Subgroups — C₂₉×#18932 #20313832

Order 7424.

892 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3251	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3212	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3206	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1646	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1645	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1644	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1643	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1624	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1623	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1622	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1622	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1548	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	Q₈²×C₂₉	C₂²	1	1	yes	characteristic
18	C₂₉×#555	C₂²	1	1	yes	characteristic
19	C₂₉×#554	C₂²	1	1	yes	characteristic
20	C₂₉×#554	C₂²	1	1	yes	characteristic
21	C₂₉×#552	—	2	1	no	—
22	C₂₉×#552	—	2	1	no	—
23	C₂₉×#547	—	2	1	no	—
24	C₂₉×#547	—	2	1	no	—
25	C₂₉×#544	—	2	1	no	—
26	C₂₉×#544	—	2	1	no	—
27	C₂₉×#542	—	2	1	no	—
28	C₂₉×#542	—	2	1	no	—
29	C₂₉×#536	—	2	2	no	—
30	C₂₉×#532	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×#495	—	2	1	no	—
35	C₂₉×#492	C₂²	1	1	yes	characteristic
36	C₂₉×#492	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×#478	—	2	1	no	—
41	C₂₉×#475	C₂²	1	1	yes	characteristic
42	C₂₉×#474	C₂²	1	1	yes	characteristic
43	C₂₉×#469	—	2	1	no	—
44	C₂₉×#468	—	2	1	no	—
45	C₂₉×#463	—	2	1	no	—
46	C₂₉×#462	C₂²	1	1	yes	characteristic
47	C₂₉×#461	—	2	2	no	—
48	C₂₉×#461	C₂²	1	1	yes	characteristic
49	C₂₉×#460	C₂²	1	1	yes	characteristic
50	C₂₉×#460	C₂²	1	1	yes	characteristic
51	C₂₉×#459	C₂²	1	1	yes	characteristic
52	C₂₉×#459	C₂²	1	1	yes	characteristic
53	C₂₉×#452	—	2	1	no	—
54	C₂₉×#449	—	2	1	no	—
55	C₂₉×#448	—	2	2	no	—
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×#333	C₂²	1	1	yes	characteristic
60	C₂₉×#333	C₂²	1	1	yes	characteristic
61	C₂₉×#333	C₂²	1	1	yes	characteristic
62	C₂₉×#333	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	2	no	—
72	C₂×#41×C₂₉	—	2	1	no	—
73	C₂²×Q₈×C₂₉	D₄	1	2	yes	—
74	C₂×Q₁₆×C₂₉	—	2	1	no	—
75	C₂×SD₁₆×C₂₉	—	2	2	no	—
76	C₂×SD₁₆×C₂₉	—	2	2	no	—
77	C₂×SD₁₆×C₂₉	—	2	1	no	—
78	C₂×SD₁₆×C₂₉	—	2	1	no	—
79	C₂×SD₁₆×C₂₉	—	2	1	no	—
80	C₂×D₈×C₂₉	—	2	1	no	—
81	C₂×D₈×C₂₉	—	2	1	no	—
82	C₂×M₁₆×C₂₉	—	2	1	no	—
83	C₂₉×C₄⋊Q₈	—	2	2	no	—
84	C₂₉×C₄⋊Q₈	—	2	2	no	—
85	C₂₉×C₄⋊Q₈	—	2	1	no	—
86	C₂₉×C₄⋊Q₈	—	2	1	no	—
87	C₂₉×C₄⋊Q₈	—	2	1	no	—
88	C₂₉×C₄⋊Q₈	—	2	1	no	—
89	C₂₉×C₄⋊Q₈	D₄	1	2	yes	—
90	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
91	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
92	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
93	C₂₉×#127	C₂³	1	1	yes	characteristic
94	C₂₉×#126	—	2	2	no	—
95	C₂₉×#126	—	2	2	no	—
96	C₂₉×#126	—	2	1	no	—
97	C₂₉×#126	—	2	1	no	—
98	C₂₉×#125	—	2	2	no	—
99	C₂₉×#125	—	2	2	no	—
100	C₂₉×#125	—	2	1	no	—
101	C₂₉×#125	—	2	1	no	—
102	C₂₉×#125	D₄	1	1	yes	characteristic
103	C₂₉×#125	D₄	1	1	yes	characteristic
104	C₂₉×#124	—	2	2	no	—
105	C₂₉×#124	—	2	2	no	—
106	C₂₉×#124	—	2	1	no	—
107	C₂₉×#124	D₄	1	1	yes	characteristic
108	C₂₉×#124	D₄	1	1	yes	characteristic
109	C₂₉×#123	—	2	2	no	—
110	C₂₉×#123	—	2	2	no	—
111	C₂₉×#123	—	2	2	no	—
112	C₂₉×#123	—	2	2	no	—
113	C₂₉×#123	—	2	1	no	—
114	C₂₉×#123	—	2	1	no	—
115	C₂₉×C₂²⋊Q₈	—	2	2	no	—
116	C₂₉×C₂²⋊Q₈	—	2	2	no	—
117	C₂₉×C₂²⋊Q₈	—	2	2	no	—
118	C₂₉×C₂²⋊Q₈	—	2	2	no	—
119	C₂₉×C₂²⋊Q₈	—	2	2	no	—
120	C₂₉×C₂²⋊Q₈	—	2	2	no	—
121	C₂₉×C₂²⋊Q₈	—	2	1	no	—
122	C₂₉×C₂²⋊Q₈	—	2	1	no	—
123	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
124	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
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	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
134	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
135	C₄×D₄×C₂₉	—	2	1	no	—
136	C₄×D₄×C₂₉	—	2	1	no	—
137	C₄×D₄×C₂₉	—	2	1	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	C₂³	1	1	yes	characteristic
142	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
143	C₂₉×#117	—	2	2	no	—
144	C₂₉×#117	—	2	1	no	—
145	C₂₉×#117	—	2	1	no	—
146	C₂₉×#117	—	2	1	no	—
147	C₂₉×#117	—	2	1	no	—
148	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
149	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
150	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
151	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
152	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
153	C₂₉×#107	—	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	2	no	—
162	C₂₉×#103	—	2	2	no	—
163	C₂₉×#103	—	2	1	no	—
164	C₂₉×#103	—	2	1	no	—
165	C₂₉×#103	—	2	1	no	—
166	C₂₉×#102	—	2	1	no	—
167	C₂₉×#102	—	2	1	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	#41×C₂₉	—	8	4	no	—
179	C₂×Q₈×C₂₉	—	2	2	no	—
180	C₂×Q₈×C₂₉	—	2	2	no	—
181	C₂×Q₈×C₂₉	—	2	1	no	—
182	C₂×Q₈×C₂₉	—	8	2	no	—
183	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
184	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
185	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
186	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
187	C₂×D₄×C₂₉	—	2	1	no	—
188	C₂×D₄×C₂₉	—	2	1	no	—
189	C₂×D₄×C₂₉	—	2	2	no	—
190	C₂×D₄×C₂₉	—	2	1	no	—
191	C₂×D₄×C₂₉	—	2	1	no	—
192	C₂×D₄×C₂₉	—	2	1	no	—
193	C₂×D₄×C₂₉	—	4	1	no	—
194	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
195	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₂₉	—	2	2	no	—
197	C₂²×C₄×C₂₉	—	2	2	no	—
198	C₂²×C₄×C₂₉	—	2	2	no	—
199	C₂²×C₄×C₂₉	—	2	1	no	—
200	C₂²×C₄×C₂₉	—	2	1	no	—
201	C₂²×C₄×C₂₉	—	4	1	no	—
202	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
205	Q₁₆×C₂₉	—	8	1	no	—
206	SD₁₆×C₂₉	—	8	1	no	—
207	SD₁₆×C₂₉	—	8	1	no	—
208	SD₁₆×C₂₉	—	8	1	no	—
209	SD₁₆×C₂₉	—	8	2	no	—
210	SD₁₆×C₂₉	—	8	2	no	—
211	D₈×C₂₉	—	8	1	no	—
212	D₈×C₂₉	—	8	1	no	—
213	M₁₆×C₂₉	—	8	1	no	—
214	C₂×C₈×C₂₉	—	2	1	no	—
215	C₂×C₈×C₂₉	—	2	1	no	—
216	C₂×C₈×C₂₉	—	2	1	no	—
217	C₂×C₈×C₂₉	—	2	1	no	—
218	C₂×C₈×C₂₉	—	2	1	no	—
219	C₂×C₈×C₂₉	—	2	1	no	—
220	C₄⋊C₄×C₂₉	—	2	2	no	—
221	C₄⋊C₄×C₂₉	—	2	2	no	—
222	C₄⋊C₄×C₂₉	—	2	2	no	—
223	C₄⋊C₄×C₂₉	—	2	2	no	—
224	C₄⋊C₄×C₂₉	—	2	2	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	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	—	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	C₂×D₄	1	1	yes	characteristic
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	C₂²⋊C₄×C₂₉	—	2	2	no	—
247	C₂²⋊C₄×C₂₉	—	2	2	no	—
248	C₂²⋊C₄×C₂₉	—	2	2	no	—
249	C₂²⋊C₄×C₂₉	—	2	2	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	—	2	1	no	—
257	C₂²⋊C₄×C₂₉	—	2	1	no	—
258	C₂²⋊C₄×C₂₉	—	2	1	no	—
259	C₂²⋊C₄×C₂₉	—	2	1	no	—
260	C₂²⋊C₄×C₂₉	—	4	1	no	—
261	C₂²⋊C₄×C₂₉	—	4	1	no	—
262	C₄²×C₂₉	—	2	2	no	—
263	C₄²×C₂₉	—	2	2	no	—
264	C₄²×C₂₉	—	2	1	no	—
265	C₄²×C₂₉	—	2	1	no	—
266	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
267	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
268	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
269	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
270	#18932	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
271	C₂³×C₂₉	—	2	1	no	—
272	C₂³×C₂₉	—	2	1	no	—
273	C₂³×C₂₉	—	4	1	no	—
274	C₂³×C₂₉	#120	1	1	yes	characteristic
275	Q₈×C₂₉	—	2	1	no	—
276	Q₈×C₂₉	—	2	1	no	—
277	Q₈×C₂₉	—	2	1	no	—
278	Q₈×C₂₉	—	2	1	no	—
279	Q₈×C₂₉	—	4	2	no	—
280	Q₈×C₂₉	—	4	2	no	—
281	Q₈×C₂₉	—	4	1	no	—
282	Q₈×C₂₉	—	4	1	no	—
283	Q₈×C₂₉	—	8	2	no	—
284	Q₈×C₂₉	—	8	2	no	—
285	D₄×C₂₉	—	2	1	no	—
286	D₄×C₂₉	—	2	1	no	—
287	D₄×C₂₉	—	2	1	no	—
288	D₄×C₂₉	—	2	1	no	—
289	D₄×C₂₉	—	4	2	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	—	8	2	no	—
297	D₄×C₂₉	—	8	2	no	—
298	C₂×C₄×C₂₉	—	2	1	no	—
299	C₂×C₄×C₂₉	—	2	1	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	—	2	1	no	—
304	C₂×C₄×C₂₉	—	2	1	no	—
305	C₂×C₄×C₂₉	—	2	1	no	—
306	C₂×C₄×C₂₉	—	2	2	no	—
307	C₂×C₄×C₂₉	—	2	1	no	—
308	C₂×C₄×C₂₉	—	2	1	no	—
309	C₂×C₄×C₂₉	—	2	2	no	—
310	C₂×C₄×C₂₉	—	4	1	no	—
311	C₂×C₄×C₂₉	—	4	4	no	—
312	C₂×C₄×C₂₉	—	4	1	no	—
313	C₂×C₄×C₂₉	—	4	1	no	—
314	C₂×C₄×C₂₉	—	4	1	no	—
315	C₂×C₄×C₂₉	—	4	1	no	—
316	C₂×C₄×C₂₉	—	4	1	no	—
317	C₂×C₄×C₂₉	—	8	2	no	—
318	C₂×C₄×C₂₉	—	8	2	no	—
319	C₂×C₄×C₂₉	—	8	2	no	—
320	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
321	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
322	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
323	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
326	C₈×C₂₉	—	4	1	no	—
327	C₈×C₂₉	—	4	1	no	—
328	C₈×C₂₉	—	4	1	no	—
329	C₈×C₂₉	—	4	1	no	—
330	C₈×C₂₉	—	4	1	no	—
331	C₈×C₂₉	—	4	1	no	—
332	#3544	C₂×C₂₉	1	1	yes	characteristic, complemented
333	#3251	C₂×C₂₉	1	1	yes	characteristic, complemented
334	#3212	C₂×C₂₉	1	1	yes	characteristic, complemented
335	#3206	C₂×C₂₉	1	1	yes	characteristic, complemented
336	#1646	C₂×C₂₉	1	1	yes	characteristic, complemented
337	#1645	C₂×C₂₉	1	1	yes	characteristic, complemented
338	#1644	C₂×C₂₉	1	1	yes	characteristic, complemented
339	#1643	C₂×C₂₉	1	1	yes	characteristic, complemented
340	#1624	C₂×C₂₉	1	1	yes	characteristic, complemented
341	#1623	C₂×C₂₉	1	1	yes	characteristic, complemented
342	#1622	C₂×C₂₉	1	1	yes	characteristic, complemented
343	#1622	C₂×C₂₉	1	1	yes	characteristic, complemented
344	#1548	C₂×C₂₉	1	1	yes	characteristic, complemented
345	#1495	C₂×C₂₉	1	1	yes	characteristic, complemented
346	#1482	C₂×C₂₉	1	1	yes	characteristic, complemented
347	C₂²×C₂₉	—	2	1	no	—
348	C₂²×C₂₉	—	2	1	no	—
349	C₂²×C₂₉	—	2	1	no	—
350	C₂²×C₂₉	—	4	1	no	—
351	C₂²×C₂₉	—	4	1	no	—
352	C₂²×C₂₉	—	4	1	no	—
353	C₂²×C₂₉	—	4	1	no	—
354	C₂²×C₂₉	—	4	1	no	—
355	C₂²×C₂₉	—	4	1	no	—
356	C₂²×C₂₉	—	8	1	no	—
357	C₂²×C₂₉	—	8	1	no	—
358	C₂²×C₂₉	—	8	1	no	—
359	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
360	C₄×C₂₉	—	2	1	no	—
361	C₄×C₂₉	—	2	1	no	—
362	C₄×C₂₉	—	2	1	no	—
363	C₄×C₂₉	—	2	1	no	—
364	C₄×C₂₉	—	4	1	no	—
365	C₄×C₂₉	—	4	1	no	—
366	C₄×C₂₉	—	4	1	no	—
367	C₄×C₂₉	—	4	1	no	—
368	C₄×C₂₉	—	4	2	no	—
369	C₄×C₂₉	—	4	2	no	—
370	C₄×C₂₉	—	4	1	no	—
371	C₄×C₂₉	—	4	1	no	—
372	C₄×C₂₉	—	8	1	no	—
373	C₄×C₂₉	#577	1	1	yes	characteristic
374	C₄×C₂₉	#577	1	1	yes	characteristic
375	C₄×C₂₉	#577	1	1	yes	characteristic
376	C₄×C₂₉	#578	1	1	yes	characteristic
377	#563	—	2	2	no	—
378	Q₈²	C₂²×C₂₉	1	1	yes	characteristic
379	#555	C₂²×C₂₉	1	1	yes	characteristic
380	#554	C₂²×C₂₉	1	1	yes	characteristic
381	#554	C₂²×C₂₉	1	1	yes	characteristic
382	#552	—	2	1	no	—
383	#552	—	2	1	no	—
384	#547	—	2	1	no	—
385	#547	—	2	1	no	—
386	#544	—	2	1	no	—
387	#544	—	2	1	no	—
388	#542	—	2	1	no	—
389	#542	—	2	1	no	—
390	#536	—	2	2	no	—
391	#532	C₂²×C₂₉	1	1	yes	characteristic
392	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
393	#529	C₂²×C₂₉	1	1	yes	characteristic
394	#529	C₂²×C₂₉	1	1	yes	characteristic
395	#495	—	2	1	no	—
396	#492	C₂²×C₂₉	1	1	yes	characteristic
397	#492	C₂²×C₂₉	1	1	yes	characteristic
398	#488	—	2	1	no	—
399	#487	C₂²×C₂₉	1	1	yes	characteristic
400	#487	C₂²×C₂₉	1	1	yes	characteristic
401	#478	—	2	1	no	—
402	#475	C₂²×C₂₉	1	1	yes	characteristic
403	#474	C₂²×C₂₉	1	1	yes	characteristic
404	#469	—	2	1	no	—
405	#468	—	2	1	no	—
406	#463	—	2	1	no	—
407	#462	C₂²×C₂₉	1	1	yes	characteristic
408	#461	—	2	2	no	—
409	#461	C₂²×C₂₉	1	1	yes	characteristic
410	#460	C₂²×C₂₉	1	1	yes	characteristic
411	#460	C₂²×C₂₉	1	1	yes	characteristic
412	#459	C₂²×C₂₉	1	1	yes	characteristic
413	#459	C₂²×C₂₉	1	1	yes	characteristic
414	#452	—	2	1	no	—
415	#449	—	2	1	no	—
416	#448	—	2	2	no	—
417	#431	C₂²×C₂₉	1	1	yes	characteristic
418	#431	C₂²×C₂₉	1	1	yes	characteristic
419	#423	C₂²×C₂₉	1	1	yes	characteristic
420	#333	C₂²×C₂₉	1	1	yes	characteristic
421	#333	C₂²×C₂₉	1	1	yes	characteristic
422	#333	C₂²×C₂₉	1	1	yes	characteristic
423	#333	C₂²×C₂₉	1	1	yes	characteristic
424	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
425	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
426	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
427	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
428	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
429	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
430	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
431	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
432	C₂×C₂₉	—	4	1	no	—
433	C₂×C₂₉	—	8	1	no	—
434	C₂×C₂₉	—	8	1	no	—
435	C₂×C₂₉	—	16	1	no	—
436	C₂×C₂₉	#3010	1	1	yes	characteristic
437	C₂×C₂₉	#3013	1	1	yes	characteristic
438	C₂×C₂₉	#3019	1	1	yes	characteristic
439	C₂×#41	—	2	2	no	—
440	C₂×#41	—	2	1	no	—
441	C₂²×Q₈	D₄×C₂₉	1	2	yes	—
442	C₂×Q₁₆	—	2	1	no	—
443	C₂×SD₁₆	—	2	2	no	—
444	C₂×SD₁₆	—	2	2	no	—
445	C₂×SD₁₆	—	2	1	no	—
446	C₂×SD₁₆	—	2	1	no	—
447	C₂×SD₁₆	—	2	1	no	—
448	C₂×D₈	—	2	1	no	—
449	C₂×D₈	—	2	1	no	—
450	C₂×M₁₆	—	2	1	no	—
451	C₄⋊Q₈	—	2	2	no	—
452	C₄⋊Q₈	—	2	2	no	—
453	C₄⋊Q₈	—	2	1	no	—
454	C₄⋊Q₈	—	2	1	no	—
455	C₄⋊Q₈	—	2	1	no	—
456	C₄⋊Q₈	—	2	1	no	—
457	C₄⋊Q₈	D₄×C₂₉	1	2	yes	—
458	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
459	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
460	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
461	#127	C₂³×C₂₉	1	1	yes	characteristic
462	#126	—	2	2	no	—
463	#126	—	2	2	no	—
464	#126	—	2	1	no	—
465	#126	—	2	1	no	—
466	#125	—	2	2	no	—
467	#125	—	2	2	no	—
468	#125	—	2	1	no	—
469	#125	—	2	1	no	—
470	#125	D₄×C₂₉	1	1	yes	characteristic
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	D₄×C₂₉	1	1	yes	characteristic
476	#124	D₄×C₂₉	1	1	yes	characteristic
477	#123	—	2	2	no	—
478	#123	—	2	2	no	—
479	#123	—	2	2	no	—
480	#123	—	2	2	no	—
481	#123	—	2	1	no	—
482	#123	—	2	1	no	—
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	—	2	2	no	—
488	C₂²⋊Q₈	—	2	2	no	—
489	C₂²⋊Q₈	—	2	1	no	—
490	C₂²⋊Q₈	—	2	1	no	—
491	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
492	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
493	#121	—	2	1	no	—
494	#121	—	2	1	no	—
495	#121	—	2	1	no	—
496	#121	—	2	1	no	—
497	#121	D₄×C₂₉	1	1	yes	characteristic
498	#121	D₄×C₂₉	1	1	yes	characteristic
499	C₄×Q₈	—	2	1	no	—
500	C₄×Q₈	—	2	1	no	—
501	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
502	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
503	C₄×D₄	—	2	1	no	—
504	C₄×D₄	—	2	1	no	—
505	C₄×D₄	—	2	1	no	—
506	C₄×D₄	—	2	1	no	—
507	C₄×D₄	—	2	1	no	—
508	C₄×D₄	—	2	1	no	—
509	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
510	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
511	#117	—	2	2	no	—
512	#117	—	2	1	no	—
513	#117	—	2	1	no	—
514	#117	—	2	1	no	—
515	#117	—	2	1	no	—
516	C₂×C₄⋊C₄	—	2	1	no	—
517	C₂×C₄⋊C₄	—	2	1	no	—
518	C₂×C₄⋊C₄	—	2	1	no	—
519	C₂×C₄⋊C₄	—	2	1	no	—
520	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
521	#107	—	2	1	no	—
522	#106	—	2	1	no	—
523	C₄⋊C₈	—	2	1	no	—
524	C₄⋊C₈	—	2	1	no	—
525	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
526	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
527	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
528	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
529	#103	—	2	2	no	—
530	#103	—	2	2	no	—
531	#103	—	2	1	no	—
532	#103	—	2	1	no	—
533	#103	—	2	1	no	—
534	#102	—	2	1	no	—
535	#102	—	2	1	no	—
536	#102	—	2	1	no	—
537	#102	—	2	1	no	—
538	#102	—	2	1	no	—
539	C₂²⋊C₈	—	2	1	no	—
540	C₂²⋊C₈	—	2	1	no	—
541	C₄×C₈	—	2	1	no	—
542	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
543	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
544	C₂₉	#18932	1	1	yes	characteristic, direct product factor, Sylow
545	#41	—	8	1	no	—
546	#41	—	8	1	no	—
547	#41	—	8	4	no	—
548	C₂×Q₈	—	2	2	no	—
549	C₂×Q₈	—	2	2	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	8	2	no	—
552	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
553	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
554	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
555	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	4	1	no	—
563	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
564	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	4	1	no	—
571	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
572	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
574	Q₁₆	—	8	1	no	—
575	SD₁₆	—	8	1	no	—
576	SD₁₆	—	8	1	no	—
577	SD₁₆	—	8	1	no	—
578	SD₁₆	—	8	2	no	—
579	SD₁₆	—	8	2	no	—
580	D₈	—	8	1	no	—
581	D₈	—	8	1	no	—
582	M₁₆	—	8	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₄⋊C₄	—	2	2	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	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	C₂×D₄×C₂₉	1	1	yes	characteristic
612	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
613	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
614	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	2	no	—
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	2	1	no	—
620	C₂²⋊C₄	—	2	1	no	—
621	C₂²⋊C₄	—	2	1	no	—
622	C₂²⋊C₄	—	2	1	no	—
623	C₂²⋊C₄	—	2	1	no	—
624	C₂²⋊C₄	—	2	1	no	—
625	C₂²⋊C₄	—	2	1	no	—
626	C₂²⋊C₄	—	2	1	no	—
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	2	1	no	—
629	C₂²⋊C₄	—	4	1	no	—
630	C₂²⋊C₄	—	4	1	no	—
631	C₄²	—	2	2	no	—
632	C₄²	—	2	2	no	—
633	C₄²	—	2	1	no	—
634	C₄²	—	2	1	no	—
635	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
636	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
637	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
638	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	4	1	no	—
642	C₂³	C₂₉×#120	1	1	yes	characteristic
643	Q₈	—	2	1	no	—
644	Q₈	—	2	1	no	—
645	Q₈	—	2	1	no	—
646	Q₈	—	2	1	no	—
647	Q₈	—	4	2	no	—
648	Q₈	—	4	2	no	—
649	Q₈	—	4	1	no	—
650	Q₈	—	4	1	no	—
651	Q₈	—	8	2	no	—
652	Q₈	—	8	2	no	—
653	D₄	—	2	1	no	—
654	D₄	—	2	1	no	—
655	D₄	—	2	1	no	—
656	D₄	—	2	1	no	—
657	D₄	—	4	2	no	—
658	D₄	—	4	2	no	—
659	D₄	—	4	2	no	—
660	D₄	—	4	1	no	—
661	D₄	—	4	1	no	—
662	D₄	—	4	1	no	—
663	D₄	—	4	1	no	—
664	D₄	—	8	2	no	—
665	D₄	—	8	2	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	4	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	8	2	no	—
686	C₂×C₄	—	8	2	no	—
687	C₂×C₄	—	8	2	no	—
688	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
689	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
690	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
691	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
692	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
693	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
694	C₈	—	4	1	no	—
695	C₈	—	4	1	no	—
696	C₈	—	4	1	no	—
697	C₈	—	4	1	no	—
698	C₈	—	4	1	no	—
699	C₈	—	4	1	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	1	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	8	1	no	—
710	C₂²	—	8	1	no	—
711	C₂²	—	8	1	no	—
712	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
713	C₄	—	2	1	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	4	1	no	—
718	C₄	—	4	1	no	—
719	C₄	—	4	1	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	1	no	—
725	C₄	—	8	1	no	—
726	C₄	C₂₉×#577	1	1	yes	characteristic
727	C₄	C₂₉×#577	1	1	yes	characteristic
728	C₄	C₂₉×#577	1	1	yes	characteristic
729	C₄	C₂₉×#578	1	1	yes	characteristic
730	C₂	—	4	1	no	—
731	C₂	—	8	1	no	—
732	C₂	—	8	1	no	—
733	C₂	—	16	1	no	—
734	C₂	C₂₉×#3010	1	1	yes	characteristic
735	C₂	C₂₉×#3013	1	1	yes	characteristic
736	C₂	C₂₉×#3019	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×#3544	C₂	semidirect
2. C₂₉×#3251	C₂	semidirect
3. C₂₉×#3212	C₂	semidirect
4. C₂₉×#3206	C₂	semidirect
5. C₂₉×#1646	C₂	semidirect
6. C₂₉×#1645	C₂	semidirect
7. C₂₉×#1644	C₂	semidirect
8. C₂₉×#1643	C₂	semidirect
9. C₂₉×#1624	C₂	semidirect
10. C₂₉×#1623	C₂	semidirect
11. C₂₉×#1622	C₂	semidirect
12. C₂₉×#1622	C₂	semidirect
13. C₂₉×#1548	C₂	semidirect
14. C₂₉×#1495	C₂	semidirect
15. C₂₉×#1482	C₂	semidirect
270. #18932	C₂₉	direct (N × H)
332. #3544	C₂×C₂₉	semidirect
333. #3251	C₂×C₂₉	semidirect
334. #3212	C₂×C₂₉	semidirect
335. #3206	C₂×C₂₉	semidirect
336. #1646	C₂×C₂₉	semidirect
337. #1645	C₂×C₂₉	semidirect
338. #1644	C₂×C₂₉	semidirect
339. #1643	C₂×C₂₉	semidirect
340. #1624	C₂×C₂₉	semidirect
341. #1623	C₂×C₂₉	semidirect
342. #1622	C₂×C₂₉	semidirect
343. #1622	C₂×C₂₉	semidirect
344. #1548	C₂×C₂₉	semidirect
345. #1495	C₂×C₂₉	semidirect
346. #1482	C₂×C₂₉	semidirect
544. C₂₉	#18932	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×#3544	2
C₂₉×#3251	2
C₂₉×#3212	2
C₂₉×#3206	2
C₂₉×#1646	2
C₂₉×#1645	2
C₂₉×#1644	2
C₂₉×#1643	2
C₂₉×#1624	2
C₂₉×#1623	2
C₂₉×#1622	2
C₂₉×#1548	2
C₂₉×#1495	2
C₂₉×#1482	2
#18932	29

Subgroups — C29×#18932 #20313832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18932 #20313832