Subgroups — C₂₉×#18881 #20313781

Order 7424.

844 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3523	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#3233	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#3231	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3104	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1653	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1652	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1649	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1648	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1638	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1637	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1636	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1636	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1544	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1482	C₂	1	1	yes	maximal, characteristic
15	C₂₉×#1479	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#557	—	2	1	no	—
17	C₂₉×#557	C₂²	1	1	yes	characteristic
18	C₂₉×#557	C₂²	1	1	yes	characteristic
19	C₂₉×#556	—	2	1	no	—
20	C₂₉×#556	C₂²	1	1	yes	characteristic
21	C₂₉×#552	—	2	2	no	—
22	C₂₉×#552	—	2	1	no	—
23	D₄×Q₈×C₂₉	—	2	1	no	—
24	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
25	C₂₉×#541	—	2	2	no	—
26	C₂₉×#541	—	2	1	no	—
27	C₂₉×#533	—	2	1	no	—
28	C₂₉×#533	C₂²	1	1	yes	characteristic
29	C₂₉×#533	C₂²	1	1	yes	characteristic
30	C₂₉×#529	—	2	1	no	—
31	C₂₉×#529	C₂²	1	1	yes	characteristic
32	C₂₉×#519	—	2	1	no	—
33	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
34	C₂₉×#500	C₂²	1	1	yes	characteristic
35	C₂₉×#499	—	2	1	no	—
36	C₂₉×#498	C₂²	1	1	yes	characteristic
37	C₂₉×#488	—	2	1	no	—
38	C₂₉×#487	C₂²	1	1	yes	characteristic
39	C₂₉×#487	C₂²	1	1	yes	characteristic
40	C₂₉×#485	—	2	1	no	—
41	C₂₉×#485	—	2	2	no	—
42	C₂₉×#484	—	2	1	no	—
43	C₂₉×#482	—	2	1	no	—
44	C₂₉×#479	—	2	2	no	—
45	C₂₉×#477	C₂²	1	1	yes	characteristic
46	C₂₉×#477	C₂²	1	1	yes	characteristic
47	C₂₉×#477	C₂²	1	1	yes	characteristic
48	C₂₉×#476	C₂²	1	1	yes	characteristic
49	C₂₉×#475	C₂²	1	1	yes	characteristic
50	C₂₉×#474	C₂²	1	1	yes	characteristic
51	C₂₉×#462	C₂²	1	1	yes	characteristic
52	C₂₉×#462	C₂²	1	1	yes	characteristic
53	C₂₉×#451	—	2	1	no	—
54	C₄×Q₁₆×C₂₉	—	2	1	no	—
55	C₄×Q₁₆×C₂₉	—	2	1	no	—
56	C₂₉×#431	C₂²	1	1	yes	characteristic
57	C₂₉×#431	C₂²	1	1	yes	characteristic
58	C₂₉×#431	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×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	C₂²×Q₈×C₂₉	—	2	1	no	—
72	C₂²×Q₈×C₂₉	D₄	1	1	yes	characteristic
73	C₂×Q₁₆×C₂₉	—	2	1	no	—
74	C₂×Q₁₆×C₂₉	—	2	1	no	—
75	C₂₉×C₄⋊Q₈	—	2	2	no	—
76	C₂₉×C₄⋊Q₈	—	2	1	no	—
77	C₂₉×C₄⋊Q₈	—	2	1	no	—
78	C₂₉×C₄⋊Q₈	—	2	1	no	—
79	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₂₉×#126	—	2	2	no	—
84	C₂₉×#126	—	2	2	no	—
85	C₂₉×#126	—	2	2	no	—
86	C₂₉×#126	—	2	2	no	—
87	C₂₉×#126	—	2	1	no	—
88	C₂₉×#125	—	2	2	no	—
89	C₂₉×#125	—	2	2	no	—
90	C₂₉×#125	—	2	2	no	—
91	C₂₉×#125	—	2	1	no	—
92	C₂₉×#125	—	2	2	no	—
93	C₂₉×#125	—	2	2	no	—
94	C₂₉×#125	—	2	1	no	—
95	C₂₉×#125	—	2	1	no	—
96	C₂₉×#125	D₄	1	2	yes	—
97	C₂₉×#125	D₄	1	1	yes	characteristic
98	C₂₉×#124	—	2	1	no	—
99	C₂₉×#124	D₄	1	1	yes	characteristic
100	C₂₉×#123	—	2	2	no	—
101	C₂₉×#123	—	2	1	no	—
102	C₂₉×C₂²⋊Q₈	—	2	2	no	—
103	C₂₉×C₂²⋊Q₈	—	2	2	no	—
104	C₂₉×C₂²⋊Q₈	—	2	1	no	—
105	C₂₉×C₂²⋊Q₈	—	2	1	no	—
106	C₂₉×C₂²⋊Q₈	—	2	1	no	—
107	C₂₉×C₂²⋊Q₈	—	2	1	no	—
108	C₂₉×C₂²⋊Q₈	—	2	2	no	—
109	C₂₉×C₂²⋊Q₈	—	2	1	no	—
110	C₂₉×C₂²⋊Q₈	—	2	1	no	—
111	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
112	C₂₉×#121	D₄	1	1	yes	characteristic
113	C₄×Q₈×C₂₉	—	2	2	no	—
114	C₄×Q₈×C₂₉	—	2	2	no	—
115	C₄×Q₈×C₂₉	—	2	1	no	—
116	C₄×Q₈×C₂₉	—	2	1	no	—
117	C₄×Q₈×C₂₉	—	2	1	no	—
118	C₄×Q₈×C₂₉	—	2	1	no	—
119	C₄×Q₈×C₂₉	—	2	1	no	—
120	C₄×Q₈×C₂₉	—	2	1	no	—
121	C₄×Q₈×C₂₉	—	2	1	no	—
122	C₄×Q₈×C₂₉	—	2	1	no	—
123	C₄×Q₈×C₂₉	—	2	1	no	—
124	C₄×Q₈×C₂₉	—	2	1	no	—
125	C₄×Q₈×C₂₉	—	2	1	no	—
126	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
127	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
128	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
129	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
130	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
131	C₄×D₄×C₂₉	—	2	2	no	—
132	C₄×D₄×C₂₉	—	2	1	no	—
133	C₄×D₄×C₂₉	—	2	1	no	—
134	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
135	C₂₉×#117	—	2	2	no	—
136	C₂₉×#117	—	2	2	no	—
137	C₂₉×#117	—	2	2	no	—
138	C₂₉×#117	—	2	1	no	—
139	C₂₉×#117	—	2	1	no	—
140	C₂₉×#117	—	2	1	no	—
141	C₂₉×#117	D₄	1	2	yes	—
142	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
143	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
144	C₂×C₄²×C₂₉	—	2	1	no	—
145	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
146	C₂₉×#107	—	2	1	no	—
147	C₂₉×#107	—	2	1	no	—
148	C₂₉×#107	—	2	1	no	—
149	C₂₉×#107	—	2	1	no	—
150	C₂₉×#107	—	2	2	no	—
151	C₂₉×#106	—	2	1	no	—
152	C₂₉×#106	—	2	1	no	—
153	C₂₉×#106	—	2	2	no	—
154	C₂₉×C₄⋊C₈	—	2	1	no	—
155	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
156	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
157	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₂₉×#103	—	2	1	no	—
160	C₂₉×#103	—	2	1	no	—
161	C₂₉×#103	—	2	1	no	—
162	C₂₉×#103	—	2	1	no	—
163	C₂₉×#103	—	2	1	no	—
164	C₂₉×#103	—	2	1	no	—
165	C₂₉×#103	—	2	2	no	—
166	C₂₉×#103	—	2	2	no	—
167	C₂₉×#102	—	2	1	no	—
168	C₂₉×#102	—	2	1	no	—
169	C₂₉×C₂²⋊C₈	—	2	1	no	—
170	C₂₉×C₂²⋊C₈	—	2	1	no	—
171	C₂₉×C₂²⋊C₈	—	2	1	no	—
172	C₄×C₈×C₂₉	—	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	C₂×Q₈×C₂₉	—	2	2	no	—
177	C₂×Q₈×C₂₉	—	2	1	no	—
178	C₂×Q₈×C₂₉	—	2	1	no	—
179	C₂×Q₈×C₂₉	—	2	1	no	—
180	C₂×Q₈×C₂₉	—	2	2	no	—
181	C₂×Q₈×C₂₉	—	2	1	no	—
182	C₂×Q₈×C₂₉	—	2	1	no	—
183	C₂×Q₈×C₂₉	—	4	1	no	—
184	C₂×Q₈×C₂₉	—	4	2	no	—
185	C₂×Q₈×C₂₉	—	4	2	no	—
186	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
187	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
188	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
189	C₂×D₄×C₂₉	—	2	1	no	—
190	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₂₉	—	2	2	no	—
192	C₂²×C₄×C₂₉	—	2	1	no	—
193	C₂²×C₄×C₂₉	—	2	1	no	—
194	C₂²×C₄×C₂₉	—	2	1	no	—
195	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
198	Q₁₆×C₂₉	—	4	2	no	—
199	Q₁₆×C₂₉	—	4	2	no	—
200	C₂×C₈×C₂₉	—	2	1	no	—
201	C₂×C₈×C₂₉	—	2	1	no	—
202	C₂×C₈×C₂₉	—	2	1	no	—
203	C₂×C₈×C₂₉	—	2	1	no	—
204	C₂×C₈×C₂₉	—	2	1	no	—
205	C₂×C₈×C₂₉	—	2	1	no	—
206	C₄⋊C₄×C₂₉	—	2	2	no	—
207	C₄⋊C₄×C₂₉	—	2	2	no	—
208	C₄⋊C₄×C₂₉	—	2	2	no	—
209	C₄⋊C₄×C₂₉	—	2	2	no	—
210	C₄⋊C₄×C₂₉	—	2	2	no	—
211	C₄⋊C₄×C₂₉	—	2	2	no	—
212	C₄⋊C₄×C₂₉	—	2	2	no	—
213	C₄⋊C₄×C₂₉	—	2	2	no	—
214	C₄⋊C₄×C₂₉	—	2	1	no	—
215	C₄⋊C₄×C₂₉	—	2	1	no	—
216	C₄⋊C₄×C₂₉	—	2	1	no	—
217	C₄⋊C₄×C₂₉	—	2	2	no	—
218	C₄⋊C₄×C₂₉	—	2	1	no	—
219	C₄⋊C₄×C₂₉	—	2	1	no	—
220	C₄⋊C₄×C₂₉	—	2	1	no	—
221	C₄⋊C₄×C₂₉	—	2	2	no	—
222	C₄⋊C₄×C₂₉	—	2	1	no	—
223	C₄⋊C₄×C₂₉	—	2	1	no	—
224	C₄⋊C₄×C₂₉	—	2	1	no	—
225	C₄⋊C₄×C₂₉	—	2	1	no	—
226	C₄⋊C₄×C₂₉	—	2	1	no	—
227	C₄⋊C₄×C₂₉	—	2	1	no	—
228	C₄⋊C₄×C₂₉	—	2	1	no	—
229	C₄⋊C₄×C₂₉	—	2	1	no	—
230	C₄⋊C₄×C₂₉	—	2	1	no	—
231	C₄⋊C₄×C₂₉	—	4	1	no	—
232	C₄⋊C₄×C₂₉	—	4	1	no	—
233	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
234	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
235	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
236	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
237	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
238	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
239	C₂²⋊C₄×C₂₉	—	2	2	no	—
240	C₂²⋊C₄×C₂₉	—	2	2	no	—
241	C₂²⋊C₄×C₂₉	—	2	2	no	—
242	C₂²⋊C₄×C₂₉	—	2	1	no	—
243	C₂²⋊C₄×C₂₉	—	2	2	no	—
244	C₂²⋊C₄×C₂₉	—	2	1	no	—
245	C₂²⋊C₄×C₂₉	—	2	1	no	—
246	C₂²⋊C₄×C₂₉	—	2	1	no	—
247	C₂²⋊C₄×C₂₉	—	2	1	no	—
248	C₂²⋊C₄×C₂₉	—	4	1	no	—
249	C₄²×C₂₉	—	2	2	no	—
250	C₄²×C₂₉	—	2	2	no	—
251	C₄²×C₂₉	—	2	2	no	—
252	C₄²×C₂₉	—	2	1	no	—
253	C₄²×C₂₉	—	2	1	no	—
254	C₄²×C₂₉	—	2	2	no	—
255	C₄²×C₂₉	—	2	1	no	—
256	C₄²×C₂₉	—	2	1	no	—
257	C₄²×C₂₉	—	2	1	no	—
258	C₄²×C₂₉	—	4	1	no	—
259	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
260	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
261	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
262	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
263	#18881	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
264	C₂³×C₂₉	—	2	1	no	—
265	C₂³×C₂₉	#120	1	1	yes	characteristic
266	Q₈×C₂₉	—	2	1	no	—
267	Q₈×C₂₉	—	2	1	no	—
268	Q₈×C₂₉	—	2	1	no	—
269	Q₈×C₂₉	—	2	1	no	—
270	Q₈×C₂₉	—	2	1	no	—
271	Q₈×C₂₉	—	4	2	no	—
272	Q₈×C₂₉	—	4	4	no	—
273	Q₈×C₂₉	—	4	2	no	—
274	Q₈×C₂₉	—	4	1	no	—
275	Q₈×C₂₉	—	4	1	no	—
276	Q₈×C₂₉	—	4	1	no	—
277	Q₈×C₂₉	—	4	1	no	—
278	Q₈×C₂₉	—	4	1	no	—
279	Q₈×C₂₉	—	4	1	no	—
280	Q₈×C₂₉	#135	1	2	yes	—
281	D₄×C₂₉	—	2	1	no	—
282	D₄×C₂₉	—	2	1	no	—
283	D₄×C₂₉	—	4	2	no	—
284	C₂×C₄×C₂₉	—	2	1	no	—
285	C₂×C₄×C₂₉	—	2	1	no	—
286	C₂×C₄×C₂₉	—	2	1	no	—
287	C₂×C₄×C₂₉	—	2	1	no	—
288	C₂×C₄×C₂₉	—	2	1	no	—
289	C₂×C₄×C₂₉	—	2	1	no	—
290	C₂×C₄×C₂₉	—	2	1	no	—
291	C₂×C₄×C₂₉	—	2	2	no	—
292	C₂×C₄×C₂₉	—	2	1	no	—
293	C₂×C₄×C₂₉	—	2	1	no	—
294	C₂×C₄×C₂₉	—	2	1	no	—
295	C₂×C₄×C₂₉	—	2	1	no	—
296	C₂×C₄×C₂₉	—	2	2	no	—
297	C₂×C₄×C₂₉	—	4	1	no	—
298	C₂×C₄×C₂₉	—	4	2	no	—
299	C₂×C₄×C₂₉	—	4	4	no	—
300	C₂×C₄×C₂₉	—	4	2	no	—
301	C₂×C₄×C₂₉	—	4	1	no	—
302	C₂×C₄×C₂₉	—	4	1	no	—
303	C₂×C₄×C₂₉	—	4	1	no	—
304	C₂×C₄×C₂₉	—	4	1	no	—
305	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
306	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
307	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
308	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
309	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
311	C₈×C₂₉	—	4	1	no	—
312	C₈×C₂₉	—	4	1	no	—
313	C₈×C₂₉	—	4	1	no	—
314	C₈×C₂₉	—	4	1	no	—
315	C₈×C₂₉	—	4	1	no	—
316	C₈×C₂₉	—	4	1	no	—
317	#3523	C₂×C₂₉	1	1	yes	characteristic
318	#3233	C₂×C₂₉	1	1	yes	characteristic
319	#3231	C₂×C₂₉	1	1	yes	characteristic, complemented
320	#3104	C₂×C₂₉	1	1	yes	characteristic, complemented
321	#1653	C₂×C₂₉	1	1	yes	characteristic, complemented
322	#1652	C₂×C₂₉	1	1	yes	characteristic, complemented
323	#1649	C₂×C₂₉	1	1	yes	characteristic, complemented
324	#1648	C₂×C₂₉	1	1	yes	characteristic, complemented
325	#1638	C₂×C₂₉	1	1	yes	characteristic, complemented
326	#1637	C₂×C₂₉	1	1	yes	characteristic, complemented
327	#1636	C₂×C₂₉	1	1	yes	characteristic, complemented
328	#1636	C₂×C₂₉	1	1	yes	characteristic, complemented
329	#1544	C₂×C₂₉	1	1	yes	characteristic, complemented
330	#1482	C₂×C₂₉	1	1	yes	characteristic
331	#1479	C₂×C₂₉	1	1	yes	characteristic, complemented
332	C₂²×C₂₉	—	2	1	no	—
333	C₂²×C₂₉	—	2	1	no	—
334	C₂²×C₂₉	—	2	1	no	—
335	C₂²×C₂₉	—	4	1	no	—
336	C₂²×C₂₉	—	4	1	no	—
337	C₂²×C₂₉	—	4	1	no	—
338	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
339	C₄×C₂₉	—	2	1	no	—
340	C₄×C₂₉	—	2	2	no	—
341	C₄×C₂₉	—	2	1	no	—
342	C₄×C₂₉	—	2	1	no	—
343	C₄×C₂₉	—	2	1	no	—
344	C₄×C₂₉	—	4	1	no	—
345	C₄×C₂₉	—	4	2	no	—
346	C₄×C₂₉	—	4	1	no	—
347	C₄×C₂₉	—	4	1	no	—
348	C₄×C₂₉	—	4	2	no	—
349	C₄×C₂₉	—	4	1	no	—
350	C₄×C₂₉	—	4	1	no	—
351	C₄×C₂₉	—	4	1	no	—
352	C₄×C₂₉	—	8	1	no	—
353	C₄×C₂₉	—	8	1	no	—
354	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
355	C₄×C₂₉	#575	1	1	yes	characteristic
356	C₄×C₂₉	#578	1	1	yes	characteristic
357	C₄×C₂₉	#578	1	1	yes	characteristic
358	#557	—	2	1	no	—
359	#557	C₂²×C₂₉	1	1	yes	characteristic
360	#557	C₂²×C₂₉	1	1	yes	characteristic
361	#556	—	2	1	no	—
362	#556	C₂²×C₂₉	1	1	yes	characteristic
363	#552	—	2	2	no	—
364	#552	—	2	1	no	—
365	D₄×Q₈	—	2	1	no	—
366	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
367	#541	—	2	2	no	—
368	#541	—	2	1	no	—
369	#533	—	2	1	no	—
370	#533	C₂²×C₂₉	1	1	yes	characteristic
371	#533	C₂²×C₂₉	1	1	yes	characteristic
372	#529	—	2	1	no	—
373	#529	C₂²×C₂₉	1	1	yes	characteristic
374	#519	—	2	1	no	—
375	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
376	#500	C₂²×C₂₉	1	1	yes	characteristic
377	#499	—	2	1	no	—
378	#498	C₂²×C₂₉	1	1	yes	characteristic
379	#488	—	2	1	no	—
380	#487	C₂²×C₂₉	1	1	yes	characteristic
381	#487	C₂²×C₂₉	1	1	yes	characteristic
382	#485	—	2	1	no	—
383	#485	—	2	2	no	—
384	#484	—	2	1	no	—
385	#482	—	2	1	no	—
386	#479	—	2	2	no	—
387	#477	C₂²×C₂₉	1	1	yes	characteristic
388	#477	C₂²×C₂₉	1	1	yes	characteristic
389	#477	C₂²×C₂₉	1	1	yes	characteristic
390	#476	C₂²×C₂₉	1	1	yes	characteristic
391	#475	C₂²×C₂₉	1	1	yes	characteristic
392	#474	C₂²×C₂₉	1	1	yes	characteristic
393	#462	C₂²×C₂₉	1	1	yes	characteristic
394	#462	C₂²×C₂₉	1	1	yes	characteristic
395	#451	—	2	1	no	—
396	C₄×Q₁₆	—	2	1	no	—
397	C₄×Q₁₆	—	2	1	no	—
398	#431	C₂²×C₂₉	1	1	yes	characteristic
399	#431	C₂²×C₂₉	1	1	yes	characteristic
400	#431	C₂²×C₂₉	1	1	yes	characteristic
401	#332	C₂²×C₂₉	1	1	yes	characteristic
402	#332	C₂²×C₂₉	1	1	yes	characteristic
403	#332	C₂²×C₂₉	1	1	yes	characteristic
404	#332	C₂²×C₂₉	1	1	yes	characteristic
405	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
406	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
407	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
408	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
409	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
410	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
411	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
412	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
413	C₂×C₂₉	—	4	1	no	—
414	C₂×C₂₉	—	8	1	no	—
415	C₂×C₂₉	#3002	1	1	yes	characteristic
416	C₂×C₂₉	#3011	1	1	yes	characteristic
417	C₂×C₂₉	#3020	1	1	yes	characteristic
418	C₂²×Q₈	—	2	1	no	—
419	C₂²×Q₈	D₄×C₂₉	1	1	yes	characteristic
420	C₂×Q₁₆	—	2	1	no	—
421	C₂×Q₁₆	—	2	1	no	—
422	C₄⋊Q₈	—	2	2	no	—
423	C₄⋊Q₈	—	2	1	no	—
424	C₄⋊Q₈	—	2	1	no	—
425	C₄⋊Q₈	—	2	1	no	—
426	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
427	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
428	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
429	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
430	#126	—	2	2	no	—
431	#126	—	2	2	no	—
432	#126	—	2	2	no	—
433	#126	—	2	2	no	—
434	#126	—	2	1	no	—
435	#125	—	2	2	no	—
436	#125	—	2	2	no	—
437	#125	—	2	2	no	—
438	#125	—	2	1	no	—
439	#125	—	2	2	no	—
440	#125	—	2	2	no	—
441	#125	—	2	1	no	—
442	#125	—	2	1	no	—
443	#125	D₄×C₂₉	1	1	yes	characteristic
444	#125	D₄×C₂₉	1	2	yes	—
445	#124	—	2	1	no	—
446	#124	D₄×C₂₉	1	1	yes	characteristic
447	#123	—	2	2	no	—
448	#123	—	2	1	no	—
449	C₂²⋊Q₈	—	2	2	no	—
450	C₂²⋊Q₈	—	2	2	no	—
451	C₂²⋊Q₈	—	2	1	no	—
452	C₂²⋊Q₈	—	2	1	no	—
453	C₂²⋊Q₈	—	2	1	no	—
454	C₂²⋊Q₈	—	2	1	no	—
455	C₂²⋊Q₈	—	2	2	no	—
456	C₂²⋊Q₈	—	2	1	no	—
457	C₂²⋊Q₈	—	2	1	no	—
458	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
459	#121	D₄×C₂₉	1	1	yes	characteristic
460	C₄×Q₈	—	2	2	no	—
461	C₄×Q₈	—	2	2	no	—
462	C₄×Q₈	—	2	1	no	—
463	C₄×Q₈	—	2	1	no	—
464	C₄×Q₈	—	2	1	no	—
465	C₄×Q₈	—	2	1	no	—
466	C₄×Q₈	—	2	1	no	—
467	C₄×Q₈	—	2	1	no	—
468	C₄×Q₈	—	2	1	no	—
469	C₄×Q₈	—	2	1	no	—
470	C₄×Q₈	—	2	1	no	—
471	C₄×Q₈	—	2	1	no	—
472	C₄×Q₈	—	2	1	no	—
473	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
474	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
475	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
476	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
477	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
478	C₄×D₄	—	2	2	no	—
479	C₄×D₄	—	2	1	no	—
480	C₄×D₄	—	2	1	no	—
481	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
482	#117	—	2	2	no	—
483	#117	—	2	2	no	—
484	#117	—	2	2	no	—
485	#117	—	2	1	no	—
486	#117	—	2	1	no	—
487	#117	—	2	1	no	—
488	#117	D₄×C₂₉	1	2	yes	—
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
491	C₂×C₄²	—	2	1	no	—
492	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
493	#107	—	2	1	no	—
494	#107	—	2	1	no	—
495	#107	—	2	1	no	—
496	#107	—	2	1	no	—
497	#107	—	2	2	no	—
498	#106	—	2	1	no	—
499	#106	—	2	1	no	—
500	#106	—	2	2	no	—
501	C₄⋊C₈	—	2	1	no	—
502	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
503	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
504	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
505	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
506	#103	—	2	1	no	—
507	#103	—	2	1	no	—
508	#103	—	2	1	no	—
509	#103	—	2	1	no	—
510	#103	—	2	1	no	—
511	#103	—	2	1	no	—
512	#103	—	2	2	no	—
513	#103	—	2	2	no	—
514	#102	—	2	1	no	—
515	#102	—	2	1	no	—
516	C₂²⋊C₈	—	2	1	no	—
517	C₂²⋊C₈	—	2	1	no	—
518	C₂²⋊C₈	—	2	1	no	—
519	C₄×C₈	—	2	1	no	—
520	C₄×C₈	—	2	1	no	—
521	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
522	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
523	C₂₉	#18881	1	1	yes	characteristic, direct product factor, Sylow
524	C₂×Q₈	—	2	2	no	—
525	C₂×Q₈	—	2	1	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	2	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	4	1	no	—
532	C₂×Q₈	—	4	2	no	—
533	C₂×Q₈	—	4	2	no	—
534	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
535	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
536	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
544	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
545	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
546	Q₁₆	—	4	2	no	—
547	Q₁₆	—	4	2	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₄⋊C₄	—	2	2	no	—
555	C₄⋊C₄	—	2	2	no	—
556	C₄⋊C₄	—	2	2	no	—
557	C₄⋊C₄	—	2	2	no	—
558	C₄⋊C₄	—	2	2	no	—
559	C₄⋊C₄	—	2	2	no	—
560	C₄⋊C₄	—	2	2	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	4	1	no	—
580	C₄⋊C₄	—	4	1	no	—
581	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
582	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
583	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
584	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
585	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
586	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
587	C₂²⋊C₄	—	2	2	no	—
588	C₂²⋊C₄	—	2	2	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	1	no	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	2	1	no	—
593	C₂²⋊C₄	—	2	1	no	—
594	C₂²⋊C₄	—	2	1	no	—
595	C₂²⋊C₄	—	2	1	no	—
596	C₂²⋊C₄	—	4	1	no	—
597	C₄²	—	2	2	no	—
598	C₄²	—	2	2	no	—
599	C₄²	—	2	2	no	—
600	C₄²	—	2	1	no	—
601	C₄²	—	2	1	no	—
602	C₄²	—	2	2	no	—
603	C₄²	—	2	1	no	—
604	C₄²	—	2	1	no	—
605	C₄²	—	2	1	no	—
606	C₄²	—	4	1	no	—
607	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
608	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
609	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
610	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
611	C₂³	—	2	1	no	—
612	C₂³	C₂₉×#120	1	1	yes	characteristic
613	Q₈	—	2	1	no	—
614	Q₈	—	2	1	no	—
615	Q₈	—	2	1	no	—
616	Q₈	—	2	1	no	—
617	Q₈	—	2	1	no	—
618	Q₈	—	4	2	no	—
619	Q₈	—	4	4	no	—
620	Q₈	—	4	2	no	—
621	Q₈	—	4	1	no	—
622	Q₈	—	4	1	no	—
623	Q₈	—	4	1	no	—
624	Q₈	—	4	1	no	—
625	Q₈	—	4	1	no	—
626	Q₈	—	4	1	no	—
627	Q₈	C₂₉×#135	1	2	yes	—
628	D₄	—	2	1	no	—
629	D₄	—	2	1	no	—
630	D₄	—	4	2	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	2	no	—
646	C₂×C₄	—	4	4	no	—
647	C₂×C₄	—	4	2	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
653	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
654	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
655	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
656	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
657	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
658	C₈	—	4	1	no	—
659	C₈	—	4	1	no	—
660	C₈	—	4	1	no	—
661	C₈	—	4	1	no	—
662	C₈	—	4	1	no	—
663	C₈	—	4	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	1	no	—
670	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
671	C₄	—	2	1	no	—
672	C₄	—	2	2	no	—
673	C₄	—	2	1	no	—
674	C₄	—	2	1	no	—
675	C₄	—	2	1	no	—
676	C₄	—	4	1	no	—
677	C₄	—	4	2	no	—
678	C₄	—	4	1	no	—
679	C₄	—	4	1	no	—
680	C₄	—	4	2	no	—
681	C₄	—	4	1	no	—
682	C₄	—	4	1	no	—
683	C₄	—	4	1	no	—
684	C₄	—	8	1	no	—
685	C₄	—	8	1	no	—
686	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
687	C₄	C₂₉×#575	1	1	yes	characteristic
688	C₄	C₂₉×#578	1	1	yes	characteristic
689	C₄	C₂₉×#578	1	1	yes	characteristic
690	C₂	—	4	1	no	—
691	C₂	—	8	1	no	—
692	C₂	C₂₉×#3002	1	1	yes	characteristic
693	C₂	C₂₉×#3011	1	1	yes	characteristic
694	C₂	C₂₉×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂₉×#121	D₄
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
3. C₂₉×#3231	C₂	semidirect
4. C₂₉×#3104	C₂	semidirect
5. C₂₉×#1653	C₂	semidirect
6. C₂₉×#1652	C₂	semidirect
7. C₂₉×#1649	C₂	semidirect
8. C₂₉×#1648	C₂	semidirect
9. C₂₉×#1638	C₂	semidirect
10. C₂₉×#1637	C₂	semidirect
11. C₂₉×#1636	C₂	semidirect
12. C₂₉×#1636	C₂	semidirect
13. C₂₉×#1544	C₂	semidirect
15. C₂₉×#1479	C₂	semidirect
263. #18881	C₂₉	direct (N × H)
319. #3231	C₂×C₂₉	semidirect
320. #3104	C₂×C₂₉	semidirect
321. #1653	C₂×C₂₉	semidirect
322. #1652	C₂×C₂₉	semidirect
323. #1649	C₂×C₂₉	semidirect
324. #1648	C₂×C₂₉	semidirect
325. #1638	C₂×C₂₉	semidirect
326. #1637	C₂×C₂₉	semidirect
327. #1636	C₂×C₂₉	semidirect
328. #1636	C₂×C₂₉	semidirect
329. #1544	C₂×C₂₉	semidirect
331. #1479	C₂×C₂₉	semidirect
523. C₂₉	#18881	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×#3523	2
C₂₉×#3233	2
C₂₉×#3231	2
C₂₉×#3104	2
C₂₉×#1653	2
C₂₉×#1652	2
C₂₉×#1649	2
C₂₉×#1648	2
C₂₉×#1638	2
C₂₉×#1637	2
C₂₉×#1636	2
C₂₉×#1544	2
C₂₉×#1482	2
C₂₉×#1479	2
#18881	29

Subgroups — C29×#18881 #20313781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18881 #20313781