Subgroups — C₂₉×#25461 #20320361

Order 7424.

792 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#476	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2566	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2085	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2084	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2067	C₂	1	1	yes	maximal, characteristic
8	C₂₉×#2065	C₂	1	1	yes	maximal, characteristic
9	C₂₉×#1989	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1949	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1948	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1940	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1926	C₂	1	1	yes	maximal, characteristic
14	C₂₉×#1925	C₂	1	1	yes	maximal, characteristic
15	C₂₉×#1762	C₂	1	1	yes	maximal, characteristic
16	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×#125	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₂₉	—	2	1	no	—
19	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
20	C₂₉×#501	—	2	4	no	—
21	C₂₉×#476	—	2	4	no	—
22	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
24	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
25	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
34	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
35	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
36	C₂₉×#396	—	2	1	no	—
37	C₂₉×#396	—	2	1	no	—
38	C₂₉×#391	—	2	1	no	—
39	C₂₉×#390	C₂²	1	1	yes	characteristic
40	C₂₉×#390	C₂²	1	1	yes	characteristic
41	C₂₉×#389	C₂²	1	1	yes	characteristic
42	C₂₉×#389	C₂²	1	1	yes	characteristic
43	C₂₉×#387	—	2	1	no	—
44	C₂₉×#387	—	2	1	no	—
45	C₂₉×#385	—	2	1	no	—
46	C₂₉×#385	—	2	1	no	—
47	C₂₉×#384	C₂²	1	1	yes	characteristic
48	C₂₉×#382	C₂²	1	1	yes	characteristic
49	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
50	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
53	C₂₉×#340	C₂²	1	1	yes	characteristic
54	C₂₉×#340	C₂²	1	1	yes	characteristic
55	C₂₉×#340	C₂²	1	1	yes	characteristic
56	C₂₉×#340	C₂²	1	1	yes	characteristic
57	C₂₉×#340	C₂²	1	1	yes	characteristic
58	C₂₉×#340	C₂²	1	1	yes	characteristic
59	C₂₉×#336	C₂²	1	1	yes	characteristic
60	C₂₉×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₂₉	—	2	1	no	—
62	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₂₉	—	2	1	no	—
64	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
68	C₂₉×C₄⋊Q₈	—	2	2	no	—
69	C₂₉×C₄⋊Q₈	D₄	1	4	yes	—
70	C₂₉×#125	—	2	2	no	—
71	C₂₉×#125	—	2	2	no	—
72	C₄×Q₈×C₂₉	—	4	4	no	—
73	C₄×D₄×C₂₉	—	2	2	no	—
74	C₄×D₄×C₂₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
96	C₂×C₄²×C₂₉	—	2	1	no	—
97	C₂×C₄²×C₂₉	—	2	1	no	—
98	C₂×C₄²×C₂₉	—	2	1	no	—
99	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
102	C₂₉×#107	—	2	2	no	—
103	C₂₉×#107	—	2	2	no	—
104	C₂₉×#106	—	2	2	no	—
105	C₂₉×#106	—	2	2	no	—
106	C₂₉×#106	—	2	2	no	—
107	C₂₉×#106	—	2	2	no	—
108	C₂₉×C₄⋊C₈	—	2	2	no	—
109	C₂₉×C₄⋊C₈	—	2	2	no	—
110	C₂₉×C₄⋊C₈	—	2	2	no	—
111	C₂₉×#102	—	2	2	no	—
112	C₂₉×#102	—	2	2	no	—
113	C₂₉×#102	—	2	2	no	—
114	C₂₉×#102	Q₈	1	4	yes	complemented
115	C₂₉×#97	—	2	2	no	—
116	C₂₉×#95	—	2	1	no	—
117	C₂₉×#95	—	2	1	no	—
118	C₂₉×#95	—	2	1	no	—
119	C₂₉×#95	—	2	1	no	—
120	C₂₉×#95	—	2	1	no	—
121	C₂₉×#95	—	2	1	no	—
122	C₂₉×#95	—	2	1	no	—
123	C₂₉×#95	D₄	1	1	yes	characteristic
124	C₂₉×#95	D₄	1	1	yes	characteristic
125	C₂⁴×C₂₉	—	2	1	no	—
126	C₂×Q₈×C₂₉	—	2	4	no	—
127	C₂×Q₈×C₂₉	—	4	2	no	—
128	C₂×Q₈×C₂₉	—	4	2	no	—
129	C₂×D₄×C₂₉	—	2	1	no	—
130	C₂×D₄×C₂₉	—	2	1	no	—
131	C₂×D₄×C₂₉	—	2	1	no	—
132	C₂×D₄×C₂₉	—	2	1	no	—
133	C₂×D₄×C₂₉	—	2	1	no	—
134	C₂×D₄×C₂₉	C₂×Q₈	1	2	yes	—
135	C₂²×C₄×C₂₉	—	2	1	no	—
136	C₂²×C₄×C₂₉	—	2	1	no	—
137	C₂²×C₄×C₂₉	—	2	1	no	—
138	C₂²×C₄×C₂₉	—	2	1	no	—
139	C₂²×C₄×C₂₉	—	2	1	no	—
140	C₂²×C₄×C₂₉	—	2	1	no	—
141	C₂²×C₄×C₂₉	—	2	1	no	—
142	C₂²×C₄×C₂₉	—	4	2	no	—
143	C₂²×C₄×C₂₉	—	8	1	no	—
144	C₂²×C₄×C₂₉	—	8	1	no	—
145	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
152	C₂×C₈×C₂₉	—	2	1	no	—
153	C₂×C₈×C₂₉	—	2	1	no	—
154	C₂×C₈×C₂₉	—	2	1	no	—
155	C₂×C₈×C₂₉	—	2	1	no	—
156	C₂×C₈×C₂₉	—	2	1	no	—
157	C₂×C₈×C₂₉	—	2	1	no	—
158	C₂×C₈×C₂₉	—	2	1	no	—
159	C₂×C₈×C₂₉	—	2	1	no	—
160	C₂×C₈×C₂₉	—	2	1	no	—
161	C₂×C₈×C₂₉	—	2	1	no	—
162	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
163	C₂×C₈×C₂₉	#41	1	2	yes	—
164	C₄⋊C₄×C₂₉	—	2	4	no	—
165	C₄⋊C₄×C₂₉	—	2	2	no	—
166	C₄⋊C₄×C₂₉	—	2	1	no	—
167	C₄⋊C₄×C₂₉	—	2	1	no	—
168	C₄⋊C₄×C₂₉	—	2	1	no	—
169	C₄⋊C₄×C₂₉	—	2	1	no	—
170	C₄⋊C₄×C₂₉	—	2	1	no	—
171	C₄⋊C₄×C₂₉	—	2	1	no	—
172	C₄⋊C₄×C₂₉	—	2	1	no	—
173	C₄⋊C₄×C₂₉	—	2	1	no	—
174	C₄⋊C₄×C₂₉	—	2	1	no	—
175	C₄⋊C₄×C₂₉	—	2	1	no	—
176	C₄⋊C₄×C₂₉	—	2	1	no	—
177	C₄⋊C₄×C₂₉	—	4	1	no	—
178	C₄⋊C₄×C₂₉	—	4	2	no	—
179	C₄⋊C₄×C₂₉	—	4	2	no	—
180	C₄⋊C₄×C₂₉	—	4	2	no	—
181	C₄⋊C₄×C₂₉	—	4	2	no	—
182	C₄⋊C₄×C₂₉	—	8	1	no	—
183	C₄⋊C₄×C₂₉	—	8	1	no	—
184	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
185	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
186	C₄⋊C₄×C₂₉	C₂×Q₈	1	2	yes	—
187	C₂²⋊C₄×C₂₉	—	4	2	no	—
188	C₂²⋊C₄×C₂₉	—	4	2	no	—
189	C₂²⋊C₄×C₂₉	—	4	2	no	—
190	C₂²⋊C₄×C₂₉	—	8	1	no	—
191	C₂²⋊C₄×C₂₉	—	8	1	no	—
192	C₄²×C₂₉	—	2	1	no	—
193	C₄²×C₂₉	—	2	1	no	—
194	C₄²×C₂₉	—	2	1	no	—
195	C₄²×C₂₉	—	2	1	no	—
196	C₄²×C₂₉	—	4	2	no	—
197	C₄²×C₂₉	—	4	2	no	—
198	C₄²×C₂₉	—	4	2	no	—
199	C₄²×C₂₉	C₂×D₄	1	2	yes	—
200	C₄²×C₂₉	#41	1	2	yes	—
201	#25461	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂³×C₂₉	—	2	2	no	—
203	C₂³×C₂₉	—	4	1	no	—
204	C₂³×C₂₉	—	4	1	no	—
205	C₂³×C₂₉	—	4	1	no	—
206	C₂³×C₂₉	—	4	1	no	—
207	C₂³×C₂₉	—	4	1	no	—
208	C₂³×C₂₉	—	4	1	no	—
209	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
210	Q₈×C₂₉	—	4	8	no	—
211	D₄×C₂₉	—	2	2	no	—
212	D₄×C₂₉	—	2	2	no	—
213	D₄×C₂₉	—	4	1	no	—
214	D₄×C₂₉	—	4	1	no	—
215	C₂×C₄×C₂₉	—	2	1	no	—
216	C₂×C₄×C₂₉	—	2	1	no	—
217	C₂×C₄×C₂₉	—	2	1	no	—
218	C₂×C₄×C₂₉	—	2	1	no	—
219	C₂×C₄×C₂₉	—	2	1	no	—
220	C₂×C₄×C₂₉	—	2	1	no	—
221	C₂×C₄×C₂₉	—	2	2	no	—
222	C₂×C₄×C₂₉	—	2	2	no	—
223	C₂×C₄×C₂₉	—	2	1	no	—
224	C₂×C₄×C₂₉	—	2	1	no	—
225	C₂×C₄×C₂₉	—	2	1	no	—
226	C₂×C₄×C₂₉	—	2	2	no	—
227	C₂×C₄×C₂₉	—	2	1	no	—
228	C₂×C₄×C₂₉	—	2	1	no	—
229	C₂×C₄×C₂₉	—	2	1	no	—
230	C₂×C₄×C₂₉	—	2	1	no	—
231	C₂×C₄×C₂₉	—	2	1	no	—
232	C₂×C₄×C₂₉	—	2	1	no	—
233	C₂×C₄×C₂₉	—	4	1	no	—
234	C₂×C₄×C₂₉	—	4	1	no	—
235	C₂×C₄×C₂₉	—	4	1	no	—
236	C₂×C₄×C₂₉	—	4	1	no	—
237	C₂×C₄×C₂₉	—	4	1	no	—
238	C₂×C₄×C₂₉	—	4	1	no	—
239	C₂×C₄×C₂₉	—	4	1	no	—
240	C₂×C₄×C₂₉	—	4	1	no	—
241	C₂×C₄×C₂₉	—	4	1	no	—
242	C₂×C₄×C₂₉	—	4	1	no	—
243	C₂×C₄×C₂₉	—	4	1	no	—
244	C₂×C₄×C₂₉	—	4	1	no	—
245	C₂×C₄×C₂₉	—	4	1	no	—
246	C₂×C₄×C₂₉	—	4	1	no	—
247	C₂×C₄×C₂₉	—	4	1	no	—
248	C₂×C₄×C₂₉	—	4	1	no	—
249	C₂×C₄×C₂₉	—	4	1	no	—
250	C₂×C₄×C₂₉	—	4	1	no	—
251	C₂×C₄×C₂₉	—	8	4	no	—
252	C₂×C₄×C₂₉	#121	1	2	yes	—
253	C₂×C₄×C₂₉	#121	1	2	yes	—
254	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
255	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
257	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
260	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
261	C₈×C₂₉	—	2	2	no	—
262	C₈×C₂₉	—	2	2	no	—
263	C₈×C₂₉	—	4	1	no	—
264	C₈×C₂₉	—	4	1	no	—
265	C₂×#501	C₂×C₂₉	1	1	yes	characteristic, complemented
266	C₂×#476	C₂×C₂₉	1	1	yes	characteristic
267	#2566	C₂×C₂₉	1	1	yes	characteristic
268	#2365	C₂×C₂₉	1	1	yes	characteristic, complemented
269	#2085	C₂×C₂₉	1	1	yes	characteristic, complemented
270	#2084	C₂×C₂₉	1	1	yes	characteristic, complemented
271	#2067	C₂×C₂₉	1	1	yes	characteristic
272	#2065	C₂×C₂₉	1	1	yes	characteristic
273	#1989	C₂×C₂₉	1	1	yes	characteristic, complemented
274	#1949	C₂×C₂₉	1	1	yes	characteristic, complemented
275	#1948	C₂×C₂₉	1	1	yes	characteristic, complemented
276	#1940	C₂×C₂₉	1	1	yes	characteristic, complemented
277	#1926	C₂×C₂₉	1	1	yes	characteristic
278	#1925	C₂×C₂₉	1	1	yes	characteristic
279	#1762	C₂×C₂₉	1	1	yes	characteristic
280	C₂²×C₂₉	—	4	2	no	—
281	C₂²×C₂₉	—	4	2	no	—
282	C₂²×C₂₉	—	4	2	no	—
283	C₂²×C₂₉	—	8	1	no	—
284	C₂²×C₂₉	—	8	1	no	—
285	C₂²×C₂₉	—	8	1	no	—
286	C₂²×C₂₉	—	8	1	no	—
287	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
288	C₂²×C₂₉	#547	1	1	yes	characteristic
289	C₂²×C₂₉	D₄×Q₈	1	1	yes	characteristic
290	C₂²×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
291	C₂²×C₂₉	#575	1	1	yes	characteristic
292	C₂²×C₂₉	#577	1	1	yes	characteristic
293	C₂²×C₂₉	#577	1	1	yes	characteristic
294	C₄×C₂₉	—	2	2	no	—
295	C₄×C₂₉	—	2	2	no	—
296	C₄×C₂₉	—	2	2	no	—
297	C₄×C₂₉	—	4	1	no	—
298	C₄×C₂₉	—	4	1	no	—
299	C₄×C₂₉	—	4	1	no	—
300	C₄×C₂₉	—	4	2	no	—
301	C₄×C₂₉	—	4	2	no	—
302	C₄×C₂₉	—	4	2	no	—
303	C₄×C₂₉	—	8	1	no	—
304	C₄×C₂₉	—	8	1	no	—
305	C₄×C₂₉	—	8	1	no	—
306	C₄×C₂₉	—	8	1	no	—
307	C₄×C₂₉	#533	1	1	yes	characteristic
308	C₄×C₂₉	#541	1	1	yes	characteristic
309	C₄×C₂₉	#548	1	1	yes	characteristic
310	C₄×C₂₉	D₄×Q₈	1	1	yes	characteristic
311	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
312	C₂×#125	C₂²×C₂₉	1	1	yes	characteristic
313	C₂×C₄×Q₈	—	2	1	no	—
314	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
315	#501	—	2	4	no	—
316	#476	—	2	4	no	—
317	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
318	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
319	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
320	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
321	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
322	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
323	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
324	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
325	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
326	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
327	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
328	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
329	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
330	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
331	#396	—	2	1	no	—
332	#396	—	2	1	no	—
333	#391	—	2	1	no	—
334	#390	C₂²×C₂₉	1	1	yes	characteristic
335	#390	C₂²×C₂₉	1	1	yes	characteristic
336	#389	C₂²×C₂₉	1	1	yes	characteristic
337	#389	C₂²×C₂₉	1	1	yes	characteristic
338	#387	—	2	1	no	—
339	#387	—	2	1	no	—
340	#385	—	2	1	no	—
341	#385	—	2	1	no	—
342	#384	C₂²×C₂₉	1	1	yes	characteristic
343	#382	C₂²×C₂₉	1	1	yes	characteristic
344	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
345	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
346	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
347	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
348	#340	C₂²×C₂₉	1	1	yes	characteristic
349	#340	C₂²×C₂₉	1	1	yes	characteristic
350	#340	C₂²×C₂₉	1	1	yes	characteristic
351	#340	C₂²×C₂₉	1	1	yes	characteristic
352	#340	C₂²×C₂₉	1	1	yes	characteristic
353	#340	C₂²×C₂₉	1	1	yes	characteristic
354	#336	C₂²×C₂₉	1	1	yes	characteristic
355	#336	C₂²×C₂₉	1	1	yes	characteristic
356	C₂×C₂₉	—	8	2	no	—
357	C₂×C₂₉	#2429	1	1	yes	characteristic
358	C₂×C₂₉	#3036	1	1	yes	characteristic
359	C₂×C₂₉	#3043	1	1	yes	characteristic
360	C₂×C₂₉	#3345	1	1	yes	characteristic
361	C₂×C₂₉	#3350	1	1	yes	characteristic
362	C₂×C₂₉	#3384	1	1	yes	characteristic
363	C₂×C₂₉	#3388	1	1	yes	characteristic
364	C₂²×Q₈	—	2	1	no	—
365	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
366	C₂³×C₄	—	2	1	no	—
367	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
368	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
369	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
370	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
371	C₄⋊Q₈	—	2	2	no	—
372	C₄⋊Q₈	D₄×C₂₉	1	4	yes	—
373	#125	—	2	2	no	—
374	#125	—	2	2	no	—
375	C₄×Q₈	—	4	4	no	—
376	C₄×D₄	—	2	2	no	—
377	C₄×D₄	—	2	2	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
386	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	—	2	1	no	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₂²⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	—	2	1	no	—
398	C₂×C₂²⋊C₄	—	2	1	no	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	—	2	1	no	—
401	C₂×C₄²	—	2	1	no	—
402	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
403	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
404	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
405	#107	—	2	2	no	—
406	#107	—	2	2	no	—
407	#106	—	2	2	no	—
408	#106	—	2	2	no	—
409	#106	—	2	2	no	—
410	#106	—	2	2	no	—
411	C₄⋊C₈	—	2	2	no	—
412	C₄⋊C₈	—	2	2	no	—
413	C₄⋊C₈	—	2	2	no	—
414	#102	—	2	2	no	—
415	#102	—	2	2	no	—
416	#102	—	2	2	no	—
417	#102	Q₈×C₂₉	1	4	yes	complemented
418	#97	—	2	2	no	—
419	#95	—	2	1	no	—
420	#95	—	2	1	no	—
421	#95	—	2	1	no	—
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	#95	—	2	1	no	—
425	#95	—	2	1	no	—
426	#95	D₄×C₂₉	1	1	yes	characteristic
427	#95	D₄×C₂₉	1	1	yes	characteristic
428	C₂₉	#25461	1	1	yes	characteristic, direct product factor, Sylow
429	C₂⁴	—	2	1	no	—
430	C₂×Q₈	—	2	4	no	—
431	C₂×Q₈	—	4	2	no	—
432	C₂×Q₈	—	4	2	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	C₂×Q₈×C₂₉	1	2	yes	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	4	2	no	—
447	C₂²×C₄	—	8	1	no	—
448	C₂²×C₄	—	8	1	no	—
449	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
455	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
467	C₂×C₈	#41×C₂₉	1	2	yes	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₄⋊C₄	—	4	2	no	—
483	C₄⋊C₄	—	4	2	no	—
484	C₄⋊C₄	—	4	2	no	—
485	C₄⋊C₄	—	4	2	no	—
486	C₄⋊C₄	—	8	1	no	—
487	C₄⋊C₄	—	8	1	no	—
488	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
489	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
490	C₄⋊C₄	C₂×Q₈×C₂₉	1	2	yes	—
491	C₂²⋊C₄	—	4	2	no	—
492	C₂²⋊C₄	—	4	2	no	—
493	C₂²⋊C₄	—	4	2	no	—
494	C₂²⋊C₄	—	8	1	no	—
495	C₂²⋊C₄	—	8	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	4	2	no	—
501	C₄²	—	4	2	no	—
502	C₄²	—	4	2	no	—
503	C₄²	C₂×D₄×C₂₉	1	2	yes	—
504	C₄²	#41×C₂₉	1	2	yes	—
505	C₂³	—	2	2	no	—
506	C₂³	—	4	1	no	—
507	C₂³	—	4	1	no	—
508	C₂³	—	4	1	no	—
509	C₂³	—	4	1	no	—
510	C₂³	—	4	1	no	—
511	C₂³	—	4	1	no	—
512	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
513	Q₈	—	4	8	no	—
514	D₄	—	2	2	no	—
515	D₄	—	2	2	no	—
516	D₄	—	4	1	no	—
517	D₄	—	4	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	8	4	no	—
555	C₂×C₄	C₂₉×#121	1	2	yes	—
556	C₂×C₄	C₂₉×#121	1	2	yes	—
557	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
558	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
559	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
560	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
561	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
562	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
563	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
564	C₈	—	2	2	no	—
565	C₈	—	2	2	no	—
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	8	1	no	—
572	C₂²	—	8	1	no	—
573	C₂²	—	8	1	no	—
574	C₂²	—	8	1	no	—
575	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
576	C₂²	C₂₉×#547	1	1	yes	characteristic
577	C₂²	D₄×Q₈×C₂₉	1	1	yes	characteristic
578	C₂²	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
579	C₂²	C₂₉×#575	1	1	yes	characteristic
580	C₂²	C₂₉×#577	1	1	yes	characteristic
581	C₂²	C₂₉×#577	1	1	yes	characteristic
582	C₄	—	2	2	no	—
583	C₄	—	2	2	no	—
584	C₄	—	2	2	no	—
585	C₄	—	4	2	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	2	no	—
591	C₄	—	8	1	no	—
592	C₄	—	8	1	no	—
593	C₄	—	8	1	no	—
594	C₄	—	8	1	no	—
595	C₄	C₂₉×#533	1	1	yes	characteristic
596	C₄	C₂₉×#541	1	1	yes	characteristic
597	C₄	C₂₉×#548	1	1	yes	characteristic
598	C₄	D₄×Q₈×C₂₉	1	1	yes	characteristic
599	C₂	—	8	2	no	—
600	C₂	C₂₉×#2429	1	1	yes	characteristic
601	C₂	C₂₉×#3036	1	1	yes	characteristic
602	C₂	C₂₉×#3043	1	1	yes	characteristic
603	C₂	C₂₉×#3345	1	1	yes	characteristic
604	C₂	C₂₉×#3350	1	1	yes	characteristic
605	C₂	C₂₉×#3384	1	1	yes	characteristic
606	C₂	C₂₉×#3388	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂²×D₄×C₂₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₄×C₄⋊C₄×C₂₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₂₉×#501	C₂	semidirect
4. C₂₉×#2365	C₂	semidirect
5. C₂₉×#2085	C₂	semidirect
6. C₂₉×#2084	C₂	semidirect
9. C₂₉×#1989	C₂	semidirect
10. C₂₉×#1949	C₂	semidirect
11. C₂₉×#1948	C₂	semidirect
12. C₂₉×#1940	C₂	semidirect
114. C₂₉×#102	Q₈	semidirect
201. #25461	C₂₉	direct (N × H)
265. C₂×#501	C₂×C₂₉	semidirect
268. #2365	C₂×C₂₉	semidirect
269. #2085	C₂×C₂₉	semidirect
270. #2084	C₂×C₂₉	semidirect
273. #1989	C₂×C₂₉	semidirect
274. #1949	C₂×C₂₉	semidirect
275. #1948	C₂×C₂₉	semidirect
276. #1940	C₂×C₂₉	semidirect
417. #102	Q₈×C₂₉	semidirect
428. C₂₉	#25461	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#501	2
C₂×C₂₉×#476	2
C₂₉×#2566	2
C₂₉×#2365	2
C₂₉×#2085	2
C₂₉×#2084	2
C₂₉×#2067	2
C₂₉×#2065	2
C₂₉×#1989	2
C₂₉×#1949	2
C₂₉×#1948	2
C₂₉×#1940	2
C₂₉×#1926	2
C₂₉×#1925	2
C₂₉×#1762	2
#25461	29

Subgroups — C29×#25461 #20320361

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#25461 #20320361