Subgroups — C₂₉×#21592 #20316492

Order 7424.

794 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3091	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2929	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#1929	C₂	1	2	yes	maximal, complemented
5	C₂₉×#1922	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1871	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#1855	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1826	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1772	C₂	1	2	yes	maximal, complemented
10	C₂₉×#1764	C₂	1	2	yes	maximal, complemented
11	C₈×C₂²⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₂₉	C₂²	1	1	yes	characteristic
15	C₂₉×#525	C₂²	1	1	yes	characteristic
16	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
17	C₂₉×#485	C₄	1	2	yes	complemented
18	C₂₉×#484	C₄	1	1	yes	characteristic, complemented
19	C₂₉×#483	C₄	1	1	yes	characteristic, complemented
20	C₂₉×#482	C₄	1	2	yes	complemented
21	C₂₉×#481	C₄	1	1	yes	characteristic, complemented
22	C₂₉×#480	C₄	1	1	yes	characteristic, complemented
23	C₂₉×#435	—	2	1	no	—
24	C₂₉×#435	—	2	1	no	—
25	C₈×D₄×C₂₉	—	2	1	no	—
26	C₈×D₄×C₂₉	—	2	1	no	—
27	C₂×C₂₉×#108	C₂²	1	2	yes	—
28	C₂₉×#427	C₂²	1	2	yes	—
29	C₂₉×#424	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×#104	C₂²	1	2	yes	—
31	C₂₉×#416	C₂²	1	2	yes	—
32	C₂₉×#408	C₂²	1	1	yes	characteristic
33	C₂₉×#407	C₂²	1	1	yes	characteristic
34	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂₉×#405	—	2	1	no	—
36	C₂₉×#405	—	2	1	no	—
37	C₂₉×#405	C₂²	1	1	yes	characteristic
38	C₂₉×#405	C₂²	1	2	yes	—
39	C₂₉×#405	C₂²	1	2	yes	—
40	C₂×C₂₉×#97	—	2	1	no	—
41	C₂×C₄×C₈×C₂₉	—	2	1	no	—
42	C₂×C₄×C₈×C₂₉	C₂²	1	2	yes	—
43	C₄×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
44	C₂₉×#341	C₂²	1	2	yes	—
45	C₂₉×#339	C₂²	1	2	yes	—
46	C₂₉×#339	C₂²	1	2	yes	—
47	C₂₉×#339	C₂²	1	2	yes	—
48	C₂₉×#336	C₂²	1	2	yes	—
49	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
51	C₂₉×#131	—	2	4	no	—
52	C₂×M₁₆×C₂₉	—	2	1	no	—
53	C₂×M₁₆×C₂₉	—	2	4	no	—
54	C₂×M₁₆×C₂₉	—	2	1	no	—
55	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
56	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
57	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
58	C₂²×C₈×C₂₉	—	2	1	no	—
59	C₂²×C₈×C₂₉	—	2	4	no	—
60	C₂²×C₈×C₂₉	—	2	1	no	—
61	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
63	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
64	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
65	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
66	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
68	C₂₉×#123	—	2	1	no	—
69	C₂₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
70	C₂₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
71	C₂₉×#121	C₂×C₄	1	1	yes	characteristic
72	C₂₉×#121	C₂×C₄	1	1	yes	characteristic
73	C₂₉×#120	—	2	1	no	—
74	C₄×D₄×C₂₉	—	2	1	no	—
75	C₄×D₄×C₂₉	—	2	1	no	—
76	C₂₉×#117	—	2	1	no	—
77	C₂₉×#117	—	2	1	no	—
78	C₂₉×#117	C₂×C₄	1	2	yes	—
79	C₂₉×#117	C₂³	1	1	yes	characteristic
80	C₂₉×#117	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
85	C₂×C₄²×C₂₉	—	2	1	no	—
86	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
87	C₂₉×#108	—	2	4	no	—
88	C₂₉×#107	C₂×C₄	1	2	yes	—
89	C₂₉×#107	C₂×C₄	1	2	yes	—
90	C₂₉×#106	C₂×C₄	1	2	yes	—
91	C₂₉×#106	C₂×C₄	1	2	yes	—
92	C₂₉×C₄⋊C₈	—	2	1	no	—
93	C₂₉×C₄⋊C₈	—	2	1	no	—
94	C₂₉×#104	—	2	4	no	—
95	C₂₉×#103	C₂×C₄	1	2	yes	—
96	C₂₉×#103	C₂×C₄	1	2	yes	—
97	C₂₉×#102	C₂×C₄	1	2	yes	—
98	C₂₉×#102	C₂×C₄	1	2	yes	—
99	C₂₉×C₂²⋊C₈	—	2	1	no	—
100	C₂₉×C₂²⋊C₈	—	2	1	no	—
101	C₂₉×C₂²⋊C₈	—	2	1	no	—
102	C₂₉×C₂²⋊C₈	—	2	1	no	—
103	C₂₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
104	C₂₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
105	C₂₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
106	C₂₉×#97	—	2	1	no	—
107	C₂₉×#97	—	2	2	no	—
108	C₂₉×#97	—	2	2	no	—
109	C₄×C₈×C₂₉	—	2	2	no	—
110	C₄×C₈×C₂₉	—	2	1	no	—
111	C₄×C₈×C₂₉	—	2	2	no	—
112	C₄×C₈×C₂₉	—	2	4	no	—
113	C₂₉×#95	—	2	1	no	—
114	C₂⁴×C₂₉	#41	1	1	yes	characteristic
115	#41×C₂₉	—	2	2	no	—
116	#41×C₂₉	—	2	2	no	—
117	C₂×Q₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
118	C₂×D₄×C₂₉	—	2	1	no	—
119	C₂×D₄×C₂₉	—	2	1	no	—
120	C₂×D₄×C₂₉	—	2	1	no	—
121	C₂×D₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₂₉	—	2	2	no	—
123	C₂²×C₄×C₂₉	—	2	2	no	—
124	C₂²×C₄×C₂₉	—	2	1	no	—
125	C₂²×C₄×C₂₉	—	2	1	no	—
126	C₂²×C₄×C₂₉	—	2	2	no	—
127	C₂²×C₄×C₂₉	—	2	1	no	—
128	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
133	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
134	M₁₆×C₂₉	—	2	4	no	—
135	M₁₆×C₂₉	—	2	2	no	—
136	M₁₆×C₂₉	—	2	2	no	—
137	M₁₆×C₂₉	—	2	2	no	—
138	M₁₆×C₂₉	—	4	2	no	—
139	M₁₆×C₂₉	#41	1	4	yes	—
140	C₂×C₈×C₂₉	—	2	4	no	—
141	C₂×C₈×C₂₉	—	2	2	no	—
142	C₂×C₈×C₂₉	—	2	2	no	—
143	C₂×C₈×C₂₉	—	2	2	no	—
144	C₂×C₈×C₂₉	—	2	2	no	—
145	C₂×C₈×C₂₉	—	2	2	no	—
146	C₂×C₈×C₂₉	—	2	2	no	—
147	C₂×C₈×C₂₉	—	2	2	no	—
148	C₂×C₈×C₂₉	—	2	2	no	—
149	C₂×C₈×C₂₉	—	2	1	no	—
150	C₂×C₈×C₂₉	—	2	1	no	—
151	C₂×C₈×C₂₉	—	4	2	no	—
152	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₂₉	#41	1	4	yes	—
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	C₂²×C₄	1	2	yes	—
164	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
165	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
166	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
167	C₂²⋊C₄×C₂₉	—	2	4	no	—
168	C₂²⋊C₄×C₂₉	—	2	2	no	—
169	C₂²⋊C₄×C₂₉	—	2	1	no	—
170	C₂²⋊C₄×C₂₉	—	2	1	no	—
171	C₂²⋊C₄×C₂₉	—	2	2	no	—
172	C₂²⋊C₄×C₂₉	—	2	1	no	—
173	C₂²⋊C₄×C₂₉	—	2	1	no	—
174	C₂²⋊C₄×C₂₉	—	2	1	no	—
175	C₄²×C₂₉	—	2	2	no	—
176	C₄²×C₂₉	—	2	2	no	—
177	C₄²×C₂₉	—	2	1	no	—
178	C₄²×C₂₉	—	2	2	no	—
179	C₄²×C₂₉	—	2	2	no	—
180	#21592	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂³×C₂₉	—	2	2	no	—
182	C₂³×C₂₉	—	2	2	no	—
183	C₂³×C₂₉	—	2	1	no	—
184	C₂³×C₂₉	—	4	1	no	—
185	C₂³×C₂₉	C₄×D₄	1	1	yes	characteristic
186	C₂³×C₂₉	C₄×D₄	1	1	yes	characteristic
187	C₂³×C₂₉	C₂×#41	1	1	yes	characteristic
188	Q₈×C₂₉	—	2	2	no	—
189	D₄×C₂₉	—	2	2	no	—
190	D₄×C₂₉	—	4	2	no	—
191	D₄×C₂₉	—	4	2	no	—
192	D₄×C₂₉	—	4	2	no	—
193	C₂×C₄×C₂₉	—	2	2	no	—
194	C₂×C₄×C₂₉	—	2	2	no	—
195	C₂×C₄×C₂₉	—	2	2	no	—
196	C₂×C₄×C₂₉	—	2	1	no	—
197	C₂×C₄×C₂₉	—	2	1	no	—
198	C₂×C₄×C₂₉	—	2	1	no	—
199	C₂×C₄×C₂₉	—	2	1	no	—
200	C₂×C₄×C₂₉	—	2	4	no	—
201	C₂×C₄×C₂₉	—	2	2	no	—
202	C₂×C₄×C₂₉	—	2	2	no	—
203	C₂×C₄×C₂₉	—	2	1	no	—
204	C₂×C₄×C₂₉	—	2	1	no	—
205	C₂×C₄×C₂₉	—	2	1	no	—
206	C₂×C₄×C₂₉	—	4	2	no	—
207	C₂×C₄×C₂₉	—	4	2	no	—
208	C₂×C₄×C₂₉	—	4	2	no	—
209	C₂×C₄×C₂₉	—	4	2	no	—
210	C₂×C₄×C₂₉	—	4	1	no	—
211	C₂×C₄×C₂₉	—	4	1	no	—
212	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
217	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
218	C₈×C₂₉	—	2	2	no	—
219	C₈×C₂₉	—	2	2	no	—
220	C₈×C₂₉	—	2	1	no	—
221	C₈×C₂₉	—	2	1	no	—
222	C₈×C₂₉	—	2	4	no	—
223	C₈×C₂₉	—	4	1	no	—
224	C₈×C₂₉	—	4	1	no	—
225	C₈×C₂₉	#123	1	2	yes	—
226	C₈×C₂₉	#123	1	2	yes	—
227	#3091	C₂×C₂₉	1	1	yes	characteristic
228	#2929	C₂×C₂₉	1	1	yes	characteristic
229	C₂×#405	C₂×C₂₉	1	1	yes	characteristic, complemented
230	#1929	C₂×C₂₉	1	2	yes	complemented
231	#1922	C₂×C₂₉	1	2	yes	complemented
232	#1871	C₂×C₂₉	1	1	yes	characteristic
233	#1855	C₂×C₂₉	1	1	yes	characteristic, complemented
234	#1826	C₂×C₂₉	1	1	yes	characteristic, complemented
235	#1772	C₂×C₂₉	1	2	yes	complemented
236	#1764	C₂×C₂₉	1	2	yes	complemented
237	C₈×C₂²⋊C₄	C₂×C₂₉	1	1	yes	characteristic, complemented
238	C₂²×C₂₉	—	2	1	no	—
239	C₂²×C₂₉	—	2	1	no	—
240	C₂²×C₂₉	—	2	1	no	—
241	C₂²×C₂₉	—	2	1	no	—
242	C₂²×C₂₉	—	2	1	no	—
243	C₂²×C₂₉	—	2	1	no	—
244	C₂²×C₂₉	—	2	1	no	—
245	C₂²×C₂₉	—	4	4	no	—
246	C₂²×C₂₉	—	4	1	no	—
247	C₂²×C₂₉	—	4	1	no	—
248	C₂²×C₂₉	—	4	1	no	—
249	C₂²×C₂₉	#443	1	2	yes	—
250	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
251	C₂²×C₂₉	#529	1	2	yes	—
252	C₄×C₂₉	—	2	1	no	—
253	C₄×C₂₉	—	2	1	no	—
254	C₄×C₂₉	—	4	4	no	—
255	C₄×C₂₉	—	4	2	no	—
256	C₄×C₂₉	—	4	1	no	—
257	C₄×C₂₉	—	4	2	no	—
258	C₄×C₂₉	—	4	1	no	—
259	C₄×C₂₉	—	4	1	no	—
260	C₄×C₂₉	C₄×#41	1	2	yes	—
261	C₄×C₂₉	C₂×#123	1	1	yes	characteristic
262	C₄×C₂₉	#525	1	1	yes	characteristic
263	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
264	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
265	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic
266	#525	C₂²×C₂₉	1	1	yes	characteristic
267	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
268	#485	C₄×C₂₉	1	2	yes	complemented
269	#484	C₄×C₂₉	1	1	yes	characteristic, complemented
270	#483	C₄×C₂₉	1	1	yes	characteristic, complemented
271	#482	C₄×C₂₉	1	2	yes	complemented
272	#481	C₄×C₂₉	1	1	yes	characteristic, complemented
273	#480	C₄×C₂₉	1	1	yes	characteristic, complemented
274	#435	—	2	1	no	—
275	#435	—	2	1	no	—
276	C₈×D₄	—	2	1	no	—
277	C₈×D₄	—	2	1	no	—
278	C₂×#108	C₂²×C₂₉	1	2	yes	—
279	#427	C₂²×C₂₉	1	2	yes	—
280	#424	C₂²×C₂₉	1	1	yes	characteristic
281	C₂×#104	C₂²×C₂₉	1	2	yes	—
282	#416	C₂²×C₂₉	1	2	yes	—
283	#408	C₂²×C₂₉	1	1	yes	characteristic
284	#407	C₂²×C₂₉	1	1	yes	characteristic
285	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
286	#405	—	2	1	no	—
287	#405	—	2	1	no	—
288	#405	C₂²×C₂₉	1	2	yes	—
289	#405	C₂²×C₂₉	1	2	yes	—
290	#405	C₂²×C₂₉	1	1	yes	characteristic
291	C₂×#97	—	2	1	no	—
292	C₂×C₄×C₈	—	2	1	no	—
293	C₂×C₄×C₈	C₂²×C₂₉	1	2	yes	—
294	C₄×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
295	#341	C₂²×C₂₉	1	2	yes	—
296	#339	C₂²×C₂₉	1	2	yes	—
297	#339	C₂²×C₂₉	1	2	yes	—
298	#339	C₂²×C₂₉	1	2	yes	—
299	#336	C₂²×C₂₉	1	2	yes	—
300	C₂×C₂₉	—	2	2	no	—
301	C₂×C₂₉	—	2	2	no	—
302	C₂×C₂₉	—	4	1	no	—
303	C₂×C₂₉	—	8	1	no	—
304	C₂×C₂₉	C₄×#123	1	1	yes	characteristic
305	C₂×C₂₉	C₂×#443	1	1	yes	characteristic
306	C₂×C₂₉	#2955	1	1	yes	characteristic
307	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
308	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
309	#131	—	2	4	no	—
310	C₂×M₁₆	—	2	1	no	—
311	C₂×M₁₆	—	2	4	no	—
312	C₂×M₁₆	—	2	1	no	—
313	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
314	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
315	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
316	C₂²×C₈	—	2	1	no	—
317	C₂²×C₈	—	2	4	no	—
318	C₂²×C₈	—	2	1	no	—
319	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
320	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
321	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
322	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
323	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
324	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
325	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
326	#123	—	2	1	no	—
327	C₂²⋊Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
328	C₂²⋊Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
329	#121	C₂×C₄×C₂₉	1	1	yes	characteristic
330	#121	C₂×C₄×C₂₉	1	1	yes	characteristic
331	#120	—	2	1	no	—
332	C₄×D₄	—	2	1	no	—
333	C₄×D₄	—	2	1	no	—
334	#117	—	2	1	no	—
335	#117	—	2	1	no	—
336	#117	C₂×C₄×C₂₉	1	2	yes	—
337	#117	C₂³×C₂₉	1	2	yes	—
338	#117	C₂³×C₂₉	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₄²	—	2	1	no	—
344	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
345	#108	—	2	4	no	—
346	#107	C₂×C₄×C₂₉	1	2	yes	—
347	#107	C₂×C₄×C₂₉	1	2	yes	—
348	#106	C₂×C₄×C₂₉	1	2	yes	—
349	#106	C₂×C₄×C₂₉	1	2	yes	—
350	C₄⋊C₈	—	2	1	no	—
351	C₄⋊C₈	—	2	1	no	—
352	#104	—	2	4	no	—
353	#103	C₂×C₄×C₂₉	1	2	yes	—
354	#103	C₂×C₄×C₂₉	1	2	yes	—
355	#102	C₂×C₄×C₂₉	1	2	yes	—
356	#102	C₂×C₄×C₂₉	1	2	yes	—
357	C₂²⋊C₈	—	2	1	no	—
358	C₂²⋊C₈	—	2	1	no	—
359	C₂²⋊C₈	—	2	1	no	—
360	C₂²⋊C₈	—	2	1	no	—
361	C₂²⋊C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
362	C₂²⋊C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
363	C₂²⋊C₈	C₂×C₄×C₂₉	1	2	yes	—
364	#97	—	2	2	no	—
365	#97	—	2	2	no	—
366	#97	—	2	1	no	—
367	C₄×C₈	—	2	2	no	—
368	C₄×C₈	—	2	2	no	—
369	C₄×C₈	—	2	1	no	—
370	C₄×C₈	—	2	4	no	—
371	#95	—	2	1	no	—
372	C₂₉	#21592	1	1	yes	characteristic, direct product factor, Sylow
373	C₂⁴	#41×C₂₉	1	1	yes	characteristic
374	#41	—	2	2	no	—
375	#41	—	2	2	no	—
376	C₂×Q₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
388	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
391	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
392	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
393	M₁₆	—	2	4	no	—
394	M₁₆	—	2	2	no	—
395	M₁₆	—	2	2	no	—
396	M₁₆	—	2	2	no	—
397	M₁₆	—	4	2	no	—
398	M₁₆	#41×C₂₉	1	4	yes	—
399	C₂×C₈	—	2	4	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	4	2	no	—
411	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
412	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
413	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
414	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
415	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
416	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
417	C₂×C₈	#41×C₂₉	1	4	yes	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
423	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
424	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
425	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	1	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	2	1	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	2	no	—
436	C₄²	—	2	1	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	C₄×D₄×C₂₉	1	1	yes	characteristic
444	C₂³	C₄×D₄×C₂₉	1	1	yes	characteristic
445	C₂³	C₂×#41×C₂₉	1	1	yes	characteristic
446	Q₈	—	2	2	no	—
447	D₄	—	2	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	4	2	no	—
450	D₄	—	4	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
471	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
472	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
473	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
474	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
475	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
476	C₈	—	2	2	no	—
477	C₈	—	2	2	no	—
478	C₈	—	2	1	no	—
479	C₈	—	2	1	no	—
480	C₈	—	2	4	no	—
481	C₈	—	4	1	no	—
482	C₈	—	4	1	no	—
483	C₈	C₂₉×#123	1	2	yes	—
484	C₈	C₂₉×#123	1	2	yes	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	1	no	—
496	C₂²	C₂₉×#443	1	2	yes	—
497	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
498	C₂²	C₂₉×#529	1	2	yes	—
499	C₄	—	2	1	no	—
500	C₄	—	2	1	no	—
501	C₄	—	4	4	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	1	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	1	no	—
506	C₄	—	4	1	no	—
507	C₄	C₄×#41×C₂₉	1	2	yes	—
508	C₄	C₂×C₂₉×#123	1	1	yes	characteristic
509	C₄	C₂₉×#525	1	1	yes	characteristic
510	C₂	—	2	2	no	—
511	C₂	—	2	2	no	—
512	C₂	—	4	1	no	—
513	C₂	—	8	1	no	—
514	C₂	C₄×C₂₉×#123	1	1	yes	characteristic
515	C₂	C₂×C₂₉×#443	1	1	yes	characteristic
516	C₂	C₂₉×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₂₉	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂×C₄×D₄
prime radical	C₂₉×#525	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₉ ◁ C₂³×C₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₂₉×#405	C₂	semidirect
4. C₂₉×#1929	C₂	semidirect
5. C₂₉×#1922	C₂	semidirect
7. C₂₉×#1855	C₂	semidirect
8. C₂₉×#1826	C₂	semidirect
9. C₂₉×#1772	C₂	semidirect
10. C₂₉×#1764	C₂	semidirect
11. C₈×C₂²⋊C₄×C₂₉	C₂	semidirect
17. C₂₉×#485	C₄	semidirect
18. C₂₉×#484	C₄	semidirect
19. C₂₉×#483	C₄	semidirect
20. C₂₉×#482	C₄	semidirect
21. C₂₉×#481	C₄	semidirect
22. C₂₉×#480	C₄	semidirect
180. #21592	C₂₉	direct (N × H)
229. C₂×#405	C₂×C₂₉	semidirect
230. #1929	C₂×C₂₉	semidirect
231. #1922	C₂×C₂₉	semidirect
233. #1855	C₂×C₂₉	semidirect
234. #1826	C₂×C₂₉	semidirect
235. #1772	C₂×C₂₉	semidirect
236. #1764	C₂×C₂₉	semidirect
237. C₈×C₂²⋊C₄	C₂×C₂₉	semidirect
268. #485	C₄×C₂₉	semidirect
269. #484	C₄×C₂₉	semidirect
270. #483	C₄×C₂₉	semidirect
271. #482	C₄×C₂₉	semidirect
272. #481	C₄×C₂₉	semidirect
273. #480	C₄×C₂₉	semidirect
372. C₂₉	#21592	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×#3091	2
C₂₉×#2929	2
C₂×C₂₉×#405	2
C₂₉×#1929	2
C₂₉×#1922	2
C₂₉×#1871	2
C₂₉×#1855	2
C₂₉×#1826	2
C₂₉×#1772	2
C₂₉×#1764	2
C₈×C₂²⋊C₄×C₂₉	2
#21592	29

Subgroups — C29×#21592 #20316492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#21592 #20316492