Subgroups — C₂₉×#18944 #20313844

Order 7424.

880 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3251	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3227	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3212	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1654	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1653	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1652	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1651	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1628	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1627	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1626	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1625	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1546	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1495	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1482	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#563	—	2	2	no	—
17	C₂₉×#557	C₂²	1	1	yes	characteristic
18	C₂₉×#556	C₂²	1	1	yes	characteristic
19	C₂₉×#554	—	2	1	no	—
20	C₂₉×#553	—	2	1	no	—
21	D₄×Q₈×C₂₉	—	2	1	no	—
22	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
23	C₂₉×#548	—	2	1	no	—
24	C₂₉×#547	C₂²	1	1	yes	characteristic
25	C₂₉×#544	—	2	1	no	—
26	C₂₉×#542	—	2	1	no	—
27	C₂₉×#541	—	2	1	no	—
28	C₂₉×#539	—	2	2	no	—
29	C₂₉×#536	—	2	1	no	—
30	C₂₉×#532	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂₉×#529	C₂²	1	1	yes	characteristic
33	C₂₉×#529	C₂²	1	1	yes	characteristic
34	C₂₉×#498	C₂²	1	1	yes	characteristic
35	C₂₉×#498	C₂²	1	1	yes	characteristic
36	C₂₉×#495	—	2	1	no	—
37	C₂₉×#488	—	2	1	no	—
38	C₂₉×#486	C₂²	1	1	yes	characteristic
39	C₂₉×#486	C₂²	1	1	yes	characteristic
40	C₂₉×#481	—	2	2	no	—
41	C₂₉×#478	—	2	1	no	—
42	C₂₉×#476	—	2	2	no	—
43	C₂₉×#475	C₂²	1	1	yes	characteristic
44	C₂₉×#474	C₂²	1	1	yes	characteristic
45	C₂₉×#469	—	2	1	no	—
46	C₂₉×#468	—	2	1	no	—
47	C₂₉×#463	—	2	1	no	—
48	C₂₉×#462	C₂²	1	1	yes	characteristic
49	C₂₉×#461	C₂²	1	1	yes	characteristic
50	C₂₉×#460	C₂²	1	1	yes	characteristic
51	C₂₉×#460	C₂²	1	1	yes	characteristic
52	C₂₉×#459	C₂²	1	1	yes	characteristic
53	C₂₉×#459	C₂²	1	1	yes	characteristic
54	C₂₉×#452	—	2	1	no	—
55	C₂₉×#449	—	2	1	no	—
56	C₂₉×#431	C₂²	1	1	yes	characteristic
57	C₂₉×#431	C₂²	1	1	yes	characteristic
58	C₂₉×#423	C₂²	1	1	yes	characteristic
59	C₂₉×#332	C₂²	1	1	yes	characteristic
60	C₂₉×#332	C₂²	1	1	yes	characteristic
61	C₂₉×#332	C₂²	1	1	yes	characteristic
62	C₂₉×#332	C₂²	1	1	yes	characteristic
63	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
67	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
69	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	C₂×#41×C₂₉	—	2	1	no	—
72	C₂×#41×C₂₉	—	2	1	no	—
73	C₂²×Q₈×C₂₉	—	2	1	no	—
74	C₂²×Q₈×C₂₉	—	2	1	no	—
75	C₂×Q₁₆×C₂₉	—	2	1	no	—
76	C₂×SD₁₆×C₂₉	—	2	1	no	—
77	C₂×SD₁₆×C₂₉	—	2	1	no	—
78	C₂×SD₁₆×C₂₉	—	2	1	no	—
79	C₂×D₈×C₂₉	—	2	1	no	—
80	C₂×D₈×C₂₉	—	2	1	no	—
81	C₂×M₁₆×C₂₉	—	2	1	no	—
82	C₂₉×C₄⋊Q₈	—	2	2	no	—
83	C₂₉×C₄⋊Q₈	—	2	1	no	—
84	C₂₉×C₄⋊Q₈	—	2	1	no	—
85	C₂₉×C₄⋊Q₈	—	2	1	no	—
86	C₂₉×C₄⋊Q₈	—	2	1	no	—
87	C₂₉×C₄⋊Q₈	D₄	1	2	yes	—
88	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
90	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
91	C₂₉×#127	C₂³	1	1	yes	characteristic
92	C₂₉×#126	—	2	2	no	—
93	C₂₉×#126	—	2	2	no	—
94	C₂₉×#126	—	2	2	no	—
95	C₂₉×#126	—	2	1	no	—
96	C₂₉×#126	—	2	1	no	—
97	C₂₉×#125	—	2	2	no	—
98	C₂₉×#125	—	2	2	no	—
99	C₂₉×#125	—	2	2	no	—
100	C₂₉×#125	—	2	1	no	—
101	C₂₉×#125	D₄	1	1	yes	characteristic
102	C₂₉×#125	D₄	1	1	yes	characteristic
103	C₂₉×#124	—	2	2	no	—
104	C₂₉×#124	—	2	1	no	—
105	C₂₉×#124	—	2	1	no	—
106	C₂₉×#124	D₄	1	1	yes	characteristic
107	C₂₉×#124	D₄	1	1	yes	characteristic
108	C₂₉×#123	—	2	2	no	—
109	C₂₉×#123	—	2	2	no	—
110	C₂₉×#123	—	2	1	no	—
111	C₂₉×#123	—	2	1	no	—
112	C₂₉×#123	—	2	2	no	—
113	C₂₉×C₂²⋊Q₈	—	2	2	no	—
114	C₂₉×C₂²⋊Q₈	—	2	2	no	—
115	C₂₉×C₂²⋊Q₈	—	2	2	no	—
116	C₂₉×C₂²⋊Q₈	—	2	2	no	—
117	C₂₉×C₂²⋊Q₈	—	2	2	no	—
118	C₂₉×C₂²⋊Q₈	—	2	1	no	—
119	C₂₉×C₂²⋊Q₈	—	2	2	no	—
120	C₂₉×C₂²⋊Q₈	—	2	1	no	—
121	C₂₉×C₂²⋊Q₈	—	2	1	no	—
122	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
123	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
124	C₂₉×#121	—	2	2	no	—
125	C₂₉×#121	—	2	1	no	—
126	C₂₉×#121	—	2	1	no	—
127	C₂₉×#121	—	2	1	no	—
128	C₂₉×#121	D₄	1	1	yes	characteristic
129	C₂₉×#121	D₄	1	1	yes	characteristic
130	C₄×Q₈×C₂₉	—	2	1	no	—
131	C₄×Q₈×C₂₉	—	2	1	no	—
132	C₄×Q₈×C₂₉	—	2	1	no	—
133	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
134	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
135	C₄×D₄×C₂₉	—	2	2	no	—
136	C₄×D₄×C₂₉	—	2	2	no	—
137	C₄×D₄×C₂₉	—	2	1	no	—
138	C₄×D₄×C₂₉	—	2	1	no	—
139	C₄×D₄×C₂₉	—	2	1	no	—
140	C₄×D₄×C₂₉	—	2	1	no	—
141	C₄×D₄×C₂₉	—	2	1	no	—
142	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
143	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
144	C₂₉×#117	—	2	1	no	—
145	C₂₉×#117	—	2	1	no	—
146	C₂₉×#117	—	2	1	no	—
147	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
148	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
149	C₂×C₄⋊C₄×C₂₉	D₄	1	2	yes	—
150	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
151	C₂₉×#107	—	2	1	no	—
152	C₂₉×#106	—	2	1	no	—
153	C₂₉×#106	—	2	2	no	—
154	C₂₉×#106	—	2	2	no	—
155	C₂₉×C₄⋊C₈	—	2	1	no	—
156	C₂₉×C₄⋊C₈	—	2	1	no	—
157	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₂₉×#103	—	2	1	no	—
162	C₂₉×#103	—	2	1	no	—
163	C₂₉×#103	—	2	1	no	—
164	C₂₉×#102	—	2	1	no	—
165	C₂₉×#102	—	2	1	no	—
166	C₂₉×#102	—	2	1	no	—
167	C₂₉×#102	—	2	1	no	—
168	C₂₉×#102	—	2	1	no	—
169	C₂₉×#102	—	2	2	no	—
170	C₂₉×#102	—	2	2	no	—
171	C₂₉×C₂²⋊C₈	—	2	1	no	—
172	C₂₉×C₂²⋊C₈	—	2	1	no	—
173	C₄×C₈×C₂₉	—	2	1	no	—
174	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
175	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
176	#41×C₂₉	—	8	1	no	—
177	#41×C₂₉	—	8	1	no	—
178	#41×C₂₉	—	8	1	no	—
179	#41×C₂₉	—	8	1	no	—
180	C₂×Q₈×C₂₉	—	2	2	no	—
181	C₂×Q₈×C₂₉	—	2	2	no	—
182	C₂×Q₈×C₂₉	—	2	1	no	—
183	C₂×Q₈×C₂₉	—	2	1	no	—
184	C₂×Q₈×C₂₉	—	2	1	no	—
185	C₂×Q₈×C₂₉	—	8	1	no	—
186	C₂×Q₈×C₂₉	—	8	1	no	—
187	C₂×Q₈×C₂₉	—	8	1	no	—
188	C₂×Q₈×C₂₉	—	8	1	no	—
189	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
190	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
191	C₂×D₄×C₂₉	—	2	1	no	—
192	C₂×D₄×C₂₉	—	2	1	no	—
193	C₂×D₄×C₂₉	—	2	2	no	—
194	C₂×D₄×C₂₉	—	2	1	no	—
195	C₂×D₄×C₂₉	—	2	1	no	—
196	C₂×D₄×C₂₉	—	2	1	no	—
197	C₂×D₄×C₂₉	—	4	1	no	—
198	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
199	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₂₉	—	2	2	no	—
201	C₂²×C₄×C₂₉	—	2	2	no	—
202	C₂²×C₄×C₂₉	—	2	2	no	—
203	C₂²×C₄×C₂₉	—	2	1	no	—
204	C₂²×C₄×C₂₉	—	2	1	no	—
205	C₂²×C₄×C₂₉	—	4	1	no	—
206	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
209	Q₁₆×C₂₉	—	8	1	no	—
210	SD₁₆×C₂₉	—	8	1	no	—
211	SD₁₆×C₂₉	—	8	1	no	—
212	SD₁₆×C₂₉	—	8	1	no	—
213	D₈×C₂₉	—	8	1	no	—
214	D₈×C₂₉	—	8	1	no	—
215	M₁₆×C₂₉	—	8	1	no	—
216	C₂×C₈×C₂₉	—	2	1	no	—
217	C₂×C₈×C₂₉	—	2	1	no	—
218	C₂×C₈×C₂₉	—	2	1	no	—
219	C₂×C₈×C₂₉	—	2	1	no	—
220	C₂×C₈×C₂₉	—	2	1	no	—
221	C₂×C₈×C₂₉	—	2	1	no	—
222	C₄⋊C₄×C₂₉	—	2	2	no	—
223	C₄⋊C₄×C₂₉	—	2	2	no	—
224	C₄⋊C₄×C₂₉	—	2	2	no	—
225	C₄⋊C₄×C₂₉	—	2	2	no	—
226	C₄⋊C₄×C₂₉	—	2	2	no	—
227	C₄⋊C₄×C₂₉	—	2	2	no	—
228	C₄⋊C₄×C₂₉	—	2	2	no	—
229	C₄⋊C₄×C₂₉	—	2	2	no	—
230	C₄⋊C₄×C₂₉	—	2	1	no	—
231	C₄⋊C₄×C₂₉	—	2	1	no	—
232	C₄⋊C₄×C₂₉	—	2	1	no	—
233	C₄⋊C₄×C₂₉	—	2	1	no	—
234	C₄⋊C₄×C₂₉	—	2	1	no	—
235	C₄⋊C₄×C₂₉	—	2	1	no	—
236	C₄⋊C₄×C₂₉	—	2	1	no	—
237	C₄⋊C₄×C₂₉	—	2	1	no	—
238	C₄⋊C₄×C₂₉	—	2	1	no	—
239	C₄⋊C₄×C₂₉	—	2	1	no	—
240	C₄⋊C₄×C₂₉	—	2	1	no	—
241	C₄⋊C₄×C₂₉	—	2	1	no	—
242	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
243	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
244	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
245	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
246	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
247	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
248	C₂²⋊C₄×C₂₉	—	2	2	no	—
249	C₂²⋊C₄×C₂₉	—	2	2	no	—
250	C₂²⋊C₄×C₂₉	—	2	2	no	—
251	C₂²⋊C₄×C₂₉	—	2	2	no	—
252	C₂²⋊C₄×C₂₉	—	2	1	no	—
253	C₂²⋊C₄×C₂₉	—	2	1	no	—
254	C₂²⋊C₄×C₂₉	—	2	1	no	—
255	C₂²⋊C₄×C₂₉	—	2	1	no	—
256	C₂²⋊C₄×C₂₉	—	2	1	no	—
257	C₂²⋊C₄×C₂₉	—	2	1	no	—
258	C₂²⋊C₄×C₂₉	—	2	1	no	—
259	C₂²⋊C₄×C₂₉	—	2	1	no	—
260	C₂²⋊C₄×C₂₉	—	2	1	no	—
261	C₂²⋊C₄×C₂₉	—	2	1	no	—
262	C₂²⋊C₄×C₂₉	—	4	1	no	—
263	C₂²⋊C₄×C₂₉	—	4	1	no	—
264	C₄²×C₂₉	—	2	2	no	—
265	C₄²×C₂₉	—	2	2	no	—
266	C₄²×C₂₉	—	2	1	no	—
267	C₄²×C₂₉	—	2	1	no	—
268	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
269	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
270	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
271	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
272	#18944	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
273	C₂³×C₂₉	—	2	1	no	—
274	C₂³×C₂₉	—	2	1	no	—
275	C₂³×C₂₉	—	4	1	no	—
276	C₂³×C₂₉	#120	1	1	yes	characteristic
277	Q₈×C₂₉	—	2	1	no	—
278	Q₈×C₂₉	—	2	1	no	—
279	Q₈×C₂₉	—	2	1	no	—
280	Q₈×C₂₉	—	2	1	no	—
281	Q₈×C₂₉	—	4	1	no	—
282	Q₈×C₂₉	—	4	1	no	—
283	Q₈×C₂₉	—	4	1	no	—
284	Q₈×C₂₉	—	4	1	no	—
285	Q₈×C₂₉	—	4	1	no	—
286	Q₈×C₂₉	—	4	1	no	—
287	Q₈×C₂₉	—	8	2	no	—
288	Q₈×C₂₉	—	8	2	no	—
289	D₄×C₂₉	—	2	1	no	—
290	D₄×C₂₉	—	2	1	no	—
291	D₄×C₂₉	—	2	1	no	—
292	D₄×C₂₉	—	2	1	no	—
293	D₄×C₂₉	—	4	2	no	—
294	D₄×C₂₉	—	4	2	no	—
295	D₄×C₂₉	—	4	2	no	—
296	D₄×C₂₉	—	4	1	no	—
297	D₄×C₂₉	—	4	1	no	—
298	D₄×C₂₉	—	4	1	no	—
299	D₄×C₂₉	—	4	1	no	—
300	D₄×C₂₉	—	8	2	no	—
301	D₄×C₂₉	—	8	2	no	—
302	C₂×C₄×C₂₉	—	2	1	no	—
303	C₂×C₄×C₂₉	—	2	1	no	—
304	C₂×C₄×C₂₉	—	2	1	no	—
305	C₂×C₄×C₂₉	—	2	1	no	—
306	C₂×C₄×C₂₉	—	2	1	no	—
307	C₂×C₄×C₂₉	—	2	1	no	—
308	C₂×C₄×C₂₉	—	2	1	no	—
309	C₂×C₄×C₂₉	—	2	1	no	—
310	C₂×C₄×C₂₉	—	2	1	no	—
311	C₂×C₄×C₂₉	—	2	2	no	—
312	C₂×C₄×C₂₉	—	2	2	no	—
313	C₂×C₄×C₂₉	—	2	1	no	—
314	C₂×C₄×C₂₉	—	4	1	no	—
315	C₂×C₄×C₂₉	—	4	1	no	—
316	C₂×C₄×C₂₉	—	4	1	no	—
317	C₂×C₄×C₂₉	—	4	1	no	—
318	C₂×C₄×C₂₉	—	4	1	no	—
319	C₂×C₄×C₂₉	—	4	1	no	—
320	C₂×C₄×C₂₉	—	8	2	no	—
321	C₂×C₄×C₂₉	—	8	2	no	—
322	C₂×C₄×C₂₉	—	8	2	no	—
323	C₂×C₄×C₂₉	—	8	2	no	—
324	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
325	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
326	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
327	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
330	C₈×C₂₉	—	4	1	no	—
331	C₈×C₂₉	—	4	1	no	—
332	C₈×C₂₉	—	4	1	no	—
333	C₈×C₂₉	—	4	1	no	—
334	C₈×C₂₉	—	4	1	no	—
335	C₈×C₂₉	—	4	1	no	—
336	#3552	C₂×C₂₉	1	1	yes	characteristic, complemented
337	#3251	C₂×C₂₉	1	1	yes	characteristic, complemented
338	#3227	C₂×C₂₉	1	1	yes	characteristic, complemented
339	#3212	C₂×C₂₉	1	1	yes	characteristic, complemented
340	#1654	C₂×C₂₉	1	1	yes	characteristic, complemented
341	#1653	C₂×C₂₉	1	1	yes	characteristic, complemented
342	#1652	C₂×C₂₉	1	1	yes	characteristic, complemented
343	#1651	C₂×C₂₉	1	1	yes	characteristic, complemented
344	#1628	C₂×C₂₉	1	1	yes	characteristic, complemented
345	#1627	C₂×C₂₉	1	1	yes	characteristic, complemented
346	#1626	C₂×C₂₉	1	1	yes	characteristic, complemented
347	#1625	C₂×C₂₉	1	1	yes	characteristic, complemented
348	#1546	C₂×C₂₉	1	1	yes	characteristic, complemented
349	#1495	C₂×C₂₉	1	1	yes	characteristic, complemented
350	#1482	C₂×C₂₉	1	1	yes	characteristic, complemented
351	C₂²×C₂₉	—	2	1	no	—
352	C₂²×C₂₉	—	2	1	no	—
353	C₂²×C₂₉	—	2	1	no	—
354	C₂²×C₂₉	—	4	1	no	—
355	C₂²×C₂₉	—	4	1	no	—
356	C₂²×C₂₉	—	4	1	no	—
357	C₂²×C₂₉	—	4	1	no	—
358	C₂²×C₂₉	—	4	1	no	—
359	C₂²×C₂₉	—	4	1	no	—
360	C₂²×C₂₉	—	8	1	no	—
361	C₂²×C₂₉	—	8	1	no	—
362	C₂²×C₂₉	—	8	1	no	—
363	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
364	C₄×C₂₉	—	2	1	no	—
365	C₄×C₂₉	—	2	1	no	—
366	C₄×C₂₉	—	2	1	no	—
367	C₄×C₂₉	—	2	1	no	—
368	C₄×C₂₉	—	4	1	no	—
369	C₄×C₂₉	—	4	1	no	—
370	C₄×C₂₉	—	4	1	no	—
371	C₄×C₂₉	—	4	2	no	—
372	C₄×C₂₉	—	4	1	no	—
373	C₄×C₂₉	—	4	2	no	—
374	C₄×C₂₉	—	4	1	no	—
375	C₄×C₂₉	—	4	1	no	—
376	C₄×C₂₉	—	8	1	no	—
377	C₄×C₂₉	#576	1	1	yes	characteristic
378	C₄×C₂₉	#577	1	1	yes	characteristic
379	C₄×C₂₉	#577	1	1	yes	characteristic
380	C₄×C₂₉	#577	1	1	yes	characteristic
381	#563	—	2	2	no	—
382	#557	C₂²×C₂₉	1	1	yes	characteristic
383	#556	C₂²×C₂₉	1	1	yes	characteristic
384	#554	—	2	1	no	—
385	#553	—	2	1	no	—
386	D₄×Q₈	—	2	1	no	—
387	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
388	#548	—	2	1	no	—
389	#547	C₂²×C₂₉	1	1	yes	characteristic
390	#544	—	2	1	no	—
391	#542	—	2	1	no	—
392	#541	—	2	1	no	—
393	#539	—	2	2	no	—
394	#536	—	2	1	no	—
395	#532	C₂²×C₂₉	1	1	yes	characteristic
396	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
397	#529	C₂²×C₂₉	1	1	yes	characteristic
398	#529	C₂²×C₂₉	1	1	yes	characteristic
399	#498	C₂²×C₂₉	1	1	yes	characteristic
400	#498	C₂²×C₂₉	1	1	yes	characteristic
401	#495	—	2	1	no	—
402	#488	—	2	1	no	—
403	#486	C₂²×C₂₉	1	1	yes	characteristic
404	#486	C₂²×C₂₉	1	1	yes	characteristic
405	#481	—	2	2	no	—
406	#478	—	2	1	no	—
407	#476	—	2	2	no	—
408	#475	C₂²×C₂₉	1	1	yes	characteristic
409	#474	C₂²×C₂₉	1	1	yes	characteristic
410	#469	—	2	1	no	—
411	#468	—	2	1	no	—
412	#463	—	2	1	no	—
413	#462	C₂²×C₂₉	1	1	yes	characteristic
414	#461	C₂²×C₂₉	1	1	yes	characteristic
415	#460	C₂²×C₂₉	1	1	yes	characteristic
416	#460	C₂²×C₂₉	1	1	yes	characteristic
417	#459	C₂²×C₂₉	1	1	yes	characteristic
418	#459	C₂²×C₂₉	1	1	yes	characteristic
419	#452	—	2	1	no	—
420	#449	—	2	1	no	—
421	#431	C₂²×C₂₉	1	1	yes	characteristic
422	#431	C₂²×C₂₉	1	1	yes	characteristic
423	#423	C₂²×C₂₉	1	1	yes	characteristic
424	#332	C₂²×C₂₉	1	1	yes	characteristic
425	#332	C₂²×C₂₉	1	1	yes	characteristic
426	#332	C₂²×C₂₉	1	1	yes	characteristic
427	#332	C₂²×C₂₉	1	1	yes	characteristic
428	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
429	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
430	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
431	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
432	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
433	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
434	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
435	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
436	C₂×C₂₉	—	4	1	no	—
437	C₂×C₂₉	—	8	1	no	—
438	C₂×C₂₉	—	8	1	no	—
439	C₂×C₂₉	—	16	1	no	—
440	C₂×C₂₉	#3010	1	1	yes	characteristic
441	C₂×C₂₉	#3012	1	1	yes	characteristic
442	C₂×C₂₉	#3020	1	1	yes	characteristic
443	C₂×#41	—	2	1	no	—
444	C₂×#41	—	2	1	no	—
445	C₂²×Q₈	—	2	1	no	—
446	C₂²×Q₈	—	2	1	no	—
447	C₂×Q₁₆	—	2	1	no	—
448	C₂×SD₁₆	—	2	1	no	—
449	C₂×SD₁₆	—	2	1	no	—
450	C₂×SD₁₆	—	2	1	no	—
451	C₂×D₈	—	2	1	no	—
452	C₂×D₈	—	2	1	no	—
453	C₂×M₁₆	—	2	1	no	—
454	C₄⋊Q₈	—	2	2	no	—
455	C₄⋊Q₈	—	2	1	no	—
456	C₄⋊Q₈	—	2	1	no	—
457	C₄⋊Q₈	—	2	1	no	—
458	C₄⋊Q₈	—	2	1	no	—
459	C₄⋊Q₈	D₄×C₂₉	1	2	yes	—
460	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
461	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
462	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
463	#127	C₂³×C₂₉	1	1	yes	characteristic
464	#126	—	2	2	no	—
465	#126	—	2	2	no	—
466	#126	—	2	2	no	—
467	#126	—	2	1	no	—
468	#126	—	2	1	no	—
469	#125	—	2	2	no	—
470	#125	—	2	2	no	—
471	#125	—	2	2	no	—
472	#125	—	2	1	no	—
473	#125	D₄×C₂₉	1	1	yes	characteristic
474	#125	D₄×C₂₉	1	1	yes	characteristic
475	#124	—	2	2	no	—
476	#124	—	2	1	no	—
477	#124	—	2	1	no	—
478	#124	D₄×C₂₉	1	1	yes	characteristic
479	#124	D₄×C₂₉	1	1	yes	characteristic
480	#123	—	2	2	no	—
481	#123	—	2	2	no	—
482	#123	—	2	1	no	—
483	#123	—	2	1	no	—
484	#123	—	2	2	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	—	2	2	no	—
488	C₂²⋊Q₈	—	2	2	no	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	—	2	1	no	—
491	C₂²⋊Q₈	—	2	2	no	—
492	C₂²⋊Q₈	—	2	1	no	—
493	C₂²⋊Q₈	—	2	1	no	—
494	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
495	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
496	#121	—	2	2	no	—
497	#121	—	2	1	no	—
498	#121	—	2	1	no	—
499	#121	—	2	1	no	—
500	#121	D₄×C₂₉	1	1	yes	characteristic
501	#121	D₄×C₂₉	1	1	yes	characteristic
502	C₄×Q₈	—	2	1	no	—
503	C₄×Q₈	—	2	1	no	—
504	C₄×Q₈	—	2	1	no	—
505	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
506	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	2	1	no	—
510	C₄×D₄	—	2	1	no	—
511	C₄×D₄	—	2	1	no	—
512	C₄×D₄	—	2	1	no	—
513	C₄×D₄	—	2	1	no	—
514	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
515	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
516	#117	—	2	1	no	—
517	#117	—	2	1	no	—
518	#117	—	2	1	no	—
519	C₂×C₄⋊C₄	—	2	1	no	—
520	C₂×C₄⋊C₄	—	2	1	no	—
521	C₂×C₄⋊C₄	D₄×C₂₉	1	2	yes	—
522	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
523	#107	—	2	1	no	—
524	#106	—	2	1	no	—
525	#106	—	2	2	no	—
526	#106	—	2	2	no	—
527	C₄⋊C₈	—	2	1	no	—
528	C₄⋊C₈	—	2	1	no	—
529	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
530	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
531	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
532	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
533	#103	—	2	1	no	—
534	#103	—	2	1	no	—
535	#103	—	2	1	no	—
536	#102	—	2	1	no	—
537	#102	—	2	1	no	—
538	#102	—	2	1	no	—
539	#102	—	2	1	no	—
540	#102	—	2	1	no	—
541	#102	—	2	2	no	—
542	#102	—	2	2	no	—
543	C₂²⋊C₈	—	2	1	no	—
544	C₂²⋊C₈	—	2	1	no	—
545	C₄×C₈	—	2	1	no	—
546	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
547	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
548	C₂₉	#18944	1	1	yes	characteristic, direct product factor, Sylow
549	#41	—	8	1	no	—
550	#41	—	8	1	no	—
551	#41	—	8	1	no	—
552	#41	—	8	1	no	—
553	C₂×Q₈	—	2	2	no	—
554	C₂×Q₈	—	2	2	no	—
555	C₂×Q₈	—	2	1	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	8	1	no	—
559	C₂×Q₈	—	8	1	no	—
560	C₂×Q₈	—	8	1	no	—
561	C₂×Q₈	—	8	1	no	—
562	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
563	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	4	1	no	—
571	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
572	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	4	1	no	—
579	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
580	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
582	Q₁₆	—	8	1	no	—
583	SD₁₆	—	8	1	no	—
584	SD₁₆	—	8	1	no	—
585	SD₁₆	—	8	1	no	—
586	D₈	—	8	1	no	—
587	D₈	—	8	1	no	—
588	M₁₆	—	8	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
616	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
617	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
618	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
619	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
620	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
621	C₂²⋊C₄	—	2	2	no	—
622	C₂²⋊C₄	—	2	2	no	—
623	C₂²⋊C₄	—	2	2	no	—
624	C₂²⋊C₄	—	2	2	no	—
625	C₂²⋊C₄	—	2	1	no	—
626	C₂²⋊C₄	—	2	1	no	—
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	2	1	no	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	2	1	no	—
631	C₂²⋊C₄	—	2	1	no	—
632	C₂²⋊C₄	—	2	1	no	—
633	C₂²⋊C₄	—	2	1	no	—
634	C₂²⋊C₄	—	2	1	no	—
635	C₂²⋊C₄	—	4	1	no	—
636	C₂²⋊C₄	—	4	1	no	—
637	C₄²	—	2	2	no	—
638	C₄²	—	2	2	no	—
639	C₄²	—	2	1	no	—
640	C₄²	—	2	1	no	—
641	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
642	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
643	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
644	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
645	C₂³	—	2	1	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	C₂₉×#120	1	1	yes	characteristic
649	Q₈	—	2	1	no	—
650	Q₈	—	2	1	no	—
651	Q₈	—	2	1	no	—
652	Q₈	—	2	1	no	—
653	Q₈	—	4	1	no	—
654	Q₈	—	4	1	no	—
655	Q₈	—	4	1	no	—
656	Q₈	—	4	1	no	—
657	Q₈	—	4	1	no	—
658	Q₈	—	4	1	no	—
659	Q₈	—	8	2	no	—
660	Q₈	—	8	2	no	—
661	D₄	—	2	1	no	—
662	D₄	—	2	1	no	—
663	D₄	—	2	1	no	—
664	D₄	—	2	1	no	—
665	D₄	—	4	2	no	—
666	D₄	—	4	2	no	—
667	D₄	—	4	2	no	—
668	D₄	—	4	1	no	—
669	D₄	—	4	1	no	—
670	D₄	—	4	1	no	—
671	D₄	—	4	1	no	—
672	D₄	—	8	2	no	—
673	D₄	—	8	2	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	8	2	no	—
693	C₂×C₄	—	8	2	no	—
694	C₂×C₄	—	8	2	no	—
695	C₂×C₄	—	8	2	no	—
696	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
697	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
698	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
699	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
700	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
701	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
702	C₈	—	4	1	no	—
703	C₈	—	4	1	no	—
704	C₈	—	4	1	no	—
705	C₈	—	4	1	no	—
706	C₈	—	4	1	no	—
707	C₈	—	4	1	no	—
708	C₂²	—	2	1	no	—
709	C₂²	—	2	1	no	—
710	C₂²	—	2	1	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	1	no	—
714	C₂²	—	4	1	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	8	1	no	—
718	C₂²	—	8	1	no	—
719	C₂²	—	8	1	no	—
720	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
721	C₄	—	2	1	no	—
722	C₄	—	2	1	no	—
723	C₄	—	2	1	no	—
724	C₄	—	2	1	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	1	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	1	no	—
732	C₄	—	4	1	no	—
733	C₄	—	8	1	no	—
734	C₄	C₂₉×#576	1	1	yes	characteristic
735	C₄	C₂₉×#577	1	1	yes	characteristic
736	C₄	C₂₉×#577	1	1	yes	characteristic
737	C₄	C₂₉×#577	1	1	yes	characteristic
738	C₂	—	4	1	no	—
739	C₂	—	8	1	no	—
740	C₂	—	8	1	no	—
741	C₂	—	16	1	no	—
742	C₂	C₂₉×#3010	1	1	yes	characteristic
743	C₂	C₂₉×#3012	1	1	yes	characteristic
744	C₂	C₂₉×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3552	C₂	semidirect
2. C₂₉×#3251	C₂	semidirect
3. C₂₉×#3227	C₂	semidirect
4. C₂₉×#3212	C₂	semidirect
5. C₂₉×#1654	C₂	semidirect
6. C₂₉×#1653	C₂	semidirect
7. C₂₉×#1652	C₂	semidirect
8. C₂₉×#1651	C₂	semidirect
9. C₂₉×#1628	C₂	semidirect
10. C₂₉×#1627	C₂	semidirect
11. C₂₉×#1626	C₂	semidirect
12. C₂₉×#1625	C₂	semidirect
13. C₂₉×#1546	C₂	semidirect
14. C₂₉×#1495	C₂	semidirect
15. C₂₉×#1482	C₂	semidirect
272. #18944	C₂₉	direct (N × H)
336. #3552	C₂×C₂₉	semidirect
337. #3251	C₂×C₂₉	semidirect
338. #3227	C₂×C₂₉	semidirect
339. #3212	C₂×C₂₉	semidirect
340. #1654	C₂×C₂₉	semidirect
341. #1653	C₂×C₂₉	semidirect
342. #1652	C₂×C₂₉	semidirect
343. #1651	C₂×C₂₉	semidirect
344. #1628	C₂×C₂₉	semidirect
345. #1627	C₂×C₂₉	semidirect
346. #1626	C₂×C₂₉	semidirect
347. #1625	C₂×C₂₉	semidirect
348. #1546	C₂×C₂₉	semidirect
349. #1495	C₂×C₂₉	semidirect
350. #1482	C₂×C₂₉	semidirect
548. C₂₉	#18944	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×#3552	2
C₂₉×#3251	2
C₂₉×#3227	2
C₂₉×#3212	2
C₂₉×#1654	2
C₂₉×#1653	2
C₂₉×#1652	2
C₂₉×#1651	2
C₂₉×#1628	2
C₂₉×#1627	2
C₂₉×#1626	2
C₂₉×#1625	2
C₂₉×#1546	2
C₂₉×#1495	2
C₂₉×#1482	2
#18944	29

Subgroups — C29×#18944 #20313844

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18944 #20313844