Subgroups — C₂₉×#18558 #20313458

Order 7424.

976 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3480	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3184	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3115	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3037	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1653	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1652	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×#1628	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1626	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1621	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1620	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1557	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1491	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1489	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×#137	—	2	1	no	—
17	C₂₉×#559	—	2	1	no	—
18	C₂₉×#559	C₂²	1	1	yes	characteristic
19	C₂₉×#557	C₂²	1	1	yes	characteristic
20	C₂₉×#556	—	2	1	no	—
21	C₂₉×#556	C₂²	1	1	yes	characteristic
22	C₂₉×#553	—	2	2	no	—
23	C₂₉×#553	—	2	1	no	—
24	C₂₉×#550	C₂²	1	1	yes	characteristic
25	C₂₉×#548	—	2	1	no	—
26	C₂₉×#532	—	2	1	no	—
27	C₂₉×#532	C₂²	1	1	yes	characteristic
28	C₂₉×#532	C₂²	1	1	yes	characteristic
29	C₂₉×#529	—	2	1	no	—
30	C₂₉×#529	—	2	2	no	—
31	C₄×#41×C₂₉	—	2	1	no	—
32	C₄×#41×C₂₉	—	2	1	no	—
33	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
35	C₂₉×#498	C₂²	1	1	yes	characteristic
36	C₂₉×#493	C₂²	1	1	yes	characteristic
37	C₂₉×#486	C₂²	1	1	yes	characteristic
38	C₂₉×#486	C₂²	1	1	yes	characteristic
39	C₂₉×#482	—	2	1	no	—
40	C₂₉×#475	C₂²	1	1	yes	characteristic
41	C₂₉×#474	C₂²	1	1	yes	characteristic
42	C₂₉×#469	—	2	2	no	—
43	C₂₉×#464	—	2	1	no	—
44	C₂₉×#464	—	2	1	no	—
45	C₂₉×#462	C₂²	1	1	yes	characteristic
46	C₂₉×#462	C₂²	1	1	yes	characteristic
47	C₂₉×#460	C₂²	1	1	yes	characteristic
48	C₂₉×#460	C₂²	1	1	yes	characteristic
49	C₂₉×#460	C₂²	1	1	yes	characteristic
50	C₂₉×#459	C₂²	1	1	yes	characteristic
51	C₂₉×#449	—	2	1	no	—
52	C₂₉×#442	—	2	2	no	—
53	C₂₉×#442	—	2	1	no	—
54	C₂₉×#440	—	2	1	no	—
55	C₂₉×#432	C₂²	1	1	yes	characteristic
56	C₂₉×#423	C₂²	1	1	yes	characteristic
57	C₂₉×#417	—	2	1	no	—
58	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
59	C₂₉×#332	C₂²	1	1	yes	characteristic
60	C₂₉×#332	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	1	no	—
72	C₂×#41×C₂₉	—	2	1	no	—
73	C₂×#41×C₂₉	—	2	1	no	—
74	C₂×#41×C₂₉	D₄	1	1	yes	characteristic
75	C₂²×Q₈×C₂₉	D₄	1	1	yes	characteristic
76	C₂₉×#137	—	4	4	no	—
77	C₂×Q₁₆×C₂₉	—	2	1	no	—
78	C₂×Q₁₆×C₂₉	—	2	1	no	—
79	C₂×SD₁₆×C₂₉	—	2	1	no	—
80	C₂×SD₁₆×C₂₉	—	2	1	no	—
81	C₂×SD₁₆×C₂₉	—	2	1	no	—
82	C₂×D₈×C₂₉	—	2	1	no	—
83	C₂×D₈×C₂₉	—	2	2	no	—
84	C₂×M₁₆×C₂₉	—	2	1	no	—
85	C₂×M₁₆×C₂₉	—	2	1	no	—
86	C₂₉×C₄⋊Q₈	—	2	1	no	—
87	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₂₉×#127	—	2	1	no	—
90	C₂₉×#127	C₂³	1	1	yes	characteristic
91	C₂₉×#127	C₂³	1	1	yes	characteristic
92	C₂₉×#126	—	2	2	no	—
93	C₂₉×#126	—	2	2	no	—
94	C₂₉×#126	—	2	2	no	—
95	C₂₉×#125	—	2	2	no	—
96	C₂₉×#125	—	2	1	no	—
97	C₂₉×#124	—	2	2	no	—
98	C₂₉×#124	—	2	1	no	—
99	C₂₉×#124	—	2	1	no	—
100	C₂₉×#124	—	2	1	no	—
101	C₂₉×#124	—	2	1	no	—
102	C₂₉×#124	—	2	1	no	—
103	C₂₉×#123	—	2	2	no	—
104	C₂₉×#123	—	2	2	no	—
105	C₂₉×#123	—	2	2	no	—
106	C₂₉×C₂²⋊Q₈	—	2	2	no	—
107	C₂₉×C₂²⋊Q₈	—	2	1	no	—
108	C₂₉×#121	—	2	2	no	—
109	C₂₉×#121	—	2	2	no	—
110	C₂₉×#121	—	2	2	no	—
111	C₂₉×#121	—	2	1	no	—
112	C₂₉×#121	—	2	1	no	—
113	C₂₉×#121	—	2	1	no	—
114	C₂₉×#121	—	2	1	no	—
115	C₂₉×#121	D₄	1	2	yes	—
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	—	2	1	no	—
121	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
122	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
123	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
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	2	no	—
130	C₄×D₄×C₂₉	—	2	2	no	—
131	C₄×D₄×C₂₉	—	2	2	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	—	2	1	no	—
139	C₄×D₄×C₂₉	—	2	1	no	—
140	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
141	C₄×D₄×C₂₉	D₄	1	2	yes	—
142	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
143	C₂₉×#117	—	2	2	no	—
144	C₂₉×#117	—	2	2	no	—
145	C₂₉×#117	—	2	1	no	—
146	C₂₉×#117	—	2	1	no	—
147	C₂₉×#117	D₄	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
149	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
150	C₂×C₄²×C₂₉	—	2	2	no	—
151	C₂×C₄²×C₂₉	—	2	1	no	—
152	C₂×C₄²×C₂₉	—	2	1	no	—
153	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
154	C₂₉×#107	—	2	1	no	—
155	C₂₉×#106	—	2	2	no	—
156	C₂₉×#106	—	2	1	no	—
157	C₂₉×C₄⋊C₈	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
162	C₂₉×#103	—	2	1	no	—
163	C₂₉×#103	—	2	1	no	—
164	C₂₉×#103	—	2	1	no	—
165	C₂₉×#102	—	2	1	no	—
166	C₂₉×#102	—	2	2	no	—
167	C₂₉×#102	—	2	1	no	—
168	C₂₉×#102	—	2	1	no	—
169	C₂₉×#102	—	2	2	no	—
170	C₂₉×#102	—	2	1	no	—
171	C₂₉×#102	—	2	1	no	—
172	C₂₉×C₂²⋊C₈	—	2	1	no	—
173	C₂₉×#97	—	2	1	no	—
174	C₂₉×#97	—	2	1	no	—
175	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
176	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
177	#41×C₂₉	—	4	1	no	—
178	#41×C₂₉	—	4	1	no	—
179	#41×C₂₉	—	4	2	no	—
180	#41×C₂₉	—	4	2	no	—
181	#41×C₂₉	—	4	2	no	—
182	#41×C₂₉	—	4	2	no	—
183	#41×C₂₉	—	4	2	no	—
184	#41×C₂₉	—	4	2	no	—
185	C₂×Q₈×C₂₉	—	2	1	no	—
186	C₂×Q₈×C₂₉	—	2	1	no	—
187	C₂×Q₈×C₂₉	—	2	2	no	—
188	C₂×Q₈×C₂₉	—	2	1	no	—
189	C₂×Q₈×C₂₉	—	4	1	no	—
190	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
191	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
192	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
193	C₂×D₄×C₂₉	—	2	2	no	—
194	C₂×D₄×C₂₉	—	2	1	no	—
195	C₂×D₄×C₂₉	—	2	2	no	—
196	C₂×D₄×C₂₉	—	2	2	no	—
197	C₂×D₄×C₂₉	—	2	1	no	—
198	C₂×D₄×C₂₉	—	2	1	no	—
199	C₂×D₄×C₂₉	—	2	1	no	—
200	C₂×D₄×C₂₉	—	2	1	no	—
201	C₂×D₄×C₂₉	—	2	1	no	—
202	C₂×D₄×C₂₉	—	4	1	no	—
203	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
204	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₂₉	—	2	2	no	—
206	C₂²×C₄×C₂₉	—	2	1	no	—
207	C₂²×C₄×C₂₉	—	2	2	no	—
208	C₂²×C₄×C₂₉	—	2	1	no	—
209	C₂²×C₄×C₂₉	—	2	1	no	—
210	C₂²×C₄×C₂₉	—	2	2	no	—
211	C₂²×C₄×C₂₉	—	2	1	no	—
212	C₂²×C₄×C₂₉	—	2	1	no	—
213	C₂²×C₄×C₂₉	—	4	1	no	—
214	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
217	Q₁₆×C₂₉	—	4	2	no	—
218	Q₁₆×C₂₉	—	4	2	no	—
219	SD₁₆×C₂₉	—	4	2	no	—
220	SD₁₆×C₂₉	—	4	2	no	—
221	SD₁₆×C₂₉	—	4	2	no	—
222	D₈×C₂₉	—	4	4	no	—
223	D₈×C₂₉	—	4	2	no	—
224	M₁₆×C₂₉	—	4	2	no	—
225	M₁₆×C₂₉	—	4	2	no	—
226	C₂×C₈×C₂₉	—	2	1	no	—
227	C₂×C₈×C₂₉	—	2	1	no	—
228	C₂×C₈×C₂₉	—	2	1	no	—
229	C₂×C₈×C₂₉	—	2	1	no	—
230	C₂×C₈×C₂₉	—	2	1	no	—
231	C₂×C₈×C₂₉	—	2	1	no	—
232	C₄⋊C₄×C₂₉	—	2	2	no	—
233	C₄⋊C₄×C₂₉	—	2	2	no	—
234	C₄⋊C₄×C₂₉	—	2	2	no	—
235	C₄⋊C₄×C₂₉	—	2	2	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	—	2	1	no	—
243	C₄⋊C₄×C₂₉	—	2	1	no	—
244	C₄⋊C₄×C₂₉	—	2	1	no	—
245	C₄⋊C₄×C₂₉	—	2	1	no	—
246	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
247	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
248	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
249	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
250	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
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	2	no	—
255	C₂²⋊C₄×C₂₉	—	2	2	no	—
256	C₂²⋊C₄×C₂₉	—	2	2	no	—
257	C₂²⋊C₄×C₂₉	—	2	1	no	—
258	C₂²⋊C₄×C₂₉	—	2	2	no	—
259	C₂²⋊C₄×C₂₉	—	2	1	no	—
260	C₂²⋊C₄×C₂₉	—	2	2	no	—
261	C₂²⋊C₄×C₂₉	—	2	1	no	—
262	C₂²⋊C₄×C₂₉	—	4	1	no	—
263	C₂²⋊C₄×C₂₉	—	4	1	no	—
264	C₄²×C₂₉	—	2	2	no	—
265	C₄²×C₂₉	—	2	2	no	—
266	C₄²×C₂₉	—	2	1	no	—
267	C₄²×C₂₉	—	2	1	no	—
268	C₄²×C₂₉	—	2	1	no	—
269	C₄²×C₂₉	—	2	1	no	—
270	C₄²×C₂₉	—	2	1	no	—
271	C₄²×C₂₉	—	2	1	no	—
272	C₄²×C₂₉	—	2	1	no	—
273	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
274	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
277	#18558	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₂³×C₂₉	—	2	1	no	—
279	C₂³×C₂₉	—	2	2	no	—
280	C₂³×C₂₉	—	4	1	no	—
281	C₂³×C₂₉	#120	1	1	yes	characteristic
282	Q₈×C₂₉	—	2	1	no	—
283	Q₈×C₂₉	—	2	1	no	—
284	Q₈×C₂₉	—	2	1	no	—
285	Q₈×C₂₉	—	2	1	no	—
286	Q₈×C₂₉	—	2	1	no	—
287	Q₈×C₂₉	—	4	2	no	—
288	Q₈×C₂₉	—	4	1	no	—
289	Q₈×C₂₉	—	4	1	no	—
290	Q₈×C₂₉	—	4	1	no	—
291	Q₈×C₂₉	—	4	1	no	—
292	Q₈×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
293	D₄×C₂₉	—	2	1	no	—
294	D₄×C₂₉	—	2	1	no	—
295	D₄×C₂₉	—	4	2	no	—
296	D₄×C₂₉	—	4	4	no	—
297	D₄×C₂₉	—	4	2	no	—
298	D₄×C₂₉	—	4	2	no	—
299	D₄×C₂₉	—	4	4	no	—
300	D₄×C₂₉	—	4	1	no	—
301	D₄×C₂₉	—	4	1	no	—
302	D₄×C₂₉	—	4	1	no	—
303	D₄×C₂₉	—	4	1	no	—
304	D₄×C₂₉	—	4	1	no	—
305	D₄×C₂₉	—	4	1	no	—
306	D₄×C₂₉	—	4	1	no	—
307	D₄×C₂₉	—	4	1	no	—
308	D₄×C₂₉	—	8	2	no	—
309	D₄×C₂₉	—	8	2	no	—
310	C₂×C₄×C₂₉	—	2	1	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	1	no	—
315	C₂×C₄×C₂₉	—	2	1	no	—
316	C₂×C₄×C₂₉	—	2	1	no	—
317	C₂×C₄×C₂₉	—	2	1	no	—
318	C₂×C₄×C₂₉	—	2	1	no	—
319	C₂×C₄×C₂₉	—	2	1	no	—
320	C₂×C₄×C₂₉	—	2	2	no	—
321	C₂×C₄×C₂₉	—	2	1	no	—
322	C₂×C₄×C₂₉	—	4	1	no	—
323	C₂×C₄×C₂₉	—	4	2	no	—
324	C₂×C₄×C₂₉	—	4	2	no	—
325	C₂×C₄×C₂₉	—	4	4	no	—
326	C₂×C₄×C₂₉	—	4	4	no	—
327	C₂×C₄×C₂₉	—	4	1	no	—
328	C₂×C₄×C₂₉	—	4	1	no	—
329	C₂×C₄×C₂₉	—	4	1	no	—
330	C₂×C₄×C₂₉	—	8	1	no	—
331	C₂×C₄×C₂₉	—	8	2	no	—
332	C₂×C₄×C₂₉	—	8	1	no	—
333	C₂×C₄×C₂₉	—	8	2	no	—
334	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
335	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
336	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
337	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
340	C₈×C₂₉	—	2	2	no	—
341	C₈×C₂₉	—	4	1	no	—
342	C₈×C₂₉	—	4	1	no	—
343	C₈×C₂₉	—	4	1	no	—
344	C₈×C₂₉	—	4	1	no	—
345	C₈×C₂₉	—	4	1	no	—
346	#3480	C₂×C₂₉	1	1	yes	characteristic, complemented
347	#3184	C₂×C₂₉	1	1	yes	characteristic, complemented
348	#3115	C₂×C₂₉	1	1	yes	characteristic, complemented
349	#3037	C₂×C₂₉	1	1	yes	characteristic, complemented
350	#1653	C₂×C₂₉	1	1	yes	characteristic, complemented
351	#1652	C₂×C₂₉	1	1	yes	characteristic, complemented
352	#1641	C₂×C₂₉	1	1	yes	characteristic, complemented
353	#1640	C₂×C₂₉	1	1	yes	characteristic, complemented
354	#1628	C₂×C₂₉	1	1	yes	characteristic, complemented
355	#1626	C₂×C₂₉	1	1	yes	characteristic, complemented
356	#1621	C₂×C₂₉	1	1	yes	characteristic, complemented
357	#1620	C₂×C₂₉	1	1	yes	characteristic, complemented
358	#1557	C₂×C₂₉	1	1	yes	characteristic, complemented
359	#1491	C₂×C₂₉	1	1	yes	characteristic, complemented
360	#1489	C₂×C₂₉	1	1	yes	characteristic, complemented
361	C₂²×C₂₉	—	2	1	no	—
362	C₂²×C₂₉	—	2	1	no	—
363	C₂²×C₂₉	—	2	1	no	—
364	C₂²×C₂₉	—	4	1	no	—
365	C₂²×C₂₉	—	4	2	no	—
366	C₂²×C₂₉	—	4	2	no	—
367	C₂²×C₂₉	—	4	1	no	—
368	C₂²×C₂₉	—	4	2	no	—
369	C₂²×C₂₉	—	4	1	no	—
370	C₂²×C₂₉	—	8	1	no	—
371	C₂²×C₂₉	—	8	1	no	—
372	C₂²×C₂₉	—	8	1	no	—
373	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
374	C₄×C₂₉	—	2	1	no	—
375	C₄×C₂₉	—	2	1	no	—
376	C₄×C₂₉	—	2	2	no	—
377	C₄×C₂₉	—	2	1	no	—
378	C₄×C₂₉	—	2	1	no	—
379	C₄×C₂₉	—	4	1	no	—
380	C₄×C₂₉	—	4	2	no	—
381	C₄×C₂₉	—	4	1	no	—
382	C₄×C₂₉	—	4	1	no	—
383	C₄×C₂₉	—	4	1	no	—
384	C₄×C₂₉	—	4	1	no	—
385	C₄×C₂₉	—	4	1	no	—
386	C₄×C₂₉	—	8	1	no	—
387	C₄×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
388	C₄×C₂₉	#575	1	1	yes	characteristic
389	C₄×C₂₉	#575	1	1	yes	characteristic
390	C₄×C₂₉	#575	1	1	yes	characteristic
391	C₂×#137	—	2	1	no	—
392	#559	—	2	1	no	—
393	#559	C₂²×C₂₉	1	1	yes	characteristic
394	#557	C₂²×C₂₉	1	1	yes	characteristic
395	#556	—	2	1	no	—
396	#556	C₂²×C₂₉	1	1	yes	characteristic
397	#553	—	2	2	no	—
398	#553	—	2	1	no	—
399	#550	C₂²×C₂₉	1	1	yes	characteristic
400	#548	—	2	1	no	—
401	#532	—	2	1	no	—
402	#532	C₂²×C₂₉	1	1	yes	characteristic
403	#532	C₂²×C₂₉	1	1	yes	characteristic
404	#529	—	2	1	no	—
405	#529	—	2	2	no	—
406	C₄×#41	—	2	1	no	—
407	C₄×#41	—	2	1	no	—
408	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
409	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
410	#498	C₂²×C₂₉	1	1	yes	characteristic
411	#493	C₂²×C₂₉	1	1	yes	characteristic
412	#486	C₂²×C₂₉	1	1	yes	characteristic
413	#486	C₂²×C₂₉	1	1	yes	characteristic
414	#482	—	2	1	no	—
415	#475	C₂²×C₂₉	1	1	yes	characteristic
416	#474	C₂²×C₂₉	1	1	yes	characteristic
417	#469	—	2	2	no	—
418	#464	—	2	1	no	—
419	#464	—	2	1	no	—
420	#462	C₂²×C₂₉	1	1	yes	characteristic
421	#462	C₂²×C₂₉	1	1	yes	characteristic
422	#460	C₂²×C₂₉	1	1	yes	characteristic
423	#460	C₂²×C₂₉	1	1	yes	characteristic
424	#460	C₂²×C₂₉	1	1	yes	characteristic
425	#459	C₂²×C₂₉	1	1	yes	characteristic
426	#449	—	2	1	no	—
427	#442	—	2	1	no	—
428	#442	—	2	2	no	—
429	#440	—	2	1	no	—
430	#432	C₂²×C₂₉	1	1	yes	characteristic
431	#423	C₂²×C₂₉	1	1	yes	characteristic
432	#417	—	2	1	no	—
433	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
434	#332	C₂²×C₂₉	1	1	yes	characteristic
435	#332	C₂²×C₂₉	1	1	yes	characteristic
436	#331	C₂²×C₂₉	1	1	yes	characteristic
437	#331	C₂²×C₂₉	1	1	yes	characteristic
438	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
439	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
440	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
441	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
442	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
443	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
444	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
445	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
446	C₂×C₂₉	—	4	1	no	—
447	C₂×C₂₉	—	8	1	no	—
448	C₂×C₂₉	—	8	2	no	—
449	C₂×C₂₉	—	16	1	no	—
450	C₂×C₂₉	#3005	1	1	yes	characteristic
451	C₂×C₂₉	#3006	1	1	yes	characteristic
452	C₂×C₂₉	#3018	1	1	yes	characteristic
453	C₂×#41	—	2	1	no	—
454	C₂×#41	—	2	1	no	—
455	C₂×#41	—	2	1	no	—
456	C₂×#41	D₄×C₂₉	1	1	yes	characteristic
457	C₂²×Q₈	D₄×C₂₉	1	1	yes	characteristic
458	#137	—	4	4	no	—
459	C₂×Q₁₆	—	2	1	no	—
460	C₂×Q₁₆	—	2	1	no	—
461	C₂×SD₁₆	—	2	1	no	—
462	C₂×SD₁₆	—	2	1	no	—
463	C₂×SD₁₆	—	2	1	no	—
464	C₂×D₈	—	2	1	no	—
465	C₂×D₈	—	2	2	no	—
466	C₂×M₁₆	—	2	1	no	—
467	C₂×M₁₆	—	2	1	no	—
468	C₄⋊Q₈	—	2	1	no	—
469	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
470	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
471	#127	—	2	1	no	—
472	#127	C₂³×C₂₉	1	1	yes	characteristic
473	#127	C₂³×C₂₉	1	1	yes	characteristic
474	#126	—	2	2	no	—
475	#126	—	2	2	no	—
476	#126	—	2	2	no	—
477	#125	—	2	2	no	—
478	#125	—	2	1	no	—
479	#124	—	2	2	no	—
480	#124	—	2	1	no	—
481	#124	—	2	1	no	—
482	#124	—	2	1	no	—
483	#124	—	2	1	no	—
484	#124	—	2	1	no	—
485	#123	—	2	2	no	—
486	#123	—	2	2	no	—
487	#123	—	2	2	no	—
488	C₂²⋊Q₈	—	2	2	no	—
489	C₂²⋊Q₈	—	2	1	no	—
490	#121	—	2	2	no	—
491	#121	—	2	2	no	—
492	#121	—	2	2	no	—
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	2	yes	—
498	C₄×Q₈	—	2	1	no	—
499	C₄×Q₈	—	2	1	no	—
500	C₄×Q₈	—	2	1	no	—
501	C₄×Q₈	—	2	1	no	—
502	C₄×Q₈	—	2	1	no	—
503	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
504	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
505	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
506	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
507	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
508	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
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	—	2	1	no	—
521	C₄×D₄	—	2	1	no	—
522	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
523	C₄×D₄	D₄×C₂₉	1	2	yes	—
524	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
525	#117	—	2	2	no	—
526	#117	—	2	2	no	—
527	#117	—	2	1	no	—
528	#117	—	2	1	no	—
529	#117	D₄×C₂₉	1	1	yes	characteristic
530	C₂×C₄⋊C₄	—	2	1	no	—
531	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
532	C₂×C₄²	—	2	2	no	—
533	C₂×C₄²	—	2	1	no	—
534	C₂×C₄²	—	2	1	no	—
535	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
536	#107	—	2	1	no	—
537	#106	—	2	2	no	—
538	#106	—	2	1	no	—
539	C₄⋊C₈	—	2	1	no	—
540	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
541	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
542	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
543	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
544	#103	—	2	1	no	—
545	#103	—	2	1	no	—
546	#103	—	2	1	no	—
547	#102	—	2	1	no	—
548	#102	—	2	2	no	—
549	#102	—	2	1	no	—
550	#102	—	2	1	no	—
551	#102	—	2	1	no	—
552	#102	—	2	1	no	—
553	#102	—	2	2	no	—
554	C₂²⋊C₈	—	2	1	no	—
555	#97	—	2	1	no	—
556	#97	—	2	1	no	—
557	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
558	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
559	C₂₉	#18558	1	1	yes	characteristic, direct product factor, Sylow
560	#41	—	4	1	no	—
561	#41	—	4	1	no	—
562	#41	—	4	2	no	—
563	#41	—	4	2	no	—
564	#41	—	4	2	no	—
565	#41	—	4	2	no	—
566	#41	—	4	2	no	—
567	#41	—	4	2	no	—
568	C₂×Q₈	—	2	1	no	—
569	C₂×Q₈	—	2	1	no	—
570	C₂×Q₈	—	2	2	no	—
571	C₂×Q₈	—	2	1	no	—
572	C₂×Q₈	—	4	1	no	—
573	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
574	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
575	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	1	no	—
583	C₂×D₄	—	2	1	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	—	4	1	no	—
586	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
587	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	4	1	no	—
597	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
600	Q₁₆	—	4	2	no	—
601	Q₁₆	—	4	2	no	—
602	SD₁₆	—	4	2	no	—
603	SD₁₆	—	4	2	no	—
604	SD₁₆	—	4	2	no	—
605	D₈	—	4	4	no	—
606	D₈	—	4	2	no	—
607	M₁₆	—	4	2	no	—
608	M₁₆	—	4	2	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	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	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
630	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
631	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
632	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
633	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	1	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	1	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	1	no	—
645	C₂²⋊C₄	—	4	1	no	—
646	C₂²⋊C₄	—	4	1	no	—
647	C₄²	—	2	2	no	—
648	C₄²	—	2	2	no	—
649	C₄²	—	2	1	no	—
650	C₄²	—	2	1	no	—
651	C₄²	—	2	1	no	—
652	C₄²	—	2	1	no	—
653	C₄²	—	2	1	no	—
654	C₄²	—	2	1	no	—
655	C₄²	—	2	1	no	—
656	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
657	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
658	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
659	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
660	C₂³	—	2	1	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	4	1	no	—
663	C₂³	C₂₉×#120	1	1	yes	characteristic
664	Q₈	—	2	1	no	—
665	Q₈	—	2	1	no	—
666	Q₈	—	2	1	no	—
667	Q₈	—	2	1	no	—
668	Q₈	—	2	1	no	—
669	Q₈	—	4	2	no	—
670	Q₈	—	4	1	no	—
671	Q₈	—	4	1	no	—
672	Q₈	—	4	1	no	—
673	Q₈	—	4	1	no	—
674	Q₈	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
675	D₄	—	2	1	no	—
676	D₄	—	2	1	no	—
677	D₄	—	4	2	no	—
678	D₄	—	4	4	no	—
679	D₄	—	4	2	no	—
680	D₄	—	4	2	no	—
681	D₄	—	4	4	no	—
682	D₄	—	4	1	no	—
683	D₄	—	4	1	no	—
684	D₄	—	4	1	no	—
685	D₄	—	4	1	no	—
686	D₄	—	4	1	no	—
687	D₄	—	4	1	no	—
688	D₄	—	4	1	no	—
689	D₄	—	4	1	no	—
690	D₄	—	8	2	no	—
691	D₄	—	8	2	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	2	no	—
706	C₂×C₄	—	4	2	no	—
707	C₂×C₄	—	4	4	no	—
708	C₂×C₄	—	4	4	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	8	1	no	—
713	C₂×C₄	—	8	2	no	—
714	C₂×C₄	—	8	1	no	—
715	C₂×C₄	—	8	2	no	—
716	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
717	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
718	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
719	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
720	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
721	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
722	C₈	—	2	2	no	—
723	C₈	—	4	1	no	—
724	C₈	—	4	1	no	—
725	C₈	—	4	1	no	—
726	C₈	—	4	1	no	—
727	C₈	—	4	1	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	8	1	no	—
738	C₂²	—	8	1	no	—
739	C₂²	—	8	1	no	—
740	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
741	C₄	—	2	1	no	—
742	C₄	—	2	1	no	—
743	C₄	—	2	2	no	—
744	C₄	—	2	1	no	—
745	C₄	—	2	1	no	—
746	C₄	—	4	1	no	—
747	C₄	—	4	2	no	—
748	C₄	—	4	1	no	—
749	C₄	—	4	1	no	—
750	C₄	—	4	1	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	1	no	—
753	C₄	—	8	1	no	—
754	C₄	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
755	C₄	C₂₉×#575	1	1	yes	characteristic
756	C₄	C₂₉×#575	1	1	yes	characteristic
757	C₄	C₂₉×#575	1	1	yes	characteristic
758	C₂	—	4	1	no	—
759	C₂	—	8	1	no	—
760	C₂	—	8	2	no	—
761	C₂	—	16	1	no	—
762	C₂	C₂₉×#3005	1	1	yes	characteristic
763	C₂	C₂₉×#3006	1	1	yes	characteristic
764	C₂	C₂₉×#3018	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×#3480	C₂	semidirect
2. C₂₉×#3184	C₂	semidirect
3. C₂₉×#3115	C₂	semidirect
4. C₂₉×#3037	C₂	semidirect
5. C₂₉×#1653	C₂	semidirect
6. C₂₉×#1652	C₂	semidirect
7. C₂₉×#1641	C₂	semidirect
8. C₂₉×#1640	C₂	semidirect
9. C₂₉×#1628	C₂	semidirect
10. C₂₉×#1626	C₂	semidirect
11. C₂₉×#1621	C₂	semidirect
12. C₂₉×#1620	C₂	semidirect
13. C₂₉×#1557	C₂	semidirect
14. C₂₉×#1491	C₂	semidirect
15. C₂₉×#1489	C₂	semidirect
277. #18558	C₂₉	direct (N × H)
346. #3480	C₂×C₂₉	semidirect
347. #3184	C₂×C₂₉	semidirect
348. #3115	C₂×C₂₉	semidirect
349. #3037	C₂×C₂₉	semidirect
350. #1653	C₂×C₂₉	semidirect
351. #1652	C₂×C₂₉	semidirect
352. #1641	C₂×C₂₉	semidirect
353. #1640	C₂×C₂₉	semidirect
354. #1628	C₂×C₂₉	semidirect
355. #1626	C₂×C₂₉	semidirect
356. #1621	C₂×C₂₉	semidirect
357. #1620	C₂×C₂₉	semidirect
358. #1557	C₂×C₂₉	semidirect
359. #1491	C₂×C₂₉	semidirect
360. #1489	C₂×C₂₉	semidirect
559. C₂₉	#18558	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×#3480	2
C₂₉×#3184	2
C₂₉×#3115	2
C₂₉×#3037	2
C₂₉×#1653	2
C₂₉×#1652	2
C₂₉×#1641	2
C₂₉×#1640	2
C₂₉×#1628	2
C₂₉×#1626	2
C₂₉×#1621	2
C₂₉×#1620	2
C₂₉×#1557	2
C₂₉×#1491	2
C₂₉×#1489	2
#18558	29

Subgroups — C29×#18558 #20313458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18558 #20313458