Subgroups — C₂₉×#34419 #20329319

Order 7424.

2182 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#542	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2379	C₂	1	2	yes	maximal, complemented
3	C₂₉×#2376	C₂	1	2	yes	maximal, complemented
4	C₂₉×#2369	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2367	C₂	1	2	yes	maximal, complemented
7	C₂₉×#2367	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2365	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#2359	C₂	1	2	yes	maximal, complemented
10	C₂₉×#2355	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#2354	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#2351	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#2349	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#2334	C₂	1	2	yes	maximal, complemented
15	C₂₉×#2334	C₂	1	2	yes	maximal, complemented
16	C₂₉×#2329	C₂	1	2	yes	maximal, complemented
17	C₂₉×#2324	C₂	1	1	yes	maximal, characteristic
18	C₂₉×#2323	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₉×#2323	C₂	1	2	yes	maximal, complemented
20	C₂₉×#2314	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂₉×#121	C₂	1	1	yes	maximal, characteristic
23	C₂₉×#2296	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₉×#542	C₄	1	16	yes	complemented
25	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×#126	C₂²	1	2	yes	—
27	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×#124	C₂²	1	2	yes	—
29	C₂×C₂₉×#123	C₂²	1	2	yes	—
30	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	2	yes	—
32	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	—
36	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
41	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
42	C₂×C₂₉×#117	C₂²	1	2	yes	—
43	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
45	C₂₉×#391	C₂²	1	1	yes	characteristic
46	C₂₉×#391	C₂²	1	1	yes	characteristic
47	C₂₉×#391	C₂²	1	2	yes	—
48	C₂₉×#391	C₂²	1	2	yes	—
49	C₂₉×#391	C₂²	1	2	yes	—
50	C₂₉×#390	C₂²	1	1	yes	characteristic
51	C₂₉×#390	C₂²	1	1	yes	characteristic
52	C₂₉×#390	C₂²	1	2	yes	—
53	C₂₉×#389	C₂²	1	1	yes	characteristic
54	C₂₉×#389	C₂²	1	1	yes	characteristic
55	C₂₉×#389	C₂²	1	1	yes	characteristic
56	C₂₉×#389	C₂²	1	1	yes	characteristic
57	C₂₉×#389	C₂²	1	1	yes	characteristic
58	C₂₉×#389	C₂²	1	1	yes	characteristic
59	C₂₉×#389	C₂²	1	2	yes	—
60	C₂₉×#389	C₂²	1	1	yes	characteristic
61	C₂₉×#389	C₂²	1	2	yes	—
62	C₂₉×#389	C₂²	1	1	yes	characteristic
63	C₂₉×#389	C₂²	1	2	yes	—
64	C₂₉×#389	C₂²	1	2	yes	—
65	C₂₉×#388	C₂²	1	2	yes	—
66	C₂₉×#388	C₂²	1	2	yes	—
67	C₂₉×#388	C₂²	1	2	yes	—
68	C₂₉×#388	C₂²	1	2	yes	—
69	C₂₉×#388	C₂²	1	2	yes	—
70	C₂₉×#388	C₂²	1	2	yes	—
71	C₂₉×#388	C₂²	1	2	yes	—
72	C₂₉×#388	C₂²	1	2	yes	—
73	C₂₉×#388	C₂²	1	2	yes	—
74	C₂₉×#388	C₂²	1	2	yes	—
75	C₂₉×#388	C₂²	1	2	yes	—
76	C₂₉×#388	C₂²	1	2	yes	—
77	C₂₉×#387	C₂²	1	2	yes	—
78	C₂₉×#387	C₂²	1	2	yes	—
79	C₂₉×#387	C₂²	1	2	yes	—
80	C₂₉×#387	C₂²	1	2	yes	—
81	C₂₉×#387	C₂²	1	2	yes	—
82	C₂₉×#387	C₂²	1	2	yes	—
83	C₂₉×#387	C₂²	1	2	yes	—
84	C₂₉×#387	C₂²	1	2	yes	—
85	C₂₉×#386	C₂²	1	2	yes	—
86	C₂₉×#386	C₂²	1	2	yes	—
87	C₂₉×#385	C₂²	1	1	yes	characteristic
88	C₂₉×#385	C₂²	1	1	yes	characteristic
89	C₂₉×#385	C₂²	1	1	yes	characteristic
90	C₂₉×#385	C₂²	1	1	yes	characteristic
91	C₂₉×#385	C₂²	1	2	yes	—
92	C₂₉×#385	C₂²	1	2	yes	—
93	C₂₉×#385	C₂²	1	2	yes	—
94	C₂₉×#385	C₂²	1	2	yes	—
95	C₂₉×#385	C₂²	1	2	yes	—
96	C₂₉×#385	C₂²	1	2	yes	—
97	C₂₉×#384	C₂²	1	1	yes	characteristic
98	C₂₉×#382	C₂²	1	1	yes	characteristic
99	C₂₉×#382	C₂²	1	2	yes	—
100	C₂₉×#382	C₂²	1	2	yes	—
101	C₂₉×#380	C₂²	1	1	yes	characteristic
102	C₂₉×#380	C₂²	1	1	yes	characteristic
103	C₂₉×#380	C₂²	1	2	yes	—
104	C₂₉×#380	C₂²	1	2	yes	—
105	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
111	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
118	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
122	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
123	C₂×C₂₉×#95	C₂²	1	2	yes	—
124	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
126	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
128	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
131	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
133	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
134	C₂₉×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
135	C₂₉×#126	C₂×C₄	1	16	yes	complemented
136	C₂₉×#124	C₂×C₄	1	8	yes	complemented
137	C₂₉×#124	C₂×C₄	1	16	yes	complemented
138	C₂₉×#123	C₂×C₄	1	16	yes	complemented
139	C₂₉×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
140	C₂₉×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
141	C₂₉×#121	C₂×C₄	1	8	yes	—
142	C₄×Q₈×C₂₉	—	4	4	no	—
143	C₄×Q₈×C₂₉	—	4	2	no	—
144	C₄×Q₈×C₂₉	—	4	2	no	—
145	C₄×Q₈×C₂₉	C₂×C₄	1	8	yes	complemented
146	C₄×D₄×C₂₉	—	4	2	no	—
147	C₄×D₄×C₂₉	—	4	2	no	—
148	C₄×D₄×C₂₉	—	4	4	no	—
149	C₄×D₄×C₂₉	C₂×C₄	1	8	yes	complemented
150	C₂₉×#117	—	4	2	no	—
151	C₂₉×#117	—	4	4	no	—
152	C₂₉×#117	C₂×C₄	1	8	yes	complemented
153	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
199	C₂×C₄²×C₂₉	—	4	2	no	—
200	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
204	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
208	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
209	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
210	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
211	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
212	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
213	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
214	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
217	C₂₉×#95	C₂³	1	1	yes	characteristic
218	C₂₉×#95	C₂³	1	2	yes	—
219	C₂₉×#95	C₂³	1	2	yes	—
220	C₂₉×#95	C₂³	1	2	yes	—
221	C₂₉×#95	C₂³	1	1	yes	characteristic
222	C₂₉×#95	C₂³	1	2	yes	—
223	C₂₉×#95	C₂³	1	1	yes	characteristic
224	C₂₉×#95	C₂³	1	2	yes	—
225	C₂₉×#95	C₂³	1	2	yes	—
226	C₂₉×#95	C₂³	1	2	yes	—
227	C₂₉×#95	C₂³	1	1	yes	characteristic
228	C₂₉×#95	C₂³	1	1	yes	characteristic
229	C₂₉×#95	C₂³	1	2	yes	—
230	C₂₉×#95	C₂³	1	2	yes	—
231	C₂₉×#95	C₂³	1	2	yes	—
232	C₂₉×#95	C₂³	1	2	yes	—
233	C₂₉×#95	C₂³	1	1	yes	characteristic
234	C₂₉×#95	C₂³	1	2	yes	—
235	C₂₉×#95	C₂³	1	2	yes	—
236	C₂₉×#95	C₂³	1	2	yes	—
237	C₂₉×#95	C₂³	1	2	yes	—
238	C₂₉×#95	C₂³	1	2	yes	—
239	C₂₉×#95	C₂³	1	1	yes	characteristic
240	C₂₉×#95	C₂³	1	2	yes	—
241	C₂₉×#95	C₂³	1	1	yes	characteristic
242	C₂₉×#95	C₂³	1	2	yes	—
243	C₂⁴×C₂₉	C₂⁴	1	2	yes	—
244	C₂⁴×C₂₉	C₂⁴	1	1	yes	characteristic
245	C₂×Q₈×C₂₉	—	2	2	no	—
246	C₂×Q₈×C₂₉	—	2	2	no	—
247	C₂×Q₈×C₂₉	—	4	2	no	—
248	C₂×Q₈×C₂₉	—	4	2	no	—
249	C₂×Q₈×C₂₉	C₂²×C₄	1	4	yes	—
250	C₂×Q₈×C₂₉	C₂²×C₄	1	8	yes	—
251	C₂×D₄×C₂₉	—	2	2	no	—
252	C₂×D₄×C₂₉	—	2	2	no	—
253	C₂×D₄×C₂₉	—	4	2	no	—
254	C₂×D₄×C₂₉	—	4	2	no	—
255	C₂×D₄×C₂₉	C₂²×C₄	1	4	yes	—
256	C₂×D₄×C₂₉	C₂²×C₄	1	8	yes	—
257	C₂²×C₄×C₂₉	—	2	2	no	—
258	C₂²×C₄×C₂₉	—	2	2	no	—
259	C₂²×C₄×C₂₉	—	2	2	no	—
260	C₂²×C₄×C₂₉	—	2	2	no	—
261	C₂²×C₄×C₂₉	—	2	4	no	—
262	C₂²×C₄×C₂₉	—	4	1	no	—
263	C₂²×C₄×C₂₉	—	4	1	no	—
264	C₂²×C₄×C₂₉	—	4	2	no	—
265	C₂²×C₄×C₂₉	—	4	2	no	—
266	C₂²×C₄×C₂₉	—	4	1	no	—
267	C₂²×C₄×C₂₉	—	4	1	no	—
268	C₂²×C₄×C₂₉	—	4	2	no	—
269	C₂²×C₄×C₂₉	—	4	2	no	—
270	C₂²×C₄×C₂₉	—	4	2	no	—
271	C₂²×C₄×C₂₉	—	4	2	no	—
272	C₂²×C₄×C₂₉	—	4	2	no	—
273	C₂²×C₄×C₂₉	C₂²×C₄	1	4	yes	—
274	C₂²×C₄×C₂₉	C₂²×C₄	1	8	yes	—
275	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
296	C₄⋊C₄×C₂₉	—	2	2	no	—
297	C₄⋊C₄×C₂₉	—	2	4	no	—
298	C₄⋊C₄×C₂₉	—	2	2	no	—
299	C₄⋊C₄×C₂₉	—	2	2	no	—
300	C₄⋊C₄×C₂₉	—	2	2	no	—
301	C₄⋊C₄×C₂₉	—	2	2	no	—
302	C₄⋊C₄×C₂₉	—	2	2	no	—
303	C₄⋊C₄×C₂₉	—	2	2	no	—
304	C₄⋊C₄×C₂₉	—	2	2	no	—
305	C₄⋊C₄×C₂₉	—	4	1	no	—
306	C₄⋊C₄×C₂₉	—	4	2	no	—
307	C₄⋊C₄×C₂₉	—	4	1	no	—
308	C₄⋊C₄×C₂₉	—	4	1	no	—
309	C₄⋊C₄×C₂₉	—	4	2	no	—
310	C₄⋊C₄×C₂₉	—	4	2	no	—
311	C₄⋊C₄×C₂₉	—	4	1	no	—
312	C₄⋊C₄×C₂₉	—	4	1	no	—
313	C₄⋊C₄×C₂₉	—	4	1	no	—
314	C₄⋊C₄×C₂₉	—	4	2	no	—
315	C₄⋊C₄×C₂₉	—	4	2	no	—
316	C₄⋊C₄×C₂₉	—	4	2	no	—
317	C₄⋊C₄×C₂₉	—	4	2	no	—
318	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
319	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
320	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
321	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
322	C₄⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
323	C₄⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
324	C₄⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
325	C₂²⋊C₄×C₂₉	—	2	4	no	—
326	C₂²⋊C₄×C₂₉	—	4	2	no	—
327	C₂²⋊C₄×C₂₉	—	4	2	no	—
328	C₂²⋊C₄×C₂₉	—	4	2	no	—
329	C₂²⋊C₄×C₂₉	—	4	1	no	—
330	C₂²⋊C₄×C₂₉	—	4	2	no	—
331	C₂²⋊C₄×C₂₉	—	4	1	no	—
332	C₂²⋊C₄×C₂₉	—	4	2	no	—
333	C₂²⋊C₄×C₂₉	—	4	2	no	—
334	C₂²⋊C₄×C₂₉	—	4	2	no	—
335	C₂²⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
336	C₂²⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
337	C₂²⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
338	C₂²⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
339	C₂²⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
340	C₂²⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
341	C₂²⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
342	C₄²×C₂₉	—	2	2	no	—
343	C₄²×C₂₉	—	2	2	no	—
344	C₄²×C₂₉	—	2	2	no	—
345	C₄²×C₂₉	—	2	4	no	—
346	C₄²×C₂₉	—	2	2	no	—
347	C₄²×C₂₉	—	4	1	no	—
348	C₄²×C₂₉	—	4	1	no	—
349	C₄²×C₂₉	—	4	2	no	—
350	C₄²×C₂₉	—	4	2	no	—
351	C₄²×C₂₉	—	4	2	no	—
352	C₄²×C₂₉	—	4	2	no	—
353	C₄²×C₂₉	—	4	2	no	—
354	C₄²×C₂₉	—	4	2	no	—
355	C₄²×C₂₉	—	4	2	no	—
356	C₄²×C₂₉	C₂²×C₄	1	4	yes	—
357	C₄²×C₂₉	C₂²×C₄	1	4	yes	—
358	C₄²×C₂₉	C₂²×C₄	1	8	yes	—
359	#34419	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
360	C₂³×C₂₉	—	2	2	no	—
361	C₂³×C₂₉	—	2	1	no	—
362	C₂³×C₂₉	—	2	1	no	—
363	C₂³×C₂₉	—	2	2	no	—
364	C₂³×C₂₉	—	2	1	no	—
365	C₂³×C₂₉	—	2	1	no	—
366	C₂³×C₂₉	—	2	2	no	—
367	C₂³×C₂₉	—	2	2	no	—
368	C₂³×C₂₉	—	2	1	no	—
369	C₂³×C₂₉	—	2	2	no	—
370	C₂³×C₂₉	—	2	2	no	—
371	C₂³×C₂₉	—	2	1	no	—
372	C₂³×C₂₉	C₂³×C₄	1	2	yes	—
373	C₂³×C₂₉	C₂³×C₄	1	4	yes	—
374	C₂³×C₂₉	C₂⁵	1	1	yes	characteristic
375	Q₈×C₂₉	—	2	8	no	—
376	Q₈×C₂₉	—	4	8	no	—
377	D₄×C₂₉	—	2	8	no	—
378	D₄×C₂₉	—	4	8	no	—
379	C₂×C₄×C₂₉	—	2	1	no	—
380	C₂×C₄×C₂₉	—	2	2	no	—
381	C₂×C₄×C₂₉	—	2	1	no	—
382	C₂×C₄×C₂₉	—	2	2	no	—
383	C₂×C₄×C₂₉	—	2	1	no	—
384	C₂×C₄×C₂₉	—	2	1	no	—
385	C₂×C₄×C₂₉	—	2	2	no	—
386	C₂×C₄×C₂₉	—	2	1	no	—
387	C₂×C₄×C₂₉	—	2	1	no	—
388	C₂×C₄×C₂₉	—	2	1	no	—
389	C₂×C₄×C₂₉	—	2	1	no	—
390	C₂×C₄×C₂₉	—	2	1	no	—
391	C₂×C₄×C₂₉	—	2	1	no	—
392	C₂×C₄×C₂₉	—	2	2	no	—
393	C₂×C₄×C₂₉	—	2	1	no	—
394	C₂×C₄×C₂₉	—	2	1	no	—
395	C₂×C₄×C₂₉	—	2	1	no	—
396	C₂×C₄×C₂₉	—	2	2	no	—
397	C₂×C₄×C₂₉	—	2	2	no	—
398	C₂×C₄×C₂₉	—	2	1	no	—
399	C₂×C₄×C₂₉	—	2	8	no	—
400	C₂×C₄×C₂₉	—	2	1	no	—
401	C₂×C₄×C₂₉	—	2	2	no	—
402	C₂×C₄×C₂₉	—	2	1	no	—
403	C₂×C₄×C₂₉	—	2	1	no	—
404	C₂×C₄×C₂₉	—	2	1	no	—
405	C₂×C₄×C₂₉	—	2	1	no	—
406	C₂×C₄×C₂₉	—	2	1	no	—
407	C₂×C₄×C₂₉	—	2	2	no	—
408	C₂×C₄×C₂₉	—	2	1	no	—
409	C₂×C₄×C₂₉	—	2	1	no	—
410	C₂×C₄×C₂₉	—	2	2	no	—
411	C₂×C₄×C₂₉	—	2	2	no	—
412	C₂×C₄×C₂₉	—	2	2	no	—
413	C₂×C₄×C₂₉	—	2	1	no	—
414	C₂×C₄×C₂₉	—	2	1	no	—
415	C₂×C₄×C₂₉	—	2	2	no	—
416	C₂×C₄×C₂₉	—	2	2	no	—
417	C₂×C₄×C₂₉	—	2	2	no	—
418	C₂×C₄×C₂₉	—	2	2	no	—
419	C₂×C₄×C₂₉	—	2	2	no	—
420	C₂×C₄×C₂₉	—	2	1	no	—
421	C₂×C₄×C₂₉	—	2	2	no	—
422	C₂×C₄×C₂₉	—	2	1	no	—
423	C₂×C₄×C₂₉	—	2	1	no	—
424	C₂×C₄×C₂₉	—	2	1	no	—
425	C₂×C₄×C₂₉	—	2	1	no	—
426	C₂×C₄×C₂₉	—	2	1	no	—
427	C₂×C₄×C₂₉	—	2	2	no	—
428	C₂×C₄×C₂₉	—	2	1	no	—
429	C₂×C₄×C₂₉	—	2	1	no	—
430	C₂×C₄×C₂₉	—	4	8	no	—
431	C₂×C₄×C₂₉	—	4	4	no	—
432	C₂×C₄×C₂₉	—	4	4	no	—
433	C₂×C₄×C₂₉	—	8	4	no	—
434	C₂×C₄×C₂₉	—	8	4	no	—
435	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
436	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
437	C₂×C₄×C₂₉	C₂³×C₄	1	4	yes	—
438	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
439	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
440	C₂×C₄×C₂₉	C₂³×C₄	1	4	yes	—
441	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
442	C₂×C₄×C₂₉	C₂³×C₄	1	4	yes	—
443	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
444	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
445	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
446	C₂×C₄×C₂₉	2₋¹⁺⁴	1	2	yes	—
447	C₂×C₄×C₂₉	2₋¹⁺⁴	1	2	yes	—
448	C₂×#542	C₂×C₂₉	1	1	yes	characteristic
449	#2379	C₂×C₂₉	1	2	yes	complemented
450	#2376	C₂×C₂₉	1	2	yes	complemented
451	#2369	C₂×C₂₉	1	1	yes	characteristic, complemented
452	#2367	C₂×C₂₉	1	1	yes	characteristic, complemented
453	#2367	C₂×C₂₉	1	1	yes	characteristic, complemented
454	#2367	C₂×C₂₉	1	2	yes	complemented
455	#2365	C₂×C₂₉	1	1	yes	characteristic, complemented
456	#2359	C₂×C₂₉	1	2	yes	complemented
457	#2355	C₂×C₂₉	1	1	yes	characteristic, complemented
458	#2354	C₂×C₂₉	1	1	yes	characteristic, complemented
459	#2351	C₂×C₂₉	1	1	yes	characteristic, complemented
460	#2349	C₂×C₂₉	1	1	yes	characteristic, complemented
461	#2334	C₂×C₂₉	1	2	yes	complemented
462	#2334	C₂×C₂₉	1	2	yes	complemented
463	#2329	C₂×C₂₉	1	2	yes	complemented
464	#2324	C₂×C₂₉	1	1	yes	characteristic
465	#2323	C₂×C₂₉	1	1	yes	characteristic, complemented
466	#2323	C₂×C₂₉	1	2	yes	complemented
467	#2314	C₂×C₂₉	1	1	yes	characteristic, complemented
468	C₄×C₂²⋊Q₈	C₂×C₂₉	1	1	yes	characteristic, complemented
469	C₄×#121	C₂×C₂₉	1	1	yes	characteristic
470	#2296	C₂×C₂₉	1	1	yes	characteristic, complemented
471	C₂²×C₂₉	—	2	2	no	—
472	C₂²×C₂₉	—	2	4	no	—
473	C₂²×C₂₉	—	2	4	no	—
474	C₂²×C₂₉	—	2	2	no	—
475	C₂²×C₂₉	—	2	2	no	—
476	C₂²×C₂₉	—	2	4	no	—
477	C₂²×C₂₉	—	4	1	no	—
478	C₂²×C₂₉	—	4	2	no	—
479	C₂²×C₂₉	—	4	1	no	—
480	C₂²×C₂₉	—	4	2	no	—
481	C₂²×C₂₉	—	4	2	no	—
482	C₂²×C₂₉	—	4	1	no	—
483	C₂²×C₂₉	—	4	1	no	—
484	C₂²×C₂₉	—	4	2	no	—
485	C₂²×C₂₉	C₂⁴×C₄	1	1	yes	characteristic
486	C₂²×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
487	C₂²×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
488	C₂²×C₂₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
489	C₂²×C₂₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
490	C₂²×C₂₉	#585	1	1	yes	characteristic
491	C₂²×C₂₉	#585	1	1	yes	characteristic
492	C₄×C₂₉	—	2	2	no	—
493	C₄×C₂₉	—	2	4	no	—
494	C₄×C₂₉	—	2	2	no	—
495	C₄×C₂₉	—	2	4	no	—
496	C₄×C₂₉	—	2	4	no	—
497	C₄×C₂₉	—	2	2	no	—
498	C₄×C₂₉	—	2	2	no	—
499	C₄×C₂₉	—	2	2	no	—
500	C₄×C₂₉	—	2	2	no	—
501	C₄×C₂₉	—	2	2	no	—
502	C₄×C₂₉	—	4	1	no	—
503	C₄×C₂₉	—	4	1	no	—
504	C₄×C₂₉	—	4	2	no	—
505	C₄×C₂₉	—	4	1	no	—
506	C₄×C₂₉	—	4	1	no	—
507	C₄×C₂₉	—	4	1	no	—
508	C₄×C₂₉	—	4	2	no	—
509	C₄×C₂₉	—	4	1	no	—
510	C₄×C₂₉	—	4	2	no	—
511	C₄×C₂₉	—	4	2	no	—
512	C₄×C₂₉	#520	1	4	yes	—
513	#542	C₄×C₂₉	1	16	yes	complemented
514	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
515	C₂×#126	C₂²×C₂₉	1	2	yes	—
516	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
517	C₂×#124	C₂²×C₂₉	1	2	yes	—
518	C₂×#123	C₂²×C₂₉	1	2	yes	—
519	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	2	yes	—
520	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
521	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic
522	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
523	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	—
524	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
525	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
526	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
527	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
528	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
529	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
530	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
531	C₂×#117	C₂²×C₂₉	1	2	yes	—
532	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
533	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
534	#391	C₂²×C₂₉	1	1	yes	characteristic
535	#391	C₂²×C₂₉	1	2	yes	—
536	#391	C₂²×C₂₉	1	2	yes	—
537	#391	C₂²×C₂₉	1	2	yes	—
538	#391	C₂²×C₂₉	1	1	yes	characteristic
539	#390	C₂²×C₂₉	1	1	yes	characteristic
540	#390	C₂²×C₂₉	1	2	yes	—
541	#390	C₂²×C₂₉	1	1	yes	characteristic
542	#389	C₂²×C₂₉	1	2	yes	—
543	#389	C₂²×C₂₉	1	1	yes	characteristic
544	#389	C₂²×C₂₉	1	1	yes	characteristic
545	#389	C₂²×C₂₉	1	2	yes	—
546	#389	C₂²×C₂₉	1	1	yes	characteristic
547	#389	C₂²×C₂₉	1	1	yes	characteristic
548	#389	C₂²×C₂₉	1	2	yes	—
549	#389	C₂²×C₂₉	1	1	yes	characteristic
550	#389	C₂²×C₂₉	1	1	yes	characteristic
551	#389	C₂²×C₂₉	1	2	yes	—
552	#389	C₂²×C₂₉	1	1	yes	characteristic
553	#389	C₂²×C₂₉	1	1	yes	characteristic
554	#388	C₂²×C₂₉	1	2	yes	—
555	#388	C₂²×C₂₉	1	2	yes	—
556	#388	C₂²×C₂₉	1	2	yes	—
557	#388	C₂²×C₂₉	1	2	yes	—
558	#388	C₂²×C₂₉	1	2	yes	—
559	#388	C₂²×C₂₉	1	2	yes	—
560	#388	C₂²×C₂₉	1	2	yes	—
561	#388	C₂²×C₂₉	1	2	yes	—
562	#388	C₂²×C₂₉	1	2	yes	—
563	#388	C₂²×C₂₉	1	2	yes	—
564	#388	C₂²×C₂₉	1	2	yes	—
565	#388	C₂²×C₂₉	1	2	yes	—
566	#387	C₂²×C₂₉	1	2	yes	—
567	#387	C₂²×C₂₉	1	2	yes	—
568	#387	C₂²×C₂₉	1	2	yes	—
569	#387	C₂²×C₂₉	1	2	yes	—
570	#387	C₂²×C₂₉	1	2	yes	—
571	#387	C₂²×C₂₉	1	2	yes	—
572	#387	C₂²×C₂₉	1	2	yes	—
573	#387	C₂²×C₂₉	1	2	yes	—
574	#386	C₂²×C₂₉	1	2	yes	—
575	#386	C₂²×C₂₉	1	2	yes	—
576	#385	C₂²×C₂₉	1	2	yes	—
577	#385	C₂²×C₂₉	1	2	yes	—
578	#385	C₂²×C₂₉	1	2	yes	—
579	#385	C₂²×C₂₉	1	2	yes	—
580	#385	C₂²×C₂₉	1	2	yes	—
581	#385	C₂²×C₂₉	1	1	yes	characteristic
582	#385	C₂²×C₂₉	1	1	yes	characteristic
583	#385	C₂²×C₂₉	1	1	yes	characteristic
584	#385	C₂²×C₂₉	1	2	yes	—
585	#385	C₂²×C₂₉	1	1	yes	characteristic
586	#384	C₂²×C₂₉	1	1	yes	characteristic
587	#382	C₂²×C₂₉	1	1	yes	characteristic
588	#382	C₂²×C₂₉	1	2	yes	—
589	#382	C₂²×C₂₉	1	2	yes	—
590	#380	C₂²×C₂₉	1	1	yes	characteristic
591	#380	C₂²×C₂₉	1	1	yes	characteristic
592	#380	C₂²×C₂₉	1	2	yes	—
593	#380	C₂²×C₂₉	1	2	yes	—
594	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
595	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
596	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
597	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
598	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
599	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
600	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
601	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
602	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
603	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
604	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
605	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
606	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
607	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
608	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
609	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
610	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
611	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
612	C₂×#95	C₂²×C₂₉	1	2	yes	—
613	C₂×C₂₉	—	4	2	no	—
614	C₂×C₂₉	—	4	4	no	—
615	C₂×C₂₉	C₂×#520	1	1	yes	characteristic
616	C₂×C₂₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic
617	C₂×C₂₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic
618	C₂×C₂₉	#3536	1	1	yes	characteristic
619	C₂×C₂₉	#3540	1	1	yes	characteristic
620	C₂×C₂₉	#3554	1	1	yes	characteristic
621	C₂×C₂₉	#3555	1	1	yes	characteristic
622	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
623	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
624	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
625	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
626	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
627	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
628	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
629	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
630	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
631	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
632	C₄⋊Q₈	C₂×C₄×C₂₉	1	8	yes	complemented
633	#126	C₂×C₄×C₂₉	1	16	yes	complemented
634	#124	C₂×C₄×C₂₉	1	8	yes	complemented
635	#124	C₂×C₄×C₂₉	1	16	yes	complemented
636	#123	C₂×C₄×C₂₉	1	16	yes	complemented
637	C₂²⋊Q₈	C₂×C₄×C₂₉	1	16	yes	complemented
638	C₂²⋊Q₈	C₂×C₄×C₂₉	1	8	yes	complemented
639	#121	C₂×C₄×C₂₉	1	8	yes	—
640	C₄×Q₈	—	4	4	no	—
641	C₄×Q₈	—	4	2	no	—
642	C₄×Q₈	—	4	2	no	—
643	C₄×Q₈	C₂×C₄×C₂₉	1	8	yes	complemented
644	C₄×D₄	—	4	2	no	—
645	C₄×D₄	—	4	2	no	—
646	C₄×D₄	—	4	4	no	—
647	C₄×D₄	C₂×C₄×C₂₉	1	8	yes	complemented
648	#117	—	4	2	no	—
649	#117	—	4	4	no	—
650	#117	C₂×C₄×C₂₉	1	8	yes	complemented
651	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
657	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
665	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
667	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
672	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
677	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
678	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
679	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
682	C₂×C₂²⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
691	C₂×C₂²⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
692	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
693	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
697	C₂×C₄²	—	4	2	no	—
698	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
700	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
702	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
703	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
704	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
705	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
706	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
707	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
708	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
709	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
710	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
711	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
712	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
713	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
714	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
715	#95	C₂³×C₂₉	1	1	yes	characteristic
716	#95	C₂³×C₂₉	1	2	yes	—
717	#95	C₂³×C₂₉	1	2	yes	—
718	#95	C₂³×C₂₉	1	2	yes	—
719	#95	C₂³×C₂₉	1	1	yes	characteristic
720	#95	C₂³×C₂₉	1	2	yes	—
721	#95	C₂³×C₂₉	1	1	yes	characteristic
722	#95	C₂³×C₂₉	1	2	yes	—
723	#95	C₂³×C₂₉	1	2	yes	—
724	#95	C₂³×C₂₉	1	2	yes	—
725	#95	C₂³×C₂₉	1	1	yes	characteristic
726	#95	C₂³×C₂₉	1	1	yes	characteristic
727	#95	C₂³×C₂₉	1	2	yes	—
728	#95	C₂³×C₂₉	1	2	yes	—
729	#95	C₂³×C₂₉	1	2	yes	—
730	#95	C₂³×C₂₉	1	2	yes	—
731	#95	C₂³×C₂₉	1	1	yes	characteristic
732	#95	C₂³×C₂₉	1	2	yes	—
733	#95	C₂³×C₂₉	1	2	yes	—
734	#95	C₂³×C₂₉	1	2	yes	—
735	#95	C₂³×C₂₉	1	2	yes	—
736	#95	C₂³×C₂₉	1	2	yes	—
737	#95	C₂³×C₂₉	1	1	yes	characteristic
738	#95	C₂³×C₂₉	1	2	yes	—
739	#95	C₂³×C₂₉	1	1	yes	characteristic
740	#95	C₂³×C₂₉	1	2	yes	—
741	C₂₉	#34419	1	1	yes	characteristic, direct product factor, Sylow
742	C₂⁴	C₂⁴×C₂₉	1	2	yes	—
743	C₂⁴	C₂⁴×C₂₉	1	1	yes	characteristic
744	C₂×Q₈	—	2	2	no	—
745	C₂×Q₈	—	2	2	no	—
746	C₂×Q₈	—	4	2	no	—
747	C₂×Q₈	—	4	2	no	—
748	C₂×Q₈	C₂²×C₄×C₂₉	1	4	yes	—
749	C₂×Q₈	C₂²×C₄×C₂₉	1	8	yes	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	2	no	—
752	C₂×D₄	—	4	2	no	—
753	C₂×D₄	—	4	2	no	—
754	C₂×D₄	C₂²×C₄×C₂₉	1	4	yes	—
755	C₂×D₄	C₂²×C₄×C₂₉	1	8	yes	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	4	no	—
761	C₂²×C₄	—	4	1	no	—
762	C₂²×C₄	—	4	1	no	—
763	C₂²×C₄	—	4	2	no	—
764	C₂²×C₄	—	4	2	no	—
765	C₂²×C₄	—	4	1	no	—
766	C₂²×C₄	—	4	1	no	—
767	C₂²×C₄	—	4	2	no	—
768	C₂²×C₄	—	4	2	no	—
769	C₂²×C₄	—	4	2	no	—
770	C₂²×C₄	—	4	2	no	—
771	C₂²×C₄	—	4	2	no	—
772	C₂²×C₄	C₂²×C₄×C₂₉	1	4	yes	—
773	C₂²×C₄	C₂²×C₄×C₂₉	1	8	yes	—
774	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
777	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
787	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
791	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	4	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	4	1	no	—
805	C₄⋊C₄	—	4	1	no	—
806	C₄⋊C₄	—	4	2	no	—
807	C₄⋊C₄	—	4	2	no	—
808	C₄⋊C₄	—	4	2	no	—
809	C₄⋊C₄	—	4	2	no	—
810	C₄⋊C₄	—	4	1	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	1	no	—
813	C₄⋊C₄	—	4	1	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	—	4	2	no	—
816	C₄⋊C₄	—	4	1	no	—
817	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
818	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
819	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
820	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
821	C₄⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
822	C₄⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
823	C₄⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	4	1	no	—
826	C₂²⋊C₄	—	4	2	no	—
827	C₂²⋊C₄	—	4	1	no	—
828	C₂²⋊C₄	—	4	2	no	—
829	C₂²⋊C₄	—	4	2	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₂²⋊C₄	—	4	2	no	—
832	C₂²⋊C₄	—	4	2	no	—
833	C₂²⋊C₄	—	4	2	no	—
834	C₂²⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
835	C₂²⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
836	C₂²⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
837	C₂²⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
838	C₂²⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
839	C₂²⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
840	C₂²⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
841	C₄²	—	2	2	no	—
842	C₄²	—	2	2	no	—
843	C₄²	—	2	2	no	—
844	C₄²	—	2	4	no	—
845	C₄²	—	2	2	no	—
846	C₄²	—	4	1	no	—
847	C₄²	—	4	1	no	—
848	C₄²	—	4	2	no	—
849	C₄²	—	4	2	no	—
850	C₄²	—	4	2	no	—
851	C₄²	—	4	2	no	—
852	C₄²	—	4	2	no	—
853	C₄²	—	4	2	no	—
854	C₄²	—	4	2	no	—
855	C₄²	C₂²×C₄×C₂₉	1	4	yes	—
856	C₄²	C₂²×C₄×C₂₉	1	4	yes	—
857	C₄²	C₂²×C₄×C₂₉	1	8	yes	—
858	C₂³	—	2	2	no	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	2	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	2	no	—
866	C₂³	—	2	1	no	—
867	C₂³	—	2	2	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	1	no	—
870	C₂³	C₂³×C₄×C₂₉	1	2	yes	—
871	C₂³	C₂³×C₄×C₂₉	1	4	yes	—
872	C₂³	C₂⁵×C₂₉	1	1	yes	characteristic
873	Q₈	—	2	8	no	—
874	Q₈	—	4	8	no	—
875	D₄	—	2	8	no	—
876	D₄	—	4	8	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	8	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	4	8	no	—
929	C₂×C₄	—	4	4	no	—
930	C₂×C₄	—	4	4	no	—
931	C₂×C₄	—	8	4	no	—
932	C₂×C₄	—	8	4	no	—
933	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
934	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
935	C₂×C₄	C₂³×C₄×C₂₉	1	4	yes	—
936	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
937	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
938	C₂×C₄	C₂³×C₄×C₂₉	1	4	yes	—
939	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
940	C₂×C₄	C₂³×C₄×C₂₉	1	4	yes	—
941	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
942	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
943	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
944	C₂×C₄	C₂₉×2₋¹⁺⁴	1	2	yes	—
945	C₂×C₄	C₂₉×2₋¹⁺⁴	1	2	yes	—
946	C₂²	—	2	2	no	—
947	C₂²	—	2	4	no	—
948	C₂²	—	2	4	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	4	no	—
952	C₂²	—	4	1	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	1	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	1	no	—
958	C₂²	—	4	1	no	—
959	C₂²	—	4	2	no	—
960	C₂²	C₂⁴×C₄×C₂₉	1	1	yes	characteristic
961	C₂²	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
962	C₂²	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
963	C₂²	C₂×C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
964	C₂²	C₂×C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
965	C₂²	C₂₉×#585	1	1	yes	characteristic
966	C₂²	C₂₉×#585	1	1	yes	characteristic
967	C₄	—	2	2	no	—
968	C₄	—	2	2	no	—
969	C₄	—	2	2	no	—
970	C₄	—	2	4	no	—
971	C₄	—	2	2	no	—
972	C₄	—	2	4	no	—
973	C₄	—	2	4	no	—
974	C₄	—	2	2	no	—
975	C₄	—	2	2	no	—
976	C₄	—	2	2	no	—
977	C₄	—	4	2	no	—
978	C₄	—	4	1	no	—
979	C₄	—	4	1	no	—
980	C₄	—	4	1	no	—
981	C₄	—	4	1	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	1	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	2	no	—
987	C₄	C₂₉×#520	1	4	yes	—
988	C₂	—	4	2	no	—
989	C₂	—	4	4	no	—
990	C₂	C₂×C₂₉×#520	1	1	yes	characteristic
991	C₂	C₄×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
992	C₂	C₄×C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
993	C₂	C₂₉×#3536	1	1	yes	characteristic
994	C₂	C₂₉×#3540	1	1	yes	characteristic
995	C₂	C₂₉×#3554	1	1	yes	characteristic
996	C₂	C₂₉×#3555	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁵×C₂₉
prime radical	C₂×C₂₉×#121	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#2379	C₂	semidirect
3. C₂₉×#2376	C₂	semidirect
4. C₂₉×#2369	C₂	semidirect
5. C₂₉×#2367	C₂	semidirect
6. C₂₉×#2367	C₂	semidirect
7. C₂₉×#2367	C₂	semidirect
8. C₂₉×#2365	C₂	semidirect
9. C₂₉×#2359	C₂	semidirect
10. C₂₉×#2355	C₂	semidirect
11. C₂₉×#2354	C₂	semidirect
12. C₂₉×#2351	C₂	semidirect
13. C₂₉×#2349	C₂	semidirect
14. C₂₉×#2334	C₂	semidirect
15. C₂₉×#2334	C₂	semidirect
16. C₂₉×#2329	C₂	semidirect
18. C₂₉×#2323	C₂	semidirect
19. C₂₉×#2323	C₂	semidirect
20. C₂₉×#2314	C₂	semidirect
21. C₄×C₂₉×C₂²⋊Q₈	C₂	semidirect
23. C₂₉×#2296	C₂	semidirect
24. C₂₉×#542	C₄	semidirect
134. C₂₉×C₄⋊Q₈	C₂×C₄	semidirect
135. C₂₉×#126	C₂×C₄	semidirect
136. C₂₉×#124	C₂×C₄	semidirect
137. C₂₉×#124	C₂×C₄	semidirect
138. C₂₉×#123	C₂×C₄	semidirect
139. C₂₉×C₂²⋊Q₈	C₂×C₄	semidirect
140. C₂₉×C₂²⋊Q₈	C₂×C₄	semidirect
145. C₄×Q₈×C₂₉	C₂×C₄	semidirect
149. C₄×D₄×C₂₉	C₂×C₄	semidirect
152. C₂₉×#117	C₂×C₄	semidirect
359. #34419	C₂₉	direct (N × H)
449. #2379	C₂×C₂₉	semidirect
450. #2376	C₂×C₂₉	semidirect
451. #2369	C₂×C₂₉	semidirect
452. #2367	C₂×C₂₉	semidirect
453. #2367	C₂×C₂₉	semidirect
454. #2367	C₂×C₂₉	semidirect
455. #2365	C₂×C₂₉	semidirect
456. #2359	C₂×C₂₉	semidirect
457. #2355	C₂×C₂₉	semidirect
458. #2354	C₂×C₂₉	semidirect
459. #2351	C₂×C₂₉	semidirect
460. #2349	C₂×C₂₉	semidirect
461. #2334	C₂×C₂₉	semidirect
462. #2334	C₂×C₂₉	semidirect
463. #2329	C₂×C₂₉	semidirect
465. #2323	C₂×C₂₉	semidirect
466. #2323	C₂×C₂₉	semidirect
467. #2314	C₂×C₂₉	semidirect
468. C₄×C₂²⋊Q₈	C₂×C₂₉	semidirect
470. #2296	C₂×C₂₉	semidirect
513. #542	C₄×C₂₉	semidirect
632. C₄⋊Q₈	C₂×C₄×C₂₉	semidirect
633. #126	C₂×C₄×C₂₉	semidirect
634. #124	C₂×C₄×C₂₉	semidirect
635. #124	C₂×C₄×C₂₉	semidirect
636. #123	C₂×C₄×C₂₉	semidirect
637. C₂²⋊Q₈	C₂×C₄×C₂₉	semidirect
638. C₂²⋊Q₈	C₂×C₄×C₂₉	semidirect
643. C₄×Q₈	C₂×C₄×C₂₉	semidirect
647. C₄×D₄	C₂×C₄×C₂₉	semidirect
650. #117	C₂×C₄×C₂₉	semidirect
741. C₂₉	#34419	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×#542	2
C₂₉×#2379	2
C₂₉×#2376	2
C₂₉×#2369	2
C₂₉×#2367	2
C₂₉×#2365	2
C₂₉×#2359	2
C₂₉×#2355	2
C₂₉×#2354	2
C₂₉×#2351	2
C₂₉×#2349	2
C₂₉×#2334	2
C₂₉×#2329	2
C₂₉×#2324	2
C₂₉×#2323	2
C₂₉×#2314	2
C₄×C₂₉×C₂²⋊Q₈	2
C₄×C₂₉×#121	2
C₂₉×#2296	2
#34419	29

Subgroups — C29×#34419 #20329319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#34419 #20329319