Subgroups — C₂₉×#26149 #20321049

Order 7424.

868 conjugacy classes of subgroups.

The subgroup lattice has 684 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×#2417	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2352	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#2097	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2085	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2076	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2036	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1927	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×#1873	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1870	C₂	1	1	yes	maximal, characteristic
14	C₂₉×#1853	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1853	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	C₂²	1	1	yes	characteristic
20	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
23	C₂₉×#483	—	2	4	no	—
24	C₂₉×#428	—	2	4	no	—
25	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×#106	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×#103	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×C₂²⋊C₈	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	C₂₉×#398	—	2	1	no	—
39	C₂₉×#396	—	2	1	no	—
40	C₂₉×#391	C₂²	1	1	yes	characteristic
41	C₂₉×#389	C₂²	1	1	yes	characteristic
42	C₂₉×#388	—	2	1	no	—
43	C₂₉×#387	—	2	1	no	—
44	C₂₉×#386	—	2	1	no	—
45	C₂₉×#386	—	2	1	no	—
46	C₂₉×#382	C₂²	1	1	yes	characteristic
47	C₂₉×#380	—	2	1	no	—
48	C₂₉×#380	C₂²	1	1	yes	characteristic
49	C₂₉×#380	C₂²	1	1	yes	characteristic
50	C₂₉×#380	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
52	C₄×C₂²⋊C₄×C₂₉	—	2	1	no	—
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	C₂₉×#117	—	2	2	no	—
81	C₂₉×#117	—	4	1	no	—
82	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
83	C₂×C₄⋊C₄×C₂₉	—	2	2	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	—	4	1	no	—
90	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
91	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₂₉	—	2	1	no	—
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	—	2	1	no	—
109	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
110	C₂₉×#107	—	2	2	no	—
111	C₂₉×#107	—	2	2	no	—
112	C₂₉×#106	—	2	2	no	—
113	C₂₉×#106	—	2	2	no	—
114	C₂₉×#106	—	4	1	no	—
115	C₂₉×#106	D₄	1	4	yes	complemented
116	C₂₉×#103	—	2	2	no	—
117	C₂₉×#103	—	2	2	no	—
118	C₂₉×#103	—	2	2	no	—
119	C₂₉×#103	—	4	1	no	—
120	C₂₉×C₂²⋊C₈	—	2	2	no	—
121	C₂₉×C₂²⋊C₈	—	2	2	no	—
122	C₂₉×C₂²⋊C₈	—	2	2	no	—
123	C₂₉×#95	—	2	1	no	—
124	C₂₉×#95	—	2	1	no	—
125	C₂₉×#95	—	2	1	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	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
133	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
134	C₂×Q₈×C₂₉	—	2	1	no	—
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×D₄×C₂₉	—	2	2	no	—
141	C₂×D₄×C₂₉	—	2	2	no	—
142	C₂×D₄×C₂₉	—	4	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	—	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	—	4	2	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	—	8	1	no	—
166	C₂²×C₄×C₂₉	—	8	1	no	—
167	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
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	#41	1	2	yes	—
172	C₂²×C₄×C₂₉	#41	1	2	yes	—
173	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
174	M₁₆×C₂₉	—	2	8	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	—	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	C₂×D₄	1	2	yes	—
186	C₂×C₈×C₂₉	#41	1	2	yes	—
187	C₄⋊C₄×C₂₉	—	2	2	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	—	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	—	4	2	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	—	8	1	no	—
205	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
206	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
207	C₂²⋊C₄×C₂₉	—	2	2	no	—
208	C₂²⋊C₄×C₂₉	—	2	2	no	—
209	C₂²⋊C₄×C₂₉	—	4	2	no	—
210	C₂²⋊C₄×C₂₉	—	4	2	no	—
211	C₂²⋊C₄×C₂₉	—	4	2	no	—
212	C₂²⋊C₄×C₂₉	—	4	2	no	—
213	C₂²⋊C₄×C₂₉	—	8	1	no	—
214	C₂²⋊C₄×C₂₉	—	8	1	no	—
215	C₄²×C₂₉	—	2	1	no	—
216	C₄²×C₂₉	—	2	1	no	—
217	C₄²×C₂₉	—	4	2	no	—
218	C₄²×C₂₉	—	8	1	no	—
219	#26149	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂³×C₂₉	—	2	1	no	—
221	C₂³×C₂₉	—	2	1	no	—
222	C₂³×C₂₉	—	2	1	no	—
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	#123	1	2	yes	—
233	C₂³×C₂₉	#137	1	2	yes	—
234	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
235	Q₈×C₂₉	—	4	1	no	—
236	Q₈×C₂₉	—	4	1	no	—
237	Q₈×C₂₉	—	4	1	no	—
238	Q₈×C₂₉	—	4	1	no	—
239	D₄×C₂₉	—	4	4	no	—
240	C₂×C₄×C₂₉	—	2	1	no	—
241	C₂×C₄×C₂₉	—	2	1	no	—
242	C₂×C₄×C₂₉	—	2	2	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	1	no	—
247	C₂×C₄×C₂₉	—	2	1	no	—
248	C₂×C₄×C₂₉	—	2	1	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	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	—	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	—	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	—	8	4	no	—
284	C₂×C₄×C₂₉	—	8	4	no	—
285	C₂×C₄×C₂₉	#123	1	2	yes	—
286	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
291	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
292	C₈×C₂₉	—	2	2	no	—
293	C₈×C₂₉	—	2	2	no	—
294	C₈×C₂₉	—	4	1	no	—
295	C₈×C₂₉	—	4	1	no	—
296	C₂×#483	C₂×C₂₉	1	1	yes	characteristic, complemented
297	C₂×#428	C₂×C₂₉	1	1	yes	characteristic, complemented
298	#2417	C₂×C₂₉	1	1	yes	characteristic
299	#2352	C₂×C₂₉	1	1	yes	characteristic
300	#2097	C₂×C₂₉	1	1	yes	characteristic, complemented
301	#2085	C₂×C₂₉	1	1	yes	characteristic, complemented
302	#2076	C₂×C₂₉	1	1	yes	characteristic, complemented
303	#2036	C₂×C₂₉	1	1	yes	characteristic, complemented
304	#1927	C₂×C₂₉	1	1	yes	characteristic, complemented
305	#1919	C₂×C₂₉	1	1	yes	characteristic, complemented
306	#1894	C₂×C₂₉	1	1	yes	characteristic, complemented
307	#1873	C₂×C₂₉	1	1	yes	characteristic, complemented
308	#1870	C₂×C₂₉	1	1	yes	characteristic
309	#1853	C₂×C₂₉	1	1	yes	characteristic, complemented
310	#1853	C₂×C₂₉	1	1	yes	characteristic, complemented
311	C₂²×C₂₉	—	2	2	no	—
312	C₂²×C₂₉	—	2	2	no	—
313	C₂²×C₂₉	—	2	2	no	—
314	C₂²×C₂₉	—	2	2	no	—
315	C₂²×C₂₉	—	2	2	no	—
316	C₂²×C₂₉	—	2	2	no	—
317	C₂²×C₂₉	—	4	1	no	—
318	C₂²×C₂₉	—	4	1	no	—
319	C₂²×C₂₉	—	4	1	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	C₂×#123	1	1	yes	characteristic
326	C₂²×C₂₉	D₄²	1	1	yes	characteristic
327	C₂²×C₂₉	#547	1	1	yes	characteristic
328	C₂²×C₂₉	C₂×#137	1	1	yes	characteristic
329	C₂²×C₂₉	#575	1	1	yes	characteristic
330	C₂²×C₂₉	#577	1	1	yes	characteristic
331	C₂²×C₂₉	#577	1	1	yes	characteristic
332	C₄×C₂₉	—	2	2	no	—
333	C₄×C₂₉	—	4	1	no	—
334	C₄×C₂₉	—	4	1	no	—
335	C₄×C₂₉	—	4	1	no	—
336	C₄×C₂₉	—	4	2	no	—
337	C₄×C₂₉	—	4	2	no	—
338	C₄×C₂₉	—	8	1	no	—
339	C₄×C₂₉	—	8	1	no	—
340	C₄×C₂₉	—	8	1	no	—
341	C₄×C₂₉	—	8	1	no	—
342	C₄×C₂₉	—	8	1	no	—
343	C₄×C₂₉	—	8	1	no	—
344	C₄×C₂₉	#525	1	1	yes	characteristic
345	C₄×C₂₉	#539	1	1	yes	characteristic
346	C₄×C₂₉	#548	1	1	yes	characteristic
347	C₄×C₂₉	#553	1	1	yes	characteristic
348	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
349	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
350	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
351	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
352	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
353	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
354	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
355	#483	—	2	4	no	—
356	#428	—	2	4	no	—
357	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
358	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
359	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
360	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
361	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
362	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
363	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
364	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
365	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
366	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
367	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
368	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
369	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
370	#398	—	2	1	no	—
371	#396	—	2	1	no	—
372	#391	C₂²×C₂₉	1	1	yes	characteristic
373	#389	C₂²×C₂₉	1	1	yes	characteristic
374	#388	—	2	1	no	—
375	#387	—	2	1	no	—
376	#386	—	2	1	no	—
377	#386	—	2	1	no	—
378	#382	C₂²×C₂₉	1	1	yes	characteristic
379	#380	—	2	1	no	—
380	#380	C₂²×C₂₉	1	1	yes	characteristic
381	#380	C₂²×C₂₉	1	1	yes	characteristic
382	#380	C₂²×C₂₉	1	1	yes	characteristic
383	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
384	C₄×C₂²⋊C₄	—	2	1	no	—
385	#340	C₂²×C₂₉	1	1	yes	characteristic
386	#340	C₂²×C₂₉	1	1	yes	characteristic
387	#340	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	#336	C₂²×C₂₉	1	1	yes	characteristic
392	#336	C₂²×C₂₉	1	1	yes	characteristic
393	C₂×C₂₉	—	4	2	no	—
394	C₂×C₂₉	—	4	2	no	—
395	C₂×C₂₉	#2443	1	1	yes	characteristic
396	C₂×C₂₉	#3095	1	1	yes	characteristic
397	C₂×C₂₉	#3099	1	1	yes	characteristic
398	C₂×C₂₉	#3266	1	1	yes	characteristic
399	C₂×C₂₉	#3275	1	1	yes	characteristic
400	C₂×C₂₉	#3344	1	1	yes	characteristic
401	C₂×C₂₉	#3351	1	1	yes	characteristic
402	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
403	C₂²×D₄	D₄×C₂₉	1	1	yes	characteristic
404	C₂³×C₄	—	2	1	no	—
405	C₂³×C₄	—	2	1	no	—
406	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
407	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
408	C₂×M₁₆	—	2	2	no	—
409	C₂×M₁₆	—	2	2	no	—
410	C₂×M₁₆	—	2	2	no	—
411	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
412	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
413	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
414	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
415	C₂²⋊Q₈	—	2	2	no	—
416	C₂²⋊Q₈	—	2	2	no	—
417	C₂²⋊Q₈	—	2	2	no	—
418	C₂²⋊Q₈	—	4	1	no	—
419	C₄×D₄	—	2	2	no	—
420	C₄×D₄	—	2	2	no	—
421	#117	—	2	2	no	—
422	#117	—	4	1	no	—
423	C₂×C₄⋊C₄	—	2	2	no	—
424	C₂×C₄⋊C₄	—	2	2	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	—	4	1	no	—
431	C₂×C₄⋊C₄	—	4	1	no	—
432	C₂×C₄⋊C₄	D₄×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×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
447	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
448	C₂×C₄²	—	2	1	no	—
449	C₂×C₄²	—	2	1	no	—
450	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
451	#107	—	2	2	no	—
452	#107	—	2	2	no	—
453	#106	—	2	2	no	—
454	#106	—	2	2	no	—
455	#106	—	4	1	no	—
456	#106	D₄×C₂₉	1	4	yes	complemented
457	#103	—	2	2	no	—
458	#103	—	2	2	no	—
459	#103	—	2	2	no	—
460	#103	—	4	1	no	—
461	C₂²⋊C₈	—	2	2	no	—
462	C₂²⋊C₈	—	2	2	no	—
463	C₂²⋊C₈	—	2	2	no	—
464	#95	—	2	1	no	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	#95	—	2	1	no	—
468	#95	—	2	1	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	#95	—	2	1	no	—
472	#95	—	2	1	no	—
473	C₂₉	#26149	1	1	yes	characteristic, direct product factor, Sylow
474	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
475	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×D₄	—	2	2	no	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	—	4	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
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	—	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	—	4	2	no	—
504	C₂²×C₄	—	4	2	no	—
505	C₂²×C₄	—	4	2	no	—
506	C₂²×C₄	—	4	2	no	—
507	C₂²×C₄	—	8	1	no	—
508	C₂²×C₄	—	8	1	no	—
509	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
510	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
511	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
512	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
513	C₂²×C₄	#41×C₂₉	1	2	yes	—
514	C₂²×C₄	#41×C₂₉	1	2	yes	—
515	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
516	M₁₆	—	2	8	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	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	C₂×D₄×C₂₉	1	2	yes	—
528	C₂×C₈	#41×C₂₉	1	2	yes	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	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	—	4	2	no	—
543	C₄⋊C₄	—	4	2	no	—
544	C₄⋊C₄	—	4	2	no	—
545	C₄⋊C₄	—	4	2	no	—
546	C₄⋊C₄	—	8	1	no	—
547	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
548	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	2	2	no	—
551	C₂²⋊C₄	—	4	2	no	—
552	C₂²⋊C₄	—	4	2	no	—
553	C₂²⋊C₄	—	4	2	no	—
554	C₂²⋊C₄	—	4	2	no	—
555	C₂²⋊C₄	—	8	1	no	—
556	C₂²⋊C₄	—	8	1	no	—
557	C₄²	—	2	1	no	—
558	C₄²	—	2	1	no	—
559	C₄²	—	4	2	no	—
560	C₄²	—	8	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	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	C₂₉×#123	1	2	yes	—
574	C₂³	C₂₉×#137	1	2	yes	—
575	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
576	Q₈	—	4	1	no	—
577	Q₈	—	4	1	no	—
578	Q₈	—	4	1	no	—
579	Q₈	—	4	1	no	—
580	D₄	—	4	4	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	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	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	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	—	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	—	8	4	no	—
625	C₂×C₄	—	8	4	no	—
626	C₂×C₄	C₂₉×#123	1	2	yes	—
627	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
628	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
629	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
630	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
631	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
632	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
633	C₈	—	2	2	no	—
634	C₈	—	2	2	no	—
635	C₈	—	4	1	no	—
636	C₈	—	4	1	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	1	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	C₂×C₂₉×#123	1	1	yes	characteristic
652	C₂²	D₄²×C₂₉	1	1	yes	characteristic
653	C₂²	C₂₉×#547	1	1	yes	characteristic
654	C₂²	C₂×C₂₉×#137	1	1	yes	characteristic
655	C₂²	C₂₉×#575	1	1	yes	characteristic
656	C₂²	C₂₉×#577	1	1	yes	characteristic
657	C₂²	C₂₉×#577	1	1	yes	characteristic
658	C₄	—	2	2	no	—
659	C₄	—	4	1	no	—
660	C₄	—	4	2	no	—
661	C₄	—	4	2	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	1	no	—
664	C₄	—	8	1	no	—
665	C₄	—	8	1	no	—
666	C₄	—	8	1	no	—
667	C₄	—	8	1	no	—
668	C₄	—	8	1	no	—
669	C₄	—	8	1	no	—
670	C₄	C₂₉×#525	1	1	yes	characteristic
671	C₄	C₂₉×#539	1	1	yes	characteristic
672	C₄	C₂₉×#548	1	1	yes	characteristic
673	C₄	C₂₉×#553	1	1	yes	characteristic
674	C₂	—	4	2	no	—
675	C₂	—	4	2	no	—
676	C₂	C₂₉×#2443	1	1	yes	characteristic
677	C₂	C₂₉×#3095	1	1	yes	characteristic
678	C₂	C₂₉×#3099	1	1	yes	characteristic
679	C₂	C₂₉×#3266	1	1	yes	characteristic
680	C₂	C₂₉×#3275	1	1	yes	characteristic
681	C₂	C₂₉×#3344	1	1	yes	characteristic
682	C₂	C₂₉×#3351	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×#2097	C₂	semidirect
6. C₂₉×#2085	C₂	semidirect
7. C₂₉×#2076	C₂	semidirect
8. C₂₉×#2036	C₂	semidirect
9. C₂₉×#1927	C₂	semidirect
10. C₂₉×#1919	C₂	semidirect
11. C₂₉×#1894	C₂	semidirect
12. C₂₉×#1873	C₂	semidirect
14. C₂₉×#1853	C₂	semidirect
15. C₂₉×#1853	C₂	semidirect
115. C₂₉×#106	D₄	semidirect
219. #26149	C₂₉	direct (N × H)
296. C₂×#483	C₂×C₂₉	semidirect
297. C₂×#428	C₂×C₂₉	semidirect
300. #2097	C₂×C₂₉	semidirect
301. #2085	C₂×C₂₉	semidirect
302. #2076	C₂×C₂₉	semidirect
303. #2036	C₂×C₂₉	semidirect
304. #1927	C₂×C₂₉	semidirect
305. #1919	C₂×C₂₉	semidirect
306. #1894	C₂×C₂₉	semidirect
307. #1873	C₂×C₂₉	semidirect
309. #1853	C₂×C₂₉	semidirect
310. #1853	C₂×C₂₉	semidirect
456. #106	D₄×C₂₉	semidirect
473. C₂₉	#26149	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×#2417	2
C₂₉×#2352	2
C₂₉×#2097	2
C₂₉×#2085	2
C₂₉×#2076	2
C₂₉×#2036	2
C₂₉×#1927	2
C₂₉×#1919	2
C₂₉×#1894	2
C₂₉×#1873	2
C₂₉×#1870	2
C₂₉×#1853	2
#26149	29

Subgroups — C29×#26149 #20321049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#26149 #20321049