Subgroups — C₂₉×#18943 #20313843

Order 7424.

846 conjugacy classes of subgroups.

The subgroup lattice has 716 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
2	C₂₉×#3252	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3233	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3229	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×#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×#1635	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1549	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×#533	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×#499	—	2	1	no	—
35	C₂₉×#498	C₂²	1	1	yes	characteristic
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×#483	—	2	2	no	—
42	C₂₉×#482	—	2	1	no	—
43	C₂₉×#479	—	2	1	no	—
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×#476	C₂²	1	1	yes	characteristic
48	C₂₉×#475	—	2	2	no	—
49	C₂₉×#475	C₂²	1	1	yes	characteristic
50	C₂₉×#474	C₂²	1	1	yes	characteristic
51	C₂₉×#470	—	2	1	no	—
52	C₂₉×#468	—	2	1	no	—
53	C₂₉×#464	—	2	1	no	—
54	C₂₉×#462	C₂²	1	1	yes	characteristic
55	C₂₉×#461	C₂²	1	1	yes	characteristic
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	C₂²×Q₈×C₂₉	—	2	1	no	—
73	C₂²×Q₈×C₂₉	—	2	1	no	—
74	C₂×Q₁₆×C₂₉	—	2	1	no	—
75	C₂×SD₁₆×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	—	2	1	no	—
82	C₂₉×C₄⋊Q₈	D₄	1	2	yes	—
83	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₂₉×#126	—	2	2	no	—
88	C₂₉×#126	—	2	2	no	—
89	C₂₉×#126	—	2	2	no	—
90	C₂₉×#126	—	2	1	no	—
91	C₂₉×#126	—	2	1	no	—
92	C₂₉×#125	—	2	2	no	—
93	C₂₉×#125	—	2	2	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×#125	D₄	1	1	yes	characteristic
99	C₂₉×#124	—	2	2	no	—
100	C₂₉×#124	—	2	1	no	—
101	C₂₉×#124	D₄	1	1	yes	characteristic
102	C₂₉×#124	D₄	1	1	yes	characteristic
103	C₂₉×#123	—	2	2	no	—
104	C₂₉×#123	—	2	2	no	—
105	C₂₉×#123	—	2	1	no	—
106	C₂₉×#123	—	2	1	no	—
107	C₂₉×#123	—	2	2	no	—
108	C₂₉×C₂²⋊Q₈	—	2	2	no	—
109	C₂₉×C₂²⋊Q₈	—	2	2	no	—
110	C₂₉×C₂²⋊Q₈	—	2	2	no	—
111	C₂₉×C₂²⋊Q₈	—	2	2	no	—
112	C₂₉×C₂²⋊Q₈	—	2	2	no	—
113	C₂₉×C₂²⋊Q₈	—	2	1	no	—
114	C₂₉×C₂²⋊Q₈	—	2	2	no	—
115	C₂₉×C₂²⋊Q₈	—	2	1	no	—
116	C₂₉×C₂²⋊Q₈	—	2	1	no	—
117	C₂₉×C₂²⋊Q₈	—	2	1	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×#121	—	2	2	no	—
122	C₂₉×#121	—	2	1	no	—
123	C₂₉×#121	D₄	1	1	yes	characteristic
124	C₂₉×#121	D₄	1	1	yes	characteristic
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	—	2	1	no	—
129	C₄×Q₈×C₂₉	—	2	1	no	—
130	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
131	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
132	C₄×D₄×C₂₉	—	2	2	no	—
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	—	2	1	no	—
137	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
138	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
139	C₂₉×#117	—	2	1	no	—
140	C₂₉×#117	—	2	1	no	—
141	C₂₉×#117	—	2	1	no	—
142	C₂₉×#117	—	2	1	no	—
143	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
144	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
145	C₂×C₄⋊C₄×C₂₉	D₄	1	2	yes	—
146	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
147	C₂₉×#107	—	2	1	no	—
148	C₂₉×#107	—	2	1	no	—
149	C₂₉×#107	—	2	1	no	—
150	C₂₉×#106	—	2	1	no	—
151	C₂₉×#106	—	2	2	no	—
152	C₂₉×#106	—	2	2	no	—
153	C₂₉×#106	—	2	1	no	—
154	C₂₉×#106	—	2	1	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×#103	—	2	1	no	—
165	C₂₉×#103	—	2	1	no	—
166	C₂₉×#103	—	2	2	no	—
167	C₂₉×#103	—	2	2	no	—
168	C₂₉×#102	—	2	1	no	—
169	C₂₉×#102	—	2	1	no	—
170	C₂₉×#102	—	2	1	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	C₂×Q₈×C₂₉	—	2	2	no	—
179	C₂×Q₈×C₂₉	—	2	2	no	—
180	C₂×Q₈×C₂₉	—	2	1	no	—
181	C₂×Q₈×C₂₉	—	2	1	no	—
182	C₂×Q₈×C₂₉	—	2	1	no	—
183	C₂×Q₈×C₂₉	—	2	1	no	—
184	C₂×Q₈×C₂₉	—	8	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	C₂×D₄	1	1	yes	characteristic
189	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
190	C₂×D₄×C₂₉	—	2	1	no	—
191	C₂×D₄×C₂₉	—	2	1	no	—
192	C₂×D₄×C₂₉	—	2	2	no	—
193	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
194	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₂₉	—	2	2	no	—
196	C₂²×C₄×C₂₉	—	2	2	no	—
197	C₂²×C₄×C₂₉	—	2	2	no	—
198	C₂²×C₄×C₂₉	—	2	1	no	—
199	C₂²×C₄×C₂₉	—	2	1	no	—
200	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
203	Q₁₆×C₂₉	—	8	1	no	—
204	SD₁₆×C₂₉	—	8	1	no	—
205	M₁₆×C₂₉	—	8	1	no	—
206	C₂×C₈×C₂₉	—	2	1	no	—
207	C₂×C₈×C₂₉	—	2	1	no	—
208	C₂×C₈×C₂₉	—	2	1	no	—
209	C₂×C₈×C₂₉	—	2	1	no	—
210	C₂×C₈×C₂₉	—	2	1	no	—
211	C₂×C₈×C₂₉	—	2	1	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	2	no	—
217	C₄⋊C₄×C₂₉	—	2	2	no	—
218	C₄⋊C₄×C₂₉	—	2	2	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	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	—	2	1	no	—
232	C₄⋊C₄×C₂₉	—	2	1	no	—
233	C₄⋊C₄×C₂₉	—	2	1	no	—
234	C₄⋊C₄×C₂₉	—	4	1	no	—
235	C₄⋊C₄×C₂₉	—	4	1	no	—
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	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
242	C₂²⋊C₄×C₂₉	—	2	2	no	—
243	C₂²⋊C₄×C₂₉	—	2	2	no	—
244	C₂²⋊C₄×C₂₉	—	2	2	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	—	2	1	no	—
251	C₂²⋊C₄×C₂₉	—	2	1	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	—	4	1	no	—
257	C₄²×C₂₉	—	2	2	no	—
258	C₄²×C₂₉	—	2	2	no	—
259	C₄²×C₂₉	—	2	1	no	—
260	C₄²×C₂₉	—	2	1	no	—
261	C₄²×C₂₉	—	4	1	no	—
262	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
263	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
264	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
265	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
266	#18943	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂³×C₂₉	—	2	1	no	—
268	C₂³×C₂₉	—	2	1	no	—
269	C₂³×C₂₉	#120	1	1	yes	characteristic
270	Q₈×C₂₉	—	2	1	no	—
271	Q₈×C₂₉	—	2	1	no	—
272	Q₈×C₂₉	—	2	1	no	—
273	Q₈×C₂₉	—	2	1	no	—
274	Q₈×C₂₉	—	4	2	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	—	4	1	no	—
281	Q₈×C₂₉	—	8	2	no	—
282	Q₈×C₂₉	—	8	2	no	—
283	D₄×C₂₉	—	2	1	no	—
284	D₄×C₂₉	—	2	1	no	—
285	D₄×C₂₉	—	2	1	no	—
286	D₄×C₂₉	—	2	1	no	—
287	D₄×C₂₉	—	4	2	no	—
288	D₄×C₂₉	—	4	2	no	—
289	D₄×C₂₉	—	8	2	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	1	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	1	no	—
299	C₂×C₄×C₂₉	—	2	2	no	—
300	C₂×C₄×C₂₉	—	2	2	no	—
301	C₂×C₄×C₂₉	—	2	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	—	4	1	no	—
306	C₂×C₄×C₂₉	—	4	1	no	—
307	C₂×C₄×C₂₉	—	4	1	no	—
308	C₂×C₄×C₂₉	—	4	1	no	—
309	C₂×C₄×C₂₉	—	8	2	no	—
310	C₂×C₄×C₂₉	—	8	2	no	—
311	C₂×C₄×C₂₉	—	8	2	no	—
312	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
313	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
314	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
315	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
318	C₈×C₂₉	—	4	1	no	—
319	C₈×C₂₉	—	4	1	no	—
320	C₈×C₂₉	—	4	1	no	—
321	C₈×C₂₉	—	4	1	no	—
322	C₈×C₂₉	—	4	1	no	—
323	C₈×C₂₉	—	4	1	no	—
324	#3552	C₂×C₂₉	1	1	yes	characteristic
325	#3252	C₂×C₂₉	1	1	yes	characteristic, complemented
326	#3233	C₂×C₂₉	1	1	yes	characteristic, complemented
327	#3229	C₂×C₂₉	1	1	yes	characteristic, complemented
328	#1654	C₂×C₂₉	1	1	yes	characteristic, complemented
329	#1653	C₂×C₂₉	1	1	yes	characteristic, complemented
330	#1652	C₂×C₂₉	1	1	yes	characteristic, complemented
331	#1651	C₂×C₂₉	1	1	yes	characteristic, complemented
332	#1638	C₂×C₂₉	1	1	yes	characteristic, complemented
333	#1637	C₂×C₂₉	1	1	yes	characteristic, complemented
334	#1636	C₂×C₂₉	1	1	yes	characteristic, complemented
335	#1635	C₂×C₂₉	1	1	yes	characteristic, complemented
336	#1549	C₂×C₂₉	1	1	yes	characteristic, complemented
337	#1495	C₂×C₂₉	1	1	yes	characteristic, complemented
338	#1482	C₂×C₂₉	1	1	yes	characteristic, complemented
339	C₂²×C₂₉	—	2	1	no	—
340	C₂²×C₂₉	—	2	1	no	—
341	C₂²×C₂₉	—	2	1	no	—
342	C₂²×C₂₉	—	4	1	no	—
343	C₂²×C₂₉	—	4	1	no	—
344	C₂²×C₂₉	—	4	1	no	—
345	C₂²×C₂₉	—	4	1	no	—
346	C₂²×C₂₉	—	4	1	no	—
347	C₂²×C₂₉	—	4	1	no	—
348	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
349	C₄×C₂₉	—	2	1	no	—
350	C₄×C₂₉	—	2	1	no	—
351	C₄×C₂₉	—	2	1	no	—
352	C₄×C₂₉	—	2	1	no	—
353	C₄×C₂₉	—	4	1	no	—
354	C₄×C₂₉	—	4	2	no	—
355	C₄×C₂₉	—	4	1	no	—
356	C₄×C₂₉	—	4	2	no	—
357	C₄×C₂₉	—	4	1	no	—
358	C₄×C₂₉	—	4	1	no	—
359	C₄×C₂₉	—	4	1	no	—
360	C₄×C₂₉	—	4	1	no	—
361	C₄×C₂₉	—	8	1	no	—
362	C₄×C₂₉	—	8	1	no	—
363	C₄×C₂₉	#577	1	1	yes	characteristic
364	C₄×C₂₉	#577	1	1	yes	characteristic
365	C₄×C₂₉	#577	1	1	yes	characteristic
366	C₄×C₂₉	#578	1	1	yes	characteristic
367	#563	—	2	2	no	—
368	#557	C₂²×C₂₉	1	1	yes	characteristic
369	#556	C₂²×C₂₉	1	1	yes	characteristic
370	#554	—	2	1	no	—
371	#553	—	2	1	no	—
372	D₄×Q₈	—	2	1	no	—
373	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
374	#548	—	2	1	no	—
375	#547	C₂²×C₂₉	1	1	yes	characteristic
376	#544	—	2	1	no	—
377	#542	—	2	1	no	—
378	#541	—	2	1	no	—
379	#539	—	2	2	no	—
380	#536	—	2	1	no	—
381	#533	C₂²×C₂₉	1	1	yes	characteristic
382	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
383	#529	C₂²×C₂₉	1	1	yes	characteristic
384	#529	C₂²×C₂₉	1	1	yes	characteristic
385	#499	—	2	1	no	—
386	#498	C₂²×C₂₉	1	1	yes	characteristic
387	#498	C₂²×C₂₉	1	1	yes	characteristic
388	#488	—	2	1	no	—
389	#487	C₂²×C₂₉	1	1	yes	characteristic
390	#487	C₂²×C₂₉	1	1	yes	characteristic
391	#485	—	2	1	no	—
392	#483	—	2	2	no	—
393	#482	—	2	1	no	—
394	#479	—	2	1	no	—
395	#477	C₂²×C₂₉	1	1	yes	characteristic
396	#477	C₂²×C₂₉	1	1	yes	characteristic
397	#476	C₂²×C₂₉	1	1	yes	characteristic
398	#476	C₂²×C₂₉	1	1	yes	characteristic
399	#475	—	2	2	no	—
400	#475	C₂²×C₂₉	1	1	yes	characteristic
401	#474	C₂²×C₂₉	1	1	yes	characteristic
402	#470	—	2	1	no	—
403	#468	—	2	1	no	—
404	#464	—	2	1	no	—
405	#462	C₂²×C₂₉	1	1	yes	characteristic
406	#461	C₂²×C₂₉	1	1	yes	characteristic
407	#431	C₂²×C₂₉	1	1	yes	characteristic
408	#431	C₂²×C₂₉	1	1	yes	characteristic
409	#423	C₂²×C₂₉	1	1	yes	characteristic
410	#332	C₂²×C₂₉	1	1	yes	characteristic
411	#332	C₂²×C₂₉	1	1	yes	characteristic
412	#332	C₂²×C₂₉	1	1	yes	characteristic
413	#332	C₂²×C₂₉	1	1	yes	characteristic
414	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
415	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
416	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
417	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
418	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
419	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
420	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
421	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
422	C₂×C₂₉	—	4	1	no	—
423	C₂×C₂₉	—	8	1	no	—
424	C₂×C₂₉	—	8	1	no	—
425	C₂×C₂₉	#3009	1	1	yes	characteristic
426	C₂×C₂₉	#3013	1	1	yes	characteristic
427	C₂×C₂₉	#3020	1	1	yes	characteristic
428	C₂×#41	—	2	1	no	—
429	C₂²×Q₈	—	2	1	no	—
430	C₂²×Q₈	—	2	1	no	—
431	C₂×Q₁₆	—	2	1	no	—
432	C₂×SD₁₆	—	2	1	no	—
433	C₂×M₁₆	—	2	1	no	—
434	C₄⋊Q₈	—	2	2	no	—
435	C₄⋊Q₈	—	2	1	no	—
436	C₄⋊Q₈	—	2	1	no	—
437	C₄⋊Q₈	—	2	1	no	—
438	C₄⋊Q₈	—	2	1	no	—
439	C₄⋊Q₈	D₄×C₂₉	1	2	yes	—
440	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
441	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
442	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
443	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
444	#126	—	2	2	no	—
445	#126	—	2	2	no	—
446	#126	—	2	2	no	—
447	#126	—	2	1	no	—
448	#126	—	2	1	no	—
449	#125	—	2	2	no	—
450	#125	—	2	2	no	—
451	#125	—	2	2	no	—
452	#125	—	2	1	no	—
453	#125	—	2	1	no	—
454	#125	D₄×C₂₉	1	1	yes	characteristic
455	#125	D₄×C₂₉	1	1	yes	characteristic
456	#124	—	2	2	no	—
457	#124	—	2	1	no	—
458	#124	D₄×C₂₉	1	1	yes	characteristic
459	#124	D₄×C₂₉	1	1	yes	characteristic
460	#123	—	2	2	no	—
461	#123	—	2	2	no	—
462	#123	—	2	1	no	—
463	#123	—	2	1	no	—
464	#123	—	2	2	no	—
465	C₂²⋊Q₈	—	2	2	no	—
466	C₂²⋊Q₈	—	2	2	no	—
467	C₂²⋊Q₈	—	2	2	no	—
468	C₂²⋊Q₈	—	2	2	no	—
469	C₂²⋊Q₈	—	2	2	no	—
470	C₂²⋊Q₈	—	2	1	no	—
471	C₂²⋊Q₈	—	2	2	no	—
472	C₂²⋊Q₈	—	2	1	no	—
473	C₂²⋊Q₈	—	2	1	no	—
474	C₂²⋊Q₈	—	2	1	no	—
475	C₂²⋊Q₈	—	2	1	no	—
476	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
477	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
478	#121	—	2	2	no	—
479	#121	—	2	1	no	—
480	#121	D₄×C₂₉	1	1	yes	characteristic
481	#121	D₄×C₂₉	1	1	yes	characteristic
482	C₄×Q₈	—	2	1	no	—
483	C₄×Q₈	—	2	1	no	—
484	C₄×Q₈	—	2	1	no	—
485	C₄×Q₈	—	2	1	no	—
486	C₄×Q₈	—	2	1	no	—
487	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
488	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
489	C₄×D₄	—	2	2	no	—
490	C₄×D₄	—	2	2	no	—
491	C₄×D₄	—	2	1	no	—
492	C₄×D₄	—	2	1	no	—
493	C₄×D₄	—	2	1	no	—
494	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
495	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
496	#117	—	2	1	no	—
497	#117	—	2	1	no	—
498	#117	—	2	1	no	—
499	#117	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	D₄×C₂₉	1	2	yes	—
503	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
504	#107	—	2	1	no	—
505	#107	—	2	1	no	—
506	#107	—	2	1	no	—
507	#106	—	2	1	no	—
508	#106	—	2	2	no	—
509	#106	—	2	2	no	—
510	#106	—	2	1	no	—
511	#106	—	2	1	no	—
512	C₄⋊C₈	—	2	1	no	—
513	C₄⋊C₈	—	2	1	no	—
514	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
515	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
516	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
517	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
518	#103	—	2	1	no	—
519	#103	—	2	1	no	—
520	#103	—	2	1	no	—
521	#103	—	2	1	no	—
522	#103	—	2	1	no	—
523	#103	—	2	2	no	—
524	#103	—	2	2	no	—
525	#102	—	2	1	no	—
526	#102	—	2	1	no	—
527	#102	—	2	1	no	—
528	C₂²⋊C₈	—	2	1	no	—
529	C₂²⋊C₈	—	2	1	no	—
530	C₄×C₈	—	2	1	no	—
531	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
532	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
533	C₂₉	#18943	1	1	yes	characteristic, direct product factor, Sylow
534	#41	—	8	1	no	—
535	#41	—	8	1	no	—
536	C₂×Q₈	—	2	2	no	—
537	C₂×Q₈	—	2	2	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	8	1	no	—
543	C₂×Q₈	—	8	1	no	—
544	C₂×Q₈	—	8	1	no	—
545	C₂×Q₈	—	8	1	no	—
546	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
547	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
552	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
559	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
560	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
561	Q₁₆	—	8	1	no	—
562	SD₁₆	—	8	1	no	—
563	M₁₆	—	8	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	2	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	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	4	1	no	—
593	C₄⋊C₄	—	4	1	no	—
594	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
595	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
596	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
597	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
598	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
599	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
600	C₂²⋊C₄	—	2	2	no	—
601	C₂²⋊C₄	—	2	2	no	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	1	no	—
605	C₂²⋊C₄	—	2	1	no	—
606	C₂²⋊C₄	—	2	1	no	—
607	C₂²⋊C₄	—	2	1	no	—
608	C₂²⋊C₄	—	2	1	no	—
609	C₂²⋊C₄	—	2	1	no	—
610	C₂²⋊C₄	—	2	1	no	—
611	C₂²⋊C₄	—	2	1	no	—
612	C₂²⋊C₄	—	2	1	no	—
613	C₂²⋊C₄	—	2	1	no	—
614	C₂²⋊C₄	—	4	1	no	—
615	C₄²	—	2	2	no	—
616	C₄²	—	2	2	no	—
617	C₄²	—	2	1	no	—
618	C₄²	—	2	1	no	—
619	C₄²	—	4	1	no	—
620	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
621	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
622	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
623	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
624	C₂³	—	2	1	no	—
625	C₂³	—	2	1	no	—
626	C₂³	C₂₉×#120	1	1	yes	characteristic
627	Q₈	—	2	1	no	—
628	Q₈	—	2	1	no	—
629	Q₈	—	2	1	no	—
630	Q₈	—	2	1	no	—
631	Q₈	—	4	2	no	—
632	Q₈	—	4	1	no	—
633	Q₈	—	4	1	no	—
634	Q₈	—	4	1	no	—
635	Q₈	—	4	1	no	—
636	Q₈	—	4	1	no	—
637	Q₈	—	4	1	no	—
638	Q₈	—	8	2	no	—
639	Q₈	—	8	2	no	—
640	D₄	—	2	1	no	—
641	D₄	—	2	1	no	—
642	D₄	—	2	1	no	—
643	D₄	—	2	1	no	—
644	D₄	—	4	2	no	—
645	D₄	—	4	2	no	—
646	D₄	—	8	2	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	8	2	no	—
667	C₂×C₄	—	8	2	no	—
668	C₂×C₄	—	8	2	no	—
669	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
670	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
671	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
672	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
673	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
674	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
675	C₈	—	4	1	no	—
676	C₈	—	4	1	no	—
677	C₈	—	4	1	no	—
678	C₈	—	4	1	no	—
679	C₈	—	4	1	no	—
680	C₈	—	4	1	no	—
681	C₂²	—	2	1	no	—
682	C₂²	—	2	1	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	4	1	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	4	1	no	—
690	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
691	C₄	—	2	1	no	—
692	C₄	—	2	1	no	—
693	C₄	—	2	1	no	—
694	C₄	—	2	1	no	—
695	C₄	—	4	1	no	—
696	C₄	—	4	2	no	—
697	C₄	—	4	1	no	—
698	C₄	—	4	2	no	—
699	C₄	—	4	1	no	—
700	C₄	—	4	1	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	1	no	—
703	C₄	—	8	1	no	—
704	C₄	—	8	1	no	—
705	C₄	C₂₉×#577	1	1	yes	characteristic
706	C₄	C₂₉×#577	1	1	yes	characteristic
707	C₄	C₂₉×#577	1	1	yes	characteristic
708	C₄	C₂₉×#578	1	1	yes	characteristic
709	C₂	—	4	1	no	—
710	C₂	—	8	1	no	—
711	C₂	—	8	1	no	—
712	C₂	C₂₉×#3009	1	1	yes	characteristic
713	C₂	C₂₉×#3013	1	1	yes	characteristic
714	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×#3552	C₂
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
2. C₂₉×#3252	C₂	semidirect
3. C₂₉×#3233	C₂	semidirect
4. C₂₉×#3229	C₂	semidirect
5. C₂₉×#1654	C₂	semidirect
6. C₂₉×#1653	C₂	semidirect
7. C₂₉×#1652	C₂	semidirect
8. C₂₉×#1651	C₂	semidirect
9. C₂₉×#1638	C₂	semidirect
10. C₂₉×#1637	C₂	semidirect
11. C₂₉×#1636	C₂	semidirect
12. C₂₉×#1635	C₂	semidirect
13. C₂₉×#1549	C₂	semidirect
14. C₂₉×#1495	C₂	semidirect
15. C₂₉×#1482	C₂	semidirect
266. #18943	C₂₉	direct (N × H)
325. #3252	C₂×C₂₉	semidirect
326. #3233	C₂×C₂₉	semidirect
327. #3229	C₂×C₂₉	semidirect
328. #1654	C₂×C₂₉	semidirect
329. #1653	C₂×C₂₉	semidirect
330. #1652	C₂×C₂₉	semidirect
331. #1651	C₂×C₂₉	semidirect
332. #1638	C₂×C₂₉	semidirect
333. #1637	C₂×C₂₉	semidirect
334. #1636	C₂×C₂₉	semidirect
335. #1635	C₂×C₂₉	semidirect
336. #1549	C₂×C₂₉	semidirect
337. #1495	C₂×C₂₉	semidirect
338. #1482	C₂×C₂₉	semidirect
533. C₂₉	#18943	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×#3252	2
C₂₉×#3233	2
C₂₉×#3229	2
C₂₉×#1654	2
C₂₉×#1653	2
C₂₉×#1652	2
C₂₉×#1651	2
C₂₉×#1638	2
C₂₉×#1637	2
C₂₉×#1636	2
C₂₉×#1635	2
C₂₉×#1549	2
C₂₉×#1495	2
C₂₉×#1482	2
#18943	29

Subgroups — C29×#18943 #20313843

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18943 #20313843