Subgroups — C₂₉×#35024 #20329924

Order 7424.

1766 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#2855	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#2854	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2851	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2850	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#2643	C₂	1	2	yes	maximal, complemented
6	C₂₉×#2623	C₂	1	2	yes	maximal, complemented
7	C₂₉×#2596	C₂	1	2	yes	maximal, complemented
8	C₂₉×#2594	C₂	1	2	yes	maximal, complemented
9	C₂₉×#2577	C₂	1	2	yes	maximal, complemented
10	C₂₉×#2575	C₂	1	2	yes	maximal, complemented
11	C₂₉×#2514	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#2513	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#2509	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#2508	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#2454	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#2453	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₉×#2448	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₉×#2447	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₉×#2322	C₂	1	2	yes	maximal, complemented
20	C₂₉×#2318	C₂	1	2	yes	maximal, complemented
21	C₄×C₂₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂₉×#121	C₂	1	1	yes	maximal, characteristic
23	C₂×C₄×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₉×#125	C₂²	1	1	yes	characteristic
25	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×#123	C₂²	1	2	yes	—
27	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×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×C₄²×C₂₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
37	C₂₉×#401	C₂²	1	2	yes	—
38	C₂₉×#400	C₂²	1	2	yes	—
39	C₂₉×#400	C₂²	1	2	yes	—
40	C₂₉×#400	C₂²	1	2	yes	—
41	C₂₉×#400	C₂²	1	2	yes	—
42	C₂₉×#400	C₂²	1	2	yes	—
43	C₂₉×#399	C₂²	1	2	yes	—
44	C₂₉×#399	C₂²	1	2	yes	—
45	C₂₉×#398	C₂²	1	2	yes	—
46	C₂₉×#398	C₂²	1	2	yes	—
47	C₂₉×#397	C₂²	1	2	yes	—
48	C₂₉×#397	C₂²	1	2	yes	—
49	C₂₉×#397	C₂²	1	2	yes	—
50	C₂₉×#397	C₂²	1	2	yes	—
51	C₂₉×#397	C₂²	1	2	yes	—
52	C₂₉×#396	C₂²	1	2	yes	—
53	C₂₉×#391	C₂²	1	1	yes	characteristic
54	C₂₉×#391	C₂²	1	1	yes	characteristic
55	C₂₉×#391	C₂²	1	1	yes	characteristic
56	C₂₉×#391	C₂²	1	1	yes	characteristic
57	C₂₉×#390	C₂²	1	1	yes	characteristic
58	C₂₉×#390	C₂²	1	1	yes	characteristic
59	C₂₉×#390	C₂²	1	1	yes	characteristic
60	C₂₉×#390	C₂²	1	1	yes	characteristic
61	C₂₉×#389	C₂²	1	1	yes	characteristic
62	C₂₉×#389	C₂²	1	1	yes	characteristic
63	C₂₉×#389	C₂²	1	1	yes	characteristic
64	C₂₉×#389	C₂²	1	1	yes	characteristic
65	C₂₉×#389	C₂²	1	2	yes	—
66	C₂₉×#389	C₂²	1	1	yes	characteristic
67	C₂₉×#389	C₂²	1	1	yes	characteristic
68	C₂₉×#389	C₂²	1	1	yes	characteristic
69	C₂₉×#389	C₂²	1	1	yes	characteristic
70	C₂₉×#389	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×#388	C₂²	1	2	yes	—
78	C₂₉×#388	C₂²	1	2	yes	—
79	C₂₉×#388	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×#387	C₂²	1	2	yes	—
86	C₂₉×#387	C₂²	1	2	yes	—
87	C₂₉×#387	C₂²	1	2	yes	—
88	C₂₉×#387	C₂²	1	2	yes	—
89	C₂₉×#386	C₂²	1	2	yes	—
90	C₂₉×#386	C₂²	1	2	yes	—
91	C₂₉×#386	C₂²	1	2	yes	—
92	C₂₉×#386	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×#385	C₂²	1	2	yes	—
98	C₂₉×#385	C₂²	1	2	yes	—
99	C₂₉×#383	C₂²	1	2	yes	—
100	C₂₉×#382	C₂²	1	1	yes	characteristic
101	C₂₉×#382	C₂²	1	2	yes	—
102	C₂₉×#382	C₂²	1	1	yes	characteristic
103	C₂₉×#381	C₂²	1	2	yes	—
104	C₂₉×#381	C₂²	1	2	yes	—
105	C₂₉×#380	C₂²	1	2	yes	—
106	C₂₉×#380	C₂²	1	1	yes	characteristic
107	C₂₉×#380	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	1	yes	characteristic
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	1	yes	characteristic
117	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
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	C₂×C₂₉×#95	C₂²	1	1	yes	characteristic
122	C₂×C₂₉×#95	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
125	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
133	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
134	C₂₉×#125	—	4	2	no	—
135	C₂₉×#124	—	4	2	no	—
136	C₂₉×#123	—	2	8	no	—
137	C₂₉×C₂²⋊Q₈	—	2	4	no	—
138	C₂₉×#121	—	2	4	no	—
139	C₄×Q₈×C₂₉	—	4	2	no	—
140	C₄×D₄×C₂₉	—	2	8	no	—
141	C₄×D₄×C₂₉	—	4	2	no	—
142	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
143	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
144	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
153	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
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	1	yes	characteristic
157	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
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	2	yes	—
164	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
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	2	yes	—
169	C₂×C₄⋊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×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
185	C₂×C₄²×C₂₉	—	2	4	no	—
186	C₂×C₄²×C₂₉	—	4	2	no	—
187	C₂×C₄²×C₂₉	—	4	2	no	—
188	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
197	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
202	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
203	C₂₉×#95	C₂³	1	1	yes	characteristic
204	C₂₉×#95	C₂³	1	1	yes	characteristic
205	C₂₉×#95	C₂³	1	1	yes	characteristic
206	C₂₉×#95	C₂³	1	1	yes	characteristic
207	C₂₉×#95	C₂³	1	1	yes	characteristic
208	C₂₉×#95	C₂³	1	1	yes	characteristic
209	C₂₉×#95	C₂³	1	1	yes	characteristic
210	C₂₉×#95	C₂³	1	1	yes	characteristic
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	C₂₉×#95	C₂³	1	2	yes	—
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	2	yes	—
222	C₂₉×#95	C₂³	1	2	yes	—
223	C₂₉×#95	C₂³	1	2	yes	—
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	2	yes	—
228	C₂₉×#95	C₂³	1	2	yes	—
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	2	yes	—
234	C₂₉×#95	C₂³	1	2	yes	—
235	C₂⁴×C₂₉	C₂⁴	1	2	yes	—
236	C₂⁴×C₂₉	C₂⁴	1	1	yes	characteristic
237	C₂×Q₈×C₂₉	—	2	2	no	—
238	C₂×Q₈×C₂₉	—	2	2	no	—
239	C₂×Q₈×C₂₉	—	2	2	no	—
240	C₂×D₄×C₂₉	—	2	4	no	—
241	C₂×D₄×C₂₉	—	2	4	no	—
242	C₂×D₄×C₂₉	—	2	4	no	—
243	C₂×D₄×C₂₉	—	2	2	no	—
244	C₂×D₄×C₂₉	—	2	2	no	—
245	C₂×D₄×C₂₉	—	2	2	no	—
246	C₂²×C₄×C₂₉	—	2	2	no	—
247	C₂²×C₄×C₂₉	—	2	2	no	—
248	C₂²×C₄×C₂₉	—	2	2	no	—
249	C₂²×C₄×C₂₉	—	2	2	no	—
250	C₂²×C₄×C₂₉	—	2	2	no	—
251	C₂²×C₄×C₂₉	—	2	2	no	—
252	C₂²×C₄×C₂₉	—	2	2	no	—
253	C₂²×C₄×C₂₉	—	2	2	no	—
254	C₂²×C₄×C₂₉	—	2	4	no	—
255	C₂²×C₄×C₂₉	—	4	1	no	—
256	C₂²×C₄×C₂₉	—	4	1	no	—
257	C₂²×C₄×C₂₉	—	4	1	no	—
258	C₂²×C₄×C₂₉	—	4	1	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	1	no	—
264	C₂²×C₄×C₂₉	—	4	1	no	—
265	C₂²×C₄×C₂₉	—	4	2	no	—
266	C₂²×C₄×C₂₉	—	4	2	no	—
267	C₂²×C₄×C₂₉	#41	1	4	yes	—
268	C₂²×C₄×C₂₉	#41	1	4	yes	—
269	C₂²×C₄×C₂₉	#41	1	4	yes	—
270	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
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	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	2	yes	—
285	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
291	C₄⋊C₄×C₂₉	—	2	2	no	—
292	C₄⋊C₄×C₂₉	—	2	2	no	—
293	C₄⋊C₄×C₂₉	—	2	2	no	—
294	C₄⋊C₄×C₂₉	—	2	2	no	—
295	C₄⋊C₄×C₂₉	—	2	2	no	—
296	C₄⋊C₄×C₂₉	—	2	2	no	—
297	C₄⋊C₄×C₂₉	—	2	2	no	—
298	C₄⋊C₄×C₂₉	—	2	2	no	—
299	C₄⋊C₄×C₂₉	—	2	4	no	—
300	C₄⋊C₄×C₂₉	—	2	2	no	—
301	C₄⋊C₄×C₂₉	—	2	2	no	—
302	C₄⋊C₄×C₂₉	—	2	4	no	—
303	C₄⋊C₄×C₂₉	—	2	4	no	—
304	C₄⋊C₄×C₂₉	—	2	4	no	—
305	C₄⋊C₄×C₂₉	—	2	2	no	—
306	C₄⋊C₄×C₂₉	—	2	2	no	—
307	C₄⋊C₄×C₂₉	—	2	2	no	—
308	C₄⋊C₄×C₂₉	—	2	2	no	—
309	C₄⋊C₄×C₂₉	—	4	2	no	—
310	C₄⋊C₄×C₂₉	—	4	2	no	—
311	C₄⋊C₄×C₂₉	—	4	2	no	—
312	C₄⋊C₄×C₂₉	—	4	2	no	—
313	C₄⋊C₄×C₂₉	—	4	2	no	—
314	C₄⋊C₄×C₂₉	—	4	2	no	—
315	C₄⋊C₄×C₂₉	—	4	2	no	—
316	C₄⋊C₄×C₂₉	—	4	2	no	—
317	C₂²⋊C₄×C₂₉	—	2	4	no	—
318	C₂²⋊C₄×C₂₉	—	2	4	no	—
319	C₂²⋊C₄×C₂₉	—	2	4	no	—
320	C₂²⋊C₄×C₂₉	—	2	4	no	—
321	C₂²⋊C₄×C₂₉	—	2	4	no	—
322	C₂²⋊C₄×C₂₉	—	2	4	no	—
323	C₂²⋊C₄×C₂₉	—	2	4	no	—
324	C₂²⋊C₄×C₂₉	—	4	2	no	—
325	C₂²⋊C₄×C₂₉	—	4	2	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	2	no	—
330	C₂²⋊C₄×C₂₉	—	4	2	no	—
331	C₂²⋊C₄×C₂₉	—	4	2	no	—
332	C₄²×C₂₉	—	2	2	no	—
333	C₄²×C₂₉	—	2	2	no	—
334	C₄²×C₂₉	—	2	2	no	—
335	C₄²×C₂₉	—	2	2	no	—
336	C₄²×C₂₉	—	2	4	no	—
337	C₄²×C₂₉	—	2	2	no	—
338	C₄²×C₂₉	—	2	2	no	—
339	C₄²×C₂₉	—	2	2	no	—
340	C₄²×C₂₉	—	2	2	no	—
341	C₄²×C₂₉	—	4	1	no	—
342	C₄²×C₂₉	—	4	1	no	—
343	C₄²×C₂₉	—	4	1	no	—
344	C₄²×C₂₉	—	4	1	no	—
345	C₄²×C₂₉	—	4	2	no	—
346	C₄²×C₂₉	—	4	2	no	—
347	#35024	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
348	C₂³×C₂₉	—	2	1	no	—
349	C₂³×C₂₉	—	2	1	no	—
350	C₂³×C₂₉	—	2	1	no	—
351	C₂³×C₂₉	—	2	1	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	C₂×#41	1	2	yes	—
360	C₂³×C₂₉	C₂×#41	1	2	yes	—
361	C₂³×C₂₉	C₂×#41	1	2	yes	—
362	C₂³×C₂₉	C₂⁵	1	1	yes	characteristic
363	Q₈×C₂₉	—	4	4	no	—
364	D₄×C₂₉	—	4	8	no	—
365	D₄×C₂₉	—	4	4	no	—
366	C₂×C₄×C₂₉	—	2	8	no	—
367	C₂×C₄×C₂₉	—	2	1	no	—
368	C₂×C₄×C₂₉	—	2	1	no	—
369	C₂×C₄×C₂₉	—	2	1	no	—
370	C₂×C₄×C₂₉	—	2	1	no	—
371	C₂×C₄×C₂₉	—	2	1	no	—
372	C₂×C₄×C₂₉	—	2	1	no	—
373	C₂×C₄×C₂₉	—	2	1	no	—
374	C₂×C₄×C₂₉	—	2	1	no	—
375	C₂×C₄×C₂₉	—	2	1	no	—
376	C₂×C₄×C₂₉	—	2	1	no	—
377	C₂×C₄×C₂₉	—	2	8	no	—
378	C₂×C₄×C₂₉	—	2	1	no	—
379	C₂×C₄×C₂₉	—	2	1	no	—
380	C₂×C₄×C₂₉	—	2	2	no	—
381	C₂×C₄×C₂₉	—	2	2	no	—
382	C₂×C₄×C₂₉	—	2	2	no	—
383	C₂×C₄×C₂₉	—	2	2	no	—
384	C₂×C₄×C₂₉	—	2	2	no	—
385	C₂×C₄×C₂₉	—	2	2	no	—
386	C₂×C₄×C₂₉	—	2	2	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	1	no	—
391	C₂×C₄×C₂₉	—	2	1	no	—
392	C₂×C₄×C₂₉	—	2	1	no	—
393	C₂×C₄×C₂₉	—	2	1	no	—
394	C₂×C₄×C₂₉	—	2	2	no	—
395	C₂×C₄×C₂₉	—	2	1	no	—
396	C₂×C₄×C₂₉	—	2	1	no	—
397	C₂×C₄×C₂₉	—	2	1	no	—
398	C₂×C₄×C₂₉	—	2	1	no	—
399	C₂×C₄×C₂₉	—	2	1	no	—
400	C₂×C₄×C₂₉	—	2	1	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	1	no	—
410	C₂×C₄×C₂₉	—	2	1	no	—
411	C₂×C₄×C₂₉	—	2	1	no	—
412	C₂×C₄×C₂₉	—	2	1	no	—
413	C₂×C₄×C₂₉	—	2	1	no	—
414	C₂×C₄×C₂₉	—	2	2	no	—
415	C₂×C₄×C₂₉	—	2	2	no	—
416	C₂×C₄×C₂₉	—	2	2	no	—
417	C₂×C₄×C₂₉	—	2	1	no	—
418	C₂×C₄×C₂₉	—	2	1	no	—
419	C₂×C₄×C₂₉	—	2	1	no	—
420	C₂×C₄×C₂₉	—	2	2	no	—
421	C₂×C₄×C₂₉	—	2	1	no	—
422	C₂×C₄×C₂₉	—	2	1	no	—
423	C₂×C₄×C₂₉	—	4	4	no	—
424	C₂×C₄×C₂₉	—	4	4	no	—
425	C₂×C₄×C₂₉	—	4	4	no	—
426	C₂×C₄×C₂₉	—	4	4	no	—
427	C₂×C₄×C₂₉	—	4	4	no	—
428	C₂×C₄×C₂₉	—	8	4	no	—
429	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
430	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
431	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
432	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
433	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
434	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
435	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
436	C₂×C₄×C₂₉	2₋¹⁺⁴	1	2	yes	—
437	#2855	C₂×C₂₉	1	1	yes	characteristic, complemented
438	#2854	C₂×C₂₉	1	1	yes	characteristic
439	#2851	C₂×C₂₉	1	1	yes	characteristic, complemented
440	#2850	C₂×C₂₉	1	1	yes	characteristic
441	#2643	C₂×C₂₉	1	2	yes	complemented
442	#2623	C₂×C₂₉	1	2	yes	complemented
443	#2596	C₂×C₂₉	1	2	yes	complemented
444	#2594	C₂×C₂₉	1	2	yes	complemented
445	#2577	C₂×C₂₉	1	2	yes	complemented
446	#2575	C₂×C₂₉	1	2	yes	complemented
447	#2514	C₂×C₂₉	1	1	yes	characteristic, complemented
448	#2513	C₂×C₂₉	1	1	yes	characteristic, complemented
449	#2509	C₂×C₂₉	1	1	yes	characteristic, complemented
450	#2508	C₂×C₂₉	1	1	yes	characteristic, complemented
451	#2454	C₂×C₂₉	1	1	yes	characteristic, complemented
452	#2453	C₂×C₂₉	1	1	yes	characteristic, complemented
453	#2448	C₂×C₂₉	1	1	yes	characteristic, complemented
454	#2447	C₂×C₂₉	1	1	yes	characteristic, complemented
455	#2322	C₂×C₂₉	1	2	yes	complemented
456	#2318	C₂×C₂₉	1	2	yes	complemented
457	C₄×C₂²⋊Q₈	C₂×C₂₉	1	1	yes	characteristic, complemented
458	C₄×#121	C₂×C₂₉	1	1	yes	characteristic
459	C₂×C₄×C₄⋊C₄	C₂×C₂₉	1	1	yes	characteristic, complemented
460	C₂²×C₂₉	—	2	2	no	—
461	C₂²×C₂₉	—	2	2	no	—
462	C₂²×C₂₉	—	2	2	no	—
463	C₂²×C₂₉	—	2	2	no	—
464	C₂²×C₂₉	—	2	2	no	—
465	C₂²×C₂₉	—	2	2	no	—
466	C₂²×C₂₉	—	4	2	no	—
467	C₂²×C₂₉	—	4	2	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	#529	1	4	yes	—
474	C₂²×C₂₉	C₂²×#41	1	1	yes	characteristic
475	C₂²×C₂₉	C₂²×#41	1	1	yes	characteristic
476	C₂²×C₂₉	C₂²×#41	1	1	yes	characteristic
477	C₂²×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
478	C₂²×C₂₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
479	C₂²×C₂₉	#585	1	1	yes	characteristic
480	C₂²×C₂₉	#585	1	1	yes	characteristic
481	C₄×C₂₉	—	2	2	no	—
482	C₄×C₂₉	—	2	2	no	—
483	C₄×C₂₉	—	2	2	no	—
484	C₄×C₂₉	—	2	2	no	—
485	C₄×C₂₉	—	2	2	no	—
486	C₄×C₂₉	—	4	2	no	—
487	C₄×C₂₉	—	4	2	no	—
488	C₄×C₂₉	—	4	2	no	—
489	C₄×C₂₉	—	4	1	no	—
490	C₄×C₂₉	—	4	1	no	—
491	C₄×C₂₉	—	4	1	no	—
492	C₄×C₂₉	—	4	1	no	—
493	C₄×C₂₉	—	4	2	no	—
494	C₄×C₂₉	—	4	2	no	—
495	C₄×C₂₉	—	4	1	no	—
496	C₄×C₂₉	—	4	1	no	—
497	C₄×C₂₉	—	4	1	no	—
498	C₄×C₂₉	—	4	1	no	—
499	C₄×C₂₉	—	4	2	no	—
500	C₄×C₂₉	—	4	2	no	—
501	C₄×C₂₉	#539	1	4	yes	—
502	C₂×#125	C₂²×C₂₉	1	1	yes	characteristic
503	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
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×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
508	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
509	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
510	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
511	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
512	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
513	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
514	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
515	#401	C₂²×C₂₉	1	2	yes	—
516	#400	C₂²×C₂₉	1	2	yes	—
517	#400	C₂²×C₂₉	1	2	yes	—
518	#400	C₂²×C₂₉	1	2	yes	—
519	#400	C₂²×C₂₉	1	2	yes	—
520	#400	C₂²×C₂₉	1	2	yes	—
521	#399	C₂²×C₂₉	1	2	yes	—
522	#399	C₂²×C₂₉	1	2	yes	—
523	#398	C₂²×C₂₉	1	2	yes	—
524	#398	C₂²×C₂₉	1	2	yes	—
525	#397	C₂²×C₂₉	1	2	yes	—
526	#397	C₂²×C₂₉	1	2	yes	—
527	#397	C₂²×C₂₉	1	2	yes	—
528	#397	C₂²×C₂₉	1	2	yes	—
529	#397	C₂²×C₂₉	1	2	yes	—
530	#396	C₂²×C₂₉	1	2	yes	—
531	#391	C₂²×C₂₉	1	1	yes	characteristic
532	#391	C₂²×C₂₉	1	1	yes	characteristic
533	#391	C₂²×C₂₉	1	1	yes	characteristic
534	#391	C₂²×C₂₉	1	1	yes	characteristic
535	#390	C₂²×C₂₉	1	1	yes	characteristic
536	#390	C₂²×C₂₉	1	1	yes	characteristic
537	#390	C₂²×C₂₉	1	1	yes	characteristic
538	#390	C₂²×C₂₉	1	1	yes	characteristic
539	#389	C₂²×C₂₉	1	2	yes	—
540	#389	C₂²×C₂₉	1	2	yes	—
541	#389	C₂²×C₂₉	1	1	yes	characteristic
542	#389	C₂²×C₂₉	1	1	yes	characteristic
543	#389	C₂²×C₂₉	1	1	yes	characteristic
544	#389	C₂²×C₂₉	1	1	yes	characteristic
545	#389	C₂²×C₂₉	1	1	yes	characteristic
546	#389	C₂²×C₂₉	1	1	yes	characteristic
547	#389	C₂²×C₂₉	1	1	yes	characteristic
548	#389	C₂²×C₂₉	1	1	yes	characteristic
549	#388	C₂²×C₂₉	1	2	yes	—
550	#388	C₂²×C₂₉	1	2	yes	—
551	#388	C₂²×C₂₉	1	2	yes	—
552	#388	C₂²×C₂₉	1	2	yes	—
553	#388	C₂²×C₂₉	1	2	yes	—
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	#387	C₂²×C₂₉	1	2	yes	—
559	#387	C₂²×C₂₉	1	2	yes	—
560	#387	C₂²×C₂₉	1	2	yes	—
561	#387	C₂²×C₂₉	1	2	yes	—
562	#387	C₂²×C₂₉	1	2	yes	—
563	#387	C₂²×C₂₉	1	2	yes	—
564	#387	C₂²×C₂₉	1	2	yes	—
565	#387	C₂²×C₂₉	1	2	yes	—
566	#387	C₂²×C₂₉	1	2	yes	—
567	#386	C₂²×C₂₉	1	2	yes	—
568	#386	C₂²×C₂₉	1	2	yes	—
569	#386	C₂²×C₂₉	1	2	yes	—
570	#386	C₂²×C₂₉	1	2	yes	—
571	#385	C₂²×C₂₉	1	2	yes	—
572	#385	C₂²×C₂₉	1	2	yes	—
573	#385	C₂²×C₂₉	1	2	yes	—
574	#385	C₂²×C₂₉	1	2	yes	—
575	#385	C₂²×C₂₉	1	2	yes	—
576	#385	C₂²×C₂₉	1	2	yes	—
577	#383	C₂²×C₂₉	1	2	yes	—
578	#382	C₂²×C₂₉	1	2	yes	—
579	#382	C₂²×C₂₉	1	1	yes	characteristic
580	#382	C₂²×C₂₉	1	1	yes	characteristic
581	#381	C₂²×C₂₉	1	2	yes	—
582	#381	C₂²×C₂₉	1	2	yes	—
583	#380	C₂²×C₂₉	1	2	yes	—
584	#380	C₂²×C₂₉	1	1	yes	characteristic
585	#380	C₂²×C₂₉	1	1	yes	characteristic
586	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
587	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
588	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
589	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
590	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
591	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
592	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
593	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
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	1	yes	characteristic
597	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
598	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
599	C₂×#95	C₂²×C₂₉	1	1	yes	characteristic
600	C₂×#95	C₂²×C₂₉	1	1	yes	characteristic
601	C₂×C₂₉	—	2	4	no	—
602	C₂×C₂₉	—	8	2	no	—
603	C₂×C₂₉	C₂×#529	1	1	yes	characteristic
604	C₂×C₂₉	C₂×#539	1	1	yes	characteristic
605	C₂×C₂₉	#3455	1	1	yes	characteristic
606	C₂×C₂₉	#3505	1	1	yes	characteristic
607	C₂×C₂₉	#3506	1	1	yes	characteristic
608	C₂×C₂₉	#3507	1	1	yes	characteristic
609	C₂×C₂₉	#3507	1	1	yes	characteristic
610	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
611	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
612	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
613	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
614	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
615	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
616	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
617	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
618	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
619	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
620	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
621	#125	—	4	2	no	—
622	#124	—	4	2	no	—
623	#123	—	2	8	no	—
624	C₂²⋊Q₈	—	2	4	no	—
625	#121	—	2	4	no	—
626	C₄×Q₈	—	4	2	no	—
627	C₄×D₄	—	2	8	no	—
628	C₄×D₄	—	4	2	no	—
629	C₂×C₄⋊C₄	—	2	4	no	—
630	C₂×C₄⋊C₄	—	2	4	no	—
631	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
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	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
643	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
656	C₂×C₄⋊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×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
672	C₂×C₄²	—	2	4	no	—
673	C₂×C₄²	—	4	2	no	—
674	C₂×C₄²	—	4	2	no	—
675	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
676	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
678	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
679	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
681	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
682	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
685	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
686	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
687	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
688	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
690	#95	C₂³×C₂₉	1	1	yes	characteristic
691	#95	C₂³×C₂₉	1	1	yes	characteristic
692	#95	C₂³×C₂₉	1	1	yes	characteristic
693	#95	C₂³×C₂₉	1	1	yes	characteristic
694	#95	C₂³×C₂₉	1	1	yes	characteristic
695	#95	C₂³×C₂₉	1	1	yes	characteristic
696	#95	C₂³×C₂₉	1	1	yes	characteristic
697	#95	C₂³×C₂₉	1	1	yes	characteristic
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	#95	C₂³×C₂₉	1	2	yes	—
708	#95	C₂³×C₂₉	1	2	yes	—
709	#95	C₂³×C₂₉	1	2	yes	—
710	#95	C₂³×C₂₉	1	2	yes	—
711	#95	C₂³×C₂₉	1	2	yes	—
712	#95	C₂³×C₂₉	1	2	yes	—
713	#95	C₂³×C₂₉	1	2	yes	—
714	#95	C₂³×C₂₉	1	2	yes	—
715	#95	C₂³×C₂₉	1	2	yes	—
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	2	yes	—
720	#95	C₂³×C₂₉	1	2	yes	—
721	#95	C₂³×C₂₉	1	2	yes	—
722	C₂₉	#35024	1	1	yes	characteristic, direct product factor, Sylow
723	C₂⁴	C₂⁴×C₂₉	1	2	yes	—
724	C₂⁴	C₂⁴×C₂₉	1	1	yes	characteristic
725	C₂×Q₈	—	2	2	no	—
726	C₂×Q₈	—	2	2	no	—
727	C₂×Q₈	—	2	2	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	4	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	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	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	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	1	no	—
748	C₂²×C₄	—	4	1	no	—
749	C₂²×C₄	—	4	1	no	—
750	C₂²×C₄	—	4	1	no	—
751	C₂²×C₄	—	4	1	no	—
752	C₂²×C₄	—	4	1	no	—
753	C₂²×C₄	—	4	2	no	—
754	C₂²×C₄	—	4	2	no	—
755	C₂²×C₄	#41×C₂₉	1	4	yes	—
756	C₂²×C₄	#41×C₂₉	1	4	yes	—
757	C₂²×C₄	#41×C₂₉	1	4	yes	—
758	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
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	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	4	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	4	no	—
791	C₄⋊C₄	—	2	4	no	—
792	C₄⋊C₄	—	2	4	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	4	2	no	—
798	C₄⋊C₄	—	4	2	no	—
799	C₄⋊C₄	—	4	2	no	—
800	C₄⋊C₄	—	4	2	no	—
801	C₄⋊C₄	—	4	2	no	—
802	C₄⋊C₄	—	4	2	no	—
803	C₄⋊C₄	—	4	2	no	—
804	C₄⋊C₄	—	4	2	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	4	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	4	no	—
812	C₂²⋊C₄	—	4	2	no	—
813	C₂²⋊C₄	—	4	2	no	—
814	C₂²⋊C₄	—	4	2	no	—
815	C₂²⋊C₄	—	4	2	no	—
816	C₂²⋊C₄	—	4	2	no	—
817	C₂²⋊C₄	—	4	2	no	—
818	C₂²⋊C₄	—	4	2	no	—
819	C₂²⋊C₄	—	4	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	2	no	—
824	C₄²	—	2	4	no	—
825	C₄²	—	2	2	no	—
826	C₄²	—	2	2	no	—
827	C₄²	—	2	2	no	—
828	C₄²	—	2	2	no	—
829	C₄²	—	4	1	no	—
830	C₄²	—	4	1	no	—
831	C₄²	—	4	1	no	—
832	C₄²	—	4	1	no	—
833	C₄²	—	4	2	no	—
834	C₄²	—	4	2	no	—
835	C₂³	—	2	1	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	1	no	—
838	C₂³	—	2	1	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	C₂×#41×C₂₉	1	2	yes	—
847	C₂³	C₂×#41×C₂₉	1	2	yes	—
848	C₂³	C₂×#41×C₂₉	1	2	yes	—
849	C₂³	C₂⁵×C₂₉	1	1	yes	characteristic
850	Q₈	—	4	4	no	—
851	D₄	—	4	8	no	—
852	D₄	—	4	4	no	—
853	C₂×C₄	—	2	8	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	8	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	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	2	no	—
889	C₂×C₄	—	2	2	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	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	4	4	no	—
911	C₂×C₄	—	4	4	no	—
912	C₂×C₄	—	4	4	no	—
913	C₂×C₄	—	4	4	no	—
914	C₂×C₄	—	4	4	no	—
915	C₂×C₄	—	8	4	no	—
916	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
917	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
918	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
919	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
920	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
921	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
922	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
923	C₂×C₄	C₂₉×2₋¹⁺⁴	1	2	yes	—
924	C₂²	—	2	2	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	2	no	—
937	C₂²	C₂₉×#529	1	4	yes	—
938	C₂²	C₂²×#41×C₂₉	1	1	yes	characteristic
939	C₂²	C₂²×#41×C₂₉	1	1	yes	characteristic
940	C₂²	C₂²×#41×C₂₉	1	1	yes	characteristic
941	C₂²	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
942	C₂²	C₂×C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
943	C₂²	C₂₉×#585	1	1	yes	characteristic
944	C₂²	C₂₉×#585	1	1	yes	characteristic
945	C₄	—	2	2	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	2	no	—
949	C₄	—	2	2	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	1	no	—
953	C₄	—	4	1	no	—
954	C₄	—	4	2	no	—
955	C₄	—	4	1	no	—
956	C₄	—	4	1	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	1	no	—
959	C₄	—	4	1	no	—
960	C₄	—	4	1	no	—
961	C₄	—	4	1	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	C₂₉×#539	1	4	yes	—
966	C₂	—	2	4	no	—
967	C₂	—	8	2	no	—
968	C₂	C₂×C₂₉×#529	1	1	yes	characteristic
969	C₂	C₂×C₂₉×#539	1	1	yes	characteristic
970	C₂	C₂₉×#3455	1	1	yes	characteristic
971	C₂	C₂₉×#3505	1	1	yes	characteristic
972	C₂	C₂₉×#3506	1	1	yes	characteristic
973	C₂	C₂₉×#3507	1	1	yes	characteristic
974	C₂	C₂₉×#3507	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂₉×#2855	C₂	semidirect
3. C₂₉×#2851	C₂	semidirect
5. C₂₉×#2643	C₂	semidirect
6. C₂₉×#2623	C₂	semidirect
7. C₂₉×#2596	C₂	semidirect
8. C₂₉×#2594	C₂	semidirect
9. C₂₉×#2577	C₂	semidirect
10. C₂₉×#2575	C₂	semidirect
11. C₂₉×#2514	C₂	semidirect
12. C₂₉×#2513	C₂	semidirect
13. C₂₉×#2509	C₂	semidirect
14. C₂₉×#2508	C₂	semidirect
15. C₂₉×#2454	C₂	semidirect
16. C₂₉×#2453	C₂	semidirect
17. C₂₉×#2448	C₂	semidirect
18. C₂₉×#2447	C₂	semidirect
19. C₂₉×#2322	C₂	semidirect
20. C₂₉×#2318	C₂	semidirect
21. C₄×C₂₉×C₂²⋊Q₈	C₂	semidirect
23. C₂×C₄×C₄⋊C₄×C₂₉	C₂	semidirect
347. #35024	C₂₉	direct (N × H)
437. #2855	C₂×C₂₉	semidirect
439. #2851	C₂×C₂₉	semidirect
441. #2643	C₂×C₂₉	semidirect
442. #2623	C₂×C₂₉	semidirect
443. #2596	C₂×C₂₉	semidirect
444. #2594	C₂×C₂₉	semidirect
445. #2577	C₂×C₂₉	semidirect
446. #2575	C₂×C₂₉	semidirect
447. #2514	C₂×C₂₉	semidirect
448. #2513	C₂×C₂₉	semidirect
449. #2509	C₂×C₂₉	semidirect
450. #2508	C₂×C₂₉	semidirect
451. #2454	C₂×C₂₉	semidirect
452. #2453	C₂×C₂₉	semidirect
453. #2448	C₂×C₂₉	semidirect
454. #2447	C₂×C₂₉	semidirect
455. #2322	C₂×C₂₉	semidirect
456. #2318	C₂×C₂₉	semidirect
457. C₄×C₂²⋊Q₈	C₂×C₂₉	semidirect
459. C₂×C₄×C₄⋊C₄	C₂×C₂₉	semidirect
722. C₂₉	#35024	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×#2855	2
C₂₉×#2854	2
C₂₉×#2851	2
C₂₉×#2850	2
C₂₉×#2643	2
C₂₉×#2623	2
C₂₉×#2596	2
C₂₉×#2594	2
C₂₉×#2577	2
C₂₉×#2575	2
C₂₉×#2514	2
C₂₉×#2513	2
C₂₉×#2509	2
C₂₉×#2508	2
C₂₉×#2454	2
C₂₉×#2453	2
C₂₉×#2448	2
C₂₉×#2447	2
C₂₉×#2322	2
C₂₉×#2318	2
C₄×C₂₉×C₂²⋊Q₈	2
C₄×C₂₉×#121	2
C₂×C₄×C₄⋊C₄×C₂₉	2
#35024	29

Subgroups — C29×#35024 #20329924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#35024 #20329924