7424.

802 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#488	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₂₉×#124	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1991	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1958	C₂	1	1	yes	maximal, characteristic
6	C₂₉×#1928	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1927	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1926	C₂	1	1	yes	maximal, characteristic
9	C₂₉×#1925	C₂	1	1	yes	maximal, characteristic
10	C₂₉×#1865	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1864	C₂	1	1	yes	maximal, characteristic
12	C₂₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1862	C₂	1	1	yes	maximal, characteristic
14	C₂₉×#1846	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1744	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×#125	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
20	C₂₉×#488	C₄	1	8	yes	complemented
21	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
24	C₂×C₂₉×#106	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×#103	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
35	C₂₉×#391	C₂²	1	1	yes	characteristic
36	C₂₉×#390	C₂²	1	1	yes	characteristic
37	C₂₉×#389	C₂²	1	1	yes	characteristic
38	C₂₉×#389	C₂²	1	1	yes	characteristic
39	C₂₉×#388	—	2	1	no	—
40	C₂₉×#388	—	2	1	no	—
41	C₂₉×#387	—	2	1	no	—
42	C₂₉×#387	—	2	1	no	—
43	C₂₉×#382	C₂²	1	1	yes	characteristic
44	C₂₉×#382	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₄×C₂₉	—	2	1	no	—
46	C₄×C₄⋊C₄×C₂₉	—	2	1	no	—
47	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
49	C₄×C₂²⋊C₄×C₂₉	—	2	1	no	—
50	C₄×C₂²⋊C₄×C₂₉	—	2	1	no	—
51	C₄³×C₂₉	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×#336	C₂²	1	1	yes	characteristic
57	C₂₉×#336	C₂²	1	1	yes	characteristic
58	C₂₉×#336	C₂²	1	1	yes	characteristic
59	C₂₉×#336	C₂²	1	1	yes	characteristic
60	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₂₉	—	2	1	no	—
63	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
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	C₂₉×#125	—	2	2	no	—
68	C₂₉×#125	C₂×C₄	1	4	yes	complemented
69	C₂₉×#124	—	2	2	no	—
70	C₂₉×#124	C₂×C₄	1	4	yes	—
71	C₄×Q₈×C₂₉	—	4	1	no	—
72	C₄×Q₈×C₂₉	—	4	1	no	—
73	C₄×D₄×C₂₉	—	4	1	no	—
74	C₄×D₄×C₂₉	—	4	1	no	—
75	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₂₉	—	2	1	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×C₂²⋊C₄×C₂₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
91	C₂×C₄²×C₂₉	—	2	1	no	—
92	C₂×C₄²×C₂₉	—	2	1	no	—
93	C₂×C₄²×C₂₉	—	2	1	no	—
94	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
101	C₂₉×#107	—	4	1	no	—
102	C₂₉×#107	—	4	1	no	—
103	C₂₉×#106	—	4	1	no	—
104	C₂₉×#106	—	4	1	no	—
105	C₂₉×#103	—	4	1	no	—
106	C₂₉×#103	—	4	1	no	—
107	C₂₉×#103	C₂×C₄	1	4	yes	complemented
108	C₂₉×#103	C₂×C₄	1	4	yes	complemented
109	C₂₉×#102	—	4	1	no	—
110	C₂₉×#102	—	4	1	no	—
111	C₂₉×#102	C₂×C₄	1	4	yes	—
112	C₂₉×#102	C₂×C₄	1	4	yes	—
113	C₄×C₈×C₂₉	—	2	2	no	—
114	C₄×C₈×C₂₉	C₂×C₄	1	4	yes	complemented
115	C₂₉×#95	—	2	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	—	2	1	no	—
124	C₂₉×#95	—	2	1	no	—
125	C₂⁴×C₂₉	—	2	1	no	—
126	C₂×Q₈×C₂₉	—	2	1	no	—
127	C₂×Q₈×C₂₉	—	2	1	no	—
128	C₂×Q₈×C₂₉	—	2	1	no	—
129	C₂×Q₈×C₂₉	—	2	1	no	—
130	C₂×Q₈×C₂₉	—	2	1	no	—
131	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
132	C₂×D₄×C₂₉	—	2	1	no	—
133	C₂×D₄×C₂₉	—	2	1	no	—
134	C₂×D₄×C₂₉	—	2	1	no	—
135	C₂×D₄×C₂₉	—	2	1	no	—
136	C₂×D₄×C₂₉	—	2	1	no	—
137	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
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	—	4	2	no	—
146	C₂²×C₄×C₂₉	—	4	2	no	—
147	C₂²×C₄×C₂₉	—	4	2	no	—
148	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
155	C₂×C₈×C₂₉	—	2	1	no	—
156	C₂×C₈×C₂₉	—	2	1	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	C₂²×C₄	1	2	yes	—
166	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
167	C₄⋊C₄×C₂₉	—	2	4	no	—
168	C₄⋊C₄×C₂₉	—	2	4	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	—	2	1	no	—
179	C₄⋊C₄×C₂₉	—	4	2	no	—
180	C₄⋊C₄×C₂₉	—	4	2	no	—
181	C₄⋊C₄×C₂₉	—	4	2	no	—
182	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
183	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
184	C₂²⋊C₄×C₂₉	—	2	4	no	—
185	C₂²⋊C₄×C₂₉	—	2	4	no	—
186	C₂²⋊C₄×C₂₉	—	4	2	no	—
187	C₂²⋊C₄×C₂₉	—	4	2	no	—
188	C₂²⋊C₄×C₂₉	—	4	2	no	—
189	C₄²×C₂₉	—	2	2	no	—
190	C₄²×C₂₉	—	2	2	no	—
191	C₄²×C₂₉	—	2	1	no	—
192	C₄²×C₂₉	—	2	1	no	—
193	C₄²×C₂₉	—	2	1	no	—
194	C₄²×C₂₉	—	2	1	no	—
195	C₄²×C₂₉	—	4	1	no	—
196	C₄²×C₂₉	—	4	1	no	—
197	C₄²×C₂₉	—	4	2	no	—
198	C₄²×C₂₉	—	4	2	no	—
199	C₄²×C₂₉	—	4	2	no	—
200	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
201	C₄²×C₂₉	#41	1	2	yes	—
202	#22222	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂³×C₂₉	—	2	2	no	—
204	C₂³×C₂₉	—	4	1	no	—
205	C₂³×C₂₉	—	4	1	no	—
206	C₂³×C₂₉	—	4	1	no	—
207	C₂³×C₂₉	—	4	1	no	—
208	C₂³×C₂₉	—	4	1	no	—
209	C₂³×C₂₉	—	4	1	no	—
210	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
211	Q₈×C₂₉	—	2	2	no	—
212	Q₈×C₂₉	—	2	2	no	—
213	Q₈×C₂₉	—	4	1	no	—
214	Q₈×C₂₉	—	4	1	no	—
215	D₄×C₂₉	—	2	2	no	—
216	D₄×C₂₉	—	2	2	no	—
217	D₄×C₂₉	—	4	1	no	—
218	D₄×C₂₉	—	4	1	no	—
219	C₂×C₄×C₂₉	—	2	1	no	—
220	C₂×C₄×C₂₉	—	2	1	no	—
221	C₂×C₄×C₂₉	—	2	1	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	2	no	—
228	C₂×C₄×C₂₉	—	2	2	no	—
229	C₂×C₄×C₂₉	—	2	2	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	—	2	1	no	—
235	C₂×C₄×C₂₉	—	2	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	—	4	1	no	—
253	C₂×C₄×C₂₉	—	4	1	no	—
254	C₂×C₄×C₂₉	—	8	4	no	—
255	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
256	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
257	C₂×C₄×C₂₉	#135	1	2	yes	—
258	C₂×C₄×C₂₉	#135	1	2	yes	—
259	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
260	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
261	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
262	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
263	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
264	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
265	C₈×C₂₉	—	2	2	no	—
266	C₈×C₂₉	—	2	2	no	—
267	C₈×C₂₉	—	4	1	no	—
268	C₈×C₂₉	—	4	1	no	—
269	C₂×#488	C₂×C₂₉	1	1	yes	characteristic
270	C₄×#125	C₂×C₂₉	1	1	yes	characteristic, complemented
271	C₄×#124	C₂×C₂₉	1	1	yes	characteristic
272	#1991	C₂×C₂₉	1	1	yes	characteristic, complemented
273	#1958	C₂×C₂₉	1	1	yes	characteristic
274	#1928	C₂×C₂₉	1	1	yes	characteristic, complemented
275	#1927	C₂×C₂₉	1	1	yes	characteristic, complemented
276	#1926	C₂×C₂₉	1	1	yes	characteristic
277	#1925	C₂×C₂₉	1	1	yes	characteristic
278	#1865	C₂×C₂₉	1	1	yes	characteristic, complemented
279	#1864	C₂×C₂₉	1	1	yes	characteristic
280	#1863	C₂×C₂₉	1	1	yes	characteristic, complemented
281	#1862	C₂×C₂₉	1	1	yes	characteristic
282	#1846	C₂×C₂₉	1	1	yes	characteristic, complemented
283	#1744	C₂×C₂₉	1	1	yes	characteristic, complemented
284	C₂²×C₂₉	—	4	2	no	—
285	C₂²×C₂₉	—	4	2	no	—
286	C₂²×C₂₉	—	4	2	no	—
287	C₂²×C₂₉	—	8	1	no	—
288	C₂²×C₂₉	—	8	1	no	—
289	C₂²×C₂₉	—	8	1	no	—
290	C₂²×C₂₉	—	8	1	no	—
291	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
292	C₂²×C₂₉	#535	1	1	yes	characteristic
293	C₂²×C₂₉	#536	1	1	yes	characteristic
294	C₂²×C₂₉	C₂×#135	1	1	yes	characteristic
295	C₂²×C₂₉	C₂×#135	1	1	yes	characteristic
296	C₂²×C₂₉	#575	1	1	yes	characteristic
297	C₂²×C₂₉	#575	1	1	yes	characteristic
298	C₄×C₂₉	—	2	2	no	—
299	C₄×C₂₉	—	2	2	no	—
300	C₄×C₂₉	—	2	2	no	—
301	C₄×C₂₉	—	2	2	no	—
302	C₄×C₂₉	—	4	2	no	—
303	C₄×C₂₉	—	4	2	no	—
304	C₄×C₂₉	—	4	2	no	—
305	C₄×C₂₉	—	4	1	no	—
306	C₄×C₂₉	—	4	1	no	—
307	C₄×C₂₉	—	8	1	no	—
308	C₄×C₂₉	—	8	1	no	—
309	C₄×C₂₉	—	8	1	no	—
310	C₄×C₂₉	—	8	1	no	—
311	C₄×C₂₉	#520	1	1	yes	characteristic
312	C₄×C₂₉	#520	1	1	yes	characteristic
313	C₄×C₂₉	#542	1	1	yes	characteristic
314	C₄×C₂₉	#542	1	1	yes	characteristic
315	C₂×#125	C₂²×C₂₉	1	1	yes	characteristic
316	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
317	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
318	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
319	#488	C₄×C₂₉	1	8	yes	complemented
320	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
321	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
322	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
323	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
324	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
325	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
326	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
327	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
328	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
329	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
330	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
331	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
332	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
333	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
334	#391	C₂²×C₂₉	1	1	yes	characteristic
335	#390	C₂²×C₂₉	1	1	yes	characteristic
336	#389	C₂²×C₂₉	1	1	yes	characteristic
337	#389	C₂²×C₂₉	1	1	yes	characteristic
338	#388	—	2	1	no	—
339	#388	—	2	1	no	—
340	#387	—	2	1	no	—
341	#387	—	2	1	no	—
342	#382	C₂²×C₂₉	1	1	yes	characteristic
343	#382	C₂²×C₂₉	1	1	yes	characteristic
344	C₄×C₄⋊C₄	—	2	1	no	—
345	C₄×C₄⋊C₄	—	2	1	no	—
346	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
347	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
348	C₄×C₂²⋊C₄	—	2	1	no	—
349	C₄×C₂²⋊C₄	—	2	1	no	—
350	C₄³	C₂²×C₂₉	1	1	yes	characteristic
351	#340	C₂²×C₂₉	1	1	yes	characteristic
352	#340	C₂²×C₂₉	1	1	yes	characteristic
353	#340	C₂²×C₂₉	1	1	yes	characteristic
354	#340	C₂²×C₂₉	1	1	yes	characteristic
355	#336	C₂²×C₂₉	1	1	yes	characteristic
356	#336	C₂²×C₂₉	1	1	yes	characteristic
357	#336	C₂²×C₂₉	1	1	yes	characteristic
358	#336	C₂²×C₂₉	1	1	yes	characteristic
359	C₂×C₂₉	—	8	2	no	—
360	C₂×C₂₉	#2326	1	1	yes	characteristic
361	C₂×C₂₉	C₄×#135	1	1	yes	characteristic
362	C₂×C₂₉	#2943	1	1	yes	characteristic
363	C₂×C₂₉	#3211	1	1	yes	characteristic
364	C₂×C₂₉	#3212	1	1	yes	characteristic
365	C₂×C₂₉	#3232	1	1	yes	characteristic
366	C₂×C₂₉	#3233	1	1	yes	characteristic
367	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
368	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
369	C₂³×C₄	—	2	1	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	#125	—	2	2	no	—
375	#125	C₂×C₄×C₂₉	1	4	yes	complemented
376	#124	—	2	2	no	—
377	#124	C₂×C₄×C₂₉	1	4	yes	—
378	C₄×Q₈	—	4	1	no	—
379	C₄×Q₈	—	4	1	no	—
380	C₄×D₄	—	4	1	no	—
381	C₄×D₄	—	4	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₂²⋊C₄	—	2	1	no	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₂²⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	—	2	1	no	—
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	—	2	1	no	—
401	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
402	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
403	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
404	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
405	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
407	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
408	#107	—	4	1	no	—
409	#107	—	4	1	no	—
410	#106	—	4	1	no	—
411	#106	—	4	1	no	—
412	#103	—	4	1	no	—
413	#103	—	4	1	no	—
414	#103	C₂×C₄×C₂₉	1	4	yes	complemented
415	#103	C₂×C₄×C₂₉	1	4	yes	complemented
416	#102	—	4	1	no	—
417	#102	—	4	1	no	—
418	#102	C₂×C₄×C₂₉	1	4	yes	—
419	#102	C₂×C₄×C₂₉	1	4	yes	—
420	C₄×C₈	—	2	2	no	—
421	C₄×C₈	C₂×C₄×C₂₉	1	4	yes	complemented
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	#95	—	2	1	no	—
425	#95	—	2	1	no	—
426	#95	—	2	1	no	—
427	#95	—	2	1	no	—
428	#95	—	2	1	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	—	2	1	no	—
432	C₂₉	#22222	1	1	yes	characteristic, direct product factor, Sylow
433	C₂⁴	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	4	2	no	—
454	C₂²×C₄	—	4	2	no	—
455	C₂²×C₄	—	4	2	no	—
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	C₂×D₄×C₂₉	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
462	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
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	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
474	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	2	4	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	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	4	2	no	—
488	C₄⋊C₄	—	4	2	no	—
489	C₄⋊C₄	—	4	2	no	—
490	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
491	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	4	2	no	—
495	C₂²⋊C₄	—	4	2	no	—
496	C₂²⋊C₄	—	4	2	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	4	1	no	—
504	C₄²	—	4	1	no	—
505	C₄²	—	4	2	no	—
506	C₄²	—	4	2	no	—
507	C₄²	—	4	2	no	—
508	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
509	C₄²	#41×C₂₉	1	2	yes	—
510	C₂³	—	2	2	no	—
511	C₂³	—	4	1	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	4	1	no	—
514	C₂³	—	4	1	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	1	no	—
517	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
518	Q₈	—	2	2	no	—
519	Q₈	—	2	2	no	—
520	Q₈	—	4	1	no	—
521	Q₈	—	4	1	no	—
522	D₄	—	2	2	no	—
523	D₄	—	2	2	no	—
524	D₄	—	4	1	no	—
525	D₄	—	4	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	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	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	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	8	4	no	—
562	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
563	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
564	C₂×C₄	C₂₉×#135	1	2	yes	—
565	C₂×C₄	C₂₉×#135	1	2	yes	—
566	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
567	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
568	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
569	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
570	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
571	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
572	C₈	—	2	2	no	—
573	C₈	—	2	2	no	—
574	C₈	—	4	1	no	—
575	C₈	—	4	1	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	8	1	no	—
580	C₂²	—	8	1	no	—
581	C₂²	—	8	1	no	—
582	C₂²	—	8	1	no	—
583	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
584	C₂²	C₂₉×#535	1	1	yes	characteristic
585	C₂²	C₂₉×#536	1	1	yes	characteristic
586	C₂²	C₂×C₂₉×#135	1	1	yes	characteristic
587	C₂²	C₂×C₂₉×#135	1	1	yes	characteristic
588	C₂²	C₂₉×#575	1	1	yes	characteristic
589	C₂²	C₂₉×#575	1	1	yes	characteristic
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	4	2	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	2	no	—
599	C₄	—	8	1	no	—
600	C₄	—	8	1	no	—
601	C₄	—	8	1	no	—
602	C₄	—	8	1	no	—
603	C₄	C₂₉×#520	1	1	yes	characteristic
604	C₄	C₂₉×#520	1	1	yes	characteristic
605	C₄	C₂₉×#542	1	1	yes	characteristic
606	C₄	C₂₉×#542	1	1	yes	characteristic
607	C₂	—	8	2	no	—
608	C₂	C₂₉×#2326	1	1	yes	characteristic
609	C₂	C₄×C₂₉×#135	1	1	yes	characteristic
610	C₂	C₂₉×#2943	1	1	yes	characteristic
611	C₂	C₂₉×#3211	1	1	yes	characteristic
612	C₂	C₂₉×#3212	1	1	yes	characteristic
613	C₂	C₂₉×#3232	1	1	yes	characteristic
614	C₂	C₂₉×#3233	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	C₂²×D₄×C₂₉	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₄³×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₂₉×#125	C₂	semidirect
4. C₂₉×#1991	C₂	semidirect
6. C₂₉×#1928	C₂	semidirect
7. C₂₉×#1927	C₂	semidirect
10. C₂₉×#1865	C₂	semidirect
12. C₂₉×#1863	C₂	semidirect
14. C₂₉×#1846	C₂	semidirect
15. C₂₉×#1744	C₂	semidirect
20. C₂₉×#488	C₄	semidirect
68. C₂₉×#125	C₂×C₄	semidirect
107. C₂₉×#103	C₂×C₄	semidirect
108. C₂₉×#103	C₂×C₄	semidirect
114. C₄×C₈×C₂₉	C₂×C₄	semidirect
202. #22222	C₂₉	direct (N × H)
270. C₄×#125	C₂×C₂₉	semidirect
272. #1991	C₂×C₂₉	semidirect
274. #1928	C₂×C₂₉	semidirect
275. #1927	C₂×C₂₉	semidirect
278. #1865	C₂×C₂₉	semidirect
280. #1863	C₂×C₂₉	semidirect
282. #1846	C₂×C₂₉	semidirect
283. #1744	C₂×C₂₉	semidirect
319. #488	C₄×C₂₉	semidirect
375. #125	C₂×C₄×C₂₉	semidirect
414. #103	C₂×C₄×C₂₉	semidirect
415. #103	C₂×C₄×C₂₉	semidirect
421. C₄×C₈	C₂×C₄×C₂₉	semidirect
432. C₂₉	#22222	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×#488	2
C₄×C₂₉×#125	2
C₄×C₂₉×#124	2
C₂₉×#1991	2
C₂₉×#1958	2
C₂₉×#1928	2
C₂₉×#1927	2
C₂₉×#1926	2
C₂₉×#1925	2
C₂₉×#1865	2
C₂₉×#1864	2
C₂₉×#1863	2
C₂₉×#1862	2
C₂₉×#1846	2
C₂₉×#1744	2
#22222	29

Subgroups — C29×#22222 #20317122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#22222 #20317122