Subgroups — C₂₉×#27066 #20321966

Order 7424.

762 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#2512	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2365	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#2096	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2055	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#2043	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2013	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#1968	C₂	1	1	yes	maximal, characteristic
8	C₂₉×#1927	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1926	C₂	1	1	yes	maximal, characteristic
10	C₂₉×#1919	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1916	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1880	C₂	1	1	yes	maximal, characteristic
13	C₂₉×#1880	C₂	1	1	yes	maximal, characteristic
14	C₂₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×#126	—	2	1	no	—
20	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
24	C₂×C₂₉×C₄⋊C₈	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×#103	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×#103	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	C₂₉×#397	—	2	1	no	—
35	C₂₉×#396	—	2	1	no	—
36	C₂₉×#391	C₂²	1	1	yes	characteristic
37	C₂₉×#391	C₂²	1	1	yes	characteristic
38	C₂₉×#390	C₂²	1	1	yes	characteristic
39	C₂₉×#390	C₂²	1	1	yes	characteristic
40	C₂₉×#390	C₂²	1	1	yes	characteristic
41	C₂₉×#389	—	2	1	no	—
42	C₂₉×#389	C₂²	1	1	yes	characteristic
43	C₂₉×#388	—	2	1	no	—
44	C₂₉×#387	—	2	1	no	—
45	C₂₉×#387	—	2	1	no	—
46	C₂₉×#384	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₂₉	—	2	1	no	—
48	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
49	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
50	C₄×C₄⋊C₄×C₂₉	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×#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×Q₈×C₂₉	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
62	C₂×SD₁₆×C₂₉	—	2	2	no	—
63	C₂×SD₁₆×C₂₉	—	2	2	no	—
64	C₂×SD₁₆×C₂₉	—	2	2	no	—
65	C₂×SD₁₆×C₂₉	—	4	1	no	—
66	C₂×SD₁₆×C₂₉	—	4	1	no	—
67	C₂×SD₁₆×C₂₉	—	4	1	no	—
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	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
72	C₂₉×C₄⋊Q₈	—	2	2	no	—
73	C₂₉×C₄⋊Q₈	—	2	2	no	—
74	C₂₉×#126	—	4	4	no	—
75	C₄×Q₈×C₂₉	—	2	2	no	—
76	C₄×Q₈×C₂₉	—	2	2	no	—
77	C₄×Q₈×C₂₉	—	4	1	no	—
78	C₄×Q₈×C₂₉	—	4	1	no	—
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	—	2	1	no	—
83	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×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	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
106	C₂₉×#106	—	2	2	no	—
107	C₂₉×#106	—	4	1	no	—
108	C₂₉×C₄⋊C₈	—	4	1	no	—
109	C₂₉×#103	—	2	2	no	—
110	C₂₉×#103	—	2	2	no	—
111	C₂₉×#103	—	2	2	no	—
112	C₂₉×#103	—	4	1	no	—
113	C₂₉×#103	—	4	1	no	—
114	C₂₉×#103	—	4	1	no	—
115	C₂₉×#102	—	2	2	no	—
116	C₂₉×#102	—	4	1	no	—
117	C₄×C₈×C₂₉	—	4	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	C₂₉×#95	D₄	1	1	yes	characteristic
126	C₂₉×#95	D₄	1	1	yes	characteristic
127	C₂⁴×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	—	2	1	no	—
132	C₂×Q₈×C₂₉	—	2	1	no	—
133	C₂×Q₈×C₂₉	—	2	1	no	—
134	C₂×Q₈×C₂₉	—	2	1	no	—
135	C₂×Q₈×C₂₉	—	2	1	no	—
136	C₂×Q₈×C₂₉	—	2	1	no	—
137	C₂×Q₈×C₂₉	—	2	1	no	—
138	C₂×Q₈×C₂₉	#41	1	2	yes	—
139	C₂×Q₈×C₂₉	#41	1	2	yes	—
140	C₂×D₄×C₂₉	—	2	1	no	—
141	C₂×D₄×C₂₉	—	2	1	no	—
142	C₂×D₄×C₂₉	—	2	1	no	—
143	C₂×D₄×C₂₉	—	2	1	no	—
144	C₂×D₄×C₂₉	—	2	1	no	—
145	C₂×D₄×C₂₉	—	2	1	no	—
146	C₂²×C₄×C₂₉	—	2	1	no	—
147	C₂²×C₄×C₂₉	—	2	1	no	—
148	C₂²×C₄×C₂₉	—	2	1	no	—
149	C₂²×C₄×C₂₉	—	2	1	no	—
150	C₂²×C₄×C₂₉	—	2	1	no	—
151	C₂²×C₄×C₂₉	—	2	1	no	—
152	C₂²×C₄×C₂₉	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
160	SD₁₆×C₂₉	—	4	4	no	—
161	SD₁₆×C₂₉	—	4	4	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	C₂×C₈×C₂₉	—	2	1	no	—
170	C₂×C₈×C₂₉	—	2	1	no	—
171	C₂×C₈×C₂₉	—	2	1	no	—
172	C₂×C₈×C₂₉	—	2	1	no	—
173	C₂×C₈×C₂₉	#41	1	2	yes	—
174	C₄⋊C₄×C₂₉	—	2	4	no	—
175	C₄⋊C₄×C₂₉	—	2	4	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	—	2	1	no	—
182	C₄⋊C₄×C₂₉	—	2	1	no	—
183	C₄⋊C₄×C₂₉	—	2	1	no	—
184	C₄⋊C₄×C₂₉	—	2	1	no	—
185	C₄⋊C₄×C₂₉	—	4	1	no	—
186	C₄⋊C₄×C₂₉	—	4	2	no	—
187	C₄⋊C₄×C₂₉	—	4	2	no	—
188	C₄⋊C₄×C₂₉	—	4	2	no	—
189	C₄⋊C₄×C₂₉	—	4	2	no	—
190	C₄⋊C₄×C₂₉	—	8	1	no	—
191	C₄⋊C₄×C₂₉	SD₁₆	1	4	yes	complemented
192	C₄⋊C₄×C₂₉	#41	1	2	yes	—
193	C₂²⋊C₄×C₂₉	—	4	2	no	—
194	C₂²⋊C₄×C₂₉	—	4	2	no	—
195	C₂²⋊C₄×C₂₉	—	4	2	no	—
196	C₂²⋊C₄×C₂₉	—	4	2	no	—
197	C₂²⋊C₄×C₂₉	—	8	1	no	—
198	C₂²⋊C₄×C₂₉	—	8	1	no	—
199	C₄²×C₂₉	—	2	1	no	—
200	C₄²×C₂₉	—	2	1	no	—
201	C₄²×C₂₉	—	2	1	no	—
202	C₄²×C₂₉	—	2	1	no	—
203	C₄²×C₂₉	—	2	1	no	—
204	C₄²×C₂₉	—	2	1	no	—
205	C₄²×C₂₉	—	4	2	no	—
206	C₄²×C₂₉	—	4	2	no	—
207	C₄²×C₂₉	—	4	2	no	—
208	C₄²×C₂₉	—	4	2	no	—
209	#27066	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂³×C₂₉	—	4	1	no	—
211	C₂³×C₂₉	—	4	1	no	—
212	C₂³×C₂₉	—	4	1	no	—
213	C₂³×C₂₉	—	4	1	no	—
214	C₂³×C₂₉	—	4	1	no	—
215	C₂³×C₂₉	—	4	1	no	—
216	C₂³×C₂₉	—	4	1	no	—
217	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
218	Q₈×C₂₉	—	2	2	no	—
219	Q₈×C₂₉	—	2	2	no	—
220	Q₈×C₂₉	—	2	2	no	—
221	Q₈×C₂₉	—	2	2	no	—
222	Q₈×C₂₉	—	4	1	no	—
223	Q₈×C₂₉	—	4	1	no	—
224	Q₈×C₂₉	—	4	1	no	—
225	Q₈×C₂₉	—	4	1	no	—
226	D₄×C₂₉	—	4	1	no	—
227	D₄×C₂₉	—	4	1	no	—
228	D₄×C₂₉	—	4	1	no	—
229	D₄×C₂₉	—	4	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	—	2	1	no	—
235	C₂×C₄×C₂₉	—	2	1	no	—
236	C₂×C₄×C₂₉	—	2	1	no	—
237	C₂×C₄×C₂₉	—	2	2	no	—
238	C₂×C₄×C₂₉	—	2	2	no	—
239	C₂×C₄×C₂₉	—	2	1	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	—	2	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	—	4	1	no	—
265	C₂×C₄×C₂₉	—	4	1	no	—
266	C₂×C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
267	C₂×C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
268	C₂×C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
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	C₂×#41	1	1	yes	characteristic
273	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
274	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
275	C₈×C₂₉	—	2	2	no	—
276	C₈×C₂₉	—	4	1	no	—
277	C₈×C₂₉	—	4	1	no	—
278	C₈×C₂₉	—	4	1	no	—
279	#2512	C₂×C₂₉	1	1	yes	characteristic
280	#2365	C₂×C₂₉	1	1	yes	characteristic, complemented
281	#2096	C₂×C₂₉	1	1	yes	characteristic, complemented
282	#2055	C₂×C₂₉	1	1	yes	characteristic
283	#2043	C₂×C₂₉	1	1	yes	characteristic, complemented
284	#2013	C₂×C₂₉	1	1	yes	characteristic
285	#1968	C₂×C₂₉	1	1	yes	characteristic
286	#1927	C₂×C₂₉	1	1	yes	characteristic, complemented
287	#1926	C₂×C₂₉	1	1	yes	characteristic
288	#1919	C₂×C₂₉	1	1	yes	characteristic, complemented
289	#1916	C₂×C₂₉	1	1	yes	characteristic, complemented
290	#1880	C₂×C₂₉	1	1	yes	characteristic
291	#1880	C₂×C₂₉	1	1	yes	characteristic
292	#1803	C₂×C₂₉	1	1	yes	characteristic, complemented
293	C₄×#103	C₂×C₂₉	1	1	yes	characteristic, complemented
294	C₂²×C₂₉	—	8	1	no	—
295	C₂²×C₂₉	—	8	1	no	—
296	C₂²×C₂₉	—	8	1	no	—
297	C₂²×C₂₉	—	8	1	no	—
298	C₂²×C₂₉	—	8	1	no	—
299	C₂²×C₂₉	—	8	1	no	—
300	C₂²×C₂₉	—	8	1	no	—
301	C₂²×C₂₉	#525	1	1	yes	characteristic
302	C₂²×C₂₉	#546	1	1	yes	characteristic
303	C₂²×C₂₉	#550	1	1	yes	characteristic
304	C₂²×C₂₉	C₂²×SD₁₆	1	1	yes	characteristic
305	C₂²×C₂₉	#575	1	1	yes	characteristic
306	C₂²×C₂₉	#577	1	1	yes	characteristic
307	C₂²×C₂₉	#578	1	1	yes	characteristic
308	C₄×C₂₉	—	2	2	no	—
309	C₄×C₂₉	—	2	2	no	—
310	C₄×C₂₉	—	2	2	no	—
311	C₄×C₂₉	—	4	1	no	—
312	C₄×C₂₉	—	4	2	no	—
313	C₄×C₂₉	—	4	2	no	—
314	C₄×C₂₉	—	4	1	no	—
315	C₄×C₂₉	—	4	1	no	—
316	C₄×C₂₉	—	4	2	no	—
317	C₄×C₂₉	—	8	1	no	—
318	C₄×C₂₉	—	8	1	no	—
319	C₄×C₂₉	—	8	1	no	—
320	C₄×C₂₉	—	8	1	no	—
321	C₄×C₂₉	#529	1	1	yes	characteristic
322	C₄×C₂₉	#538	1	1	yes	characteristic
323	C₄×C₂₉	#551	1	1	yes	characteristic
324	C₄×C₂₉	#553	1	1	yes	characteristic
325	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
326	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
327	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
328	C₂×#126	—	2	1	no	—
329	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
330	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
331	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
332	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
333	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
334	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
335	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
336	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
337	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
338	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
339	C₂×#103	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×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
343	#397	—	2	1	no	—
344	#396	—	2	1	no	—
345	#391	C₂²×C₂₉	1	1	yes	characteristic
346	#391	C₂²×C₂₉	1	1	yes	characteristic
347	#390	C₂²×C₂₉	1	1	yes	characteristic
348	#390	C₂²×C₂₉	1	1	yes	characteristic
349	#390	C₂²×C₂₉	1	1	yes	characteristic
350	#389	—	2	1	no	—
351	#389	C₂²×C₂₉	1	1	yes	characteristic
352	#388	—	2	1	no	—
353	#387	—	2	1	no	—
354	#387	—	2	1	no	—
355	#384	C₂²×C₂₉	1	1	yes	characteristic
356	C₄×C₄⋊C₄	—	2	1	no	—
357	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
358	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
359	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
360	#340	C₂²×C₂₉	1	1	yes	characteristic
361	#340	C₂²×C₂₉	1	1	yes	characteristic
362	#340	C₂²×C₂₉	1	1	yes	characteristic
363	#340	C₂²×C₂₉	1	1	yes	characteristic
364	#336	C₂²×C₂₉	1	1	yes	characteristic
365	#336	C₂²×C₂₉	1	1	yes	characteristic
366	#336	C₂²×C₂₉	1	1	yes	characteristic
367	#336	C₂²×C₂₉	1	1	yes	characteristic
368	C₂×C₂₉	—	16	1	no	—
369	C₂×C₂₉	#2467	1	1	yes	characteristic
370	C₂×C₂₉	#3103	1	1	yes	characteristic
371	C₂×C₂₉	#3121	1	1	yes	characteristic
372	C₂×C₂₉	#3298	1	1	yes	characteristic
373	C₂×C₂₉	#3307	1	1	yes	characteristic
374	C₂×C₂₉	#3392	1	1	yes	characteristic
375	C₂×C₂₉	#3402	1	1	yes	characteristic
376	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
377	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
378	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
379	C₂×SD₁₆	—	2	2	no	—
380	C₂×SD₁₆	—	2	2	no	—
381	C₂×SD₁₆	—	2	2	no	—
382	C₂×SD₁₆	—	4	1	no	—
383	C₂×SD₁₆	—	4	1	no	—
384	C₂×SD₁₆	—	4	1	no	—
385	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
386	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
387	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
388	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
389	C₄⋊Q₈	—	2	2	no	—
390	C₄⋊Q₈	—	2	2	no	—
391	#126	—	4	4	no	—
392	C₄×Q₈	—	2	2	no	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	4	1	no	—
395	C₄×Q₈	—	4	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
404	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₂²⋊C₄	—	2	1	no	—
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×C₄²	—	2	1	no	—
417	C₂×C₄²	—	2	1	no	—
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	—	2	1	no	—
420	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
421	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
423	#106	—	2	2	no	—
424	#106	—	4	1	no	—
425	C₄⋊C₈	—	4	1	no	—
426	#103	—	2	2	no	—
427	#103	—	2	2	no	—
428	#103	—	2	2	no	—
429	#103	—	4	1	no	—
430	#103	—	4	1	no	—
431	#103	—	4	1	no	—
432	#102	—	2	2	no	—
433	#102	—	4	1	no	—
434	C₄×C₈	—	4	1	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	D₄×C₂₉	1	1	yes	characteristic
443	#95	D₄×C₂₉	1	1	yes	characteristic
444	C₂₉	#27066	1	1	yes	characteristic, direct product factor, Sylow
445	C₂⁴	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	#41×C₂₉	1	2	yes	—
457	C₂×Q₈	#41×C₂₉	1	2	yes	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	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	C₂×D₄×C₂₉	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
473	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
477	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
478	SD₁₆	—	4	4	no	—
479	SD₁₆	—	4	4	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
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	#41×C₂₉	1	2	yes	—
492	C₄⋊C₄	—	2	4	no	—
493	C₄⋊C₄	—	2	4	no	—
494	C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
504	C₄⋊C₄	—	4	2	no	—
505	C₄⋊C₄	—	4	2	no	—
506	C₄⋊C₄	—	4	2	no	—
507	C₄⋊C₄	—	4	2	no	—
508	C₄⋊C₄	—	8	1	no	—
509	C₄⋊C₄	SD₁₆×C₂₉	1	4	yes	complemented
510	C₄⋊C₄	#41×C₂₉	1	2	yes	—
511	C₂²⋊C₄	—	4	2	no	—
512	C₂²⋊C₄	—	4	2	no	—
513	C₂²⋊C₄	—	4	2	no	—
514	C₂²⋊C₄	—	4	2	no	—
515	C₂²⋊C₄	—	8	1	no	—
516	C₂²⋊C₄	—	8	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	4	2	no	—
524	C₄²	—	4	2	no	—
525	C₄²	—	4	2	no	—
526	C₄²	—	4	2	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	4	1	no	—
530	C₂³	—	4	1	no	—
531	C₂³	—	4	1	no	—
532	C₂³	—	4	1	no	—
533	C₂³	—	4	1	no	—
534	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
535	Q₈	—	2	2	no	—
536	Q₈	—	2	2	no	—
537	Q₈	—	2	2	no	—
538	Q₈	—	2	2	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	4	1	no	—
541	Q₈	—	4	1	no	—
542	Q₈	—	4	1	no	—
543	D₄	—	4	1	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	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	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	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	C₂×SD₁₆×C₂₉	1	2	yes	—
584	C₂×C₄	C₂×SD₁₆×C₂₉	1	2	yes	—
585	C₂×C₄	C₂×SD₁₆×C₂₉	1	2	yes	—
586	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
587	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
588	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
589	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
590	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
591	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
592	C₈	—	2	2	no	—
593	C₈	—	4	1	no	—
594	C₈	—	4	1	no	—
595	C₈	—	4	1	no	—
596	C₂²	—	8	1	no	—
597	C₂²	—	8	1	no	—
598	C₂²	—	8	1	no	—
599	C₂²	—	8	1	no	—
600	C₂²	—	8	1	no	—
601	C₂²	—	8	1	no	—
602	C₂²	—	8	1	no	—
603	C₂²	C₂₉×#525	1	1	yes	characteristic
604	C₂²	C₂₉×#546	1	1	yes	characteristic
605	C₂²	C₂₉×#550	1	1	yes	characteristic
606	C₂²	C₂²×SD₁₆×C₂₉	1	1	yes	characteristic
607	C₂²	C₂₉×#575	1	1	yes	characteristic
608	C₂²	C₂₉×#577	1	1	yes	characteristic
609	C₂²	C₂₉×#578	1	1	yes	characteristic
610	C₄	—	2	2	no	—
611	C₄	—	2	2	no	—
612	C₄	—	2	2	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	2	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	1	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	1	no	—
619	C₄	—	8	1	no	—
620	C₄	—	8	1	no	—
621	C₄	—	8	1	no	—
622	C₄	—	8	1	no	—
623	C₄	C₂₉×#529	1	1	yes	characteristic
624	C₄	C₂₉×#538	1	1	yes	characteristic
625	C₄	C₂₉×#551	1	1	yes	characteristic
626	C₄	C₂₉×#553	1	1	yes	characteristic
627	C₂	—	16	1	no	—
628	C₂	C₂₉×#2467	1	1	yes	characteristic
629	C₂	C₂₉×#3103	1	1	yes	characteristic
630	C₂	C₂₉×#3121	1	1	yes	characteristic
631	C₂	C₂₉×#3298	1	1	yes	characteristic
632	C₂	C₂₉×#3307	1	1	yes	characteristic
633	C₂	C₂₉×#3392	1	1	yes	characteristic
634	C₂	C₂₉×#3402	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 ◁ C₄×C₄⋊C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#2365	C₂	semidirect
3. C₂₉×#2096	C₂	semidirect
5. C₂₉×#2043	C₂	semidirect
8. C₂₉×#1927	C₂	semidirect
10. C₂₉×#1919	C₂	semidirect
11. C₂₉×#1916	C₂	semidirect
14. C₂₉×#1803	C₂	semidirect
15. C₄×C₂₉×#103	C₂	semidirect
191. C₄⋊C₄×C₂₉	SD₁₆	semidirect
209. #27066	C₂₉	direct (N × H)
280. #2365	C₂×C₂₉	semidirect
281. #2096	C₂×C₂₉	semidirect
283. #2043	C₂×C₂₉	semidirect
286. #1927	C₂×C₂₉	semidirect
288. #1919	C₂×C₂₉	semidirect
289. #1916	C₂×C₂₉	semidirect
292. #1803	C₂×C₂₉	semidirect
293. C₄×#103	C₂×C₂₉	semidirect
444. C₂₉	#27066	direct (N × H)
509. C₄⋊C₄	SD₁₆×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#2512	2
C₂₉×#2365	2
C₂₉×#2096	2
C₂₉×#2055	2
C₂₉×#2043	2
C₂₉×#2013	2
C₂₉×#1968	2
C₂₉×#1927	2
C₂₉×#1926	2
C₂₉×#1919	2
C₂₉×#1916	2
C₂₉×#1880	2
C₂₉×#1803	2
C₄×C₂₉×#103	2
#27066	29

Subgroups — C29×#27066 #20321966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#27066 #20321966