Subgroups — C₂₉×#18869 #20313769

Order 7424.

912 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3522	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#3233	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3210	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3104	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1645	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1644	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1641	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1640	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1633	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1632	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1631	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1630	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1543	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1482	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1479	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#559	—	2	1	no	—
17	C₂₉×#559	C₂²	1	1	yes	characteristic
18	Q₈²×C₂₉	C₂²	1	1	yes	characteristic
19	C₂₉×#554	—	2	1	no	—
20	C₂₉×#554	C₂²	1	1	yes	characteristic
21	C₂₉×#550	C₂²	1	1	yes	characteristic
22	C₂₉×#548	—	2	1	no	—
23	C₂₉×#547	—	2	2	no	—
24	C₂₉×#547	—	2	1	no	—
25	C₂₉×#542	—	2	2	no	—
26	C₂₉×#542	—	2	1	no	—
27	C₂₉×#533	C₂²	1	1	yes	characteristic
28	C₂₉×#532	—	2	1	no	—
29	C₂₉×#532	C₂²	1	1	yes	characteristic
30	C₂₉×#529	—	2	1	no	—
31	C₂₉×#529	C₂²	1	1	yes	characteristic
32	C₂₉×#520	—	2	1	no	—
33	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
34	C₂₉×#499	—	2	1	no	—
35	C₂₉×#494	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×#486	C₂²	1	1	yes	characteristic
40	C₂₉×#485	—	2	1	no	—
41	C₂₉×#484	—	2	1	no	—
42	C₂₉×#482	—	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×#474	C₂²	1	1	yes	characteristic
49	C₂₉×#464	—	2	2	no	—
50	C₂₉×#462	C₂²	1	1	yes	characteristic
51	C₂₉×#462	C₂²	1	1	yes	characteristic
52	C₂₉×#452	—	2	2	no	—
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×#333	C₂²	1	1	yes	characteristic
60	C₂₉×#333	C₂²	1	1	yes	characteristic
61	C₂₉×#331	C₂²	1	1	yes	characteristic
62	C₂₉×#331	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	—	2	2	no	—
72	C₂×#41×C₂₉	—	2	1	no	—
73	C₂×#41×C₂₉	D₄	1	2	yes	—
74	C₂²×Q₈×C₂₉	D₄	1	1	yes	characteristic
75	C₂×Q₁₆×C₂₉	—	2	1	no	—
76	C₂×Q₁₆×C₂₉	—	2	1	no	—
77	C₂×Q₁₆×C₂₉	—	2	2	no	—
78	C₂×SD₁₆×C₂₉	—	2	2	no	—
79	C₂₉×C₄⋊Q₈	—	2	2	no	—
80	C₂₉×C₄⋊Q₈	—	2	1	no	—
81	C₂₉×C₄⋊Q₈	—	2	1	no	—
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×#127	—	2	1	no	—
86	C₂₉×#127	C₂³	1	1	yes	characteristic
87	C₂₉×#126	—	2	2	no	—
88	C₂₉×#126	—	2	1	no	—
89	C₂₉×#125	—	2	1	no	—
90	C₂₉×#125	—	2	1	no	—
91	C₂₉×#125	D₄	1	1	yes	characteristic
92	C₂₉×#124	—	2	2	no	—
93	C₂₉×#124	—	2	2	no	—
94	C₂₉×#124	—	2	1	no	—
95	C₂₉×#124	—	2	1	no	—
96	C₂₉×#124	D₄	1	2	yes	—
97	C₂₉×#124	D₄	1	1	yes	characteristic
98	C₂₉×#123	—	2	2	no	—
99	C₂₉×#123	—	2	2	no	—
100	C₂₉×#123	—	2	2	no	—
101	C₂₉×#123	—	2	2	no	—
102	C₂₉×#123	—	2	1	no	—
103	C₂₉×C₂²⋊Q₈	—	2	2	no	—
104	C₂₉×C₂²⋊Q₈	—	2	2	no	—
105	C₂₉×C₂²⋊Q₈	—	2	2	no	—
106	C₂₉×C₂²⋊Q₈	—	2	2	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	D₄	1	1	yes	characteristic
111	C₂₉×#121	—	2	2	no	—
112	C₂₉×#121	—	2	2	no	—
113	C₂₉×#121	—	2	1	no	—
114	C₂₉×#121	—	2	1	no	—
115	C₂₉×#121	—	2	1	no	—
116	C₂₉×#121	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
124	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
125	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
126	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
127	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
128	C₄×D₄×C₂₉	—	2	2	no	—
129	C₄×D₄×C₂₉	—	2	2	no	—
130	C₄×D₄×C₂₉	—	2	2	no	—
131	C₄×D₄×C₂₉	—	2	1	no	—
132	C₄×D₄×C₂₉	—	2	1	no	—
133	C₄×D₄×C₂₉	—	2	1	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	—	2	1	no	—
138	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
139	C₂₉×#117	—	2	2	no	—
140	C₂₉×#117	—	2	1	no	—
141	C₂₉×#117	—	2	1	no	—
142	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
143	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
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	1	no	—
152	C₂₉×#106	—	2	1	no	—
153	C₂₉×#106	—	2	1	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	2	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×#102	—	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	#41×C₂₉	—	4	2	no	—
177	#41×C₂₉	—	4	2	no	—
178	#41×C₂₉	—	8	4	no	—
179	#41×C₂₉	—	8	2	no	—
180	C₂×Q₈×C₂₉	—	2	2	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	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×Q₈×C₂₉	C₂×D₄	1	2	yes	—
190	C₂×D₄×C₂₉	—	2	2	no	—
191	C₂×D₄×C₂₉	—	2	2	no	—
192	C₂×D₄×C₂₉	—	2	1	no	—
193	C₂×D₄×C₂₉	—	2	2	no	—
194	C₂×D₄×C₂₉	—	2	1	no	—
195	C₂×D₄×C₂₉	—	2	1	no	—
196	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
197	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
202	C₂²×C₄×C₂₉	—	2	2	no	—
203	C₂²×C₄×C₂₉	—	2	1	no	—
204	C₂²×C₄×C₂₉	—	2	2	no	—
205	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
208	Q₁₆×C₂₉	—	4	2	no	—
209	Q₁₆×C₂₉	—	4	2	no	—
210	Q₁₆×C₂₉	—	8	2	no	—
211	SD₁₆×C₂₉	—	8	2	no	—
212	C₂×C₈×C₂₉	—	2	1	no	—
213	C₂×C₈×C₂₉	—	2	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	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	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	—	2	1	no	—
235	C₄⋊C₄×C₂₉	—	2	1	no	—
236	C₄⋊C₄×C₂₉	—	2	1	no	—
237	C₄⋊C₄×C₂₉	—	4	1	no	—
238	C₄⋊C₄×C₂₉	—	4	1	no	—
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	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
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	2	no	—
247	C₂²⋊C₄×C₂₉	—	2	2	no	—
248	C₂²⋊C₄×C₂₉	—	2	1	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	2	no	—
253	C₂²⋊C₄×C₂₉	—	2	1	no	—
254	C₂²⋊C₄×C₂₉	—	2	1	no	—
255	C₂²⋊C₄×C₂₉	—	4	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	—	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	#18869	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
268	C₂³×C₂₉	—	2	1	no	—
269	C₂³×C₂₉	—	2	2	no	—
270	C₂³×C₂₉	#120	1	1	yes	characteristic
271	Q₈×C₂₉	—	2	1	no	—
272	Q₈×C₂₉	—	2	1	no	—
273	Q₈×C₂₉	—	2	1	no	—
274	Q₈×C₂₉	—	2	1	no	—
275	Q₈×C₂₉	—	2	1	no	—
276	Q₈×C₂₉	—	4	2	no	—
277	Q₈×C₂₉	—	4	2	no	—
278	Q₈×C₂₉	—	4	2	no	—
279	Q₈×C₂₉	—	4	1	no	—
280	Q₈×C₂₉	—	4	1	no	—
281	Q₈×C₂₉	—	8	2	no	—
282	Q₈×C₂₉	#135	1	2	yes	—
283	D₄×C₂₉	—	2	1	no	—
284	D₄×C₂₉	—	2	1	no	—
285	D₄×C₂₉	—	4	2	no	—
286	D₄×C₂₉	—	4	4	no	—
287	D₄×C₂₉	—	4	4	no	—
288	D₄×C₂₉	—	4	2	no	—
289	D₄×C₂₉	—	4	1	no	—
290	D₄×C₂₉	—	4	1	no	—
291	D₄×C₂₉	—	4	1	no	—
292	D₄×C₂₉	—	4	1	no	—
293	D₄×C₂₉	—	8	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	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	2	no	—
304	C₂×C₄×C₂₉	—	2	1	no	—
305	C₂×C₄×C₂₉	—	2	1	no	—
306	C₂×C₄×C₂₉	—	4	1	no	—
307	C₂×C₄×C₂₉	—	4	2	no	—
308	C₂×C₄×C₂₉	—	4	4	no	—
309	C₂×C₄×C₂₉	—	4	2	no	—
310	C₂×C₄×C₂₉	—	4	1	no	—
311	C₂×C₄×C₂₉	—	4	1	no	—
312	C₂×C₄×C₂₉	—	4	1	no	—
313	C₂×C₄×C₂₉	—	4	1	no	—
314	C₂×C₄×C₂₉	—	8	2	no	—
315	C₂×C₄×C₂₉	—	8	2	no	—
316	C₂×C₄×C₂₉	—	8	2	no	—
317	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
318	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
319	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
320	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
323	C₈×C₂₉	—	4	1	no	—
324	C₈×C₂₉	—	4	1	no	—
325	C₈×C₂₉	—	4	1	no	—
326	C₈×C₂₉	—	4	1	no	—
327	C₈×C₂₉	—	4	1	no	—
328	C₈×C₂₉	—	4	1	no	—
329	#3522	C₂×C₂₉	1	1	yes	characteristic
330	#3233	C₂×C₂₉	1	1	yes	characteristic, complemented
331	#3210	C₂×C₂₉	1	1	yes	characteristic, complemented
332	#3104	C₂×C₂₉	1	1	yes	characteristic, complemented
333	#1645	C₂×C₂₉	1	1	yes	characteristic, complemented
334	#1644	C₂×C₂₉	1	1	yes	characteristic, complemented
335	#1641	C₂×C₂₉	1	1	yes	characteristic, complemented
336	#1640	C₂×C₂₉	1	1	yes	characteristic, complemented
337	#1633	C₂×C₂₉	1	1	yes	characteristic, complemented
338	#1632	C₂×C₂₉	1	1	yes	characteristic, complemented
339	#1631	C₂×C₂₉	1	1	yes	characteristic, complemented
340	#1630	C₂×C₂₉	1	1	yes	characteristic, complemented
341	#1543	C₂×C₂₉	1	1	yes	characteristic, complemented
342	#1482	C₂×C₂₉	1	1	yes	characteristic, complemented
343	#1479	C₂×C₂₉	1	1	yes	characteristic, complemented
344	C₂²×C₂₉	—	2	1	no	—
345	C₂²×C₂₉	—	2	1	no	—
346	C₂²×C₂₉	—	2	1	no	—
347	C₂²×C₂₉	—	4	2	no	—
348	C₂²×C₂₉	—	4	1	no	—
349	C₂²×C₂₉	—	4	1	no	—
350	C₂²×C₂₉	—	4	2	no	—
351	C₂²×C₂₉	—	4	2	no	—
352	C₂²×C₂₉	—	4	1	no	—
353	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
354	C₄×C₂₉	—	2	1	no	—
355	C₄×C₂₉	—	2	2	no	—
356	C₄×C₂₉	—	2	1	no	—
357	C₄×C₂₉	—	2	1	no	—
358	C₄×C₂₉	—	2	1	no	—
359	C₄×C₂₉	—	4	1	no	—
360	C₄×C₂₉	—	4	1	no	—
361	C₄×C₂₉	—	4	1	no	—
362	C₄×C₂₉	—	4	1	no	—
363	C₄×C₂₉	—	4	1	no	—
364	C₄×C₂₉	—	4	2	no	—
365	C₄×C₂₉	—	4	1	no	—
366	C₄×C₂₉	—	8	1	no	—
367	C₄×C₂₉	—	8	1	no	—
368	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
369	C₄×C₂₉	#575	1	1	yes	characteristic
370	C₄×C₂₉	#578	1	1	yes	characteristic
371	C₄×C₂₉	#578	1	1	yes	characteristic
372	#559	—	2	1	no	—
373	#559	C₂²×C₂₉	1	1	yes	characteristic
374	Q₈²	C₂²×C₂₉	1	1	yes	characteristic
375	#554	—	2	1	no	—
376	#554	C₂²×C₂₉	1	1	yes	characteristic
377	#550	C₂²×C₂₉	1	1	yes	characteristic
378	#548	—	2	1	no	—
379	#547	—	2	2	no	—
380	#547	—	2	1	no	—
381	#542	—	2	2	no	—
382	#542	—	2	1	no	—
383	#533	C₂²×C₂₉	1	1	yes	characteristic
384	#532	—	2	1	no	—
385	#532	C₂²×C₂₉	1	1	yes	characteristic
386	#529	—	2	1	no	—
387	#529	C₂²×C₂₉	1	1	yes	characteristic
388	#520	—	2	1	no	—
389	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
390	#499	—	2	1	no	—
391	#494	C₂²×C₂₉	1	1	yes	characteristic
392	#492	C₂²×C₂₉	1	1	yes	characteristic
393	#488	—	2	1	no	—
394	#487	C₂²×C₂₉	1	1	yes	characteristic
395	#486	C₂²×C₂₉	1	1	yes	characteristic
396	#485	—	2	1	no	—
397	#484	—	2	1	no	—
398	#482	—	2	1	no	—
399	#477	C₂²×C₂₉	1	1	yes	characteristic
400	#477	C₂²×C₂₉	1	1	yes	characteristic
401	#477	C₂²×C₂₉	1	1	yes	characteristic
402	#476	C₂²×C₂₉	1	1	yes	characteristic
403	#475	C₂²×C₂₉	1	1	yes	characteristic
404	#474	C₂²×C₂₉	1	1	yes	characteristic
405	#464	—	2	2	no	—
406	#462	C₂²×C₂₉	1	1	yes	characteristic
407	#462	C₂²×C₂₉	1	1	yes	characteristic
408	#452	—	2	2	no	—
409	#451	—	2	1	no	—
410	C₄×Q₁₆	—	2	1	no	—
411	C₄×Q₁₆	—	2	1	no	—
412	#431	C₂²×C₂₉	1	1	yes	characteristic
413	#431	C₂²×C₂₉	1	1	yes	characteristic
414	#431	C₂²×C₂₉	1	1	yes	characteristic
415	#333	C₂²×C₂₉	1	1	yes	characteristic
416	#333	C₂²×C₂₉	1	1	yes	characteristic
417	#331	C₂²×C₂₉	1	1	yes	characteristic
418	#331	C₂²×C₂₉	1	1	yes	characteristic
419	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
420	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
421	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
422	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
423	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
424	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
425	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
426	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
427	C₂×C₂₉	—	4	1	no	—
428	C₂×C₂₉	—	8	1	no	—
429	C₂×C₂₉	—	8	2	no	—
430	C₂×C₂₉	#3002	1	1	yes	characteristic
431	C₂×C₂₉	#3011	1	1	yes	characteristic
432	C₂×C₂₉	#3019	1	1	yes	characteristic
433	C₂×#41	—	2	2	no	—
434	C₂×#41	—	2	1	no	—
435	C₂×#41	D₄×C₂₉	1	2	yes	—
436	C₂²×Q₈	D₄×C₂₉	1	1	yes	characteristic
437	C₂×Q₁₆	—	2	1	no	—
438	C₂×Q₁₆	—	2	1	no	—
439	C₂×Q₁₆	—	2	2	no	—
440	C₂×SD₁₆	—	2	2	no	—
441	C₄⋊Q₈	—	2	2	no	—
442	C₄⋊Q₈	—	2	1	no	—
443	C₄⋊Q₈	—	2	1	no	—
444	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
445	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
446	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
447	#127	—	2	1	no	—
448	#127	C₂³×C₂₉	1	1	yes	characteristic
449	#126	—	2	2	no	—
450	#126	—	2	1	no	—
451	#125	—	2	1	no	—
452	#125	—	2	1	no	—
453	#125	D₄×C₂₉	1	1	yes	characteristic
454	#124	—	2	2	no	—
455	#124	—	2	2	no	—
456	#124	—	2	1	no	—
457	#124	—	2	1	no	—
458	#124	D₄×C₂₉	1	1	yes	characteristic
459	#124	D₄×C₂₉	1	2	yes	—
460	#123	—	2	2	no	—
461	#123	—	2	2	no	—
462	#123	—	2	2	no	—
463	#123	—	2	2	no	—
464	#123	—	2	1	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	1	no	—
470	C₂²⋊Q₈	—	2	1	no	—
471	C₂²⋊Q₈	—	2	1	no	—
472	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
473	#121	—	2	2	no	—
474	#121	—	2	2	no	—
475	#121	—	2	1	no	—
476	#121	—	2	1	no	—
477	#121	—	2	1	no	—
478	#121	D₄×C₂₉	1	1	yes	characteristic
479	C₄×Q₈	—	2	1	no	—
480	C₄×Q₈	—	2	1	no	—
481	C₄×Q₈	—	2	1	no	—
482	C₄×Q₈	—	2	1	no	—
483	C₄×Q₈	—	2	1	no	—
484	C₄×Q₈	—	2	1	no	—
485	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
486	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
487	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
488	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
489	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
490	C₄×D₄	—	2	2	no	—
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	—	2	2	no	—
493	C₄×D₄	—	2	1	no	—
494	C₄×D₄	—	2	1	no	—
495	C₄×D₄	—	2	1	no	—
496	C₄×D₄	—	2	1	no	—
497	C₄×D₄	—	2	1	no	—
498	C₄×D₄	—	2	1	no	—
499	C₄×D₄	—	2	1	no	—
500	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
501	#117	—	2	2	no	—
502	#117	—	2	1	no	—
503	#117	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	2	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	—	2	1	no	—
507	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
508	C₂×C₄²	—	2	1	no	—
509	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
510	#107	—	2	1	no	—
511	#107	—	2	1	no	—
512	#107	—	2	1	no	—
513	#107	—	2	1	no	—
514	#106	—	2	1	no	—
515	#106	—	2	1	no	—
516	C₄⋊C₈	—	2	1	no	—
517	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
518	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
519	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
520	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
521	#103	—	2	1	no	—
522	#103	—	2	1	no	—
523	#103	—	2	2	no	—
524	#103	—	2	1	no	—
525	#103	—	2	1	no	—
526	#103	—	2	1	no	—
527	#103	—	2	1	no	—
528	#102	—	2	2	no	—
529	#102	—	2	1	no	—
530	#102	—	2	1	no	—
531	C₂²⋊C₈	—	2	1	no	—
532	C₂²⋊C₈	—	2	1	no	—
533	C₂²⋊C₈	—	2	1	no	—
534	C₄×C₈	—	2	1	no	—
535	C₄×C₈	—	2	1	no	—
536	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
537	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
538	C₂₉	#18869	1	1	yes	characteristic, direct product factor, Sylow
539	#41	—	4	2	no	—
540	#41	—	4	2	no	—
541	#41	—	8	4	no	—
542	#41	—	8	2	no	—
543	C₂×Q₈	—	2	2	no	—
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	—	2	2	no	—
546	C₂×Q₈	—	2	1	no	—
547	C₂×Q₈	—	2	1	no	—
548	C₂×Q₈	—	4	1	no	—
549	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
550	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
551	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
552	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
560	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
569	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
570	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
571	Q₁₆	—	4	2	no	—
572	Q₁₆	—	4	2	no	—
573	Q₁₆	—	8	2	no	—
574	SD₁₆	—	8	2	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₄⋊C₄	—	2	2	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	2	no	—
584	C₄⋊C₄	—	2	2	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	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	4	1	no	—
601	C₄⋊C₄	—	4	1	no	—
602	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
603	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
604	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
605	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	1	no	—
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	—	2	1	no	—
614	C₂²⋊C₄	—	2	1	no	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	2	1	no	—
617	C₂²⋊C₄	—	2	1	no	—
618	C₂²⋊C₄	—	4	1	no	—
619	C₄²	—	2	2	no	—
620	C₄²	—	2	1	no	—
621	C₄²	—	2	1	no	—
622	C₄²	—	2	1	no	—
623	C₄²	—	2	1	no	—
624	C₄²	—	2	1	no	—
625	C₄²	—	4	1	no	—
626	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
627	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
628	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
629	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
630	C₂³	—	2	1	no	—
631	C₂³	—	2	2	no	—
632	C₂³	C₂₉×#120	1	1	yes	characteristic
633	Q₈	—	2	1	no	—
634	Q₈	—	2	1	no	—
635	Q₈	—	2	1	no	—
636	Q₈	—	2	1	no	—
637	Q₈	—	2	1	no	—
638	Q₈	—	4	2	no	—
639	Q₈	—	4	2	no	—
640	Q₈	—	4	2	no	—
641	Q₈	—	4	1	no	—
642	Q₈	—	4	1	no	—
643	Q₈	—	8	2	no	—
644	Q₈	C₂₉×#135	1	2	yes	—
645	D₄	—	2	1	no	—
646	D₄	—	2	1	no	—
647	D₄	—	4	2	no	—
648	D₄	—	4	4	no	—
649	D₄	—	4	4	no	—
650	D₄	—	4	2	no	—
651	D₄	—	4	1	no	—
652	D₄	—	4	1	no	—
653	D₄	—	4	1	no	—
654	D₄	—	4	1	no	—
655	D₄	—	8	2	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	2	no	—
670	C₂×C₄	—	4	4	no	—
671	C₂×C₄	—	4	2	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	8	2	no	—
677	C₂×C₄	—	8	2	no	—
678	C₂×C₄	—	8	2	no	—
679	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
680	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
681	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
682	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
683	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
684	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
685	C₈	—	4	1	no	—
686	C₈	—	4	1	no	—
687	C₈	—	4	1	no	—
688	C₈	—	4	1	no	—
689	C₈	—	4	1	no	—
690	C₈	—	4	1	no	—
691	C₂²	—	2	1	no	—
692	C₂²	—	2	1	no	—
693	C₂²	—	2	1	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	1	no	—
700	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
701	C₄	—	2	1	no	—
702	C₄	—	2	2	no	—
703	C₄	—	2	1	no	—
704	C₄	—	2	1	no	—
705	C₄	—	2	1	no	—
706	C₄	—	4	1	no	—
707	C₄	—	4	1	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	1	no	—
710	C₄	—	4	1	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	1	no	—
713	C₄	—	8	1	no	—
714	C₄	—	8	1	no	—
715	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
716	C₄	C₂₉×#575	1	1	yes	characteristic
717	C₄	C₂₉×#578	1	1	yes	characteristic
718	C₄	C₂₉×#578	1	1	yes	characteristic
719	C₂	—	4	1	no	—
720	C₂	—	8	1	no	—
721	C₂	—	8	2	no	—
722	C₂	C₂₉×#3002	1	1	yes	characteristic
723	C₂	C₂₉×#3011	1	1	yes	characteristic
724	C₂	C₂₉×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂₉×#3522	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×#3233	C₂	semidirect
3. C₂₉×#3210	C₂	semidirect
4. C₂₉×#3104	C₂	semidirect
5. C₂₉×#1645	C₂	semidirect
6. C₂₉×#1644	C₂	semidirect
7. C₂₉×#1641	C₂	semidirect
8. C₂₉×#1640	C₂	semidirect
9. C₂₉×#1633	C₂	semidirect
10. C₂₉×#1632	C₂	semidirect
11. C₂₉×#1631	C₂	semidirect
12. C₂₉×#1630	C₂	semidirect
13. C₂₉×#1543	C₂	semidirect
14. C₂₉×#1482	C₂	semidirect
15. C₂₉×#1479	C₂	semidirect
267. #18869	C₂₉	direct (N × H)
330. #3233	C₂×C₂₉	semidirect
331. #3210	C₂×C₂₉	semidirect
332. #3104	C₂×C₂₉	semidirect
333. #1645	C₂×C₂₉	semidirect
334. #1644	C₂×C₂₉	semidirect
335. #1641	C₂×C₂₉	semidirect
336. #1640	C₂×C₂₉	semidirect
337. #1633	C₂×C₂₉	semidirect
338. #1632	C₂×C₂₉	semidirect
339. #1631	C₂×C₂₉	semidirect
340. #1630	C₂×C₂₉	semidirect
341. #1543	C₂×C₂₉	semidirect
342. #1482	C₂×C₂₉	semidirect
343. #1479	C₂×C₂₉	semidirect
538. C₂₉	#18869	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×#3522	2
C₂₉×#3233	2
C₂₉×#3210	2
C₂₉×#3104	2
C₂₉×#1645	2
C₂₉×#1644	2
C₂₉×#1641	2
C₂₉×#1640	2
C₂₉×#1633	2
C₂₉×#1632	2
C₂₉×#1631	2
C₂₉×#1630	2
C₂₉×#1543	2
C₂₉×#1482	2
C₂₉×#1479	2
#18869	29

Subgroups — C29×#18869 #20313769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18869 #20313769