Subgroups — C₂₉×#18965 #20313865

Order 7424.

900 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3253	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3247	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3210	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1637	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1635	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1634	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1632	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1627	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1625	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1624	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1622	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1550	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1495	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1480	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#562	—	2	2	no	—
17	C₂₉×#555	—	2	1	no	—
18	C₂₉×#555	C₂²	1	1	yes	characteristic
19	C₂₉×#554	C₂²	1	1	yes	characteristic
20	C₂₉×#553	—	2	1	no	—
21	C₂₉×#552	—	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	2	no	—
27	C₂₉×#540	—	2	1	no	—
28	C₂₉×#537	—	2	1	no	—
29	C₂₉×#536	—	2	1	no	—
30	C₂₉×#533	C₂²	1	1	yes	characteristic
31	C₂₉×#532	C₂²	1	1	yes	characteristic
32	C₂₉×#532	C₂²	1	1	yes	characteristic
33	C₂₉×#529	C₂²	1	1	yes	characteristic
34	C₂₉×#494	C₂²	1	1	yes	characteristic
35	C₂₉×#492	C₂²	1	1	yes	characteristic
36	C₂₉×#487	C₂²	1	1	yes	characteristic
37	C₂₉×#486	C₂²	1	1	yes	characteristic
38	C₂₉×#478	—	2	1	no	—
39	C₂₉×#477	C₂²	1	1	yes	characteristic
40	C₂₉×#476	—	2	1	no	—
41	C₂₉×#476	C₂²	1	1	yes	characteristic
42	C₂₉×#476	C₂²	1	1	yes	characteristic
43	C₂₉×#476	C₂²	1	1	yes	characteristic
44	C₂₉×#469	—	2	1	no	—
45	C₂₉×#469	—	2	1	no	—
46	C₂₉×#466	—	2	1	no	—
47	C₂₉×#465	—	2	1	no	—
48	C₂₉×#464	—	2	2	no	—
49	C₂₉×#463	—	2	1	no	—
50	C₂₉×#460	C₂²	1	1	yes	characteristic
51	C₂₉×#459	—	2	1	no	—
52	C₂₉×#459	C₂²	1	1	yes	characteristic
53	C₂₉×#459	C₂²	1	1	yes	characteristic
54	C₂₉×#459	C₂²	1	1	yes	characteristic
55	C₂₉×#452	—	2	2	no	—
56	C₂₉×#431	C₂²	1	1	yes	characteristic
57	C₂₉×#423	C₂²	1	1	yes	characteristic
58	C₂×C₂₉×C₄⋊C₈	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×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₂₉×D₄⋊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	C₂×#41×C₂₉	—	2	1	no	—
73	C₂×#41×C₂₉	—	2	1	no	—
74	C₂²×Q₈×C₂₉	—	2	1	no	—
75	C₂×Q₁₆×C₂₉	—	2	2	no	—
76	C₂×SD₁₆×C₂₉	—	2	2	no	—
77	C₂×SD₁₆×C₂₉	—	2	1	no	—
78	C₂×D₈×C₂₉	—	2	1	no	—
79	C₂×D₈×C₂₉	—	2	1	no	—
80	C₂×D₈×C₂₉	—	2	1	no	—
81	C₂×M₁₆×C₂₉	—	2	1	no	—
82	C₂²×C₈×C₂₉	—	2	1	no	—
83	C₂₉×C₄⋊Q₈	—	2	2	no	—
84	C₂₉×C₄⋊Q₈	—	2	1	no	—
85	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
86	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₂₉×#127	D₄	1	1	yes	characteristic
90	C₂₉×#127	C₂³	1	1	yes	characteristic
91	C₂₉×#126	—	2	2	no	—
92	C₂₉×#126	—	2	1	no	—
93	C₂₉×#125	—	2	2	no	—
94	C₂₉×#125	—	2	1	no	—
95	C₂₉×#125	—	2	1	no	—
96	C₂₉×#125	D₄	1	1	yes	characteristic
97	C₂₉×#124	—	2	2	no	—
98	C₂₉×#124	—	2	2	no	—
99	C₂₉×#124	—	2	2	no	—
100	C₂₉×#124	—	2	1	no	—
101	C₂₉×#124	—	2	1	no	—
102	C₂₉×#124	D₄	1	1	yes	characteristic
103	C₂₉×#123	—	2	2	no	—
104	C₂₉×#123	—	2	2	no	—
105	C₂₉×#123	—	2	2	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	1	no	—
111	C₂₉×C₂²⋊Q₈	—	2	2	no	—
112	C₂₉×C₂²⋊Q₈	—	2	1	no	—
113	C₂₉×C₂²⋊Q₈	—	2	1	no	—
114	C₂₉×C₂²⋊Q₈	—	2	1	no	—
115	C₂₉×C₂²⋊Q₈	—	2	2	no	—
116	C₂₉×C₂²⋊Q₈	D₄	1	2	yes	—
117	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
118	C₂₉×#121	—	2	2	no	—
119	C₂₉×#121	—	2	2	no	—
120	C₂₉×#121	—	2	2	no	—
121	C₂₉×#121	—	2	2	no	—
122	C₂₉×#121	—	2	1	no	—
123	C₂₉×#121	—	2	1	no	—
124	C₂₉×#121	—	2	1	no	—
125	C₂₉×#121	—	2	1	no	—
126	C₂₉×#121	—	2	1	no	—
127	C₂₉×#121	—	2	1	no	—
128	C₂₉×#121	D₄	1	1	yes	characteristic
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	D₄	1	2	yes	—
133	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
134	C₄×D₄×C₂₉	—	2	2	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	—	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	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
144	C₂₉×#117	—	2	2	no	—
145	C₂₉×#117	—	2	1	no	—
146	C₂₉×#117	—	2	1	no	—
147	C₂₉×#117	—	2	1	no	—
148	C₂₉×#117	—	2	1	no	—
149	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
150	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
151	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
152	C₂₉×#107	—	2	1	no	—
153	C₂₉×#106	—	2	1	no	—
154	C₂₉×#106	—	2	1	no	—
155	C₂₉×#106	—	2	1	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	2	no	—
165	C₂₉×#102	—	2	1	no	—
166	C₂₉×#102	—	2	1	no	—
167	C₂₉×#102	—	2	1	no	—
168	C₂₉×#102	—	2	2	no	—
169	C₂₉×#102	—	2	1	no	—
170	C₂₉×#102	—	2	1	no	—
171	C₂₉×#102	—	2	1	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	#41×C₂₉	—	8	1	no	—
177	#41×C₂₉	—	8	1	no	—
178	#41×C₂₉	—	8	1	no	—
179	#41×C₂₉	—	8	1	no	—
180	#41×C₂₉	—	8	2	no	—
181	C₂×Q₈×C₂₉	—	2	2	no	—
182	C₂×Q₈×C₂₉	—	2	1	no	—
183	C₂×Q₈×C₂₉	—	2	1	no	—
184	C₂×Q₈×C₂₉	—	2	1	no	—
185	C₂×Q₈×C₂₉	—	8	1	no	—
186	C₂×Q₈×C₂₉	—	8	1	no	—
187	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
188	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
189	C₂×D₄×C₂₉	—	2	2	no	—
190	C₂×D₄×C₂₉	—	2	2	no	—
191	C₂×D₄×C₂₉	—	2	1	no	—
192	C₂×D₄×C₂₉	—	2	1	no	—
193	C₂×D₄×C₂₉	—	2	1	no	—
194	C₂×D₄×C₂₉	—	2	1	no	—
195	C₂×D₄×C₂₉	—	2	1	no	—
196	C₂×D₄×C₂₉	—	2	1	no	—
197	C₂×D₄×C₂₉	—	2	1	no	—
198	C₂×D₄×C₂₉	—	2	1	no	—
199	C₂×D₄×C₂₉	—	4	1	no	—
200	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
201	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
202	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₂₉	—	2	2	no	—
204	C₂²×C₄×C₂₉	—	2	2	no	—
205	C₂²×C₄×C₂₉	—	2	2	no	—
206	C₂²×C₄×C₂₉	—	2	1	no	—
207	C₂²×C₄×C₂₉	—	2	1	no	—
208	C₂²×C₄×C₂₉	—	2	1	no	—
209	C₂²×C₄×C₂₉	—	4	1	no	—
210	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
213	Q₁₆×C₂₉	—	8	2	no	—
214	SD₁₆×C₂₉	—	8	1	no	—
215	SD₁₆×C₂₉	—	8	2	no	—
216	D₈×C₂₉	—	8	1	no	—
217	D₈×C₂₉	—	8	1	no	—
218	D₈×C₂₉	—	8	1	no	—
219	M₁₆×C₂₉	—	8	1	no	—
220	C₂×C₈×C₂₉	—	2	1	no	—
221	C₂×C₈×C₂₉	—	2	1	no	—
222	C₂×C₈×C₂₉	—	2	1	no	—
223	C₂×C₈×C₂₉	—	2	1	no	—
224	C₂×C₈×C₂₉	—	2	1	no	—
225	C₂×C₈×C₂₉	—	2	1	no	—
226	C₂×C₈×C₂₉	—	8	1	no	—
227	C₄⋊C₄×C₂₉	—	2	2	no	—
228	C₄⋊C₄×C₂₉	—	2	2	no	—
229	C₄⋊C₄×C₂₉	—	2	2	no	—
230	C₄⋊C₄×C₂₉	—	2	2	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	2	no	—
236	C₄⋊C₄×C₂₉	—	2	2	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	—	2	1	no	—
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	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
247	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
248	C₂²⋊C₄×C₂₉	—	2	2	no	—
249	C₂²⋊C₄×C₂₉	—	2	2	no	—
250	C₂²⋊C₄×C₂₉	—	2	2	no	—
251	C₂²⋊C₄×C₂₉	—	2	2	no	—
252	C₂²⋊C₄×C₂₉	—	2	2	no	—
253	C₂²⋊C₄×C₂₉	—	2	2	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	—	2	1	no	—
261	C₂²⋊C₄×C₂₉	—	2	1	no	—
262	C₂²⋊C₄×C₂₉	—	2	1	no	—
263	C₂²⋊C₄×C₂₉	—	4	1	no	—
264	C₂²⋊C₄×C₂₉	—	4	1	no	—
265	C₄²×C₂₉	—	2	2	no	—
266	C₄²×C₂₉	—	2	2	no	—
267	C₄²×C₂₉	—	2	1	no	—
268	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
269	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
270	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
271	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
272	#18965	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
273	C₂³×C₂₉	—	2	1	no	—
274	C₂³×C₂₉	—	2	1	no	—
275	C₂³×C₂₉	—	2	1	no	—
276	C₂³×C₂₉	—	4	1	no	—
277	C₂³×C₂₉	#120	1	1	yes	characteristic
278	Q₈×C₂₉	—	2	1	no	—
279	Q₈×C₂₉	—	2	1	no	—
280	Q₈×C₂₉	—	4	2	no	—
281	Q₈×C₂₉	—	4	2	no	—
282	Q₈×C₂₉	—	4	1	no	—
283	Q₈×C₂₉	—	4	1	no	—
284	Q₈×C₂₉	—	8	1	no	—
285	Q₈×C₂₉	—	8	2	no	—
286	D₄×C₂₉	—	2	1	no	—
287	D₄×C₂₉	—	2	1	no	—
288	D₄×C₂₉	—	2	1	no	—
289	D₄×C₂₉	—	2	1	no	—
290	D₄×C₂₉	—	2	1	no	—
291	D₄×C₂₉	—	2	1	no	—
292	D₄×C₂₉	—	4	2	no	—
293	D₄×C₂₉	—	4	1	no	—
294	D₄×C₂₉	—	4	1	no	—
295	D₄×C₂₉	—	4	1	no	—
296	D₄×C₂₉	—	4	1	no	—
297	D₄×C₂₉	—	8	1	no	—
298	D₄×C₂₉	—	8	1	no	—
299	D₄×C₂₉	—	8	1	no	—
300	D₄×C₂₉	—	8	1	no	—
301	D₄×C₂₉	—	8	1	no	—
302	D₄×C₂₉	—	8	2	no	—
303	D₄×C₂₉	—	8	2	no	—
304	D₄×C₂₉	—	8	2	no	—
305	C₂×C₄×C₂₉	—	2	1	no	—
306	C₂×C₄×C₂₉	—	2	1	no	—
307	C₂×C₄×C₂₉	—	2	1	no	—
308	C₂×C₄×C₂₉	—	2	1	no	—
309	C₂×C₄×C₂₉	—	2	1	no	—
310	C₂×C₄×C₂₉	—	2	2	no	—
311	C₂×C₄×C₂₉	—	2	1	no	—
312	C₂×C₄×C₂₉	—	2	1	no	—
313	C₂×C₄×C₂₉	—	2	1	no	—
314	C₂×C₄×C₂₉	—	2	2	no	—
315	C₂×C₄×C₂₉	—	2	1	no	—
316	C₂×C₄×C₂₉	—	4	1	no	—
317	C₂×C₄×C₂₉	—	4	1	no	—
318	C₂×C₄×C₂₉	—	4	1	no	—
319	C₂×C₄×C₂₉	—	4	1	no	—
320	C₂×C₄×C₂₉	—	4	1	no	—
321	C₂×C₄×C₂₉	—	4	1	no	—
322	C₂×C₄×C₂₉	—	4	1	no	—
323	C₂×C₄×C₂₉	—	4	1	no	—
324	C₂×C₄×C₂₉	—	8	2	no	—
325	C₂×C₄×C₂₉	—	8	2	no	—
326	C₂×C₄×C₂₉	—	8	2	no	—
327	C₂×C₄×C₂₉	—	8	2	no	—
328	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
329	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
330	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
331	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
334	C₈×C₂₉	—	4	1	no	—
335	C₈×C₂₉	—	4	1	no	—
336	C₈×C₂₉	—	4	1	no	—
337	C₈×C₂₉	—	4	1	no	—
338	C₈×C₂₉	—	4	1	no	—
339	C₈×C₂₉	—	4	1	no	—
340	#3547	C₂×C₂₉	1	1	yes	characteristic, complemented
341	#3253	C₂×C₂₉	1	1	yes	characteristic, complemented
342	#3247	C₂×C₂₉	1	1	yes	characteristic, complemented
343	#3210	C₂×C₂₉	1	1	yes	characteristic, complemented
344	#1637	C₂×C₂₉	1	1	yes	characteristic, complemented
345	#1635	C₂×C₂₉	1	1	yes	characteristic, complemented
346	#1634	C₂×C₂₉	1	1	yes	characteristic, complemented
347	#1632	C₂×C₂₉	1	1	yes	characteristic, complemented
348	#1627	C₂×C₂₉	1	1	yes	characteristic, complemented
349	#1625	C₂×C₂₉	1	1	yes	characteristic, complemented
350	#1624	C₂×C₂₉	1	1	yes	characteristic, complemented
351	#1622	C₂×C₂₉	1	1	yes	characteristic, complemented
352	#1550	C₂×C₂₉	1	1	yes	characteristic, complemented
353	#1495	C₂×C₂₉	1	1	yes	characteristic, complemented
354	#1480	C₂×C₂₉	1	1	yes	characteristic, complemented
355	C₂²×C₂₉	—	2	1	no	—
356	C₂²×C₂₉	—	2	1	no	—
357	C₂²×C₂₉	—	2	1	no	—
358	C₂²×C₂₉	—	4	1	no	—
359	C₂²×C₂₉	—	4	1	no	—
360	C₂²×C₂₉	—	4	1	no	—
361	C₂²×C₂₉	—	4	1	no	—
362	C₂²×C₂₉	—	4	1	no	—
363	C₂²×C₂₉	—	4	1	no	—
364	C₂²×C₂₉	—	4	1	no	—
365	C₂²×C₂₉	—	4	1	no	—
366	C₂²×C₂₉	—	4	1	no	—
367	C₂²×C₂₉	—	8	1	no	—
368	C₂²×C₂₉	—	8	1	no	—
369	C₂²×C₂₉	—	8	1	no	—
370	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
371	C₄×C₂₉	—	2	1	no	—
372	C₄×C₂₉	—	2	1	no	—
373	C₄×C₂₉	—	2	1	no	—
374	C₄×C₂₉	—	2	1	no	—
375	C₄×C₂₉	—	4	1	no	—
376	C₄×C₂₉	—	4	1	no	—
377	C₄×C₂₉	—	4	2	no	—
378	C₄×C₂₉	—	4	1	no	—
379	C₄×C₂₉	—	4	1	no	—
380	C₄×C₂₉	—	4	1	no	—
381	C₄×C₂₉	—	4	2	no	—
382	C₄×C₂₉	—	8	1	no	—
383	C₄×C₂₉	#576	1	1	yes	characteristic
384	C₄×C₂₉	#577	1	1	yes	characteristic
385	C₄×C₂₉	#577	1	1	yes	characteristic
386	C₄×C₂₉	#578	1	1	yes	characteristic
387	#562	—	2	2	no	—
388	#555	—	2	1	no	—
389	#555	C₂²×C₂₉	1	1	yes	characteristic
390	#554	C₂²×C₂₉	1	1	yes	characteristic
391	#553	—	2	1	no	—
392	#552	—	2	1	no	—
393	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
394	#548	—	2	1	no	—
395	#547	C₂²×C₂₉	1	1	yes	characteristic
396	#544	—	2	1	no	—
397	#542	—	2	2	no	—
398	#540	—	2	1	no	—
399	#537	—	2	1	no	—
400	#536	—	2	1	no	—
401	#533	C₂²×C₂₉	1	1	yes	characteristic
402	#532	C₂²×C₂₉	1	1	yes	characteristic
403	#532	C₂²×C₂₉	1	1	yes	characteristic
404	#529	C₂²×C₂₉	1	1	yes	characteristic
405	#494	C₂²×C₂₉	1	1	yes	characteristic
406	#492	C₂²×C₂₉	1	1	yes	characteristic
407	#487	C₂²×C₂₉	1	1	yes	characteristic
408	#486	C₂²×C₂₉	1	1	yes	characteristic
409	#478	—	2	1	no	—
410	#477	C₂²×C₂₉	1	1	yes	characteristic
411	#476	—	2	1	no	—
412	#476	C₂²×C₂₉	1	1	yes	characteristic
413	#476	C₂²×C₂₉	1	1	yes	characteristic
414	#476	C₂²×C₂₉	1	1	yes	characteristic
415	#469	—	2	1	no	—
416	#469	—	2	1	no	—
417	#466	—	2	1	no	—
418	#465	—	2	1	no	—
419	#464	—	2	2	no	—
420	#463	—	2	1	no	—
421	#460	C₂²×C₂₉	1	1	yes	characteristic
422	#459	—	2	1	no	—
423	#459	C₂²×C₂₉	1	1	yes	characteristic
424	#459	C₂²×C₂₉	1	1	yes	characteristic
425	#459	C₂²×C₂₉	1	1	yes	characteristic
426	#452	—	2	2	no	—
427	#431	C₂²×C₂₉	1	1	yes	characteristic
428	#423	C₂²×C₂₉	1	1	yes	characteristic
429	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
430	#333	C₂²×C₂₉	1	1	yes	characteristic
431	#333	C₂²×C₂₉	1	1	yes	characteristic
432	#332	C₂²×C₂₉	1	1	yes	characteristic
433	#332	C₂²×C₂₉	1	1	yes	characteristic
434	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
435	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
436	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
437	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
438	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
439	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
440	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
441	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
442	C₂×C₂₉	—	4	1	no	—
443	C₂×C₂₉	—	8	1	no	—
444	C₂×C₂₉	—	8	1	no	—
445	C₂×C₂₉	—	8	1	no	—
446	C₂×C₂₉	—	16	1	no	—
447	C₂×C₂₉	#3012	1	1	yes	characteristic
448	C₂×C₂₉	#3013	1	1	yes	characteristic
449	C₂×C₂₉	#3021	1	1	yes	characteristic
450	C₂×#41	—	2	1	no	—
451	C₂×#41	—	2	1	no	—
452	C₂×#41	—	2	1	no	—
453	C₂²×Q₈	—	2	1	no	—
454	C₂×Q₁₆	—	2	2	no	—
455	C₂×SD₁₆	—	2	2	no	—
456	C₂×SD₁₆	—	2	1	no	—
457	C₂×D₈	—	2	1	no	—
458	C₂×D₈	—	2	1	no	—
459	C₂×D₈	—	2	1	no	—
460	C₂×M₁₆	—	2	1	no	—
461	C₂²×C₈	—	2	1	no	—
462	C₄⋊Q₈	—	2	2	no	—
463	C₄⋊Q₈	—	2	1	no	—
464	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
465	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
466	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
467	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
468	#127	D₄×C₂₉	1	1	yes	characteristic
469	#127	C₂³×C₂₉	1	1	yes	characteristic
470	#126	—	2	2	no	—
471	#126	—	2	1	no	—
472	#125	—	2	2	no	—
473	#125	—	2	1	no	—
474	#125	—	2	1	no	—
475	#125	D₄×C₂₉	1	1	yes	characteristic
476	#124	—	2	2	no	—
477	#124	—	2	2	no	—
478	#124	—	2	2	no	—
479	#124	—	2	1	no	—
480	#124	—	2	1	no	—
481	#124	D₄×C₂₉	1	1	yes	characteristic
482	#123	—	2	2	no	—
483	#123	—	2	2	no	—
484	#123	—	2	2	no	—
485	#123	—	2	1	no	—
486	#123	—	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	2	no	—
491	C₂²⋊Q₈	—	2	1	no	—
492	C₂²⋊Q₈	—	2	1	no	—
493	C₂²⋊Q₈	—	2	1	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
496	C₂²⋊Q₈	D₄×C₂₉	1	2	yes	—
497	#121	—	2	2	no	—
498	#121	—	2	2	no	—
499	#121	—	2	2	no	—
500	#121	—	2	2	no	—
501	#121	—	2	1	no	—
502	#121	—	2	1	no	—
503	#121	—	2	1	no	—
504	#121	—	2	1	no	—
505	#121	—	2	1	no	—
506	#121	—	2	1	no	—
507	#121	D₄×C₂₉	1	1	yes	characteristic
508	#121	D₄×C₂₉	1	1	yes	characteristic
509	#121	D₄×C₂₉	1	1	yes	characteristic
510	C₄×Q₈	—	2	1	no	—
511	C₄×Q₈	D₄×C₂₉	1	2	yes	—
512	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
513	C₄×D₄	—	2	2	no	—
514	C₄×D₄	—	2	1	no	—
515	C₄×D₄	—	2	1	no	—
516	C₄×D₄	—	2	1	no	—
517	C₄×D₄	—	2	1	no	—
518	C₄×D₄	—	2	1	no	—
519	C₄×D₄	—	2	1	no	—
520	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
521	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
522	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
523	#117	—	2	2	no	—
524	#117	—	2	1	no	—
525	#117	—	2	1	no	—
526	#117	—	2	1	no	—
527	#117	—	2	1	no	—
528	C₂×C₄⋊C₄	—	2	1	no	—
529	C₂×C₄⋊C₄	—	2	1	no	—
530	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
531	#107	—	2	1	no	—
532	#106	—	2	1	no	—
533	#106	—	2	1	no	—
534	#106	—	2	1	no	—
535	C₄⋊C₈	—	2	1	no	—
536	C₄⋊C₈	—	2	1	no	—
537	C₄⋊C₈	—	2	1	no	—
538	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
539	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
540	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
541	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
542	#103	—	2	1	no	—
543	#103	—	2	2	no	—
544	#102	—	2	1	no	—
545	#102	—	2	1	no	—
546	#102	—	2	1	no	—
547	#102	—	2	2	no	—
548	#102	—	2	1	no	—
549	#102	—	2	1	no	—
550	#102	—	2	1	no	—
551	#102	—	2	1	no	—
552	C₂²⋊C₈	—	2	1	no	—
553	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
554	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
555	C₂₉	#18965	1	1	yes	characteristic, direct product factor, Sylow
556	#41	—	8	1	no	—
557	#41	—	8	1	no	—
558	#41	—	8	1	no	—
559	#41	—	8	1	no	—
560	#41	—	8	2	no	—
561	C₂×Q₈	—	2	2	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	8	1	no	—
566	C₂×Q₈	—	8	1	no	—
567	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
568	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	4	1	no	—
580	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
581	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
582	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	4	1	no	—
590	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
591	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
592	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
593	Q₁₆	—	8	2	no	—
594	SD₁₆	—	8	1	no	—
595	SD₁₆	—	8	2	no	—
596	D₈	—	8	1	no	—
597	D₈	—	8	1	no	—
598	D₈	—	8	1	no	—
599	M₁₆	—	8	1	no	—
600	C₂×C₈	—	2	1	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	8	1	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
624	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
625	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
626	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
627	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	2	1	no	—
635	C₂²⋊C₄	—	2	1	no	—
636	C₂²⋊C₄	—	2	1	no	—
637	C₂²⋊C₄	—	2	1	no	—
638	C₂²⋊C₄	—	2	1	no	—
639	C₂²⋊C₄	—	2	1	no	—
640	C₂²⋊C₄	—	2	1	no	—
641	C₂²⋊C₄	—	2	1	no	—
642	C₂²⋊C₄	—	2	1	no	—
643	C₂²⋊C₄	—	4	1	no	—
644	C₂²⋊C₄	—	4	1	no	—
645	C₄²	—	2	2	no	—
646	C₄²	—	2	2	no	—
647	C₄²	—	2	1	no	—
648	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
649	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
650	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
651	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
652	C₂³	—	2	1	no	—
653	C₂³	—	2	1	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	4	1	no	—
656	C₂³	C₂₉×#120	1	1	yes	characteristic
657	Q₈	—	2	1	no	—
658	Q₈	—	2	1	no	—
659	Q₈	—	4	2	no	—
660	Q₈	—	4	2	no	—
661	Q₈	—	4	1	no	—
662	Q₈	—	4	1	no	—
663	Q₈	—	8	1	no	—
664	Q₈	—	8	2	no	—
665	D₄	—	2	1	no	—
666	D₄	—	2	1	no	—
667	D₄	—	2	1	no	—
668	D₄	—	2	1	no	—
669	D₄	—	2	1	no	—
670	D₄	—	2	1	no	—
671	D₄	—	4	2	no	—
672	D₄	—	4	1	no	—
673	D₄	—	4	1	no	—
674	D₄	—	4	1	no	—
675	D₄	—	4	1	no	—
676	D₄	—	8	1	no	—
677	D₄	—	8	1	no	—
678	D₄	—	8	1	no	—
679	D₄	—	8	1	no	—
680	D₄	—	8	1	no	—
681	D₄	—	8	2	no	—
682	D₄	—	8	2	no	—
683	D₄	—	8	2	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	8	2	no	—
704	C₂×C₄	—	8	2	no	—
705	C₂×C₄	—	8	2	no	—
706	C₂×C₄	—	8	2	no	—
707	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
708	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
709	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
710	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
711	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
712	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
713	C₈	—	4	1	no	—
714	C₈	—	4	1	no	—
715	C₈	—	4	1	no	—
716	C₈	—	4	1	no	—
717	C₈	—	4	1	no	—
718	C₈	—	4	1	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	4	1	no	—
723	C₂²	—	4	1	no	—
724	C₂²	—	4	1	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	8	1	no	—
732	C₂²	—	8	1	no	—
733	C₂²	—	8	1	no	—
734	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
735	C₄	—	2	1	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	1	no	—
739	C₄	—	4	1	no	—
740	C₄	—	4	1	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	1	no	—
744	C₄	—	4	1	no	—
745	C₄	—	4	2	no	—
746	C₄	—	8	1	no	—
747	C₄	C₂₉×#576	1	1	yes	characteristic
748	C₄	C₂₉×#577	1	1	yes	characteristic
749	C₄	C₂₉×#577	1	1	yes	characteristic
750	C₄	C₂₉×#578	1	1	yes	characteristic
751	C₂	—	4	1	no	—
752	C₂	—	8	1	no	—
753	C₂	—	8	1	no	—
754	C₂	—	8	1	no	—
755	C₂	—	16	1	no	—
756	C₂	C₂₉×#3012	1	1	yes	characteristic
757	C₂	C₂₉×#3013	1	1	yes	characteristic
758	C₂	C₂₉×#3021	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×#3547	C₂	semidirect
2. C₂₉×#3253	C₂	semidirect
3. C₂₉×#3247	C₂	semidirect
4. C₂₉×#3210	C₂	semidirect
5. C₂₉×#1637	C₂	semidirect
6. C₂₉×#1635	C₂	semidirect
7. C₂₉×#1634	C₂	semidirect
8. C₂₉×#1632	C₂	semidirect
9. C₂₉×#1627	C₂	semidirect
10. C₂₉×#1625	C₂	semidirect
11. C₂₉×#1624	C₂	semidirect
12. C₂₉×#1622	C₂	semidirect
13. C₂₉×#1550	C₂	semidirect
14. C₂₉×#1495	C₂	semidirect
15. C₂₉×#1480	C₂	semidirect
272. #18965	C₂₉	direct (N × H)
340. #3547	C₂×C₂₉	semidirect
341. #3253	C₂×C₂₉	semidirect
342. #3247	C₂×C₂₉	semidirect
343. #3210	C₂×C₂₉	semidirect
344. #1637	C₂×C₂₉	semidirect
345. #1635	C₂×C₂₉	semidirect
346. #1634	C₂×C₂₉	semidirect
347. #1632	C₂×C₂₉	semidirect
348. #1627	C₂×C₂₉	semidirect
349. #1625	C₂×C₂₉	semidirect
350. #1624	C₂×C₂₉	semidirect
351. #1622	C₂×C₂₉	semidirect
352. #1550	C₂×C₂₉	semidirect
353. #1495	C₂×C₂₉	semidirect
354. #1480	C₂×C₂₉	semidirect
555. C₂₉	#18965	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×#3547	2
C₂₉×#3253	2
C₂₉×#3247	2
C₂₉×#3210	2
C₂₉×#1637	2
C₂₉×#1635	2
C₂₉×#1634	2
C₂₉×#1632	2
C₂₉×#1627	2
C₂₉×#1625	2
C₂₉×#1624	2
C₂₉×#1622	2
C₂₉×#1550	2
C₂₉×#1495	2
C₂₉×#1480	2
#18965	29

Subgroups — C29×#18965 #20313865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18965 #20313865