Subgroups — C₂₉×#60314 #20355214

Order 7424.

1900 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3481	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2995	C₂	1	2	yes	maximal, complemented
3	C₂₉×#2992	C₂	1	2	yes	maximal, complemented
4	C₂₉×#2989	C₂	1	2	yes	maximal, complemented
5	C₂₉×#2980	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2978	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2977	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2976	C₂	1	2	yes	maximal, complemented
9	C₂₉×#2974	C₂	1	2	yes	maximal, complemented
10	C₂₉×#2973	C₂	1	2	yes	maximal, complemented
11	C₂₉×#2970	C₂	1	2	yes	maximal, complemented
12	C₂₉×#2968	C₂	1	2	yes	maximal, complemented
13	C₂₉×#2967	C₂	1	2	yes	maximal, complemented
14	D₄×M₁₆×C₂₉	C₂	1	2	yes	maximal, complemented
15	C₂₉×#2933	C₂	1	2	yes	maximal, complemented
16	C₂₉×#2932	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₉×#2930	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₉×#2929	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₂₉×#435	C₂	1	2	yes	maximal, complemented
20	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic, complemented
22	C₂²×M₁₆×C₂₉	C₂²	1	2	yes	complemented
23	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
24	C₂³×C₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
25	C₂₉×#559	C₄	1	1	yes	characteristic
26	C₂₉×#554	C₄	1	2	yes	—
27	C₂₉×#553	C₄	1	2	yes	—
28	C₂₉×#553	C₄	1	2	yes	—
29	C₂₉×#551	C₄	1	1	yes	characteristic
30	C₂₉×#551	C₄	1	2	yes	—
31	C₂₉×#551	C₄	1	1	yes	characteristic
32	C₂₉×#546	C₄	1	2	yes	—
33	C₂₉×#546	C₄	1	2	yes	—
34	D₄²×C₂₉	C₄	1	1	yes	characteristic
35	C₂₉×#532	C₂²	1	1	yes	characteristic
36	C₂₉×#529	C₂²	1	2	yes	—
37	C₂₉×#529	C₂²	1	2	yes	—
38	C₂₉×#525	C₂²	1	1	yes	characteristic
39	C₂₉×#525	C₂²	1	1	yes	characteristic
40	C₂₉×#525	C₂²	1	2	yes	—
41	C₄×#41×C₂₉	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
44	C₂₉×#446	C₂²	1	2	yes	complemented
45	C₂₉×#446	C₂²	1	2	yes	complemented
46	C₂₉×#446	C₂²	1	2	yes	complemented
47	C₂₉×#446	C₂²	1	2	yes	complemented
48	C₂₉×#436	C₂²	1	2	yes	complemented
49	C₂₉×#436	C₂²	1	2	yes	complemented
50	C₂₉×#436	C₂²	1	2	yes	complemented
51	C₂₉×#436	C₂²	1	2	yes	complemented
52	C₂₉×#436	C₂²	1	2	yes	complemented
53	C₂₉×#436	C₂²	1	2	yes	complemented
54	C₂₉×#435	C₂²	1	2	yes	—
55	C₂₉×#435	C₂²	1	2	yes	—
56	C₂₉×#435	C₂²	1	2	yes	—
57	C₂₉×#435	C₂²	1	2	yes	—
58	C₂₉×#435	C₂²	1	2	yes	complemented
59	C₂₉×#435	C₂²	1	2	yes	complemented
60	C₂₉×#435	C₂²	1	2	yes	complemented
61	C₂₉×#435	C₂²	1	2	yes	complemented
62	C₂₉×#435	C₂²	1	2	yes	complemented
63	C₂₉×#435	C₂²	1	2	yes	complemented
64	C₂₉×#435	C₂²	1	2	yes	complemented
65	C₂₉×#435	C₂²	1	2	yes	complemented
66	C₂₉×#435	C₂²	1	2	yes	complemented
67	C₂₉×#435	C₂²	1	2	yes	complemented
68	C₂₉×#435	C₂²	1	2	yes	complemented
69	C₂₉×#435	C₂²	1	2	yes	complemented
70	C₂₉×#435	C₂²	1	2	yes	complemented
71	C₂₉×#435	C₂²	1	2	yes	complemented
72	C₂₉×#435	C₂²	1	2	yes	complemented
73	C₂₉×#435	C₂²	1	2	yes	complemented
74	C₂₉×#435	C₂²	1	2	yes	complemented
75	C₂₉×#435	C₂²	1	2	yes	complemented
76	C₂₉×#435	C₂²	1	2	yes	complemented
77	C₂₉×#435	C₂²	1	2	yes	complemented
78	C₈×D₄×C₂₉	C₂²	1	2	yes	complemented
79	C₈×D₄×C₂₉	C₂²	1	2	yes	complemented
80	C₈×D₄×C₂₉	C₂²	1	2	yes	complemented
81	C₈×D₄×C₂₉	C₂²	1	2	yes	complemented
82	C₈×D₄×C₂₉	C₂²	1	2	yes	complemented
83	C₈×D₄×C₂₉	C₂²	1	2	yes	complemented
84	C₂₉×#433	C₂²	1	2	yes	complemented
85	C₂₉×#433	C₂²	1	2	yes	complemented
86	C₂₉×#433	C₂²	1	2	yes	complemented
87	C₂₉×#433	C₂²	1	2	yes	complemented
88	C₂₉×#432	C₂²	1	2	yes	complemented
89	C₂₉×#432	C₂²	1	2	yes	complemented
90	C₂₉×#432	C₂²	1	2	yes	complemented
91	C₂₉×#432	C₂²	1	2	yes	complemented
92	C₂₉×#431	C₂²	1	2	yes	complemented
93	C₂₉×#424	C₂²	1	1	yes	characteristic, complemented
94	C₂₉×#424	C₂²	1	1	yes	characteristic, complemented
95	C₂₉×#424	C₂²	1	2	yes	complemented
96	C₂₉×#423	C₂²	1	1	yes	characteristic, complemented
97	C₂₉×#423	C₂²	1	2	yes	complemented
98	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	complemented
99	C₂₉×#408	C₂²	1	1	yes	characteristic, complemented
100	C₂₉×#408	C₂²	1	1	yes	characteristic, complemented
101	C₂₉×#408	C₂²	1	1	yes	characteristic, complemented
102	C₂₉×#408	C₂²	1	1	yes	characteristic, complemented
103	C₂₉×#408	C₂²	1	2	yes	complemented
104	C₂₉×#407	C₂²	1	1	yes	characteristic, complemented
105	C₂₉×#407	C₂²	1	1	yes	characteristic, complemented
106	C₂₉×#407	C₂²	1	2	yes	complemented
107	C₂₉×#407	C₂²	1	2	yes	complemented
108	C₂×C₂₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
109	C₂×C₂₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
110	C₂×C₂₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
111	C₂₉×#405	C₂²	1	1	yes	characteristic, complemented
112	C₂₉×#405	C₂²	1	1	yes	characteristic, complemented
113	C₂₉×#405	C₂²	1	2	yes	complemented
114	C₄×M₁₆×C₂₉	C₂²	1	2	yes	complemented
115	C₂×C₂₉×#97	C₂²	1	2	yes	complemented
116	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic, complemented
117	C₂×#41×C₂₉	C₂×C₄	1	2	yes	—
118	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
119	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
120	C₂²×D₄×C₂₉	C₂×C₄	1	2	yes	—
121	C₂²×D₄×C₂₉	C₂×C₄	1	2	yes	—
122	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
124	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
125	C₂₉×#131	—	4	2	no	—
126	C₂₉×#131	—	4	2	no	—
127	C₂×M₁₆×C₂₉	—	4	4	no	—
128	C₂×M₁₆×C₂₉	—	4	2	no	—
129	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
130	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
131	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
132	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
133	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
134	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
135	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
136	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
137	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
138	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
139	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
140	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₂₉	—	4	2	no	—
142	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
143	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
144	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
145	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
146	C₂²×C₈×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	1	yes	characteristic
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×#127	C₂×C₄	1	1	yes	characteristic
156	C₂₉×#126	C₂×C₄	1	2	yes	—
157	C₂₉×#126	C₂×C₄	1	2	yes	—
158	C₂₉×#126	C₂×C₄	1	2	yes	—
159	C₂₉×#126	C₂×C₄	1	2	yes	—
160	C₂₉×#125	C₂×C₄	1	2	yes	—
161	C₂₉×#125	C₂×C₄	1	2	yes	—
162	C₂₉×#124	C₂×C₄	1	2	yes	—
163	C₂₉×#124	C₂×C₄	1	2	yes	—
164	C₂₉×#124	C₂×C₄	1	1	yes	characteristic
165	C₂₉×#124	C₂×C₄	1	1	yes	characteristic
166	C₂₉×#123	C₂×C₄	1	1	yes	characteristic
167	C₂₉×#123	C₂×C₄	1	1	yes	characteristic
168	C₂₉×#123	C₂×C₄	1	2	yes	—
169	C₂₉×#123	C₂×C₄	1	1	yes	characteristic
170	C₂₉×#123	C₂×C₄	1	1	yes	characteristic
171	C₂₉×#123	C₂×C₄	1	2	yes	—
172	C₂₉×#123	C₂×C₄	1	2	yes	—
173	C₂₉×#123	C₂×C₄	1	2	yes	—
174	C₂₉×#123	C₂×C₄	1	2	yes	—
175	C₂₉×#123	C₂×C₄	1	2	yes	—
176	C₂₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
177	C₂₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
178	C₂₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
179	C₂₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
180	C₂₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
181	C₂₉×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
182	C₂₉×#121	C₂×C₄	1	2	yes	—
183	C₂₉×#121	C₂×C₄	1	2	yes	—
184	C₂₉×#121	C₂×C₄	1	2	yes	—
185	C₂₉×#121	C₂×C₄	1	2	yes	—
186	C₂₉×#121	C₂×C₄	1	2	yes	—
187	C₂₉×#121	C₂×C₄	1	2	yes	—
188	C₂₉×#121	C₂×C₄	1	2	yes	—
189	C₂₉×#121	C₂×C₄	1	2	yes	—
190	C₂₉×#120	C₂×C₄	1	1	yes	characteristic
191	C₂₉×#120	C₂×C₄	1	2	yes	—
192	C₂₉×#120	C₂×C₄	1	1	yes	characteristic
193	C₂₉×#120	C₂×C₄	1	1	yes	characteristic
194	C₂₉×#120	C₂×C₄	1	2	yes	—
195	C₂₉×#120	C₂×C₄	1	1	yes	characteristic
196	C₄×Q₈×C₂₉	C₂×C₄	1	2	yes	—
197	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
198	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
199	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
200	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
201	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
202	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
203	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
204	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
205	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
206	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
207	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
208	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
209	C₄×D₄×C₂₉	C₂³	1	2	yes	—
210	C₄×D₄×C₂₉	C₂³	1	2	yes	—
211	C₄×D₄×C₂₉	C₂³	1	2	yes	—
212	C₄×D₄×C₂₉	C₂³	1	2	yes	—
213	C₄×D₄×C₂₉	C₂³	1	2	yes	—
214	C₄×D₄×C₂₉	C₂³	1	2	yes	—
215	C₄×D₄×C₂₉	C₂³	1	2	yes	—
216	C₄×D₄×C₂₉	C₂³	1	2	yes	—
217	C₄×D₄×C₂₉	C₂³	1	2	yes	—
218	C₂₉×#117	C₂×C₄	1	2	yes	—
219	C₂₉×#117	C₂×C₄	1	2	yes	—
220	C₂₉×#117	C₂×C₄	1	2	yes	—
221	C₂₉×#117	C₂³	1	2	yes	—
222	C₂₉×#117	C₂³	1	1	yes	characteristic
223	C₂₉×#117	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
225	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
226	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
227	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
228	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
229	C₂×C₂²⋊C₄×C₂₉	C₂×C₄	1	2	yes	—
230	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
231	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
232	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
233	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
234	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
235	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
236	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
237	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
238	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
239	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
240	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
241	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
242	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
243	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
244	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
245	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
246	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
247	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
248	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
249	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
250	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
251	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
252	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
253	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
254	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
255	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
256	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
260	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
261	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
262	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
263	C₂₉×#97	C₂³	1	2	yes	—
264	C₂₉×#97	C₂³	1	2	yes	—
265	C₂₉×#97	C₂³	1	2	yes	—
266	C₂₉×#97	C₂³	1	2	yes	—
267	C₂₉×#97	C₂³	1	2	yes	—
268	C₂₉×#97	C₂³	1	2	yes	—
269	C₂₉×#97	C₂³	1	2	yes	—
270	C₂₉×#97	C₂³	1	2	yes	—
271	C₄×C₈×C₂₉	C₂³	1	2	yes	—
272	C₄×C₈×C₂₉	C₂³	1	2	yes	—
273	C₄×C₈×C₂₉	C₂³	1	2	yes	—
274	C₄×C₈×C₂₉	C₂³	1	2	yes	—
275	C₂⁴×C₂₉	C₂²×C₄	1	1	yes	characteristic
276	C₂⁴×C₂₉	C₂²×C₄	1	2	yes	—
277	C₂⁴×C₂₉	C₂²×C₄	1	1	yes	characteristic
278	#41×C₂₉	—	4	1	no	—
279	#41×C₂₉	—	4	1	no	—
280	#41×C₂₉	—	4	1	no	—
281	#41×C₂₉	—	4	1	no	—
282	#41×C₂₉	—	4	4	no	—
283	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
284	C₂×Q₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
285	C₂×Q₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
286	C₂×D₄×C₂₉	—	4	4	no	—
287	C₂×D₄×C₂₉	—	4	4	no	—
288	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
289	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
290	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
291	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
292	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
293	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
294	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
295	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
296	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
297	C₂×D₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
298	C₂×D₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
299	C₂×D₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
300	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
301	C₂×D₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
302	C₂²×C₄×C₂₉	—	4	1	no	—
303	C₂²×C₄×C₂₉	—	4	2	no	—
304	C₂²×C₄×C₂₉	—	4	1	no	—
305	C₂²×C₄×C₂₉	—	4	1	no	—
306	C₂²×C₄×C₂₉	—	4	2	no	—
307	C₂²×C₄×C₂₉	—	4	1	no	—
308	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
309	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
310	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
311	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
312	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
313	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
314	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
315	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
316	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
317	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
318	C₂²×C₄×C₂₉	C₂²×C₄	1	2	yes	—
319	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
320	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
326	M₁₆×C₂₉	—	2	4	no	—
327	M₁₆×C₂₉	—	2	4	no	—
328	M₁₆×C₂₉	—	4	2	no	—
329	M₁₆×C₂₉	—	4	2	no	—
330	M₁₆×C₂₉	—	4	2	no	—
331	M₁₆×C₂₉	—	4	1	no	—
332	M₁₆×C₂₉	—	4	2	no	—
333	M₁₆×C₂₉	—	4	1	no	—
334	M₁₆×C₂₉	—	4	1	no	—
335	M₁₆×C₂₉	—	4	1	no	—
336	M₁₆×C₂₉	—	4	1	no	—
337	M₁₆×C₂₉	—	4	1	no	—
338	C₂×C₈×C₂₉	—	2	4	no	—
339	C₂×C₈×C₂₉	—	2	2	no	—
340	C₂×C₈×C₂₉	—	2	2	no	—
341	C₂×C₈×C₂₉	—	2	2	no	—
342	C₂×C₈×C₂₉	—	4	2	no	—
343	C₂×C₈×C₂₉	—	4	1	no	—
344	C₂×C₈×C₂₉	—	4	2	no	—
345	C₂×C₈×C₂₉	—	4	1	no	—
346	C₂×C₈×C₂₉	—	4	2	no	—
347	C₂×C₈×C₂₉	—	4	2	no	—
348	C₂×C₈×C₂₉	—	4	1	no	—
349	C₂×C₈×C₂₉	—	4	2	no	—
350	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
351	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
354	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
355	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
356	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
357	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
359	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
360	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
361	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
362	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
363	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
364	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
365	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
366	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
367	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
368	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
369	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
370	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
371	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
372	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
373	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
374	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
375	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
376	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
377	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
378	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
379	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
380	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
381	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
382	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
383	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
384	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
385	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
386	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
387	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
388	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
389	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
390	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
391	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
392	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
393	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
394	C₂²⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
395	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
396	C₂²⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
397	C₂²⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
398	C₂²⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
399	C₂²⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
400	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
401	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
402	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
403	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
404	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
405	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
406	C₄²×C₂₉	C₂⁴	1	2	yes	—
407	C₄²×C₂₉	C₂⁴	1	2	yes	—
408	C₄²×C₂₉	C₂⁴	1	2	yes	—
409	#60314	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
410	C₂³×C₂₉	—	2	4	no	—
411	C₂³×C₂₉	—	2	4	no	—
412	C₂³×C₂₉	—	4	1	no	—
413	C₂³×C₂₉	—	4	2	no	—
414	C₂³×C₂₉	—	4	1	no	—
415	C₂³×C₂₉	—	4	2	no	—
416	C₂³×C₂₉	—	4	2	no	—
417	C₂³×C₂₉	C₂³×C₄	1	1	yes	characteristic
418	C₂³×C₂₉	C₂³×C₄	1	2	yes	—
419	C₂³×C₂₉	C₂³×C₄	1	1	yes	characteristic
420	C₂³×C₂₉	C₂³×C₄	1	2	yes	—
421	C₂³×C₂₉	C₂³×C₄	1	1	yes	characteristic
422	C₂³×C₂₉	C₂³×C₄	1	2	yes	—
423	Q₈×C₂₉	—	4	1	no	—
424	Q₈×C₂₉	—	4	1	no	—
425	Q₈×C₂₉	—	4	2	no	—
426	D₄×C₂₉	—	2	4	no	—
427	D₄×C₂₉	—	2	4	no	—
428	D₄×C₂₉	—	2	4	no	—
429	D₄×C₂₉	—	2	4	no	—
430	D₄×C₂₉	—	4	2	no	—
431	D₄×C₂₉	—	4	2	no	—
432	D₄×C₂₉	—	4	2	no	—
433	D₄×C₂₉	—	4	2	no	—
434	D₄×C₂₉	—	4	1	no	—
435	D₄×C₂₉	—	4	1	no	—
436	D₄×C₂₉	—	4	2	no	—
437	D₄×C₂₉	—	4	1	no	—
438	D₄×C₂₉	—	4	1	no	—
439	D₄×C₂₉	—	4	2	no	—
440	C₂×C₄×C₂₉	—	2	4	no	—
441	C₂×C₄×C₂₉	—	2	2	no	—
442	C₂×C₄×C₂₉	—	2	1	no	—
443	C₂×C₄×C₂₉	—	2	1	no	—
444	C₂×C₄×C₂₉	—	2	1	no	—
445	C₂×C₄×C₂₉	—	2	2	no	—
446	C₂×C₄×C₂₉	—	2	2	no	—
447	C₂×C₄×C₂₉	—	2	2	no	—
448	C₂×C₄×C₂₉	—	2	2	no	—
449	C₂×C₄×C₂₉	—	2	1	no	—
450	C₂×C₄×C₂₉	—	2	2	no	—
451	C₂×C₄×C₂₉	—	2	1	no	—
452	C₂×C₄×C₂₉	—	2	1	no	—
453	C₂×C₄×C₂₉	—	4	1	no	—
454	C₂×C₄×C₂₉	—	4	2	no	—
455	C₂×C₄×C₂₉	—	4	1	no	—
456	C₂×C₄×C₂₉	—	4	2	no	—
457	C₂×C₄×C₂₉	—	4	2	no	—
458	C₂×C₄×C₂₉	—	4	2	no	—
459	C₂×C₄×C₂₉	—	4	2	no	—
460	C₂×C₄×C₂₉	—	4	2	no	—
461	C₂×C₄×C₂₉	—	4	2	no	—
462	C₂×C₄×C₂₉	—	4	2	no	—
463	C₂×C₄×C₂₉	—	4	2	no	—
464	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
465	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
466	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
467	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
468	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
469	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
470	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
471	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
472	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
473	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
474	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
475	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
476	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
477	C₈×C₂₉	—	2	2	no	—
478	C₈×C₂₉	—	2	1	no	—
479	C₈×C₂₉	—	2	1	no	—
480	C₈×C₂₉	—	2	1	no	—
481	C₈×C₂₉	—	2	2	no	—
482	C₈×C₂₉	—	2	2	no	—
483	C₈×C₂₉	—	2	2	no	—
484	C₈×C₂₉	—	2	2	no	—
485	C₈×C₂₉	—	2	2	no	—
486	C₈×C₂₉	H(5,𝔽₂)	1	2	yes	—
487	#3481	C₂×C₂₉	1	1	yes	characteristic
488	#2995	C₂×C₂₉	1	2	yes	complemented
489	#2992	C₂×C₂₉	1	2	yes	complemented
490	#2989	C₂×C₂₉	1	2	yes	complemented
491	#2980	C₂×C₂₉	1	1	yes	characteristic, complemented
492	#2978	C₂×C₂₉	1	1	yes	characteristic, complemented
493	#2977	C₂×C₂₉	1	1	yes	characteristic, complemented
494	#2976	C₂×C₂₉	1	2	yes	complemented
495	#2974	C₂×C₂₉	1	2	yes	complemented
496	#2973	C₂×C₂₉	1	2	yes	complemented
497	#2970	C₂×C₂₉	1	2	yes	complemented
498	#2968	C₂×C₂₉	1	2	yes	complemented
499	#2967	C₂×C₂₉	1	2	yes	complemented
500	D₄×M₁₆	C₂×C₂₉	1	2	yes	complemented
501	#2933	C₂×C₂₉	1	2	yes	complemented
502	#2932	C₂×C₂₉	1	1	yes	characteristic, complemented
503	#2930	C₂×C₂₉	1	1	yes	characteristic, complemented
504	#2929	C₂×C₂₉	1	1	yes	characteristic, complemented
505	C₂×#435	C₂×C₂₉	1	2	yes	complemented
506	C₂²×C₂₉	—	2	2	no	—
507	C₂²×C₂₉	—	2	2	no	—
508	C₂²×C₂₉	—	2	2	no	—
509	C₂²×C₂₉	—	2	1	no	—
510	C₂²×C₂₉	—	2	1	no	—
511	C₂²×C₂₉	—	2	2	no	—
512	C₂²×C₂₉	—	2	1	no	—
513	C₂²×C₂₉	—	2	2	no	—
514	C₂²×C₂₉	—	2	2	no	—
515	C₂²×C₂₉	—	2	2	no	—
516	C₂²×C₂₉	—	2	2	no	—
517	C₂²×C₂₉	—	2	2	no	—
518	C₂²×C₂₉	—	2	2	no	—
519	C₂²×C₂₉	—	2	2	no	—
520	C₂²×C₂₉	—	4	4	no	—
521	C₂²×C₂₉	—	8	4	no	—
522	C₂²×C₂₉	—	8	2	no	—
523	C₂²×C₂₉	#568	1	4	yes	—
524	C₂²×C₂₉	C₂⁴×C₄	1	1	yes	characteristic
525	C₄×C₂₉	—	2	2	no	—
526	C₄×C₂₉	—	2	2	no	—
527	C₄×C₂₉	—	2	1	no	—
528	C₄×C₂₉	—	2	1	no	—
529	C₄×C₂₉	—	2	2	no	—
530	C₄×C₂₉	—	2	1	no	—
531	C₄×C₂₉	—	2	2	no	—
532	C₄×C₂₉	—	2	2	no	—
533	C₄×C₂₉	—	2	2	no	—
534	C₄×C₂₉	—	2	2	no	—
535	C₄×C₂₉	—	2	2	no	—
536	C₄×C₂₉	—	2	2	no	—
537	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
538	C₄×C₂₉	#585	1	1	yes	characteristic
539	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic, complemented
540	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic, complemented
541	C₂²×M₁₆	C₂²×C₂₉	1	2	yes	complemented
542	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
543	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
544	#559	C₄×C₂₉	1	1	yes	characteristic
545	#554	C₄×C₂₉	1	2	yes	—
546	#553	C₄×C₂₉	1	2	yes	—
547	#553	C₄×C₂₉	1	2	yes	—
548	#551	C₄×C₂₉	1	1	yes	characteristic
549	#551	C₄×C₂₉	1	2	yes	—
550	#551	C₄×C₂₉	1	1	yes	characteristic
551	#546	C₄×C₂₉	1	2	yes	—
552	#546	C₄×C₂₉	1	2	yes	—
553	D₄²	C₄×C₂₉	1	1	yes	characteristic
554	#532	C₂²×C₂₉	1	1	yes	characteristic
555	#529	C₂²×C₂₉	1	2	yes	—
556	#529	C₂²×C₂₉	1	2	yes	—
557	#525	C₂²×C₂₉	1	1	yes	characteristic
558	#525	C₂²×C₂₉	1	1	yes	characteristic
559	#525	C₂²×C₂₉	1	2	yes	—
560	C₄×#41	C₂²×C₂₉	1	2	yes	—
561	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
562	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
563	#446	C₂²×C₂₉	1	2	yes	complemented
564	#446	C₂²×C₂₉	1	2	yes	complemented
565	#446	C₂²×C₂₉	1	2	yes	complemented
566	#446	C₂²×C₂₉	1	2	yes	complemented
567	#436	C₂²×C₂₉	1	2	yes	complemented
568	#436	C₂²×C₂₉	1	2	yes	complemented
569	#436	C₂²×C₂₉	1	2	yes	complemented
570	#436	C₂²×C₂₉	1	2	yes	complemented
571	#436	C₂²×C₂₉	1	2	yes	complemented
572	#436	C₂²×C₂₉	1	2	yes	complemented
573	#435	C₂²×C₂₉	1	2	yes	—
574	#435	C₂²×C₂₉	1	2	yes	—
575	#435	C₂²×C₂₉	1	2	yes	—
576	#435	C₂²×C₂₉	1	2	yes	—
577	#435	C₂²×C₂₉	1	2	yes	complemented
578	#435	C₂²×C₂₉	1	2	yes	complemented
579	#435	C₂²×C₂₉	1	2	yes	complemented
580	#435	C₂²×C₂₉	1	2	yes	complemented
581	#435	C₂²×C₂₉	1	2	yes	complemented
582	#435	C₂²×C₂₉	1	2	yes	complemented
583	#435	C₂²×C₂₉	1	2	yes	complemented
584	#435	C₂²×C₂₉	1	2	yes	complemented
585	#435	C₂²×C₂₉	1	2	yes	complemented
586	#435	C₂²×C₂₉	1	2	yes	complemented
587	#435	C₂²×C₂₉	1	2	yes	complemented
588	#435	C₂²×C₂₉	1	2	yes	complemented
589	#435	C₂²×C₂₉	1	2	yes	complemented
590	#435	C₂²×C₂₉	1	2	yes	complemented
591	#435	C₂²×C₂₉	1	2	yes	complemented
592	#435	C₂²×C₂₉	1	2	yes	complemented
593	#435	C₂²×C₂₉	1	2	yes	complemented
594	#435	C₂²×C₂₉	1	2	yes	complemented
595	#435	C₂²×C₂₉	1	2	yes	complemented
596	#435	C₂²×C₂₉	1	2	yes	complemented
597	C₈×D₄	C₂²×C₂₉	1	2	yes	complemented
598	C₈×D₄	C₂²×C₂₉	1	2	yes	complemented
599	C₈×D₄	C₂²×C₂₉	1	2	yes	complemented
600	C₈×D₄	C₂²×C₂₉	1	2	yes	complemented
601	C₈×D₄	C₂²×C₂₉	1	2	yes	complemented
602	C₈×D₄	C₂²×C₂₉	1	2	yes	complemented
603	#433	C₂²×C₂₉	1	2	yes	complemented
604	#433	C₂²×C₂₉	1	2	yes	complemented
605	#433	C₂²×C₂₉	1	2	yes	complemented
606	#433	C₂²×C₂₉	1	2	yes	complemented
607	#432	C₂²×C₂₉	1	2	yes	complemented
608	#432	C₂²×C₂₉	1	2	yes	complemented
609	#432	C₂²×C₂₉	1	2	yes	complemented
610	#432	C₂²×C₂₉	1	2	yes	complemented
611	#431	C₂²×C₂₉	1	2	yes	complemented
612	#424	C₂²×C₂₉	1	1	yes	characteristic, complemented
613	#424	C₂²×C₂₉	1	1	yes	characteristic, complemented
614	#424	C₂²×C₂₉	1	2	yes	complemented
615	#423	C₂²×C₂₉	1	1	yes	characteristic, complemented
616	#423	C₂²×C₂₉	1	2	yes	complemented
617	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	complemented
618	#408	C₂²×C₂₉	1	1	yes	characteristic, complemented
619	#408	C₂²×C₂₉	1	1	yes	characteristic, complemented
620	#408	C₂²×C₂₉	1	1	yes	characteristic, complemented
621	#408	C₂²×C₂₉	1	1	yes	characteristic, complemented
622	#408	C₂²×C₂₉	1	2	yes	complemented
623	#407	C₂²×C₂₉	1	1	yes	characteristic, complemented
624	#407	C₂²×C₂₉	1	1	yes	characteristic, complemented
625	#407	C₂²×C₂₉	1	2	yes	complemented
626	#407	C₂²×C₂₉	1	2	yes	complemented
627	C₂×C₂²⋊C₈	C₂²×C₂₉	1	2	yes	complemented
628	C₂×C₂²⋊C₈	C₂²×C₂₉	1	2	yes	complemented
629	C₂×C₂²⋊C₈	C₂²×C₂₉	1	2	yes	complemented
630	#405	C₂²×C₂₉	1	1	yes	characteristic, complemented
631	#405	C₂²×C₂₉	1	1	yes	characteristic, complemented
632	#405	C₂²×C₂₉	1	2	yes	complemented
633	C₄×M₁₆	C₂²×C₂₉	1	2	yes	complemented
634	C₂×#97	C₂²×C₂₉	1	2	yes	complemented
635	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic, complemented
636	C₂×C₂₉	—	2	4	no	—
637	C₂×C₂₉	—	4	1	no	—
638	C₂×C₂₉	—	4	1	no	—
639	C₂×C₂₉	—	4	1	no	—
640	C₂×C₂₉	—	4	2	no	—
641	C₂×C₂₉	—	4	2	no	—
642	C₂×C₂₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic
643	C₂×C₂₉	C₂×#568	1	2	yes	—
644	C₂×#41	C₂×C₄×C₂₉	1	2	yes	—
645	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
646	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
647	C₂²×D₄	C₂×C₄×C₂₉	1	2	yes	—
648	C₂²×D₄	C₂×C₄×C₂₉	1	2	yes	—
649	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
650	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
651	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
652	#131	—	4	2	no	—
653	#131	—	4	2	no	—
654	C₂×M₁₆	—	4	4	no	—
655	C₂×M₁₆	—	4	2	no	—
656	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
657	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
658	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
659	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
660	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
661	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
662	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
663	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
664	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
665	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
666	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
667	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
668	C₂²×C₈	—	4	2	no	—
669	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
670	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
671	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
672	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
673	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
674	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
675	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
676	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
677	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
678	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
679	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
680	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
681	C₄⋊Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
682	#127	C₂×C₄×C₂₉	1	1	yes	characteristic
683	#126	C₂×C₄×C₂₉	1	2	yes	—
684	#126	C₂×C₄×C₂₉	1	2	yes	—
685	#126	C₂×C₄×C₂₉	1	2	yes	—
686	#126	C₂×C₄×C₂₉	1	2	yes	—
687	#125	C₂×C₄×C₂₉	1	2	yes	—
688	#125	C₂×C₄×C₂₉	1	2	yes	—
689	#124	C₂×C₄×C₂₉	1	2	yes	—
690	#124	C₂×C₄×C₂₉	1	2	yes	—
691	#124	C₂×C₄×C₂₉	1	1	yes	characteristic
692	#124	C₂×C₄×C₂₉	1	1	yes	characteristic
693	#123	C₂×C₄×C₂₉	1	1	yes	characteristic
694	#123	C₂×C₄×C₂₉	1	1	yes	characteristic
695	#123	C₂×C₄×C₂₉	1	2	yes	—
696	#123	C₂×C₄×C₂₉	1	1	yes	characteristic
697	#123	C₂×C₄×C₂₉	1	1	yes	characteristic
698	#123	C₂×C₄×C₂₉	1	2	yes	—
699	#123	C₂×C₄×C₂₉	1	2	yes	—
700	#123	C₂×C₄×C₂₉	1	2	yes	—
701	#123	C₂×C₄×C₂₉	1	2	yes	—
702	#123	C₂×C₄×C₂₉	1	2	yes	—
703	C₂²⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
704	C₂²⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
705	C₂²⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
706	C₂²⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
707	C₂²⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
708	C₂²⋊Q₈	C₂×C₄×C₂₉	1	2	yes	—
709	#121	C₂×C₄×C₂₉	1	2	yes	—
710	#121	C₂×C₄×C₂₉	1	2	yes	—
711	#121	C₂×C₄×C₂₉	1	2	yes	—
712	#121	C₂×C₄×C₂₉	1	2	yes	—
713	#121	C₂×C₄×C₂₉	1	2	yes	—
714	#121	C₂×C₄×C₂₉	1	2	yes	—
715	#121	C₂×C₄×C₂₉	1	2	yes	—
716	#121	C₂×C₄×C₂₉	1	2	yes	—
717	#120	C₂×C₄×C₂₉	1	1	yes	characteristic
718	#120	C₂×C₄×C₂₉	1	2	yes	—
719	#120	C₂×C₄×C₂₉	1	1	yes	characteristic
720	#120	C₂×C₄×C₂₉	1	1	yes	characteristic
721	#120	C₂×C₄×C₂₉	1	2	yes	—
722	#120	C₂×C₄×C₂₉	1	1	yes	characteristic
723	C₄×Q₈	C₂×C₄×C₂₉	1	2	yes	—
724	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
725	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
726	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
727	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
728	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
729	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
730	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
731	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
732	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
733	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
734	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
735	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
736	C₄×D₄	C₂³×C₂₉	1	2	yes	—
737	C₄×D₄	C₂³×C₂₉	1	2	yes	—
738	C₄×D₄	C₂³×C₂₉	1	2	yes	—
739	C₄×D₄	C₂³×C₂₉	1	2	yes	—
740	C₄×D₄	C₂³×C₂₉	1	2	yes	—
741	C₄×D₄	C₂³×C₂₉	1	2	yes	—
742	C₄×D₄	C₂³×C₂₉	1	2	yes	—
743	C₄×D₄	C₂³×C₂₉	1	2	yes	—
744	C₄×D₄	C₂³×C₂₉	1	2	yes	—
745	#117	C₂×C₄×C₂₉	1	2	yes	—
746	#117	C₂×C₄×C₂₉	1	2	yes	—
747	#117	C₂×C₄×C₂₉	1	2	yes	—
748	#117	C₂³×C₂₉	1	1	yes	characteristic
749	#117	C₂³×C₂₉	1	1	yes	characteristic
750	#117	C₂³×C₂₉	1	2	yes	—
751	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
752	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂×C₄×C₂₉	1	2	yes	—
757	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
758	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
759	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
760	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
761	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
762	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
763	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
764	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
765	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
766	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
767	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
768	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
769	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
770	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
771	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
772	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
773	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
774	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
775	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
776	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
777	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
778	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
779	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
780	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
781	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
782	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
783	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
784	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
785	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
786	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
787	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
788	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
789	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
790	#97	C₂³×C₂₉	1	2	yes	—
791	#97	C₂³×C₂₉	1	2	yes	—
792	#97	C₂³×C₂₉	1	2	yes	—
793	#97	C₂³×C₂₉	1	2	yes	—
794	#97	C₂³×C₂₉	1	2	yes	—
795	#97	C₂³×C₂₉	1	2	yes	—
796	#97	C₂³×C₂₉	1	2	yes	—
797	#97	C₂³×C₂₉	1	2	yes	—
798	C₄×C₈	C₂³×C₂₉	1	2	yes	—
799	C₄×C₈	C₂³×C₂₉	1	2	yes	—
800	C₄×C₈	C₂³×C₂₉	1	2	yes	—
801	C₄×C₈	C₂³×C₂₉	1	2	yes	—
802	C₂₉	#60314	1	1	yes	characteristic, direct product factor, Sylow
803	C₂⁴	C₂²×C₄×C₂₉	1	1	yes	characteristic
804	C₂⁴	C₂²×C₄×C₂₉	1	2	yes	—
805	C₂⁴	C₂²×C₄×C₂₉	1	1	yes	characteristic
806	#41	—	4	1	no	—
807	#41	—	4	1	no	—
808	#41	—	4	1	no	—
809	#41	—	4	1	no	—
810	#41	—	4	4	no	—
811	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
812	C₂×Q₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
813	C₂×Q₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
814	C₂×D₄	—	4	4	no	—
815	C₂×D₄	—	4	4	no	—
816	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
817	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
818	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
819	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
820	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
821	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
822	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
823	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
824	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
825	C₂×D₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
826	C₂×D₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
827	C₂×D₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
828	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
829	C₂×D₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
830	C₂²×C₄	—	4	1	no	—
831	C₂²×C₄	—	4	2	no	—
832	C₂²×C₄	—	4	1	no	—
833	C₂²×C₄	—	4	1	no	—
834	C₂²×C₄	—	4	2	no	—
835	C₂²×C₄	—	4	1	no	—
836	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
837	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
838	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
839	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
840	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
841	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
842	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
843	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
844	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
845	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
846	C₂²×C₄	C₂²×C₄×C₂₉	1	2	yes	—
847	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
848	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
849	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
850	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
851	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
852	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
853	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
854	M₁₆	—	2	4	no	—
855	M₁₆	—	2	4	no	—
856	M₁₆	—	4	2	no	—
857	M₁₆	—	4	2	no	—
858	M₁₆	—	4	2	no	—
859	M₁₆	—	4	1	no	—
860	M₁₆	—	4	1	no	—
861	M₁₆	—	4	1	no	—
862	M₁₆	—	4	1	no	—
863	M₁₆	—	4	1	no	—
864	M₁₆	—	4	2	no	—
865	M₁₆	—	4	1	no	—
866	C₂×C₈	—	2	4	no	—
867	C₂×C₈	—	2	2	no	—
868	C₂×C₈	—	2	2	no	—
869	C₂×C₈	—	2	2	no	—
870	C₂×C₈	—	4	2	no	—
871	C₂×C₈	—	4	1	no	—
872	C₂×C₈	—	4	2	no	—
873	C₂×C₈	—	4	1	no	—
874	C₂×C₈	—	4	2	no	—
875	C₂×C₈	—	4	2	no	—
876	C₂×C₈	—	4	1	no	—
877	C₂×C₈	—	4	2	no	—
878	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
879	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
880	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
881	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
882	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
883	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
884	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
885	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
886	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
887	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
888	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
889	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
890	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
891	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
892	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
893	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
894	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
895	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
896	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
897	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
898	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
899	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
900	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
901	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
902	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
903	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
904	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
905	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
906	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
907	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
908	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
909	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
910	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
911	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
912	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
913	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
914	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
915	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
916	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
917	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
918	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
919	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
920	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
921	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
922	C₂²⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
923	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
924	C₂²⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
925	C₂²⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
926	C₂²⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
927	C₂²⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
928	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
929	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
930	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
931	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
932	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
933	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
934	C₄²	C₂⁴×C₂₉	1	2	yes	—
935	C₄²	C₂⁴×C₂₉	1	2	yes	—
936	C₄²	C₂⁴×C₂₉	1	2	yes	—
937	C₂³	—	2	4	no	—
938	C₂³	—	2	4	no	—
939	C₂³	—	4	1	no	—
940	C₂³	—	4	2	no	—
941	C₂³	—	4	1	no	—
942	C₂³	—	4	2	no	—
943	C₂³	—	4	2	no	—
944	C₂³	C₂³×C₄×C₂₉	1	1	yes	characteristic
945	C₂³	C₂³×C₄×C₂₉	1	2	yes	—
946	C₂³	C₂³×C₄×C₂₉	1	1	yes	characteristic
947	C₂³	C₂³×C₄×C₂₉	1	2	yes	—
948	C₂³	C₂³×C₄×C₂₉	1	1	yes	characteristic
949	C₂³	C₂³×C₄×C₂₉	1	2	yes	—
950	Q₈	—	4	2	no	—
951	Q₈	—	4	1	no	—
952	Q₈	—	4	1	no	—
953	D₄	—	2	4	no	—
954	D₄	—	2	4	no	—
955	D₄	—	2	4	no	—
956	D₄	—	2	4	no	—
957	D₄	—	4	2	no	—
958	D₄	—	4	2	no	—
959	D₄	—	4	2	no	—
960	D₄	—	4	2	no	—
961	D₄	—	4	2	no	—
962	D₄	—	4	1	no	—
963	D₄	—	4	1	no	—
964	D₄	—	4	2	no	—
965	D₄	—	4	1	no	—
966	D₄	—	4	1	no	—
967	C₂×C₄	—	2	4	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	4	1	no	—
981	C₂×C₄	—	4	2	no	—
982	C₂×C₄	—	4	1	no	—
983	C₂×C₄	—	4	2	no	—
984	C₂×C₄	—	4	2	no	—
985	C₂×C₄	—	4	2	no	—
986	C₂×C₄	—	4	2	no	—
987	C₂×C₄	—	4	2	no	—
988	C₂×C₄	—	4	2	no	—
989	C₂×C₄	—	4	2	no	—
990	C₂×C₄	—	4	2	no	—
991	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
992	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
993	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
994	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
995	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
996	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
997	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
998	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
999	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
1000	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
1001	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
1002	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
1003	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1004	C₈	—	2	2	no	—
1005	C₈	—	2	1	no	—
1006	C₈	—	2	1	no	—
1007	C₈	—	2	1	no	—
1008	C₈	—	2	2	no	—
1009	C₈	—	2	2	no	—
1010	C₈	—	2	2	no	—
1011	C₈	—	2	2	no	—
1012	C₈	—	2	2	no	—
1013	C₈	C₂₉×H(5,𝔽₂)	1	2	yes	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	2	2	no	—
1017	C₂²	—	2	2	no	—
1018	C₂²	—	2	2	no	—
1019	C₂²	—	2	2	no	—
1020	C₂²	—	2	2	no	—
1021	C₂²	—	2	2	no	—
1022	C₂²	—	2	2	no	—
1023	C₂²	—	2	2	no	—
1024	C₂²	—	2	1	no	—
1025	C₂²	—	2	1	no	—
1026	C₂²	—	2	2	no	—
1027	C₂²	—	2	1	no	—
1028	C₂²	—	4	4	no	—
1029	C₂²	—	8	4	no	—
1030	C₂²	—	8	2	no	—
1031	C₂²	C₂₉×#568	1	4	yes	—
1032	C₂²	C₂⁴×C₄×C₂₉	1	1	yes	characteristic
1033	C₄	—	2	2	no	—
1034	C₄	—	2	2	no	—
1035	C₄	—	2	2	no	—
1036	C₄	—	2	2	no	—
1037	C₄	—	2	2	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	2	2	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	1	no	—
1042	C₄	—	2	1	no	—
1043	C₄	—	2	2	no	—
1044	C₄	—	2	1	no	—
1045	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
1046	C₄	C₂₉×#585	1	1	yes	characteristic
1047	C₂	—	2	4	no	—
1048	C₂	—	4	1	no	—
1049	C₂	—	4	2	no	—
1050	C₂	—	4	1	no	—
1051	C₂	—	4	2	no	—
1052	C₂	—	4	1	no	—
1053	C₂	C₄×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
1054	C₂	C₂×C₂₉×#568	1	2	yes	—

	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×#3481	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×#2992	C₂	semidirect
4. C₂₉×#2989	C₂	semidirect
5. C₂₉×#2980	C₂	semidirect
6. C₂₉×#2978	C₂	semidirect
7. C₂₉×#2977	C₂	semidirect
8. C₂₉×#2976	C₂	semidirect
9. C₂₉×#2974	C₂	semidirect
10. C₂₉×#2973	C₂	semidirect
11. C₂₉×#2970	C₂	semidirect
12. C₂₉×#2968	C₂	semidirect
13. C₂₉×#2967	C₂	semidirect
14. D₄×M₁₆×C₂₉	C₂	semidirect
15. C₂₉×#2933	C₂	semidirect
16. C₂₉×#2932	C₂	semidirect
17. C₂₉×#2930	C₂	semidirect
18. C₂₉×#2929	C₂	semidirect
19. C₂×C₂₉×#435	C₂	semidirect
20. C₂×C₂₉×#131	C₂²	semidirect
21. C₂×C₂₉×#131	C₂²	semidirect
22. C₂²×M₁₆×C₂₉	C₂²	semidirect
23. C₂²×M₁₆×C₂₉	C₂²	semidirect
24. C₂³×C₈×C₂₉	C₂²	semidirect
44. C₂₉×#446	C₂²	semidirect
45. C₂₉×#446	C₂²	semidirect
46. C₂₉×#446	C₂²	semidirect
47. C₂₉×#446	C₂²	semidirect
48. C₂₉×#436	C₂²	semidirect
49. C₂₉×#436	C₂²	semidirect
50. C₂₉×#436	C₂²	semidirect
51. C₂₉×#436	C₂²	semidirect
52. C₂₉×#436	C₂²	semidirect
53. C₂₉×#436	C₂²	semidirect
58. C₂₉×#435	C₂²	semidirect
59. C₂₉×#435	C₂²	semidirect
60. C₂₉×#435	C₂²	semidirect
61. C₂₉×#435	C₂²	semidirect
62. C₂₉×#435	C₂²	semidirect
63. C₂₉×#435	C₂²	semidirect
64. C₂₉×#435	C₂²	semidirect
65. C₂₉×#435	C₂²	semidirect
66. C₂₉×#435	C₂²	semidirect
67. C₂₉×#435	C₂²	semidirect
68. C₂₉×#435	C₂²	semidirect
69. C₂₉×#435	C₂²	semidirect
70. C₂₉×#435	C₂²	semidirect
71. C₂₉×#435	C₂²	semidirect
72. C₂₉×#435	C₂²	semidirect
73. C₂₉×#435	C₂²	semidirect
74. C₂₉×#435	C₂²	semidirect
75. C₂₉×#435	C₂²	semidirect
76. C₂₉×#435	C₂²	semidirect
77. C₂₉×#435	C₂²	semidirect
78. C₈×D₄×C₂₉	C₂²	semidirect
79. C₈×D₄×C₂₉	C₂²	semidirect
80. C₈×D₄×C₂₉	C₂²	semidirect
81. C₈×D₄×C₂₉	C₂²	semidirect
82. C₈×D₄×C₂₉	C₂²	semidirect
83. C₈×D₄×C₂₉	C₂²	semidirect
84. C₂₉×#433	C₂²	semidirect
85. C₂₉×#433	C₂²	semidirect
86. C₂₉×#433	C₂²	semidirect
87. C₂₉×#433	C₂²	semidirect
88. C₂₉×#432	C₂²	semidirect
89. C₂₉×#432	C₂²	semidirect
90. C₂₉×#432	C₂²	semidirect
91. C₂₉×#432	C₂²	semidirect
92. C₂₉×#431	C₂²	semidirect
93. C₂₉×#424	C₂²	semidirect
94. C₂₉×#424	C₂²	semidirect
95. C₂₉×#424	C₂²	semidirect
96. C₂₉×#423	C₂²	semidirect
97. C₂₉×#423	C₂²	semidirect
98. C₂×C₂₉×C₄⋊C₈	C₂²	semidirect
99. C₂₉×#408	C₂²	semidirect
100. C₂₉×#408	C₂²	semidirect
101. C₂₉×#408	C₂²	semidirect
102. C₂₉×#408	C₂²	semidirect
103. C₂₉×#408	C₂²	semidirect
104. C₂₉×#407	C₂²	semidirect
105. C₂₉×#407	C₂²	semidirect
106. C₂₉×#407	C₂²	semidirect
107. C₂₉×#407	C₂²	semidirect
108. C₂×C₂₉×C₂²⋊C₈	C₂²	semidirect
109. C₂×C₂₉×C₂²⋊C₈	C₂²	semidirect
110. C₂×C₂₉×C₂²⋊C₈	C₂²	semidirect
111. C₂₉×#405	C₂²	semidirect
112. C₂₉×#405	C₂²	semidirect
113. C₂₉×#405	C₂²	semidirect
114. C₄×M₁₆×C₂₉	C₂²	semidirect
115. C₂×C₂₉×#97	C₂²	semidirect
116. C₂×C₂₉×#97	C₂²	semidirect
409. #60314	C₂₉	direct (N × H)
488. #2995	C₂×C₂₉	semidirect
489. #2992	C₂×C₂₉	semidirect
490. #2989	C₂×C₂₉	semidirect
491. #2980	C₂×C₂₉	semidirect
492. #2978	C₂×C₂₉	semidirect
493. #2977	C₂×C₂₉	semidirect
494. #2976	C₂×C₂₉	semidirect
495. #2974	C₂×C₂₉	semidirect
496. #2973	C₂×C₂₉	semidirect
497. #2970	C₂×C₂₉	semidirect
498. #2968	C₂×C₂₉	semidirect
499. #2967	C₂×C₂₉	semidirect
500. D₄×M₁₆	C₂×C₂₉	semidirect
501. #2933	C₂×C₂₉	semidirect
502. #2932	C₂×C₂₉	semidirect
503. #2930	C₂×C₂₉	semidirect
504. #2929	C₂×C₂₉	semidirect
505. C₂×#435	C₂×C₂₉	semidirect
539. C₂×#131	C₂²×C₂₉	semidirect
540. C₂×#131	C₂²×C₂₉	semidirect
541. C₂²×M₁₆	C₂²×C₂₉	semidirect
542. C₂²×M₁₆	C₂²×C₂₉	semidirect
543. C₂³×C₈	C₂²×C₂₉	semidirect
563. #446	C₂²×C₂₉	semidirect
564. #446	C₂²×C₂₉	semidirect
565. #446	C₂²×C₂₉	semidirect
566. #446	C₂²×C₂₉	semidirect
567. #436	C₂²×C₂₉	semidirect
568. #436	C₂²×C₂₉	semidirect
569. #436	C₂²×C₂₉	semidirect
570. #436	C₂²×C₂₉	semidirect
571. #436	C₂²×C₂₉	semidirect
572. #436	C₂²×C₂₉	semidirect
577. #435	C₂²×C₂₉	semidirect
578. #435	C₂²×C₂₉	semidirect
579. #435	C₂²×C₂₉	semidirect
580. #435	C₂²×C₂₉	semidirect
581. #435	C₂²×C₂₉	semidirect
582. #435	C₂²×C₂₉	semidirect
583. #435	C₂²×C₂₉	semidirect
584. #435	C₂²×C₂₉	semidirect
585. #435	C₂²×C₂₉	semidirect
586. #435	C₂²×C₂₉	semidirect
587. #435	C₂²×C₂₉	semidirect
588. #435	C₂²×C₂₉	semidirect
589. #435	C₂²×C₂₉	semidirect
590. #435	C₂²×C₂₉	semidirect
591. #435	C₂²×C₂₉	semidirect
592. #435	C₂²×C₂₉	semidirect
593. #435	C₂²×C₂₉	semidirect
594. #435	C₂²×C₂₉	semidirect
595. #435	C₂²×C₂₉	semidirect
596. #435	C₂²×C₂₉	semidirect
597. C₈×D₄	C₂²×C₂₉	semidirect
598. C₈×D₄	C₂²×C₂₉	semidirect
599. C₈×D₄	C₂²×C₂₉	semidirect
600. C₈×D₄	C₂²×C₂₉	semidirect
601. C₈×D₄	C₂²×C₂₉	semidirect
602. C₈×D₄	C₂²×C₂₉	semidirect
603. #433	C₂²×C₂₉	semidirect
604. #433	C₂²×C₂₉	semidirect
605. #433	C₂²×C₂₉	semidirect
606. #433	C₂²×C₂₉	semidirect
607. #432	C₂²×C₂₉	semidirect
608. #432	C₂²×C₂₉	semidirect
609. #432	C₂²×C₂₉	semidirect
610. #432	C₂²×C₂₉	semidirect
611. #431	C₂²×C₂₉	semidirect
612. #424	C₂²×C₂₉	semidirect
613. #424	C₂²×C₂₉	semidirect
614. #424	C₂²×C₂₉	semidirect
615. #423	C₂²×C₂₉	semidirect
616. #423	C₂²×C₂₉	semidirect
617. C₂×C₄⋊C₈	C₂²×C₂₉	semidirect
618. #408	C₂²×C₂₉	semidirect
619. #408	C₂²×C₂₉	semidirect
620. #408	C₂²×C₂₉	semidirect
621. #408	C₂²×C₂₉	semidirect
622. #408	C₂²×C₂₉	semidirect
623. #407	C₂²×C₂₉	semidirect
624. #407	C₂²×C₂₉	semidirect
625. #407	C₂²×C₂₉	semidirect
626. #407	C₂²×C₂₉	semidirect
627. C₂×C₂²⋊C₈	C₂²×C₂₉	semidirect
628. C₂×C₂²⋊C₈	C₂²×C₂₉	semidirect
629. C₂×C₂²⋊C₈	C₂²×C₂₉	semidirect
630. #405	C₂²×C₂₉	semidirect
631. #405	C₂²×C₂₉	semidirect
632. #405	C₂²×C₂₉	semidirect
633. C₄×M₁₆	C₂²×C₂₉	semidirect
634. C₂×#97	C₂²×C₂₉	semidirect
635. C₂×#97	C₂²×C₂₉	semidirect
802. C₂₉	#60314	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×#3481	2
C₂₉×#2995	2
C₂₉×#2992	2
C₂₉×#2989	2
C₂₉×#2980	2
C₂₉×#2978	2
C₂₉×#2977	2
C₂₉×#2976	2
C₂₉×#2974	2
C₂₉×#2973	2
C₂₉×#2970	2
C₂₉×#2968	2
C₂₉×#2967	2
D₄×M₁₆×C₂₉	2
C₂₉×#2933	2
C₂₉×#2932	2
C₂₉×#2930	2
C₂₉×#2929	2
C₂×C₂₉×#435	2
#60314	29

Subgroups — C29×#60314 #20355214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#60314 #20355214