Subgroups — C₂₉×#18809 #20313709

Order 7424.

890 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#41×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#3231	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3113	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3107	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#1653	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1651	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×#1645	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1645	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1644	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1643	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1554	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1488	C₂	1	1	yes	maximal, characteristic
15	C₂₉×#1479	C₂	1	1	yes	maximal, characteristic, complemented
16	Q₈²×C₂₉	C₂²	1	1	yes	characteristic
17	C₂₉×#557	—	2	1	no	—
18	C₂₉×#557	C₂²	1	1	yes	characteristic
19	C₂₉×#554	—	2	2	no	—
20	C₂₉×#554	—	2	1	no	—
21	C₂₉×#554	—	2	1	no	—
22	C₂₉×#554	C₂²	1	1	yes	characteristic
23	D₄×Q₈×C₂₉	—	2	1	no	—
24	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
25	C₂₉×#533	—	2	2	no	—
26	C₂₉×#533	—	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	C₄×#41×C₂₉	—	2	1	no	—
31	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₂₉	—	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×#485	—	2	1	no	—
40	C₂₉×#483	—	2	1	no	—
41	C₂₉×#479	—	2	2	no	—
42	C₂₉×#475	C₂²	1	1	yes	characteristic
43	C₂₉×#475	C₂²	1	1	yes	characteristic
44	C₂₉×#475	C₂²	1	1	yes	characteristic
45	C₂₉×#474	C₂²	1	1	yes	characteristic
46	C₂₉×#462	C₂²	1	1	yes	characteristic
47	C₂₉×#462	C₂²	1	1	yes	characteristic
48	C₂₉×#462	C₂²	1	1	yes	characteristic
49	C₂₉×#461	C₂²	1	1	yes	characteristic
50	C₂₉×#452	—	2	1	no	—
51	C₂₉×#451	—	2	1	no	—
52	C₂₉×#441	—	2	1	no	—
53	C₂₉×#441	—	2	1	no	—
54	C₄×Q₁₆×C₂₉	—	2	1	no	—
55	C₄×SD₁₆×C₂₉	—	2	1	no	—
56	C₂₉×#432	C₂²	1	1	yes	characteristic
57	C₂₉×#431	C₂²	1	1	yes	characteristic
58	C₂₉×#431	C₂²	1	1	yes	characteristic
59	C₂₉×#333	C₂²	1	1	yes	characteristic
60	C₂₉×#333	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	C₂×#41×C₂₉	D₄	1	1	yes	characteristic
72	C₂²×Q₈×C₂₉	—	2	1	no	—
73	C₂²×Q₈×C₂₉	D₄	1	1	yes	characteristic
74	C₂×Q₁₆×C₂₉	—	2	1	no	—
75	C₂×Q₁₆×C₂₉	—	2	1	no	—
76	C₂×Q₁₆×C₂₉	—	2	1	no	—
77	C₂×SD₁₆×C₂₉	—	2	1	no	—
78	C₂₉×C₄⋊Q₈	—	2	2	no	—
79	C₂₉×C₄⋊Q₈	—	2	1	no	—
80	C₂₉×C₄⋊Q₈	—	2	2	no	—
81	C₂₉×C₄⋊Q₈	—	2	1	no	—
82	C₂₉×C₄⋊Q₈	—	2	1	no	—
83	C₂₉×C₄⋊Q₈	—	2	1	no	—
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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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	1	no	—
93	C₂₉×#125	—	2	1	no	—
94	C₂₉×#125	—	2	1	no	—
95	C₂₉×C₂²⋊Q₈	—	2	2	no	—
96	C₂₉×C₂²⋊Q₈	—	2	2	no	—
97	C₂₉×C₂²⋊Q₈	—	2	2	no	—
98	C₂₉×C₂²⋊Q₈	—	2	2	no	—
99	C₂₉×C₂²⋊Q₈	—	2	2	no	—
100	C₂₉×C₂²⋊Q₈	—	2	1	no	—
101	C₂₉×C₂²⋊Q₈	—	2	2	no	—
102	C₂₉×C₂²⋊Q₈	—	2	1	no	—
103	C₂₉×C₂²⋊Q₈	—	2	1	no	—
104	C₂₉×C₂²⋊Q₈	—	2	2	no	—
105	C₂₉×C₂²⋊Q₈	—	2	1	no	—
106	C₂₉×C₂²⋊Q₈	—	2	1	no	—
107	C₂₉×C₂²⋊Q₈	D₄	1	2	yes	—
108	C₄×Q₈×C₂₉	—	2	2	no	—
109	C₄×Q₈×C₂₉	—	2	2	no	—
110	C₄×Q₈×C₂₉	—	2	2	no	—
111	C₄×Q₈×C₂₉	—	2	1	no	—
112	C₄×Q₈×C₂₉	—	2	1	no	—
113	C₄×Q₈×C₂₉	—	2	1	no	—
114	C₄×Q₈×C₂₉	—	2	1	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	D₄	1	1	yes	characteristic
121	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
122	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
123	C₄×Q₈×C₂₉	D₄	1	2	yes	—
124	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
125	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
126	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
127	C₄×D₄×C₂₉	—	2	2	no	—
128	C₄×D₄×C₂₉	—	2	2	no	—
129	C₄×D₄×C₂₉	—	2	1	no	—
130	C₄×D₄×C₂₉	—	2	1	no	—
131	C₄×D₄×C₂₉	—	2	1	no	—
132	C₄×D₄×C₂₉	—	2	1	no	—
133	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
134	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
135	C₂₉×#117	—	2	2	no	—
136	C₂₉×#117	—	2	1	no	—
137	C₂₉×#117	—	2	1	no	—
138	C₂₉×#117	—	2	1	no	—
139	C₂₉×#117	D₄	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
141	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
142	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
143	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
144	C₂×C₄²×C₂₉	—	2	2	no	—
145	C₂×C₄²×C₂₉	—	2	1	no	—
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	2	no	—
150	C₂₉×#106	—	2	1	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	2	no	—
163	C₂₉×#103	—	2	2	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×#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	C₂₉×#97	—	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	—	2	2	no	—
177	#41×C₂₉	—	2	2	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	2	no	—
183	C₂×Q₈×C₂₉	—	2	1	no	—
184	C₂×Q₈×C₂₉	—	2	1	no	—
185	C₂×Q₈×C₂₉	—	4	1	no	—
186	C₂×Q₈×C₂₉	—	4	2	no	—
187	C₂×Q₈×C₂₉	—	4	2	no	—
188	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
189	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
190	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
191	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
192	C₂×D₄×C₂₉	—	2	1	no	—
193	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₂₉	—	2	1	no	—
195	C₂²×C₄×C₂₉	—	2	2	no	—
196	C₂²×C₄×C₂₉	—	2	1	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	—	2	1	no	—
201	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
204	Q₁₆×C₂₉	—	4	2	no	—
205	Q₁₆×C₂₉	—	4	2	no	—
206	Q₁₆×C₂₉	—	4	2	no	—
207	SD₁₆×C₂₉	—	4	2	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	C₂×C₈×C₂₉	—	2	1	no	—
213	C₂×C₈×C₂₉	—	2	1	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	2	no	—
221	C₄⋊C₄×C₂₉	—	2	2	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	2	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	—	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	—	4	1	no	—
239	C₄⋊C₄×C₂₉	—	4	1	no	—
240	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
241	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
242	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
243	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
244	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
245	C₂²⋊C₄×C₂₉	—	2	2	no	—
246	C₂²⋊C₄×C₂₉	—	2	2	no	—
247	C₂²⋊C₄×C₂₉	—	2	2	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	—	4	1	no	—
252	C₄²×C₂₉	—	2	2	no	—
253	C₄²×C₂₉	—	2	2	no	—
254	C₄²×C₂₉	—	2	1	no	—
255	C₄²×C₂₉	—	2	2	no	—
256	C₄²×C₂₉	—	2	1	no	—
257	C₄²×C₂₉	—	2	1	no	—
258	C₄²×C₂₉	—	2	1	no	—
259	C₄²×C₂₉	—	2	1	no	—
260	C₄²×C₂₉	—	2	1	no	—
261	C₄²×C₂₉	—	2	1	no	—
262	C₄²×C₂₉	—	4	1	no	—
263	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
264	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
265	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
266	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
267	#18809	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	2	no	—
276	Q₈×C₂₉	—	4	4	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	—	4	1	no	—
283	Q₈×C₂₉	—	8	2	no	—
284	Q₈×C₂₉	#135	1	2	yes	—
285	Q₈×C₂₉	#137	1	2	yes	—
286	D₄×C₂₉	—	2	4	no	—
287	D₄×C₂₉	—	2	1	no	—
288	D₄×C₂₉	#137	1	2	yes	—
289	C₂×C₄×C₂₉	—	2	4	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	2	no	—
299	C₂×C₄×C₂₉	—	2	2	no	—
300	C₂×C₄×C₂₉	—	2	1	no	—
301	C₂×C₄×C₂₉	—	2	1	no	—
302	C₂×C₄×C₂₉	—	2	1	no	—
303	C₂×C₄×C₂₉	—	4	1	no	—
304	C₂×C₄×C₂₉	—	4	2	no	—
305	C₂×C₄×C₂₉	—	4	4	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	—	4	1	no	—
310	C₂×C₄×C₂₉	—	8	1	no	—
311	C₂×C₄×C₂₉	—	8	1	no	—
312	C₂×C₄×C₂₉	—	8	2	no	—
313	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
314	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
315	C₂×C₄×C₂₉	#120	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	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
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	C₈×C₂₉	—	4	1	no	—
325	Q₈×#41	C₂×C₂₉	1	1	yes	characteristic
326	#3231	C₂×C₂₉	1	1	yes	characteristic, complemented
327	#3113	C₂×C₂₉	1	1	yes	characteristic, complemented
328	#3107	C₂×C₂₉	1	1	yes	characteristic
329	#1653	C₂×C₂₉	1	1	yes	characteristic, complemented
330	#1651	C₂×C₂₉	1	1	yes	characteristic, complemented
331	#1649	C₂×C₂₉	1	1	yes	characteristic, complemented
332	#1648	C₂×C₂₉	1	1	yes	characteristic, complemented
333	#1645	C₂×C₂₉	1	1	yes	characteristic, complemented
334	#1645	C₂×C₂₉	1	1	yes	characteristic, complemented
335	#1644	C₂×C₂₉	1	1	yes	characteristic, complemented
336	#1643	C₂×C₂₉	1	1	yes	characteristic, complemented
337	#1554	C₂×C₂₉	1	1	yes	characteristic, complemented
338	#1488	C₂×C₂₉	1	1	yes	characteristic
339	#1479	C₂×C₂₉	1	1	yes	characteristic, complemented
340	C₂²×C₂₉	—	2	1	no	—
341	C₂²×C₂₉	—	2	1	no	—
342	C₂²×C₂₉	—	2	2	no	—
343	C₂²×C₂₉	—	2	1	no	—
344	C₂²×C₂₉	—	4	1	no	—
345	C₂²×C₂₉	—	4	1	no	—
346	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
347	C₄×C₂₉	—	2	1	no	—
348	C₄×C₂₉	—	2	2	no	—
349	C₄×C₂₉	—	2	1	no	—
350	C₄×C₂₉	—	2	2	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	1	no	—
357	C₄×C₂₉	—	4	2	no	—
358	C₄×C₂₉	—	4	1	no	—
359	C₄×C₂₉	—	4	1	no	—
360	C₄×C₂₉	—	8	1	no	—
361	C₄×C₂₉	—	8	1	no	—
362	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
363	C₄×C₂₉	C₂×#137	1	1	yes	characteristic
364	C₄×C₂₉	C₂×#137	1	1	yes	characteristic
365	C₄×C₂₉	#575	1	1	yes	characteristic
366	Q₈²	C₂²×C₂₉	1	1	yes	characteristic
367	#557	—	2	1	no	—
368	#557	C₂²×C₂₉	1	1	yes	characteristic
369	#554	—	2	2	no	—
370	#554	—	2	1	no	—
371	#554	—	2	1	no	—
372	#554	C₂²×C₂₉	1	1	yes	characteristic
373	D₄×Q₈	—	2	1	no	—
374	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
375	#533	—	2	2	no	—
376	#533	—	2	1	no	—
377	#533	—	2	1	no	—
378	#533	C₂²×C₂₉	1	1	yes	characteristic
379	#533	C₂²×C₂₉	1	1	yes	characteristic
380	C₄×#41	—	2	1	no	—
381	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
382	C₂×C₄×Q₈	—	2	1	no	—
383	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
384	#500	C₂²×C₂₉	1	1	yes	characteristic
385	#498	C₂²×C₂₉	1	1	yes	characteristic
386	#487	C₂²×C₂₉	1	1	yes	characteristic
387	#487	C₂²×C₂₉	1	1	yes	characteristic
388	#485	—	2	2	no	—
389	#485	—	2	1	no	—
390	#483	—	2	1	no	—
391	#479	—	2	2	no	—
392	#475	C₂²×C₂₉	1	1	yes	characteristic
393	#475	C₂²×C₂₉	1	1	yes	characteristic
394	#475	C₂²×C₂₉	1	1	yes	characteristic
395	#474	C₂²×C₂₉	1	1	yes	characteristic
396	#462	C₂²×C₂₉	1	1	yes	characteristic
397	#462	C₂²×C₂₉	1	1	yes	characteristic
398	#462	C₂²×C₂₉	1	1	yes	characteristic
399	#461	C₂²×C₂₉	1	1	yes	characteristic
400	#452	—	2	1	no	—
401	#451	—	2	1	no	—
402	#441	—	2	1	no	—
403	#441	—	2	1	no	—
404	C₄×Q₁₆	—	2	1	no	—
405	C₄×SD₁₆	—	2	1	no	—
406	#432	C₂²×C₂₉	1	1	yes	characteristic
407	#431	C₂²×C₂₉	1	1	yes	characteristic
408	#431	C₂²×C₂₉	1	1	yes	characteristic
409	#333	C₂²×C₂₉	1	1	yes	characteristic
410	#333	C₂²×C₂₉	1	1	yes	characteristic
411	#332	C₂²×C₂₉	1	1	yes	characteristic
412	#332	C₂²×C₂₉	1	1	yes	characteristic
413	Q₈⋊C₈	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	Q₈⋊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	C₂×C₂₉	—	4	1	no	—
422	C₂×C₂₉	—	4	2	no	—
423	C₂×C₂₉	#3002	1	1	yes	characteristic
424	C₂×C₂₉	#3004	1	1	yes	characteristic
425	C₂×C₂₉	#3022	1	1	yes	characteristic
426	C₂×#41	D₄×C₂₉	1	1	yes	characteristic
427	C₂²×Q₈	—	2	1	no	—
428	C₂²×Q₈	D₄×C₂₉	1	1	yes	characteristic
429	C₂×Q₁₆	—	2	1	no	—
430	C₂×Q₁₆	—	2	1	no	—
431	C₂×Q₁₆	—	2	1	no	—
432	C₂×SD₁₆	—	2	1	no	—
433	C₄⋊Q₈	—	2	2	no	—
434	C₄⋊Q₈	—	2	1	no	—
435	C₄⋊Q₈	—	2	2	no	—
436	C₄⋊Q₈	—	2	1	no	—
437	C₄⋊Q₈	—	2	1	no	—
438	C₄⋊Q₈	—	2	1	no	—
439	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
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	#125	—	2	2	no	—
444	#125	—	2	2	no	—
445	#125	—	2	2	no	—
446	#125	—	2	1	no	—
447	#125	—	2	1	no	—
448	#125	—	2	1	no	—
449	#125	—	2	1	no	—
450	C₂²⋊Q₈	—	2	2	no	—
451	C₂²⋊Q₈	—	2	2	no	—
452	C₂²⋊Q₈	—	2	2	no	—
453	C₂²⋊Q₈	—	2	2	no	—
454	C₂²⋊Q₈	—	2	2	no	—
455	C₂²⋊Q₈	—	2	1	no	—
456	C₂²⋊Q₈	—	2	2	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	2	yes	—
463	C₄×Q₈	—	2	2	no	—
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	D₄×C₂₉	1	1	yes	characteristic
476	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
477	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
478	C₄×Q₈	D₄×C₂₉	1	2	yes	—
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	2	no	—
484	C₄×D₄	—	2	1	no	—
485	C₄×D₄	—	2	1	no	—
486	C₄×D₄	—	2	1	no	—
487	C₄×D₄	—	2	1	no	—
488	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
489	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
490	#117	—	2	2	no	—
491	#117	—	2	1	no	—
492	#117	—	2	1	no	—
493	#117	—	2	1	no	—
494	#117	D₄×C₂₉	1	1	yes	characteristic
495	C₂×C₄⋊C₄	—	2	2	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
499	C₂×C₄²	—	2	2	no	—
500	C₂×C₄²	—	2	1	no	—
501	C₂×C₄²	—	2	1	no	—
502	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
503	#107	—	2	1	no	—
504	#107	—	2	2	no	—
505	#106	—	2	1	no	—
506	#106	—	2	1	no	—
507	#106	—	2	1	no	—
508	#106	—	2	2	no	—
509	C₄⋊C₈	—	2	1	no	—
510	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
511	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
512	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
513	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
514	#103	—	2	1	no	—
515	#103	—	2	1	no	—
516	#103	—	2	1	no	—
517	#103	—	2	2	no	—
518	#103	—	2	2	no	—
519	#103	—	2	1	no	—
520	#103	—	2	1	no	—
521	#103	—	2	1	no	—
522	#103	—	2	1	no	—
523	#102	—	2	1	no	—
524	C₂²⋊C₈	—	2	1	no	—
525	C₂²⋊C₈	—	2	1	no	—
526	C₂²⋊C₈	—	2	1	no	—
527	#97	—	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	C₂₉	#18809	1	1	yes	characteristic, direct product factor, Sylow
532	#41	—	2	2	no	—
533	#41	—	2	2	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	2	2	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	2	2	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	4	1	no	—
542	C₂×Q₈	—	4	2	no	—
543	C₂×Q₈	—	4	2	no	—
544	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
545	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
546	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
547	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
558	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
559	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
560	Q₁₆	—	4	2	no	—
561	Q₁₆	—	4	2	no	—
562	Q₁₆	—	4	2	no	—
563	SD₁₆	—	4	2	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	2	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	2	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	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	4	1	no	—
595	C₄⋊C₄	—	4	1	no	—
596	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
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	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
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	—	4	1	no	—
608	C₄²	—	2	2	no	—
609	C₄²	—	2	2	no	—
610	C₄²	—	2	1	no	—
611	C₄²	—	2	2	no	—
612	C₄²	—	2	1	no	—
613	C₄²	—	2	1	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	2	1	no	—
617	C₄²	—	2	1	no	—
618	C₄²	—	4	1	no	—
619	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
620	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
621	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
622	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
623	C₂³	—	2	1	no	—
624	C₂³	C₂₉×#120	1	1	yes	characteristic
625	Q₈	—	2	1	no	—
626	Q₈	—	2	1	no	—
627	Q₈	—	2	1	no	—
628	Q₈	—	2	1	no	—
629	Q₈	—	4	2	no	—
630	Q₈	—	4	2	no	—
631	Q₈	—	4	4	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	C₂₉×#135	1	2	yes	—
640	Q₈	C₂₉×#137	1	2	yes	—
641	D₄	—	2	4	no	—
642	D₄	—	2	1	no	—
643	D₄	C₂₉×#137	1	2	yes	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	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	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	2	no	—
660	C₂×C₄	—	4	4	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	—	8	1	no	—
666	C₂×C₄	—	8	1	no	—
667	C₂×C₄	—	8	2	no	—
668	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
669	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
670	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
671	C₂×C₄	C₂²×D₄×C₂₉	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	C₈	—	4	1	no	—
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	C₂²	—	2	1	no	—
681	C₂²	—	2	1	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	4	1	no	—
685	C₂²	—	4	1	no	—
686	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
687	C₄	—	2	1	no	—
688	C₄	—	2	2	no	—
689	C₄	—	2	1	no	—
690	C₄	—	2	2	no	—
691	C₄	—	2	1	no	—
692	C₄	—	2	1	no	—
693	C₄	—	4	1	no	—
694	C₄	—	4	2	no	—
695	C₄	—	4	1	no	—
696	C₄	—	4	1	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	1	no	—
699	C₄	—	4	1	no	—
700	C₄	—	8	1	no	—
701	C₄	—	8	1	no	—
702	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
703	C₄	C₂×C₂₉×#137	1	1	yes	characteristic
704	C₄	C₂×C₂₉×#137	1	1	yes	characteristic
705	C₄	C₂₉×#575	1	1	yes	characteristic
706	C₂	—	4	1	no	—
707	C₂	—	4	2	no	—
708	C₂	C₂₉×#3002	1	1	yes	characteristic
709	C₂	C₂₉×#3004	1	1	yes	characteristic
710	C₂	C₂₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂×#41×C₂₉	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
2. C₂₉×#3231	C₂	semidirect
3. C₂₉×#3113	C₂	semidirect
5. C₂₉×#1653	C₂	semidirect
6. C₂₉×#1651	C₂	semidirect
7. C₂₉×#1649	C₂	semidirect
8. C₂₉×#1648	C₂	semidirect
9. C₂₉×#1645	C₂	semidirect
10. C₂₉×#1645	C₂	semidirect
11. C₂₉×#1644	C₂	semidirect
12. C₂₉×#1643	C₂	semidirect
13. C₂₉×#1554	C₂	semidirect
15. C₂₉×#1479	C₂	semidirect
267. #18809	C₂₉	direct (N × H)
326. #3231	C₂×C₂₉	semidirect
327. #3113	C₂×C₂₉	semidirect
329. #1653	C₂×C₂₉	semidirect
330. #1651	C₂×C₂₉	semidirect
331. #1649	C₂×C₂₉	semidirect
332. #1648	C₂×C₂₉	semidirect
333. #1645	C₂×C₂₉	semidirect
334. #1645	C₂×C₂₉	semidirect
335. #1644	C₂×C₂₉	semidirect
336. #1643	C₂×C₂₉	semidirect
337. #1554	C₂×C₂₉	semidirect
339. #1479	C₂×C₂₉	semidirect
531. C₂₉	#18809	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
Q₈×#41×C₂₉	2
C₂₉×#3231	2
C₂₉×#3113	2
C₂₉×#3107	2
C₂₉×#1653	2
C₂₉×#1651	2
C₂₉×#1649	2
C₂₉×#1648	2
C₂₉×#1645	2
C₂₉×#1644	2
C₂₉×#1643	2
C₂₉×#1554	2
C₂₉×#1488	2
C₂₉×#1479	2
#18809	29

Subgroups — C29×#18809 #20313709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18809 #20313709