Subgroups — C₂₉×#26410 #20321310

Order 7424.

902 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#2440	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#2361	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2088	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2065	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2023	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1920	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1893	C₂	1	1	yes	maximal, characteristic
10	C₂₉×#1874	C₂	1	1	yes	maximal, characteristic
11	C₂₉×#1864	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1853	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1850	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1802	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₈×C₂₉	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₂₉	—	2	1	no	—
21	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₂₉	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×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂₉×#398	—	2	1	no	—
34	C₂₉×#395	—	2	1	no	—
35	C₂₉×#390	C₂²	1	1	yes	characteristic
36	C₂₉×#389	C₂²	1	1	yes	characteristic
37	C₂₉×#389	C₂²	1	1	yes	characteristic
38	C₂₉×#389	C₂²	1	1	yes	characteristic
39	C₂₉×#388	—	2	1	no	—
40	C₂₉×#386	—	2	1	no	—
41	C₂₉×#385	—	2	1	no	—
42	C₂₉×#385	—	2	1	no	—
43	C₂₉×#384	C₂²	1	1	yes	characteristic
44	C₂₉×#380	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
47	C₂₉×#340	C₂²	1	1	yes	characteristic
48	C₂₉×#340	C₂²	1	1	yes	characteristic
49	C₂₉×#340	C₂²	1	1	yes	characteristic
50	C₂₉×#340	C₂²	1	1	yes	characteristic
51	C₂₉×#340	C₂²	1	1	yes	characteristic
52	C₂₉×#340	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×#336	C₂²	1	1	yes	characteristic
58	C₂₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₂₉	—	2	1	no	—
60	C₂²×D₄×C₂₉	—	2	1	no	—
61	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₂₉	—	2	1	no	—
63	C₂³×C₄×C₂₉	—	2	1	no	—
64	C₂³×C₄×C₂₉	—	2	1	no	—
65	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₂₉	—	2	2	no	—
67	C₂²×C₈×C₂₉	—	4	1	no	—
68	C₂²×C₈×C₂₉	—	4	1	no	—
69	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
73	C₂₉×C₄⋊Q₈	—	2	2	no	—
74	C₂₉×C₄⋊Q₈	—	4	1	no	—
75	C₂₉×C₂²⋊Q₈	—	4	4	no	—
76	C₂₉×#121	—	2	2	no	—
77	C₂₉×#121	Q₈	1	4	yes	complemented
78	C₄×D₄×C₂₉	—	2	2	no	—
79	C₄×D₄×C₂₉	—	4	1	no	—
80	C₄×D₄×C₂₉	—	4	4	no	—
81	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
82	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
83	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
92	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
93	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₂₉	—	2	1	no	—
108	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
110	C₂₉×#106	—	2	2	no	—
111	C₂₉×#106	—	4	1	no	—
112	C₂₉×C₄⋊C₈	—	4	1	no	—
113	C₂₉×C₄⋊C₈	—	4	1	no	—
114	C₂₉×#102	—	2	2	no	—
115	C₂₉×#102	—	4	1	no	—
116	C₂₉×#102	—	4	1	no	—
117	C₂₉×#102	—	4	1	no	—
118	C₂₉×C₂²⋊C₈	—	2	2	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	—	2	1	no	—
124	C₂₉×#95	D₄	1	1	yes	characteristic
125	C₂₉×#95	D₄	1	1	yes	characteristic
126	C₂⁴×C₂₉	—	2	1	no	—
127	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
128	C₂×Q₈×C₂₉	—	4	2	no	—
129	C₂×Q₈×C₂₉	—	4	2	no	—
130	C₂×Q₈×C₂₉	—	8	1	no	—
131	C₂×D₄×C₂₉	—	2	4	no	—
132	C₂×D₄×C₂₉	—	2	1	no	—
133	C₂×D₄×C₂₉	—	2	1	no	—
134	C₂×D₄×C₂₉	—	2	1	no	—
135	C₂×D₄×C₂₉	—	2	1	no	—
136	C₂×D₄×C₂₉	—	2	1	no	—
137	C₂×D₄×C₂₉	—	4	2	no	—
138	C₂×D₄×C₂₉	—	4	2	no	—
139	C₂×D₄×C₂₉	C₂×Q₈	1	2	yes	—
140	C₂²×C₄×C₂₉	—	2	1	no	—
141	C₂²×C₄×C₂₉	—	2	1	no	—
142	C₂²×C₄×C₂₉	—	2	1	no	—
143	C₂²×C₄×C₂₉	—	2	1	no	—
144	C₂²×C₄×C₂₉	—	2	1	no	—
145	C₂²×C₄×C₂₉	—	2	1	no	—
146	C₂²×C₄×C₂₉	—	2	1	no	—
147	C₂²×C₄×C₂₉	—	2	1	no	—
148	C₂²×C₄×C₂₉	—	2	1	no	—
149	C₂²×C₄×C₂₉	—	2	1	no	—
150	C₂²×C₄×C₂₉	—	2	1	no	—
151	C₂²×C₄×C₂₉	—	4	2	no	—
152	C₂²×C₄×C₂₉	—	4	2	no	—
153	C₂²×C₄×C₂₉	—	4	2	no	—
154	C₂²×C₄×C₂₉	—	4	2	no	—
155	C₂²×C₄×C₂₉	—	4	2	no	—
156	C₂²×C₄×C₂₉	—	4	2	no	—
157	C₂²×C₄×C₂₉	—	8	1	no	—
158	C₂²×C₄×C₂₉	—	8	1	no	—
159	C₂²×C₄×C₂₉	—	8	1	no	—
160	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₂₉	C₂×Q₈	1	2	yes	—
166	C₂²×C₄×C₂₉	#41	1	2	yes	—
167	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
168	C₂×C₈×C₂₉	—	2	1	no	—
169	C₂×C₈×C₂₉	—	2	1	no	—
170	C₂×C₈×C₂₉	—	2	1	no	—
171	C₂×C₈×C₂₉	—	2	1	no	—
172	C₂×C₈×C₂₉	—	2	1	no	—
173	C₂×C₈×C₂₉	—	2	1	no	—
174	C₂×C₈×C₂₉	—	2	1	no	—
175	C₂×C₈×C₂₉	—	2	1	no	—
176	C₂×C₈×C₂₉	—	2	1	no	—
177	C₂×C₈×C₂₉	—	2	1	no	—
178	C₂×C₈×C₂₉	—	2	1	no	—
179	C₂×C₈×C₂₉	—	2	1	no	—
180	C₂×C₈×C₂₉	—	4	4	no	—
181	C₄⋊C₄×C₂₉	—	2	1	no	—
182	C₄⋊C₄×C₂₉	—	2	1	no	—
183	C₄⋊C₄×C₂₉	—	2	1	no	—
184	C₄⋊C₄×C₂₉	—	2	1	no	—
185	C₄⋊C₄×C₂₉	—	2	1	no	—
186	C₄⋊C₄×C₂₉	—	2	1	no	—
187	C₄⋊C₄×C₂₉	—	2	1	no	—
188	C₄⋊C₄×C₂₉	—	2	1	no	—
189	C₄⋊C₄×C₂₉	—	2	1	no	—
190	C₄⋊C₄×C₂₉	—	2	1	no	—
191	C₄⋊C₄×C₂₉	—	2	1	no	—
192	C₄⋊C₄×C₂₉	—	4	2	no	—
193	C₄⋊C₄×C₂₉	—	4	2	no	—
194	C₄⋊C₄×C₂₉	—	4	2	no	—
195	C₄⋊C₄×C₂₉	—	4	2	no	—
196	C₄⋊C₄×C₂₉	—	4	2	no	—
197	C₄⋊C₄×C₂₉	—	4	2	no	—
198	C₄⋊C₄×C₂₉	—	4	2	no	—
199	C₄⋊C₄×C₂₉	—	8	1	no	—
200	C₄⋊C₄×C₂₉	C₂×Q₈	1	2	yes	—
201	C₄⋊C₄×C₂₉	#41	1	2	yes	—
202	C₄⋊C₄×C₂₉	#41	1	2	yes	—
203	C₂²⋊C₄×C₂₉	—	2	2	no	—
204	C₂²⋊C₄×C₂₉	—	2	4	no	—
205	C₂²⋊C₄×C₂₉	—	4	2	no	—
206	C₂²⋊C₄×C₂₉	—	4	2	no	—
207	C₂²⋊C₄×C₂₉	—	4	2	no	—
208	C₂²⋊C₄×C₂₉	—	8	1	no	—
209	C₂²⋊C₄×C₂₉	SD₁₆	1	4	yes	—
210	C₄²×C₂₉	—	2	1	no	—
211	C₄²×C₂₉	—	2	1	no	—
212	C₄²×C₂₉	—	2	1	no	—
213	C₄²×C₂₉	—	2	1	no	—
214	C₄²×C₂₉	—	4	2	no	—
215	#26410	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂³×C₂₉	—	2	1	no	—
217	C₂³×C₂₉	—	2	1	no	—
218	C₂³×C₂₉	—	2	1	no	—
219	C₂³×C₂₉	—	2	1	no	—
220	C₂³×C₂₉	—	2	2	no	—
221	C₂³×C₂₉	—	4	1	no	—
222	C₂³×C₂₉	—	4	1	no	—
223	C₂³×C₂₉	—	4	1	no	—
224	C₂³×C₂₉	—	4	1	no	—
225	C₂³×C₂₉	—	4	1	no	—
226	C₂³×C₂₉	—	4	1	no	—
227	C₂³×C₂₉	C₂²⋊Q₈	1	2	yes	—
228	C₂³×C₂₉	C₂×SD₁₆	1	2	yes	—
229	C₂³×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
230	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
231	Q₈×C₂₉	—	8	4	no	—
232	D₄×C₂₉	—	2	2	no	—
233	D₄×C₂₉	—	2	2	no	—
234	D₄×C₂₉	—	4	8	no	—
235	D₄×C₂₉	—	4	1	no	—
236	D₄×C₂₉	—	4	1	no	—
237	C₂×C₄×C₂₉	—	2	1	no	—
238	C₂×C₄×C₂₉	—	2	1	no	—
239	C₂×C₄×C₂₉	—	2	1	no	—
240	C₂×C₄×C₂₉	—	2	1	no	—
241	C₂×C₄×C₂₉	—	2	1	no	—
242	C₂×C₄×C₂₉	—	2	1	no	—
243	C₂×C₄×C₂₉	—	2	2	no	—
244	C₂×C₄×C₂₉	—	2	2	no	—
245	C₂×C₄×C₂₉	—	2	2	no	—
246	C₂×C₄×C₂₉	—	2	2	no	—
247	C₂×C₄×C₂₉	—	2	2	no	—
248	C₂×C₄×C₂₉	—	2	1	no	—
249	C₂×C₄×C₂₉	—	2	1	no	—
250	C₂×C₄×C₂₉	—	2	2	no	—
251	C₂×C₄×C₂₉	—	2	2	no	—
252	C₂×C₄×C₂₉	—	2	1	no	—
253	C₂×C₄×C₂₉	—	2	1	no	—
254	C₂×C₄×C₂₉	—	2	1	no	—
255	C₂×C₄×C₂₉	—	2	1	no	—
256	C₂×C₄×C₂₉	—	4	1	no	—
257	C₂×C₄×C₂₉	—	4	1	no	—
258	C₂×C₄×C₂₉	—	4	1	no	—
259	C₂×C₄×C₂₉	—	4	1	no	—
260	C₂×C₄×C₂₉	—	4	1	no	—
261	C₂×C₄×C₂₉	—	4	1	no	—
262	C₂×C₄×C₂₉	—	4	1	no	—
263	C₂×C₄×C₂₉	—	4	1	no	—
264	C₂×C₄×C₂₉	—	4	1	no	—
265	C₂×C₄×C₂₉	—	4	1	no	—
266	C₂×C₄×C₂₉	—	4	1	no	—
267	C₂×C₄×C₂₉	—	4	1	no	—
268	C₂×C₄×C₂₉	—	4	1	no	—
269	C₂×C₄×C₂₉	—	4	1	no	—
270	C₂×C₄×C₂₉	—	4	1	no	—
271	C₂×C₄×C₂₉	—	4	1	no	—
272	C₂×C₄×C₂₉	—	4	1	no	—
273	C₂×C₄×C₂₉	—	4	1	no	—
274	C₂×C₄×C₂₉	—	8	4	no	—
275	C₂×C₄×C₂₉	—	8	4	no	—
276	C₂×C₄×C₂₉	—	8	4	no	—
277	C₂×C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
278	C₂×C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
279	C₂×C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
280	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
281	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
282	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
283	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
285	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
286	C₈×C₂₉	—	4	1	no	—
287	C₈×C₂₉	—	4	1	no	—
288	C₈×C₂₉	—	4	1	no	—
289	C₈×C₂₉	—	4	1	no	—
290	#2440	C₂×C₂₉	1	1	yes	characteristic, complemented
291	#2361	C₂×C₂₉	1	1	yes	characteristic
292	#2100	C₂×C₂₉	1	1	yes	characteristic, complemented
293	#2088	C₂×C₂₉	1	1	yes	characteristic, complemented
294	#2065	C₂×C₂₉	1	1	yes	characteristic, complemented
295	#2023	C₂×C₂₉	1	1	yes	characteristic, complemented
296	#1987	C₂×C₂₉	1	1	yes	characteristic, complemented
297	#1920	C₂×C₂₉	1	1	yes	characteristic, complemented
298	#1893	C₂×C₂₉	1	1	yes	characteristic
299	#1874	C₂×C₂₉	1	1	yes	characteristic
300	#1864	C₂×C₂₉	1	1	yes	characteristic, complemented
301	#1853	C₂×C₂₉	1	1	yes	characteristic, complemented
302	#1850	C₂×C₂₉	1	1	yes	characteristic, complemented
303	#1802	C₂×C₂₉	1	1	yes	characteristic, complemented
304	C₂×#340	C₂×C₂₉	1	1	yes	characteristic, complemented
305	C₂²×C₂₉	—	2	2	no	—
306	C₂²×C₂₉	—	2	2	no	—
307	C₂²×C₂₉	—	2	2	no	—
308	C₂²×C₂₉	—	2	2	no	—
309	C₂²×C₂₉	—	2	2	no	—
310	C₂²×C₂₉	—	2	2	no	—
311	C₂²×C₂₉	—	4	2	no	—
312	C₂²×C₂₉	—	4	2	no	—
313	C₂²×C₂₉	—	4	2	no	—
314	C₂²×C₂₉	—	8	1	no	—
315	C₂²×C₂₉	—	8	1	no	—
316	C₂²×C₂₉	—	8	1	no	—
317	C₂²×C₂₉	—	8	1	no	—
318	C₂²×C₂₉	#476	1	4	yes	—
319	C₂²×C₂₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
320	C₂²×C₂₉	#546	1	1	yes	characteristic
321	C₂²×C₂₉	#546	1	1	yes	characteristic
322	C₂²×C₂₉	C₂²×SD₁₆	1	1	yes	characteristic
323	C₂²×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
324	C₂²×C₂₉	#576	1	1	yes	characteristic
325	C₂²×C₂₉	#578	1	1	yes	characteristic
326	C₄×C₂₉	—	2	2	no	—
327	C₄×C₂₉	—	2	2	no	—
328	C₄×C₂₉	—	2	2	no	—
329	C₄×C₂₉	—	4	2	no	—
330	C₄×C₂₉	—	4	1	no	—
331	C₄×C₂₉	—	4	1	no	—
332	C₄×C₂₉	—	4	2	no	—
333	C₄×C₂₉	—	4	2	no	—
334	C₄×C₂₉	—	8	1	no	—
335	C₄×C₂₉	—	8	1	no	—
336	C₄×C₂₉	—	8	1	no	—
337	C₄×C₂₉	—	8	1	no	—
338	C₄×C₂₉	#529	1	1	yes	characteristic
339	C₄×C₂₉	#538	1	1	yes	characteristic
340	C₄×C₂₉	#554	1	1	yes	characteristic
341	C₄×C₂₉	#554	1	1	yes	characteristic
342	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic
343	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
344	C₂×C₂²⋊Q₈	—	2	1	no	—
345	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic
346	C₂×C₄×D₄	—	2	1	no	—
347	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
348	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
349	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
350	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
351	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
352	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
353	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
354	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
355	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
356	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
357	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
358	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
359	#398	—	2	1	no	—
360	#395	—	2	1	no	—
361	#390	C₂²×C₂₉	1	1	yes	characteristic
362	#389	C₂²×C₂₉	1	1	yes	characteristic
363	#389	C₂²×C₂₉	1	1	yes	characteristic
364	#389	C₂²×C₂₉	1	1	yes	characteristic
365	#388	—	2	1	no	—
366	#386	—	2	1	no	—
367	#385	—	2	1	no	—
368	#385	—	2	1	no	—
369	#384	C₂²×C₂₉	1	1	yes	characteristic
370	#380	C₂²×C₂₉	1	1	yes	characteristic
371	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
372	C₄×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
373	#340	C₂²×C₂₉	1	1	yes	characteristic
374	#340	C₂²×C₂₉	1	1	yes	characteristic
375	#340	C₂²×C₂₉	1	1	yes	characteristic
376	#340	C₂²×C₂₉	1	1	yes	characteristic
377	#340	C₂²×C₂₉	1	1	yes	characteristic
378	#340	C₂²×C₂₉	1	1	yes	characteristic
379	#340	C₂²×C₂₉	1	1	yes	characteristic
380	#340	C₂²×C₂₉	1	1	yes	characteristic
381	#340	C₂²×C₂₉	1	1	yes	characteristic
382	#340	C₂²×C₂₉	1	1	yes	characteristic
383	#336	C₂²×C₂₉	1	1	yes	characteristic
384	#336	C₂²×C₂₉	1	1	yes	characteristic
385	C₂×C₂₉	—	2	4	no	—
386	C₂×C₂₉	—	8	2	no	—
387	C₂×C₂₉	#2450	1	1	yes	characteristic
388	C₂×C₂₉	C₂×#476	1	1	yes	characteristic
389	C₂×C₂₉	#3083	1	1	yes	characteristic
390	C₂×C₂₉	#3295	1	1	yes	characteristic
391	C₂×C₂₉	#3298	1	1	yes	characteristic
392	C₂×C₂₉	#3308	1	1	yes	characteristic
393	C₂×C₂₉	#3318	1	1	yes	characteristic
394	C₂²×Q₈	—	2	1	no	—
395	C₂²×D₄	—	2	1	no	—
396	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
397	C₂³×C₄	—	2	1	no	—
398	C₂³×C₄	—	2	1	no	—
399	C₂³×C₄	—	2	1	no	—
400	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
401	C₂²×C₈	—	2	2	no	—
402	C₂²×C₈	—	4	1	no	—
403	C₂²×C₈	—	4	1	no	—
404	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
405	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
406	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
407	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
408	C₄⋊Q₈	—	2	2	no	—
409	C₄⋊Q₈	—	4	1	no	—
410	C₂²⋊Q₈	—	4	4	no	—
411	#121	—	2	2	no	—
412	#121	Q₈×C₂₉	1	4	yes	complemented
413	C₄×D₄	—	2	2	no	—
414	C₄×D₄	—	4	1	no	—
415	C₄×D₄	—	4	4	no	—
416	C₂×C₄⋊C₄	—	2	2	no	—
417	C₂×C₄⋊C₄	—	2	2	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	—	2	1	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	4	1	no	—
427	C₂×C₄⋊C₄	—	4	1	no	—
428	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₂²⋊C₄	—	2	1	no	—
437	C₂×C₂²⋊C₄	—	2	1	no	—
438	C₂×C₂²⋊C₄	—	2	1	no	—
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
441	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
442	C₂×C₄²	—	2	1	no	—
443	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
444	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
445	#106	—	2	2	no	—
446	#106	—	4	1	no	—
447	C₄⋊C₈	—	4	1	no	—
448	C₄⋊C₈	—	4	1	no	—
449	#102	—	2	2	no	—
450	#102	—	4	1	no	—
451	#102	—	4	1	no	—
452	#102	—	4	1	no	—
453	C₂²⋊C₈	—	2	2	no	—
454	#95	—	2	1	no	—
455	#95	—	2	1	no	—
456	#95	—	2	1	no	—
457	#95	—	2	1	no	—
458	#95	—	2	1	no	—
459	#95	D₄×C₂₉	1	1	yes	characteristic
460	#95	D₄×C₂₉	1	1	yes	characteristic
461	C₂₉	#26410	1	1	yes	characteristic, direct product factor, Sylow
462	C₂⁴	—	2	1	no	—
463	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
464	C₂×Q₈	—	4	2	no	—
465	C₂×Q₈	—	4	2	no	—
466	C₂×Q₈	—	8	1	no	—
467	C₂×D₄	—	2	4	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	4	2	no	—
474	C₂×D₄	—	4	2	no	—
475	C₂×D₄	C₂×Q₈×C₂₉	1	2	yes	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	4	2	no	—
488	C₂²×C₄	—	4	2	no	—
489	C₂²×C₄	—	4	2	no	—
490	C₂²×C₄	—	4	2	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	—	8	1	no	—
494	C₂²×C₄	—	8	1	no	—
495	C₂²×C₄	—	8	1	no	—
496	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
500	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
501	C₂²×C₄	C₂×Q₈×C₂₉	1	2	yes	—
502	C₂²×C₄	#41×C₂₉	1	2	yes	—
503	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	4	4	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	4	2	no	—
529	C₄⋊C₄	—	4	2	no	—
530	C₄⋊C₄	—	4	2	no	—
531	C₄⋊C₄	—	4	2	no	—
532	C₄⋊C₄	—	4	2	no	—
533	C₄⋊C₄	—	4	2	no	—
534	C₄⋊C₄	—	4	2	no	—
535	C₄⋊C₄	—	8	1	no	—
536	C₄⋊C₄	C₂×Q₈×C₂₉	1	2	yes	—
537	C₄⋊C₄	#41×C₂₉	1	2	yes	—
538	C₄⋊C₄	#41×C₂₉	1	2	yes	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	4	no	—
541	C₂²⋊C₄	—	4	2	no	—
542	C₂²⋊C₄	—	4	2	no	—
543	C₂²⋊C₄	—	4	2	no	—
544	C₂²⋊C₄	—	8	1	no	—
545	C₂²⋊C₄	SD₁₆×C₂₉	1	4	yes	—
546	C₄²	—	2	1	no	—
547	C₄²	—	2	1	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	4	2	no	—
551	C₂³	—	2	1	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	4	1	no	—
559	C₂³	—	4	1	no	—
560	C₂³	—	4	1	no	—
561	C₂³	—	4	1	no	—
562	C₂³	C₂₉×C₂²⋊Q₈	1	2	yes	—
563	C₂³	C₂×SD₁₆×C₂₉	1	2	yes	—
564	C₂³	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
565	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
566	Q₈	—	8	4	no	—
567	D₄	—	2	2	no	—
568	D₄	—	2	2	no	—
569	D₄	—	4	8	no	—
570	D₄	—	4	1	no	—
571	D₄	—	4	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	8	4	no	—
610	C₂×C₄	—	8	4	no	—
611	C₂×C₄	—	8	4	no	—
612	C₂×C₄	C₂₉×C₂²⋊Q₈	1	2	yes	—
613	C₂×C₄	C₂×SD₁₆×C₂₉	1	2	yes	—
614	C₂×C₄	C₂×SD₁₆×C₂₉	1	2	yes	—
615	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
616	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
617	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
618	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
619	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
620	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
621	C₈	—	4	1	no	—
622	C₈	—	4	1	no	—
623	C₈	—	4	1	no	—
624	C₈	—	4	1	no	—
625	C₂²	—	2	2	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	4	2	no	—
633	C₂²	—	4	2	no	—
634	C₂²	—	8	1	no	—
635	C₂²	—	8	1	no	—
636	C₂²	—	8	1	no	—
637	C₂²	—	8	1	no	—
638	C₂²	C₂₉×#476	1	4	yes	—
639	C₂²	C₂×C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
640	C₂²	C₂₉×#546	1	1	yes	characteristic
641	C₂²	C₂₉×#546	1	1	yes	characteristic
642	C₂²	C₂²×SD₁₆×C₂₉	1	1	yes	characteristic
643	C₂²	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
644	C₂²	C₂₉×#576	1	1	yes	characteristic
645	C₂²	C₂₉×#578	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	4	2	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	2	no	—
653	C₄	—	4	2	no	—
654	C₄	—	8	1	no	—
655	C₄	—	8	1	no	—
656	C₄	—	8	1	no	—
657	C₄	—	8	1	no	—
658	C₄	C₂₉×#529	1	1	yes	characteristic
659	C₄	C₂₉×#538	1	1	yes	characteristic
660	C₄	C₂₉×#554	1	1	yes	characteristic
661	C₄	C₂₉×#554	1	1	yes	characteristic
662	C₂	—	2	4	no	—
663	C₂	—	8	2	no	—
664	C₂	C₂₉×#2450	1	1	yes	characteristic
665	C₂	C₂×C₂₉×#476	1	1	yes	characteristic
666	C₂	C₂₉×#3083	1	1	yes	characteristic
667	C₂	C₂₉×#3295	1	1	yes	characteristic
668	C₂	C₂₉×#3298	1	1	yes	characteristic
669	C₂	C₂₉×#3308	1	1	yes	characteristic
670	C₂	C₂₉×#3318	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₄×C₂²⋊C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#2440	C₂	semidirect
3. C₂₉×#2100	C₂	semidirect
4. C₂₉×#2088	C₂	semidirect
5. C₂₉×#2065	C₂	semidirect
6. C₂₉×#2023	C₂	semidirect
7. C₂₉×#1987	C₂	semidirect
8. C₂₉×#1920	C₂	semidirect
11. C₂₉×#1864	C₂	semidirect
12. C₂₉×#1853	C₂	semidirect
13. C₂₉×#1850	C₂	semidirect
14. C₂₉×#1802	C₂	semidirect
15. C₂×C₂₉×#340	C₂	semidirect
77. C₂₉×#121	Q₈	semidirect
215. #26410	C₂₉	direct (N × H)
290. #2440	C₂×C₂₉	semidirect
292. #2100	C₂×C₂₉	semidirect
293. #2088	C₂×C₂₉	semidirect
294. #2065	C₂×C₂₉	semidirect
295. #2023	C₂×C₂₉	semidirect
296. #1987	C₂×C₂₉	semidirect
297. #1920	C₂×C₂₉	semidirect
300. #1864	C₂×C₂₉	semidirect
301. #1853	C₂×C₂₉	semidirect
302. #1850	C₂×C₂₉	semidirect
303. #1802	C₂×C₂₉	semidirect
304. C₂×#340	C₂×C₂₉	semidirect
412. #121	Q₈×C₂₉	semidirect
461. C₂₉	#26410	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×#2440	2
C₂₉×#2361	2
C₂₉×#2100	2
C₂₉×#2088	2
C₂₉×#2065	2
C₂₉×#2023	2
C₂₉×#1987	2
C₂₉×#1920	2
C₂₉×#1893	2
C₂₉×#1874	2
C₂₉×#1864	2
C₂₉×#1853	2
C₂₉×#1850	2
C₂₉×#1802	2
C₂×C₂₉×#340	2
#26410	29

Subgroups — C29×#26410 #20321310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#26410 #20321310