Subgroups — C₂₉×#28881 #20323781

Order 7424.

788 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#2514	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#2445	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2085	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2067	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2055	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2014	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#1973	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1968	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1961	C₂	1	1	yes	maximal, characteristic
10	C₂₉×#1935	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1934	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1926	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1770	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1762	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×#123	—	2	1	no	—
20	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
25	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×#102	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×#97	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
35	C₂₉×#401	—	2	1	no	—
36	C₂₉×#400	—	2	1	no	—
37	C₂₉×#394	—	2	1	no	—
38	C₂₉×#394	—	2	1	no	—
39	C₂₉×#391	C₂²	1	1	yes	characteristic
40	C₂₉×#391	C₂²	1	1	yes	characteristic
41	C₂₉×#391	C₂²	1	1	yes	characteristic
42	C₂₉×#390	C₂²	1	1	yes	characteristic
43	C₂₉×#390	C₂²	1	1	yes	characteristic
44	C₂₉×#390	C₂²	1	1	yes	characteristic
45	C₂₉×#389	C₂²	1	1	yes	characteristic
46	C₂₉×#389	C₂²	1	1	yes	characteristic
47	C₂₉×#387	—	2	1	no	—
48	C₂₉×#386	—	2	1	no	—
49	C₂₉×#383	—	2	1	no	—
50	C₂₉×#382	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×#336	C₂²	1	1	yes	characteristic
58	C₂₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₂₉	—	2	1	no	—
61	C₂²×D₄×C₂₉	—	2	1	no	—
62	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₂₉	—	2	1	no	—
65	C₂×SD₁₆×C₂₉	—	2	2	no	—
66	C₂×SD₁₆×C₂₉	—	2	2	no	—
67	C₂×SD₁₆×C₂₉	—	2	2	no	—
68	C₂×SD₁₆×C₂₉	—	4	1	no	—
69	C₂×SD₁₆×C₂₉	—	4	1	no	—
70	C₂×SD₁₆×C₂₉	—	4	1	no	—
71	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
75	C₂₉×#127	—	2	2	no	—
76	C₂₉×#127	—	4	1	no	—
77	C₂₉×#123	—	4	4	no	—
78	C₄×D₄×C₂₉	—	2	2	no	—
79	C₄×D₄×C₂₉	—	4	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×C₂²⋊C₄×C₂₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
100	C₂₉×#107	—	4	1	no	—
101	C₂₉×#106	—	4	1	no	—
102	C₂₉×C₄⋊C₈	—	2	2	no	—
103	C₂₉×#103	—	2	2	no	—
104	C₂₉×#103	—	4	1	no	—
105	C₂₉×#102	—	2	2	no	—
106	C₂₉×#102	—	2	2	no	—
107	C₂₉×#102	—	2	2	no	—
108	C₂₉×#102	—	2	2	no	—
109	C₂₉×#102	—	4	1	no	—
110	C₂₉×#102	—	4	1	no	—
111	C₂₉×#97	—	4	1	no	—
112	C₂₉×#97	—	4	1	no	—
113	C₄×C₈×C₂₉	—	2	2	no	—
114	C₂₉×#95	—	2	1	no	—
115	C₂₉×#95	—	2	1	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	—	2	1	no	—
124	C₂₉×#95	—	2	1	no	—
125	C₂₉×#95	D₄	1	1	yes	characteristic
126	C₂₉×#95	D₄	1	1	yes	characteristic
127	C₂⁴×C₂₉	—	2	1	no	—
128	C₂⁴×C₂₉	—	2	1	no	—
129	C₂×Q₈×C₂₉	—	2	1	no	—
130	C₂×Q₈×C₂₉	—	2	1	no	—
131	C₂×Q₈×C₂₉	—	2	1	no	—
132	C₂×Q₈×C₂₉	—	2	1	no	—
133	C₂×Q₈×C₂₉	—	2	1	no	—
134	C₂×Q₈×C₂₉	—	2	1	no	—
135	C₂×D₄×C₂₉	—	2	1	no	—
136	C₂×D₄×C₂₉	—	2	1	no	—
137	C₂×D₄×C₂₉	—	2	1	no	—
138	C₂×D₄×C₂₉	—	2	1	no	—
139	C₂×D₄×C₂₉	—	2	1	no	—
140	C₂×D₄×C₂₉	—	2	1	no	—
141	C₂×D₄×C₂₉	—	2	1	no	—
142	C₂×D₄×C₂₉	—	2	1	no	—
143	C₂×D₄×C₂₉	—	2	1	no	—
144	C₂×D₄×C₂₉	—	2	1	no	—
145	C₂×D₄×C₂₉	—	2	1	no	—
146	C₂×D₄×C₂₉	—	4	2	no	—
147	C₂×D₄×C₂₉	—	4	2	no	—
148	C₂×D₄×C₂₉	—	4	2	no	—
149	C₂×D₄×C₂₉	—	4	2	no	—
150	C₂×D₄×C₂₉	—	8	1	no	—
151	C₂×D₄×C₂₉	—	8	1	no	—
152	C₂×D₄×C₂₉	#41	1	2	yes	—
153	C₂²×C₄×C₂₉	—	2	1	no	—
154	C₂²×C₄×C₂₉	—	2	1	no	—
155	C₂²×C₄×C₂₉	—	2	1	no	—
156	C₂²×C₄×C₂₉	—	2	1	no	—
157	C₂²×C₄×C₂₉	—	2	1	no	—
158	C₂²×C₄×C₂₉	—	2	1	no	—
159	C₂²×C₄×C₂₉	—	4	2	no	—
160	C₂²×C₄×C₂₉	—	4	2	no	—
161	C₂²×C₄×C₂₉	—	8	1	no	—
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×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
169	SD₁₆×C₂₉	—	4	4	no	—
170	SD₁₆×C₂₉	—	4	4	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	#41	1	2	yes	—
181	C₂×C₈×C₂₉	#41	1	2	yes	—
182	C₂×C₈×C₂₉	#41	1	2	yes	—
183	C₄⋊C₄×C₂₉	—	2	2	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	—	2	1	no	—
193	C₄⋊C₄×C₂₉	—	2	1	no	—
194	C₄⋊C₄×C₂₉	—	4	1	no	—
195	C₄⋊C₄×C₂₉	—	4	2	no	—
196	C₄⋊C₄×C₂₉	—	4	2	no	—
197	C₂²⋊C₄×C₂₉	—	4	2	no	—
198	C₂²⋊C₄×C₂₉	—	4	2	no	—
199	C₂²⋊C₄×C₂₉	—	4	2	no	—
200	C₂²⋊C₄×C₂₉	—	4	2	no	—
201	C₂²⋊C₄×C₂₉	—	8	1	no	—
202	C₂²⋊C₄×C₂₉	—	8	1	no	—
203	C₂²⋊C₄×C₂₉	—	8	1	no	—
204	C₄²×C₂₉	—	2	1	no	—
205	C₄²×C₂₉	—	2	1	no	—
206	C₄²×C₂₉	—	2	1	no	—
207	C₄²×C₂₉	—	2	1	no	—
208	C₄²×C₂₉	—	2	1	no	—
209	C₄²×C₂₉	—	2	1	no	—
210	C₄²×C₂₉	—	4	2	no	—
211	#28881	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂³×C₂₉	—	2	2	no	—
213	C₂³×C₂₉	—	4	1	no	—
214	C₂³×C₂₉	—	4	1	no	—
215	C₂³×C₂₉	—	4	1	no	—
216	C₂³×C₂₉	—	4	1	no	—
217	C₂³×C₂₉	—	4	1	no	—
218	C₂³×C₂₉	—	4	1	no	—
219	C₂³×C₂₉	—	4	1	no	—
220	C₂³×C₂₉	—	4	1	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	C₂²×D₄	1	1	yes	characteristic
227	Q₈×C₂₉	—	4	1	no	—
228	Q₈×C₂₉	—	4	1	no	—
229	Q₈×C₂₉	—	4	1	no	—
230	Q₈×C₂₉	—	4	1	no	—
231	D₄×C₂₉	—	2	2	no	—
232	D₄×C₂₉	—	2	2	no	—
233	D₄×C₂₉	—	4	1	no	—
234	D₄×C₂₉	—	4	1	no	—
235	D₄×C₂₉	—	4	1	no	—
236	D₄×C₂₉	—	4	1	no	—
237	D₄×C₂₉	—	4	1	no	—
238	D₄×C₂₉	—	4	1	no	—
239	D₄×C₂₉	—	8	4	no	—
240	D₄×C₂₉	—	8	4	no	—
241	C₂×C₄×C₂₉	—	2	1	no	—
242	C₂×C₄×C₂₉	—	2	1	no	—
243	C₂×C₄×C₂₉	—	2	1	no	—
244	C₂×C₄×C₂₉	—	2	1	no	—
245	C₂×C₄×C₂₉	—	2	1	no	—
246	C₂×C₄×C₂₉	—	2	1	no	—
247	C₂×C₄×C₂₉	—	2	1	no	—
248	C₂×C₄×C₂₉	—	2	1	no	—
249	C₂×C₄×C₂₉	—	2	1	no	—
250	C₂×C₄×C₂₉	—	2	1	no	—
251	C₂×C₄×C₂₉	—	2	1	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	—	2	1	no	—
257	C₂×C₄×C₂₉	—	2	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	—	4	1	no	—
275	C₂×C₄×C₂₉	—	4	1	no	—
276	C₂×C₄×C₂₉	—	8	4	no	—
277	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
278	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
279	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
280	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
281	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
282	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
283	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
284	C₈×C₂₉	—	2	2	no	—
285	C₈×C₂₉	—	2	2	no	—
286	C₈×C₂₉	—	2	2	no	—
287	C₈×C₂₉	—	4	1	no	—
288	#2514	C₂×C₂₉	1	1	yes	characteristic, complemented
289	#2445	C₂×C₂₉	1	1	yes	characteristic
290	#2085	C₂×C₂₉	1	1	yes	characteristic, complemented
291	#2067	C₂×C₂₉	1	1	yes	characteristic, complemented
292	#2055	C₂×C₂₉	1	1	yes	characteristic, complemented
293	#2014	C₂×C₂₉	1	1	yes	characteristic
294	#1973	C₂×C₂₉	1	1	yes	characteristic, complemented
295	#1968	C₂×C₂₉	1	1	yes	characteristic, complemented
296	#1961	C₂×C₂₉	1	1	yes	characteristic
297	#1935	C₂×C₂₉	1	1	yes	characteristic, complemented
298	#1934	C₂×C₂₉	1	1	yes	characteristic, complemented
299	#1926	C₂×C₂₉	1	1	yes	characteristic, complemented
300	#1877	C₂×C₂₉	1	1	yes	characteristic, complemented
301	#1770	C₂×C₂₉	1	1	yes	characteristic, complemented
302	#1762	C₂×C₂₉	1	1	yes	characteristic, complemented
303	C₂²×C₂₉	—	4	2	no	—
304	C₂²×C₂₉	—	4	2	no	—
305	C₂²×C₂₉	—	4	2	no	—
306	C₂²×C₂₉	—	8	1	no	—
307	C₂²×C₂₉	—	8	1	no	—
308	C₂²×C₂₉	—	8	1	no	—
309	C₂²×C₂₉	—	8	1	no	—
310	C₂²×C₂₉	—	8	1	no	—
311	C₂²×C₂₉	—	8	1	no	—
312	C₂²×C₂₉	—	8	1	no	—
313	C₂²×C₂₉	—	8	1	no	—
314	C₂²×C₂₉	—	8	1	no	—
315	C₂²×C₂₉	—	8	1	no	—
316	C₂²×C₂₉	—	8	1	no	—
317	C₂²×C₂₉	#532	1	1	yes	characteristic
318	C₂²×C₂₉	#546	1	1	yes	characteristic
319	C₂²×C₂₉	#550	1	1	yes	characteristic
320	C₂²×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
321	C₂²×C₂₉	#575	1	1	yes	characteristic
322	C₂²×C₂₉	#577	1	1	yes	characteristic
323	C₂²×C₂₉	#577	1	1	yes	characteristic
324	C₄×C₂₉	—	2	2	no	—
325	C₄×C₂₉	—	4	1	no	—
326	C₄×C₂₉	—	4	1	no	—
327	C₄×C₂₉	—	4	1	no	—
328	C₄×C₂₉	—	4	1	no	—
329	C₄×C₂₉	—	4	1	no	—
330	C₄×C₂₉	—	8	1	no	—
331	C₄×C₂₉	—	8	1	no	—
332	C₄×C₂₉	—	8	1	no	—
333	C₄×C₂₉	—	8	1	no	—
334	C₄×C₂₉	—	8	1	no	—
335	C₄×C₂₉	—	8	1	no	—
336	C₄×C₂₉	#529	1	1	yes	characteristic
337	C₄×C₂₉	#538	1	1	yes	characteristic
338	C₄×C₂₉	#551	1	1	yes	characteristic
339	C₄×C₂₉	#553	1	1	yes	characteristic
340	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
341	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
342	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
343	C₂×#123	—	2	1	no	—
344	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
345	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
346	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
347	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
348	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
349	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
350	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
351	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
352	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
353	C₂×#102	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×#97	C₂²×C₂₉	1	1	yes	characteristic
357	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
358	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
359	#401	—	2	1	no	—
360	#400	—	2	1	no	—
361	#394	—	2	1	no	—
362	#394	—	2	1	no	—
363	#391	C₂²×C₂₉	1	1	yes	characteristic
364	#391	C₂²×C₂₉	1	1	yes	characteristic
365	#391	C₂²×C₂₉	1	1	yes	characteristic
366	#390	C₂²×C₂₉	1	1	yes	characteristic
367	#390	C₂²×C₂₉	1	1	yes	characteristic
368	#390	C₂²×C₂₉	1	1	yes	characteristic
369	#389	C₂²×C₂₉	1	1	yes	characteristic
370	#389	C₂²×C₂₉	1	1	yes	characteristic
371	#387	—	2	1	no	—
372	#386	—	2	1	no	—
373	#383	—	2	1	no	—
374	#382	C₂²×C₂₉	1	1	yes	characteristic
375	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
376	C₄×C₄⋊C₄	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	#336	C₂²×C₂₉	1	1	yes	characteristic
382	#336	C₂²×C₂₉	1	1	yes	characteristic
383	C₂×C₂₉	—	8	2	no	—
384	C₂×C₂₉	—	16	1	no	—
385	C₂×C₂₉	#2554	1	1	yes	characteristic
386	C₂×C₂₉	#3174	1	1	yes	characteristic
387	C₂×C₂₉	#3180	1	1	yes	characteristic
388	C₂×C₂₉	#3323	1	1	yes	characteristic
389	C₂×C₂₉	#3324	1	1	yes	characteristic
390	C₂×C₂₉	#3397	1	1	yes	characteristic
391	C₂×C₂₉	#3401	1	1	yes	characteristic
392	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
393	C₂²×D₄	—	2	1	no	—
394	C₂²×D₄	—	2	1	no	—
395	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
396	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
397	C₂³×C₄	—	2	1	no	—
398	C₂×SD₁₆	—	2	2	no	—
399	C₂×SD₁₆	—	2	2	no	—
400	C₂×SD₁₆	—	2	2	no	—
401	C₂×SD₁₆	—	4	1	no	—
402	C₂×SD₁₆	—	4	1	no	—
403	C₂×SD₁₆	—	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	#127	—	2	2	no	—
409	#127	—	4	1	no	—
410	#123	—	4	4	no	—
411	C₄×D₄	—	2	2	no	—
412	C₄×D₄	—	4	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
416	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₄²	—	2	1	no	—
430	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
433	#107	—	4	1	no	—
434	#106	—	4	1	no	—
435	C₄⋊C₈	—	2	2	no	—
436	#103	—	2	2	no	—
437	#103	—	4	1	no	—
438	#102	—	2	2	no	—
439	#102	—	2	2	no	—
440	#102	—	2	2	no	—
441	#102	—	2	2	no	—
442	#102	—	4	1	no	—
443	#102	—	4	1	no	—
444	#97	—	4	1	no	—
445	#97	—	4	1	no	—
446	C₄×C₈	—	2	2	no	—
447	#95	—	2	1	no	—
448	#95	—	2	1	no	—
449	#95	—	2	1	no	—
450	#95	—	2	1	no	—
451	#95	—	2	1	no	—
452	#95	—	2	1	no	—
453	#95	—	2	1	no	—
454	#95	—	2	1	no	—
455	#95	—	2	1	no	—
456	#95	—	2	1	no	—
457	#95	—	2	1	no	—
458	#95	D₄×C₂₉	1	1	yes	characteristic
459	#95	D₄×C₂₉	1	1	yes	characteristic
460	C₂₉	#28881	1	1	yes	characteristic, direct product factor, Sylow
461	C₂⁴	—	2	1	no	—
462	C₂⁴	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	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	—	2	1	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	4	2	no	—
481	C₂×D₄	—	4	2	no	—
482	C₂×D₄	—	4	2	no	—
483	C₂×D₄	—	4	2	no	—
484	C₂×D₄	—	8	1	no	—
485	C₂×D₄	—	8	1	no	—
486	C₂×D₄	#41×C₂₉	1	2	yes	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	4	2	no	—
494	C₂²×C₄	—	4	2	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×D₄×C₂₉	1	1	yes	characteristic
502	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
503	SD₁₆	—	4	4	no	—
504	SD₁₆	—	4	4	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	#41×C₂₉	1	2	yes	—
515	C₂×C₈	#41×C₂₉	1	2	yes	—
516	C₂×C₈	#41×C₂₉	1	2	yes	—
517	C₄⋊C₄	—	2	2	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	1	no	—
529	C₄⋊C₄	—	4	2	no	—
530	C₄⋊C₄	—	4	2	no	—
531	C₂²⋊C₄	—	4	2	no	—
532	C₂²⋊C₄	—	4	2	no	—
533	C₂²⋊C₄	—	4	2	no	—
534	C₂²⋊C₄	—	4	2	no	—
535	C₂²⋊C₄	—	8	1	no	—
536	C₂²⋊C₄	—	8	1	no	—
537	C₂²⋊C₄	—	8	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	4	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	4	1	no	—
547	C₂³	—	4	1	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	4	1	no	—
550	C₂³	—	4	1	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	4	1	no	—
554	C₂³	—	4	1	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	4	1	no	—
559	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
560	Q₈	—	4	1	no	—
561	Q₈	—	4	1	no	—
562	Q₈	—	4	1	no	—
563	Q₈	—	4	1	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	2	no	—
566	D₄	—	4	1	no	—
567	D₄	—	4	1	no	—
568	D₄	—	4	1	no	—
569	D₄	—	4	1	no	—
570	D₄	—	4	1	no	—
571	D₄	—	4	1	no	—
572	D₄	—	8	4	no	—
573	D₄	—	8	4	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	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	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	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
611	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
612	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
613	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
614	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
615	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
616	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
617	C₈	—	2	2	no	—
618	C₈	—	2	2	no	—
619	C₈	—	2	2	no	—
620	C₈	—	4	1	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	8	1	no	—
625	C₂²	—	8	1	no	—
626	C₂²	—	8	1	no	—
627	C₂²	—	8	1	no	—
628	C₂²	—	8	1	no	—
629	C₂²	—	8	1	no	—
630	C₂²	—	8	1	no	—
631	C₂²	—	8	1	no	—
632	C₂²	—	8	1	no	—
633	C₂²	—	8	1	no	—
634	C₂²	—	8	1	no	—
635	C₂²	C₂₉×#532	1	1	yes	characteristic
636	C₂²	C₂₉×#546	1	1	yes	characteristic
637	C₂²	C₂₉×#550	1	1	yes	characteristic
638	C₂²	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
639	C₂²	C₂₉×#575	1	1	yes	characteristic
640	C₂²	C₂₉×#577	1	1	yes	characteristic
641	C₂²	C₂₉×#577	1	1	yes	characteristic
642	C₄	—	2	2	no	—
643	C₄	—	4	1	no	—
644	C₄	—	4	1	no	—
645	C₄	—	4	1	no	—
646	C₄	—	4	1	no	—
647	C₄	—	4	1	no	—
648	C₄	—	8	1	no	—
649	C₄	—	8	1	no	—
650	C₄	—	8	1	no	—
651	C₄	—	8	1	no	—
652	C₄	—	8	1	no	—
653	C₄	—	8	1	no	—
654	C₄	C₂₉×#529	1	1	yes	characteristic
655	C₄	C₂₉×#538	1	1	yes	characteristic
656	C₄	C₂₉×#551	1	1	yes	characteristic
657	C₄	C₂₉×#553	1	1	yes	characteristic
658	C₂	—	8	2	no	—
659	C₂	—	16	1	no	—
660	C₂	C₂₉×#2554	1	1	yes	characteristic
661	C₂	C₂₉×#3174	1	1	yes	characteristic
662	C₂	C₂₉×#3180	1	1	yes	characteristic
663	C₂	C₂₉×#3323	1	1	yes	characteristic
664	C₂	C₂₉×#3324	1	1	yes	characteristic
665	C₂	C₂₉×#3397	1	1	yes	characteristic
666	C₂	C₂₉×#3401	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#127	C₂²
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. C₂₉×#2514	C₂	semidirect
3. C₂₉×#2085	C₂	semidirect
4. C₂₉×#2067	C₂	semidirect
5. C₂₉×#2055	C₂	semidirect
7. C₂₉×#1973	C₂	semidirect
8. C₂₉×#1968	C₂	semidirect
10. C₂₉×#1935	C₂	semidirect
11. C₂₉×#1934	C₂	semidirect
12. C₂₉×#1926	C₂	semidirect
13. C₂₉×#1877	C₂	semidirect
14. C₂₉×#1770	C₂	semidirect
15. C₂₉×#1762	C₂	semidirect
211. #28881	C₂₉	direct (N × H)
288. #2514	C₂×C₂₉	semidirect
290. #2085	C₂×C₂₉	semidirect
291. #2067	C₂×C₂₉	semidirect
292. #2055	C₂×C₂₉	semidirect
294. #1973	C₂×C₂₉	semidirect
295. #1968	C₂×C₂₉	semidirect
297. #1935	C₂×C₂₉	semidirect
298. #1934	C₂×C₂₉	semidirect
299. #1926	C₂×C₂₉	semidirect
300. #1877	C₂×C₂₉	semidirect
301. #1770	C₂×C₂₉	semidirect
302. #1762	C₂×C₂₉	semidirect
460. C₂₉	#28881	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×#2514	2
C₂₉×#2445	2
C₂₉×#2085	2
C₂₉×#2067	2
C₂₉×#2055	2
C₂₉×#2014	2
C₂₉×#1973	2
C₂₉×#1968	2
C₂₉×#1961	2
C₂₉×#1935	2
C₂₉×#1934	2
C₂₉×#1926	2
C₂₉×#1877	2
C₂₉×#1770	2
C₂₉×#1762	2
#28881	29

Subgroups — C29×#28881 #20323781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#28881 #20323781