Subgroups — C₂₉×#61561 #20356461

Order 7424.

2282 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3505	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3297	C₂	1	4	yes	maximal, complemented
4	C₂₉×#3296	C₂	1	4	yes	maximal, complemented
5	C₂₉×#3282	C₂	1	4	yes	maximal, complemented
6	C₂₉×#3280	C₂	1	4	yes	maximal, complemented
7	C₂₉×#3211	C₂	1	2	yes	maximal, complemented
8	C₂₉×#3189	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#3188	C₂	1	2	yes	maximal, complemented
10	C₂₉×#3187	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#3105	C₂	1	2	yes	maximal, complemented
12	C₂₉×#3002	C₂	1	2	yes	maximal, complemented
13	C₂×C₂₉×#450	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₉×#447	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#2972	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₉	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₄×C₂₉	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×#135	C₂²	1	4	yes	complemented
19	C₂²×SD₁₆×C₂₉	C₂²	1	2	yes	complemented
20	C₂²×D₈×C₂₉	C₂²	1	2	yes	complemented
21	C₂₉×#553	—	2	2	no	—
22	C₂₉×#553	C₂²	1	2	yes	complemented
23	C₂₉×#552	C₂²	1	2	yes	complemented
24	C₂₉×#551	—	2	2	no	—
25	C₂₉×#548	C₂²	1	2	yes	complemented
26	C₂₉×#546	—	2	2	no	—
27	C₂₉×#546	—	2	2	no	—
28	C₂₉×#546	C₂²	1	4	yes	—
29	C₂₉×#546	C₂²	1	4	yes	complemented
30	C₂₉×#546	C₂²	1	2	yes	complemented
31	C₂₉×#539	—	2	1	no	—
32	C₂₉×#538	—	2	1	no	—
33	C₂₉×#534	—	2	1	no	—
34	C₂₉×#529	C₂²	1	2	yes	complemented
35	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic, complemented
36	C₂₉×#525	C₂²	1	2	yes	complemented
37	C₂×C₂₉×#123	—	2	1	no	—
38	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₉×#121	—	2	1	no	—
41	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic
42	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₂₉×#120	—	2	1	no	—
44	C₂₉×#518	—	2	1	no	—
45	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
47	C₂²×C₂²⋊C₄×C₂₉	—	2	1	no	—
48	C₂₉×#495	C₂²	1	4	yes	complemented
49	C₂₉×#488	C₂²	1	4	yes	complemented
50	C₂₉×#484	C₂²	1	2	yes	complemented
51	C₂₉×#484	C₂²	1	2	yes	complemented
52	C₂₉×#483	C₂²	1	2	yes	complemented
53	C₂₉×#482	C₂²	1	4	yes	complemented
54	C₂₉×#481	C₂²	1	2	yes	complemented
55	C₂₉×#478	C₂²	1	4	yes	complemented
56	C₂₉×#467	C₂²	1	4	yes	complemented
57	C₂₉×#466	C₂²	1	4	yes	complemented
58	C₂₉×#465	C₂²	1	4	yes	complemented
59	C₂₉×#465	C₂²	1	4	yes	complemented
60	C₂₉×#464	C₂²	1	4	yes	complemented
61	C₂₉×#463	C₂²	1	4	yes	complemented
62	C₂₉×#463	C₂²	1	4	yes	complemented
63	C₂₉×#452	C₂²	1	4	yes	complemented
64	C₂₉×#451	C₂²	1	2	yes	complemented
65	C₂₉×#451	C₂²	1	2	yes	complemented
66	C₂₉×#450	C₂²	1	2	yes	complemented
67	C₂₉×#450	C₂²	1	2	yes	complemented
68	C₂₉×#450	C₂²	1	4	yes	complemented
69	C₂₉×#450	C₂²	1	2	yes	complemented
70	C₂₉×#449	C₂²	1	4	yes	complemented
71	C₂₉×#449	C₂²	1	4	yes	complemented
72	C₂₉×#448	C₂²	1	2	yes	complemented
73	C₂₉×#447	C₂²	1	2	yes	—
74	C₂₉×#447	C₂²	1	2	yes	—
75	C₂₉×#447	C₂²	1	4	yes	complemented
76	C₄×SD₁₆×C₂₉	C₂²	1	4	yes	complemented
77	C₄×D₈×C₂₉	C₂²	1	4	yes	complemented
78	C₈×D₄×C₂₉	C₂²	1	4	yes	complemented
79	C₈×D₄×C₂₉	C₂²	1	4	yes	complemented
80	C₂₉×#431	C₂²	1	2	yes	complemented
81	C₂₉×#416	C₂²	1	4	yes	complemented
82	C₂×C₂₉×#102	C₂²	1	2	yes	complemented
83	C₂×C₂₉×#102	C₂²	1	2	yes	complemented
84	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
85	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
86	C₂×C₂₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
87	C₂⁵×C₂₉	—	2	1	no	—
88	C₂×#41×C₂₉	—	2	2	no	—
89	C₂×#41×C₂₉	—	4	4	no	—
90	C₂×#41×C₂₉	C₂³	1	4	yes	—
91	C₂×#41×C₂₉	C₂³	1	2	yes	complemented
92	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
93	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₂₉	—	2	1	no	—
95	C₂²×D₄×C₂₉	—	2	1	no	—
96	C₂²×D₄×C₂₉	—	2	1	no	—
97	C₂²×D₄×C₂₉	—	2	1	no	—
98	C₂²×D₄×C₂₉	—	2	1	no	—
99	C₂²×D₄×C₂₉	—	2	1	no	—
100	C₂²×D₄×C₂₉	—	4	4	no	—
101	C₂²×D₄×C₂₉	D₄	1	1	yes	characteristic
102	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
104	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
105	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₂₉	—	2	1	no	—
108	C₂³×C₄×C₂₉	—	2	1	no	—
109	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
111	C₂₉×#135	—	4	8	no	—
112	C₂×Q₁₆×C₂₉	C₂³	1	4	yes	complemented
113	C₂×SD₁₆×C₂₉	—	4	4	no	—
114	C₂×SD₁₆×C₂₉	C₂³	1	4	yes	—
115	C₂×SD₁₆×C₂₉	C₂³	1	4	yes	—
116	C₂×SD₁₆×C₂₉	C₂³	1	4	yes	complemented
117	C₂×D₈×C₂₉	—	4	4	no	—
118	C₂×D₈×C₂₉	C₂³	1	4	yes	—
119	C₂×D₈×C₂₉	C₂³	1	4	yes	—
120	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
121	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
122	C₂²×C₈×C₂₉	C₂³	1	4	yes	complemented
123	C₂₉×#126	—	2	2	no	—
124	C₂₉×#126	—	2	2	no	—
125	C₂₉×#126	—	2	2	no	—
126	C₂₉×#125	—	2	2	no	—
127	C₂₉×#125	C₂³	1	2	yes	complemented
128	C₂₉×#124	—	2	2	no	—
129	C₂₉×#124	—	2	2	no	—
130	C₂₉×#124	C₂³	1	4	yes	—
131	C₂₉×#124	C₂³	1	2	yes	complemented
132	C₂₉×#123	—	2	2	no	—
133	C₂₉×#123	—	2	2	no	—
134	C₂₉×#123	—	2	2	no	—
135	C₂₉×#123	—	2	4	no	—
136	C₂₉×#123	—	2	4	no	—
137	C₂₉×#123	—	2	2	no	—
138	C₂₉×#123	—	2	2	no	—
139	C₂₉×C₂²⋊Q₈	—	2	1	no	—
140	C₂₉×C₂²⋊Q₈	—	2	1	no	—
141	C₂₉×C₂²⋊Q₈	—	2	1	no	—
142	C₂₉×C₂²⋊Q₈	—	2	1	no	—
143	C₂₉×C₂²⋊Q₈	—	2	2	no	—
144	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
145	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
148	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	complemented
149	C₂₉×#121	—	2	2	no	—
150	C₂₉×#121	—	2	2	no	—
151	C₂₉×#121	—	2	1	no	—
152	C₂₉×#121	—	2	1	no	—
153	C₂₉×#121	—	2	2	no	—
154	C₂₉×#121	—	2	4	no	—
155	C₂₉×#121	—	2	4	no	—
156	C₂₉×#121	—	2	2	no	—
157	C₂₉×#121	C₂³	1	2	yes	—
158	C₂₉×#121	C₂³	1	2	yes	—
159	C₂₉×#121	C₂³	1	4	yes	—
160	C₂₉×#121	C₂³	1	2	yes	complemented
161	C₂₉×#120	—	2	2	no	—
162	C₂₉×#120	—	2	4	no	—
163	C₂₉×#120	—	2	4	no	—
164	C₂₉×#120	—	2	2	no	—
165	C₄×Q₈×C₂₉	C₂³	1	2	yes	complemented
166	C₄×D₄×C₂₉	—	2	2	no	—
167	C₄×D₄×C₂₉	—	2	2	no	—
168	C₄×D₄×C₂₉	—	2	2	no	—
169	C₄×D₄×C₂₉	—	2	2	no	—
170	C₄×D₄×C₂₉	—	2	2	no	—
171	C₄×D₄×C₂₉	—	2	2	no	—
172	C₄×D₄×C₂₉	D₄	1	2	yes	—
173	C₄×D₄×C₂₉	D₄	1	2	yes	—
174	C₄×D₄×C₂₉	C₂³	1	4	yes	—
175	C₄×D₄×C₂₉	C₂³	1	2	yes	—
176	C₄×D₄×C₂₉	C₂³	1	2	yes	—
177	C₄×D₄×C₂₉	C₂³	1	2	yes	complemented
178	C₂₉×#117	—	2	2	no	—
179	C₂₉×#117	—	2	2	no	—
180	C₂₉×#117	C₂³	1	2	yes	complemented
181	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
182	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
183	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
188	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
189	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
190	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
191	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
192	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
193	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
194	C₂×C₂²⋊C₄×C₂₉	—	2	4	no	—
195	C₂×C₂²⋊C₄×C₂₉	—	2	4	no	—
196	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
197	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
199	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
200	C₂₉×#107	C₂³	1	4	yes	complemented
201	C₂₉×#106	C₂³	1	4	yes	complemented
202	C₂₉×C₄⋊C₈	C₂³	1	4	yes	complemented
203	C₂₉×#103	C₂³	1	4	yes	complemented
204	C₂₉×#103	C₂³	1	4	yes	complemented
205	C₂₉×#103	C₂³	1	4	yes	complemented
206	C₂₉×#102	C₂³	1	4	yes	—
207	C₂₉×#102	C₂³	1	4	yes	—
208	C₂₉×#102	C₂³	1	4	yes	—
209	C₂₉×#102	C₂³	1	4	yes	—
210	C₂₉×#102	C₂³	1	4	yes	complemented
211	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
212	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
213	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
214	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
215	C₂₉×C₂²⋊C₈	C₂³	1	4	yes	complemented
216	C₄×C₈×C₂₉	C₂³	1	4	yes	complemented
217	C₂⁴×C₂₉	—	2	1	no	—
218	C₂⁴×C₂₉	—	2	1	no	—
219	C₂⁴×C₂₉	—	2	2	no	—
220	C₂⁴×C₂₉	—	2	2	no	—
221	C₂⁴×C₂₉	—	2	1	no	—
222	C₂⁴×C₂₉	—	4	4	no	—
223	C₂⁴×C₂₉	—	4	4	no	—
224	C₂⁴×C₂₉	—	8	2	no	—
225	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
226	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
227	#41×C₂₉	—	2	8	no	—
228	#41×C₂₉	—	4	4	no	—
229	#41×C₂₉	—	4	4	no	—
230	#41×C₂₉	—	4	8	no	—
231	C₂×Q₈×C₂₉	—	2	1	no	—
232	C₂×Q₈×C₂₉	—	2	1	no	—
233	C₂×Q₈×C₂₉	—	4	2	no	—
234	C₂×Q₈×C₂₉	—	4	2	no	—
235	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
236	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
237	C₂×D₄×C₂₉	—	2	4	no	—
238	C₂×D₄×C₂₉	—	2	4	no	—
239	C₂×D₄×C₂₉	—	2	4	no	—
240	C₂×D₄×C₂₉	—	2	4	no	—
241	C₂×D₄×C₂₉	—	2	2	no	—
242	C₂×D₄×C₂₉	—	2	2	no	—
243	C₂×D₄×C₂₉	—	2	4	no	—
244	C₂×D₄×C₂₉	—	2	2	no	—
245	C₂×D₄×C₂₉	—	2	4	no	—
246	C₂×D₄×C₂₉	—	2	2	no	—
247	C₂×D₄×C₂₉	—	2	1	no	—
248	C₂×D₄×C₂₉	—	2	2	no	—
249	C₂×D₄×C₂₉	—	2	2	no	—
250	C₂×D₄×C₂₉	—	2	1	no	—
251	C₂×D₄×C₂₉	—	2	1	no	—
252	C₂×D₄×C₂₉	—	4	2	no	—
253	C₂×D₄×C₂₉	—	4	2	no	—
254	C₂×D₄×C₂₉	—	4	2	no	—
255	C₂×D₄×C₂₉	—	4	2	no	—
256	C₂×D₄×C₂₉	—	4	4	no	—
257	C₂×D₄×C₂₉	—	4	4	no	—
258	C₂×D₄×C₂₉	—	4	4	no	—
259	C₂×D₄×C₂₉	—	4	4	no	—
260	C₂×D₄×C₂₉	—	4	4	no	—
261	C₂×D₄×C₂₉	—	8	2	no	—
262	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
263	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
264	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
265	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
266	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₂₉	—	2	1	no	—
268	C₂²×C₄×C₂₉	—	2	1	no	—
269	C₂²×C₄×C₂₉	—	2	1	no	—
270	C₂²×C₄×C₂₉	—	2	1	no	—
271	C₂²×C₄×C₂₉	—	2	1	no	—
272	C₂²×C₄×C₂₉	—	2	4	no	—
273	C₂²×C₄×C₂₉	—	2	4	no	—
274	C₂²×C₄×C₂₉	—	2	2	no	—
275	C₂²×C₄×C₂₉	—	2	2	no	—
276	C₂²×C₄×C₂₉	—	4	2	no	—
277	C₂²×C₄×C₂₉	—	4	2	no	—
278	C₂²×C₄×C₂₉	—	4	4	no	—
279	C₂²×C₄×C₂₉	—	8	2	no	—
280	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
291	Q₁₆×C₂₉	—	4	4	no	—
292	SD₁₆×C₂₉	—	2	8	no	—
293	SD₁₆×C₂₉	—	4	4	no	—
294	SD₁₆×C₂₉	—	4	4	no	—
295	D₈×C₂₉	—	2	8	no	—
296	D₈×C₂₉	—	4	4	no	—
297	C₂×C₈×C₂₉	—	4	2	no	—
298	C₂×C₈×C₂₉	—	4	2	no	—
299	C₂×C₈×C₂₉	—	4	4	no	—
300	C₂×C₈×C₂₉	C₂⁴	1	4	yes	—
301	C₂×C₈×C₂₉	C₂⁴	1	4	yes	—
302	C₄⋊C₄×C₂₉	—	2	2	no	—
303	C₄⋊C₄×C₂₉	—	2	2	no	—
304	C₄⋊C₄×C₂₉	—	2	2	no	—
305	C₄⋊C₄×C₂₉	—	2	2	no	—
306	C₄⋊C₄×C₂₉	—	2	1	no	—
307	C₄⋊C₄×C₂₉	—	2	1	no	—
308	C₄⋊C₄×C₂₉	—	2	1	no	—
309	C₄⋊C₄×C₂₉	—	2	2	no	—
310	C₄⋊C₄×C₂₉	—	2	2	no	—
311	C₄⋊C₄×C₂₉	—	2	2	no	—
312	C₄⋊C₄×C₂₉	—	2	2	no	—
313	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
314	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
315	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
316	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
317	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
318	C₂²⋊C₄×C₂₉	—	2	2	no	—
319	C₂²⋊C₄×C₂₉	—	2	2	no	—
320	C₂²⋊C₄×C₂₉	—	2	2	no	—
321	C₂²⋊C₄×C₂₉	—	2	2	no	—
322	C₂²⋊C₄×C₂₉	—	2	2	no	—
323	C₂²⋊C₄×C₂₉	—	2	2	no	—
324	C₂²⋊C₄×C₂₉	—	2	4	no	—
325	C₂²⋊C₄×C₂₉	—	2	4	no	—
326	C₂²⋊C₄×C₂₉	—	2	2	no	—
327	C₂²⋊C₄×C₂₉	—	2	2	no	—
328	C₂²⋊C₄×C₂₉	—	2	2	no	—
329	C₂²⋊C₄×C₂₉	—	2	4	no	—
330	C₂²⋊C₄×C₂₉	—	2	4	no	—
331	C₂²⋊C₄×C₂₉	—	2	2	no	—
332	C₂²⋊C₄×C₂₉	—	2	2	no	—
333	C₂²⋊C₄×C₂₉	—	2	2	no	—
334	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
335	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
336	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
337	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
338	C₄²×C₂₉	—	2	2	no	—
339	C₄²×C₂₉	—	2	2	no	—
340	C₄²×C₂₉	C₂×D₄	1	2	yes	—
341	C₄²×C₂₉	C₂⁴	1	2	yes	—
342	#61561	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
343	C₂³×C₂₉	—	2	4	no	—
344	C₂³×C₂₉	—	2	2	no	—
345	C₂³×C₂₉	—	2	2	no	—
346	C₂³×C₂₉	—	2	2	no	—
347	C₂³×C₂₉	—	2	2	no	—
348	C₂³×C₂₉	—	4	1	no	—
349	C₂³×C₂₉	—	4	1	no	—
350	C₂³×C₂₉	—	4	1	no	—
351	C₂³×C₂₉	—	4	1	no	—
352	C₂³×C₂₉	—	4	4	no	—
353	C₂³×C₂₉	—	4	4	no	—
354	C₂³×C₂₉	—	4	2	no	—
355	C₂³×C₂₉	—	4	2	no	—
356	C₂³×C₂₉	—	4	2	no	—
357	C₂³×C₂₉	—	4	2	no	—
358	C₂³×C₂₉	—	4	4	no	—
359	C₂³×C₂₉	—	4	4	no	—
360	C₂³×C₂₉	—	4	2	no	—
361	C₂³×C₂₉	—	4	2	no	—
362	C₂³×C₂₉	—	8	2	no	—
363	C₂³×C₂₉	—	8	2	no	—
364	C₂³×C₂₉	—	8	1	no	—
365	C₂³×C₂₉	—	8	1	no	—
366	C₂³×C₂₉	—	8	16	no	—
367	C₂³×C₂₉	#135	1	4	yes	complemented
368	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
369	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
370	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
371	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
372	Q₈×C₂₉	—	2	4	no	—
373	Q₈×C₂₉	—	2	4	no	—
374	Q₈×C₂₉	—	4	2	no	—
375	Q₈×C₂₉	—	8	1	no	—
376	D₄×C₂₉	—	2	4	no	—
377	D₄×C₂₉	—	2	4	no	—
378	D₄×C₂₉	—	2	4	no	—
379	D₄×C₂₉	—	2	2	no	—
380	D₄×C₂₉	—	2	4	no	—
381	D₄×C₂₉	—	2	2	no	—
382	D₄×C₂₉	—	2	2	no	—
383	D₄×C₂₉	—	4	4	no	—
384	D₄×C₂₉	—	4	4	no	—
385	D₄×C₂₉	—	4	2	no	—
386	D₄×C₂₉	—	4	8	no	—
387	D₄×C₂₉	—	4	4	no	—
388	D₄×C₂₉	—	4	4	no	—
389	D₄×C₂₉	—	8	1	no	—
390	D₄×C₂₉	—	8	2	no	—
391	D₄×C₂₉	—	8	4	no	—
392	D₄×C₂₉	—	8	2	no	—
393	D₄×C₂₉	H(5,𝔽₂)	1	4	yes	—
394	C₂×C₄×C₂₉	—	2	2	no	—
395	C₂×C₄×C₂₉	—	2	2	no	—
396	C₂×C₄×C₂₉	—	2	2	no	—
397	C₂×C₄×C₂₉	—	2	4	no	—
398	C₂×C₄×C₂₉	—	2	2	no	—
399	C₂×C₄×C₂₉	—	2	2	no	—
400	C₂×C₄×C₂₉	—	2	2	no	—
401	C₂×C₄×C₂₉	—	2	2	no	—
402	C₂×C₄×C₂₉	—	2	2	no	—
403	C₂×C₄×C₂₉	—	2	2	no	—
404	C₂×C₄×C₂₉	—	4	1	no	—
405	C₂×C₄×C₂₉	—	4	1	no	—
406	C₂×C₄×C₂₉	—	4	1	no	—
407	C₂×C₄×C₂₉	—	4	1	no	—
408	C₂×C₄×C₂₉	—	4	2	no	—
409	C₂×C₄×C₂₉	—	4	1	no	—
410	C₂×C₄×C₂₉	—	4	8	no	—
411	C₂×C₄×C₂₉	—	4	2	no	—
412	C₂×C₄×C₂₉	—	4	2	no	—
413	C₂×C₄×C₂₉	—	4	2	no	—
414	C₂×C₄×C₂₉	—	8	2	no	—
415	C₂×C₄×C₂₉	—	8	4	no	—
416	C₂×C₄×C₂₉	—	8	2	no	—
417	C₂×C₄×C₂₉	—	8	1	no	—
418	C₂×C₄×C₂₉	—	8	1	no	—
419	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
421	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
423	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
426	C₈×C₂₉	—	2	4	no	—
427	C₈×C₂₉	—	2	4	no	—
428	#3505	C₂×C₂₉	1	1	yes	characteristic, complemented
429	C₂×#546	C₂×C₂₉	1	1	yes	characteristic, complemented
430	#3297	C₂×C₂₉	1	4	yes	complemented
431	#3296	C₂×C₂₉	1	4	yes	complemented
432	#3282	C₂×C₂₉	1	4	yes	complemented
433	#3280	C₂×C₂₉	1	4	yes	complemented
434	#3211	C₂×C₂₉	1	2	yes	complemented
435	#3189	C₂×C₂₉	1	1	yes	characteristic, complemented
436	#3188	C₂×C₂₉	1	2	yes	complemented
437	#3187	C₂×C₂₉	1	1	yes	characteristic, complemented
438	#3105	C₂×C₂₉	1	2	yes	complemented
439	#3002	C₂×C₂₉	1	2	yes	complemented
440	C₂×#450	C₂×C₂₉	1	1	yes	characteristic, complemented
441	C₂×#447	C₂×C₂₉	1	1	yes	characteristic, complemented
442	#2972	C₂×C₂₉	1	1	yes	characteristic, complemented
443	C₂²×C₂₉	—	2	1	no	—
444	C₂²×C₂₉	—	2	1	no	—
445	C₂²×C₂₉	—	2	1	no	—
446	C₂²×C₂₉	—	2	1	no	—
447	C₂²×C₂₉	—	2	1	no	—
448	C₂²×C₂₉	—	2	1	no	—
449	C₂²×C₂₉	—	2	2	no	—
450	C₂²×C₂₉	—	2	2	no	—
451	C₂²×C₂₉	—	2	4	no	—
452	C₂²×C₂₉	—	2	2	no	—
453	C₂²×C₂₉	—	4	4	no	—
454	C₂²×C₂₉	—	4	8	no	—
455	C₂²×C₂₉	—	4	2	no	—
456	C₂²×C₂₉	—	4	2	no	—
457	C₂²×C₂₉	—	4	2	no	—
458	C₂²×C₂₉	—	4	2	no	—
459	C₂²×C₂₉	—	4	2	no	—
460	C₂²×C₂₉	—	4	2	no	—
461	C₂²×C₂₉	—	4	2	no	—
462	C₂²×C₂₉	—	4	2	no	—
463	C₂²×C₂₉	—	8	2	no	—
464	C₂²×C₂₉	—	8	8	no	—
465	C₂²×C₂₉	—	8	8	no	—
466	C₂²×C₂₉	—	8	4	no	—
467	C₂²×C₂₉	—	16	2	no	—
468	C₂²×C₂₉	C₂×#135	1	2	yes	—
469	C₂²×C₂₉	C₂×#135	1	2	yes	—
470	C₂²×C₂₉	C₂×#135	1	2	yes	—
471	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
472	C₄×C₂₉	—	2	2	no	—
473	C₄×C₂₉	—	2	2	no	—
474	C₄×C₂₉	—	2	1	no	—
475	C₄×C₂₉	—	2	1	no	—
476	C₄×C₂₉	—	2	1	no	—
477	C₄×C₂₉	—	2	2	no	—
478	C₄×C₂₉	—	4	2	no	—
479	C₄×C₂₉	—	4	2	no	—
480	C₄×C₂₉	—	4	2	no	—
481	C₄×C₂₉	—	4	2	no	—
482	C₄×C₂₉	—	4	2	no	—
483	C₄×C₂₉	C₂×H(5,𝔽₂)	1	2	yes	—
484	C₂²×#41	C₂²×C₂₉	1	1	yes	characteristic, complemented
485	C₂³×D₄	C₂²×C₂₉	1	1	yes	characteristic
486	C₂×#135	C₂²×C₂₉	1	4	yes	complemented
487	C₂²×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
488	C₂²×D₈	C₂²×C₂₉	1	2	yes	complemented
489	#553	—	2	2	no	—
490	#553	C₂²×C₂₉	1	2	yes	complemented
491	#552	C₂²×C₂₉	1	2	yes	complemented
492	#551	—	2	2	no	—
493	#548	C₂²×C₂₉	1	2	yes	complemented
494	#546	—	2	2	no	—
495	#546	—	2	2	no	—
496	#546	C₂²×C₂₉	1	4	yes	—
497	#546	C₂²×C₂₉	1	4	yes	complemented
498	#546	C₂²×C₂₉	1	2	yes	complemented
499	#539	—	2	1	no	—
500	#538	—	2	1	no	—
501	#534	—	2	1	no	—
502	#529	C₂²×C₂₉	1	2	yes	complemented
503	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic, complemented
504	#525	C₂²×C₂₉	1	2	yes	complemented
505	C₂×#123	—	2	1	no	—
506	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
507	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
508	C₂×#121	—	2	1	no	—
509	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic
510	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic, complemented
511	C₂×#120	—	2	1	no	—
512	#518	—	2	1	no	—
513	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
514	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
515	C₂²×C₂²⋊C₄	—	2	1	no	—
516	#495	C₂²×C₂₉	1	4	yes	complemented
517	#488	C₂²×C₂₉	1	4	yes	complemented
518	#484	C₂²×C₂₉	1	2	yes	complemented
519	#484	C₂²×C₂₉	1	2	yes	complemented
520	#483	C₂²×C₂₉	1	2	yes	complemented
521	#482	C₂²×C₂₉	1	4	yes	complemented
522	#481	C₂²×C₂₉	1	2	yes	complemented
523	#478	C₂²×C₂₉	1	4	yes	complemented
524	#467	C₂²×C₂₉	1	4	yes	complemented
525	#466	C₂²×C₂₉	1	4	yes	complemented
526	#465	C₂²×C₂₉	1	4	yes	complemented
527	#465	C₂²×C₂₉	1	4	yes	complemented
528	#464	C₂²×C₂₉	1	4	yes	complemented
529	#463	C₂²×C₂₉	1	4	yes	complemented
530	#463	C₂²×C₂₉	1	4	yes	complemented
531	#452	C₂²×C₂₉	1	4	yes	complemented
532	#451	C₂²×C₂₉	1	2	yes	complemented
533	#451	C₂²×C₂₉	1	2	yes	complemented
534	#450	C₂²×C₂₉	1	2	yes	complemented
535	#450	C₂²×C₂₉	1	2	yes	complemented
536	#450	C₂²×C₂₉	1	4	yes	complemented
537	#450	C₂²×C₂₉	1	2	yes	complemented
538	#449	C₂²×C₂₉	1	4	yes	complemented
539	#449	C₂²×C₂₉	1	4	yes	complemented
540	#448	C₂²×C₂₉	1	2	yes	complemented
541	#447	C₂²×C₂₉	1	2	yes	—
542	#447	C₂²×C₂₉	1	2	yes	—
543	#447	C₂²×C₂₉	1	4	yes	complemented
544	C₄×SD₁₆	C₂²×C₂₉	1	4	yes	complemented
545	C₄×D₈	C₂²×C₂₉	1	4	yes	complemented
546	C₈×D₄	C₂²×C₂₉	1	4	yes	complemented
547	C₈×D₄	C₂²×C₂₉	1	4	yes	complemented
548	#431	C₂²×C₂₉	1	2	yes	complemented
549	#416	C₂²×C₂₉	1	4	yes	complemented
550	C₂×#102	C₂²×C₂₉	1	2	yes	complemented
551	C₂×#102	C₂²×C₂₉	1	2	yes	complemented
552	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
553	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
554	C₂×C₂²⋊C₈	C₂²×C₂₉	1	2	yes	complemented
555	C₂×C₂₉	—	2	2	no	—
556	C₂×C₂₉	—	2	2	no	—
557	C₂×C₂₉	—	2	2	no	—
558	C₂×C₂₉	—	4	2	no	—
559	C₂×C₂₉	—	4	4	no	—
560	C₂×C₂₉	—	8	2	no	—
561	C₂×C₂₉	—	8	2	no	—
562	C₂×C₂₉	#3484	1	1	yes	characteristic
563	C₂×C₂₉	C₂²×#135	1	1	yes	characteristic
564	C₂×C₂₉	#3585	1	1	yes	characteristic
565	C₂⁵	—	2	1	no	—
566	C₂×#41	—	2	2	no	—
567	C₂×#41	—	4	4	no	—
568	C₂×#41	C₂³×C₂₉	1	4	yes	—
569	C₂×#41	C₂³×C₂₉	1	2	yes	complemented
570	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
571	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
572	C₂²×D₄	—	2	1	no	—
573	C₂²×D₄	—	2	1	no	—
574	C₂²×D₄	—	2	1	no	—
575	C₂²×D₄	—	2	1	no	—
576	C₂²×D₄	—	2	1	no	—
577	C₂²×D₄	—	2	1	no	—
578	C₂²×D₄	—	4	4	no	—
579	C₂²×D₄	D₄×C₂₉	1	1	yes	characteristic
580	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
581	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
582	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
583	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
584	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
585	C₂³×C₄	—	2	1	no	—
586	C₂³×C₄	—	2	1	no	—
587	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
588	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
589	#135	—	4	8	no	—
590	C₂×Q₁₆	C₂³×C₂₉	1	4	yes	complemented
591	C₂×SD₁₆	—	4	4	no	—
592	C₂×SD₁₆	C₂³×C₂₉	1	4	yes	—
593	C₂×SD₁₆	C₂³×C₂₉	1	4	yes	—
594	C₂×SD₁₆	C₂³×C₂₉	1	4	yes	complemented
595	C₂×D₈	—	4	4	no	—
596	C₂×D₈	C₂³×C₂₉	1	4	yes	—
597	C₂×D₈	C₂³×C₂₉	1	4	yes	—
598	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
599	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
600	C₂²×C₈	C₂³×C₂₉	1	4	yes	complemented
601	#126	—	2	2	no	—
602	#126	—	2	2	no	—
603	#126	—	2	2	no	—
604	#125	—	2	2	no	—
605	#125	C₂³×C₂₉	1	2	yes	complemented
606	#124	—	2	2	no	—
607	#124	—	2	2	no	—
608	#124	C₂³×C₂₉	1	4	yes	—
609	#124	C₂³×C₂₉	1	2	yes	complemented
610	#123	—	2	2	no	—
611	#123	—	2	2	no	—
612	#123	—	2	2	no	—
613	#123	—	2	4	no	—
614	#123	—	2	4	no	—
615	#123	—	2	2	no	—
616	#123	—	2	2	no	—
617	C₂²⋊Q₈	—	2	1	no	—
618	C₂²⋊Q₈	—	2	1	no	—
619	C₂²⋊Q₈	—	2	1	no	—
620	C₂²⋊Q₈	—	2	1	no	—
621	C₂²⋊Q₈	—	2	2	no	—
622	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
623	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
624	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
625	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
626	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	complemented
627	#121	—	2	2	no	—
628	#121	—	2	2	no	—
629	#121	—	2	1	no	—
630	#121	—	2	1	no	—
631	#121	—	2	2	no	—
632	#121	—	2	4	no	—
633	#121	—	2	4	no	—
634	#121	—	2	2	no	—
635	#121	C₂³×C₂₉	1	2	yes	—
636	#121	C₂³×C₂₉	1	2	yes	—
637	#121	C₂³×C₂₉	1	4	yes	—
638	#121	C₂³×C₂₉	1	2	yes	complemented
639	#120	—	2	2	no	—
640	#120	—	2	4	no	—
641	#120	—	2	4	no	—
642	#120	—	2	2	no	—
643	C₄×Q₈	C₂³×C₂₉	1	2	yes	complemented
644	C₄×D₄	—	2	2	no	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	—	2	2	no	—
648	C₄×D₄	—	2	2	no	—
649	C₄×D₄	—	2	2	no	—
650	C₄×D₄	D₄×C₂₉	1	2	yes	—
651	C₄×D₄	D₄×C₂₉	1	2	yes	—
652	C₄×D₄	C₂³×C₂₉	1	4	yes	—
653	C₄×D₄	C₂³×C₂₉	1	2	yes	—
654	C₄×D₄	C₂³×C₂₉	1	2	yes	—
655	C₄×D₄	C₂³×C₂₉	1	2	yes	complemented
656	#117	—	2	2	no	—
657	#117	—	2	2	no	—
658	#117	C₂³×C₂₉	1	2	yes	complemented
659	C₂×C₄⋊C₄	—	2	1	no	—
660	C₂×C₄⋊C₄	—	2	1	no	—
661	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
662	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
663	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
664	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
665	C₂×C₂²⋊C₄	—	2	1	no	—
666	C₂×C₂²⋊C₄	—	2	1	no	—
667	C₂×C₂²⋊C₄	—	2	1	no	—
668	C₂×C₂²⋊C₄	—	2	1	no	—
669	C₂×C₂²⋊C₄	—	2	1	no	—
670	C₂×C₂²⋊C₄	—	2	1	no	—
671	C₂×C₂²⋊C₄	—	2	1	no	—
672	C₂×C₂²⋊C₄	—	2	4	no	—
673	C₂×C₂²⋊C₄	—	2	4	no	—
674	C₂×C₂²⋊C₄	—	2	2	no	—
675	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
676	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
678	#107	C₂³×C₂₉	1	4	yes	complemented
679	#106	C₂³×C₂₉	1	4	yes	complemented
680	C₄⋊C₈	C₂³×C₂₉	1	4	yes	complemented
681	#103	C₂³×C₂₉	1	4	yes	complemented
682	#103	C₂³×C₂₉	1	4	yes	complemented
683	#103	C₂³×C₂₉	1	4	yes	complemented
684	#102	C₂³×C₂₉	1	4	yes	—
685	#102	C₂³×C₂₉	1	4	yes	—
686	#102	C₂³×C₂₉	1	4	yes	—
687	#102	C₂³×C₂₉	1	4	yes	—
688	#102	C₂³×C₂₉	1	4	yes	complemented
689	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
690	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
691	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
692	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
693	C₂²⋊C₈	C₂³×C₂₉	1	4	yes	complemented
694	C₄×C₈	C₂³×C₂₉	1	4	yes	complemented
695	C₂₉	#61561	1	1	yes	characteristic, direct product factor, Sylow
696	C₂⁴	—	2	1	no	—
697	C₂⁴	—	2	1	no	—
698	C₂⁴	—	2	2	no	—
699	C₂⁴	—	2	2	no	—
700	C₂⁴	—	2	1	no	—
701	C₂⁴	—	4	4	no	—
702	C₂⁴	—	4	4	no	—
703	C₂⁴	—	8	2	no	—
704	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
705	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
706	#41	—	2	8	no	—
707	#41	—	4	4	no	—
708	#41	—	4	4	no	—
709	#41	—	4	8	no	—
710	C₂×Q₈	—	2	1	no	—
711	C₂×Q₈	—	2	1	no	—
712	C₂×Q₈	—	4	2	no	—
713	C₂×Q₈	—	4	2	no	—
714	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
715	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	4	no	—
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	2	4	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	4	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	2	no	—
729	C₂×D₄	—	2	1	no	—
730	C₂×D₄	—	2	1	no	—
731	C₂×D₄	—	4	2	no	—
732	C₂×D₄	—	4	2	no	—
733	C₂×D₄	—	4	2	no	—
734	C₂×D₄	—	4	2	no	—
735	C₂×D₄	—	4	4	no	—
736	C₂×D₄	—	4	4	no	—
737	C₂×D₄	—	4	4	no	—
738	C₂×D₄	—	4	4	no	—
739	C₂×D₄	—	4	4	no	—
740	C₂×D₄	—	8	2	no	—
741	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
742	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
743	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
744	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
745	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
746	C₂²×C₄	—	2	1	no	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	1	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	4	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	4	2	no	—
756	C₂²×C₄	—	4	2	no	—
757	C₂²×C₄	—	4	4	no	—
758	C₂²×C₄	—	8	2	no	—
759	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
760	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
761	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
762	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
763	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
764	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
765	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
770	Q₁₆	—	4	4	no	—
771	SD₁₆	—	2	8	no	—
772	SD₁₆	—	4	4	no	—
773	SD₁₆	—	4	4	no	—
774	D₈	—	2	8	no	—
775	D₈	—	4	4	no	—
776	C₂×C₈	—	4	2	no	—
777	C₂×C₈	—	4	2	no	—
778	C₂×C₈	—	4	4	no	—
779	C₂×C₈	C₂⁴×C₂₉	1	4	yes	—
780	C₂×C₈	C₂⁴×C₂₉	1	4	yes	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	1	no	—
786	C₄⋊C₄	—	2	1	no	—
787	C₄⋊C₄	—	2	1	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
793	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
794	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
795	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
796	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
814	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
815	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
816	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
817	C₄²	—	2	2	no	—
818	C₄²	—	2	2	no	—
819	C₄²	C₂×D₄×C₂₉	1	2	yes	—
820	C₄²	C₂⁴×C₂₉	1	2	yes	—
821	C₂³	—	2	4	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	4	1	no	—
827	C₂³	—	4	1	no	—
828	C₂³	—	4	1	no	—
829	C₂³	—	4	1	no	—
830	C₂³	—	4	4	no	—
831	C₂³	—	4	4	no	—
832	C₂³	—	4	2	no	—
833	C₂³	—	4	2	no	—
834	C₂³	—	4	2	no	—
835	C₂³	—	4	2	no	—
836	C₂³	—	4	4	no	—
837	C₂³	—	4	4	no	—
838	C₂³	—	4	2	no	—
839	C₂³	—	4	2	no	—
840	C₂³	—	8	2	no	—
841	C₂³	—	8	2	no	—
842	C₂³	—	8	1	no	—
843	C₂³	—	8	1	no	—
844	C₂³	—	8	16	no	—
845	C₂³	C₂₉×#135	1	4	yes	complemented
846	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
847	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
848	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
849	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
850	Q₈	—	2	4	no	—
851	Q₈	—	2	4	no	—
852	Q₈	—	4	2	no	—
853	Q₈	—	8	1	no	—
854	D₄	—	2	4	no	—
855	D₄	—	2	4	no	—
856	D₄	—	2	4	no	—
857	D₄	—	2	2	no	—
858	D₄	—	2	4	no	—
859	D₄	—	2	2	no	—
860	D₄	—	2	2	no	—
861	D₄	—	4	4	no	—
862	D₄	—	4	4	no	—
863	D₄	—	4	2	no	—
864	D₄	—	4	8	no	—
865	D₄	—	4	4	no	—
866	D₄	—	4	4	no	—
867	D₄	—	8	1	no	—
868	D₄	—	8	4	no	—
869	D₄	—	8	2	no	—
870	D₄	—	8	2	no	—
871	D₄	C₂₉×H(5,𝔽₂)	1	4	yes	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	4	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	4	1	no	—
883	C₂×C₄	—	4	1	no	—
884	C₂×C₄	—	4	1	no	—
885	C₂×C₄	—	4	1	no	—
886	C₂×C₄	—	4	2	no	—
887	C₂×C₄	—	4	1	no	—
888	C₂×C₄	—	4	8	no	—
889	C₂×C₄	—	4	2	no	—
890	C₂×C₄	—	4	2	no	—
891	C₂×C₄	—	4	2	no	—
892	C₂×C₄	—	8	4	no	—
893	C₂×C₄	—	8	2	no	—
894	C₂×C₄	—	8	2	no	—
895	C₂×C₄	—	8	1	no	—
896	C₂×C₄	—	8	1	no	—
897	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
898	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
899	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
901	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
903	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
904	C₈	—	2	4	no	—
905	C₈	—	2	4	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	1	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	4	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	4	4	no	—
917	C₂²	—	4	8	no	—
918	C₂²	—	4	2	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	8	2	no	—
927	C₂²	—	8	8	no	—
928	C₂²	—	8	8	no	—
929	C₂²	—	8	4	no	—
930	C₂²	—	16	2	no	—
931	C₂²	C₂×C₂₉×#135	1	2	yes	—
932	C₂²	C₂×C₂₉×#135	1	2	yes	—
933	C₂²	C₂×C₂₉×#135	1	2	yes	—
934	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
935	C₄	—	2	2	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	1	no	—
939	C₄	—	2	2	no	—
940	C₄	—	2	2	no	—
941	C₄	—	4	2	no	—
942	C₄	—	4	2	no	—
943	C₄	—	4	2	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	2	no	—
946	C₄	C₂×C₂₉×H(5,𝔽₂)	1	2	yes	—
947	C₂	—	2	2	no	—
948	C₂	—	2	2	no	—
949	C₂	—	2	2	no	—
950	C₂	—	4	2	no	—
951	C₂	—	4	4	no	—
952	C₂	—	8	2	no	—
953	C₂	—	8	2	no	—
954	C₂	C₂₉×#3484	1	1	yes	characteristic
955	C₂	C₂²×C₂₉×#135	1	1	yes	characteristic
956	C₂	C₂₉×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄×D₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3505	C₂	semidirect
2. C₂×C₂₉×#546	C₂	semidirect
3. C₂₉×#3297	C₂	semidirect
4. C₂₉×#3296	C₂	semidirect
5. C₂₉×#3282	C₂	semidirect
6. C₂₉×#3280	C₂	semidirect
7. C₂₉×#3211	C₂	semidirect
8. C₂₉×#3189	C₂	semidirect
9. C₂₉×#3188	C₂	semidirect
10. C₂₉×#3187	C₂	semidirect
11. C₂₉×#3105	C₂	semidirect
12. C₂₉×#3002	C₂	semidirect
13. C₂×C₂₉×#450	C₂	semidirect
14. C₂×C₂₉×#447	C₂	semidirect
15. C₂₉×#2972	C₂	semidirect
16. C₂²×#41×C₂₉	C₂²	semidirect
18. C₂×C₂₉×#135	C₂²	semidirect
19. C₂²×SD₁₆×C₂₉	C₂²	semidirect
20. C₂²×D₈×C₂₉	C₂²	semidirect
22. C₂₉×#553	C₂²	semidirect
23. C₂₉×#552	C₂²	semidirect
25. C₂₉×#548	C₂²	semidirect
29. C₂₉×#546	C₂²	semidirect
30. C₂₉×#546	C₂²	semidirect
34. C₂₉×#529	C₂²	semidirect
35. C₂×C₂₉×#124	C₂²	semidirect
36. C₂₉×#525	C₂²	semidirect
42. C₂×C₂₉×#121	C₂²	semidirect
46. C₂×C₄×D₄×C₂₉	C₂²	semidirect
48. C₂₉×#495	C₂²	semidirect
49. C₂₉×#488	C₂²	semidirect
50. C₂₉×#484	C₂²	semidirect
51. C₂₉×#484	C₂²	semidirect
52. C₂₉×#483	C₂²	semidirect
53. C₂₉×#482	C₂²	semidirect
54. C₂₉×#481	C₂²	semidirect
55. C₂₉×#478	C₂²	semidirect
56. C₂₉×#467	C₂²	semidirect
57. C₂₉×#466	C₂²	semidirect
58. C₂₉×#465	C₂²	semidirect
59. C₂₉×#465	C₂²	semidirect
60. C₂₉×#464	C₂²	semidirect
61. C₂₉×#463	C₂²	semidirect
62. C₂₉×#463	C₂²	semidirect
63. C₂₉×#452	C₂²	semidirect
64. C₂₉×#451	C₂²	semidirect
65. C₂₉×#451	C₂²	semidirect
66. C₂₉×#450	C₂²	semidirect
67. C₂₉×#450	C₂²	semidirect
68. C₂₉×#450	C₂²	semidirect
69. C₂₉×#450	C₂²	semidirect
70. C₂₉×#449	C₂²	semidirect
71. C₂₉×#449	C₂²	semidirect
72. C₂₉×#448	C₂²	semidirect
75. C₂₉×#447	C₂²	semidirect
76. C₄×SD₁₆×C₂₉	C₂²	semidirect
77. C₄×D₈×C₂₉	C₂²	semidirect
78. C₈×D₄×C₂₉	C₂²	semidirect
79. C₈×D₄×C₂₉	C₂²	semidirect
80. C₂₉×#431	C₂²	semidirect
81. C₂₉×#416	C₂²	semidirect
82. C₂×C₂₉×#102	C₂²	semidirect
83. C₂×C₂₉×#102	C₂²	semidirect
86. C₂×C₂₉×C₂²⋊C₈	C₂²	semidirect
91. C₂×#41×C₂₉	C₂³	semidirect
112. C₂×Q₁₆×C₂₉	C₂³	semidirect
116. C₂×SD₁₆×C₂₉	C₂³	semidirect
122. C₂²×C₈×C₂₉	C₂³	semidirect
127. C₂₉×#125	C₂³	semidirect
131. C₂₉×#124	C₂³	semidirect
148. C₂₉×C₂²⋊Q₈	C₂³	semidirect
160. C₂₉×#121	C₂³	semidirect
165. C₄×Q₈×C₂₉	C₂³	semidirect
177. C₄×D₄×C₂₉	C₂³	semidirect
180. C₂₉×#117	C₂³	semidirect
200. C₂₉×#107	C₂³	semidirect
201. C₂₉×#106	C₂³	semidirect
202. C₂₉×C₄⋊C₈	C₂³	semidirect
203. C₂₉×#103	C₂³	semidirect
204. C₂₉×#103	C₂³	semidirect
205. C₂₉×#103	C₂³	semidirect
210. C₂₉×#102	C₂³	semidirect
215. C₂₉×C₂²⋊C₈	C₂³	semidirect
216. C₄×C₈×C₂₉	C₂³	semidirect
342. #61561	C₂₉	direct (N × H)
367. C₂³×C₂₉	#135	semidirect
428. #3505	C₂×C₂₉	semidirect
429. C₂×#546	C₂×C₂₉	semidirect
430. #3297	C₂×C₂₉	semidirect
431. #3296	C₂×C₂₉	semidirect
432. #3282	C₂×C₂₉	semidirect
433. #3280	C₂×C₂₉	semidirect
434. #3211	C₂×C₂₉	semidirect
435. #3189	C₂×C₂₉	semidirect
436. #3188	C₂×C₂₉	semidirect
437. #3187	C₂×C₂₉	semidirect
438. #3105	C₂×C₂₉	semidirect
439. #3002	C₂×C₂₉	semidirect
440. C₂×#450	C₂×C₂₉	semidirect
441. C₂×#447	C₂×C₂₉	semidirect
442. #2972	C₂×C₂₉	semidirect
484. C₂²×#41	C₂²×C₂₉	semidirect
486. C₂×#135	C₂²×C₂₉	semidirect
487. C₂²×SD₁₆	C₂²×C₂₉	semidirect
488. C₂²×D₈	C₂²×C₂₉	semidirect
490. #553	C₂²×C₂₉	semidirect
491. #552	C₂²×C₂₉	semidirect
493. #548	C₂²×C₂₉	semidirect
497. #546	C₂²×C₂₉	semidirect
498. #546	C₂²×C₂₉	semidirect
502. #529	C₂²×C₂₉	semidirect
503. C₂×#124	C₂²×C₂₉	semidirect
504. #525	C₂²×C₂₉	semidirect
510. C₂×#121	C₂²×C₂₉	semidirect
514. C₂×C₄×D₄	C₂²×C₂₉	semidirect
516. #495	C₂²×C₂₉	semidirect
517. #488	C₂²×C₂₉	semidirect
518. #484	C₂²×C₂₉	semidirect
519. #484	C₂²×C₂₉	semidirect
520. #483	C₂²×C₂₉	semidirect
521. #482	C₂²×C₂₉	semidirect
522. #481	C₂²×C₂₉	semidirect
523. #478	C₂²×C₂₉	semidirect
524. #467	C₂²×C₂₉	semidirect
525. #466	C₂²×C₂₉	semidirect
526. #465	C₂²×C₂₉	semidirect
527. #465	C₂²×C₂₉	semidirect
528. #464	C₂²×C₂₉	semidirect
529. #463	C₂²×C₂₉	semidirect
530. #463	C₂²×C₂₉	semidirect
531. #452	C₂²×C₂₉	semidirect
532. #451	C₂²×C₂₉	semidirect
533. #451	C₂²×C₂₉	semidirect
534. #450	C₂²×C₂₉	semidirect
535. #450	C₂²×C₂₉	semidirect
536. #450	C₂²×C₂₉	semidirect
537. #450	C₂²×C₂₉	semidirect
538. #449	C₂²×C₂₉	semidirect
539. #449	C₂²×C₂₉	semidirect
540. #448	C₂²×C₂₉	semidirect
543. #447	C₂²×C₂₉	semidirect
544. C₄×SD₁₆	C₂²×C₂₉	semidirect
545. C₄×D₈	C₂²×C₂₉	semidirect
546. C₈×D₄	C₂²×C₂₉	semidirect
547. C₈×D₄	C₂²×C₂₉	semidirect
548. #431	C₂²×C₂₉	semidirect
549. #416	C₂²×C₂₉	semidirect
550. C₂×#102	C₂²×C₂₉	semidirect
551. C₂×#102	C₂²×C₂₉	semidirect
554. C₂×C₂²⋊C₈	C₂²×C₂₉	semidirect
569. C₂×#41	C₂³×C₂₉	semidirect
590. C₂×Q₁₆	C₂³×C₂₉	semidirect
594. C₂×SD₁₆	C₂³×C₂₉	semidirect
600. C₂²×C₈	C₂³×C₂₉	semidirect
605. #125	C₂³×C₂₉	semidirect
609. #124	C₂³×C₂₉	semidirect
626. C₂²⋊Q₈	C₂³×C₂₉	semidirect
638. #121	C₂³×C₂₉	semidirect
643. C₄×Q₈	C₂³×C₂₉	semidirect
655. C₄×D₄	C₂³×C₂₉	semidirect
658. #117	C₂³×C₂₉	semidirect
678. #107	C₂³×C₂₉	semidirect
679. #106	C₂³×C₂₉	semidirect
680. C₄⋊C₈	C₂³×C₂₉	semidirect
681. #103	C₂³×C₂₉	semidirect
682. #103	C₂³×C₂₉	semidirect
683. #103	C₂³×C₂₉	semidirect
688. #102	C₂³×C₂₉	semidirect
693. C₂²⋊C₈	C₂³×C₂₉	semidirect
694. C₄×C₈	C₂³×C₂₉	semidirect
695. C₂₉	#61561	direct (N × H)
845. C₂³	C₂₉×#135	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#3505	2
C₂×C₂₉×#546	2
C₂₉×#3297	2
C₂₉×#3296	2
C₂₉×#3282	2
C₂₉×#3280	2
C₂₉×#3211	2
C₂₉×#3189	2
C₂₉×#3188	2
C₂₉×#3187	2
C₂₉×#3105	2
C₂₉×#3002	2
C₂×C₂₉×#450	2
C₂×C₂₉×#447	2
C₂₉×#2972	2
#61561	29

Subgroups — C29×#61561 #20356461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#61561 #20356461