Subgroups — C₂₉×#18825 #20313725

Order 7424.

846 conjugacy classes of subgroups.

The subgroup lattice has 700 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×#3252	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#3231	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3078	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1653	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1651	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1650	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×#1561	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1495	C₂	1	1	yes	maximal, characteristic
15	C₂₉×#1487	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×#498	C₂²	1	1	yes	characteristic
36	C₂₉×#487	C₂²	1	1	yes	characteristic
37	C₂₉×#487	C₂²	1	1	yes	characteristic
38	C₂₉×#485	—	2	2	no	—
39	C₂₉×#479	—	2	2	no	—
40	C₂₉×#479	—	2	1	no	—
41	C₂₉×#479	—	2	1	no	—
42	C₂₉×#479	—	2	1	no	—
43	C₂₉×#477	C₂²	1	1	yes	characteristic
44	C₂₉×#477	C₂²	1	1	yes	characteristic
45	C₂₉×#477	C₂²	1	1	yes	characteristic
46	C₂₉×#476	C₂²	1	1	yes	characteristic
47	C₂₉×#475	C₂²	1	1	yes	characteristic
48	C₂₉×#475	C₂²	1	1	yes	characteristic
49	C₂₉×#470	—	2	1	no	—
50	C₂₉×#468	—	2	1	no	—
51	C₂₉×#464	—	2	1	no	—
52	C₂₉×#462	C₂²	1	1	yes	characteristic
53	C₂₉×#461	C₂²	1	1	yes	characteristic
54	C₂₉×#431	C₂²	1	1	yes	characteristic
55	C₂₉×#428	—	2	1	no	—
56	C₂₉×#423	C₂²	1	1	yes	characteristic
57	C₂₉×#423	C₂²	1	1	yes	characteristic
58	C₂₉×#419	—	2	1	no	—
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×SD₁₆×C₂₉	—	2	1	no	—
75	C₂×M₁₆×C₂₉	—	2	1	no	—
76	C₂×M₁₆×C₂₉	—	2	1	no	—
77	C₂₉×C₄⋊Q₈	—	2	2	no	—
78	C₂₉×C₄⋊Q₈	—	2	1	no	—
79	C₂₉×C₄⋊Q₈	—	2	1	no	—
80	C₂₉×C₄⋊Q₈	—	2	1	no	—
81	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₂₉×#126	—	2	2	no	—
86	C₂₉×#126	—	2	2	no	—
87	C₂₉×#126	—	2	2	no	—
88	C₂₉×#126	—	2	2	no	—
89	C₂₉×#126	—	2	1	no	—
90	C₂₉×#125	—	2	2	no	—
91	C₂₉×#125	—	2	2	no	—
92	C₂₉×#125	—	2	2	no	—
93	C₂₉×#125	—	2	1	no	—
94	C₂₉×#125	—	2	2	no	—
95	C₂₉×#125	—	2	2	no	—
96	C₂₉×#125	—	2	1	no	—
97	C₂₉×#125	—	2	1	no	—
98	C₂₉×#125	D₄	1	1	yes	characteristic
99	C₂₉×#125	D₄	1	2	yes	—
100	C₂₉×#124	—	2	1	no	—
101	C₂₉×#124	D₄	1	1	yes	characteristic
102	C₂₉×#123	—	2	2	no	—
103	C₂₉×#123	—	2	1	no	—
104	C₂₉×C₂²⋊Q₈	—	2	2	no	—
105	C₂₉×C₂²⋊Q₈	—	2	2	no	—
106	C₂₉×C₂²⋊Q₈	—	2	1	no	—
107	C₂₉×C₂²⋊Q₈	—	2	1	no	—
108	C₂₉×C₂²⋊Q₈	—	2	1	no	—
109	C₂₉×C₂²⋊Q₈	—	2	1	no	—
110	C₂₉×C₂²⋊Q₈	—	2	2	no	—
111	C₂₉×C₂²⋊Q₈	—	2	1	no	—
112	C₂₉×C₂²⋊Q₈	—	2	1	no	—
113	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
114	C₂₉×#121	D₄	1	1	yes	characteristic
115	C₄×Q₈×C₂₉	—	2	2	no	—
116	C₄×Q₈×C₂₉	—	2	2	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	—	2	1	no	—
127	C₄×Q₈×C₂₉	—	2	1	no	—
128	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
129	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
130	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
131	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
132	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
133	C₄×D₄×C₂₉	—	2	2	no	—
134	C₄×D₄×C₂₉	—	2	1	no	—
135	C₄×D₄×C₂₉	—	2	1	no	—
136	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
137	C₂₉×#117	—	2	2	no	—
138	C₂₉×#117	—	2	2	no	—
139	C₂₉×#117	—	2	2	no	—
140	C₂₉×#117	—	2	1	no	—
141	C₂₉×#117	—	2	1	no	—
142	C₂₉×#117	—	2	1	no	—
143	C₂₉×#117	D₄	1	2	yes	—
144	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
145	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
146	C₂×C₄²×C₂₉	—	2	1	no	—
147	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
148	C₂₉×#107	—	2	1	no	—
149	C₂₉×#107	—	2	1	no	—
150	C₂₉×#107	—	2	1	no	—
151	C₂₉×#107	—	2	2	no	—
152	C₂₉×#106	—	2	1	no	—
153	C₂₉×#106	—	2	1	no	—
154	C₂₉×#106	—	2	1	no	—
155	C₂₉×#106	—	2	2	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	1	no	—
167	C₂₉×#103	—	2	1	no	—
168	C₂₉×#103	—	2	1	no	—
169	C₂₉×#103	—	2	1	no	—
170	C₂₉×#103	—	2	2	no	—
171	C₂₉×#103	—	2	2	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	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	—	8	1	no	—
199	SD₁₆×C₂₉	—	8	1	no	—
200	M₁₆×C₂₉	—	4	2	no	—
201	M₁₆×C₂₉	—	8	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	C₂×C₈×C₂₉	—	2	1	no	—
207	C₂×C₈×C₂₉	—	2	1	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	2	no	—
215	C₄⋊C₄×C₂₉	—	2	2	no	—
216	C₄⋊C₄×C₂₉	—	2	1	no	—
217	C₄⋊C₄×C₂₉	—	2	1	no	—
218	C₄⋊C₄×C₂₉	—	2	1	no	—
219	C₄⋊C₄×C₂₉	—	2	2	no	—
220	C₄⋊C₄×C₂₉	—	2	1	no	—
221	C₄⋊C₄×C₂₉	—	2	1	no	—
222	C₄⋊C₄×C₂₉	—	2	1	no	—
223	C₄⋊C₄×C₂₉	—	2	2	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	—	2	1	no	—
232	C₄⋊C₄×C₂₉	—	2	1	no	—
233	C₄⋊C₄×C₂₉	—	4	1	no	—
234	C₄⋊C₄×C₂₉	—	4	1	no	—
235	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
236	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
237	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
238	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
239	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
240	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
241	C₂²⋊C₄×C₂₉	—	2	2	no	—
242	C₂²⋊C₄×C₂₉	—	2	2	no	—
243	C₂²⋊C₄×C₂₉	—	2	2	no	—
244	C₂²⋊C₄×C₂₉	—	2	1	no	—
245	C₂²⋊C₄×C₂₉	—	2	2	no	—
246	C₂²⋊C₄×C₂₉	—	2	1	no	—
247	C₂²⋊C₄×C₂₉	—	2	1	no	—
248	C₂²⋊C₄×C₂₉	—	2	1	no	—
249	C₂²⋊C₄×C₂₉	—	2	1	no	—
250	C₂²⋊C₄×C₂₉	—	4	1	no	—
251	C₄²×C₂₉	—	2	2	no	—
252	C₄²×C₂₉	—	2	2	no	—
253	C₄²×C₂₉	—	2	2	no	—
254	C₄²×C₂₉	—	2	1	no	—
255	C₄²×C₂₉	—	2	1	no	—
256	C₄²×C₂₉	—	2	2	no	—
257	C₄²×C₂₉	—	2	1	no	—
258	C₄²×C₂₉	—	2	1	no	—
259	C₄²×C₂₉	—	2	1	no	—
260	C₄²×C₂₉	—	4	1	no	—
261	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
262	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
263	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
264	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
265	#18825	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
266	C₂³×C₂₉	—	2	1	no	—
267	C₂³×C₂₉	#120	1	1	yes	characteristic
268	Q₈×C₂₉	—	2	1	no	—
269	Q₈×C₂₉	—	2	1	no	—
270	Q₈×C₂₉	—	2	1	no	—
271	Q₈×C₂₉	—	2	1	no	—
272	Q₈×C₂₉	—	2	1	no	—
273	Q₈×C₂₉	—	4	2	no	—
274	Q₈×C₂₉	—	4	4	no	—
275	Q₈×C₂₉	—	4	2	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	—	4	1	no	—
281	Q₈×C₂₉	—	4	1	no	—
282	Q₈×C₂₉	#137	1	2	yes	—
283	D₄×C₂₉	—	2	1	no	—
284	D₄×C₂₉	—	2	1	no	—
285	D₄×C₂₉	—	4	2	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	1	no	—
292	C₂×C₄×C₂₉	—	2	1	no	—
293	C₂×C₄×C₂₉	—	2	2	no	—
294	C₂×C₄×C₂₉	—	2	1	no	—
295	C₂×C₄×C₂₉	—	2	1	no	—
296	C₂×C₄×C₂₉	—	2	1	no	—
297	C₂×C₄×C₂₉	—	2	1	no	—
298	C₂×C₄×C₂₉	—	2	2	no	—
299	C₂×C₄×C₂₉	—	4	1	no	—
300	C₂×C₄×C₂₉	—	4	2	no	—
301	C₂×C₄×C₂₉	—	4	4	no	—
302	C₂×C₄×C₂₉	—	4	2	no	—
303	C₂×C₄×C₂₉	—	4	1	no	—
304	C₂×C₄×C₂₉	—	4	1	no	—
305	C₂×C₄×C₂₉	—	4	1	no	—
306	C₂×C₄×C₂₉	—	4	1	no	—
307	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
308	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
309	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
310	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
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	C₈×C₂₉	—	4	1	no	—
318	C₈×C₂₉	—	4	1	no	—
319	#3523	C₂×C₂₉	1	1	yes	characteristic
320	#3252	C₂×C₂₉	1	1	yes	characteristic
321	#3231	C₂×C₂₉	1	1	yes	characteristic, complemented
322	#3078	C₂×C₂₉	1	1	yes	characteristic, complemented
323	#1653	C₂×C₂₉	1	1	yes	characteristic, complemented
324	#1651	C₂×C₂₉	1	1	yes	characteristic, complemented
325	#1650	C₂×C₂₉	1	1	yes	characteristic, complemented
326	#1648	C₂×C₂₉	1	1	yes	characteristic, complemented
327	#1638	C₂×C₂₉	1	1	yes	characteristic, complemented
328	#1637	C₂×C₂₉	1	1	yes	characteristic, complemented
329	#1636	C₂×C₂₉	1	1	yes	characteristic, complemented
330	#1636	C₂×C₂₉	1	1	yes	characteristic, complemented
331	#1561	C₂×C₂₉	1	1	yes	characteristic, complemented
332	#1495	C₂×C₂₉	1	1	yes	characteristic
333	#1487	C₂×C₂₉	1	1	yes	characteristic, complemented
334	C₂²×C₂₉	—	2	1	no	—
335	C₂²×C₂₉	—	2	1	no	—
336	C₂²×C₂₉	—	2	1	no	—
337	C₂²×C₂₉	—	4	1	no	—
338	C₂²×C₂₉	—	4	1	no	—
339	C₂²×C₂₉	—	4	1	no	—
340	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
341	C₄×C₂₉	—	2	1	no	—
342	C₄×C₂₉	—	2	2	no	—
343	C₄×C₂₉	—	2	1	no	—
344	C₄×C₂₉	—	2	1	no	—
345	C₄×C₂₉	—	2	1	no	—
346	C₄×C₂₉	—	4	1	no	—
347	C₄×C₂₉	—	4	2	no	—
348	C₄×C₂₉	—	4	1	no	—
349	C₄×C₂₉	—	4	1	no	—
350	C₄×C₂₉	—	4	2	no	—
351	C₄×C₂₉	—	4	1	no	—
352	C₄×C₂₉	—	4	1	no	—
353	C₄×C₂₉	—	4	1	no	—
354	C₄×C₂₉	—	8	1	no	—
355	C₄×C₂₉	—	8	1	no	—
356	C₄×C₂₉	C₂×#137	1	1	yes	characteristic
357	C₄×C₂₉	#575	1	1	yes	characteristic
358	C₄×C₂₉	#577	1	1	yes	characteristic
359	C₄×C₂₉	#578	1	1	yes	characteristic
360	#557	—	2	1	no	—
361	#557	C₂²×C₂₉	1	1	yes	characteristic
362	#557	C₂²×C₂₉	1	1	yes	characteristic
363	#556	—	2	1	no	—
364	#556	C₂²×C₂₉	1	1	yes	characteristic
365	#552	—	2	2	no	—
366	#552	—	2	1	no	—
367	D₄×Q₈	—	2	1	no	—
368	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
369	#541	—	2	2	no	—
370	#541	—	2	1	no	—
371	#533	—	2	1	no	—
372	#533	C₂²×C₂₉	1	1	yes	characteristic
373	#533	C₂²×C₂₉	1	1	yes	characteristic
374	#529	—	2	1	no	—
375	#529	C₂²×C₂₉	1	1	yes	characteristic
376	#519	—	2	1	no	—
377	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
378	#500	C₂²×C₂₉	1	1	yes	characteristic
379	#498	C₂²×C₂₉	1	1	yes	characteristic
380	#487	C₂²×C₂₉	1	1	yes	characteristic
381	#487	C₂²×C₂₉	1	1	yes	characteristic
382	#485	—	2	2	no	—
383	#479	—	2	2	no	—
384	#479	—	2	1	no	—
385	#479	—	2	1	no	—
386	#479	—	2	1	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	#475	C₂²×C₂₉	1	1	yes	characteristic
393	#470	—	2	1	no	—
394	#468	—	2	1	no	—
395	#464	—	2	1	no	—
396	#462	C₂²×C₂₉	1	1	yes	characteristic
397	#461	C₂²×C₂₉	1	1	yes	characteristic
398	#431	C₂²×C₂₉	1	1	yes	characteristic
399	#428	—	2	1	no	—
400	#423	C₂²×C₂₉	1	1	yes	characteristic
401	#423	C₂²×C₂₉	1	1	yes	characteristic
402	#419	—	2	1	no	—
403	#332	C₂²×C₂₉	1	1	yes	characteristic
404	#332	C₂²×C₂₉	1	1	yes	characteristic
405	#332	C₂²×C₂₉	1	1	yes	characteristic
406	#332	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	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
412	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
413	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
414	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
415	C₂×C₂₉	—	4	1	no	—
416	C₂×C₂₉	—	8	1	no	—
417	C₂×C₂₉	#3007	1	1	yes	characteristic
418	C₂×C₂₉	#3013	1	1	yes	characteristic
419	C₂×C₂₉	#3020	1	1	yes	characteristic
420	C₂²×Q₈	—	2	1	no	—
421	C₂²×Q₈	D₄×C₂₉	1	1	yes	characteristic
422	C₂×Q₁₆	—	2	1	no	—
423	C₂×SD₁₆	—	2	1	no	—
424	C₂×M₁₆	—	2	1	no	—
425	C₂×M₁₆	—	2	1	no	—
426	C₄⋊Q₈	—	2	2	no	—
427	C₄⋊Q₈	—	2	1	no	—
428	C₄⋊Q₈	—	2	1	no	—
429	C₄⋊Q₈	—	2	1	no	—
430	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
431	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
432	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
433	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
434	#126	—	2	2	no	—
435	#126	—	2	2	no	—
436	#126	—	2	2	no	—
437	#126	—	2	2	no	—
438	#126	—	2	1	no	—
439	#125	—	2	2	no	—
440	#125	—	2	2	no	—
441	#125	—	2	2	no	—
442	#125	—	2	1	no	—
443	#125	—	2	2	no	—
444	#125	—	2	2	no	—
445	#125	—	2	1	no	—
446	#125	—	2	1	no	—
447	#125	D₄×C₂₉	1	1	yes	characteristic
448	#125	D₄×C₂₉	1	2	yes	—
449	#124	—	2	1	no	—
450	#124	D₄×C₂₉	1	1	yes	characteristic
451	#123	—	2	2	no	—
452	#123	—	2	1	no	—
453	C₂²⋊Q₈	—	2	2	no	—
454	C₂²⋊Q₈	—	2	2	no	—
455	C₂²⋊Q₈	—	2	1	no	—
456	C₂²⋊Q₈	—	2	1	no	—
457	C₂²⋊Q₈	—	2	1	no	—
458	C₂²⋊Q₈	—	2	1	no	—
459	C₂²⋊Q₈	—	2	2	no	—
460	C₂²⋊Q₈	—	2	1	no	—
461	C₂²⋊Q₈	—	2	1	no	—
462	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
463	#121	D₄×C₂₉	1	1	yes	characteristic
464	C₄×Q₈	—	2	2	no	—
465	C₄×Q₈	—	2	2	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	—	2	1	no	—
474	C₄×Q₈	—	2	1	no	—
475	C₄×Q₈	—	2	1	no	—
476	C₄×Q₈	—	2	1	no	—
477	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
478	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
479	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
480	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
481	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
482	C₄×D₄	—	2	2	no	—
483	C₄×D₄	—	2	1	no	—
484	C₄×D₄	—	2	1	no	—
485	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
486	#117	—	2	2	no	—
487	#117	—	2	2	no	—
488	#117	—	2	2	no	—
489	#117	—	2	1	no	—
490	#117	—	2	1	no	—
491	#117	—	2	1	no	—
492	#117	D₄×C₂₉	1	2	yes	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
495	C₂×C₄²	—	2	1	no	—
496	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
497	#107	—	2	1	no	—
498	#107	—	2	1	no	—
499	#107	—	2	1	no	—
500	#107	—	2	2	no	—
501	#106	—	2	1	no	—
502	#106	—	2	1	no	—
503	#106	—	2	1	no	—
504	#106	—	2	2	no	—
505	C₄⋊C₈	—	2	1	no	—
506	C₄⋊C₈	—	2	1	no	—
507	C₄⋊C₈	—	2	1	no	—
508	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
509	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
510	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
511	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
512	#103	—	2	1	no	—
513	#103	—	2	1	no	—
514	#103	—	2	1	no	—
515	#103	—	2	1	no	—
516	#103	—	2	1	no	—
517	#103	—	2	1	no	—
518	#103	—	2	1	no	—
519	#103	—	2	2	no	—
520	#103	—	2	2	no	—
521	#102	—	2	1	no	—
522	C₂²⋊C₈	—	2	1	no	—
523	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
524	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
525	C₂₉	#18825	1	1	yes	characteristic, direct product factor, Sylow
526	C₂×Q₈	—	2	2	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	2	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	—	4	1	no	—
534	C₂×Q₈	—	4	2	no	—
535	C₂×Q₈	—	4	2	no	—
536	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
537	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
538	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
546	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
547	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
548	Q₁₆	—	8	1	no	—
549	SD₁₆	—	8	1	no	—
550	M₁₆	—	4	2	no	—
551	M₁₆	—	8	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	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	2	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	2	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	2	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	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	4	1	no	—
584	C₄⋊C₄	—	4	1	no	—
585	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
586	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
587	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
588	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
589	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
590	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	—	2	1	no	—
595	C₂²⋊C₄	—	2	2	no	—
596	C₂²⋊C₄	—	2	1	no	—
597	C₂²⋊C₄	—	2	1	no	—
598	C₂²⋊C₄	—	2	1	no	—
599	C₂²⋊C₄	—	2	1	no	—
600	C₂²⋊C₄	—	4	1	no	—
601	C₄²	—	2	2	no	—
602	C₄²	—	2	2	no	—
603	C₄²	—	2	2	no	—
604	C₄²	—	2	1	no	—
605	C₄²	—	2	1	no	—
606	C₄²	—	2	2	no	—
607	C₄²	—	2	1	no	—
608	C₄²	—	2	1	no	—
609	C₄²	—	2	1	no	—
610	C₄²	—	4	1	no	—
611	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
612	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
613	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
614	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
615	C₂³	—	2	1	no	—
616	C₂³	C₂₉×#120	1	1	yes	characteristic
617	Q₈	—	2	1	no	—
618	Q₈	—	2	1	no	—
619	Q₈	—	2	1	no	—
620	Q₈	—	2	1	no	—
621	Q₈	—	2	1	no	—
622	Q₈	—	4	2	no	—
623	Q₈	—	4	4	no	—
624	Q₈	—	4	2	no	—
625	Q₈	—	4	1	no	—
626	Q₈	—	4	1	no	—
627	Q₈	—	4	1	no	—
628	Q₈	—	4	1	no	—
629	Q₈	—	4	1	no	—
630	Q₈	—	4	1	no	—
631	Q₈	C₂₉×#137	1	2	yes	—
632	D₄	—	2	1	no	—
633	D₄	—	2	1	no	—
634	D₄	—	4	2	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	2	no	—
650	C₂×C₄	—	4	4	no	—
651	C₂×C₄	—	4	2	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
657	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
658	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
659	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
660	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
661	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
662	C₈	—	4	1	no	—
663	C₈	—	4	1	no	—
664	C₈	—	4	1	no	—
665	C₈	—	4	1	no	—
666	C₈	—	4	1	no	—
667	C₈	—	4	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	4	1	no	—
672	C₂²	—	4	1	no	—
673	C₂²	—	4	1	no	—
674	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
675	C₄	—	2	1	no	—
676	C₄	—	2	2	no	—
677	C₄	—	2	1	no	—
678	C₄	—	2	1	no	—
679	C₄	—	2	1	no	—
680	C₄	—	4	1	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	1	no	—
683	C₄	—	4	1	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	1	no	—
686	C₄	—	4	1	no	—
687	C₄	—	4	1	no	—
688	C₄	—	8	1	no	—
689	C₄	—	8	1	no	—
690	C₄	C₂×C₂₉×#137	1	1	yes	characteristic
691	C₄	C₂₉×#575	1	1	yes	characteristic
692	C₄	C₂₉×#577	1	1	yes	characteristic
693	C₄	C₂₉×#578	1	1	yes	characteristic
694	C₂	—	4	1	no	—
695	C₂	—	8	1	no	—
696	C₂	C₂₉×#3007	1	1	yes	characteristic
697	C₂	C₂₉×#3013	1	1	yes	characteristic
698	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×#3078	C₂	semidirect
5. C₂₉×#1653	C₂	semidirect
6. C₂₉×#1651	C₂	semidirect
7. C₂₉×#1650	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×#1561	C₂	semidirect
15. C₂₉×#1487	C₂	semidirect
265. #18825	C₂₉	direct (N × H)
321. #3231	C₂×C₂₉	semidirect
322. #3078	C₂×C₂₉	semidirect
323. #1653	C₂×C₂₉	semidirect
324. #1651	C₂×C₂₉	semidirect
325. #1650	C₂×C₂₉	semidirect
326. #1648	C₂×C₂₉	semidirect
327. #1638	C₂×C₂₉	semidirect
328. #1637	C₂×C₂₉	semidirect
329. #1636	C₂×C₂₉	semidirect
330. #1636	C₂×C₂₉	semidirect
331. #1561	C₂×C₂₉	semidirect
333. #1487	C₂×C₂₉	semidirect
525. C₂₉	#18825	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×#3252	2
C₂₉×#3231	2
C₂₉×#3078	2
C₂₉×#1653	2
C₂₉×#1651	2
C₂₉×#1650	2
C₂₉×#1648	2
C₂₉×#1638	2
C₂₉×#1637	2
C₂₉×#1636	2
C₂₉×#1561	2
C₂₉×#1495	2
C₂₉×#1487	2
#18825	29

Subgroups — C29×#18825 #20313725

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18825 #20313725