Subgroups — C₄×C₂₉×#529 #20328935

Order 7424.

2670 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#529	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₉×#125	C₂	1	2	yes	maximal, complemented
3	C₄×C₂₉×#126	C₂	1	4	yes	maximal, complemented
4	C₄×C₂₉×#124	C₂	1	2	yes	maximal, complemented
5	C₄×C₂₉×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
6	C₄×C₂₉×#123	C₂	1	4	yes	maximal, complemented
7	C₄×C₂₉×#121	C₂	1	2	yes	maximal
8	C₂₉×#2298	C₂	1	2	yes	maximal, complemented
9	C₂₉×#2295	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#2293	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#2290	C₂	1	2	yes	maximal, complemented
12	C₂₉×#2283	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄²×Q₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄²×D₄×C₂₉	C₂	1	2	yes	maximal, complemented
15	C₄²×D₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₂₉×#117	C₂	1	2	yes	maximal, complemented
17	C₂×C₄³×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₉×#529	C₄	1	16	yes	direct product factor
19	C₂×C₂₉×#126	C₂²	1	2	yes	—
20	C₂×C₂₉×#125	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×#123	C₂²	1	2	yes	—
23	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₂₉	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×#117	C₂²	1	2	yes	—
32	C₂×C₂₉×#117	C₂²	1	2	yes	—
33	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₂₉	C₂²	1	2	yes	—
35	C₂²×C₄²×C₂₉	C₂²	1	2	yes	—
36	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₂₉	C₂²	1	2	yes	—
38	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
39	C₂₉×#391	C₂²	1	2	yes	—
40	C₂₉×#390	C₂²	1	2	yes	—
41	C₂₉×#389	C₂²	1	2	yes	—
42	C₂₉×#389	C₂²	1	2	yes	—
43	C₂₉×#388	C₂²	1	4	yes	—
44	C₂₉×#388	C₂²	1	4	yes	—
45	C₂₉×#388	C₂²	1	4	yes	—
46	C₂₉×#388	C₂²	1	4	yes	—
47	C₂₉×#387	C₂²	1	4	yes	—
48	C₂₉×#387	C₂²	1	4	yes	—
49	C₂₉×#387	C₂²	1	4	yes	—
50	C₂₉×#387	C₂²	1	4	yes	—
51	C₂₉×#386	C₂²	1	4	yes	—
52	C₂₉×#385	C₂²	1	4	yes	—
53	C₂₉×#383	C₂²	1	2	yes	—
54	C₂₉×#382	C₂²	1	2	yes	—
55	C₂₉×#381	C₂²	1	2	yes	—
56	C₂₉×#380	C₂²	1	2	yes	—
57	C₄×C₄⋊C₄×C₂₉	C₂²	1	4	yes	—
58	C₄×C₄⋊C₄×C₂₉	C₂²	1	4	yes	—
59	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
60	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
61	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
62	C₄×C₄⋊C₄×C₂₉	C₂²	1	4	yes	—
63	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
64	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
65	C₄×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
66	C₄×C₄⋊C₄×C₂₉	C₂²	1	4	yes	—
67	C₄×C₂²⋊C₄×C₂₉	C₂²	1	4	yes	—
68	C₄×C₂²⋊C₄×C₂₉	C₂²	1	4	yes	—
69	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
70	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
71	C₄×C₂²⋊C₄×C₂₉	C₂²	1	2	yes	—
72	C₄×C₂²⋊C₄×C₂₉	C₂²	1	4	yes	—
73	C₄×C₂²⋊C₄×C₂₉	C₂²	1	4	yes	—
74	C₄×C₂²⋊C₄×C₂₉	C₂²	1	4	yes	—
75	C₂₉×#376	C₂²	1	2	yes	—
76	C₂₉×#376	C₂²	1	2	yes	—
77	C₄³×C₂₉	C₂²	1	1	yes	characteristic
78	C₄³×C₂₉	C₂²	1	1	yes	characteristic
79	C₄³×C₂₉	C₂²	1	2	yes	—
80	C₄³×C₂₉	C₂²	1	2	yes	—
81	C₄³×C₂₉	C₂²	1	1	yes	characteristic
82	C₄³×C₂₉	C₂²	1	1	yes	characteristic
83	C₄³×C₂₉	C₂²	1	2	yes	—
84	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
86	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
88	C₂³×C₄×C₂₉	C₂³	1	4	yes	—
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	2	yes	—
93	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
94	C₂₉×#126	C₂×C₄	1	16	yes	complemented
95	C₂₉×#125	C₂×C₄	1	8	yes	complemented
96	C₂₉×#124	C₂×C₄	1	8	yes	complemented
97	C₂₉×#123	C₂×C₄	1	16	yes	complemented
98	C₂₉×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
99	C₂₉×#121	C₂×C₄	1	8	yes	—
100	C₄×Q₈×C₂₉	—	2	8	no	—
101	C₄×Q₈×C₂₉	C₂×C₄	1	8	yes	complemented
102	C₄×D₄×C₂₉	—	2	16	no	—
103	C₄×D₄×C₂₉	—	2	8	no	—
104	C₄×D₄×C₂₉	C₂×C₄	1	8	yes	complemented
105	C₄×D₄×C₂₉	C₂×C₄	1	16	yes	complemented
106	C₂₉×#117	—	2	8	no	—
107	C₂₉×#117	C₂×C₄	1	16	yes	complemented
108	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₂₉	C₂³	1	2	yes	—
128	C₂×C₄²×C₂₉	—	2	8	no	—
129	C₂×C₄²×C₂₉	—	2	4	no	—
130	C₂×C₄²×C₂₉	—	2	8	no	—
131	C₂×C₄²×C₂₉	—	2	4	no	—
132	C₂×C₄²×C₂₉	—	2	8	no	—
133	C₂×C₄²×C₂₉	C₂×C₄	1	8	yes	complemented
134	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
135	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
136	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
137	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
138	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
141	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
142	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
143	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
144	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
145	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
146	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
147	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
148	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
149	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
150	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
158	C₂₉×#95	C₂³	1	4	yes	—
159	C₂₉×#95	C₂³	1	4	yes	—
160	C₂₉×#95	C₂³	1	4	yes	—
161	C₂₉×#95	C₂³	1	4	yes	—
162	C₂₉×#95	C₂³	1	2	yes	—
163	C₂₉×#95	C₂³	1	4	yes	—
164	C₂₉×#95	C₂³	1	4	yes	—
165	C₂₉×#95	C₂³	1	4	yes	—
166	C₂₉×#95	C₂³	1	4	yes	—
167	C₂₉×#95	C₂³	1	2	yes	—
168	C₂₉×#95	C₂³	1	4	yes	—
169	C₂⁴×C₂₉	C₂⁴	1	2	yes	—
170	C₂⁴×C₂₉	C₂⁴	1	1	yes	characteristic
171	C₂×Q₈×C₂₉	—	2	4	no	—
172	C₂×Q₈×C₂₉	C₂²×C₄	1	4	yes	—
173	C₂×D₄×C₂₉	—	2	8	no	—
174	C₂×D₄×C₂₉	—	2	4	no	—
175	C₂×D₄×C₂₉	C₂²×C₄	1	8	yes	—
176	C₂×D₄×C₂₉	C₂²×C₄	1	4	yes	—
177	C₂²×C₄×C₂₉	—	2	4	no	—
178	C₂²×C₄×C₂₉	—	2	4	no	—
179	C₂²×C₄×C₂₉	—	2	4	no	—
180	C₂²×C₄×C₂₉	—	2	4	no	—
181	C₂²×C₄×C₂₉	—	2	2	no	—
182	C₂²×C₄×C₂₉	—	2	2	no	—
183	C₂²×C₄×C₂₉	—	2	4	no	—
184	C₂²×C₄×C₂₉	—	2	4	no	—
185	C₂²×C₄×C₂₉	—	2	4	no	—
186	C₂²×C₄×C₂₉	—	2	4	no	—
187	C₂²×C₄×C₂₉	—	2	4	no	—
188	C₂²×C₄×C₂₉	—	2	8	no	—
189	C₂²×C₄×C₂₉	—	2	8	no	—
190	C₂²×C₄×C₂₉	—	2	8	no	—
191	C₂²×C₄×C₂₉	C₂²×C₄	1	4	yes	—
192	C₂²×C₄×C₂₉	C₂²×C₄	1	4	yes	—
193	C₂²×C₄×C₂₉	C₂²×C₄	1	4	yes	—
194	C₂²×C₄×C₂₉	C₂²×C₄	1	8	yes	—
195	C₂²×C₄×C₂₉	#41	1	8	yes	—
196	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
211	C₄⋊C₄×C₂₉	—	2	8	no	—
212	C₄⋊C₄×C₂₉	—	2	8	no	—
213	C₄⋊C₄×C₂₉	—	2	4	no	—
214	C₄⋊C₄×C₂₉	—	2	8	no	—
215	C₄⋊C₄×C₂₉	—	2	4	no	—
216	C₄⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
217	C₄⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
218	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
219	C₄⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
220	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
221	C₄⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
222	C₂²⋊C₄×C₂₉	—	2	8	no	—
223	C₂²⋊C₄×C₂₉	—	2	8	no	—
224	C₂²⋊C₄×C₂₉	—	2	8	no	—
225	C₂²⋊C₄×C₂₉	—	2	8	no	—
226	C₂²⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
227	C₂²⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
228	C₂²⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
229	C₂²⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
230	C₂²⋊C₄×C₂₉	C₂²×C₄	1	8	yes	—
231	C₄²×C₂₉	—	2	4	no	—
232	C₄²×C₂₉	—	2	4	no	—
233	C₄²×C₂₉	—	2	4	no	—
234	C₄²×C₂₉	—	2	4	no	—
235	C₄²×C₂₉	—	2	2	no	—
236	C₄²×C₂₉	—	2	2	no	—
237	C₄²×C₂₉	—	2	4	no	—
238	C₄²×C₂₉	—	2	4	no	—
239	C₄²×C₂₉	—	2	4	no	—
240	C₄²×C₂₉	—	2	4	no	—
241	C₄²×C₂₉	—	2	4	no	—
242	C₄²×C₂₉	—	2	8	no	—
243	C₄²×C₂₉	—	2	4	no	—
244	C₄²×C₂₉	—	2	4	no	—
245	C₄²×C₂₉	—	2	8	no	—
246	C₄²×C₂₉	—	2	8	no	—
247	C₄²×C₂₉	C₂²×C₄	1	4	yes	—
248	C₄²×C₂₉	C₂²×C₄	1	4	yes	—
249	C₄²×C₂₉	C₂²×C₄	1	4	yes	—
250	C₄²×C₂₉	C₂²×C₄	1	4	yes	—
251	C₄²×C₂₉	C₂²×C₄	1	8	yes	—
252	C₄²×C₂₉	#41	1	4	yes	—
253	C₄²×C₂₉	#41	1	4	yes	—
254	C₄²×C₂₉	#41	1	8	yes	—
255	C₄×#529	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂³×C₂₉	—	2	1	no	—
257	C₂³×C₂₉	—	2	2	no	—
258	C₂³×C₂₉	—	2	1	no	—
259	C₂³×C₂₉	—	2	2	no	—
260	C₂³×C₂₉	—	2	4	no	—
261	C₂³×C₂₉	—	2	4	no	—
262	C₂³×C₂₉	—	2	2	no	—
263	C₂³×C₂₉	C₂³×C₄	1	4	yes	—
264	C₂³×C₂₉	C₂³×C₄	1	2	yes	—
265	C₂³×C₂₉	C₂×#41	1	4	yes	—
266	C₂³×C₂₉	C₂⁵	1	1	yes	characteristic
267	Q₈×C₂₉	—	2	8	no	—
268	D₄×C₂₉	—	2	16	no	—
269	D₄×C₂₉	—	2	8	no	—
270	C₂×C₄×C₂₉	—	2	16	no	—
271	C₂×C₄×C₂₉	—	2	8	no	—
272	C₂×C₄×C₂₉	—	2	1	no	—
273	C₂×C₄×C₂₉	—	2	2	no	—
274	C₂×C₄×C₂₉	—	2	2	no	—
275	C₂×C₄×C₂₉	—	2	2	no	—
276	C₂×C₄×C₂₉	—	2	2	no	—
277	C₂×C₄×C₂₉	—	2	1	no	—
278	C₂×C₄×C₂₉	—	2	2	no	—
279	C₂×C₄×C₂₉	—	2	2	no	—
280	C₂×C₄×C₂₉	—	2	2	no	—
281	C₂×C₄×C₂₉	—	2	2	no	—
282	C₂×C₄×C₂₉	—	2	2	no	—
283	C₂×C₄×C₂₉	—	2	2	no	—
284	C₂×C₄×C₂₉	—	2	4	no	—
285	C₂×C₄×C₂₉	—	2	4	no	—
286	C₂×C₄×C₂₉	—	2	2	no	—
287	C₂×C₄×C₂₉	—	2	8	no	—
288	C₂×C₄×C₂₉	—	2	16	no	—
289	C₂×C₄×C₂₉	—	2	8	no	—
290	C₂×C₄×C₂₉	—	2	16	no	—
291	C₂×C₄×C₂₉	—	2	4	no	—
292	C₂×C₄×C₂₉	—	2	4	no	—
293	C₂×C₄×C₂₉	—	2	4	no	—
294	C₂×C₄×C₂₉	—	2	4	no	—
295	C₂×C₄×C₂₉	—	2	4	no	—
296	C₂×C₄×C₂₉	—	2	4	no	—
297	C₂×C₄×C₂₉	—	4	16	no	—
298	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
299	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
300	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
301	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
302	C₂×C₄×C₂₉	C₂³×C₄	1	4	yes	—
303	C₂×C₄×C₂₉	C₂³×C₄	1	4	yes	—
304	C₂×C₄×C₂₉	C₂³×C₄	1	4	yes	—
305	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
306	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
307	C₂×C₄×C₂₉	C₂×#41	1	4	yes	—
308	C₂×C₄×C₂₉	C₂×#41	1	4	yes	—
309	C₂×C₄×C₂₉	C₂×#41	1	4	yes	—
310	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
311	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
312	C₂×C₄×C₂₉	C₂×#41	1	4	yes	—
313	C₂×C₄×C₂₉	C₂×#41	1	4	yes	—
314	C₂×C₄×C₂₉	C₂×#41	1	4	yes	—
315	C₂×C₄×C₂₉	C₂×#41	1	4	yes	—
316	C₂×#529	C₂×C₂₉	1	1	yes	characteristic
317	C₄×#125	C₂×C₂₉	1	2	yes	complemented
318	C₄×#126	C₂×C₂₉	1	4	yes	complemented
319	C₄×#124	C₂×C₂₉	1	2	yes	complemented
320	C₄×C₂²⋊Q₈	C₂×C₂₉	1	2	yes	complemented
321	C₄×#123	C₂×C₂₉	1	4	yes	complemented
322	C₄×#121	C₂×C₂₉	1	2	yes	—
323	#2298	C₂×C₂₉	1	2	yes	complemented
324	#2295	C₂×C₂₉	1	1	yes	characteristic, complemented
325	#2293	C₂×C₂₉	1	1	yes	characteristic, complemented
326	#2290	C₂×C₂₉	1	2	yes	complemented
327	#2283	C₂×C₂₉	1	1	yes	characteristic, complemented
328	C₄²×Q₈	C₂×C₂₉	1	1	yes	characteristic, complemented
329	C₄²×D₄	C₂×C₂₉	1	2	yes	complemented
330	C₄²×D₄	C₂×C₂₉	1	1	yes	characteristic, complemented
331	C₄×#117	C₂×C₂₉	1	2	yes	complemented
332	C₂×C₄³	C₂×C₂₉	1	1	yes	characteristic, complemented
333	C₂²×C₂₉	—	2	2	no	—
334	C₂²×C₂₉	—	2	2	no	—
335	C₂²×C₂₉	—	2	4	no	—
336	C₂²×C₂₉	—	2	4	no	—
337	C₂²×C₂₉	—	2	4	no	—
338	C₂²×C₂₉	—	2	4	no	—
339	C₂²×C₂₉	—	2	4	no	—
340	C₂²×C₂₉	—	4	4	no	—
341	C₂²×C₂₉	—	4	4	no	—
342	C₂²×C₂₉	C₄×#41	1	4	yes	—
343	C₂²×C₂₉	C₂⁴×C₄	1	1	yes	characteristic
344	C₂²×C₂₉	C₂²×#41	1	1	yes	characteristic
345	C₂²×C₂₉	C₂²×#41	1	2	yes	—
346	C₂²×C₂₉	C₂²×#41	1	2	yes	—
347	C₂²×C₂₉	C₂²×#41	1	1	yes	characteristic
348	C₄×C₂₉	—	2	2	no	—
349	C₄×C₂₉	—	2	2	no	—
350	C₄×C₂₉	—	2	2	no	—
351	C₄×C₂₉	—	2	2	no	—
352	C₄×C₂₉	—	2	4	no	—
353	C₄×C₂₉	—	2	4	no	—
354	C₄×C₂₉	—	2	4	no	—
355	C₄×C₂₉	—	2	4	no	—
356	C₄×C₂₉	—	2	4	no	—
357	C₄×C₂₉	—	2	4	no	—
358	C₄×C₂₉	—	4	4	no	—
359	C₄×C₂₉	—	4	4	no	—
360	C₄×C₂₉	C₄×#41	1	4	yes	—
361	C₄×C₂₉	C₄×#41	1	4	yes	—
362	C₄×C₂₉	#529	1	8	yes	direct product factor
363	#529	C₄×C₂₉	1	16	yes	direct product factor
364	C₂×#126	C₂²×C₂₉	1	2	yes	—
365	C₂×#125	C₂²×C₂₉	1	1	yes	characteristic
366	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
367	C₂×#123	C₂²×C₂₉	1	2	yes	—
368	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
369	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic
370	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	—
371	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
372	C₂×C₄×D₄	C₂²×C₂₉	1	4	yes	—
373	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
374	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
375	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
376	C₂×#117	C₂²×C₂₉	1	2	yes	—
377	C₂×#117	C₂²×C₂₉	1	2	yes	—
378	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
379	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
380	C₂²×C₄²	C₂²×C₂₉	1	2	yes	—
381	C₂²×C₄²	C₂²×C₂₉	1	2	yes	—
382	C₂²×C₄²	C₂²×C₂₉	1	2	yes	—
383	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
384	#391	C₂²×C₂₉	1	2	yes	—
385	#390	C₂²×C₂₉	1	2	yes	—
386	#389	C₂²×C₂₉	1	2	yes	—
387	#389	C₂²×C₂₉	1	2	yes	—
388	#388	C₂²×C₂₉	1	4	yes	—
389	#388	C₂²×C₂₉	1	4	yes	—
390	#388	C₂²×C₂₉	1	4	yes	—
391	#388	C₂²×C₂₉	1	4	yes	—
392	#387	C₂²×C₂₉	1	4	yes	—
393	#387	C₂²×C₂₉	1	4	yes	—
394	#387	C₂²×C₂₉	1	4	yes	—
395	#387	C₂²×C₂₉	1	4	yes	—
396	#386	C₂²×C₂₉	1	4	yes	—
397	#385	C₂²×C₂₉	1	4	yes	—
398	#383	C₂²×C₂₉	1	2	yes	—
399	#382	C₂²×C₂₉	1	2	yes	—
400	#381	C₂²×C₂₉	1	2	yes	—
401	#380	C₂²×C₂₉	1	2	yes	—
402	C₄×C₄⋊C₄	C₂²×C₂₉	1	4	yes	—
403	C₄×C₄⋊C₄	C₂²×C₂₉	1	4	yes	—
404	C₄×C₄⋊C₄	C₂²×C₂₉	1	4	yes	—
405	C₄×C₄⋊C₄	C₂²×C₂₉	1	4	yes	—
406	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
407	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
408	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
409	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
410	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
411	C₄×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
412	C₄×C₂²⋊C₄	C₂²×C₂₉	1	4	yes	—
413	C₄×C₂²⋊C₄	C₂²×C₂₉	1	4	yes	—
414	C₄×C₂²⋊C₄	C₂²×C₂₉	1	4	yes	—
415	C₄×C₂²⋊C₄	C₂²×C₂₉	1	4	yes	—
416	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
417	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
418	C₄×C₂²⋊C₄	C₂²×C₂₉	1	2	yes	—
419	C₄×C₂²⋊C₄	C₂²×C₂₉	1	4	yes	—
420	#376	C₂²×C₂₉	1	2	yes	—
421	#376	C₂²×C₂₉	1	2	yes	—
422	C₄³	C₂²×C₂₉	1	2	yes	—
423	C₄³	C₂²×C₂₉	1	2	yes	—
424	C₄³	C₂²×C₂₉	1	1	yes	characteristic
425	C₄³	C₂²×C₂₉	1	1	yes	characteristic
426	C₄³	C₂²×C₂₉	1	1	yes	characteristic
427	C₄³	C₂²×C₂₉	1	1	yes	characteristic
428	C₄³	C₂²×C₂₉	1	2	yes	—
429	C₂×C₂₉	—	2	4	no	—
430	C₂×C₂₉	—	4	4	no	—
431	C₂×C₂₉	C₂×C₄×#41	1	1	yes	characteristic
432	C₂×C₂₉	C₂×C₄×#41	1	1	yes	characteristic
433	C₂×C₂₉	C₂×C₄×#41	1	1	yes	characteristic
434	C₂×C₂₉	C₂×#529	1	2	yes	—
435	C₂×C₂₉	#3444	1	2	yes	—
436	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
437	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
438	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
439	C₂³×C₄	C₂³×C₂₉	1	4	yes	—
440	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
441	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
442	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
443	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
444	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
445	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
446	#126	C₂×C₄×C₂₉	1	16	yes	complemented
447	#125	C₂×C₄×C₂₉	1	8	yes	complemented
448	#124	C₂×C₄×C₂₉	1	8	yes	complemented
449	#123	C₂×C₄×C₂₉	1	16	yes	complemented
450	C₂²⋊Q₈	C₂×C₄×C₂₉	1	8	yes	complemented
451	#121	C₂×C₄×C₂₉	1	8	yes	—
452	C₄×Q₈	—	2	8	no	—
453	C₄×Q₈	C₂×C₄×C₂₉	1	8	yes	complemented
454	C₄×D₄	—	2	16	no	—
455	C₄×D₄	—	2	8	no	—
456	C₄×D₄	C₂×C₄×C₂₉	1	8	yes	complemented
457	C₄×D₄	C₂×C₄×C₂₉	1	16	yes	complemented
458	#117	—	2	8	no	—
459	#117	C₂×C₄×C₂₉	1	16	yes	complemented
460	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
461	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
462	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
463	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
465	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₂₉	1	2	yes	—
480	C₂×C₄²	—	2	8	no	—
481	C₂×C₄²	—	2	4	no	—
482	C₂×C₄²	—	2	8	no	—
483	C₂×C₄²	—	2	4	no	—
484	C₂×C₄²	—	2	8	no	—
485	C₂×C₄²	C₂×C₄×C₂₉	1	8	yes	complemented
486	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
487	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
488	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
489	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
490	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
491	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
492	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
493	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
495	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
496	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
497	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
498	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
499	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
500	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
501	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
502	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
503	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
504	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
506	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
507	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
509	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
510	#95	C₂³×C₂₉	1	4	yes	—
511	#95	C₂³×C₂₉	1	4	yes	—
512	#95	C₂³×C₂₉	1	4	yes	—
513	#95	C₂³×C₂₉	1	4	yes	—
514	#95	C₂³×C₂₉	1	2	yes	—
515	#95	C₂³×C₂₉	1	4	yes	—
516	#95	C₂³×C₂₉	1	4	yes	—
517	#95	C₂³×C₂₉	1	4	yes	—
518	#95	C₂³×C₂₉	1	4	yes	—
519	#95	C₂³×C₂₉	1	2	yes	—
520	#95	C₂³×C₂₉	1	4	yes	—
521	C₂₉	C₄×#529	1	1	yes	characteristic, direct product factor, Sylow
522	C₂⁴	C₂⁴×C₂₉	1	2	yes	—
523	C₂⁴	C₂⁴×C₂₉	1	1	yes	characteristic
524	C₂×Q₈	—	2	4	no	—
525	C₂×Q₈	C₂²×C₄×C₂₉	1	4	yes	—
526	C₂×D₄	—	2	8	no	—
527	C₂×D₄	—	2	4	no	—
528	C₂×D₄	C₂²×C₄×C₂₉	1	8	yes	—
529	C₂×D₄	C₂²×C₄×C₂₉	1	4	yes	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	2	8	no	—
542	C₂²×C₄	—	2	8	no	—
543	C₂²×C₄	—	2	8	no	—
544	C₂²×C₄	C₂²×C₄×C₂₉	1	4	yes	—
545	C₂²×C₄	C₂²×C₄×C₂₉	1	4	yes	—
546	C₂²×C₄	C₂²×C₄×C₂₉	1	4	yes	—
547	C₂²×C₄	C₂²×C₄×C₂₉	1	8	yes	—
548	C₂²×C₄	#41×C₂₉	1	8	yes	—
549	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
550	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
551	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
557	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
560	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
563	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
564	C₄⋊C₄	—	2	8	no	—
565	C₄⋊C₄	—	2	8	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	8	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
570	C₄⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
571	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
572	C₄⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
573	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
574	C₄⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
575	C₂²⋊C₄	—	2	8	no	—
576	C₂²⋊C₄	—	2	8	no	—
577	C₂²⋊C₄	—	2	8	no	—
578	C₂²⋊C₄	—	2	8	no	—
579	C₂²⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
580	C₂²⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
581	C₂²⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
582	C₂²⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
583	C₂²⋊C₄	C₂²×C₄×C₂₉	1	8	yes	—
584	C₄²	—	2	4	no	—
585	C₄²	—	2	4	no	—
586	C₄²	—	2	4	no	—
587	C₄²	—	2	4	no	—
588	C₄²	—	2	2	no	—
589	C₄²	—	2	2	no	—
590	C₄²	—	2	4	no	—
591	C₄²	—	2	4	no	—
592	C₄²	—	2	4	no	—
593	C₄²	—	2	4	no	—
594	C₄²	—	2	4	no	—
595	C₄²	—	2	8	no	—
596	C₄²	—	2	4	no	—
597	C₄²	—	2	4	no	—
598	C₄²	—	2	8	no	—
599	C₄²	—	2	8	no	—
600	C₄²	C₂²×C₄×C₂₉	1	4	yes	—
601	C₄²	C₂²×C₄×C₂₉	1	4	yes	—
602	C₄²	C₂²×C₄×C₂₉	1	4	yes	—
603	C₄²	C₂²×C₄×C₂₉	1	4	yes	—
604	C₄²	C₂²×C₄×C₂₉	1	8	yes	—
605	C₄²	#41×C₂₉	1	4	yes	—
606	C₄²	#41×C₂₉	1	4	yes	—
607	C₄²	#41×C₂₉	1	8	yes	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	2	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	4	no	—
613	C₂³	—	2	4	no	—
614	C₂³	—	2	2	no	—
615	C₂³	C₂³×C₄×C₂₉	1	4	yes	—
616	C₂³	C₂³×C₄×C₂₉	1	2	yes	—
617	C₂³	C₂×#41×C₂₉	1	4	yes	—
618	C₂³	C₂⁵×C₂₉	1	1	yes	characteristic
619	Q₈	—	2	8	no	—
620	D₄	—	2	16	no	—
621	D₄	—	2	8	no	—
622	C₂×C₄	—	2	16	no	—
623	C₂×C₄	—	2	8	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	8	no	—
640	C₂×C₄	—	2	16	no	—
641	C₂×C₄	—	2	8	no	—
642	C₂×C₄	—	2	16	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	2	4	no	—
649	C₂×C₄	—	4	16	no	—
650	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
651	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
652	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
653	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
654	C₂×C₄	C₂³×C₄×C₂₉	1	4	yes	—
655	C₂×C₄	C₂³×C₄×C₂₉	1	4	yes	—
656	C₂×C₄	C₂³×C₄×C₂₉	1	4	yes	—
657	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
658	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
659	C₂×C₄	C₂×#41×C₂₉	1	4	yes	—
660	C₂×C₄	C₂×#41×C₂₉	1	4	yes	—
661	C₂×C₄	C₂×#41×C₂₉	1	4	yes	—
662	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
663	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
664	C₂×C₄	C₂×#41×C₂₉	1	4	yes	—
665	C₂×C₄	C₂×#41×C₂₉	1	4	yes	—
666	C₂×C₄	C₂×#41×C₂₉	1	4	yes	—
667	C₂×C₄	C₂×#41×C₂₉	1	4	yes	—
668	C₂²	—	2	4	no	—
669	C₂²	—	2	4	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	4	no	—
673	C₂²	—	2	4	no	—
674	C₂²	—	2	4	no	—
675	C₂²	—	4	4	no	—
676	C₂²	—	4	4	no	—
677	C₂²	C₄×#41×C₂₉	1	4	yes	—
678	C₂²	C₂⁴×C₄×C₂₉	1	1	yes	characteristic
679	C₂²	C₂²×#41×C₂₉	1	1	yes	characteristic
680	C₂²	C₂²×#41×C₂₉	1	2	yes	—
681	C₂²	C₂²×#41×C₂₉	1	2	yes	—
682	C₂²	C₂²×#41×C₂₉	1	1	yes	characteristic
683	C₄	—	2	4	no	—
684	C₄	—	2	4	no	—
685	C₄	—	2	4	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	2	no	—
688	C₄	—	2	2	no	—
689	C₄	—	2	2	no	—
690	C₄	—	2	4	no	—
691	C₄	—	2	4	no	—
692	C₄	—	2	4	no	—
693	C₄	—	4	4	no	—
694	C₄	—	4	4	no	—
695	C₄	C₄×#41×C₂₉	1	4	yes	—
696	C₄	C₄×#41×C₂₉	1	4	yes	—
697	C₄	C₂₉×#529	1	8	yes	direct product factor
698	C₂	—	2	4	no	—
699	C₂	—	4	4	no	—
700	C₂	C₂×C₄×#41×C₂₉	1	1	yes	characteristic
701	C₂	C₂×C₄×#41×C₂₉	1	1	yes	characteristic
702	C₂	C₂×C₄×#41×C₂₉	1	1	yes	characteristic
703	C₂	C₂×C₂₉×#529	1	2	yes	—
704	C₂	C₂₉×#3444	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²×C₂₉	C₂³
commutator	C₂²	C₂⁴×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁵×C₂₉
socle	C₂³×C₂₉	C₂⁵
prime radical	C₂×C₂₉×#121	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₂₉×#125	C₂	semidirect
3. C₄×C₂₉×#126	C₂	semidirect
4. C₄×C₂₉×#124	C₂	semidirect
5. C₄×C₂₉×C₂²⋊Q₈	C₂	semidirect
6. C₄×C₂₉×#123	C₂	semidirect
8. C₂₉×#2298	C₂	semidirect
9. C₂₉×#2295	C₂	semidirect
10. C₂₉×#2293	C₂	semidirect
11. C₂₉×#2290	C₂	semidirect
12. C₂₉×#2283	C₂	semidirect
13. C₄²×Q₈×C₂₉	C₂	semidirect
14. C₄²×D₄×C₂₉	C₂	semidirect
15. C₄²×D₄×C₂₉	C₂	semidirect
16. C₄×C₂₉×#117	C₂	semidirect
17. C₂×C₄³×C₂₉	C₂	semidirect
18. C₂₉×#529	C₄	direct (N × H)
94. C₂₉×#126	C₂×C₄	semidirect
95. C₂₉×#125	C₂×C₄	semidirect
96. C₂₉×#124	C₂×C₄	semidirect
97. C₂₉×#123	C₂×C₄	semidirect
98. C₂₉×C₂²⋊Q₈	C₂×C₄	semidirect
101. C₄×Q₈×C₂₉	C₂×C₄	semidirect
104. C₄×D₄×C₂₉	C₂×C₄	semidirect
105. C₄×D₄×C₂₉	C₂×C₄	semidirect
107. C₂₉×#117	C₂×C₄	semidirect
133. C₂×C₄²×C₂₉	C₂×C₄	semidirect
255. C₄×#529	C₂₉	direct (N × H)
317. C₄×#125	C₂×C₂₉	semidirect
318. C₄×#126	C₂×C₂₉	semidirect
319. C₄×#124	C₂×C₂₉	semidirect
320. C₄×C₂²⋊Q₈	C₂×C₂₉	semidirect
321. C₄×#123	C₂×C₂₉	semidirect
323. #2298	C₂×C₂₉	semidirect
324. #2295	C₂×C₂₉	semidirect
325. #2293	C₂×C₂₉	semidirect
326. #2290	C₂×C₂₉	semidirect
327. #2283	C₂×C₂₉	semidirect
328. C₄²×Q₈	C₂×C₂₉	semidirect
329. C₄²×D₄	C₂×C₂₉	semidirect
330. C₄²×D₄	C₂×C₂₉	semidirect
331. C₄×#117	C₂×C₂₉	semidirect
332. C₂×C₄³	C₂×C₂₉	semidirect
362. C₄×C₂₉	#529	direct (N × H)
363. #529	C₄×C₂₉	direct (N × H)
446. #126	C₂×C₄×C₂₉	semidirect
447. #125	C₂×C₄×C₂₉	semidirect
448. #124	C₂×C₄×C₂₉	semidirect
449. #123	C₂×C₄×C₂₉	semidirect
450. C₂²⋊Q₈	C₂×C₄×C₂₉	semidirect
453. C₄×Q₈	C₂×C₄×C₂₉	semidirect
456. C₄×D₄	C₂×C₄×C₂₉	semidirect
457. C₄×D₄	C₂×C₄×C₂₉	semidirect
459. #117	C₂×C₄×C₂₉	semidirect
485. C₂×C₄²	C₂×C₄×C₂₉	semidirect
521. C₂₉	C₄×#529	direct (N × H)
697. C₄	C₂₉×#529	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#529	2
C₄×C₂₉×#125	2
C₄×C₂₉×#126	2
C₄×C₂₉×#124	2
C₄×C₂₉×C₂²⋊Q₈	2
C₄×C₂₉×#123	2
C₄×C₂₉×#121	2
C₂₉×#2298	2
C₂₉×#2295	2
C₂₉×#2293	2
C₂₉×#2290	2
C₂₉×#2283	2
C₄²×Q₈×C₂₉	2
C₄²×D₄×C₂₉	2
C₄×C₂₉×#117	2
C₂×C₄³×C₂₉	2
C₄×#529	29

Subgroups — C4×C29×#529 #20328935

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₉×#529 #20328935