Subgroups — C₂₉×#26144 #20321044

Order 7424.

904 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#483	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#2415	C₂	1	1	yes	maximal, characteristic
4	D₄×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#2095	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2084	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2075	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1928	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1919	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1894	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1872	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1870	C₂	1	1	yes	maximal, characteristic
14	C₂₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1852	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₂₉	—	2	1	no	—
20	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#117	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	C₂₉×#483	—	2	4	no	—
25	C₂₉×#428	—	2	4	no	—
26	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
34	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
35	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
36	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂₉×#397	—	2	1	no	—
40	C₂₉×#394	—	2	1	no	—
41	C₂₉×#391	C₂²	1	1	yes	characteristic
42	C₂₉×#389	—	2	1	no	—
43	C₂₉×#389	—	2	1	no	—
44	C₂₉×#389	C₂²	1	1	yes	characteristic
45	C₂₉×#388	—	2	1	no	—
46	C₂₉×#385	—	2	1	no	—
47	C₂₉×#385	—	2	1	no	—
48	C₂₉×#384	C₂²	1	1	yes	characteristic
49	C₂₉×#380	C₂²	1	1	yes	characteristic
50	C₂₉×#380	C₂²	1	1	yes	characteristic
51	C₂₉×#380	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	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₂₉	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₂₉	—	2	1	no	—
64	C₂³×C₄×C₂₉	—	2	1	no	—
65	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₂₉	—	2	2	no	—
68	C₂×M₁₆×C₂₉	—	2	2	no	—
69	C₂×M₁₆×C₂₉	—	2	2	no	—
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	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
74	C₂₉×C₂²⋊Q₈	—	2	2	no	—
75	C₂₉×C₂²⋊Q₈	—	2	2	no	—
76	C₂₉×C₂²⋊Q₈	—	2	2	no	—
77	C₂₉×C₂²⋊Q₈	—	4	1	no	—
78	C₄×D₄×C₂₉	—	2	2	no	—
79	C₄×D₄×C₂₉	—	2	2	no	—
80	C₄×D₄×C₂₉	—	4	4	no	—
81	C₂₉×#117	—	2	2	no	—
82	C₂₉×#117	—	4	1	no	—
83	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
84	C₂×C₄⋊C₄×C₂₉	—	2	2	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	—	2	1	no	—
92	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
93	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
94	C₂×C₄⋊C₄×C₂₉	D₄	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×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₂₉	—	2	1	no	—
111	C₂×C₄²×C₂₉	—	2	1	no	—
112	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
113	C₂₉×#107	—	2	2	no	—
114	C₂₉×#107	—	2	2	no	—
115	C₂₉×#107	—	4	1	no	—
116	C₂₉×#106	—	2	2	no	—
117	C₂₉×#106	—	2	2	no	—
118	C₂₉×#106	D₄	1	4	yes	complemented
119	C₂₉×#103	—	2	2	no	—
120	C₂₉×#103	—	2	2	no	—
121	C₂₉×#103	—	2	2	no	—
122	C₂₉×#103	—	4	1	no	—
123	C₂₉×C₂²⋊C₈	—	2	2	no	—
124	C₂₉×C₂²⋊C₈	—	2	2	no	—
125	C₂₉×C₂²⋊C₈	—	2	2	no	—
126	C₂₉×#95	—	2	1	no	—
127	C₂₉×#95	—	2	1	no	—
128	C₂₉×#95	—	2	1	no	—
129	C₂₉×#95	—	2	1	no	—
130	C₂₉×#95	—	2	1	no	—
131	C₂₉×#95	—	2	1	no	—
132	C₂₉×#95	—	2	1	no	—
133	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
134	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
135	C₂×Q₈×C₂₉	—	2	1	no	—
136	C₂×Q₈×C₂₉	—	2	1	no	—
137	C₂×Q₈×C₂₉	—	2	1	no	—
138	C₂×Q₈×C₂₉	—	2	1	no	—
139	C₂×Q₈×C₂₉	—	2	1	no	—
140	C₂×Q₈×C₂₉	—	2	1	no	—
141	C₂×D₄×C₂₉	—	2	2	no	—
142	C₂×D₄×C₂₉	—	2	2	no	—
143	C₂×D₄×C₂₉	—	2	2	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	—	2	1	no	—
152	C₂²×C₄×C₂₉	—	2	1	no	—
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	—	2	1	no	—
160	C₂²×C₄×C₂₉	—	2	1	no	—
161	C₂²×C₄×C₂₉	—	2	1	no	—
162	C₂²×C₄×C₂₉	—	4	2	no	—
163	C₂²×C₄×C₂₉	—	4	2	no	—
164	C₂²×C₄×C₂₉	—	4	2	no	—
165	C₂²×C₄×C₂₉	—	4	2	no	—
166	C₂²×C₄×C₂₉	—	8	1	no	—
167	C₂²×C₄×C₂₉	—	8	1	no	—
168	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₂₉	#41	1	2	yes	—
173	C₂²×C₄×C₂₉	#41	1	2	yes	—
174	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
175	M₁₆×C₂₉	—	2	8	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	—	2	1	no	—
181	C₂×C₈×C₂₉	—	2	1	no	—
182	C₂×C₈×C₂₉	—	2	1	no	—
183	C₂×C₈×C₂₉	—	2	1	no	—
184	C₂×C₈×C₂₉	—	2	1	no	—
185	C₂×C₈×C₂₉	—	2	1	no	—
186	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
187	C₂×C₈×C₂₉	#41	1	2	yes	—
188	C₄⋊C₄×C₂₉	—	2	2	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	—	2	1	no	—
195	C₄⋊C₄×C₂₉	—	2	1	no	—
196	C₄⋊C₄×C₂₉	—	2	1	no	—
197	C₄⋊C₄×C₂₉	—	2	1	no	—
198	C₄⋊C₄×C₂₉	—	2	1	no	—
199	C₄⋊C₄×C₂₉	—	2	1	no	—
200	C₄⋊C₄×C₂₉	—	2	1	no	—
201	C₄⋊C₄×C₂₉	—	4	2	no	—
202	C₄⋊C₄×C₂₉	—	4	2	no	—
203	C₄⋊C₄×C₂₉	—	4	2	no	—
204	C₄⋊C₄×C₂₉	—	4	2	no	—
205	C₄⋊C₄×C₂₉	—	4	2	no	—
206	C₄⋊C₄×C₂₉	—	4	2	no	—
207	C₄⋊C₄×C₂₉	—	8	1	no	—
208	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
209	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
210	C₂²⋊C₄×C₂₉	—	2	2	no	—
211	C₂²⋊C₄×C₂₉	—	2	2	no	—
212	C₂²⋊C₄×C₂₉	—	4	2	no	—
213	C₂²⋊C₄×C₂₉	—	4	2	no	—
214	C₂²⋊C₄×C₂₉	—	4	2	no	—
215	C₂²⋊C₄×C₂₉	—	4	2	no	—
216	C₂²⋊C₄×C₂₉	—	4	2	no	—
217	C₂²⋊C₄×C₂₉	—	4	2	no	—
218	C₄²×C₂₉	—	2	1	no	—
219	C₄²×C₂₉	—	2	1	no	—
220	C₄²×C₂₉	—	4	2	no	—
221	C₄²×C₂₉	—	4	2	no	—
222	#26144	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂³×C₂₉	—	2	1	no	—
224	C₂³×C₂₉	—	2	1	no	—
225	C₂³×C₂₉	—	2	1	no	—
226	C₂³×C₂₉	—	2	1	no	—
227	C₂³×C₂₉	—	2	1	no	—
228	C₂³×C₂₉	—	2	1	no	—
229	C₂³×C₂₉	—	2	1	no	—
230	C₂³×C₂₉	—	2	1	no	—
231	C₂³×C₂₉	—	2	1	no	—
232	C₂³×C₂₉	—	2	1	no	—
233	C₂³×C₂₉	—	2	1	no	—
234	C₂³×C₂₉	—	2	1	no	—
235	C₂³×C₂₉	#123	1	2	yes	—
236	C₂³×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
237	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
238	Q₈×C₂₉	—	4	1	no	—
239	Q₈×C₂₉	—	4	1	no	—
240	Q₈×C₂₉	—	4	1	no	—
241	Q₈×C₂₉	—	4	1	no	—
242	D₄×C₂₉	—	2	8	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	2	no	—
248	C₂×C₄×C₂₉	—	2	2	no	—
249	C₂×C₄×C₂₉	—	2	2	no	—
250	C₂×C₄×C₂₉	—	2	2	no	—
251	C₂×C₄×C₂₉	—	2	1	no	—
252	C₂×C₄×C₂₉	—	2	1	no	—
253	C₂×C₄×C₂₉	—	2	2	no	—
254	C₂×C₄×C₂₉	—	2	2	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	—	2	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	—	4	1	no	—
277	C₂×C₄×C₂₉	—	4	1	no	—
278	C₂×C₄×C₂₉	—	4	1	no	—
279	C₂×C₄×C₂₉	—	4	1	no	—
280	C₂×C₄×C₂₉	—	4	1	no	—
281	C₂×C₄×C₂₉	—	4	1	no	—
282	C₂×C₄×C₂₉	—	4	1	no	—
283	C₂×C₄×C₂₉	—	4	1	no	—
284	C₂×C₄×C₂₉	—	4	1	no	—
285	C₂×C₄×C₂₉	—	8	4	no	—
286	C₂×C₄×C₂₉	—	8	4	no	—
287	C₂×C₄×C₂₉	#123	1	2	yes	—
288	C₂×C₄×C₂₉	#137	1	2	yes	—
289	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
292	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
293	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
294	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
295	C₈×C₂₉	—	2	2	no	—
296	C₈×C₂₉	—	2	2	no	—
297	C₈×C₂₉	—	4	1	no	—
298	C₈×C₂₉	—	4	1	no	—
299	C₂×#483	C₂×C₂₉	1	1	yes	characteristic, complemented
300	C₂×#428	C₂×C₂₉	1	1	yes	characteristic, complemented
301	#2415	C₂×C₂₉	1	1	yes	characteristic
302	D₄×C₄⋊C₄	C₂×C₂₉	1	1	yes	characteristic
303	#2095	C₂×C₂₉	1	1	yes	characteristic, complemented
304	#2084	C₂×C₂₉	1	1	yes	characteristic, complemented
305	#2075	C₂×C₂₉	1	1	yes	characteristic, complemented
306	#2035	C₂×C₂₉	1	1	yes	characteristic, complemented
307	#1928	C₂×C₂₉	1	1	yes	characteristic, complemented
308	#1919	C₂×C₂₉	1	1	yes	characteristic, complemented
309	#1894	C₂×C₂₉	1	1	yes	characteristic, complemented
310	#1872	C₂×C₂₉	1	1	yes	characteristic, complemented
311	#1870	C₂×C₂₉	1	1	yes	characteristic
312	#1854	C₂×C₂₉	1	1	yes	characteristic, complemented
313	#1852	C₂×C₂₉	1	1	yes	characteristic, complemented
314	C₂²×C₂₉	—	2	2	no	—
315	C₂²×C₂₉	—	2	2	no	—
316	C₂²×C₂₉	—	2	2	no	—
317	C₂²×C₂₉	—	2	2	no	—
318	C₂²×C₂₉	—	2	2	no	—
319	C₂²×C₂₉	—	2	2	no	—
320	C₂²×C₂₉	—	4	1	no	—
321	C₂²×C₂₉	—	4	1	no	—
322	C₂²×C₂₉	—	4	1	no	—
323	C₂²×C₂₉	—	4	1	no	—
324	C₂²×C₂₉	—	4	1	no	—
325	C₂²×C₂₉	—	4	1	no	—
326	C₂²×C₂₉	—	4	1	no	—
327	C₂²×C₂₉	—	4	1	no	—
328	C₂²×C₂₉	C₂×#123	1	1	yes	characteristic
329	C₂²×C₂₉	D₄²	1	1	yes	characteristic
330	C₂²×C₂₉	#547	1	1	yes	characteristic
331	C₂²×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
332	C₂²×C₂₉	C₂×#137	1	1	yes	characteristic
333	C₂²×C₂₉	#577	1	1	yes	characteristic
334	C₂²×C₂₉	#578	1	1	yes	characteristic
335	C₄×C₂₉	—	2	2	no	—
336	C₄×C₂₉	—	2	2	no	—
337	C₄×C₂₉	—	4	1	no	—
338	C₄×C₂₉	—	4	1	no	—
339	C₄×C₂₉	—	4	2	no	—
340	C₄×C₂₉	—	4	2	no	—
341	C₄×C₂₉	—	8	1	no	—
342	C₄×C₂₉	—	8	1	no	—
343	C₄×C₂₉	—	8	1	no	—
344	C₄×C₂₉	—	8	1	no	—
345	C₄×C₂₉	—	8	1	no	—
346	C₄×C₂₉	—	8	1	no	—
347	C₄×C₂₉	#525	1	1	yes	characteristic
348	C₄×C₂₉	#539	1	1	yes	characteristic
349	C₄×C₂₉	#548	1	1	yes	characteristic
350	C₄×C₂₉	#553	1	1	yes	characteristic
351	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
352	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
353	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
354	C₂×C₄×D₄	—	2	1	no	—
355	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
356	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
357	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
358	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
359	#483	—	2	4	no	—
360	#428	—	2	4	no	—
361	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
362	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
363	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
364	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
365	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
366	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
367	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
368	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
369	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
370	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
371	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
372	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
373	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
374	#397	—	2	1	no	—
375	#394	—	2	1	no	—
376	#391	C₂²×C₂₉	1	1	yes	characteristic
377	#389	—	2	1	no	—
378	#389	—	2	1	no	—
379	#389	C₂²×C₂₉	1	1	yes	characteristic
380	#388	—	2	1	no	—
381	#385	—	2	1	no	—
382	#385	—	2	1	no	—
383	#384	C₂²×C₂₉	1	1	yes	characteristic
384	#380	C₂²×C₂₉	1	1	yes	characteristic
385	#380	C₂²×C₂₉	1	1	yes	characteristic
386	#380	C₂²×C₂₉	1	1	yes	characteristic
387	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
388	#340	C₂²×C₂₉	1	1	yes	characteristic
389	#340	C₂²×C₂₉	1	1	yes	characteristic
390	#340	C₂²×C₂₉	1	1	yes	characteristic
391	#340	C₂²×C₂₉	1	1	yes	characteristic
392	#340	C₂²×C₂₉	1	1	yes	characteristic
393	#340	C₂²×C₂₉	1	1	yes	characteristic
394	#336	C₂²×C₂₉	1	1	yes	characteristic
395	#336	C₂²×C₂₉	1	1	yes	characteristic
396	C₂×C₂₉	—	4	2	no	—
397	C₂×C₂₉	—	4	2	no	—
398	C₂×C₂₉	#2443	1	1	yes	characteristic
399	C₂×C₂₉	#3092	1	1	yes	characteristic
400	C₂×C₂₉	#3097	1	1	yes	characteristic
401	C₂×C₂₉	#3265	1	1	yes	characteristic
402	C₂×C₂₉	#3276	1	1	yes	characteristic
403	C₂×C₂₉	#3343	1	1	yes	characteristic
404	C₂×C₂₉	#3356	1	1	yes	characteristic
405	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
406	C₂²×D₄	D₄×C₂₉	1	1	yes	characteristic
407	C₂³×C₄	—	2	1	no	—
408	C₂³×C₄	—	2	1	no	—
409	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
410	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
411	C₂×M₁₆	—	2	2	no	—
412	C₂×M₁₆	—	2	2	no	—
413	C₂×M₁₆	—	2	2	no	—
414	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
415	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
416	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
417	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
418	C₂²⋊Q₈	—	2	2	no	—
419	C₂²⋊Q₈	—	2	2	no	—
420	C₂²⋊Q₈	—	2	2	no	—
421	C₂²⋊Q₈	—	4	1	no	—
422	C₄×D₄	—	2	2	no	—
423	C₄×D₄	—	2	2	no	—
424	C₄×D₄	—	4	4	no	—
425	#117	—	2	2	no	—
426	#117	—	4	1	no	—
427	C₂×C₄⋊C₄	—	2	2	no	—
428	C₂×C₄⋊C₄	—	2	2	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	—	4	1	no	—
437	C₂×C₄⋊C₄	—	4	1	no	—
438	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
453	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
454	C₂×C₄²	—	2	1	no	—
455	C₂×C₄²	—	2	1	no	—
456	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
457	#107	—	2	2	no	—
458	#107	—	2	2	no	—
459	#107	—	4	1	no	—
460	#106	—	2	2	no	—
461	#106	—	2	2	no	—
462	#106	D₄×C₂₉	1	4	yes	complemented
463	#103	—	2	2	no	—
464	#103	—	2	2	no	—
465	#103	—	2	2	no	—
466	#103	—	4	1	no	—
467	C₂²⋊C₈	—	2	2	no	—
468	C₂²⋊C₈	—	2	2	no	—
469	C₂²⋊C₈	—	2	2	no	—
470	#95	—	2	1	no	—
471	#95	—	2	1	no	—
472	#95	—	2	1	no	—
473	#95	—	2	1	no	—
474	#95	—	2	1	no	—
475	#95	—	2	1	no	—
476	#95	—	2	1	no	—
477	C₂₉	#26144	1	1	yes	characteristic, direct product factor, Sylow
478	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
479	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×D₄	—	2	2	no	—
487	C₂×D₄	—	2	2	no	—
488	C₂×D₄	—	2	2	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	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	4	2	no	—
508	C₂²×C₄	—	4	2	no	—
509	C₂²×C₄	—	4	2	no	—
510	C₂²×C₄	—	4	2	no	—
511	C₂²×C₄	—	8	1	no	—
512	C₂²×C₄	—	8	1	no	—
513	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
514	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
515	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
516	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
517	C₂²×C₄	#41×C₂₉	1	2	yes	—
518	C₂²×C₄	#41×C₂₉	1	2	yes	—
519	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
520	M₁₆	—	2	8	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
532	C₂×C₈	#41×C₂₉	1	2	yes	—
533	C₄⋊C₄	—	2	2	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	4	2	no	—
547	C₄⋊C₄	—	4	2	no	—
548	C₄⋊C₄	—	4	2	no	—
549	C₄⋊C₄	—	4	2	no	—
550	C₄⋊C₄	—	4	2	no	—
551	C₄⋊C₄	—	4	2	no	—
552	C₄⋊C₄	—	8	1	no	—
553	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
554	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
555	C₂²⋊C₄	—	2	2	no	—
556	C₂²⋊C₄	—	2	2	no	—
557	C₂²⋊C₄	—	4	2	no	—
558	C₂²⋊C₄	—	4	2	no	—
559	C₂²⋊C₄	—	4	2	no	—
560	C₂²⋊C₄	—	4	2	no	—
561	C₂²⋊C₄	—	4	2	no	—
562	C₂²⋊C₄	—	4	2	no	—
563	C₄²	—	2	1	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	4	2	no	—
566	C₄²	—	4	2	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	—	2	1	no	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	1	no	—
579	C₂³	C₂₉×#123	1	2	yes	—
580	C₂³	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
581	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
582	Q₈	—	4	1	no	—
583	Q₈	—	4	1	no	—
584	Q₈	—	4	1	no	—
585	Q₈	—	4	1	no	—
586	D₄	—	2	8	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	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	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	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	8	4	no	—
630	C₂×C₄	—	8	4	no	—
631	C₂×C₄	C₂₉×#123	1	2	yes	—
632	C₂×C₄	C₂₉×#137	1	2	yes	—
633	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
634	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
635	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
636	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
637	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
638	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
639	C₈	—	2	2	no	—
640	C₈	—	2	2	no	—
641	C₈	—	4	1	no	—
642	C₈	—	4	1	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	1	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	4	1	no	—
655	C₂²	—	4	1	no	—
656	C₂²	—	4	1	no	—
657	C₂²	C₂×C₂₉×#123	1	1	yes	characteristic
658	C₂²	D₄²×C₂₉	1	1	yes	characteristic
659	C₂²	C₂₉×#547	1	1	yes	characteristic
660	C₂²	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
661	C₂²	C₂×C₂₉×#137	1	1	yes	characteristic
662	C₂²	C₂₉×#577	1	1	yes	characteristic
663	C₂²	C₂₉×#578	1	1	yes	characteristic
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	2	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	1	no	—
670	C₄	—	8	1	no	—
671	C₄	—	8	1	no	—
672	C₄	—	8	1	no	—
673	C₄	—	8	1	no	—
674	C₄	—	8	1	no	—
675	C₄	—	8	1	no	—
676	C₄	C₂₉×#525	1	1	yes	characteristic
677	C₄	C₂₉×#539	1	1	yes	characteristic
678	C₄	C₂₉×#548	1	1	yes	characteristic
679	C₄	C₂₉×#553	1	1	yes	characteristic
680	C₂	—	4	2	no	—
681	C₂	—	4	2	no	—
682	C₂	C₂₉×#2443	1	1	yes	characteristic
683	C₂	C₂₉×#3092	1	1	yes	characteristic
684	C₂	C₂₉×#3097	1	1	yes	characteristic
685	C₂	C₂₉×#3265	1	1	yes	characteristic
686	C₂	C₂₉×#3276	1	1	yes	characteristic
687	C₂	C₂₉×#3343	1	1	yes	characteristic
688	C₂	C₂₉×#3356	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	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₄×D₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#483	C₂	semidirect
2. C₂×C₂₉×#428	C₂	semidirect
5. C₂₉×#2095	C₂	semidirect
6. C₂₉×#2084	C₂	semidirect
7. C₂₉×#2075	C₂	semidirect
8. C₂₉×#2035	C₂	semidirect
9. C₂₉×#1928	C₂	semidirect
10. C₂₉×#1919	C₂	semidirect
11. C₂₉×#1894	C₂	semidirect
12. C₂₉×#1872	C₂	semidirect
14. C₂₉×#1854	C₂	semidirect
15. C₂₉×#1852	C₂	semidirect
118. C₂₉×#106	D₄	semidirect
222. #26144	C₂₉	direct (N × H)
299. C₂×#483	C₂×C₂₉	semidirect
300. C₂×#428	C₂×C₂₉	semidirect
303. #2095	C₂×C₂₉	semidirect
304. #2084	C₂×C₂₉	semidirect
305. #2075	C₂×C₂₉	semidirect
306. #2035	C₂×C₂₉	semidirect
307. #1928	C₂×C₂₉	semidirect
308. #1919	C₂×C₂₉	semidirect
309. #1894	C₂×C₂₉	semidirect
310. #1872	C₂×C₂₉	semidirect
312. #1854	C₂×C₂₉	semidirect
313. #1852	C₂×C₂₉	semidirect
462. #106	D₄×C₂₉	semidirect
477. C₂₉	#26144	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×#483	2
C₂×C₂₉×#428	2
C₂₉×#2415	2
D₄×C₄⋊C₄×C₂₉	2
C₂₉×#2095	2
C₂₉×#2084	2
C₂₉×#2075	2
C₂₉×#2035	2
C₂₉×#1928	2
C₂₉×#1919	2
C₂₉×#1894	2
C₂₉×#1872	2
C₂₉×#1870	2
C₂₉×#1854	2
C₂₉×#1852	2
#26144	29

Subgroups — C29×#26144 #20321044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#26144 #20321044