Subgroups — C₂₉×#60302 #20355202

Order 7424.

1716 conjugacy classes of subgroups.

The subgroup lattice has 1122 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×#2995	C₂	1	2	yes	maximal, complemented
3	C₂₉×#2994	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2992	C₂	1	2	yes	maximal, complemented
6	C₂₉×#2990	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2989	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2984	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#2983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#2981	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#2981	C₂	1	2	yes	maximal, complemented
12	C₂₉×#2980	C₂	1	2	yes	maximal, complemented
13	C₂₉×#2979	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#2970	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#2969	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#2968	C₂	1	2	yes	maximal, complemented
17	C₂₉×#2967	C₂	1	2	yes	maximal, complemented
18	C₂₉×#2966	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₉×#2965	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₉×#2925	C₂	1	2	yes	maximal, complemented
21	C₂₉×#2925	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₉×#2923	C₂	1	2	yes	maximal, complemented
23	C₂₉×#2922	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₉×#559	C₄	1	1	yes	characteristic
25	C₂₉×#559	C₄	1	2	yes	—
26	C₂₉×#557	C₄	1	1	yes	characteristic
27	C₂₉×#556	C₄	1	1	yes	characteristic
28	C₂₉×#556	C₄	1	2	yes	—
29	C₂₉×#553	C₄	1	1	yes	characteristic
30	C₂₉×#553	C₄	1	1	yes	characteristic
31	C₂₉×#553	C₄	1	2	yes	—
32	C₂₉×#553	C₄	1	2	yes	—
33	C₂₉×#550	C₄	1	1	yes	characteristic
34	C₂₉×#548	C₄	1	1	yes	characteristic
35	C₂₉×#548	C₄	1	1	yes	characteristic
36	C₂₉×#532	C₂²	1	1	yes	characteristic
37	C₂₉×#532	C₂²	1	2	yes	—
38	C₂₉×#529	C₂²	1	1	yes	characteristic
39	C₂₉×#529	C₂²	1	2	yes	—
40	C₂₉×#529	C₂²	1	2	yes	—
41	C₂₉×#529	C₂²	1	1	yes	characteristic
42	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
43	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
44	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
45	C₄×#41×C₂₉	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
47	C₂₉×#446	C₂²	1	1	yes	characteristic
48	C₂₉×#446	C₂²	1	1	yes	characteristic
49	C₂₉×#446	C₂²	1	1	yes	characteristic
50	C₂₉×#446	C₂²	1	2	yes	—
51	C₂₉×#446	C₂²	1	2	yes	—
52	C₂₉×#446	C₂²	1	2	yes	—
53	C₂₉×#446	C₂²	1	2	yes	—
54	C₂₉×#446	C₂²	1	1	yes	characteristic
55	C₂₉×#446	C₂²	1	1	yes	characteristic
56	C₂₉×#446	C₂²	1	1	yes	characteristic
57	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
58	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
59	C₂₉×#436	C₂²	1	1	yes	characteristic
60	C₂₉×#436	C₂²	1	1	yes	characteristic
61	C₂₉×#436	C₂²	1	1	yes	characteristic
62	C₂₉×#436	C₂²	1	2	yes	—
63	C₂₉×#436	C₂²	1	2	yes	—
64	C₂₉×#436	C₂²	1	1	yes	characteristic
65	C₂₉×#436	C₂²	1	2	yes	—
66	C₂₉×#435	C₂²	1	2	yes	—
67	C₂₉×#435	C₂²	1	2	yes	—
68	C₂₉×#435	C₂²	1	2	yes	—
69	C₂₉×#435	C₂²	1	2	yes	—
70	C₂₉×#435	C₂²	1	2	yes	—
71	C₂₉×#435	C₂²	1	2	yes	—
72	C₂₉×#435	C₂²	1	2	yes	—
73	C₂₉×#435	C₂²	1	2	yes	—
74	C₂₉×#435	C₂²	1	2	yes	—
75	C₂₉×#435	C₂²	1	2	yes	—
76	C₂₉×#435	C₂²	1	2	yes	—
77	C₂₉×#435	C₂²	1	2	yes	—
78	C₂₉×#435	C₂²	1	2	yes	—
79	C₂₉×#435	C₂²	1	2	yes	—
80	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
81	C₈×D₄×C₂₉	C₂²	1	2	yes	—
82	C₈×D₄×C₂₉	C₂²	1	2	yes	—
83	C₈×D₄×C₂₉	C₂²	1	2	yes	—
84	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
85	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
86	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
87	C₂₉×#433	C₂²	1	2	yes	—
88	C₂₉×#433	C₂²	1	1	yes	characteristic
89	C₂₉×#433	C₂²	1	1	yes	characteristic
90	C₂₉×#433	C₂²	1	2	yes	—
91	C₂₉×#433	C₂²	1	2	yes	—
92	C₂₉×#433	C₂²	1	2	yes	—
93	C₂₉×#433	C₂²	1	2	yes	—
94	C₂₉×#433	C₂²	1	1	yes	characteristic
95	C₂₉×#433	C₂²	1	1	yes	characteristic
96	C₂₉×#433	C₂²	1	2	yes	—
97	C₂₉×#432	C₂²	1	1	yes	characteristic
98	C₂₉×#432	C₂²	1	2	yes	—
99	C₂₉×#432	C₂²	1	2	yes	—
100	C₂₉×#432	C₂²	1	2	yes	—
101	C₂₉×#432	C₂²	1	2	yes	—
102	C₂₉×#432	C₂²	1	1	yes	characteristic
103	C₂₉×#432	C₂²	1	2	yes	—
104	C₂₉×#432	C₂²	1	2	yes	—
105	C₂₉×#431	C₂²	1	2	yes	—
106	C₂₉×#431	C₂²	1	1	yes	characteristic
107	C₂₉×#431	C₂²	1	1	yes	characteristic
108	C₂₉×#431	C₂²	1	1	yes	characteristic
109	C₂₉×#431	C₂²	1	1	yes	characteristic
110	C₂₉×#431	C₂²	1	2	yes	—
111	C₂₉×#431	C₂²	1	1	yes	characteristic
112	C₂₉×#431	C₂²	1	1	yes	characteristic
113	C₂₉×#424	C₂²	1	1	yes	characteristic
114	C₂₉×#424	C₂²	1	2	yes	—
115	C₂₉×#424	C₂²	1	2	yes	—
116	C₂₉×#424	C₂²	1	1	yes	characteristic
117	C₂₉×#423	C₂²	1	2	yes	—
118	C₂₉×#423	C₂²	1	1	yes	characteristic
119	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
120	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	—
121	C₂₉×#408	C₂²	1	2	yes	—
122	C₂₉×#408	C₂²	1	2	yes	—
123	C₂₉×#408	C₂²	1	1	yes	characteristic
124	C₂₉×#408	C₂²	1	2	yes	—
125	C₂₉×#408	C₂²	1	2	yes	—
126	C₂₉×#408	C₂²	1	1	yes	characteristic
127	C₂₉×#408	C₂²	1	2	yes	—
128	C₂₉×#405	C₂²	1	2	yes	—
129	C₂₉×#405	C₂²	1	2	yes	—
130	C₂₉×#405	C₂²	1	2	yes	—
131	C₄×M₁₆×C₂₉	C₂²	1	2	yes	—
132	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
133	C₂×C₂₉×#97	C₂²	1	2	yes	—
134	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
135	C₂×#41×C₂₉	C₂×C₄	1	1	yes	characteristic
136	C₂×#41×C₂₉	C₂×C₄	1	1	yes	characteristic
137	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
138	C₂×#41×C₂₉	C₂³	1	2	yes	—
139	C₂²×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
140	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
141	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
142	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
143	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
144	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
145	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
146	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
147	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
148	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
150	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
151	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
152	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
153	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
154	C₂₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
155	C₂₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
156	C₂₉×#127	C₂×C₄	1	1	yes	characteristic
157	C₂₉×#127	C₂×C₄	1	2	yes	—
158	C₂₉×#126	C₂×C₄	1	2	yes	—
159	C₂₉×#126	C₂×C₄	1	2	yes	—
160	C₂₉×#126	C₂×C₄	1	2	yes	—
161	C₂₉×#126	C₂×C₄	1	2	yes	—
162	C₂₉×#126	C₂×C₄	1	2	yes	—
163	C₂₉×#126	C₂×C₄	1	2	yes	—
164	C₂₉×#125	C₂×C₄	1	1	yes	characteristic
165	C₂₉×#125	C₂×C₄	1	2	yes	—
166	C₂₉×#125	C₂×C₄	1	2	yes	—
167	C₂₉×#125	C₂×C₄	1	1	yes	characteristic
168	C₂₉×#124	C₂×C₄	1	1	yes	characteristic
169	C₂₉×#124	C₂×C₄	1	1	yes	characteristic
170	C₂₉×#124	C₂×C₄	1	2	yes	—
171	C₂₉×#124	C₂×C₄	1	2	yes	—
172	C₂₉×#124	C₂×C₄	1	2	yes	—
173	C₂₉×#124	C₂×C₄	1	2	yes	—
174	C₂₉×#124	C₂×C₄	1	2	yes	—
175	C₂₉×#123	C₂×C₄	1	2	yes	—
176	C₂₉×#123	C₂×C₄	1	2	yes	—
177	C₂₉×#123	C₂×C₄	1	2	yes	—
178	C₂₉×#123	C₂×C₄	1	2	yes	—
179	C₂₉×#123	C₂×C₄	1	2	yes	—
180	C₂₉×#123	C₂×C₄	1	2	yes	—
181	C₂₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
182	C₂₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
183	C₂₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
184	C₂₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
185	C₂₉×#121	C₂×C₄	1	1	yes	characteristic
186	C₂₉×#121	C₂×C₄	1	1	yes	characteristic
187	C₂₉×#121	C₂×C₄	1	2	yes	—
188	C₂₉×#121	C₂×C₄	1	2	yes	—
189	C₂₉×#121	C₂×C₄	1	1	yes	characteristic
190	C₂₉×#121	C₂×C₄	1	1	yes	characteristic
191	C₂₉×#121	C₂×C₄	1	2	yes	—
192	C₂₉×#121	C₂×C₄	1	2	yes	—
193	C₂₉×#121	C₂×C₄	1	2	yes	—
194	C₂₉×#121	C₂×C₄	1	2	yes	—
195	C₂₉×#121	C₂×C₄	1	2	yes	—
196	C₄×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
197	C₄×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
198	C₄×Q₈×C₂₉	C₂×C₄	1	2	yes	—
199	C₄×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
200	C₄×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
201	C₄×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
202	C₄×Q₈×C₂₉	C₂×C₄	1	2	yes	—
203	C₄×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
204	C₄×Q₈×C₂₉	C₂×C₄	1	2	yes	—
205	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
206	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
207	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
208	C₄×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
209	C₄×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
210	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
211	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
212	C₄×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
213	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
214	C₄×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
215	C₄×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
216	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
217	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
218	C₄×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
219	C₄×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
220	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
221	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
222	C₄×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
223	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
224	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
226	C₄×D₄×C₂₉	C₂³	1	2	yes	—
227	C₄×D₄×C₂₉	C₂³	1	2	yes	—
228	C₄×D₄×C₂₉	C₂³	1	2	yes	—
229	C₄×D₄×C₂₉	C₂³	1	2	yes	—
230	C₄×D₄×C₂₉	C₂³	1	2	yes	—
231	C₂₉×#117	C₂×C₄	1	1	yes	characteristic
232	C₂₉×#117	C₂×C₄	1	1	yes	characteristic
233	C₂₉×#117	C₂×C₄	1	2	yes	—
234	C₂₉×#117	C₂×C₄	1	2	yes	—
235	C₂₉×#117	C₂³	1	1	yes	characteristic
236	C₂₉×#117	C₂³	1	2	yes	—
237	C₂₉×#117	C₂³	1	1	yes	characteristic
238	C₂₉×#117	C₂³	1	2	yes	—
239	C₂₉×#117	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
241	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
242	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
243	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
244	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
245	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
246	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
247	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
248	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
249	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
250	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
251	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
252	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
253	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
254	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
255	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
256	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
257	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
258	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
264	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
265	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
266	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
267	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
268	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
269	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
270	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
271	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
272	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
274	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
275	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
276	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
277	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
278	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
279	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
280	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
282	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
283	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
284	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
285	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
286	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
287	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
288	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
289	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
290	C₂₉×#97	C₂³	1	2	yes	—
291	C₂₉×#97	C₂³	1	1	yes	characteristic
292	C₂₉×#97	C₂³	1	2	yes	—
293	C₂₉×#97	C₂³	1	2	yes	—
294	C₂₉×#97	C₂³	1	2	yes	—
295	C₂₉×#97	C₂³	1	2	yes	—
296	C₂₉×#97	C₂³	1	2	yes	—
297	C₂₉×#97	C₂³	1	2	yes	—
298	C₂₉×#97	C₂³	1	2	yes	—
299	C₂₉×#97	C₂³	1	1	yes	characteristic
300	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
301	C₄×C₈×C₂₉	C₂³	1	2	yes	—
302	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
303	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
304	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
305	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
306	C₄×C₈×C₂₉	C₂³	1	2	yes	—
307	C₄×C₈×C₂₉	C₂³	1	2	yes	—
308	C₄×C₈×C₂₉	C₂³	1	2	yes	—
309	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
310	#41×C₂₉	—	4	1	no	—
311	#41×C₂₉	—	4	2	no	—
312	#41×C₂₉	—	4	1	no	—
313	#41×C₂₉	—	4	2	no	—
314	#41×C₂₉	—	4	2	no	—
315	#41×C₂₉	—	4	2	no	—
316	C₂×Q₈×C₂₉	—	4	2	no	—
317	C₂×Q₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
318	C₂×Q₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
319	C₂×Q₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
320	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
321	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
322	C₂×D₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
323	C₂×D₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
324	C₂×D₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
325	C₂×D₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
326	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
327	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
328	C₂×D₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
329	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
330	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
331	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
332	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
333	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
334	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
335	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
336	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
337	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
338	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
339	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
340	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
341	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
342	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
343	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
344	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
345	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
346	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
347	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
350	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
352	M₁₆×C₂₉	—	4	1	no	—
353	M₁₆×C₂₉	—	4	2	no	—
354	M₁₆×C₂₉	—	4	2	no	—
355	M₁₆×C₂₉	—	4	1	no	—
356	M₁₆×C₂₉	—	4	2	no	—
357	M₁₆×C₂₉	—	4	2	no	—
358	M₁₆×C₂₉	—	4	2	no	—
359	C₂×C₈×C₂₉	—	4	2	no	—
360	C₂×C₈×C₂₉	—	4	1	no	—
361	C₂×C₈×C₂₉	—	4	2	no	—
362	C₂×C₈×C₂₉	—	4	2	no	—
363	C₂×C₈×C₂₉	—	4	2	no	—
364	C₂×C₈×C₂₉	—	4	2	no	—
365	C₂×C₈×C₂₉	—	4	1	no	—
366	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
368	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
371	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
374	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
375	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
379	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
380	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
381	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
382	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
383	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
384	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
385	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
386	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
387	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
388	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
389	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
390	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
391	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
392	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
393	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
394	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
395	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
396	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
397	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
398	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
399	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
400	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
401	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
402	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
403	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
404	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
405	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
406	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
407	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
408	C₂²⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
409	C₂²⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
410	C₂²⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
411	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
412	C₂²⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
413	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
414	C₂²⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
415	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
416	C₂²⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
417	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
418	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
419	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
420	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
421	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
422	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
423	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
424	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
425	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
426	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
427	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
428	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
429	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
430	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
431	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
432	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
433	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
434	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
435	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
436	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
437	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
438	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
439	C₄²×C₂₉	C₂⁴	1	2	yes	—
440	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
441	C₄²×C₂₉	C₂⁴	1	2	yes	—
442	#60302	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
443	C₂³×C₂₉	C₂³×C₄	1	1	yes	characteristic
444	C₂³×C₂₉	C₂³×C₄	1	1	yes	characteristic
445	C₂³×C₂₉	C₂³×C₄	1	2	yes	—
446	C₂³×C₂₉	C₂³×C₄	1	2	yes	—
447	C₂³×C₂₉	C₂³×C₄	1	1	yes	characteristic
448	Q₈×C₂₉	—	2	2	no	—
449	Q₈×C₂₉	—	2	2	no	—
450	Q₈×C₂₉	—	4	2	no	—
451	Q₈×C₂₉	—	4	1	no	—
452	Q₈×C₂₉	—	4	2	no	—
453	D₄×C₂₉	—	2	2	no	—
454	D₄×C₂₉	—	2	2	no	—
455	D₄×C₂₉	—	4	2	no	—
456	D₄×C₂₉	—	4	2	no	—
457	D₄×C₂₉	—	4	2	no	—
458	D₄×C₂₉	—	4	1	no	—
459	D₄×C₂₉	—	4	2	no	—
460	D₄×C₂₉	—	4	1	no	—
461	D₄×C₂₉	—	4	2	no	—
462	D₄×C₂₉	—	4	1	no	—
463	D₄×C₂₉	—	4	2	no	—
464	D₄×C₂₉	—	4	2	no	—
465	D₄×C₂₉	—	4	2	no	—
466	C₂×C₄×C₂₉	—	2	2	no	—
467	C₂×C₄×C₂₉	—	2	2	no	—
468	C₂×C₄×C₂₉	—	2	2	no	—
469	C₂×C₄×C₂₉	—	2	2	no	—
470	C₂×C₄×C₂₉	—	2	1	no	—
471	C₂×C₄×C₂₉	—	2	1	no	—
472	C₂×C₄×C₂₉	—	2	2	no	—
473	C₂×C₄×C₂₉	—	2	2	no	—
474	C₂×C₄×C₂₉	—	2	1	no	—
475	C₂×C₄×C₂₉	—	2	1	no	—
476	C₂×C₄×C₂₉	—	2	2	no	—
477	C₂×C₄×C₂₉	—	2	1	no	—
478	C₂×C₄×C₂₉	—	2	1	no	—
479	C₂×C₄×C₂₉	—	4	1	no	—
480	C₂×C₄×C₂₉	—	4	1	no	—
481	C₂×C₄×C₂₉	—	4	2	no	—
482	C₂×C₄×C₂₉	—	4	2	no	—
483	C₂×C₄×C₂₉	—	4	1	no	—
484	C₂×C₄×C₂₉	—	4	2	no	—
485	C₂×C₄×C₂₉	—	4	2	no	—
486	C₂×C₄×C₂₉	—	4	2	no	—
487	C₂×C₄×C₂₉	—	4	2	no	—
488	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
489	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
490	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
491	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
492	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
493	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
494	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
495	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
496	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
497	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
498	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
499	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
500	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
501	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
502	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
503	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
504	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
505	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
506	C₈×C₂₉	—	2	1	no	—
507	C₈×C₂₉	—	2	2	no	—
508	C₈×C₂₉	—	2	1	no	—
509	C₈×C₂₉	—	2	1	no	—
510	C₈×C₂₉	—	2	1	no	—
511	C₈×C₂₉	—	2	2	no	—
512	C₈×C₂₉	—	2	1	no	—
513	C₈×C₂₉	—	2	2	no	—
514	C₈×C₂₉	—	2	2	no	—
515	C₈×C₂₉	—	2	1	no	—
516	C₈×C₂₉	—	2	1	no	—
517	C₈×C₂₉	—	2	1	no	—
518	#3480	C₂×C₂₉	1	1	yes	characteristic
519	#2995	C₂×C₂₉	1	2	yes	complemented
520	#2994	C₂×C₂₉	1	1	yes	characteristic, complemented
521	#2993	C₂×C₂₉	1	1	yes	characteristic, complemented
522	#2992	C₂×C₂₉	1	2	yes	complemented
523	#2990	C₂×C₂₉	1	1	yes	characteristic, complemented
524	#2989	C₂×C₂₉	1	1	yes	characteristic, complemented
525	#2984	C₂×C₂₉	1	1	yes	characteristic, complemented
526	#2983	C₂×C₂₉	1	1	yes	characteristic, complemented
527	#2981	C₂×C₂₉	1	1	yes	characteristic, complemented
528	#2981	C₂×C₂₉	1	2	yes	complemented
529	#2980	C₂×C₂₉	1	2	yes	complemented
530	#2979	C₂×C₂₉	1	1	yes	characteristic, complemented
531	#2970	C₂×C₂₉	1	1	yes	characteristic, complemented
532	#2969	C₂×C₂₉	1	1	yes	characteristic, complemented
533	#2968	C₂×C₂₉	1	2	yes	complemented
534	#2967	C₂×C₂₉	1	2	yes	complemented
535	#2966	C₂×C₂₉	1	1	yes	characteristic, complemented
536	#2965	C₂×C₂₉	1	1	yes	characteristic, complemented
537	#2925	C₂×C₂₉	1	1	yes	characteristic, complemented
538	#2925	C₂×C₂₉	1	2	yes	complemented
539	#2923	C₂×C₂₉	1	2	yes	complemented
540	#2922	C₂×C₂₉	1	1	yes	characteristic, complemented
541	C₂²×C₂₉	—	2	1	no	—
542	C₂²×C₂₉	—	2	1	no	—
543	C₂²×C₂₉	—	2	2	no	—
544	C₂²×C₂₉	—	2	1	no	—
545	C₂²×C₂₉	—	2	2	no	—
546	C₂²×C₂₉	—	2	1	no	—
547	C₂²×C₂₉	—	2	1	no	—
548	C₂²×C₂₉	—	2	1	no	—
549	C₂²×C₂₉	—	2	2	no	—
550	C₂²×C₂₉	—	2	2	no	—
551	C₂²×C₂₉	—	2	1	no	—
552	C₂²×C₂₉	—	2	1	no	—
553	C₂²×C₂₉	—	2	1	no	—
554	C₂²×C₂₉	—	2	2	no	—
555	C₂²×C₂₉	—	2	2	no	—
556	C₂²×C₂₉	C₂⁴×C₄	1	1	yes	characteristic
557	C₄×C₂₉	—	2	1	no	—
558	C₄×C₂₉	—	2	2	no	—
559	C₄×C₂₉	—	2	1	no	—
560	C₄×C₂₉	—	2	1	no	—
561	C₄×C₂₉	—	2	2	no	—
562	C₄×C₂₉	—	2	1	no	—
563	C₄×C₂₉	—	2	1	no	—
564	C₄×C₂₉	—	2	1	no	—
565	C₄×C₂₉	—	2	2	no	—
566	C₄×C₂₉	—	2	2	no	—
567	C₄×C₂₉	—	2	1	no	—
568	C₄×C₂₉	—	2	1	no	—
569	C₄×C₂₉	—	2	1	no	—
570	C₄×C₂₉	—	2	2	no	—
571	C₄×C₂₉	—	2	1	no	—
572	C₄×C₂₉	—	2	2	no	—
573	C₄×C₂₉	#568	1	2	yes	—
574	C₄×C₂₉	#585	1	1	yes	characteristic
575	C₄×C₂₉	#585	1	1	yes	characteristic
576	#559	C₄×C₂₉	1	1	yes	characteristic
577	#559	C₄×C₂₉	1	2	yes	—
578	#557	C₄×C₂₉	1	1	yes	characteristic
579	#556	C₄×C₂₉	1	1	yes	characteristic
580	#556	C₄×C₂₉	1	2	yes	—
581	#553	C₄×C₂₉	1	1	yes	characteristic
582	#553	C₄×C₂₉	1	1	yes	characteristic
583	#553	C₄×C₂₉	1	2	yes	—
584	#553	C₄×C₂₉	1	2	yes	—
585	#550	C₄×C₂₉	1	1	yes	characteristic
586	#548	C₄×C₂₉	1	1	yes	characteristic
587	#548	C₄×C₂₉	1	1	yes	characteristic
588	#532	C₂²×C₂₉	1	1	yes	characteristic
589	#532	C₂²×C₂₉	1	2	yes	—
590	#529	C₂²×C₂₉	1	1	yes	characteristic
591	#529	C₂²×C₂₉	1	2	yes	—
592	#529	C₂²×C₂₉	1	2	yes	—
593	#529	C₂²×C₂₉	1	1	yes	characteristic
594	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
595	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
596	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
597	C₄×#41	C₂²×C₂₉	1	2	yes	—
598	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
599	#446	C₂²×C₂₉	1	1	yes	characteristic
600	#446	C₂²×C₂₉	1	1	yes	characteristic
601	#446	C₂²×C₂₉	1	1	yes	characteristic
602	#446	C₂²×C₂₉	1	2	yes	—
603	#446	C₂²×C₂₉	1	2	yes	—
604	#446	C₂²×C₂₉	1	2	yes	—
605	#446	C₂²×C₂₉	1	2	yes	—
606	#446	C₂²×C₂₉	1	1	yes	characteristic
607	#446	C₂²×C₂₉	1	1	yes	characteristic
608	#446	C₂²×C₂₉	1	1	yes	characteristic
609	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
610	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
611	#436	C₂²×C₂₉	1	1	yes	characteristic
612	#436	C₂²×C₂₉	1	1	yes	characteristic
613	#436	C₂²×C₂₉	1	1	yes	characteristic
614	#436	C₂²×C₂₉	1	2	yes	—
615	#436	C₂²×C₂₉	1	2	yes	—
616	#436	C₂²×C₂₉	1	1	yes	characteristic
617	#436	C₂²×C₂₉	1	2	yes	—
618	#435	C₂²×C₂₉	1	2	yes	—
619	#435	C₂²×C₂₉	1	2	yes	—
620	#435	C₂²×C₂₉	1	2	yes	—
621	#435	C₂²×C₂₉	1	2	yes	—
622	#435	C₂²×C₂₉	1	2	yes	—
623	#435	C₂²×C₂₉	1	2	yes	—
624	#435	C₂²×C₂₉	1	2	yes	—
625	#435	C₂²×C₂₉	1	2	yes	—
626	#435	C₂²×C₂₉	1	2	yes	—
627	#435	C₂²×C₂₉	1	2	yes	—
628	#435	C₂²×C₂₉	1	2	yes	—
629	#435	C₂²×C₂₉	1	2	yes	—
630	#435	C₂²×C₂₉	1	2	yes	—
631	#435	C₂²×C₂₉	1	2	yes	—
632	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
633	C₈×D₄	C₂²×C₂₉	1	2	yes	—
634	C₈×D₄	C₂²×C₂₉	1	2	yes	—
635	C₈×D₄	C₂²×C₂₉	1	2	yes	—
636	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
637	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
638	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
639	#433	C₂²×C₂₉	1	1	yes	characteristic
640	#433	C₂²×C₂₉	1	1	yes	characteristic
641	#433	C₂²×C₂₉	1	1	yes	characteristic
642	#433	C₂²×C₂₉	1	1	yes	characteristic
643	#433	C₂²×C₂₉	1	2	yes	—
644	#433	C₂²×C₂₉	1	2	yes	—
645	#433	C₂²×C₂₉	1	2	yes	—
646	#433	C₂²×C₂₉	1	2	yes	—
647	#433	C₂²×C₂₉	1	2	yes	—
648	#433	C₂²×C₂₉	1	2	yes	—
649	#432	C₂²×C₂₉	1	2	yes	—
650	#432	C₂²×C₂₉	1	2	yes	—
651	#432	C₂²×C₂₉	1	2	yes	—
652	#432	C₂²×C₂₉	1	2	yes	—
653	#432	C₂²×C₂₉	1	1	yes	characteristic
654	#432	C₂²×C₂₉	1	2	yes	—
655	#432	C₂²×C₂₉	1	2	yes	—
656	#432	C₂²×C₂₉	1	1	yes	characteristic
657	#431	C₂²×C₂₉	1	1	yes	characteristic
658	#431	C₂²×C₂₉	1	1	yes	characteristic
659	#431	C₂²×C₂₉	1	1	yes	characteristic
660	#431	C₂²×C₂₉	1	1	yes	characteristic
661	#431	C₂²×C₂₉	1	2	yes	—
662	#431	C₂²×C₂₉	1	1	yes	characteristic
663	#431	C₂²×C₂₉	1	1	yes	characteristic
664	#431	C₂²×C₂₉	1	2	yes	—
665	#424	C₂²×C₂₉	1	1	yes	characteristic
666	#424	C₂²×C₂₉	1	1	yes	characteristic
667	#424	C₂²×C₂₉	1	2	yes	—
668	#424	C₂²×C₂₉	1	2	yes	—
669	#423	C₂²×C₂₉	1	2	yes	—
670	#423	C₂²×C₂₉	1	1	yes	characteristic
671	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
672	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	—
673	#408	C₂²×C₂₉	1	1	yes	characteristic
674	#408	C₂²×C₂₉	1	1	yes	characteristic
675	#408	C₂²×C₂₉	1	2	yes	—
676	#408	C₂²×C₂₉	1	2	yes	—
677	#408	C₂²×C₂₉	1	2	yes	—
678	#408	C₂²×C₂₉	1	2	yes	—
679	#408	C₂²×C₂₉	1	2	yes	—
680	#405	C₂²×C₂₉	1	2	yes	—
681	#405	C₂²×C₂₉	1	2	yes	—
682	#405	C₂²×C₂₉	1	2	yes	—
683	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
684	C₄×M₁₆	C₂²×C₂₉	1	2	yes	—
685	C₂×#97	C₂²×C₂₉	1	2	yes	—
686	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
687	C₂×C₂₉	—	4	1	no	—
688	C₂×C₂₉	—	4	1	no	—
689	C₂×C₂₉	—	4	1	no	—
690	C₂×C₂₉	—	4	2	no	—
691	C₂×C₂₉	—	4	2	no	—
692	C₂×C₂₉	#3428	1	1	yes	characteristic
693	C₂×C₂₉	C₂×#568	1	1	yes	characteristic
694	C₂×C₂₉	#3573	1	1	yes	characteristic
695	C₂×#41	C₂×C₄×C₂₉	1	1	yes	characteristic
696	C₂×#41	C₂×C₄×C₂₉	1	1	yes	characteristic
697	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
698	C₂×#41	C₂³×C₂₉	1	2	yes	—
699	C₂²×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
700	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
701	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
702	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
703	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
704	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
705	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
706	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
707	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
708	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
709	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
710	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
711	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
712	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
713	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
714	C₄⋊Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
715	C₄⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
716	#127	C₂×C₄×C₂₉	1	1	yes	characteristic
717	#127	C₂×C₄×C₂₉	1	2	yes	—
718	#126	C₂×C₄×C₂₉	1	2	yes	—
719	#126	C₂×C₄×C₂₉	1	2	yes	—
720	#126	C₂×C₄×C₂₉	1	2	yes	—
721	#126	C₂×C₄×C₂₉	1	2	yes	—
722	#126	C₂×C₄×C₂₉	1	2	yes	—
723	#126	C₂×C₄×C₂₉	1	2	yes	—
724	#125	C₂×C₄×C₂₉	1	1	yes	characteristic
725	#125	C₂×C₄×C₂₉	1	2	yes	—
726	#125	C₂×C₄×C₂₉	1	2	yes	—
727	#125	C₂×C₄×C₂₉	1	1	yes	characteristic
728	#124	C₂×C₄×C₂₉	1	1	yes	characteristic
729	#124	C₂×C₄×C₂₉	1	1	yes	characteristic
730	#124	C₂×C₄×C₂₉	1	2	yes	—
731	#124	C₂×C₄×C₂₉	1	2	yes	—
732	#124	C₂×C₄×C₂₉	1	2	yes	—
733	#124	C₂×C₄×C₂₉	1	2	yes	—
734	#124	C₂×C₄×C₂₉	1	2	yes	—
735	#123	C₂×C₄×C₂₉	1	2	yes	—
736	#123	C₂×C₄×C₂₉	1	2	yes	—
737	#123	C₂×C₄×C₂₉	1	2	yes	—
738	#123	C₂×C₄×C₂₉	1	2	yes	—
739	#123	C₂×C₄×C₂₉	1	2	yes	—
740	#123	C₂×C₄×C₂₉	1	2	yes	—
741	C₂²⋊Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
742	C₂²⋊Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
743	C₂²⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
744	C₂²⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
745	#121	C₂×C₄×C₂₉	1	1	yes	characteristic
746	#121	C₂×C₄×C₂₉	1	1	yes	characteristic
747	#121	C₂×C₄×C₂₉	1	2	yes	—
748	#121	C₂×C₄×C₂₉	1	2	yes	—
749	#121	C₂×C₄×C₂₉	1	1	yes	characteristic
750	#121	C₂×C₄×C₂₉	1	1	yes	characteristic
751	#121	C₂×C₄×C₂₉	1	2	yes	—
752	#121	C₂×C₄×C₂₉	1	2	yes	—
753	#121	C₂×C₄×C₂₉	1	2	yes	—
754	#121	C₂×C₄×C₂₉	1	2	yes	—
755	#121	C₂×C₄×C₂₉	1	2	yes	—
756	C₄×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
757	C₄×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
758	C₄×Q₈	C₂×C₄×C₂₉	1	2	yes	—
759	C₄×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
760	C₄×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
761	C₄×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
762	C₄×Q₈	C₂×C₄×C₂₉	1	2	yes	—
763	C₄×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
764	C₄×Q₈	C₂×C₄×C₂₉	1	2	yes	—
765	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
766	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
767	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
768	C₄×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
769	C₄×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
770	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
771	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
772	C₄×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
773	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
774	C₄×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
775	C₄×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
776	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
777	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
778	C₄×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
779	C₄×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
780	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
781	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
782	C₄×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
783	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
784	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
785	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
786	C₄×D₄	C₂³×C₂₉	1	2	yes	—
787	C₄×D₄	C₂³×C₂₉	1	2	yes	—
788	C₄×D₄	C₂³×C₂₉	1	2	yes	—
789	C₄×D₄	C₂³×C₂₉	1	2	yes	—
790	C₄×D₄	C₂³×C₂₉	1	2	yes	—
791	#117	C₂×C₄×C₂₉	1	1	yes	characteristic
792	#117	C₂×C₄×C₂₉	1	1	yes	characteristic
793	#117	C₂×C₄×C₂₉	1	2	yes	—
794	#117	C₂×C₄×C₂₉	1	2	yes	—
795	#117	C₂³×C₂₉	1	1	yes	characteristic
796	#117	C₂³×C₂₉	1	1	yes	characteristic
797	#117	C₂³×C₂₉	1	2	yes	—
798	#117	C₂³×C₂₉	1	1	yes	characteristic
799	#117	C₂³×C₂₉	1	2	yes	—
800	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
801	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
802	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
803	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
804	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
805	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
806	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
807	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
808	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
809	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
810	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
811	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
812	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
813	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
814	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
815	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
816	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
817	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
818	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
819	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
820	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
821	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
822	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
823	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
824	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
825	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
826	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
827	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
828	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
829	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
830	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
831	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
832	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
833	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
834	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
835	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
836	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
837	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
838	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
839	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
840	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
841	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
842	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
843	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
844	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
845	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
846	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
847	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
848	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
849	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
850	#97	C₂³×C₂₉	1	1	yes	characteristic
851	#97	C₂³×C₂₉	1	2	yes	—
852	#97	C₂³×C₂₉	1	2	yes	—
853	#97	C₂³×C₂₉	1	2	yes	—
854	#97	C₂³×C₂₉	1	1	yes	characteristic
855	#97	C₂³×C₂₉	1	2	yes	—
856	#97	C₂³×C₂₉	1	2	yes	—
857	#97	C₂³×C₂₉	1	2	yes	—
858	#97	C₂³×C₂₉	1	2	yes	—
859	#97	C₂³×C₂₉	1	2	yes	—
860	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
861	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
862	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
863	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
864	C₄×C₈	C₂³×C₂₉	1	2	yes	—
865	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
866	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
867	C₄×C₈	C₂³×C₂₉	1	2	yes	—
868	C₄×C₈	C₂³×C₂₉	1	2	yes	—
869	C₄×C₈	C₂³×C₂₉	1	2	yes	—
870	C₂₉	#60302	1	1	yes	characteristic, direct product factor, Sylow
871	#41	—	4	1	no	—
872	#41	—	4	2	no	—
873	#41	—	4	1	no	—
874	#41	—	4	2	no	—
875	#41	—	4	2	no	—
876	#41	—	4	2	no	—
877	C₂×Q₈	—	4	2	no	—
878	C₂×Q₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
879	C₂×Q₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
880	C₂×Q₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
881	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
882	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
883	C₂×D₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
884	C₂×D₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
885	C₂×D₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
886	C₂×D₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
887	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
888	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
889	C₂×D₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
890	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
891	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
892	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
893	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
894	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
895	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
896	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
897	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
898	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
899	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
900	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
901	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
902	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
903	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
904	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
905	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
906	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
907	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
908	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
909	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
911	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
912	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
913	M₁₆	—	4	1	no	—
914	M₁₆	—	4	2	no	—
915	M₁₆	—	4	2	no	—
916	M₁₆	—	4	1	no	—
917	M₁₆	—	4	2	no	—
918	M₁₆	—	4	2	no	—
919	M₁₆	—	4	2	no	—
920	C₂×C₈	—	4	2	no	—
921	C₂×C₈	—	4	1	no	—
922	C₂×C₈	—	4	2	no	—
923	C₂×C₈	—	4	2	no	—
924	C₂×C₈	—	4	2	no	—
925	C₂×C₈	—	4	2	no	—
926	C₂×C₈	—	4	1	no	—
927	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
928	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
929	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
930	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
933	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
934	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
936	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
937	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
938	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
939	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
940	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
941	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
942	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
943	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
944	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
945	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
946	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
947	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
948	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
949	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
950	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
951	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
952	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
953	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
954	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
955	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
956	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
957	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
958	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
959	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
960	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
961	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
962	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
963	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
964	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
965	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
966	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
967	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
968	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
969	C₂²⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
970	C₂²⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
971	C₂²⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
972	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
973	C₂²⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
974	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
975	C₂²⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
976	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
977	C₂²⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
978	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
979	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
980	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
981	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
982	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
983	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
984	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
985	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
986	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
987	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
988	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
989	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
990	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
991	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
992	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
993	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
994	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
995	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
996	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
997	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
998	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
999	C₄²	C₂⁴×C₂₉	1	2	yes	—
1000	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1001	C₄²	C₂⁴×C₂₉	1	2	yes	—
1002	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1003	C₂³	C₂³×C₄×C₂₉	1	1	yes	characteristic
1004	C₂³	C₂³×C₄×C₂₉	1	1	yes	characteristic
1005	C₂³	C₂³×C₄×C₂₉	1	2	yes	—
1006	C₂³	C₂³×C₄×C₂₉	1	2	yes	—
1007	C₂³	C₂³×C₄×C₂₉	1	1	yes	characteristic
1008	Q₈	—	2	2	no	—
1009	Q₈	—	2	2	no	—
1010	Q₈	—	4	2	no	—
1011	Q₈	—	4	1	no	—
1012	Q₈	—	4	2	no	—
1013	D₄	—	2	2	no	—
1014	D₄	—	2	2	no	—
1015	D₄	—	4	2	no	—
1016	D₄	—	4	2	no	—
1017	D₄	—	4	1	no	—
1018	D₄	—	4	2	no	—
1019	D₄	—	4	1	no	—
1020	D₄	—	4	2	no	—
1021	D₄	—	4	1	no	—
1022	D₄	—	4	2	no	—
1023	D₄	—	4	2	no	—
1024	D₄	—	4	2	no	—
1025	D₄	—	4	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	4	2	no	—
1040	C₂×C₄	—	4	2	no	—
1041	C₂×C₄	—	4	2	no	—
1042	C₂×C₄	—	4	1	no	—
1043	C₂×C₄	—	4	2	no	—
1044	C₂×C₄	—	4	1	no	—
1045	C₂×C₄	—	4	2	no	—
1046	C₂×C₄	—	4	1	no	—
1047	C₂×C₄	—	4	2	no	—
1048	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
1049	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
1050	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
1051	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
1052	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
1053	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
1054	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
1055	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
1056	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
1057	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
1058	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
1059	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
1060	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
1061	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
1062	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
1063	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
1064	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
1065	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1066	C₈	—	2	1	no	—
1067	C₈	—	2	2	no	—
1068	C₈	—	2	1	no	—
1069	C₈	—	2	1	no	—
1070	C₈	—	2	1	no	—
1071	C₈	—	2	2	no	—
1072	C₈	—	2	1	no	—
1073	C₈	—	2	2	no	—
1074	C₈	—	2	2	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	1	no	—
1077	C₈	—	2	1	no	—
1078	C₂²	—	2	1	no	—
1079	C₂²	—	2	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	C₂⁴×C₄×C₂₉	1	1	yes	characteristic
1094	C₄	—	2	1	no	—
1095	C₄	—	2	1	no	—
1096	C₄	—	2	1	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	2	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	2	2	no	—
1110	C₄	C₂₉×#568	1	2	yes	—
1111	C₄	C₂₉×#585	1	1	yes	characteristic
1112	C₄	C₂₉×#585	1	1	yes	characteristic
1113	C₂	—	4	1	no	—
1114	C₂	—	4	1	no	—
1115	C₂	—	4	1	no	—
1116	C₂	—	4	2	no	—
1117	C₂	—	4	2	no	—
1118	C₂	C₂₉×#3428	1	1	yes	characteristic
1119	C₂	C₂×C₂₉×#568	1	1	yes	characteristic
1120	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×#2995	C₂	semidirect
3. C₂₉×#2994	C₂	semidirect
4. C₂₉×#2993	C₂	semidirect
5. C₂₉×#2992	C₂	semidirect
6. C₂₉×#2990	C₂	semidirect
7. C₂₉×#2989	C₂	semidirect
8. C₂₉×#2984	C₂	semidirect
9. C₂₉×#2983	C₂	semidirect
10. C₂₉×#2981	C₂	semidirect
11. C₂₉×#2981	C₂	semidirect
12. C₂₉×#2980	C₂	semidirect
13. C₂₉×#2979	C₂	semidirect
14. C₂₉×#2970	C₂	semidirect
15. C₂₉×#2969	C₂	semidirect
16. C₂₉×#2968	C₂	semidirect
17. C₂₉×#2967	C₂	semidirect
18. C₂₉×#2966	C₂	semidirect
19. C₂₉×#2965	C₂	semidirect
20. C₂₉×#2925	C₂	semidirect
21. C₂₉×#2925	C₂	semidirect
22. C₂₉×#2923	C₂	semidirect
23. C₂₉×#2922	C₂	semidirect
442. #60302	C₂₉	direct (N × H)
519. #2995	C₂×C₂₉	semidirect
520. #2994	C₂×C₂₉	semidirect
521. #2993	C₂×C₂₉	semidirect
522. #2992	C₂×C₂₉	semidirect
523. #2990	C₂×C₂₉	semidirect
524. #2989	C₂×C₂₉	semidirect
525. #2984	C₂×C₂₉	semidirect
526. #2983	C₂×C₂₉	semidirect
527. #2981	C₂×C₂₉	semidirect
528. #2981	C₂×C₂₉	semidirect
529. #2980	C₂×C₂₉	semidirect
530. #2979	C₂×C₂₉	semidirect
531. #2970	C₂×C₂₉	semidirect
532. #2969	C₂×C₂₉	semidirect
533. #2968	C₂×C₂₉	semidirect
534. #2967	C₂×C₂₉	semidirect
535. #2966	C₂×C₂₉	semidirect
536. #2965	C₂×C₂₉	semidirect
537. #2925	C₂×C₂₉	semidirect
538. #2925	C₂×C₂₉	semidirect
539. #2923	C₂×C₂₉	semidirect
540. #2922	C₂×C₂₉	semidirect
870. C₂₉	#60302	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×#3480	2
C₂₉×#2995	2
C₂₉×#2994	2
C₂₉×#2993	2
C₂₉×#2992	2
C₂₉×#2990	2
C₂₉×#2989	2
C₂₉×#2984	2
C₂₉×#2983	2
C₂₉×#2981	2
C₂₉×#2980	2
C₂₉×#2979	2
C₂₉×#2970	2
C₂₉×#2969	2
C₂₉×#2968	2
C₂₉×#2967	2
C₂₉×#2966	2
C₂₉×#2965	2
C₂₉×#2925	2
C₂₉×#2923	2
C₂₉×#2922	2
#60302	29

Subgroups — C29×#60302 #20355202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#60302 #20355202