Subgroups — C₂₉×#34277 #20329177

Order 7424.

2634 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#538	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2374	C₂	1	2	yes	maximal, complemented
3	C₂₉×#2373	C₂	1	2	yes	maximal, complemented
4	C₂₉×#2373	C₂	1	2	yes	maximal, complemented
5	C₂₉×#2372	C₂	1	2	yes	maximal, complemented
6	C₂₉×#2367	C₂	1	2	yes	maximal, complemented
7	C₂₉×#2364	C₂	1	2	yes	maximal, complemented
8	C₂₉×#2363	C₂	1	2	yes	maximal, complemented
9	C₂₉×#2359	C₂	1	2	yes	maximal, complemented
10	C₂₉×#2329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#2325	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#2321	C₂	1	2	yes	maximal, complemented
13	C₂₉×#2312	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₂₉×#120	C₂	1	2	yes	maximal, complemented
17	C₂₉×#2290	C₂	1	2	yes	maximal, complemented
18	C₂₉×#2275	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₂²⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₂₉	C₂²	1	1	yes	characteristic
21	C₂₉×#538	C₄	1	16	yes	complemented
22	C₂×C₂₉×#126	C₂²	1	2	yes	—
23	C₂×C₂₉×#124	C₂²	1	2	yes	—
24	C₂×C₂₉×#123	C₂²	1	2	yes	—
25	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×#121	C₂²	1	2	yes	—
28	C₂×C₂₉×#120	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₂₉×#117	C₂²	1	2	yes	complemented
37	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
41	C₂₉×#391	C₂²	1	1	yes	characteristic, complemented
42	C₂₉×#391	C₂²	1	2	yes	complemented
43	C₂₉×#390	C₂²	1	2	yes	—
44	C₂₉×#390	C₂²	1	2	yes	—
45	C₂₉×#390	C₂²	1	1	yes	characteristic, complemented
46	C₂₉×#389	C₂²	1	1	yes	characteristic, complemented
47	C₂₉×#389	C₂²	1	1	yes	characteristic, complemented
48	C₂₉×#389	C₂²	1	2	yes	complemented
49	C₂₉×#388	C₂²	1	2	yes	—
50	C₂₉×#388	C₂²	1	2	yes	—
51	C₂₉×#388	C₂²	1	2	yes	—
52	C₂₉×#388	C₂²	1	2	yes	—
53	C₂₉×#388	C₂²	1	2	yes	—
54	C₂₉×#388	C₂²	1	2	yes	—
55	C₂₉×#388	C₂²	1	2	yes	—
56	C₂₉×#388	C₂²	1	2	yes	—
57	C₂₉×#388	C₂²	1	2	yes	complemented
58	C₂₉×#388	C₂²	1	2	yes	complemented
59	C₂₉×#388	C₂²	1	2	yes	complemented
60	C₂₉×#388	C₂²	1	2	yes	complemented
61	C₂₉×#387	C₂²	1	2	yes	complemented
62	C₂₉×#387	C₂²	1	2	yes	complemented
63	C₂₉×#387	C₂²	1	2	yes	complemented
64	C₂₉×#387	C₂²	1	2	yes	complemented
65	C₂₉×#387	C₂²	1	2	yes	complemented
66	C₂₉×#387	C₂²	1	2	yes	complemented
67	C₂₉×#386	C₂²	1	2	yes	—
68	C₂₉×#386	C₂²	1	2	yes	—
69	C₂₉×#386	C₂²	1	2	yes	—
70	C₂₉×#386	C₂²	1	2	yes	—
71	C₂₉×#386	C₂²	1	2	yes	—
72	C₂₉×#386	C₂²	1	2	yes	—
73	C₂₉×#386	C₂²	1	2	yes	complemented
74	C₂₉×#385	C₂²	1	2	yes	—
75	C₂₉×#385	C₂²	1	2	yes	—
76	C₂₉×#385	C₂²	1	2	yes	—
77	C₂₉×#385	C₂²	1	2	yes	—
78	C₂₉×#385	C₂²	1	2	yes	complemented
79	C₂₉×#380	C₂²	1	1	yes	characteristic
80	C₂₉×#380	C₂²	1	1	yes	characteristic
81	C₂₉×#379	C₂²	1	2	yes	—
82	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	complemented
83	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	complemented
84	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	complemented
85	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	complemented
86	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
87	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	complemented
88	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
89	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
90	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
91	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
92	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
93	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
94	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
95	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	complemented
99	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	complemented
103	C₂₉×#376	C₂²	1	2	yes	complemented
104	C₂₉×#376	C₂²	1	2	yes	complemented
105	C₂×C₂₉×#95	C₂²	1	1	yes	characteristic
106	C₂×C₂₉×#95	C₂²	1	1	yes	characteristic
107	C₂×C₂₉×#95	C₂²	1	2	yes	complemented
108	C₂⁵×C₂₉	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
111	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
112	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
113	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₂₉	—	2	4	no	—
115	C₂³×C₄×C₂₉	—	4	2	no	—
116	C₂³×C₄×C₂₉	—	4	2	no	—
117	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
119	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
120	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
122	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
123	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
126	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
128	C₂₉×#126	C₂×C₄	1	16	yes	complemented
129	C₂₉×#124	C₂×C₄	1	16	yes	complemented
130	C₂₉×#123	C₂×C₄	1	16	yes	complemented
131	C₂₉×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
132	C₂₉×#121	C₂×C₄	1	16	yes	complemented
133	C₂₉×#121	C₂×C₄	1	8	yes	complemented
134	C₂₉×#120	C₂×C₄	1	16	yes	complemented
135	C₄×Q₈×C₂₉	—	4	2	no	—
136	C₄×D₄×C₂₉	—	2	8	no	—
137	C₄×D₄×C₂₉	—	2	8	no	—
138	C₄×D₄×C₂₉	—	4	2	no	—
139	C₄×D₄×C₂₉	—	4	4	no	—
140	C₄×D₄×C₂₉	—	4	4	no	—
141	C₄×D₄×C₂₉	C₂×C₄	1	16	yes	complemented
142	C₂₉×#117	—	4	4	no	—
143	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₂₉	—	2	4	no	—
158	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	8	yes	complemented
159	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
180	C₂×C₄²×C₂₉	—	4	2	no	—
181	C₂×C₄²×C₂₉	—	4	2	no	—
182	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
183	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
186	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
187	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
189	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
191	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
192	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
193	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
194	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
195	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
196	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
197	C₂₉×#95	C₂³	1	2	yes	—
198	C₂₉×#95	C₂³	1	2	yes	—
199	C₂₉×#95	C₂³	1	2	yes	—
200	C₂₉×#95	C₂³	1	2	yes	—
201	C₂₉×#95	C₂³	1	2	yes	—
202	C₂₉×#95	C₂³	1	2	yes	—
203	C₂₉×#95	C₂³	1	2	yes	—
204	C₂₉×#95	C₂³	1	2	yes	—
205	C₂₉×#95	C₂³	1	2	yes	—
206	C₂₉×#95	C₂³	1	2	yes	—
207	C₂₉×#95	C₂³	1	2	yes	—
208	C₂₉×#95	C₂³	1	2	yes	—
209	C₂₉×#95	C₂³	1	2	yes	—
210	C₂₉×#95	C₂³	1	2	yes	—
211	C₂₉×#95	C₂³	1	2	yes	—
212	C₂₉×#95	C₂³	1	2	yes	—
213	C₂₉×#95	C₂³	1	2	yes	—
214	C₂₉×#95	C₂³	1	2	yes	—
215	C₂₉×#95	C₂³	1	2	yes	—
216	C₂₉×#95	C₂³	1	2	yes	—
217	C₂⁴×C₂₉	—	2	2	no	—
218	C₂⁴×C₂₉	—	2	2	no	—
219	C₂⁴×C₂₉	—	4	1	no	—
220	C₂⁴×C₂₉	—	4	1	no	—
221	C₂⁴×C₂₉	—	4	1	no	—
222	C₂⁴×C₂₉	—	4	1	no	—
223	C₂⁴×C₂₉	C₂²×C₄	1	4	yes	—
224	C₂⁴×C₂₉	C₂⁴	1	2	yes	—
225	C₂⁴×C₂₉	C₂⁴	1	2	yes	—
226	C₂⁴×C₂₉	C₂⁴	1	1	yes	characteristic
227	C₂×Q₈×C₂₉	—	4	1	no	—
228	C₂×Q₈×C₂₉	—	4	1	no	—
229	C₂×Q₈×C₂₉	C₂²×C₄	1	4	yes	complemented
230	C₂×D₄×C₂₉	—	2	4	no	—
231	C₂×D₄×C₂₉	—	2	4	no	—
232	C₂×D₄×C₂₉	—	4	1	no	—
233	C₂×D₄×C₂₉	—	4	2	no	—
234	C₂×D₄×C₂₉	—	4	2	no	—
235	C₂×D₄×C₂₉	—	4	2	no	—
236	C₂×D₄×C₂₉	—	4	1	no	—
237	C₂×D₄×C₂₉	—	4	2	no	—
238	C₂×D₄×C₂₉	C₂²×C₄	1	8	yes	—
239	C₂×D₄×C₂₉	C₂²×C₄	1	8	yes	—
240	C₂×D₄×C₂₉	C₂²×C₄	1	8	yes	—
241	C₂×D₄×C₂₉	C₂²×C₄	1	4	yes	complemented
242	C₂²×C₄×C₂₉	—	2	2	no	—
243	C₂²×C₄×C₂₉	—	2	2	no	—
244	C₂²×C₄×C₂₉	—	2	2	no	—
245	C₂²×C₄×C₂₉	—	2	2	no	—
246	C₂²×C₄×C₂₉	—	2	4	no	—
247	C₂²×C₄×C₂₉	—	2	4	no	—
248	C₂²×C₄×C₂₉	—	2	4	no	—
249	C₂²×C₄×C₂₉	—	2	4	no	—
250	C₂²×C₄×C₂₉	—	2	4	no	—
251	C₂²×C₄×C₂₉	—	2	4	no	—
252	C₂²×C₄×C₂₉	—	4	1	no	—
253	C₂²×C₄×C₂₉	—	4	1	no	—
254	C₂²×C₄×C₂₉	—	4	1	no	—
255	C₂²×C₄×C₂₉	—	4	1	no	—
256	C₂²×C₄×C₂₉	—	4	2	no	—
257	C₂²×C₄×C₂₉	—	4	2	no	—
258	C₂²×C₄×C₂₉	—	4	2	no	—
259	C₂²×C₄×C₂₉	—	4	1	no	—
260	C₂²×C₄×C₂₉	—	4	1	no	—
261	C₂²×C₄×C₂₉	—	4	1	no	—
262	C₂²×C₄×C₂₉	—	4	1	no	—
263	C₂²×C₄×C₂₉	—	4	2	no	—
264	C₂²×C₄×C₂₉	—	4	1	no	—
265	C₂²×C₄×C₂₉	—	4	1	no	—
266	C₂²×C₄×C₂₉	—	4	2	no	—
267	C₂²×C₄×C₂₉	—	4	2	no	—
268	C₂²×C₄×C₂₉	—	4	2	no	—
269	C₂²×C₄×C₂₉	—	4	2	no	—
270	C₂²×C₄×C₂₉	—	4	16	no	—
271	C₂²×C₄×C₂₉	C₂²×C₄	1	4	yes	—
272	C₂²×C₄×C₂₉	C₂²×C₄	1	4	yes	—
273	C₂²×C₄×C₂₉	C₂²×C₄	1	8	yes	complemented
274	C₂²×C₄×C₂₉	#41	1	4	yes	—
275	C₂²×C₄×C₂₉	#41	1	4	yes	—
276	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
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	2	yes	—
287	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
292	C₄⋊C₄×C₂₉	—	2	4	no	—
293	C₄⋊C₄×C₂₉	—	2	4	no	—
294	C₄⋊C₄×C₂₉	—	2	4	no	—
295	C₄⋊C₄×C₂₉	—	2	4	no	—
296	C₄⋊C₄×C₂₉	—	4	1	no	—
297	C₄⋊C₄×C₂₉	—	4	1	no	—
298	C₄⋊C₄×C₂₉	—	4	2	no	—
299	C₄⋊C₄×C₂₉	—	4	2	no	—
300	C₄⋊C₄×C₂₉	—	4	1	no	—
301	C₄⋊C₄×C₂₉	—	4	1	no	—
302	C₄⋊C₄×C₂₉	C₂²×C₄	1	8	yes	complemented
303	C₄⋊C₄×C₂₉	C₂²×C₄	1	8	yes	complemented
304	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	complemented
305	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	complemented
306	C₂²⋊C₄×C₂₉	—	2	4	no	—
307	C₂²⋊C₄×C₂₉	—	2	4	no	—
308	C₂²⋊C₄×C₂₉	—	2	4	no	—
309	C₂²⋊C₄×C₂₉	—	2	4	no	—
310	C₂²⋊C₄×C₂₉	—	2	4	no	—
311	C₂²⋊C₄×C₂₉	—	2	4	no	—
312	C₂²⋊C₄×C₂₉	—	2	4	no	—
313	C₂²⋊C₄×C₂₉	—	2	4	no	—
314	C₂²⋊C₄×C₂₉	—	4	2	no	—
315	C₂²⋊C₄×C₂₉	—	4	2	no	—
316	C₂²⋊C₄×C₂₉	—	4	2	no	—
317	C₂²⋊C₄×C₂₉	—	4	2	no	—
318	C₂²⋊C₄×C₂₉	—	4	2	no	—
319	C₂²⋊C₄×C₂₉	—	4	2	no	—
320	C₂²⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
321	C₂²⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
322	C₂²⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
323	C₂²⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
324	C₂²⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
325	C₂²⋊C₄×C₂₉	C₂²×C₄	1	8	yes	complemented
326	C₂²⋊C₄×C₂₉	C₂²×C₄	1	8	yes	complemented
327	C₄²×C₂₉	—	2	4	no	—
328	C₄²×C₂₉	—	2	4	no	—
329	C₄²×C₂₉	—	2	4	no	—
330	C₄²×C₂₉	—	2	2	no	—
331	C₄²×C₂₉	—	2	2	no	—
332	C₄²×C₂₉	—	4	1	no	—
333	C₄²×C₂₉	—	4	2	no	—
334	C₄²×C₂₉	—	4	1	no	—
335	C₄²×C₂₉	—	4	2	no	—
336	C₄²×C₂₉	—	4	2	no	—
337	C₄²×C₂₉	—	4	2	no	—
338	C₄²×C₂₉	—	4	2	no	—
339	C₄²×C₂₉	—	4	2	no	—
340	C₄²×C₂₉	—	4	2	no	—
341	C₄²×C₂₉	C₂²×C₄	1	8	yes	complemented
342	#34277	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
343	C₂³×C₂₉	—	2	1	no	—
344	C₂³×C₂₉	—	2	1	no	—
345	C₂³×C₂₉	—	2	1	no	—
346	C₂³×C₂₉	—	2	1	no	—
347	C₂³×C₂₉	—	2	8	no	—
348	C₂³×C₂₉	—	2	2	no	—
349	C₂³×C₂₉	—	2	2	no	—
350	C₂³×C₂₉	—	2	2	no	—
351	C₂³×C₂₉	—	2	2	no	—
352	C₂³×C₂₉	—	2	2	no	—
353	C₂³×C₂₉	—	2	2	no	—
354	C₂³×C₂₉	—	2	2	no	—
355	C₂³×C₂₉	—	2	2	no	—
356	C₂³×C₂₉	—	2	2	no	—
357	C₂³×C₂₉	—	2	2	no	—
358	C₂³×C₂₉	—	2	2	no	—
359	C₂³×C₂₉	—	2	2	no	—
360	C₂³×C₂₉	—	4	4	no	—
361	C₂³×C₂₉	—	4	4	no	—
362	C₂³×C₂₉	—	4	4	no	—
363	C₂³×C₂₉	—	4	4	no	—
364	C₂³×C₂₉	—	4	4	no	—
365	C₂³×C₂₉	—	4	4	no	—
366	C₂³×C₂₉	C₂³×C₄	1	4	yes	—
367	C₂³×C₂₉	C₂³×C₄	1	4	yes	—
368	C₂³×C₂₉	C₂³×C₄	1	2	yes	—
369	C₂³×C₂₉	C₂×#41	1	2	yes	—
370	C₂³×C₂₉	C₂×#41	1	2	yes	—
371	C₂³×C₂₉	C₂⁵	1	1	yes	characteristic
372	Q₈×C₂₉	—	4	4	no	—
373	D₄×C₂₉	—	2	16	no	—
374	D₄×C₂₉	—	4	8	no	—
375	D₄×C₂₉	—	4	8	no	—
376	D₄×C₂₉	—	4	4	no	—
377	C₂×C₄×C₂₉	—	2	8	no	—
378	C₂×C₄×C₂₉	—	2	2	no	—
379	C₂×C₄×C₂₉	—	2	2	no	—
380	C₂×C₄×C₂₉	—	2	1	no	—
381	C₂×C₄×C₂₉	—	2	1	no	—
382	C₂×C₄×C₂₉	—	2	1	no	—
383	C₂×C₄×C₂₉	—	2	2	no	—
384	C₂×C₄×C₂₉	—	2	1	no	—
385	C₂×C₄×C₂₉	—	2	1	no	—
386	C₂×C₄×C₂₉	—	2	1	no	—
387	C₂×C₄×C₂₉	—	2	2	no	—
388	C₂×C₄×C₂₉	—	2	1	no	—
389	C₂×C₄×C₂₉	—	2	1	no	—
390	C₂×C₄×C₂₉	—	2	2	no	—
391	C₂×C₄×C₂₉	—	2	2	no	—
392	C₂×C₄×C₂₉	—	2	2	no	—
393	C₂×C₄×C₂₉	—	2	1	no	—
394	C₂×C₄×C₂₉	—	2	2	no	—
395	C₂×C₄×C₂₉	—	2	2	no	—
396	C₂×C₄×C₂₉	—	2	1	no	—
397	C₂×C₄×C₂₉	—	2	1	no	—
398	C₂×C₄×C₂₉	—	2	2	no	—
399	C₂×C₄×C₂₉	—	2	1	no	—
400	C₂×C₄×C₂₉	—	2	2	no	—
401	C₂×C₄×C₂₉	—	2	2	no	—
402	C₂×C₄×C₂₉	—	2	2	no	—
403	C₂×C₄×C₂₉	—	2	2	no	—
404	C₂×C₄×C₂₉	—	2	2	no	—
405	C₂×C₄×C₂₉	—	2	2	no	—
406	C₂×C₄×C₂₉	—	2	2	no	—
407	C₂×C₄×C₂₉	—	2	2	no	—
408	C₂×C₄×C₂₉	—	2	2	no	—
409	C₂×C₄×C₂₉	—	2	2	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	2	no	—
414	C₂×C₄×C₂₉	—	2	2	no	—
415	C₂×C₄×C₂₉	—	4	4	no	—
416	C₂×C₄×C₂₉	—	4	4	no	—
417	C₂×C₄×C₂₉	—	4	4	no	—
418	C₂×C₄×C₂₉	—	4	8	no	—
419	C₂×C₄×C₂₉	—	4	4	no	—
420	C₂×C₄×C₂₉	—	4	8	no	—
421	C₂×C₄×C₂₉	—	4	8	no	—
422	C₂×C₄×C₂₉	—	4	4	no	—
423	C₂×C₄×C₂₉	—	8	4	no	—
424	C₂×C₄×C₂₉	—	8	4	no	—
425	C₂×C₄×C₂₉	C₂³×C₄	1	4	yes	—
426	C₂×C₄×C₂₉	C₂³×C₄	1	4	yes	—
427	C₂×C₄×C₂₉	C₂³×C₄	1	4	yes	—
428	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
429	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
430	C₂×C₄×C₂₉	C₂³×C₄	1	4	yes	—
431	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
432	C₂×C₄×C₂₉	C₂×#41	1	4	yes	—
433	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
434	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
435	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
436	C₂×#538	C₂×C₂₉	1	1	yes	characteristic
437	#2374	C₂×C₂₉	1	2	yes	complemented
438	#2373	C₂×C₂₉	1	2	yes	complemented
439	#2373	C₂×C₂₉	1	2	yes	complemented
440	#2372	C₂×C₂₉	1	2	yes	complemented
441	#2367	C₂×C₂₉	1	2	yes	complemented
442	#2364	C₂×C₂₉	1	2	yes	complemented
443	#2363	C₂×C₂₉	1	2	yes	complemented
444	#2359	C₂×C₂₉	1	2	yes	complemented
445	#2329	C₂×C₂₉	1	1	yes	characteristic, complemented
446	#2325	C₂×C₂₉	1	1	yes	characteristic, complemented
447	#2321	C₂×C₂₉	1	2	yes	complemented
448	#2312	C₂×C₂₉	1	1	yes	characteristic, complemented
449	C₄×C₂²⋊Q₈	C₂×C₂₉	1	1	yes	characteristic, complemented
450	C₄×#121	C₂×C₂₉	1	1	yes	characteristic, complemented
451	C₄×#120	C₂×C₂₉	1	2	yes	complemented
452	#2290	C₂×C₂₉	1	2	yes	complemented
453	#2275	C₂×C₂₉	1	2	yes	complemented
454	C₂×C₄×C₂²⋊C₄	C₂×C₂₉	1	1	yes	characteristic, complemented
455	C₂²×C₂₉	—	2	2	no	—
456	C₂²×C₂₉	—	2	2	no	—
457	C₂²×C₂₉	—	2	2	no	—
458	C₂²×C₂₉	—	2	2	no	—
459	C₂²×C₂₉	—	2	2	no	—
460	C₂²×C₂₉	—	2	2	no	—
461	C₂²×C₂₉	—	2	4	no	—
462	C₂²×C₂₉	—	2	4	no	—
463	C₂²×C₂₉	—	2	4	no	—
464	C₂²×C₂₉	—	2	4	no	—
465	C₂²×C₂₉	—	2	4	no	—
466	C₂²×C₂₉	—	2	4	no	—
467	C₂²×C₂₉	—	4	16	no	—
468	C₂²×C₂₉	—	4	2	no	—
469	C₂²×C₂₉	—	4	2	no	—
470	C₂²×C₂₉	—	4	2	no	—
471	C₂²×C₂₉	—	4	2	no	—
472	C₂²×C₂₉	—	4	2	no	—
473	C₂²×C₂₉	—	4	2	no	—
474	C₂²×C₂₉	—	4	2	no	—
475	C₂²×C₂₉	—	4	2	no	—
476	C₂²×C₂₉	C₄×#41	1	4	yes	—
477	C₂²×C₂₉	C₂⁴×C₄	1	1	yes	characteristic
478	C₂²×C₂₉	C₂²×#41	1	1	yes	characteristic
479	C₂²×C₂₉	C₂²×#41	1	1	yes	characteristic
480	C₂²×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
481	C₂²×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
482	C₂²×C₂₉	#585	1	1	yes	characteristic
483	C₂²×C₂₉	#585	1	1	yes	characteristic
484	C₄×C₂₉	—	2	4	no	—
485	C₄×C₂₉	—	2	4	no	—
486	C₄×C₂₉	—	2	2	no	—
487	C₄×C₂₉	—	2	4	no	—
488	C₄×C₂₉	—	2	2	no	—
489	C₄×C₂₉	—	2	4	no	—
490	C₄×C₂₉	—	2	2	no	—
491	C₄×C₂₉	—	2	2	no	—
492	C₄×C₂₉	—	2	4	no	—
493	C₄×C₂₉	—	2	2	no	—
494	C₄×C₂₉	—	2	2	no	—
495	C₄×C₂₉	—	4	2	no	—
496	C₄×C₂₉	—	4	2	no	—
497	C₄×C₂₉	—	4	2	no	—
498	C₄×C₂₉	—	4	2	no	—
499	C₄×C₂₉	—	4	2	no	—
500	C₂⁴×C₄	C₂²×C₂₉	1	1	yes	characteristic
501	#538	C₄×C₂₉	1	16	yes	complemented
502	C₂×#126	C₂²×C₂₉	1	2	yes	—
503	C₂×#124	C₂²×C₂₉	1	2	yes	—
504	C₂×#123	C₂²×C₂₉	1	2	yes	—
505	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
506	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic
507	C₂×#121	C₂²×C₂₉	1	2	yes	—
508	C₂×#120	C₂²×C₂₉	1	2	yes	—
509	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
510	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
511	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
512	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
513	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
514	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
515	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
516	C₂×#117	C₂²×C₂₉	1	2	yes	complemented
517	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
518	C₂²×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
519	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
520	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
521	#391	C₂²×C₂₉	1	2	yes	complemented
522	#391	C₂²×C₂₉	1	1	yes	characteristic, complemented
523	#390	C₂²×C₂₉	1	2	yes	—
524	#390	C₂²×C₂₉	1	2	yes	—
525	#390	C₂²×C₂₉	1	1	yes	characteristic, complemented
526	#389	C₂²×C₂₉	1	2	yes	complemented
527	#389	C₂²×C₂₉	1	1	yes	characteristic, complemented
528	#389	C₂²×C₂₉	1	1	yes	characteristic, complemented
529	#388	C₂²×C₂₉	1	2	yes	—
530	#388	C₂²×C₂₉	1	2	yes	—
531	#388	C₂²×C₂₉	1	2	yes	—
532	#388	C₂²×C₂₉	1	2	yes	—
533	#388	C₂²×C₂₉	1	2	yes	—
534	#388	C₂²×C₂₉	1	2	yes	—
535	#388	C₂²×C₂₉	1	2	yes	—
536	#388	C₂²×C₂₉	1	2	yes	—
537	#388	C₂²×C₂₉	1	2	yes	complemented
538	#388	C₂²×C₂₉	1	2	yes	complemented
539	#388	C₂²×C₂₉	1	2	yes	complemented
540	#388	C₂²×C₂₉	1	2	yes	complemented
541	#387	C₂²×C₂₉	1	2	yes	complemented
542	#387	C₂²×C₂₉	1	2	yes	complemented
543	#387	C₂²×C₂₉	1	2	yes	complemented
544	#387	C₂²×C₂₉	1	2	yes	complemented
545	#387	C₂²×C₂₉	1	2	yes	complemented
546	#387	C₂²×C₂₉	1	2	yes	complemented
547	#386	C₂²×C₂₉	1	2	yes	—
548	#386	C₂²×C₂₉	1	2	yes	—
549	#386	C₂²×C₂₉	1	2	yes	—
550	#386	C₂²×C₂₉	1	2	yes	—
551	#386	C₂²×C₂₉	1	2	yes	—
552	#386	C₂²×C₂₉	1	2	yes	—
553	#386	C₂²×C₂₉	1	2	yes	complemented
554	#385	C₂²×C₂₉	1	2	yes	—
555	#385	C₂²×C₂₉	1	2	yes	—
556	#385	C₂²×C₂₉	1	2	yes	—
557	#385	C₂²×C₂₉	1	2	yes	—
558	#385	C₂²×C₂₉	1	2	yes	complemented
559	#380	C₂²×C₂₉	1	1	yes	characteristic
560	#380	C₂²×C₂₉	1	1	yes	characteristic
561	#379	C₂²×C₂₉	1	2	yes	—
562	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	complemented
563	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	complemented
564	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	complemented
565	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	complemented
566	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
567	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	complemented
568	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
569	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
570	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
571	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
572	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
573	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
574	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
575	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
576	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
577	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
578	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	complemented
579	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	complemented
580	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	complemented
581	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	complemented
582	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	complemented
583	#376	C₂²×C₂₉	1	2	yes	complemented
584	#376	C₂²×C₂₉	1	2	yes	complemented
585	C₂×#95	C₂²×C₂₉	1	1	yes	characteristic
586	C₂×#95	C₂²×C₂₉	1	1	yes	characteristic
587	C₂×#95	C₂²×C₂₉	1	2	yes	complemented
588	C₂×C₂₉	—	2	4	no	—
589	C₂×C₂₉	—	4	4	no	—
590	C₂×C₂₉	—	4	4	no	—
591	C₂×C₂₉	C₂×C₄×#41	1	1	yes	characteristic
592	C₂×C₂₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic
593	C₂×C₂₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic
594	C₂×C₂₉	#3490	1	1	yes	characteristic
595	C₂×C₂₉	#3493	1	1	yes	characteristic
596	C₂×C₂₉	#3505	1	1	yes	characteristic
597	C₂×C₂₉	#3506	1	1	yes	characteristic
598	C₂⁵	C₂³×C₂₉	1	1	yes	characteristic
599	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
600	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
601	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
602	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
603	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
604	C₂³×C₄	—	2	4	no	—
605	C₂³×C₄	—	4	2	no	—
606	C₂³×C₄	—	4	2	no	—
607	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
608	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
609	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
610	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
612	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
613	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
614	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
615	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
616	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
617	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
618	#126	C₂×C₄×C₂₉	1	16	yes	complemented
619	#124	C₂×C₄×C₂₉	1	16	yes	complemented
620	#123	C₂×C₄×C₂₉	1	16	yes	complemented
621	C₂²⋊Q₈	C₂×C₄×C₂₉	1	8	yes	complemented
622	#121	C₂×C₄×C₂₉	1	16	yes	complemented
623	#121	C₂×C₄×C₂₉	1	8	yes	complemented
624	#120	C₂×C₄×C₂₉	1	16	yes	complemented
625	C₄×Q₈	—	4	2	no	—
626	C₄×D₄	—	2	8	no	—
627	C₄×D₄	—	2	8	no	—
628	C₄×D₄	—	4	2	no	—
629	C₄×D₄	—	4	4	no	—
630	C₄×D₄	—	4	4	no	—
631	C₄×D₄	C₂×C₄×C₂₉	1	16	yes	complemented
632	#117	—	4	4	no	—
633	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	—	2	4	no	—
648	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	8	yes	complemented
649	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
670	C₂×C₄²	—	4	2	no	—
671	C₂×C₄²	—	4	2	no	—
672	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
673	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
674	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
675	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
678	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
679	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
680	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
681	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
682	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
684	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
685	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
686	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
687	#95	C₂³×C₂₉	1	2	yes	—
688	#95	C₂³×C₂₉	1	2	yes	—
689	#95	C₂³×C₂₉	1	2	yes	—
690	#95	C₂³×C₂₉	1	2	yes	—
691	#95	C₂³×C₂₉	1	2	yes	—
692	#95	C₂³×C₂₉	1	2	yes	—
693	#95	C₂³×C₂₉	1	2	yes	—
694	#95	C₂³×C₂₉	1	2	yes	—
695	#95	C₂³×C₂₉	1	2	yes	—
696	#95	C₂³×C₂₉	1	2	yes	—
697	#95	C₂³×C₂₉	1	2	yes	—
698	#95	C₂³×C₂₉	1	2	yes	—
699	#95	C₂³×C₂₉	1	2	yes	—
700	#95	C₂³×C₂₉	1	2	yes	—
701	#95	C₂³×C₂₉	1	2	yes	—
702	#95	C₂³×C₂₉	1	2	yes	—
703	#95	C₂³×C₂₉	1	2	yes	—
704	#95	C₂³×C₂₉	1	2	yes	—
705	#95	C₂³×C₂₉	1	2	yes	—
706	#95	C₂³×C₂₉	1	2	yes	—
707	C₂₉	#34277	1	1	yes	characteristic, direct product factor, Sylow
708	C₂⁴	—	2	2	no	—
709	C₂⁴	—	2	2	no	—
710	C₂⁴	—	4	1	no	—
711	C₂⁴	—	4	1	no	—
712	C₂⁴	—	4	1	no	—
713	C₂⁴	—	4	1	no	—
714	C₂⁴	C₂²×C₄×C₂₉	1	4	yes	—
715	C₂⁴	C₂⁴×C₂₉	1	2	yes	—
716	C₂⁴	C₂⁴×C₂₉	1	2	yes	—
717	C₂⁴	C₂⁴×C₂₉	1	1	yes	characteristic
718	C₂×Q₈	—	4	1	no	—
719	C₂×Q₈	—	4	1	no	—
720	C₂×Q₈	C₂²×C₄×C₂₉	1	4	yes	complemented
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	4	1	no	—
724	C₂×D₄	—	4	2	no	—
725	C₂×D₄	—	4	2	no	—
726	C₂×D₄	—	4	2	no	—
727	C₂×D₄	—	4	1	no	—
728	C₂×D₄	—	4	2	no	—
729	C₂×D₄	C₂²×C₄×C₂₉	1	8	yes	—
730	C₂×D₄	C₂²×C₄×C₂₉	1	8	yes	—
731	C₂×D₄	C₂²×C₄×C₂₉	1	8	yes	—
732	C₂×D₄	C₂²×C₄×C₂₉	1	4	yes	complemented
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	4	no	—
738	C₂²×C₄	—	2	4	no	—
739	C₂²×C₄	—	2	4	no	—
740	C₂²×C₄	—	2	4	no	—
741	C₂²×C₄	—	2	4	no	—
742	C₂²×C₄	—	2	4	no	—
743	C₂²×C₄	—	4	1	no	—
744	C₂²×C₄	—	4	1	no	—
745	C₂²×C₄	—	4	1	no	—
746	C₂²×C₄	—	4	1	no	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	—	4	2	no	—
750	C₂²×C₄	—	4	1	no	—
751	C₂²×C₄	—	4	1	no	—
752	C₂²×C₄	—	4	1	no	—
753	C₂²×C₄	—	4	1	no	—
754	C₂²×C₄	—	4	2	no	—
755	C₂²×C₄	—	4	1	no	—
756	C₂²×C₄	—	4	1	no	—
757	C₂²×C₄	—	4	2	no	—
758	C₂²×C₄	—	4	2	no	—
759	C₂²×C₄	—	4	2	no	—
760	C₂²×C₄	—	4	2	no	—
761	C₂²×C₄	—	4	16	no	—
762	C₂²×C₄	C₂²×C₄×C₂₉	1	4	yes	—
763	C₂²×C₄	C₂²×C₄×C₂₉	1	4	yes	—
764	C₂²×C₄	C₂²×C₄×C₂₉	1	8	yes	complemented
765	C₂²×C₄	#41×C₂₉	1	4	yes	—
766	C₂²×C₄	#41×C₂₉	1	4	yes	—
767	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
781	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
783	C₄⋊C₄	—	2	4	no	—
784	C₄⋊C₄	—	2	4	no	—
785	C₄⋊C₄	—	2	4	no	—
786	C₄⋊C₄	—	2	4	no	—
787	C₄⋊C₄	—	4	2	no	—
788	C₄⋊C₄	—	4	1	no	—
789	C₄⋊C₄	—	4	1	no	—
790	C₄⋊C₄	—	4	1	no	—
791	C₄⋊C₄	—	4	1	no	—
792	C₄⋊C₄	—	4	2	no	—
793	C₄⋊C₄	C₂²×C₄×C₂₉	1	8	yes	complemented
794	C₄⋊C₄	C₂²×C₄×C₂₉	1	8	yes	complemented
795	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	complemented
796	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	complemented
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	4	2	no	—
806	C₂²⋊C₄	—	4	2	no	—
807	C₂²⋊C₄	—	4	2	no	—
808	C₂²⋊C₄	—	4	2	no	—
809	C₂²⋊C₄	—	4	2	no	—
810	C₂²⋊C₄	—	4	2	no	—
811	C₂²⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
812	C₂²⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
813	C₂²⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
814	C₂²⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
815	C₂²⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
816	C₂²⋊C₄	C₂²×C₄×C₂₉	1	8	yes	complemented
817	C₂²⋊C₄	C₂²×C₄×C₂₉	1	8	yes	complemented
818	C₄²	—	2	4	no	—
819	C₄²	—	2	4	no	—
820	C₄²	—	2	4	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	—	4	1	no	—
824	C₄²	—	4	2	no	—
825	C₄²	—	4	1	no	—
826	C₄²	—	4	2	no	—
827	C₄²	—	4	2	no	—
828	C₄²	—	4	2	no	—
829	C₄²	—	4	2	no	—
830	C₄²	—	4	2	no	—
831	C₄²	—	4	2	no	—
832	C₄²	C₂²×C₄×C₂₉	1	8	yes	complemented
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	1	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	8	no	—
838	C₂³	—	2	2	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	4	4	no	—
851	C₂³	—	4	4	no	—
852	C₂³	—	4	4	no	—
853	C₂³	—	4	4	no	—
854	C₂³	—	4	4	no	—
855	C₂³	—	4	4	no	—
856	C₂³	C₂³×C₄×C₂₉	1	4	yes	—
857	C₂³	C₂³×C₄×C₂₉	1	4	yes	—
858	C₂³	C₂³×C₄×C₂₉	1	2	yes	—
859	C₂³	C₂×#41×C₂₉	1	2	yes	—
860	C₂³	C₂×#41×C₂₉	1	2	yes	—
861	C₂³	C₂⁵×C₂₉	1	1	yes	characteristic
862	Q₈	—	4	4	no	—
863	D₄	—	2	16	no	—
864	D₄	—	4	8	no	—
865	D₄	—	4	8	no	—
866	D₄	—	4	4	no	—
867	C₂×C₄	—	2	8	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	4	4	no	—
906	C₂×C₄	—	4	4	no	—
907	C₂×C₄	—	4	4	no	—
908	C₂×C₄	—	4	8	no	—
909	C₂×C₄	—	4	4	no	—
910	C₂×C₄	—	4	8	no	—
911	C₂×C₄	—	4	8	no	—
912	C₂×C₄	—	4	4	no	—
913	C₂×C₄	—	8	4	no	—
914	C₂×C₄	—	8	4	no	—
915	C₂×C₄	C₂³×C₄×C₂₉	1	4	yes	—
916	C₂×C₄	C₂³×C₄×C₂₉	1	4	yes	—
917	C₂×C₄	C₂³×C₄×C₂₉	1	4	yes	—
918	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
919	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
920	C₂×C₄	C₂³×C₄×C₂₉	1	4	yes	—
921	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
922	C₂×C₄	C₂×#41×C₂₉	1	4	yes	—
923	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
924	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
925	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	2	no	—
932	C₂²	—	2	4	no	—
933	C₂²	—	2	4	no	—
934	C₂²	—	2	4	no	—
935	C₂²	—	2	4	no	—
936	C₂²	—	2	4	no	—
937	C₂²	—	2	4	no	—
938	C₂²	—	4	16	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	C₄×#41×C₂₉	1	4	yes	—
948	C₂²	C₂⁴×C₄×C₂₉	1	1	yes	characteristic
949	C₂²	C₂²×#41×C₂₉	1	1	yes	characteristic
950	C₂²	C₂²×#41×C₂₉	1	1	yes	characteristic
951	C₂²	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
952	C₂²	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
953	C₂²	C₂₉×#585	1	1	yes	characteristic
954	C₂²	C₂₉×#585	1	1	yes	characteristic
955	C₄	—	2	2	no	—
956	C₄	—	2	2	no	—
957	C₄	—	2	4	no	—
958	C₄	—	2	2	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	4	no	—
961	C₄	—	2	4	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	4	no	—
964	C₄	—	2	2	no	—
965	C₄	—	2	4	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₂	—	2	4	no	—
972	C₂	—	4	4	no	—
973	C₂	—	4	4	no	—
974	C₂	C₂×C₄×#41×C₂₉	1	1	yes	characteristic
975	C₂	C₄×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
976	C₂	C₄×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
977	C₂	C₂₉×#3490	1	1	yes	characteristic
978	C₂	C₂₉×#3493	1	1	yes	characteristic
979	C₂	C₂₉×#3505	1	1	yes	characteristic
980	C₂	C₂₉×#3506	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×#538	C₂
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×#2374	C₂	semidirect
3. C₂₉×#2373	C₂	semidirect
4. C₂₉×#2373	C₂	semidirect
5. C₂₉×#2372	C₂	semidirect
6. C₂₉×#2367	C₂	semidirect
7. C₂₉×#2364	C₂	semidirect
8. C₂₉×#2363	C₂	semidirect
9. C₂₉×#2359	C₂	semidirect
10. C₂₉×#2329	C₂	semidirect
11. C₂₉×#2325	C₂	semidirect
12. C₂₉×#2321	C₂	semidirect
13. C₂₉×#2312	C₂	semidirect
14. C₄×C₂₉×C₂²⋊Q₈	C₂	semidirect
15. C₄×C₂₉×#121	C₂	semidirect
16. C₄×C₂₉×#120	C₂	semidirect
17. C₂₉×#2290	C₂	semidirect
18. C₂₉×#2275	C₂	semidirect
19. C₂×C₄×C₂²⋊C₄×C₂₉	C₂	semidirect
21. C₂₉×#538	C₄	semidirect
29. C₂×C₄×Q₈×C₂₉	C₂²	semidirect
35. C₂×C₄×D₄×C₂₉	C₂²	semidirect
36. C₂×C₂₉×#117	C₂²	semidirect
41. C₂₉×#391	C₂²	semidirect
42. C₂₉×#391	C₂²	semidirect
45. C₂₉×#390	C₂²	semidirect
46. C₂₉×#389	C₂²	semidirect
47. C₂₉×#389	C₂²	semidirect
48. C₂₉×#389	C₂²	semidirect
57. C₂₉×#388	C₂²	semidirect
58. C₂₉×#388	C₂²	semidirect
59. C₂₉×#388	C₂²	semidirect
60. C₂₉×#388	C₂²	semidirect
61. C₂₉×#387	C₂²	semidirect
62. C₂₉×#387	C₂²	semidirect
63. C₂₉×#387	C₂²	semidirect
64. C₂₉×#387	C₂²	semidirect
65. C₂₉×#387	C₂²	semidirect
66. C₂₉×#387	C₂²	semidirect
73. C₂₉×#386	C₂²	semidirect
78. C₂₉×#385	C₂²	semidirect
82. C₄×C₄⋊C₄×C₂₉	C₂²	semidirect
83. C₄×C₄⋊C₄×C₂₉	C₂²	semidirect
84. C₄×C₄⋊C₄×C₂₉	C₂²	semidirect
85. C₄×C₄⋊C₄×C₂₉	C₂²	semidirect
86. C₄×C₄⋊C₄×C₂₉	C₂²	semidirect
87. C₄×C₄⋊C₄×C₂₉	C₂²	semidirect
88. C₄×C₄⋊C₄×C₂₉	C₂²	semidirect
98. C₄×C₂²⋊C₄×C₂₉	C₂²	semidirect
99. C₄×C₂²⋊C₄×C₂₉	C₂²	semidirect
100. C₄×C₂²⋊C₄×C₂₉	C₂²	semidirect
101. C₄×C₂²⋊C₄×C₂₉	C₂²	semidirect
102. C₄×C₂²⋊C₄×C₂₉	C₂²	semidirect
103. C₂₉×#376	C₂²	semidirect
104. C₂₉×#376	C₂²	semidirect
107. C₂×C₂₉×#95	C₂²	semidirect
128. C₂₉×#126	C₂×C₄	semidirect
129. C₂₉×#124	C₂×C₄	semidirect
130. C₂₉×#123	C₂×C₄	semidirect
131. C₂₉×C₂²⋊Q₈	C₂×C₄	semidirect
132. C₂₉×#121	C₂×C₄	semidirect
133. C₂₉×#121	C₂×C₄	semidirect
134. C₂₉×#120	C₂×C₄	semidirect
141. C₄×D₄×C₂₉	C₂×C₄	semidirect
158. C₂×C₂²⋊C₄×C₂₉	C₂×C₄	semidirect
229. C₂×Q₈×C₂₉	C₂²×C₄	semidirect
241. C₂×D₄×C₂₉	C₂²×C₄	semidirect
273. C₂²×C₄×C₂₉	C₂²×C₄	semidirect
302. C₄⋊C₄×C₂₉	C₂²×C₄	semidirect
303. C₄⋊C₄×C₂₉	C₂²×C₄	semidirect
304. C₄⋊C₄×C₂₉	C₂²×C₄	semidirect
305. C₄⋊C₄×C₂₉	C₂²×C₄	semidirect
325. C₂²⋊C₄×C₂₉	C₂²×C₄	semidirect
326. C₂²⋊C₄×C₂₉	C₂²×C₄	semidirect
341. C₄²×C₂₉	C₂²×C₄	semidirect
342. #34277	C₂₉	direct (N × H)
437. #2374	C₂×C₂₉	semidirect
438. #2373	C₂×C₂₉	semidirect
439. #2373	C₂×C₂₉	semidirect
440. #2372	C₂×C₂₉	semidirect
441. #2367	C₂×C₂₉	semidirect
442. #2364	C₂×C₂₉	semidirect
443. #2363	C₂×C₂₉	semidirect
444. #2359	C₂×C₂₉	semidirect
445. #2329	C₂×C₂₉	semidirect
446. #2325	C₂×C₂₉	semidirect
447. #2321	C₂×C₂₉	semidirect
448. #2312	C₂×C₂₉	semidirect
449. C₄×C₂²⋊Q₈	C₂×C₂₉	semidirect
450. C₄×#121	C₂×C₂₉	semidirect
451. C₄×#120	C₂×C₂₉	semidirect
452. #2290	C₂×C₂₉	semidirect
453. #2275	C₂×C₂₉	semidirect
454. C₂×C₄×C₂²⋊C₄	C₂×C₂₉	semidirect
501. #538	C₄×C₂₉	semidirect
509. C₂×C₄×Q₈	C₂²×C₂₉	semidirect
515. C₂×C₄×D₄	C₂²×C₂₉	semidirect
516. C₂×#117	C₂²×C₂₉	semidirect
521. #391	C₂²×C₂₉	semidirect
522. #391	C₂²×C₂₉	semidirect
525. #390	C₂²×C₂₉	semidirect
526. #389	C₂²×C₂₉	semidirect
527. #389	C₂²×C₂₉	semidirect
528. #389	C₂²×C₂₉	semidirect
537. #388	C₂²×C₂₉	semidirect
538. #388	C₂²×C₂₉	semidirect
539. #388	C₂²×C₂₉	semidirect
540. #388	C₂²×C₂₉	semidirect
541. #387	C₂²×C₂₉	semidirect
542. #387	C₂²×C₂₉	semidirect
543. #387	C₂²×C₂₉	semidirect
544. #387	C₂²×C₂₉	semidirect
545. #387	C₂²×C₂₉	semidirect
546. #387	C₂²×C₂₉	semidirect
553. #386	C₂²×C₂₉	semidirect
558. #385	C₂²×C₂₉	semidirect
562. C₄×C₄⋊C₄	C₂²×C₂₉	semidirect
563. C₄×C₄⋊C₄	C₂²×C₂₉	semidirect
564. C₄×C₄⋊C₄	C₂²×C₂₉	semidirect
565. C₄×C₄⋊C₄	C₂²×C₂₉	semidirect
566. C₄×C₄⋊C₄	C₂²×C₂₉	semidirect
567. C₄×C₄⋊C₄	C₂²×C₂₉	semidirect
568. C₄×C₄⋊C₄	C₂²×C₂₉	semidirect
578. C₄×C₂²⋊C₄	C₂²×C₂₉	semidirect
579. C₄×C₂²⋊C₄	C₂²×C₂₉	semidirect
580. C₄×C₂²⋊C₄	C₂²×C₂₉	semidirect
581. C₄×C₂²⋊C₄	C₂²×C₂₉	semidirect
582. C₄×C₂²⋊C₄	C₂²×C₂₉	semidirect
583. #376	C₂²×C₂₉	semidirect
584. #376	C₂²×C₂₉	semidirect
587. C₂×#95	C₂²×C₂₉	semidirect
618. #126	C₂×C₄×C₂₉	semidirect
619. #124	C₂×C₄×C₂₉	semidirect
620. #123	C₂×C₄×C₂₉	semidirect
621. C₂²⋊Q₈	C₂×C₄×C₂₉	semidirect
622. #121	C₂×C₄×C₂₉	semidirect
623. #121	C₂×C₄×C₂₉	semidirect
624. #120	C₂×C₄×C₂₉	semidirect
631. C₄×D₄	C₂×C₄×C₂₉	semidirect
648. C₂×C₂²⋊C₄	C₂×C₄×C₂₉	semidirect
707. C₂₉	#34277	direct (N × H)
720. C₂×Q₈	C₂²×C₄×C₂₉	semidirect
732. C₂×D₄	C₂²×C₄×C₂₉	semidirect
764. C₂²×C₄	C₂²×C₄×C₂₉	semidirect
793. C₄⋊C₄	C₂²×C₄×C₂₉	semidirect
794. C₄⋊C₄	C₂²×C₄×C₂₉	semidirect
795. C₄⋊C₄	C₂²×C₄×C₂₉	semidirect
796. C₄⋊C₄	C₂²×C₄×C₂₉	semidirect
816. C₂²⋊C₄	C₂²×C₄×C₂₉	semidirect
817. C₂²⋊C₄	C₂²×C₄×C₂₉	semidirect
832. C₄²	C₂²×C₄×C₂₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₂₉×#538	2
C₂₉×#2374	2
C₂₉×#2373	2
C₂₉×#2372	2
C₂₉×#2367	2
C₂₉×#2364	2
C₂₉×#2363	2
C₂₉×#2359	2
C₂₉×#2329	2
C₂₉×#2325	2
C₂₉×#2321	2
C₂₉×#2312	2
C₄×C₂₉×C₂²⋊Q₈	2
C₄×C₂₉×#121	2
C₄×C₂₉×#120	2
C₂₉×#2290	2
C₂₉×#2275	2
C₂×C₄×C₂²⋊C₄×C₂₉	2
#34277	29

Subgroups — C29×#34277 #20329177

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#34277 #20329177