Subgroups — C₂×C₂₉×#2359 #20329031

Order 7424.

3830 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, socle	C₂⁴×C₂₉	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁵×C₂₉
prime radical	C₂³×D₄×C₂₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂²×C₂₉×#117	C₂	semidirect
4. C₂₉×#2359	C₂	direct (N × H)
5. C₂×C₂₉×#389	C₂	semidirect
6. C₂×C₂₉×#388	C₂	semidirect
7. C₂×C₂₉×#388	C₂	semidirect
8. C₂×C₂₉×#387	C₂	semidirect
9. C₂×C₂₉×#387	C₂	semidirect
11. C₂×C₂₉×#385	C₂	semidirect
12. C₂×C₂₉×#385	C₂	semidirect
13. C₂×C₄×C₄⋊C₄×C₂₉	C₂	semidirect
14. C₂×C₄×C₂²⋊C₄×C₂₉	C₂	semidirect
15. C₂×C₄×C₂²⋊C₄×C₂₉	C₂	semidirect
16. C₂²×C₂₉×#95	C₂	semidirect
22. C₂×C₂₉×#123	C₄	semidirect
27. C₂×C₂₉×#117	C₂²	semidirect
48. C₂₉×#389	C₂²	semidirect
49. C₂₉×#388	C₂²	semidirect
50. C₂₉×#388	C₂²	semidirect
51. C₂₉×#387	C₂²	semidirect
52. C₂₉×#387	C₂²	semidirect
54. C₂₉×#385	C₂²	semidirect
55. C₂₉×#385	C₂²	semidirect
56. C₄×C₄⋊C₄×C₂₉	C₂²	semidirect
57. C₄×C₂²⋊C₄×C₂₉	C₂²	semidirect
58. C₄×C₂²⋊C₄×C₂₉	C₂²	semidirect
69. C₂×C₂₉×#95	C₂²	semidirect
87. C₂³×C₄×C₂₉	C₂×C₄	semidirect
105. C₂₉×#123	C₂×C₄	semidirect
113. C₂×C₄⋊C₄×C₂₉	C₂×C₄	semidirect
114. C₂×C₄⋊C₄×C₂₉	C₂×C₄	semidirect
126. C₂×C₂²⋊C₄×C₂₉	C₂×C₄	semidirect
127. C₂×C₂²⋊C₄×C₂₉	C₂×C₄	semidirect
128. C₂×C₂²⋊C₄×C₂₉	C₂×C₄	semidirect
229. C₂²×C₄×C₂₉	C₂²×C₄	semidirect
252. C₄⋊C₄×C₂₉	C₂²×C₄	semidirect
253. C₄⋊C₄×C₂₉	C₂²×C₄	semidirect
258. C₂²⋊C₄×C₂₉	C₂²×C₄	semidirect
259. C₂²⋊C₄×C₂₉	C₂²×C₄	semidirect
260. C₂²⋊C₄×C₂₉	C₂²×C₄	semidirect
267. C₂×#2359	C₂₉	direct (N × H)
363. C₂²×#117	C₂×C₂₉	semidirect
364. #2359	C₂×C₂₉	direct (N × H)
365. C₂×#389	C₂×C₂₉	semidirect
366. C₂×#388	C₂×C₂₉	semidirect
367. C₂×#388	C₂×C₂₉	semidirect
368. C₂×#387	C₂×C₂₉	semidirect
369. C₂×#387	C₂×C₂₉	semidirect
371. C₂×#385	C₂×C₂₉	semidirect
372. C₂×#385	C₂×C₂₉	semidirect
373. C₂×C₄×C₄⋊C₄	C₂×C₂₉	semidirect
374. C₂×C₄×C₂²⋊C₄	C₂×C₂₉	semidirect
375. C₂×C₄×C₂²⋊C₄	C₂×C₂₉	semidirect
376. C₂²×#95	C₂×C₂₉	semidirect
425. C₂×#123	C₄×C₂₉	semidirect
430. C₂×#117	C₂²×C₂₉	semidirect
451. #389	C₂²×C₂₉	semidirect
452. #388	C₂²×C₂₉	semidirect
453. #388	C₂²×C₂₉	semidirect
454. #387	C₂²×C₂₉	semidirect
455. #387	C₂²×C₂₉	semidirect
457. #385	C₂²×C₂₉	semidirect
458. #385	C₂²×C₂₉	semidirect
459. C₄×C₄⋊C₄	C₂²×C₂₉	semidirect
460. C₄×C₂²⋊C₄	C₂²×C₂₉	semidirect
461. C₄×C₂²⋊C₄	C₂²×C₂₉	semidirect
472. C₂×#95	C₂²×C₂₉	semidirect
475. C₂×C₂₉	#2359	direct (N × H)
500. C₂³×C₄	C₂×C₄×C₂₉	semidirect
518. #123	C₂×C₄×C₂₉	semidirect
526. C₂×C₄⋊C₄	C₂×C₄×C₂₉	semidirect
527. C₂×C₄⋊C₄	C₂×C₄×C₂₉	semidirect
539. C₂×C₂²⋊C₄	C₂×C₄×C₂₉	semidirect
540. C₂×C₂²⋊C₄	C₂×C₄×C₂₉	semidirect
541. C₂×C₂²⋊C₄	C₂×C₄×C₂₉	semidirect
571. C₂₉	C₂×#2359	direct (N × H)
643. C₂²×C₄	C₂²×C₄×C₂₉	semidirect
666. C₄⋊C₄	C₂²×C₄×C₂₉	semidirect
667. C₄⋊C₄	C₂²×C₄×C₂₉	semidirect
672. C₂²⋊C₄	C₂²×C₄×C₂₉	semidirect
673. C₂²⋊C₄	C₂²×C₄×C₂₉	semidirect
674. C₂²⋊C₄	C₂²×C₄×C₂₉	semidirect
819. C₂	C₂₉×#2359	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂₉×#123	2
C₂²×C₄×D₄×C₂₉	2
C₂²×C₂₉×#117	2
C₂₉×#2359	2
C₂×C₂₉×#389	2
C₂×C₂₉×#388	2
C₂×C₂₉×#387	2
C₂×C₂₉×#386	2
C₂×C₂₉×#385	2
C₂×C₄×C₄⋊C₄×C₂₉	2
C₂×C₄×C₂²⋊C₄×C₂₉	2
C₂²×C₂₉×#95	2
C₂×#2359	29

Subgroups — C2×C29×#2359 #20329031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#2359 #20329031