Subgroups — C₂₉×#18964 #20313864

Order 7424.

900 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3247	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3207	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1637	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1636	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1631	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1630	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1627	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1626	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1621	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1620	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1547	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1495	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1481	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#562	—	2	2	no	—
17	C₂₉×#559	—	2	1	no	—
18	C₂₉×#559	C₂²	1	1	yes	characteristic
19	C₂₉×#557	C₂²	1	1	yes	characteristic
20	C₂₉×#554	—	2	1	no	—
21	C₂₉×#550	C₂²	1	1	yes	characteristic
22	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
23	C₂₉×#548	—	2	1	no	—
24	C₂₉×#547	—	2	1	no	—
25	C₂₉×#542	—	2	1	no	—
26	C₂₉×#542	—	2	1	no	—
27	C₂₉×#540	—	2	1	no	—
28	C₂₉×#539	—	2	2	no	—
29	C₂₉×#536	—	2	1	no	—
30	C₂₉×#533	C₂²	1	1	yes	characteristic
31	C₂₉×#532	C₂²	1	1	yes	characteristic
32	C₂₉×#532	C₂²	1	1	yes	characteristic
33	C₂₉×#529	C₂²	1	1	yes	characteristic
34	C₂₉×#493	C₂²	1	1	yes	characteristic
35	C₂₉×#492	C₂²	1	1	yes	characteristic
36	C₂₉×#487	C₂²	1	1	yes	characteristic
37	C₂₉×#486	C₂²	1	1	yes	characteristic
38	C₂₉×#478	—	2	1	no	—
39	C₂₉×#477	C₂²	1	1	yes	characteristic
40	C₂₉×#477	C₂²	1	1	yes	characteristic
41	C₂₉×#477	C₂²	1	1	yes	characteristic
42	C₂₉×#476	C₂²	1	1	yes	characteristic
43	C₂₉×#474	—	2	1	no	—
44	C₂₉×#468	—	2	1	no	—
45	C₂₉×#468	—	2	1	no	—
46	C₂₉×#466	—	2	1	no	—
47	C₂₉×#465	—	2	1	no	—
48	C₂₉×#463	—	2	1	no	—
49	C₂₉×#463	—	2	2	no	—
50	C₂₉×#461	—	2	1	no	—
51	C₂₉×#460	C₂²	1	1	yes	characteristic
52	C₂₉×#460	C₂²	1	1	yes	characteristic
53	C₂₉×#460	C₂²	1	1	yes	characteristic
54	C₂₉×#459	C₂²	1	1	yes	characteristic
55	C₂₉×#449	—	2	2	no	—
56	C₂₉×#431	C₂²	1	1	yes	characteristic
57	C₂₉×#423	C₂²	1	1	yes	characteristic
58	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
59	C₂₉×#332	C₂²	1	1	yes	characteristic
60	C₂₉×#332	C₂²	1	1	yes	characteristic
61	C₂₉×#331	C₂²	1	1	yes	characteristic
62	C₂₉×#331	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×Q₈⋊C₈	C₂²	1	1	yes	characteristic
68	C₂₉×Q₈⋊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	C₂×#41×C₂₉	—	2	1	no	—
74	C₂²×Q₈×C₂₉	—	2	1	no	—
75	C₂×SD₁₆×C₂₉	—	2	1	no	—
76	C₂×SD₁₆×C₂₉	—	2	1	no	—
77	C₂×SD₁₆×C₂₉	—	2	1	no	—
78	C₂×SD₁₆×C₂₉	—	2	2	no	—
79	C₂×D₈×C₂₉	—	2	2	no	—
80	C₂×D₈×C₂₉	—	2	1	no	—
81	C₂×M₁₆×C₂₉	—	2	1	no	—
82	C₂²×C₈×C₂₉	—	2	1	no	—
83	C₂₉×C₄⋊Q₈	—	2	1	no	—
84	C₂₉×C₄⋊Q₈	—	2	1	no	—
85	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
86	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
87	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₂₉×#127	—	2	1	no	—
90	C₂₉×#127	C₂³	1	1	yes	characteristic
91	C₂₉×#127	C₂³	1	1	yes	characteristic
92	C₂₉×#126	—	2	2	no	—
93	C₂₉×#126	—	2	1	no	—
94	C₂₉×#125	—	2	2	no	—
95	C₂₉×#125	—	2	1	no	—
96	C₂₉×#125	—	2	1	no	—
97	C₂₉×#125	D₄	1	1	yes	characteristic
98	C₂₉×#124	—	2	2	no	—
99	C₂₉×#124	—	2	2	no	—
100	C₂₉×#124	—	2	1	no	—
101	C₂₉×#124	—	2	1	no	—
102	C₂₉×#124	—	2	1	no	—
103	C₂₉×#124	—	2	1	no	—
104	C₂₉×#124	D₄	1	1	yes	characteristic
105	C₂₉×#123	—	2	2	no	—
106	C₂₉×#123	—	2	2	no	—
107	C₂₉×#123	—	2	2	no	—
108	C₂₉×#123	—	2	2	no	—
109	C₂₉×#123	—	2	2	no	—
110	C₂₉×#123	—	2	2	no	—
111	C₂₉×#123	—	2	1	no	—
112	C₂₉×C₂²⋊Q₈	—	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	1	no	—
117	C₂₉×C₂²⋊Q₈	—	2	2	no	—
118	C₂₉×C₂²⋊Q₈	—	2	1	no	—
119	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
120	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
121	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
122	C₂₉×#121	—	2	2	no	—
123	C₂₉×#121	—	2	2	no	—
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	—	2	1	no	—
129	C₂₉×#121	D₄	1	2	yes	—
130	C₂₉×#121	D₄	1	1	yes	characteristic
131	C₄×Q₈×C₂₉	—	2	1	no	—
132	C₄×Q₈×C₂₉	—	2	1	no	—
133	C₄×Q₈×C₂₉	—	2	1	no	—
134	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
135	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
136	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
137	C₄×D₄×C₂₉	—	2	2	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	—	2	1	no	—
143	C₄×D₄×C₂₉	—	2	1	no	—
144	C₄×D₄×C₂₉	—	2	1	no	—
145	C₄×D₄×C₂₉	—	2	1	no	—
146	C₄×D₄×C₂₉	D₄	1	2	yes	—
147	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
148	C₂₉×#117	—	2	1	no	—
149	C₂₉×#117	—	2	1	no	—
150	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
151	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
152	C₂₉×#107	—	2	1	no	—
153	C₂₉×#107	—	2	1	no	—
154	C₂₉×#107	—	2	1	no	—
155	C₂₉×#106	—	2	1	no	—
156	C₂₉×C₄⋊C₈	—	2	1	no	—
157	C₂₉×C₄⋊C₈	—	2	1	no	—
158	C₂₉×C₄⋊C₈	—	2	1	no	—
159	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
162	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
163	C₂₉×#103	—	2	1	no	—
164	C₂₉×#103	—	2	1	no	—
165	C₂₉×#103	—	2	1	no	—
166	C₂₉×#103	—	2	2	no	—
167	C₂₉×#102	—	2	1	no	—
168	C₂₉×#102	—	2	2	no	—
169	C₂₉×#102	—	2	1	no	—
170	C₂₉×#102	—	2	1	no	—
171	C₂₉×#102	—	2	1	no	—
172	C₂₉×#102	—	2	1	no	—
173	C₂₉×C₂²⋊C₈	—	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	#41×C₂₉	—	8	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	C₂×D₄	1	1	yes	characteristic
188	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
189	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
190	C₂×D₄×C₂₉	—	2	2	no	—
191	C₂×D₄×C₂₉	—	2	2	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	—	2	1	no	—
198	C₂×D₄×C₂₉	—	2	1	no	—
199	C₂×D₄×C₂₉	—	4	1	no	—
200	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
201	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
202	C₂²×C₄×C₂₉	—	2	2	no	—
203	C₂²×C₄×C₂₉	—	2	2	no	—
204	C₂²×C₄×C₂₉	—	2	2	no	—
205	C₂²×C₄×C₂₉	—	2	1	no	—
206	C₂²×C₄×C₂₉	—	2	2	no	—
207	C₂²×C₄×C₂₉	—	4	1	no	—
208	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
211	SD₁₆×C₂₉	—	8	1	no	—
212	SD₁₆×C₂₉	—	8	1	no	—
213	SD₁₆×C₂₉	—	8	1	no	—
214	SD₁₆×C₂₉	—	8	2	no	—
215	D₈×C₂₉	—	8	1	no	—
216	D₈×C₂₉	—	8	2	no	—
217	M₁₆×C₂₉	—	8	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	C₂×C₈×C₂₉	—	2	1	no	—
223	C₂×C₈×C₂₉	—	2	1	no	—
224	C₂×C₈×C₂₉	—	8	1	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	1	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	—	2	1	no	—
243	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
244	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
245	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
246	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
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	2	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	2	no	—
260	C₂²⋊C₄×C₂₉	—	2	2	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	1	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	#18964	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
273	C₂³×C₂₉	—	2	1	no	—
274	C₂³×C₂₉	—	2	2	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	—	2	1	no	—
282	Q₈×C₂₉	—	2	1	no	—
283	Q₈×C₂₉	—	4	2	no	—
284	Q₈×C₂₉	—	4	1	no	—
285	Q₈×C₂₉	—	4	1	no	—
286	Q₈×C₂₉	—	8	1	no	—
287	Q₈×C₂₉	—	8	2	no	—
288	D₄×C₂₉	—	2	1	no	—
289	D₄×C₂₉	—	2	1	no	—
290	D₄×C₂₉	—	4	2	no	—
291	D₄×C₂₉	—	4	2	no	—
292	D₄×C₂₉	—	4	1	no	—
293	D₄×C₂₉	—	4	1	no	—
294	D₄×C₂₉	—	4	1	no	—
295	D₄×C₂₉	—	4	1	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	1	no	—
301	D₄×C₂₉	—	8	2	no	—
302	D₄×C₂₉	—	8	2	no	—
303	D₄×C₂₉	—	8	2	no	—
304	D₄×C₂₉	—	8	2	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	1	no	—
312	C₂×C₄×C₂₉	—	2	1	no	—
313	C₂×C₄×C₂₉	—	2	1	no	—
314	C₂×C₄×C₂₉	—	2	2	no	—
315	C₂×C₄×C₂₉	—	2	1	no	—
316	C₂×C₄×C₂₉	—	2	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	—	4	1	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	—	8	2	no	—
325	C₂×C₄×C₂₉	—	8	2	no	—
326	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
327	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
328	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
329	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
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	C₈×C₂₉	—	4	1	no	—
337	C₈×C₂₉	—	4	1	no	—
338	#3554	C₂×C₂₉	1	1	yes	characteristic, complemented
339	#3254	C₂×C₂₉	1	1	yes	characteristic, complemented
340	#3247	C₂×C₂₉	1	1	yes	characteristic, complemented
341	#3207	C₂×C₂₉	1	1	yes	characteristic, complemented
342	#1637	C₂×C₂₉	1	1	yes	characteristic, complemented
343	#1636	C₂×C₂₉	1	1	yes	characteristic, complemented
344	#1631	C₂×C₂₉	1	1	yes	characteristic, complemented
345	#1630	C₂×C₂₉	1	1	yes	characteristic, complemented
346	#1627	C₂×C₂₉	1	1	yes	characteristic, complemented
347	#1626	C₂×C₂₉	1	1	yes	characteristic, complemented
348	#1621	C₂×C₂₉	1	1	yes	characteristic, complemented
349	#1620	C₂×C₂₉	1	1	yes	characteristic, complemented
350	#1547	C₂×C₂₉	1	1	yes	characteristic, complemented
351	#1495	C₂×C₂₉	1	1	yes	characteristic, complemented
352	#1481	C₂×C₂₉	1	1	yes	characteristic, complemented
353	C₂²×C₂₉	—	2	1	no	—
354	C₂²×C₂₉	—	2	1	no	—
355	C₂²×C₂₉	—	2	1	no	—
356	C₂²×C₂₉	—	4	1	no	—
357	C₂²×C₂₉	—	4	2	no	—
358	C₂²×C₂₉	—	4	1	no	—
359	C₂²×C₂₉	—	4	2	no	—
360	C₂²×C₂₉	—	4	2	no	—
361	C₂²×C₂₉	—	4	1	no	—
362	C₂²×C₂₉	—	8	1	no	—
363	C₂²×C₂₉	—	8	1	no	—
364	C₂²×C₂₉	—	8	1	no	—
365	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
366	C₄×C₂₉	—	2	1	no	—
367	C₄×C₂₉	—	2	1	no	—
368	C₄×C₂₉	—	2	1	no	—
369	C₄×C₂₉	—	2	1	no	—
370	C₄×C₂₉	—	4	1	no	—
371	C₄×C₂₉	—	4	1	no	—
372	C₄×C₂₉	—	4	2	no	—
373	C₄×C₂₉	—	4	1	no	—
374	C₄×C₂₉	—	4	1	no	—
375	C₄×C₂₉	—	4	1	no	—
376	C₄×C₂₉	—	4	1	no	—
377	C₄×C₂₉	—	4	1	no	—
378	C₄×C₂₉	—	8	1	no	—
379	C₄×C₂₉	#576	1	1	yes	characteristic
380	C₄×C₂₉	#577	1	1	yes	characteristic
381	C₄×C₂₉	#577	1	1	yes	characteristic
382	C₄×C₂₉	#578	1	1	yes	characteristic
383	#562	—	2	2	no	—
384	#559	—	2	1	no	—
385	#559	C₂²×C₂₉	1	1	yes	characteristic
386	#557	C₂²×C₂₉	1	1	yes	characteristic
387	#554	—	2	1	no	—
388	#550	C₂²×C₂₉	1	1	yes	characteristic
389	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
390	#548	—	2	1	no	—
391	#547	—	2	1	no	—
392	#542	—	2	1	no	—
393	#542	—	2	1	no	—
394	#540	—	2	1	no	—
395	#539	—	2	2	no	—
396	#536	—	2	1	no	—
397	#533	C₂²×C₂₉	1	1	yes	characteristic
398	#532	C₂²×C₂₉	1	1	yes	characteristic
399	#532	C₂²×C₂₉	1	1	yes	characteristic
400	#529	C₂²×C₂₉	1	1	yes	characteristic
401	#493	C₂²×C₂₉	1	1	yes	characteristic
402	#492	C₂²×C₂₉	1	1	yes	characteristic
403	#487	C₂²×C₂₉	1	1	yes	characteristic
404	#486	C₂²×C₂₉	1	1	yes	characteristic
405	#478	—	2	1	no	—
406	#477	C₂²×C₂₉	1	1	yes	characteristic
407	#477	C₂²×C₂₉	1	1	yes	characteristic
408	#477	C₂²×C₂₉	1	1	yes	characteristic
409	#476	C₂²×C₂₉	1	1	yes	characteristic
410	#474	—	2	1	no	—
411	#468	—	2	1	no	—
412	#468	—	2	1	no	—
413	#466	—	2	1	no	—
414	#465	—	2	1	no	—
415	#463	—	2	1	no	—
416	#463	—	2	2	no	—
417	#461	—	2	1	no	—
418	#460	C₂²×C₂₉	1	1	yes	characteristic
419	#460	C₂²×C₂₉	1	1	yes	characteristic
420	#460	C₂²×C₂₉	1	1	yes	characteristic
421	#459	C₂²×C₂₉	1	1	yes	characteristic
422	#449	—	2	2	no	—
423	#431	C₂²×C₂₉	1	1	yes	characteristic
424	#423	C₂²×C₂₉	1	1	yes	characteristic
425	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
426	#332	C₂²×C₂₉	1	1	yes	characteristic
427	#332	C₂²×C₂₉	1	1	yes	characteristic
428	#331	C₂²×C₂₉	1	1	yes	characteristic
429	#331	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	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
433	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
434	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
435	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
436	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
437	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
438	C₂×C₂₉	—	4	1	no	—
439	C₂×C₂₉	—	8	1	no	—
440	C₂×C₂₉	—	8	2	no	—
441	C₂×C₂₉	—	16	1	no	—
442	C₂×C₂₉	#3012	1	1	yes	characteristic
443	C₂×C₂₉	#3013	1	1	yes	characteristic
444	C₂×C₂₉	#3021	1	1	yes	characteristic
445	C₂×#41	—	2	1	no	—
446	C₂×#41	—	2	1	no	—
447	C₂×#41	—	2	1	no	—
448	C₂²×Q₈	—	2	1	no	—
449	C₂×SD₁₆	—	2	1	no	—
450	C₂×SD₁₆	—	2	1	no	—
451	C₂×SD₁₆	—	2	1	no	—
452	C₂×SD₁₆	—	2	2	no	—
453	C₂×D₈	—	2	2	no	—
454	C₂×D₈	—	2	1	no	—
455	C₂×M₁₆	—	2	1	no	—
456	C₂²×C₈	—	2	1	no	—
457	C₄⋊Q₈	—	2	1	no	—
458	C₄⋊Q₈	—	2	1	no	—
459	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
460	C₄⋊Q₈	D₄×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	—	2	1	no	—
464	#127	C₂³×C₂₉	1	1	yes	characteristic
465	#127	C₂³×C₂₉	1	1	yes	characteristic
466	#126	—	2	2	no	—
467	#126	—	2	1	no	—
468	#125	—	2	2	no	—
469	#125	—	2	1	no	—
470	#125	—	2	1	no	—
471	#125	D₄×C₂₉	1	1	yes	characteristic
472	#124	—	2	2	no	—
473	#124	—	2	2	no	—
474	#124	—	2	1	no	—
475	#124	—	2	1	no	—
476	#124	—	2	1	no	—
477	#124	—	2	1	no	—
478	#124	D₄×C₂₉	1	1	yes	characteristic
479	#123	—	2	2	no	—
480	#123	—	2	2	no	—
481	#123	—	2	2	no	—
482	#123	—	2	2	no	—
483	#123	—	2	2	no	—
484	#123	—	2	2	no	—
485	#123	—	2	1	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	D₄×C₂₉	1	1	yes	characteristic
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	2	no	—
498	#121	—	2	2	no	—
499	#121	—	2	1	no	—
500	#121	—	2	1	no	—
501	#121	—	2	1	no	—
502	#121	—	2	1	no	—
503	#121	D₄×C₂₉	1	1	yes	characteristic
504	#121	D₄×C₂₉	1	2	yes	—
505	C₄×Q₈	—	2	1	no	—
506	C₄×Q₈	—	2	1	no	—
507	C₄×Q₈	—	2	1	no	—
508	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
509	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
510	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	1	no	—
513	C₄×D₄	—	2	1	no	—
514	C₄×D₄	—	2	1	no	—
515	C₄×D₄	—	2	1	no	—
516	C₄×D₄	—	2	1	no	—
517	C₄×D₄	—	2	1	no	—
518	C₄×D₄	—	2	1	no	—
519	C₄×D₄	—	2	1	no	—
520	C₄×D₄	D₄×C₂₉	1	2	yes	—
521	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
522	#117	—	2	1	no	—
523	#117	—	2	1	no	—
524	C₂×C₄⋊C₄	—	2	2	no	—
525	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
526	#107	—	2	1	no	—
527	#107	—	2	1	no	—
528	#107	—	2	1	no	—
529	#106	—	2	1	no	—
530	C₄⋊C₈	—	2	1	no	—
531	C₄⋊C₈	—	2	1	no	—
532	C₄⋊C₈	—	2	1	no	—
533	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
534	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
535	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
536	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
537	#103	—	2	1	no	—
538	#103	—	2	1	no	—
539	#103	—	2	1	no	—
540	#103	—	2	2	no	—
541	#102	—	2	1	no	—
542	#102	—	2	2	no	—
543	#102	—	2	1	no	—
544	#102	—	2	1	no	—
545	#102	—	2	1	no	—
546	#102	—	2	1	no	—
547	C₂²⋊C₈	—	2	1	no	—
548	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
549	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
550	C₂₉	#18964	1	1	yes	characteristic, direct product factor, Sylow
551	#41	—	8	1	no	—
552	#41	—	8	1	no	—
553	#41	—	8	1	no	—
554	#41	—	8	1	no	—
555	#41	—	8	2	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	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×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	4	1	no	—
575	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
576	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	4	1	no	—
583	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
584	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
585	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
586	SD₁₆	—	8	1	no	—
587	SD₁₆	—	8	1	no	—
588	SD₁₆	—	8	1	no	—
589	SD₁₆	—	8	2	no	—
590	D₈	—	8	1	no	—
591	D₈	—	8	2	no	—
592	M₁₆	—	8	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	8	1	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	2	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	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
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	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
622	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
623	C₂²⋊C₄	—	2	2	no	—
624	C₂²⋊C₄	—	2	2	no	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	2	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	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	1	no	—
637	C₂²⋊C₄	—	4	1	no	—
638	C₂²⋊C₄	—	4	1	no	—
639	C₄²	—	2	2	no	—
640	C₄²	—	2	1	no	—
641	C₄²	—	2	1	no	—
642	C₄²	—	2	1	no	—
643	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
644	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
645	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
646	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
647	C₂³	—	2	1	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	4	1	no	—
650	C₂³	C₂₉×#120	1	1	yes	characteristic
651	Q₈	—	2	1	no	—
652	Q₈	—	2	1	no	—
653	Q₈	—	2	1	no	—
654	Q₈	—	2	1	no	—
655	Q₈	—	2	1	no	—
656	Q₈	—	2	1	no	—
657	Q₈	—	4	2	no	—
658	Q₈	—	4	1	no	—
659	Q₈	—	4	1	no	—
660	Q₈	—	8	1	no	—
661	Q₈	—	8	2	no	—
662	D₄	—	2	1	no	—
663	D₄	—	2	1	no	—
664	D₄	—	4	2	no	—
665	D₄	—	4	2	no	—
666	D₄	—	4	1	no	—
667	D₄	—	4	1	no	—
668	D₄	—	4	1	no	—
669	D₄	—	4	1	no	—
670	D₄	—	4	1	no	—
671	D₄	—	4	1	no	—
672	D₄	—	4	1	no	—
673	D₄	—	4	1	no	—
674	D₄	—	8	2	no	—
675	D₄	—	8	1	no	—
676	D₄	—	8	2	no	—
677	D₄	—	8	2	no	—
678	D₄	—	8	2	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	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	8	2	no	—
696	C₂×C₄	—	8	2	no	—
697	C₂×C₄	—	8	2	no	—
698	C₂×C₄	—	8	2	no	—
699	C₂×C₄	—	8	2	no	—
700	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
701	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
702	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
703	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
705	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
706	C₈	—	4	1	no	—
707	C₈	—	4	1	no	—
708	C₈	—	4	1	no	—
709	C₈	—	4	1	no	—
710	C₈	—	4	1	no	—
711	C₈	—	4	1	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	2	1	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	8	1	no	—
722	C₂²	—	8	1	no	—
723	C₂²	—	8	1	no	—
724	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
725	C₄	—	2	1	no	—
726	C₄	—	2	1	no	—
727	C₄	—	2	1	no	—
728	C₄	—	2	1	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	1	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	1	no	—
733	C₄	—	4	1	no	—
734	C₄	—	4	1	no	—
735	C₄	—	4	1	no	—
736	C₄	—	4	1	no	—
737	C₄	—	8	1	no	—
738	C₄	C₂₉×#576	1	1	yes	characteristic
739	C₄	C₂₉×#577	1	1	yes	characteristic
740	C₄	C₂₉×#577	1	1	yes	characteristic
741	C₄	C₂₉×#578	1	1	yes	characteristic
742	C₂	—	4	1	no	—
743	C₂	—	8	1	no	—
744	C₂	—	8	2	no	—
745	C₂	—	16	1	no	—
746	C₂	C₂₉×#3012	1	1	yes	characteristic
747	C₂	C₂₉×#3013	1	1	yes	characteristic
748	C₂	C₂₉×#3021	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×#3554	C₂	semidirect
2. C₂₉×#3254	C₂	semidirect
3. C₂₉×#3247	C₂	semidirect
4. C₂₉×#3207	C₂	semidirect
5. C₂₉×#1637	C₂	semidirect
6. C₂₉×#1636	C₂	semidirect
7. C₂₉×#1631	C₂	semidirect
8. C₂₉×#1630	C₂	semidirect
9. C₂₉×#1627	C₂	semidirect
10. C₂₉×#1626	C₂	semidirect
11. C₂₉×#1621	C₂	semidirect
12. C₂₉×#1620	C₂	semidirect
13. C₂₉×#1547	C₂	semidirect
14. C₂₉×#1495	C₂	semidirect
15. C₂₉×#1481	C₂	semidirect
272. #18964	C₂₉	direct (N × H)
338. #3554	C₂×C₂₉	semidirect
339. #3254	C₂×C₂₉	semidirect
340. #3247	C₂×C₂₉	semidirect
341. #3207	C₂×C₂₉	semidirect
342. #1637	C₂×C₂₉	semidirect
343. #1636	C₂×C₂₉	semidirect
344. #1631	C₂×C₂₉	semidirect
345. #1630	C₂×C₂₉	semidirect
346. #1627	C₂×C₂₉	semidirect
347. #1626	C₂×C₂₉	semidirect
348. #1621	C₂×C₂₉	semidirect
349. #1620	C₂×C₂₉	semidirect
350. #1547	C₂×C₂₉	semidirect
351. #1495	C₂×C₂₉	semidirect
352. #1481	C₂×C₂₉	semidirect
550. C₂₉	#18964	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×#3554	2
C₂₉×#3254	2
C₂₉×#3247	2
C₂₉×#3207	2
C₂₉×#1637	2
C₂₉×#1636	2
C₂₉×#1631	2
C₂₉×#1630	2
C₂₉×#1627	2
C₂₉×#1626	2
C₂₉×#1621	2
C₂₉×#1620	2
C₂₉×#1547	2
C₂₉×#1495	2
C₂₉×#1481	2
#18964	29

Subgroups — C29×#18964 #20313864

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18964 #20313864