Subgroups — C₂₉×#60219 #20355119

Order 7424.

1906 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3480	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2970	C₂	1	2	yes	maximal, complemented
3	C₂₉×#2969	C₂	1	2	yes	maximal, complemented
4	C₂₉×#2968	C₂	1	4	yes	maximal, complemented
5	C₂₉×#2967	C₂	1	4	yes	maximal, complemented
6	C₂₉×#2966	C₂	1	2	yes	maximal, complemented
7	C₂₉×#2965	C₂	1	2	yes	maximal, complemented
8	Q₈×M₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₉×#446	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#2935	C₂	1	2	yes	maximal, complemented
11	C₂₉×#2935	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#2932	C₂	1	2	yes	maximal, complemented
13	C₂₉×#2931	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#2925	C₂	1	2	yes	maximal, complemented
15	C₂₉×#2925	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#2875	C₂	1	2	yes	maximal, complemented
17	C₄×C₂₉×#131	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₉×#131	C₂²	1	2	yes	—
19	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
20	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#131	C₂²	1	2	yes	—
22	C₂₉×#559	C₄	1	1	yes	characteristic
23	C₂₉×#559	C₄	1	2	yes	—
24	C₂₉×#557	C₄	1	1	yes	characteristic
25	C₂₉×#556	C₄	1	1	yes	characteristic
26	C₂₉×#556	C₄	1	2	yes	—
27	C₂₉×#553	C₄	1	2	yes	—
28	C₂₉×#553	C₄	1	4	yes	—
29	C₂₉×#550	C₄	1	1	yes	characteristic
30	C₂₉×#548	C₄	1	2	yes	—
31	C₂₉×#532	C₂²	1	1	yes	characteristic
32	C₂₉×#532	C₂²	1	2	yes	—
33	C₂₉×#529	C₂²	1	2	yes	—
34	C₂₉×#529	C₂²	1	4	yes	—
35	C₄×#41×C₂₉	C₂²	1	2	yes	—
36	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
37	C₄×#41×C₂₉	C₂²	1	2	yes	—
38	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
39	C₂₉×#446	C₂²	1	1	yes	characteristic
40	C₂₉×#446	C₂²	1	1	yes	characteristic
41	C₂₉×#446	C₂²	1	2	yes	—
42	C₂₉×#446	C₂²	1	2	yes	—
43	C₂₉×#446	C₂²	1	1	yes	characteristic
44	C₂₉×#446	C₂²	1	1	yes	characteristic
45	C₂₉×#446	C₂²	1	2	yes	—
46	C₂₉×#446	C₂²	1	4	yes	—
47	C₈×Q₈×C₂₉	C₂²	1	2	yes	—
48	C₂₉×#436	C₂²	1	2	yes	—
49	C₂₉×#436	C₂²	1	2	yes	—
50	C₂₉×#436	C₂²	1	2	yes	—
51	C₂₉×#436	C₂²	1	4	yes	—
52	C₂₉×#435	C₂²	1	4	yes	—
53	C₂₉×#435	C₂²	1	4	yes	—
54	C₂₉×#435	C₂²	1	4	yes	—
55	C₂₉×#435	C₂²	1	4	yes	—
56	C₂₉×#435	C₂²	1	4	yes	—
57	C₂₉×#435	C₂²	1	4	yes	—
58	C₂₉×#435	C₂²	1	4	yes	—
59	C₈×D₄×C₂₉	C₂²	1	2	yes	—
60	C₈×D₄×C₂₉	C₂²	1	2	yes	—
61	C₈×D₄×C₂₉	C₂²	1	4	yes	—
62	C₈×D₄×C₂₉	C₂²	1	2	yes	—
63	C₂₉×#433	C₂²	1	4	yes	—
64	C₂₉×#433	C₂²	1	4	yes	—
65	C₂₉×#433	C₂²	1	4	yes	—
66	C₂₉×#432	C₂²	1	2	yes	—
67	C₂₉×#432	C₂²	1	4	yes	—
68	C₂₉×#431	C₂²	1	4	yes	—
69	C₂₉×#431	C₂²	1	2	yes	—
70	C₂₉×#423	C₂²	1	1	yes	characteristic
71	C₂₉×#423	C₂²	1	2	yes	—
72	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
73	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
74	C₂₉×#408	C₂²	1	2	yes	—
75	C₂₉×#408	C₂²	1	2	yes	—
76	C₂₉×#408	C₂²	1	2	yes	—
77	C₂₉×#405	C₂²	1	4	yes	—
78	C₂₉×#405	C₂²	1	2	yes	—
79	C₂₉×#405	C₂²	1	2	yes	—
80	C₂₉×#405	C₂²	1	4	yes	—
81	C₂₉×#405	C₂²	1	1	yes	characteristic
82	C₂₉×#405	C₂²	1	1	yes	characteristic
83	C₂₉×#405	C₂²	1	2	yes	—
84	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
85	C₄×M₁₆×C₂₉	C₂²	1	2	yes	—
86	C₄×M₁₆×C₂₉	C₂²	1	4	yes	—
87	C₄×M₁₆×C₂₉	C₂²	1	2	yes	—
88	C₂×C₂₉×#97	C₂²	1	2	yes	—
89	C₂×C₂₉×#97	C₂²	1	4	yes	—
90	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
91	C₂×C₄×C₈×C₂₉	C₂²	1	2	yes	—
92	C₂×#41×C₂₉	C₂×C₄	1	2	yes	—
93	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
94	C₂×#41×C₂₉	C₂³	1	2	yes	—
95	C₂²×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
96	C₂₉×#131	—	2	4	no	—
97	C₂₉×#131	—	2	8	no	—
98	C₂₉×#131	—	2	8	no	—
99	C₂₉×#131	—	2	4	no	—
100	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
101	C₂×M₁₆×C₂₉	C₂³	1	4	yes	—
102	C₂×M₁₆×C₂₉	C₂³	1	4	yes	—
103	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
104	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
105	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
106	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
108	C₂²×C₈×C₂₉	C₂³	1	4	yes	—
109	C₂²×C₈×C₂₉	C₂³	1	4	yes	—
110	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
111	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
113	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
114	C₂₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
115	C₂₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
116	C₂₉×#127	C₂×C₄	1	1	yes	characteristic
117	C₂₉×#127	C₂×C₄	1	2	yes	—
118	C₂₉×#126	C₂×C₄	1	4	yes	—
119	C₂₉×#126	C₂×C₄	1	4	yes	—
120	C₂₉×#126	C₂×C₄	1	4	yes	—
121	C₂₉×#125	C₂×C₄	1	2	yes	—
122	C₂₉×#125	C₂×C₄	1	4	yes	—
123	C₂₉×#124	C₂×C₄	1	2	yes	—
124	C₂₉×#124	C₂×C₄	1	4	yes	—
125	C₂₉×#124	C₂×C₄	1	2	yes	—
126	C₂₉×#124	C₂×C₄	1	2	yes	—
127	C₂₉×#124	C₂×C₄	1	2	yes	—
128	C₂₉×#123	C₂×C₄	1	4	yes	—
129	C₂₉×#123	C₂×C₄	1	4	yes	—
130	C₂₉×#123	C₂×C₄	1	4	yes	—
131	C₂₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
132	C₂₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
133	C₂₉×#121	C₂×C₄	1	2	yes	—
134	C₂₉×#121	C₂×C₄	1	4	yes	—
135	C₂₉×#121	C₂×C₄	1	2	yes	—
136	C₂₉×#121	C₂×C₄	1	4	yes	—
137	C₂₉×#121	C₂×C₄	1	2	yes	—
138	C₂₉×#121	C₂×C₄	1	4	yes	—
139	C₄×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
140	C₄×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
141	C₄×Q₈×C₂₉	C₂×C₄	1	2	yes	—
142	C₄×Q₈×C₂₉	C₂×C₄	1	2	yes	—
143	C₄×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
144	C₄×Q₈×C₂₉	C₂×C₄	1	2	yes	—
145	C₄×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
146	C₄×Q₈×C₂₉	C₂×C₄	1	2	yes	—
147	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
148	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
149	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
150	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
151	C₄×D₄×C₂₉	C₂×C₄	1	4	yes	—
152	C₄×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
153	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
154	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
155	C₄×D₄×C₂₉	C₂×C₄	1	4	yes	—
156	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
157	C₄×D₄×C₂₉	C₂×C₄	1	4	yes	—
158	C₄×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
159	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
160	C₄×D₄×C₂₉	C₂³	1	2	yes	—
161	C₄×D₄×C₂₉	C₂³	1	2	yes	—
162	C₄×D₄×C₂₉	C₂³	1	4	yes	—
163	C₄×D₄×C₂₉	C₂³	1	4	yes	—
164	C₂₉×#117	C₂×C₄	1	2	yes	—
165	C₂₉×#117	C₂×C₄	1	4	yes	—
166	C₂₉×#117	C₂³	1	4	yes	—
167	C₂₉×#117	C₂³	1	2	yes	—
168	C₂₉×#117	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
171	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
172	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
173	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
175	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
176	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
177	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
178	C₂₉×C₄⋊C₈	C₂³	1	4	yes	—
179	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
180	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
181	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
182	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
183	C₂₉×C₄⋊C₈	C₂³	1	4	yes	—
184	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
185	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
186	C₂₉×C₂²⋊C₈	C₂³	1	4	yes	—
187	C₂₉×C₂²⋊C₈	C₂³	1	4	yes	—
188	C₂₉×C₂²⋊C₈	C₂³	1	4	yes	—
189	C₂₉×C₂²⋊C₈	C₂³	1	4	yes	—
190	C₂₉×C₂²⋊C₈	C₂³	1	4	yes	—
191	C₂₉×C₂²⋊C₈	C₂³	1	4	yes	—
192	C₂₉×#97	C₂³	1	4	yes	—
193	C₂₉×#97	C₂³	1	2	yes	—
194	C₂₉×#97	C₂³	1	2	yes	—
195	C₂₉×#97	C₂³	1	2	yes	—
196	C₂₉×#97	C₂³	1	4	yes	—
197	C₂₉×#97	C₂³	1	2	yes	—
198	C₂₉×#97	C₂³	1	2	yes	—
199	C₂₉×#97	C₂³	1	2	yes	—
200	C₂₉×#97	C₂³	1	2	yes	—
201	C₄×C₈×C₂₉	C₂³	1	2	yes	—
202	C₄×C₈×C₂₉	C₂³	1	4	yes	—
203	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
204	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
205	C₄×C₈×C₂₉	C₂³	1	2	yes	—
206	C₄×C₈×C₂₉	C₂³	1	4	yes	—
207	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
208	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
209	C₄×C₈×C₂₉	C₂³	1	2	yes	—
210	#41×C₂₉	—	2	2	no	—
211	#41×C₂₉	—	2	4	no	—
212	#41×C₂₉	—	2	4	no	—
213	#41×C₂₉	—	2	2	no	—
214	#41×C₂₉	—	4	4	no	—
215	C₂×Q₈×C₂₉	—	4	2	no	—
216	C₂×Q₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
217	C₂×Q₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
218	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
219	C₂×Q₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
220	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
221	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
222	C₂×D₄×C₂₉	C₂²×C₄	1	4	yes	—
223	C₂×D₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
224	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
225	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
226	C₂×D₄×C₂₉	C₂²×C₄	1	4	yes	—
227	C₂×D₄×C₂₉	C₂²×C₄	1	4	yes	—
228	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
229	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
230	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
231	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
232	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
233	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
234	C₂²×C₄×C₂₉	C₂²×C₄	1	4	yes	—
235	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
236	C₂²×C₄×C₂₉	C₂²×C₄	1	4	yes	—
237	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
239	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
240	M₁₆×C₂₉	—	2	4	no	—
241	M₁₆×C₂₉	—	2	2	no	—
242	M₁₆×C₂₉	—	2	4	no	—
243	M₁₆×C₂₉	—	2	8	no	—
244	M₁₆×C₂₉	—	2	4	no	—
245	M₁₆×C₂₉	—	2	8	no	—
246	M₁₆×C₂₉	#41	1	4	yes	complemented
247	C₂×C₈×C₂₉	—	2	2	no	—
248	C₂×C₈×C₂₉	—	2	4	no	—
249	C₂×C₈×C₂₉	—	2	4	no	—
250	C₂×C₈×C₂₉	—	2	8	no	—
251	C₂×C₈×C₂₉	—	2	8	no	—
252	C₂×C₈×C₂₉	—	2	4	no	—
253	C₂×C₈×C₂₉	#41	1	4	yes	complemented
254	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
255	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
256	C₂×C₈×C₂₉	C₂⁴	1	4	yes	—
257	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
258	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
259	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
260	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
261	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
262	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
263	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
264	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
265	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
266	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
267	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
268	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
269	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
270	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
271	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
272	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
273	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
274	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
275	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
276	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
277	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
278	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
279	C₄⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
280	C₂²⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
281	C₂²⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
282	C₂²⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
283	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
284	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
285	C₂²⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
286	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
287	C₂²⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
288	C₂²⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
289	C₂²⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
290	C₂²⋊C₄×C₂₉	C₂²×C₄	1	4	yes	—
291	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
292	C₄²×C₂₉	C₂²×C₄	1	4	yes	—
293	C₄²×C₂₉	C₂²×C₄	1	4	yes	—
294	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
295	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
296	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
297	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
298	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
299	C₄²×C₂₉	C₂⁴	1	2	yes	—
300	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
301	C₄²×C₂₉	C₂⁴	1	2	yes	—
302	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
303	C₄²×C₂₉	C₂⁴	1	2	yes	—
304	#60219	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
305	C₂³×C₂₉	C₂³×C₄	1	2	yes	—
306	C₂³×C₂₉	C₂³×C₄	1	4	yes	—
307	C₂³×C₂₉	C₂³×C₄	1	1	yes	characteristic
308	Q₈×C₂₉	—	2	2	no	—
309	Q₈×C₂₉	—	2	4	no	—
310	Q₈×C₂₉	—	2	2	no	—
311	Q₈×C₂₉	—	2	2	no	—
312	Q₈×C₂₉	—	4	2	no	—
313	D₄×C₂₉	—	2	4	no	—
314	D₄×C₂₉	—	2	8	no	—
315	D₄×C₂₉	—	2	2	no	—
316	D₄×C₂₉	—	2	4	no	—
317	D₄×C₂₉	—	2	4	no	—
318	D₄×C₂₉	—	4	4	no	—
319	D₄×C₂₉	—	4	2	no	—
320	D₄×C₂₉	—	4	4	no	—
321	C₂×C₄×C₂₉	—	2	2	no	—
322	C₂×C₄×C₂₉	—	2	4	no	—
323	C₂×C₄×C₂₉	—	2	2	no	—
324	C₂×C₄×C₂₉	—	2	4	no	—
325	C₂×C₄×C₂₉	—	2	4	no	—
326	C₂×C₄×C₂₉	—	2	2	no	—
327	C₂×C₄×C₂₉	—	4	2	no	—
328	C₂×C₄×C₂₉	—	4	4	no	—
329	C₂×C₄×C₂₉	—	4	1	no	—
330	C₂×C₄×C₂₉	—	4	2	no	—
331	C₂×C₄×C₂₉	—	4	2	no	—
332	C₂×C₄×C₂₉	—	4	4	no	—
333	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
334	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
335	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
336	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
337	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
338	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
339	C₂×C₄×C₂₉	C₂³×C₄	1	4	yes	—
340	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
341	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
342	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
343	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
344	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
345	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
346	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
347	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
348	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
349	C₈×C₂₉	—	2	1	no	—
350	C₈×C₂₉	—	2	2	no	—
351	C₈×C₂₉	—	2	1	no	—
352	C₈×C₂₉	—	2	2	no	—
353	C₈×C₂₉	—	2	4	no	—
354	C₈×C₂₉	—	2	2	no	—
355	C₈×C₂₉	C₂×#41	1	2	yes	—
356	C₈×C₂₉	C₂×#41	1	4	yes	—
357	C₈×C₂₉	C₂×#41	1	2	yes	—
358	#3480	C₂×C₂₉	1	1	yes	characteristic
359	#2970	C₂×C₂₉	1	2	yes	complemented
360	#2969	C₂×C₂₉	1	2	yes	complemented
361	#2968	C₂×C₂₉	1	4	yes	complemented
362	#2967	C₂×C₂₉	1	4	yes	complemented
363	#2966	C₂×C₂₉	1	2	yes	complemented
364	#2965	C₂×C₂₉	1	2	yes	complemented
365	Q₈×M₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
366	C₂×#446	C₂×C₂₉	1	1	yes	characteristic, complemented
367	#2935	C₂×C₂₉	1	1	yes	characteristic, complemented
368	#2935	C₂×C₂₉	1	2	yes	complemented
369	#2932	C₂×C₂₉	1	2	yes	complemented
370	#2931	C₂×C₂₉	1	1	yes	characteristic, complemented
371	#2925	C₂×C₂₉	1	1	yes	characteristic, complemented
372	#2925	C₂×C₂₉	1	2	yes	complemented
373	#2875	C₂×C₂₉	1	2	yes	complemented
374	C₄×#131	C₂×C₂₉	1	1	yes	characteristic, complemented
375	C₂²×C₂₉	—	2	1	no	—
376	C₂²×C₂₉	—	2	1	no	—
377	C₂²×C₂₉	—	2	2	no	—
378	C₂²×C₂₉	—	2	4	no	—
379	C₂²×C₂₉	—	2	2	no	—
380	C₂²×C₂₉	—	2	4	no	—
381	C₂²×C₂₉	—	2	2	no	—
382	C₂²×C₂₉	—	2	4	no	—
383	C₂²×C₂₉	C₄×#41	1	2	yes	—
384	C₂²×C₂₉	C₂⁴×C₄	1	1	yes	characteristic
385	C₄×C₂₉	—	2	2	no	—
386	C₄×C₂₉	—	2	4	no	—
387	C₄×C₂₉	—	2	2	no	—
388	C₄×C₂₉	—	2	1	no	—
389	C₄×C₂₉	—	2	2	no	—
390	C₄×C₂₉	—	2	2	no	—
391	C₄×C₂₉	—	2	2	no	—
392	C₄×C₂₉	—	2	1	no	—
393	C₄×C₂₉	—	2	2	no	—
394	C₄×C₂₉	—	2	1	no	—
395	C₄×C₂₉	—	2	2	no	—
396	C₄×C₂₉	C₄×#41	1	2	yes	—
397	C₄×C₂₉	#568	1	2	yes	—
398	C₄×C₂₉	C₂²×#41	1	1	yes	characteristic
399	C₄×C₂₉	C₂²×#41	1	1	yes	characteristic
400	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
401	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
402	C₂×#131	C₂²×C₂₉	1	2	yes	—
403	C₂×#131	C₂²×C₂₉	1	2	yes	—
404	#559	C₄×C₂₉	1	1	yes	characteristic
405	#559	C₄×C₂₉	1	2	yes	—
406	#557	C₄×C₂₉	1	1	yes	characteristic
407	#556	C₄×C₂₉	1	1	yes	characteristic
408	#556	C₄×C₂₉	1	2	yes	—
409	#553	C₄×C₂₉	1	2	yes	—
410	#553	C₄×C₂₉	1	4	yes	—
411	#550	C₄×C₂₉	1	1	yes	characteristic
412	#548	C₄×C₂₉	1	2	yes	—
413	#532	C₂²×C₂₉	1	1	yes	characteristic
414	#532	C₂²×C₂₉	1	2	yes	—
415	#529	C₂²×C₂₉	1	2	yes	—
416	#529	C₂²×C₂₉	1	4	yes	—
417	C₄×#41	C₂²×C₂₉	1	2	yes	—
418	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
419	C₄×#41	C₂²×C₂₉	1	2	yes	—
420	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
421	#446	C₂²×C₂₉	1	1	yes	characteristic
422	#446	C₂²×C₂₉	1	1	yes	characteristic
423	#446	C₂²×C₂₉	1	2	yes	—
424	#446	C₂²×C₂₉	1	2	yes	—
425	#446	C₂²×C₂₉	1	1	yes	characteristic
426	#446	C₂²×C₂₉	1	1	yes	characteristic
427	#446	C₂²×C₂₉	1	2	yes	—
428	#446	C₂²×C₂₉	1	4	yes	—
429	C₈×Q₈	C₂²×C₂₉	1	2	yes	—
430	#436	C₂²×C₂₉	1	2	yes	—
431	#436	C₂²×C₂₉	1	2	yes	—
432	#436	C₂²×C₂₉	1	2	yes	—
433	#436	C₂²×C₂₉	1	4	yes	—
434	#435	C₂²×C₂₉	1	4	yes	—
435	#435	C₂²×C₂₉	1	4	yes	—
436	#435	C₂²×C₂₉	1	4	yes	—
437	#435	C₂²×C₂₉	1	4	yes	—
438	#435	C₂²×C₂₉	1	4	yes	—
439	#435	C₂²×C₂₉	1	4	yes	—
440	#435	C₂²×C₂₉	1	4	yes	—
441	C₈×D₄	C₂²×C₂₉	1	2	yes	—
442	C₈×D₄	C₂²×C₂₉	1	2	yes	—
443	C₈×D₄	C₂²×C₂₉	1	4	yes	—
444	C₈×D₄	C₂²×C₂₉	1	2	yes	—
445	#433	C₂²×C₂₉	1	4	yes	—
446	#433	C₂²×C₂₉	1	4	yes	—
447	#433	C₂²×C₂₉	1	4	yes	—
448	#432	C₂²×C₂₉	1	2	yes	—
449	#432	C₂²×C₂₉	1	4	yes	—
450	#431	C₂²×C₂₉	1	4	yes	—
451	#431	C₂²×C₂₉	1	2	yes	—
452	#423	C₂²×C₂₉	1	1	yes	characteristic
453	#423	C₂²×C₂₉	1	2	yes	—
454	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
455	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
456	#408	C₂²×C₂₉	1	2	yes	—
457	#408	C₂²×C₂₉	1	2	yes	—
458	#408	C₂²×C₂₉	1	2	yes	—
459	#405	C₂²×C₂₉	1	1	yes	characteristic
460	#405	C₂²×C₂₉	1	1	yes	characteristic
461	#405	C₂²×C₂₉	1	2	yes	—
462	#405	C₂²×C₂₉	1	2	yes	—
463	#405	C₂²×C₂₉	1	2	yes	—
464	#405	C₂²×C₂₉	1	4	yes	—
465	#405	C₂²×C₂₉	1	4	yes	—
466	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
467	C₄×M₁₆	C₂²×C₂₉	1	2	yes	—
468	C₄×M₁₆	C₂²×C₂₉	1	2	yes	—
469	C₄×M₁₆	C₂²×C₂₉	1	4	yes	—
470	C₂×#97	C₂²×C₂₉	1	2	yes	—
471	C₂×#97	C₂²×C₂₉	1	4	yes	—
472	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
473	C₂×C₄×C₈	C₂²×C₂₉	1	2	yes	—
474	C₂×C₂₉	—	2	2	no	—
475	C₂×C₂₉	—	4	2	no	—
476	C₂×C₂₉	—	4	4	no	—
477	C₂×C₂₉	C₂×C₄×#41	1	1	yes	characteristic
478	C₂×C₂₉	C₂×#568	1	1	yes	characteristic
479	C₂×C₂₉	#3573	1	1	yes	characteristic
480	C₂×#41	C₂×C₄×C₂₉	1	2	yes	—
481	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
482	C₂×#41	C₂³×C₂₉	1	2	yes	—
483	C₂²×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
484	#131	—	2	4	no	—
485	#131	—	2	8	no	—
486	#131	—	2	4	no	—
487	#131	—	2	8	no	—
488	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
489	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
490	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
491	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
492	C₂×M₁₆	C₂³×C₂₉	1	4	yes	—
493	C₂×M₁₆	C₂³×C₂₉	1	4	yes	—
494	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
496	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
497	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
498	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
499	C₂²×C₈	C₂³×C₂₉	1	4	yes	—
500	C₂²×C₈	C₂³×C₂₉	1	4	yes	—
501	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
502	C₄⋊Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
503	C₄⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
504	#127	C₂×C₄×C₂₉	1	1	yes	characteristic
505	#127	C₂×C₄×C₂₉	1	2	yes	—
506	#126	C₂×C₄×C₂₉	1	4	yes	—
507	#126	C₂×C₄×C₂₉	1	4	yes	—
508	#126	C₂×C₄×C₂₉	1	4	yes	—
509	#125	C₂×C₄×C₂₉	1	2	yes	—
510	#125	C₂×C₄×C₂₉	1	4	yes	—
511	#124	C₂×C₄×C₂₉	1	2	yes	—
512	#124	C₂×C₄×C₂₉	1	4	yes	—
513	#124	C₂×C₄×C₂₉	1	2	yes	—
514	#124	C₂×C₄×C₂₉	1	2	yes	—
515	#124	C₂×C₄×C₂₉	1	2	yes	—
516	#123	C₂×C₄×C₂₉	1	4	yes	—
517	#123	C₂×C₄×C₂₉	1	4	yes	—
518	#123	C₂×C₄×C₂₉	1	4	yes	—
519	C₂²⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
520	C₂²⋊Q₈	C₂×C₄×C₂₉	1	4	yes	—
521	#121	C₂×C₄×C₂₉	1	2	yes	—
522	#121	C₂×C₄×C₂₉	1	4	yes	—
523	#121	C₂×C₄×C₂₉	1	2	yes	—
524	#121	C₂×C₄×C₂₉	1	4	yes	—
525	#121	C₂×C₄×C₂₉	1	2	yes	—
526	#121	C₂×C₄×C₂₉	1	4	yes	—
527	C₄×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
528	C₄×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
529	C₄×Q₈	C₂×C₄×C₂₉	1	2	yes	—
530	C₄×Q₈	C₂×C₄×C₂₉	1	2	yes	—
531	C₄×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
532	C₄×Q₈	C₂×C₄×C₂₉	1	2	yes	—
533	C₄×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
534	C₄×Q₈	C₂×C₄×C₂₉	1	2	yes	—
535	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
536	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
537	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
538	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
539	C₄×D₄	C₂×C₄×C₂₉	1	4	yes	—
540	C₄×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
541	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
542	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
543	C₄×D₄	C₂×C₄×C₂₉	1	4	yes	—
544	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
545	C₄×D₄	C₂×C₄×C₂₉	1	4	yes	—
546	C₄×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
547	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
548	C₄×D₄	C₂³×C₂₉	1	2	yes	—
549	C₄×D₄	C₂³×C₂₉	1	4	yes	—
550	C₄×D₄	C₂³×C₂₉	1	4	yes	—
551	C₄×D₄	C₂³×C₂₉	1	2	yes	—
552	#117	C₂×C₄×C₂₉	1	2	yes	—
553	#117	C₂×C₄×C₂₉	1	4	yes	—
554	#117	C₂³×C₂₉	1	1	yes	characteristic
555	#117	C₂³×C₂₉	1	2	yes	—
556	#117	C₂³×C₂₉	1	4	yes	—
557	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
559	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
561	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
562	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
563	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
564	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
565	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
566	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
567	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
568	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
569	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
570	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
571	C₄⋊C₈	C₂³×C₂₉	1	4	yes	—
572	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
573	C₄⋊C₈	C₂³×C₂₉	1	4	yes	—
574	C₂²⋊C₈	C₂³×C₂₉	1	4	yes	—
575	C₂²⋊C₈	C₂³×C₂₉	1	4	yes	—
576	C₂²⋊C₈	C₂³×C₂₉	1	4	yes	—
577	C₂²⋊C₈	C₂³×C₂₉	1	4	yes	—
578	C₂²⋊C₈	C₂³×C₂₉	1	4	yes	—
579	C₂²⋊C₈	C₂³×C₂₉	1	4	yes	—
580	#97	C₂³×C₂₉	1	2	yes	—
581	#97	C₂³×C₂₉	1	2	yes	—
582	#97	C₂³×C₂₉	1	2	yes	—
583	#97	C₂³×C₂₉	1	4	yes	—
584	#97	C₂³×C₂₉	1	4	yes	—
585	#97	C₂³×C₂₉	1	2	yes	—
586	#97	C₂³×C₂₉	1	2	yes	—
587	#97	C₂³×C₂₉	1	2	yes	—
588	#97	C₂³×C₂₉	1	2	yes	—
589	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
590	C₄×C₈	C₂³×C₂₉	1	2	yes	—
591	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
592	C₄×C₈	C₂³×C₂₉	1	2	yes	—
593	C₄×C₈	C₂³×C₂₉	1	2	yes	—
594	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
595	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
596	C₄×C₈	C₂³×C₂₉	1	4	yes	—
597	C₄×C₈	C₂³×C₂₉	1	4	yes	—
598	C₂₉	#60219	1	1	yes	characteristic, direct product factor, Sylow
599	#41	—	2	2	no	—
600	#41	—	2	4	no	—
601	#41	—	2	2	no	—
602	#41	—	2	4	no	—
603	#41	—	4	4	no	—
604	C₂×Q₈	—	4	2	no	—
605	C₂×Q₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
606	C₂×Q₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
607	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
608	C₂×Q₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
609	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
610	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
611	C₂×D₄	C₂²×C₄×C₂₉	1	4	yes	—
612	C₂×D₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
613	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
614	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
615	C₂×D₄	C₂²×C₄×C₂₉	1	4	yes	—
616	C₂×D₄	C₂²×C₄×C₂₉	1	4	yes	—
617	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
618	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
619	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
620	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
621	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
622	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
623	C₂²×C₄	C₂²×C₄×C₂₉	1	4	yes	—
624	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
625	C₂²×C₄	C₂²×C₄×C₂₉	1	4	yes	—
626	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
627	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
629	M₁₆	—	2	2	no	—
630	M₁₆	—	2	4	no	—
631	M₁₆	—	2	4	no	—
632	M₁₆	—	2	4	no	—
633	M₁₆	—	2	8	no	—
634	M₁₆	—	2	8	no	—
635	M₁₆	#41×C₂₉	1	4	yes	complemented
636	C₂×C₈	—	2	2	no	—
637	C₂×C₈	—	2	4	no	—
638	C₂×C₈	—	2	4	no	—
639	C₂×C₈	—	2	8	no	—
640	C₂×C₈	—	2	8	no	—
641	C₂×C₈	—	2	4	no	—
642	C₂×C₈	#41×C₂₉	1	4	yes	complemented
643	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
644	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
645	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
646	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
647	C₂×C₈	C₂⁴×C₂₉	1	4	yes	—
648	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
649	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
650	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
651	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
652	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
653	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
654	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
655	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
656	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
657	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
658	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
659	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
660	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
661	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
662	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
663	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
664	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
665	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
666	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
667	C₄⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
668	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
669	C₂²⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
670	C₂²⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
671	C₂²⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
672	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
673	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
674	C₂²⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
675	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
676	C₂²⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
677	C₂²⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
678	C₂²⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
679	C₂²⋊C₄	C₂²×C₄×C₂₉	1	4	yes	—
680	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
681	C₄²	C₂²×C₄×C₂₉	1	4	yes	—
682	C₄²	C₂²×C₄×C₂₉	1	4	yes	—
683	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
684	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
685	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
686	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
687	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
688	C₄²	C₂⁴×C₂₉	1	2	yes	—
689	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
690	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
691	C₄²	C₂⁴×C₂₉	1	2	yes	—
692	C₄²	C₂⁴×C₂₉	1	2	yes	—
693	C₂³	C₂³×C₄×C₂₉	1	2	yes	—
694	C₂³	C₂³×C₄×C₂₉	1	4	yes	—
695	C₂³	C₂³×C₄×C₂₉	1	1	yes	characteristic
696	Q₈	—	2	2	no	—
697	Q₈	—	2	4	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	2	2	no	—
700	Q₈	—	4	2	no	—
701	D₄	—	2	4	no	—
702	D₄	—	2	8	no	—
703	D₄	—	2	2	no	—
704	D₄	—	2	4	no	—
705	D₄	—	2	4	no	—
706	D₄	—	4	4	no	—
707	D₄	—	4	4	no	—
708	D₄	—	4	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	2	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	2	no	—
721	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
722	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
723	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
724	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
725	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
726	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
727	C₂×C₄	C₂³×C₄×C₂₉	1	4	yes	—
728	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
729	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
730	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
731	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
732	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
733	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
734	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
735	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
736	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
737	C₈	—	2	1	no	—
738	C₈	—	2	2	no	—
739	C₈	—	2	1	no	—
740	C₈	—	2	2	no	—
741	C₈	—	2	4	no	—
742	C₈	—	2	2	no	—
743	C₈	C₂×#41×C₂₉	1	2	yes	—
744	C₈	C₂×#41×C₂₉	1	4	yes	—
745	C₈	C₂×#41×C₂₉	1	2	yes	—
746	C₂²	—	2	1	no	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	2	4	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	4	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	4	no	—
754	C₂²	C₄×#41×C₂₉	1	2	yes	—
755	C₂²	C₂⁴×C₄×C₂₉	1	1	yes	characteristic
756	C₄	—	2	2	no	—
757	C₄	—	2	1	no	—
758	C₄	—	2	2	no	—
759	C₄	—	2	2	no	—
760	C₄	—	2	2	no	—
761	C₄	—	2	1	no	—
762	C₄	—	2	2	no	—
763	C₄	—	2	1	no	—
764	C₄	—	2	2	no	—
765	C₄	—	2	2	no	—
766	C₄	—	2	4	no	—
767	C₄	C₄×#41×C₂₉	1	2	yes	—
768	C₄	C₂₉×#568	1	2	yes	—
769	C₄	C₂²×#41×C₂₉	1	1	yes	characteristic
770	C₄	C₂²×#41×C₂₉	1	1	yes	characteristic
771	C₂	—	2	2	no	—
772	C₂	—	4	2	no	—
773	C₂	—	4	4	no	—
774	C₂	C₂×C₄×#41×C₂₉	1	1	yes	characteristic
775	C₂	C₂×C₂₉×#568	1	1	yes	characteristic
776	C₂	C₂₉×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
socle	C₂²×C₂₉	C₂⁴×C₄
prime radical	C₂₉×#3480	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#2970	C₂	semidirect
3. C₂₉×#2969	C₂	semidirect
4. C₂₉×#2968	C₂	semidirect
5. C₂₉×#2967	C₂	semidirect
6. C₂₉×#2966	C₂	semidirect
7. C₂₉×#2965	C₂	semidirect
8. Q₈×M₁₆×C₂₉	C₂	semidirect
9. C₂×C₂₉×#446	C₂	semidirect
10. C₂₉×#2935	C₂	semidirect
11. C₂₉×#2935	C₂	semidirect
12. C₂₉×#2932	C₂	semidirect
13. C₂₉×#2931	C₂	semidirect
14. C₂₉×#2925	C₂	semidirect
15. C₂₉×#2925	C₂	semidirect
16. C₂₉×#2875	C₂	semidirect
17. C₄×C₂₉×#131	C₂	semidirect
246. M₁₆×C₂₉	#41	semidirect
253. C₂×C₈×C₂₉	#41	semidirect
304. #60219	C₂₉	direct (N × H)
359. #2970	C₂×C₂₉	semidirect
360. #2969	C₂×C₂₉	semidirect
361. #2968	C₂×C₂₉	semidirect
362. #2967	C₂×C₂₉	semidirect
363. #2966	C₂×C₂₉	semidirect
364. #2965	C₂×C₂₉	semidirect
365. Q₈×M₁₆	C₂×C₂₉	semidirect
366. C₂×#446	C₂×C₂₉	semidirect
367. #2935	C₂×C₂₉	semidirect
368. #2935	C₂×C₂₉	semidirect
369. #2932	C₂×C₂₉	semidirect
370. #2931	C₂×C₂₉	semidirect
371. #2925	C₂×C₂₉	semidirect
372. #2925	C₂×C₂₉	semidirect
373. #2875	C₂×C₂₉	semidirect
374. C₄×#131	C₂×C₂₉	semidirect
598. C₂₉	#60219	direct (N × H)
635. M₁₆	#41×C₂₉	semidirect
642. C₂×C₈	#41×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#3480	2
C₂₉×#2970	2
C₂₉×#2969	2
C₂₉×#2968	2
C₂₉×#2967	2
C₂₉×#2966	2
C₂₉×#2965	2
Q₈×M₁₆×C₂₉	2
C₂×C₂₉×#446	2
C₂₉×#2935	2
C₂₉×#2932	2
C₂₉×#2931	2
C₂₉×#2925	2
C₂₉×#2875	2
C₄×C₂₉×#131	2
#60219	29

Subgroups — C29×#60219 #20355119

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#60219 #20355119