Subgroups — C₂₉×#27126 #20322026

Order 7424.

714 conjugacy classes of subgroups.

The subgroup lattice has 584 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×#2099	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2067	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#2057	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2023	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#1947	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1934	C₂	1	1	yes	maximal, characteristic
9	C₂₉×#1925	C₂	1	1	yes	maximal, characteristic
10	C₂₉×#1925	C₂	1	1	yes	maximal, characteristic
11	C₂₉×#1925	C₂	1	1	yes	maximal, characteristic
12	C₂₉×#1918	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1918	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1916	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×#126	—	2	1	no	—
18	C₂×C₄×Q₈×C₂₉	—	2	1	no	—
19	C₂×C₂₉×#107	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×#107	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
25	C₂×C₂₉×#102	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×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
29	C₂₉×#397	—	2	1	no	—
30	C₂₉×#396	—	2	1	no	—
31	C₂₉×#391	—	2	1	no	—
32	C₂₉×#390	C₂²	1	1	yes	characteristic
33	C₂₉×#390	C₂²	1	1	yes	characteristic
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×#387	—	2	1	no	—
40	C₂₉×#387	—	2	1	no	—
41	C₂₉×#384	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
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×#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	—	2	1	no	—
60	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
65	C₂₉×C₄⋊Q₈	—	2	2	no	—
66	C₂₉×C₄⋊Q₈	—	2	2	no	—
67	C₂₉×#126	—	4	4	no	—
68	C₄×Q₈×C₂₉	—	4	4	no	—
69	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₂₉	—	2	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	D₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
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	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
90	C₂×C₄²×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	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
97	C₂₉×#107	—	2	2	no	—
98	C₂₉×#107	—	2	2	no	—
99	C₂₉×#107	—	2	2	no	—
100	C₂₉×#107	—	2	2	no	—
101	C₂₉×C₄⋊C₈	—	2	2	no	—
102	C₂₉×#102	—	2	2	no	—
103	C₂₉×#102	—	2	2	no	—
104	C₂₉×#102	—	2	2	no	—
105	C₂₉×#102	—	2	2	no	—
106	C₄×C₈×C₂₉	—	2	2	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	D₄	1	1	yes	characteristic
115	C₂₉×#95	D₄	1	1	yes	characteristic
116	C₂⁴×C₂₉	—	2	1	no	—
117	C₂×Q₈×C₂₉	—	2	4	no	—
118	C₂×Q₈×C₂₉	—	4	2	no	—
119	C₂×Q₈×C₂₉	—	4	2	no	—
120	C₂×D₄×C₂₉	—	2	1	no	—
121	C₂×D₄×C₂₉	—	2	1	no	—
122	C₂×D₄×C₂₉	—	2	1	no	—
123	C₂×D₄×C₂₉	—	2	1	no	—
124	C₂×D₄×C₂₉	—	2	1	no	—
125	C₂×D₄×C₂₉	—	2	1	no	—
126	C₂²×C₄×C₂₉	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
140	C₂×C₈×C₂₉	—	2	1	no	—
141	C₂×C₈×C₂₉	—	2	1	no	—
142	C₂×C₈×C₂₉	—	2	1	no	—
143	C₂×C₈×C₂₉	—	2	1	no	—
144	C₂×C₈×C₂₉	—	2	1	no	—
145	C₂×C₈×C₂₉	—	2	1	no	—
146	C₂×C₈×C₂₉	—	2	1	no	—
147	C₂×C₈×C₂₉	—	2	1	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	#41	1	2	yes	—
152	C₄⋊C₄×C₂₉	—	2	4	no	—
153	C₄⋊C₄×C₂₉	—	2	1	no	—
154	C₄⋊C₄×C₂₉	—	2	1	no	—
155	C₄⋊C₄×C₂₉	—	2	1	no	—
156	C₄⋊C₄×C₂₉	—	2	1	no	—
157	C₄⋊C₄×C₂₉	—	2	1	no	—
158	C₄⋊C₄×C₂₉	—	2	1	no	—
159	C₄⋊C₄×C₂₉	—	2	1	no	—
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	—	4	1	no	—
165	C₄⋊C₄×C₂₉	—	4	2	no	—
166	C₄⋊C₄×C₂₉	—	4	2	no	—
167	C₄⋊C₄×C₂₉	—	4	2	no	—
168	C₄⋊C₄×C₂₉	—	4	2	no	—
169	C₄⋊C₄×C₂₉	—	8	1	no	—
170	C₄⋊C₄×C₂₉	D₈	1	4	yes	—
171	C₄⋊C₄×C₂₉	#41	1	2	yes	—
172	C₄⋊C₄×C₂₉	#41	1	2	yes	—
173	C₄⋊C₄×C₂₉	#41	1	2	yes	—
174	C₂²⋊C₄×C₂₉	—	4	2	no	—
175	C₂²⋊C₄×C₂₉	—	4	2	no	—
176	C₂²⋊C₄×C₂₉	—	4	2	no	—
177	C₂²⋊C₄×C₂₉	—	4	2	no	—
178	C₂²⋊C₄×C₂₉	—	8	1	no	—
179	C₂²⋊C₄×C₂₉	—	8	1	no	—
180	C₄²×C₂₉	—	2	1	no	—
181	C₄²×C₂₉	—	2	1	no	—
182	C₄²×C₂₉	—	2	1	no	—
183	C₄²×C₂₉	—	2	1	no	—
184	C₄²×C₂₉	—	2	1	no	—
185	C₄²×C₂₉	—	2	1	no	—
186	C₄²×C₂₉	—	4	2	no	—
187	C₄²×C₂₉	—	4	2	no	—
188	C₄²×C₂₉	—	4	2	no	—
189	C₄²×C₂₉	—	4	2	no	—
190	#27126	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂³×C₂₉	—	4	1	no	—
192	C₂³×C₂₉	—	4	1	no	—
193	C₂³×C₂₉	—	4	1	no	—
194	C₂³×C₂₉	—	4	1	no	—
195	C₂³×C₂₉	—	4	1	no	—
196	C₂³×C₂₉	—	4	1	no	—
197	C₂³×C₂₉	—	4	1	no	—
198	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
199	Q₈×C₂₉	—	4	8	no	—
200	D₄×C₂₉	—	4	1	no	—
201	D₄×C₂₉	—	4	1	no	—
202	D₄×C₂₉	—	4	1	no	—
203	D₄×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	1	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	2	no	—
212	C₂×C₄×C₂₉	—	2	2	no	—
213	C₂×C₄×C₂₉	—	2	1	no	—
214	C₂×C₄×C₂₉	—	2	1	no	—
215	C₂×C₄×C₂₉	—	2	2	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	—	2	1	no	—
221	C₂×C₄×C₂₉	—	2	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	C₂×D₈	1	2	yes	—
241	C₂×C₄×C₂₉	C₂×D₈	1	2	yes	—
242	C₂×C₄×C₂₉	C₂×D₈	1	2	yes	—
243	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
246	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
248	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
249	C₈×C₂₉	—	2	2	no	—
250	C₈×C₂₉	—	4	1	no	—
251	C₈×C₂₉	—	4	1	no	—
252	C₈×C₂₉	—	4	1	no	—
253	#2512	C₂×C₂₉	1	1	yes	characteristic
254	#2365	C₂×C₂₉	1	1	yes	characteristic, complemented
255	#2099	C₂×C₂₉	1	1	yes	characteristic, complemented
256	#2067	C₂×C₂₉	1	1	yes	characteristic
257	#2057	C₂×C₂₉	1	1	yes	characteristic, complemented
258	#2023	C₂×C₂₉	1	1	yes	characteristic
259	#1947	C₂×C₂₉	1	1	yes	characteristic, complemented
260	#1934	C₂×C₂₉	1	1	yes	characteristic
261	#1925	C₂×C₂₉	1	1	yes	characteristic
262	#1925	C₂×C₂₉	1	1	yes	characteristic
263	#1925	C₂×C₂₉	1	1	yes	characteristic
264	#1918	C₂×C₂₉	1	1	yes	characteristic, complemented
265	#1918	C₂×C₂₉	1	1	yes	characteristic, complemented
266	#1916	C₂×C₂₉	1	1	yes	characteristic, complemented
267	C₄×#107	C₂×C₂₉	1	1	yes	characteristic, complemented
268	C₂²×C₂₉	—	8	1	no	—
269	C₂²×C₂₉	—	8	1	no	—
270	C₂²×C₂₉	—	8	1	no	—
271	C₂²×C₂₉	—	8	1	no	—
272	C₂²×C₂₉	—	8	1	no	—
273	C₂²×C₂₉	—	8	1	no	—
274	C₂²×C₂₉	—	8	1	no	—
275	C₂²×C₂₉	#525	1	1	yes	characteristic
276	C₂²×C₂₉	#547	1	1	yes	characteristic
277	C₂²×C₂₉	#548	1	1	yes	characteristic
278	C₂²×C₂₉	C₂²×D₈	1	1	yes	characteristic
279	C₂²×C₂₉	#575	1	1	yes	characteristic
280	C₂²×C₂₉	#577	1	1	yes	characteristic
281	C₂²×C₂₉	#578	1	1	yes	characteristic
282	C₄×C₂₉	—	2	2	no	—
283	C₄×C₂₉	—	2	2	no	—
284	C₄×C₂₉	—	2	2	no	—
285	C₄×C₂₉	—	4	1	no	—
286	C₄×C₂₉	—	4	1	no	—
287	C₄×C₂₉	—	4	2	no	—
288	C₄×C₂₉	—	4	2	no	—
289	C₄×C₂₉	—	4	2	no	—
290	C₄×C₂₉	—	4	1	no	—
291	C₄×C₂₉	—	8	1	no	—
292	C₄×C₂₉	—	8	1	no	—
293	C₄×C₂₉	—	8	1	no	—
294	C₄×C₂₉	—	8	1	no	—
295	C₄×C₂₉	#529	1	1	yes	characteristic
296	C₄×C₂₉	#541	1	1	yes	characteristic
297	C₄×C₂₉	#556	1	1	yes	characteristic
298	C₄×C₂₉	#556	1	1	yes	characteristic
299	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
300	C₂×#126	—	2	1	no	—
301	C₂×C₄×Q₈	—	2	1	no	—
302	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
303	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
304	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
305	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
306	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
307	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
308	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
309	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
310	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
311	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
312	#397	—	2	1	no	—
313	#396	—	2	1	no	—
314	#391	—	2	1	no	—
315	#390	C₂²×C₂₉	1	1	yes	characteristic
316	#390	C₂²×C₂₉	1	1	yes	characteristic
317	#390	C₂²×C₂₉	1	1	yes	characteristic
318	#389	C₂²×C₂₉	1	1	yes	characteristic
319	#389	C₂²×C₂₉	1	1	yes	characteristic
320	#389	C₂²×C₂₉	1	1	yes	characteristic
321	#388	—	2	1	no	—
322	#387	—	2	1	no	—
323	#387	—	2	1	no	—
324	#384	C₂²×C₂₉	1	1	yes	characteristic
325	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
326	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
327	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
328	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
329	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
330	#340	C₂²×C₂₉	1	1	yes	characteristic
331	#340	C₂²×C₂₉	1	1	yes	characteristic
332	#340	C₂²×C₂₉	1	1	yes	characteristic
333	#340	C₂²×C₂₉	1	1	yes	characteristic
334	#340	C₂²×C₂₉	1	1	yes	characteristic
335	#340	C₂²×C₂₉	1	1	yes	characteristic
336	#340	C₂²×C₂₉	1	1	yes	characteristic
337	#340	C₂²×C₂₉	1	1	yes	characteristic
338	#336	C₂²×C₂₉	1	1	yes	characteristic
339	#336	C₂²×C₂₉	1	1	yes	characteristic
340	#336	C₂²×C₂₉	1	1	yes	characteristic
341	#336	C₂²×C₂₉	1	1	yes	characteristic
342	C₂×C₂₉	—	16	1	no	—
343	C₂×C₂₉	#2469	1	1	yes	characteristic
344	C₂×C₂₉	#3100	1	1	yes	characteristic
345	C₂×C₂₉	#3121	1	1	yes	characteristic
346	C₂×C₂₉	#3334	1	1	yes	characteristic
347	C₂×C₂₉	#3350	1	1	yes	characteristic
348	C₂×C₂₉	#3358	1	1	yes	characteristic
349	C₂×C₂₉	#3377	1	1	yes	characteristic
350	C₂²×Q₈	—	2	1	no	—
351	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
352	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
353	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
355	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
356	C₄⋊Q₈	—	2	2	no	—
357	C₄⋊Q₈	—	2	2	no	—
358	#126	—	4	4	no	—
359	C₄×Q₈	—	4	4	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
367	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	1	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₄²	—	2	1	no	—
382	C₂×C₄²	—	2	1	no	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
387	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
388	#107	—	2	2	no	—
389	#107	—	2	2	no	—
390	#107	—	2	2	no	—
391	#107	—	2	2	no	—
392	C₄⋊C₈	—	2	2	no	—
393	#102	—	2	2	no	—
394	#102	—	2	2	no	—
395	#102	—	2	2	no	—
396	#102	—	2	2	no	—
397	C₄×C₈	—	2	2	no	—
398	#95	—	2	1	no	—
399	#95	—	2	1	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	D₄×C₂₉	1	1	yes	characteristic
406	#95	D₄×C₂₉	1	1	yes	characteristic
407	C₂₉	#27126	1	1	yes	characteristic, direct product factor, Sylow
408	C₂⁴	—	2	1	no	—
409	C₂×Q₈	—	2	4	no	—
410	C₂×Q₈	—	4	2	no	—
411	C₂×Q₈	—	4	2	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
431	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	#41×C₂₉	1	2	yes	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	4	1	no	—
457	C₄⋊C₄	—	4	2	no	—
458	C₄⋊C₄	—	4	2	no	—
459	C₄⋊C₄	—	4	2	no	—
460	C₄⋊C₄	—	4	2	no	—
461	C₄⋊C₄	—	8	1	no	—
462	C₄⋊C₄	D₈×C₂₉	1	4	yes	—
463	C₄⋊C₄	#41×C₂₉	1	2	yes	—
464	C₄⋊C₄	#41×C₂₉	1	2	yes	—
465	C₄⋊C₄	#41×C₂₉	1	2	yes	—
466	C₂²⋊C₄	—	4	2	no	—
467	C₂²⋊C₄	—	4	2	no	—
468	C₂²⋊C₄	—	4	2	no	—
469	C₂²⋊C₄	—	4	2	no	—
470	C₂²⋊C₄	—	8	1	no	—
471	C₂²⋊C₄	—	8	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	4	2	no	—
479	C₄²	—	4	2	no	—
480	C₄²	—	4	2	no	—
481	C₄²	—	4	2	no	—
482	C₂³	—	4	1	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	1	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	1	no	—
488	C₂³	—	4	1	no	—
489	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
490	Q₈	—	4	8	no	—
491	D₄	—	4	1	no	—
492	D₄	—	4	1	no	—
493	D₄	—	4	1	no	—
494	D₄	—	4	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	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	2	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	2	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	—	4	1	no	—
514	C₂×C₄	—	4	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	C₂×D₈×C₂₉	1	2	yes	—
532	C₂×C₄	C₂×D₈×C₂₉	1	2	yes	—
533	C₂×C₄	C₂×D₈×C₂₉	1	2	yes	—
534	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
535	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
536	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
537	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
538	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
539	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
540	C₈	—	2	2	no	—
541	C₈	—	4	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	1	no	—
546	C₂²	—	8	1	no	—
547	C₂²	—	8	1	no	—
548	C₂²	—	8	1	no	—
549	C₂²	—	8	1	no	—
550	C₂²	—	8	1	no	—
551	C₂²	C₂₉×#525	1	1	yes	characteristic
552	C₂²	C₂₉×#547	1	1	yes	characteristic
553	C₂²	C₂₉×#548	1	1	yes	characteristic
554	C₂²	C₂²×D₈×C₂₉	1	1	yes	characteristic
555	C₂²	C₂₉×#575	1	1	yes	characteristic
556	C₂²	C₂₉×#577	1	1	yes	characteristic
557	C₂²	C₂₉×#578	1	1	yes	characteristic
558	C₄	—	2	2	no	—
559	C₄	—	2	2	no	—
560	C₄	—	2	2	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	2	no	—
566	C₄	—	4	1	no	—
567	C₄	—	8	1	no	—
568	C₄	—	8	1	no	—
569	C₄	—	8	1	no	—
570	C₄	—	8	1	no	—
571	C₄	C₂₉×#529	1	1	yes	characteristic
572	C₄	C₂₉×#541	1	1	yes	characteristic
573	C₄	C₂₉×#556	1	1	yes	characteristic
574	C₄	C₂₉×#556	1	1	yes	characteristic
575	C₂	—	16	1	no	—
576	C₂	C₂₉×#2469	1	1	yes	characteristic
577	C₂	C₂₉×#3100	1	1	yes	characteristic
578	C₂	C₂₉×#3121	1	1	yes	characteristic
579	C₂	C₂₉×#3334	1	1	yes	characteristic
580	C₂	C₂₉×#3350	1	1	yes	characteristic
581	C₂	C₂₉×#3358	1	1	yes	characteristic
582	C₂	C₂₉×#3377	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×#2099	C₂	semidirect
5. C₂₉×#2057	C₂	semidirect
7. C₂₉×#1947	C₂	semidirect
12. C₂₉×#1918	C₂	semidirect
13. C₂₉×#1918	C₂	semidirect
14. C₂₉×#1916	C₂	semidirect
15. C₄×C₂₉×#107	C₂	semidirect
190. #27126	C₂₉	direct (N × H)
254. #2365	C₂×C₂₉	semidirect
255. #2099	C₂×C₂₉	semidirect
257. #2057	C₂×C₂₉	semidirect
259. #1947	C₂×C₂₉	semidirect
264. #1918	C₂×C₂₉	semidirect
265. #1918	C₂×C₂₉	semidirect
266. #1916	C₂×C₂₉	semidirect
267. C₄×#107	C₂×C₂₉	semidirect
407. C₂₉	#27126	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×#2512	2
C₂₉×#2365	2
C₂₉×#2099	2
C₂₉×#2067	2
C₂₉×#2057	2
C₂₉×#2023	2
C₂₉×#1947	2
C₂₉×#1934	2
C₂₉×#1925	2
C₂₉×#1918	2
C₂₉×#1916	2
C₄×C₂₉×#107	2
#27126	29

Subgroups — C29×#27126 #20322026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#27126 #20322026