Subgroups — C₂₉×#62755 #20357655

Order 7424.

6644 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3566	C₂	1	8	yes	maximal, complemented
2	C₂₉×#3564	C₂	1	4	yes	maximal, complemented
3	C₂₉×#3560	C₂	1	4	yes	maximal, complemented
4	C₂₉×#3553	C₂	1	4	yes	maximal, complemented
5	C₂₉×#3545	C₂	1	4	yes	maximal, complemented
6	C₂₉×#3535	C₂	1	4	yes	maximal, complemented
7	C₂₉×#3534	C₂	1	4	yes	maximal, complemented
8	C₂₉×#3531	C₂	1	2	yes	maximal, complemented
9	C₂₉×#3529	C₂	1	2	yes	maximal, complemented
10	C₂₉×#3481	C₂	1	4	yes	maximal, complemented
11	C₂₉×#3475	C₂	1	8	yes	maximal, complemented
12	C₂₉×#3461	C₂	1	4	yes	maximal, complemented
13	C₂₉×#3459	C₂	1	4	yes	maximal, complemented
14	C₂₉×#3455	C₂	1	4	yes	maximal, complemented
15	C₂₉×#3444	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×#529	C₂	1	2	yes	maximal, complemented
17	C₂₉×#564	C₂²	1	2	yes	complemented
18	C₂₉×#563	C₂²	1	2	yes	complemented
19	C₂₉×#563	C₂²	1	4	yes	complemented
20	C₂₉×#563	C₂²	1	8	yes	complemented
21	C₂₉×#563	C₂²	1	4	yes	complemented
22	C₂₉×#563	C₂²	1	8	yes	complemented
23	C₂₉×#562	C₂²	1	8	yes	complemented
24	C₂₉×#562	C₂²	1	4	yes	complemented
25	C₂₉×#562	C₂²	1	8	yes	complemented
26	C₂₉×#562	C₂²	1	2	yes	complemented
27	C₂₉×H(3,𝔽₄)	C₂²	1	2	yes	complemented
28	C₂₉×#560	C₂²	1	8	yes	complemented
29	C₂₉×#560	C₂²	1	4	yes	complemented
30	C₂₉×#559	C₂²	1	4	yes	complemented
31	C₂₉×#556	C₂²	1	8	yes	complemented
32	C₂₉×#555	C₂²	1	8	yes	complemented
33	C₂₉×#554	C₂²	1	8	yes	complemented
34	C₂₉×#554	C₂²	1	8	yes	complemented
35	C₂₉×#553	C₂²	1	8	yes	complemented
36	C₂₉×#553	C₂²	1	8	yes	complemented
37	C₂₉×#553	C₂²	1	8	yes	complemented
38	C₂₉×#553	C₂²	1	8	yes	complemented
39	C₂₉×#552	C₂²	1	8	yes	complemented
40	C₂₉×#552	C₂²	1	8	yes	complemented
41	C₂₉×#552	C₂²	1	8	yes	complemented
42	C₂₉×#552	C₂²	1	8	yes	complemented
43	C₂₉×#551	C₂²	1	8	yes	complemented
44	C₂₉×#551	C₂²	1	8	yes	complemented
45	C₂₉×#551	C₂²	1	8	yes	complemented
46	C₂₉×#551	C₂²	1	8	yes	complemented
47	C₂₉×#551	C₂²	1	4	yes	complemented
48	C₂₉×#551	C₂²	1	8	yes	complemented
49	C₂₉×#551	C₂²	1	4	yes	complemented
50	C₂₉×#547	C₂²	1	8	yes	complemented
51	C₂₉×#546	C₂²	1	8	yes	complemented
52	C₂₉×#546	C₂²	1	8	yes	complemented
53	C₂₉×#546	C₂²	1	8	yes	complemented
54	C₂₉×#546	C₂²	1	8	yes	complemented
55	D₄²×C₂₉	C₂²	1	4	yes	complemented
56	C₂₉×#544	C₂²	1	4	yes	complemented
57	C₂₉×#543	C₂²	1	4	yes	complemented
58	C₂₉×#542	C₂²	1	8	yes	complemented
59	C₂₉×#542	C₂²	1	8	yes	complemented
60	C₂₉×#542	C₂²	1	8	yes	complemented
61	C₂₉×#542	C₂²	1	8	yes	complemented
62	C₂₉×#541	C₂²	1	8	yes	complemented
63	C₂₉×#541	C₂²	1	8	yes	complemented
64	C₂₉×#541	C₂²	1	8	yes	complemented
65	C₂₉×#540	C₂²	1	8	yes	complemented
66	C₂₉×#539	C₂²	1	8	yes	complemented
67	C₂₉×#539	C₂²	1	8	yes	complemented
68	C₂₉×#539	C₂²	1	8	yes	complemented
69	C₂₉×#539	C₂²	1	8	yes	complemented
70	C₂₉×#539	C₂²	1	8	yes	complemented
71	C₂₉×#539	C₂²	1	8	yes	complemented
72	C₂₉×#539	C₂²	1	4	yes	complemented
73	C₂₉×#539	C₂²	1	4	yes	complemented
74	C₂₉×#538	C₂²	1	4	yes	—
75	C₂₉×#538	C₂²	1	8	yes	complemented
76	C₂₉×#538	C₂²	1	8	yes	complemented
77	C₂₉×#538	C₂²	1	4	yes	complemented
78	C₂₉×#538	C₂²	1	8	yes	complemented
79	C₂₉×#538	C₂²	1	8	yes	complemented
80	C₂₉×#537	C₂²	1	4	yes	—
81	C₂₉×#536	C₂²	1	8	yes	complemented
82	C₂₉×#534	C₂²	1	8	yes	complemented
83	C₂₉×#534	C₂²	1	4	yes	complemented
84	C₂₉×#533	C₂²	1	1	yes	characteristic, complemented
85	C₂₉×#533	C₂²	1	2	yes	complemented
86	C₂₉×#533	C₂²	1	4	yes	complemented
87	C₂₉×#533	C₂²	1	8	yes	complemented
88	C₂₉×#532	C₂²	1	1	yes	characteristic, complemented
89	C₂₉×#532	C₂²	1	2	yes	complemented
90	C₂₉×#532	C₂²	1	4	yes	complemented
91	C₂₉×#529	C₂²	1	4	yes	complemented
92	C₂₉×#529	C₂²	1	4	yes	complemented
93	C₂₉×#529	C₂²	1	4	yes	complemented
94	C₂₉×#529	C₂²	1	4	yes	complemented
95	C₂₉×#529	C₂²	1	4	yes	complemented
96	C₂₉×#529	C₂²	1	4	yes	complemented
97	C₂₉×#529	C₂²	1	4	yes	complemented
98	C₂₉×#529	C₂²	1	4	yes	complemented
99	C₂₉×#529	C₂²	1	4	yes	complemented
100	C₂₉×#529	C₂²	1	4	yes	complemented
101	C₂₉×#529	C₂²	1	4	yes	complemented
102	C₂₉×#529	C₂²	1	8	yes	complemented
103	C₂₉×#529	C₂²	1	8	yes	complemented
104	C₂₉×#529	C₂²	1	8	yes	complemented
105	C₂₉×#529	C₂²	1	8	yes	complemented
106	C₂₉×#529	C₂²	1	8	yes	complemented
107	C₂₉×#529	C₂²	1	8	yes	complemented
108	C₂×C₂₉×#126	C₂²	1	4	yes	complemented
109	C₂×C₂₉×#125	C₂²	1	2	yes	complemented
110	C₂×C₂₉×#124	C₂²	1	2	yes	complemented
111	C₂₉×#525	C₂²	1	2	yes	complemented
112	C₂₉×#525	C₂²	1	4	yes	complemented
113	C₂₉×#525	C₂²	1	4	yes	complemented
114	C₂₉×#525	C₂²	1	4	yes	complemented
115	C₂₉×#525	C₂²	1	8	yes	complemented
116	C₂₉×#525	C₂²	1	8	yes	complemented
117	C₂×C₂₉×#123	C₂²	1	4	yes	complemented
118	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
119	C₂×C₂₉×#121	C₂²	1	2	yes	—
120	C₄×#41×C₂₉	C₂²	1	2	yes	complemented
121	C₄×#41×C₂₉	C₂²	1	4	yes	complemented
122	C₄×#41×C₂₉	C₂²	1	4	yes	complemented
123	C₄×#41×C₂₉	C₂²	1	8	yes	complemented
124	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	complemented
125	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	complemented
126	C₂×C₄×D₄×C₂₉	C₂²	1	4	yes	complemented
127	C₂×C₄×D₄×C₂₉	C₂²	1	8	yes	complemented
128	C₂×C₂₉×#117	C₂²	1	4	yes	complemented
129	C₂×C₂₉×#117	C₂²	1	4	yes	complemented
130	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic, complemented
131	C₂×#41×C₂₉	C₂³	1	4	yes	—
132	C₂×#41×C₂₉	C₂³	1	2	yes	—
133	C₂×#41×C₂₉	C₂³	1	4	yes	—
134	C₂×#41×C₂₉	C₂³	1	8	yes	—
135	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
136	C₂²×D₄×C₂₉	C₂³	1	4	yes	—
137	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
138	C₂²×D₄×C₂₉	C₂³	1	8	yes	—
139	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₂₉	C₂³	1	2	yes	—
141	C₂³×C₄×C₂₉	C₂³	1	4	yes	—
142	C₂³×C₄×C₂₉	C₂³	1	4	yes	—
143	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
144	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
145	C₂₉×C₄⋊Q₈	C₂³	1	4	yes	—
146	C₂₉×C₄⋊Q₈	C₂³	1	8	yes	—
147	C₂₉×C₄⋊Q₈	C₂³	1	8	yes	—
148	C₂₉×C₄⋊Q₈	C₂³	1	8	yes	—
149	C₂₉×#127	C₂³	1	1	yes	characteristic
150	C₂₉×#127	C₂³	1	4	yes	—
151	C₂₉×#126	C₂³	1	8	yes	—
152	C₂₉×#126	C₂³	1	8	yes	—
153	C₂₉×#126	C₂³	1	8	yes	—
154	C₂₉×#126	C₂³	1	8	yes	—
155	C₂₉×#126	C₂³	1	8	yes	—
156	C₂₉×#126	C₂³	1	8	yes	—
157	C₂₉×#126	C₂³	1	8	yes	—
158	C₂₉×#126	C₂³	1	8	yes	—
159	C₂₉×#126	C₂³	1	8	yes	—
160	C₂₉×#126	C₂³	1	8	yes	—
161	C₂₉×#126	C₂³	1	8	yes	—
162	C₂₉×#126	C₂³	1	8	yes	—
163	C₂₉×#126	C₂³	1	8	yes	—
164	C₂₉×#126	C₂³	1	8	yes	—
165	C₂₉×#126	C₂³	1	8	yes	—
166	C₂₉×#126	C₂³	1	8	yes	—
167	C₂₉×#126	C₂³	1	8	yes	—
168	C₂₉×#125	C₂³	1	4	yes	—
169	C₂₉×#125	C₂³	1	4	yes	—
170	C₂₉×#125	C₂³	1	4	yes	—
171	C₂₉×#125	C₂³	1	4	yes	—
172	C₂₉×#125	C₂³	1	4	yes	—
173	C₂₉×#125	C₂³	1	2	yes	—
174	C₂₉×#125	C₂³	1	8	yes	—
175	C₂₉×#125	C₂³	1	8	yes	—
176	C₂₉×#125	C₂³	1	8	yes	—
177	C₂₉×#125	C₂³	1	8	yes	—
178	C₂₉×#125	C₂³	1	8	yes	—
179	C₂₉×#125	C₂³	1	8	yes	—
180	C₂₉×#125	C₂³	1	8	yes	—
181	C₂₉×#125	C₂³	1	8	yes	—
182	C₂₉×#125	C₂³	1	8	yes	—
183	C₂₉×#124	C₂³	1	4	yes	—
184	C₂₉×#124	C₂³	1	4	yes	—
185	C₂₉×#124	C₂³	1	4	yes	—
186	C₂₉×#124	C₂³	1	4	yes	—
187	C₂₉×#124	C₂³	1	4	yes	—
188	C₂₉×#124	C₂³	1	2	yes	—
189	C₂₉×#124	C₂³	1	8	yes	—
190	C₂₉×#124	C₂³	1	8	yes	—
191	C₂₉×#124	C₂³	1	8	yes	—
192	C₂₉×#124	C₂³	1	8	yes	—
193	C₂₉×#124	C₂³	1	8	yes	—
194	C₂₉×#124	C₂³	1	8	yes	—
195	C₂₉×#124	C₂³	1	4	yes	—
196	C₂₉×#124	C₂³	1	4	yes	—
197	C₂₉×#123	C₂³	1	8	yes	—
198	C₂₉×#123	C₂³	1	8	yes	—
199	C₂₉×#123	C₂³	1	8	yes	—
200	C₂₉×#123	C₂³	1	8	yes	—
201	C₂₉×#123	C₂³	1	8	yes	—
202	C₂₉×#123	C₂³	1	4	yes	—
203	C₂₉×#123	C₂³	1	8	yes	—
204	C₂₉×#123	C₂³	1	8	yes	—
205	C₂₉×#123	C₂³	1	8	yes	—
206	C₂₉×#123	C₂³	1	8	yes	—
207	C₂₉×#123	C₂³	1	8	yes	—
208	C₂₉×#123	C₂³	1	4	yes	—
209	C₂₉×#123	C₂³	1	4	yes	—
210	C₂₉×#123	C₂³	1	8	yes	—
211	C₂₉×#123	C₂³	1	8	yes	—
212	C₂₉×#123	C₂³	1	8	yes	—
213	C₂₉×#123	C₂³	1	8	yes	—
214	C₂₉×#123	C₂³	1	8	yes	—
215	C₂₉×#123	C₂³	1	8	yes	—
216	C₂₉×#123	C₂³	1	8	yes	—
217	C₂₉×#123	C₂³	1	8	yes	—
218	C₂₉×#123	C₂³	1	8	yes	—
219	C₂₉×#123	C₂³	1	8	yes	—
220	C₂₉×#123	C₂³	1	8	yes	—
221	C₂₉×#123	C₂³	1	8	yes	—
222	C₂₉×C₂²⋊Q₈	C₂³	1	4	yes	—
223	C₂₉×C₂²⋊Q₈	C₂³	1	4	yes	—
224	C₂₉×C₂²⋊Q₈	C₂³	1	4	yes	—
225	C₂₉×C₂²⋊Q₈	C₂³	1	4	yes	—
226	C₂₉×C₂²⋊Q₈	C₂³	1	4	yes	—
227	C₂₉×C₂²⋊Q₈	C₂³	1	4	yes	—
228	C₂₉×C₂²⋊Q₈	C₂³	1	4	yes	—
229	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
230	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
231	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
232	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
233	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
234	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
235	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
236	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
237	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
238	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
239	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
240	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
241	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
242	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
243	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
244	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
245	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
246	C₂₉×C₂²⋊Q₈	C₂³	1	8	yes	—
247	C₂₉×#121	C₂³	1	4	yes	—
248	C₂₉×#121	C₂³	1	4	yes	—
249	C₂₉×#121	C₂³	1	4	yes	—
250	C₂₉×#121	C₂³	1	4	yes	—
251	C₂₉×#121	C₂³	1	4	yes	—
252	C₂₉×#121	C₂³	1	4	yes	—
253	C₂₉×#121	C₂³	1	4	yes	—
254	C₂₉×#121	C₂³	1	8	yes	—
255	C₂₉×#121	C₂³	1	8	yes	—
256	C₂₉×#121	C₂³	1	8	yes	—
257	C₂₉×#121	C₂³	1	8	yes	—
258	C₂₉×#121	C₂³	1	8	yes	—
259	C₂₉×#121	C₂³	1	8	yes	—
260	C₂₉×#121	C₂³	1	8	yes	—
261	C₂₉×#121	C₂³	1	8	yes	—
262	C₂₉×#121	C₂³	1	8	yes	—
263	C₂₉×#121	C₂³	1	8	yes	—
264	C₂₉×#121	C₂³	1	8	yes	—
265	C₂₉×#121	C₂³	1	8	yes	—
266	C₂₉×#121	C₂³	1	8	yes	—
267	C₂₉×#121	C₂³	1	8	yes	—
268	C₂₉×#120	C₂³	1	4	yes	—
269	C₂₉×#120	C₂³	1	8	yes	—
270	C₂₉×#120	C₂³	1	8	yes	—
271	C₂₉×#120	C₂³	1	8	yes	—
272	C₂₉×#120	C₂³	1	8	yes	—
273	C₂₉×#120	C₂³	1	8	yes	—
274	C₂₉×#120	C₂³	1	4	yes	—
275	C₂₉×#120	C₂³	1	4	yes	—
276	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
277	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
278	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
279	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
280	C₄×Q₈×C₂₉	C₂³	1	8	yes	—
281	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
282	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
283	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
284	C₄×Q₈×C₂₉	C₂³	1	8	yes	—
285	C₄×Q₈×C₂₉	C₂³	1	8	yes	—
286	C₄×D₄×C₂₉	C₂³	1	8	yes	—
287	C₄×D₄×C₂₉	C₂³	1	8	yes	—
288	C₄×D₄×C₂₉	C₂³	1	4	yes	—
289	C₄×D₄×C₂₉	C₂³	1	4	yes	—
290	C₄×D₄×C₂₉	C₂³	1	8	yes	—
291	C₄×D₄×C₂₉	C₂³	1	8	yes	—
292	C₄×D₄×C₂₉	C₂³	1	8	yes	—
293	C₄×D₄×C₂₉	C₂³	1	4	yes	—
294	C₄×D₄×C₂₉	C₂³	1	4	yes	—
295	C₄×D₄×C₂₉	C₂³	1	8	yes	—
296	C₄×D₄×C₂₉	C₂³	1	8	yes	—
297	C₄×D₄×C₂₉	C₂³	1	8	yes	—
298	C₄×D₄×C₂₉	C₂³	1	8	yes	—
299	C₄×D₄×C₂₉	C₂³	1	8	yes	—
300	C₄×D₄×C₂₉	C₂³	1	8	yes	—
301	C₄×D₄×C₂₉	C₂³	1	8	yes	—
302	C₄×D₄×C₂₉	C₂³	1	4	yes	—
303	C₄×D₄×C₂₉	C₂³	1	8	yes	—
304	C₄×D₄×C₂₉	C₂³	1	8	yes	—
305	C₄×D₄×C₂₉	C₂³	1	4	yes	—
306	C₄×D₄×C₂₉	C₂³	1	4	yes	—
307	C₄×D₄×C₂₉	C₂³	1	8	yes	—
308	C₄×D₄×C₂₉	C₂³	1	8	yes	—
309	C₄×D₄×C₂₉	C₂³	1	8	yes	—
310	C₄×D₄×C₂₉	C₂³	1	8	yes	—
311	C₄×D₄×C₂₉	C₂³	1	8	yes	—
312	C₄×D₄×C₂₉	C₂³	1	8	yes	—
313	C₂₉×#117	C₂³	1	8	yes	—
314	C₂₉×#117	C₂³	1	8	yes	—
315	C₂₉×#117	C₂³	1	8	yes	—
316	C₂₉×#117	C₂³	1	8	yes	—
317	C₂₉×#117	C₂³	1	8	yes	—
318	C₂₉×#117	C₂³	1	8	yes	—
319	C₂₉×#117	C₂³	1	8	yes	—
320	C₂₉×#117	C₂³	1	4	yes	—
321	C₂₉×#117	C₂³	1	2	yes	—
322	C₂₉×#117	C₂³	1	4	yes	—
323	C₂₉×#117	C₂³	1	4	yes	—
324	C₂₉×#117	C₂³	1	8	yes	—
325	C₂₉×#117	C₂³	1	8	yes	—
326	C₂₉×#117	C₂³	1	8	yes	—
327	C₂₉×#117	C₂³	1	8	yes	—
328	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
329	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
330	C₂×C₄⋊C₄×C₂₉	C₂³	1	8	yes	—
331	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
332	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
333	C₂×C₄⋊C₄×C₂₉	C₂³	1	8	yes	—
334	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
335	C₂×C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
336	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
337	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
338	C₂×C₂²⋊C₄×C₂₉	C₂³	1	8	yes	—
339	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
340	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
341	C₂×C₂²⋊C₄×C₂₉	C₂³	1	4	yes	—
342	C₂×C₂²⋊C₄×C₂₉	C₂³	1	8	yes	—
343	C₂×C₂²⋊C₄×C₂₉	C₂³	1	8	yes	—
344	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
345	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
346	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
347	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
348	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
349	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
350	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
351	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
352	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
353	C₂×C₄²×C₂₉	C₂³	1	4	yes	—
354	C₂×C₄²×C₂₉	C₂³	1	8	yes	—
355	C₂⁴×C₂₉	C₂⁴	1	1	yes	characteristic
356	C₂⁴×C₂₉	C₂⁴	1	4	yes	—
357	C₂⁴×C₂₉	C₂⁴	1	4	yes	—
358	#41×C₂₉	—	4	8	no	—
359	#41×C₂₉	—	4	4	no	—
360	#41×C₂₉	—	4	8	no	—
361	#41×C₂₉	—	4	16	no	—
362	C₂×Q₈×C₂₉	—	4	4	no	—
363	C₂×Q₈×C₂₉	C₂⁴	1	4	yes	—
364	C₂×Q₈×C₂₉	C₂⁴	1	4	yes	—
365	C₂×Q₈×C₂₉	C₂⁴	1	4	yes	—
366	C₂×Q₈×C₂₉	C₂⁴	1	8	yes	—
367	C₂×Q₈×C₂₉	C₂⁴	1	4	yes	—
368	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
369	C₂×D₄×C₂₉	—	4	4	no	—
370	C₂×D₄×C₂₉	—	4	8	no	—
371	C₂×D₄×C₂₉	—	4	16	no	—
372	C₂×D₄×C₂₉	C₂⁴	1	8	yes	—
373	C₂×D₄×C₂₉	C₂⁴	1	8	yes	—
374	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
375	C₂×D₄×C₂₉	C₂⁴	1	8	yes	—
376	C₂×D₄×C₂₉	C₂⁴	1	8	yes	—
377	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
378	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
379	C₂×D₄×C₂₉	C₂⁴	1	8	yes	—
380	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
381	C₂×D₄×C₂₉	C₂⁴	1	4	yes	—
382	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
383	C₂×D₄×C₂₉	C₂⁴	1	8	yes	—
384	C₂×D₄×C₂₉	C₂⁴	1	8	yes	—
385	C₂²×C₄×C₂₉	—	4	2	no	—
386	C₂²×C₄×C₂₉	—	4	8	no	—
387	C₂²×C₄×C₂₉	—	4	8	no	—
388	C₂²×C₄×C₂₉	—	4	4	no	—
389	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
390	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
391	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
392	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
393	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
395	C₂²×C₄×C₂₉	C₂⁴	1	8	yes	—
396	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
397	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
398	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
399	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
401	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
402	C₂²×C₄×C₂₉	C₂⁴	1	8	yes	—
403	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
404	C₂²×C₄×C₂₉	C₂⁴	1	8	yes	—
405	C₂²×C₄×C₂₉	C₂⁴	1	8	yes	—
406	C₂²×C₄×C₂₉	C₂⁴	1	8	yes	—
407	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
408	C₂²×C₄×C₂₉	C₂⁴	1	8	yes	—
409	C₂²×C₄×C₂₉	C₂⁴	1	8	yes	—
410	C₂²×C₄×C₂₉	C₂⁴	1	4	yes	—
411	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
412	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
413	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
414	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
415	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
416	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
417	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
418	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
419	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
420	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
421	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
422	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
423	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
424	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
425	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
426	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
427	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
428	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
429	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
430	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
431	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
432	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
433	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
434	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
435	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
436	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
437	C₄⋊C₄×C₂₉	C₂⁴	1	8	yes	—
438	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
439	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
440	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
441	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
442	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
443	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
444	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
445	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
446	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
447	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
448	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
449	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
450	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
451	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
452	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
453	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
454	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
455	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
456	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
457	C₂²⋊C₄×C₂₉	C₂⁴	1	4	yes	—
458	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
459	C₂²⋊C₄×C₂₉	C₂⁴	1	4	yes	—
460	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
461	C₂²⋊C₄×C₂₉	C₂⁴	1	8	yes	—
462	C₂²⋊C₄×C₂₉	C₂⁴	1	4	yes	—
463	C₄²×C₂₉	C₂⁴	1	2	yes	—
464	C₄²×C₂₉	C₂⁴	1	2	yes	—
465	C₄²×C₂₉	C₂⁴	1	2	yes	—
466	C₄²×C₂₉	C₂⁴	1	2	yes	—
467	C₄²×C₂₉	C₂⁴	1	2	yes	—
468	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
469	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
470	C₄²×C₂₉	C₂⁴	1	4	yes	—
471	C₄²×C₂₉	C₂⁴	1	8	yes	—
472	C₄²×C₂₉	C₂⁴	1	8	yes	—
473	C₄²×C₂₉	C₂⁴	1	8	yes	—
474	C₄²×C₂₉	C₂⁴	1	4	yes	—
475	C₄²×C₂₉	C₂⁴	1	8	yes	—
476	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
477	C₄²×C₂₉	C₂⁴	1	8	yes	—
478	C₄²×C₂₉	C₂⁴	1	2	yes	—
479	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
480	C₄²×C₂₉	C₂⁴	1	4	yes	—
481	#62755	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
482	C₂³×C₂₉	—	2	4	no	—
483	C₂³×C₂₉	—	2	8	no	—
484	C₂³×C₂₉	—	4	1	no	—
485	C₂³×C₂₉	—	4	4	no	—
486	C₂³×C₂₉	—	4	4	no	—
487	C₂³×C₂₉	—	4	4	no	—
488	C₂³×C₂₉	—	4	8	no	—
489	C₂³×C₂₉	C₂⁵	1	8	yes	—
490	C₂³×C₂₉	C₂⁵	1	4	yes	—
491	C₂³×C₂₉	C₂⁵	1	1	yes	characteristic
492	C₂³×C₂₉	C₂⁵	1	2	yes	—
493	Q₈×C₂₉	—	4	4	no	—
494	Q₈×C₂₉	—	4	4	no	—
495	Q₈×C₂₉	—	4	4	no	—
496	Q₈×C₂₉	—	4	2	no	—
497	Q₈×C₂₉	—	4	4	no	—
498	Q₈×C₂₉	—	4	8	no	—
499	D₄×C₂₉	—	2	16	no	—
500	D₄×C₂₉	—	2	16	no	—
501	D₄×C₂₉	—	4	4	no	—
502	D₄×C₂₉	—	4	4	no	—
503	D₄×C₂₉	—	4	8	no	—
504	D₄×C₂₉	—	4	8	no	—
505	D₄×C₂₉	—	4	8	no	—
506	D₄×C₂₉	—	4	8	no	—
507	D₄×C₂₉	—	4	4	no	—
508	D₄×C₂₉	—	4	4	no	—
509	D₄×C₂₉	—	4	2	no	—
510	D₄×C₂₉	—	4	4	no	—
511	D₄×C₂₉	—	4	8	no	—
512	C₂×C₄×C₂₉	—	2	4	no	—
513	C₂×C₄×C₂₉	—	2	4	no	—
514	C₂×C₄×C₂₉	—	2	8	no	—
515	C₂×C₄×C₂₉	—	2	4	no	—
516	C₂×C₄×C₂₉	—	2	16	no	—
517	C₂×C₄×C₂₉	—	2	2	no	—
518	C₂×C₄×C₂₉	—	2	8	no	—
519	C₂×C₄×C₂₉	—	4	1	no	—
520	C₂×C₄×C₂₉	—	4	8	no	—
521	C₂×C₄×C₂₉	—	4	2	no	—
522	C₂×C₄×C₂₉	—	4	2	no	—
523	C₂×C₄×C₂₉	—	4	2	no	—
524	C₂×C₄×C₂₉	—	4	4	no	—
525	C₂×C₄×C₂₉	—	4	4	no	—
526	C₂×C₄×C₂₉	—	4	8	no	—
527	C₂×C₄×C₂₉	—	4	2	no	—
528	C₂×C₄×C₂₉	—	4	2	no	—
529	C₂×C₄×C₂₉	—	4	4	no	—
530	C₂×C₄×C₂₉	—	4	8	no	—
531	C₂×C₄×C₂₉	—	4	8	no	—
532	C₂×C₄×C₂₉	—	4	8	no	—
533	C₂×C₄×C₂₉	—	4	8	no	—
534	C₂×C₄×C₂₉	C₂⁵	1	2	yes	—
535	C₂×C₄×C₂₉	C₂⁵	1	2	yes	—
536	C₂×C₄×C₂₉	C₂⁵	1	8	yes	—
537	C₂×C₄×C₂₉	C₂⁵	1	2	yes	—
538	C₂×C₄×C₂₉	C₂⁵	1	2	yes	—
539	C₂×C₄×C₂₉	C₂⁵	1	2	yes	—
540	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
541	C₂×C₄×C₂₉	C₂⁵	1	4	yes	—
542	C₂×C₄×C₂₉	C₂⁵	1	8	yes	—
543	C₂×C₄×C₂₉	C₂⁵	1	8	yes	—
544	C₂×C₄×C₂₉	C₂⁵	1	8	yes	—
545	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
546	#3566	C₂×C₂₉	1	8	yes	complemented
547	#3564	C₂×C₂₉	1	4	yes	complemented
548	#3560	C₂×C₂₉	1	4	yes	complemented
549	#3553	C₂×C₂₉	1	4	yes	complemented
550	#3545	C₂×C₂₉	1	4	yes	complemented
551	#3535	C₂×C₂₉	1	4	yes	complemented
552	#3534	C₂×C₂₉	1	4	yes	complemented
553	#3531	C₂×C₂₉	1	2	yes	complemented
554	#3529	C₂×C₂₉	1	2	yes	complemented
555	#3481	C₂×C₂₉	1	4	yes	complemented
556	#3475	C₂×C₂₉	1	8	yes	complemented
557	#3461	C₂×C₂₉	1	4	yes	complemented
558	#3459	C₂×C₂₉	1	4	yes	complemented
559	#3455	C₂×C₂₉	1	4	yes	complemented
560	#3444	C₂×C₂₉	1	1	yes	characteristic, complemented
561	C₂×#529	C₂×C₂₉	1	2	yes	complemented
562	C₂²×C₂₉	—	2	2	no	—
563	C₂²×C₂₉	—	2	2	no	—
564	C₂²×C₂₉	—	2	8	no	—
565	C₂²×C₂₉	—	2	1	no	—
566	C₂²×C₂₉	—	2	4	no	—
567	C₂²×C₂₉	—	2	8	no	—
568	C₂²×C₂₉	—	2	2	no	—
569	C₂²×C₂₉	—	2	8	no	—
570	C₂²×C₂₉	—	2	8	no	—
571	C₂²×C₂₉	—	4	4	no	—
572	C₂²×C₂₉	—	8	8	no	—
573	C₂²×C₂₉	—	8	8	no	—
574	C₂²×C₂₉	#585	1	4	yes	—
575	C₂²×C₂₉	C₂⁶	1	1	yes	characteristic
576	C₄×C₂₉	—	2	2	no	—
577	C₄×C₂₉	—	2	2	no	—
578	C₄×C₂₉	—	2	8	no	—
579	C₄×C₂₉	—	2	2	no	—
580	C₄×C₂₉	—	2	2	no	—
581	C₄×C₂₉	—	2	2	no	—
582	C₄×C₂₉	—	2	1	no	—
583	C₄×C₂₉	—	2	4	no	—
584	C₄×C₂₉	—	2	8	no	—
585	C₄×C₂₉	—	2	8	no	—
586	C₄×C₂₉	—	2	8	no	—
587	C₄×C₂₉	#585	1	2	yes	—
588	#564	C₂²×C₂₉	1	2	yes	complemented
589	#563	C₂²×C₂₉	1	2	yes	complemented
590	#563	C₂²×C₂₉	1	4	yes	complemented
591	#563	C₂²×C₂₉	1	8	yes	complemented
592	#563	C₂²×C₂₉	1	4	yes	complemented
593	#563	C₂²×C₂₉	1	8	yes	complemented
594	#562	C₂²×C₂₉	1	8	yes	complemented
595	#562	C₂²×C₂₉	1	4	yes	complemented
596	#562	C₂²×C₂₉	1	8	yes	complemented
597	#562	C₂²×C₂₉	1	2	yes	complemented
598	H(3,𝔽₄)	C₂²×C₂₉	1	2	yes	complemented
599	#560	C₂²×C₂₉	1	8	yes	complemented
600	#560	C₂²×C₂₉	1	4	yes	complemented
601	#559	C₂²×C₂₉	1	4	yes	complemented
602	#556	C₂²×C₂₉	1	8	yes	complemented
603	#555	C₂²×C₂₉	1	8	yes	complemented
604	#554	C₂²×C₂₉	1	8	yes	complemented
605	#554	C₂²×C₂₉	1	8	yes	complemented
606	#553	C₂²×C₂₉	1	8	yes	complemented
607	#553	C₂²×C₂₉	1	8	yes	complemented
608	#553	C₂²×C₂₉	1	8	yes	complemented
609	#553	C₂²×C₂₉	1	8	yes	complemented
610	#552	C₂²×C₂₉	1	8	yes	complemented
611	#552	C₂²×C₂₉	1	8	yes	complemented
612	#552	C₂²×C₂₉	1	8	yes	complemented
613	#552	C₂²×C₂₉	1	8	yes	complemented
614	#551	C₂²×C₂₉	1	8	yes	complemented
615	#551	C₂²×C₂₉	1	8	yes	complemented
616	#551	C₂²×C₂₉	1	8	yes	complemented
617	#551	C₂²×C₂₉	1	8	yes	complemented
618	#551	C₂²×C₂₉	1	4	yes	complemented
619	#551	C₂²×C₂₉	1	8	yes	complemented
620	#551	C₂²×C₂₉	1	4	yes	complemented
621	#547	C₂²×C₂₉	1	8	yes	complemented
622	#546	C₂²×C₂₉	1	8	yes	complemented
623	#546	C₂²×C₂₉	1	8	yes	complemented
624	#546	C₂²×C₂₉	1	8	yes	complemented
625	#546	C₂²×C₂₉	1	8	yes	complemented
626	D₄²	C₂²×C₂₉	1	4	yes	complemented
627	#544	C₂²×C₂₉	1	4	yes	complemented
628	#543	C₂²×C₂₉	1	4	yes	complemented
629	#542	C₂²×C₂₉	1	8	yes	complemented
630	#542	C₂²×C₂₉	1	8	yes	complemented
631	#542	C₂²×C₂₉	1	8	yes	complemented
632	#542	C₂²×C₂₉	1	8	yes	complemented
633	#541	C₂²×C₂₉	1	8	yes	complemented
634	#541	C₂²×C₂₉	1	8	yes	complemented
635	#541	C₂²×C₂₉	1	8	yes	complemented
636	#540	C₂²×C₂₉	1	8	yes	complemented
637	#539	C₂²×C₂₉	1	8	yes	complemented
638	#539	C₂²×C₂₉	1	8	yes	complemented
639	#539	C₂²×C₂₉	1	8	yes	complemented
640	#539	C₂²×C₂₉	1	8	yes	complemented
641	#539	C₂²×C₂₉	1	8	yes	complemented
642	#539	C₂²×C₂₉	1	8	yes	complemented
643	#539	C₂²×C₂₉	1	4	yes	complemented
644	#539	C₂²×C₂₉	1	4	yes	complemented
645	#538	C₂²×C₂₉	1	4	yes	—
646	#538	C₂²×C₂₉	1	8	yes	complemented
647	#538	C₂²×C₂₉	1	8	yes	complemented
648	#538	C₂²×C₂₉	1	4	yes	complemented
649	#538	C₂²×C₂₉	1	8	yes	complemented
650	#538	C₂²×C₂₉	1	8	yes	complemented
651	#537	C₂²×C₂₉	1	4	yes	—
652	#536	C₂²×C₂₉	1	8	yes	complemented
653	#534	C₂²×C₂₉	1	8	yes	complemented
654	#534	C₂²×C₂₉	1	4	yes	complemented
655	#533	C₂²×C₂₉	1	1	yes	characteristic, complemented
656	#533	C₂²×C₂₉	1	2	yes	complemented
657	#533	C₂²×C₂₉	1	4	yes	complemented
658	#533	C₂²×C₂₉	1	8	yes	complemented
659	#532	C₂²×C₂₉	1	1	yes	characteristic, complemented
660	#532	C₂²×C₂₉	1	2	yes	complemented
661	#532	C₂²×C₂₉	1	4	yes	complemented
662	#529	C₂²×C₂₉	1	4	yes	complemented
663	#529	C₂²×C₂₉	1	4	yes	complemented
664	#529	C₂²×C₂₉	1	4	yes	complemented
665	#529	C₂²×C₂₉	1	4	yes	complemented
666	#529	C₂²×C₂₉	1	4	yes	complemented
667	#529	C₂²×C₂₉	1	4	yes	complemented
668	#529	C₂²×C₂₉	1	4	yes	complemented
669	#529	C₂²×C₂₉	1	4	yes	complemented
670	#529	C₂²×C₂₉	1	4	yes	complemented
671	#529	C₂²×C₂₉	1	4	yes	complemented
672	#529	C₂²×C₂₉	1	4	yes	complemented
673	#529	C₂²×C₂₉	1	8	yes	complemented
674	#529	C₂²×C₂₉	1	8	yes	complemented
675	#529	C₂²×C₂₉	1	8	yes	complemented
676	#529	C₂²×C₂₉	1	8	yes	complemented
677	#529	C₂²×C₂₉	1	8	yes	complemented
678	#529	C₂²×C₂₉	1	8	yes	complemented
679	C₂×#126	C₂²×C₂₉	1	4	yes	complemented
680	C₂×#125	C₂²×C₂₉	1	2	yes	complemented
681	C₂×#124	C₂²×C₂₉	1	2	yes	complemented
682	#525	C₂²×C₂₉	1	2	yes	complemented
683	#525	C₂²×C₂₉	1	4	yes	complemented
684	#525	C₂²×C₂₉	1	4	yes	complemented
685	#525	C₂²×C₂₉	1	4	yes	complemented
686	#525	C₂²×C₂₉	1	8	yes	complemented
687	#525	C₂²×C₂₉	1	8	yes	complemented
688	C₂×#123	C₂²×C₂₉	1	4	yes	complemented
689	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	2	yes	complemented
690	C₂×#121	C₂²×C₂₉	1	2	yes	—
691	C₄×#41	C₂²×C₂₉	1	2	yes	complemented
692	C₄×#41	C₂²×C₂₉	1	4	yes	complemented
693	C₄×#41	C₂²×C₂₉	1	4	yes	complemented
694	C₄×#41	C₂²×C₂₉	1	8	yes	complemented
695	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	complemented
696	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	complemented
697	C₂×C₄×D₄	C₂²×C₂₉	1	4	yes	complemented
698	C₂×C₄×D₄	C₂²×C₂₉	1	8	yes	complemented
699	C₂×#117	C₂²×C₂₉	1	4	yes	complemented
700	C₂×#117	C₂²×C₂₉	1	4	yes	complemented
701	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic, complemented
702	C₂×C₂₉	—	2	4	no	—
703	C₂×C₂₉	—	4	1	no	—
704	C₂×C₂₉	—	4	4	no	—
705	C₂×C₂₉	—	4	8	no	—
706	C₂×C₂₉	C₂×#585	1	2	yes	—
707	C₂×C₂₉	C₂×#585	1	1	yes	characteristic
708	C₂×#41	C₂³×C₂₉	1	4	yes	—
709	C₂×#41	C₂³×C₂₉	1	2	yes	—
710	C₂×#41	C₂³×C₂₉	1	4	yes	—
711	C₂×#41	C₂³×C₂₉	1	8	yes	—
712	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
713	C₂²×D₄	C₂³×C₂₉	1	4	yes	—
714	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
715	C₂²×D₄	C₂³×C₂₉	1	8	yes	—
716	C₂³×C₄	C₂³×C₂₉	1	4	yes	—
717	C₂³×C₄	C₂³×C₂₉	1	4	yes	—
718	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
719	C₂³×C₄	C₂³×C₂₉	1	2	yes	—
720	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
721	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
722	C₄⋊Q₈	C₂³×C₂₉	1	4	yes	—
723	C₄⋊Q₈	C₂³×C₂₉	1	8	yes	—
724	C₄⋊Q₈	C₂³×C₂₉	1	8	yes	—
725	C₄⋊Q₈	C₂³×C₂₉	1	8	yes	—
726	#127	C₂³×C₂₉	1	1	yes	characteristic
727	#127	C₂³×C₂₉	1	4	yes	—
728	#126	C₂³×C₂₉	1	8	yes	—
729	#126	C₂³×C₂₉	1	8	yes	—
730	#126	C₂³×C₂₉	1	8	yes	—
731	#126	C₂³×C₂₉	1	8	yes	—
732	#126	C₂³×C₂₉	1	8	yes	—
733	#126	C₂³×C₂₉	1	8	yes	—
734	#126	C₂³×C₂₉	1	8	yes	—
735	#126	C₂³×C₂₉	1	8	yes	—
736	#126	C₂³×C₂₉	1	8	yes	—
737	#126	C₂³×C₂₉	1	8	yes	—
738	#126	C₂³×C₂₉	1	8	yes	—
739	#126	C₂³×C₂₉	1	8	yes	—
740	#126	C₂³×C₂₉	1	8	yes	—
741	#126	C₂³×C₂₉	1	8	yes	—
742	#126	C₂³×C₂₉	1	8	yes	—
743	#126	C₂³×C₂₉	1	8	yes	—
744	#126	C₂³×C₂₉	1	8	yes	—
745	#125	C₂³×C₂₉	1	4	yes	—
746	#125	C₂³×C₂₉	1	4	yes	—
747	#125	C₂³×C₂₉	1	4	yes	—
748	#125	C₂³×C₂₉	1	4	yes	—
749	#125	C₂³×C₂₉	1	4	yes	—
750	#125	C₂³×C₂₉	1	2	yes	—
751	#125	C₂³×C₂₉	1	8	yes	—
752	#125	C₂³×C₂₉	1	8	yes	—
753	#125	C₂³×C₂₉	1	8	yes	—
754	#125	C₂³×C₂₉	1	8	yes	—
755	#125	C₂³×C₂₉	1	8	yes	—
756	#125	C₂³×C₂₉	1	8	yes	—
757	#125	C₂³×C₂₉	1	8	yes	—
758	#125	C₂³×C₂₉	1	8	yes	—
759	#125	C₂³×C₂₉	1	8	yes	—
760	#124	C₂³×C₂₉	1	4	yes	—
761	#124	C₂³×C₂₉	1	4	yes	—
762	#124	C₂³×C₂₉	1	4	yes	—
763	#124	C₂³×C₂₉	1	4	yes	—
764	#124	C₂³×C₂₉	1	4	yes	—
765	#124	C₂³×C₂₉	1	2	yes	—
766	#124	C₂³×C₂₉	1	8	yes	—
767	#124	C₂³×C₂₉	1	8	yes	—
768	#124	C₂³×C₂₉	1	8	yes	—
769	#124	C₂³×C₂₉	1	8	yes	—
770	#124	C₂³×C₂₉	1	8	yes	—
771	#124	C₂³×C₂₉	1	8	yes	—
772	#124	C₂³×C₂₉	1	4	yes	—
773	#124	C₂³×C₂₉	1	4	yes	—
774	#123	C₂³×C₂₉	1	8	yes	—
775	#123	C₂³×C₂₉	1	8	yes	—
776	#123	C₂³×C₂₉	1	8	yes	—
777	#123	C₂³×C₂₉	1	8	yes	—
778	#123	C₂³×C₂₉	1	8	yes	—
779	#123	C₂³×C₂₉	1	4	yes	—
780	#123	C₂³×C₂₉	1	8	yes	—
781	#123	C₂³×C₂₉	1	8	yes	—
782	#123	C₂³×C₂₉	1	8	yes	—
783	#123	C₂³×C₂₉	1	8	yes	—
784	#123	C₂³×C₂₉	1	8	yes	—
785	#123	C₂³×C₂₉	1	4	yes	—
786	#123	C₂³×C₂₉	1	4	yes	—
787	#123	C₂³×C₂₉	1	8	yes	—
788	#123	C₂³×C₂₉	1	8	yes	—
789	#123	C₂³×C₂₉	1	8	yes	—
790	#123	C₂³×C₂₉	1	8	yes	—
791	#123	C₂³×C₂₉	1	8	yes	—
792	#123	C₂³×C₂₉	1	8	yes	—
793	#123	C₂³×C₂₉	1	8	yes	—
794	#123	C₂³×C₂₉	1	8	yes	—
795	#123	C₂³×C₂₉	1	8	yes	—
796	#123	C₂³×C₂₉	1	8	yes	—
797	#123	C₂³×C₂₉	1	8	yes	—
798	#123	C₂³×C₂₉	1	8	yes	—
799	C₂²⋊Q₈	C₂³×C₂₉	1	4	yes	—
800	C₂²⋊Q₈	C₂³×C₂₉	1	4	yes	—
801	C₂²⋊Q₈	C₂³×C₂₉	1	4	yes	—
802	C₂²⋊Q₈	C₂³×C₂₉	1	4	yes	—
803	C₂²⋊Q₈	C₂³×C₂₉	1	4	yes	—
804	C₂²⋊Q₈	C₂³×C₂₉	1	4	yes	—
805	C₂²⋊Q₈	C₂³×C₂₉	1	4	yes	—
806	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
807	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
808	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
809	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
810	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
811	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
812	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
813	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
814	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
815	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
816	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
817	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
818	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
819	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
820	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
821	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
822	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
823	C₂²⋊Q₈	C₂³×C₂₉	1	8	yes	—
824	#121	C₂³×C₂₉	1	4	yes	—
825	#121	C₂³×C₂₉	1	4	yes	—
826	#121	C₂³×C₂₉	1	4	yes	—
827	#121	C₂³×C₂₉	1	4	yes	—
828	#121	C₂³×C₂₉	1	4	yes	—
829	#121	C₂³×C₂₉	1	4	yes	—
830	#121	C₂³×C₂₉	1	4	yes	—
831	#121	C₂³×C₂₉	1	8	yes	—
832	#121	C₂³×C₂₉	1	8	yes	—
833	#121	C₂³×C₂₉	1	8	yes	—
834	#121	C₂³×C₂₉	1	8	yes	—
835	#121	C₂³×C₂₉	1	8	yes	—
836	#121	C₂³×C₂₉	1	8	yes	—
837	#121	C₂³×C₂₉	1	8	yes	—
838	#121	C₂³×C₂₉	1	8	yes	—
839	#121	C₂³×C₂₉	1	8	yes	—
840	#121	C₂³×C₂₉	1	8	yes	—
841	#121	C₂³×C₂₉	1	8	yes	—
842	#121	C₂³×C₂₉	1	8	yes	—
843	#121	C₂³×C₂₉	1	8	yes	—
844	#121	C₂³×C₂₉	1	8	yes	—
845	#120	C₂³×C₂₉	1	4	yes	—
846	#120	C₂³×C₂₉	1	8	yes	—
847	#120	C₂³×C₂₉	1	8	yes	—
848	#120	C₂³×C₂₉	1	8	yes	—
849	#120	C₂³×C₂₉	1	8	yes	—
850	#120	C₂³×C₂₉	1	8	yes	—
851	#120	C₂³×C₂₉	1	4	yes	—
852	#120	C₂³×C₂₉	1	4	yes	—
853	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
854	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
855	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
856	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
857	C₄×Q₈	C₂³×C₂₉	1	8	yes	—
858	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
859	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
860	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
861	C₄×Q₈	C₂³×C₂₉	1	8	yes	—
862	C₄×Q₈	C₂³×C₂₉	1	8	yes	—
863	C₄×D₄	C₂³×C₂₉	1	8	yes	—
864	C₄×D₄	C₂³×C₂₉	1	8	yes	—
865	C₄×D₄	C₂³×C₂₉	1	4	yes	—
866	C₄×D₄	C₂³×C₂₉	1	4	yes	—
867	C₄×D₄	C₂³×C₂₉	1	8	yes	—
868	C₄×D₄	C₂³×C₂₉	1	8	yes	—
869	C₄×D₄	C₂³×C₂₉	1	8	yes	—
870	C₄×D₄	C₂³×C₂₉	1	4	yes	—
871	C₄×D₄	C₂³×C₂₉	1	4	yes	—
872	C₄×D₄	C₂³×C₂₉	1	8	yes	—
873	C₄×D₄	C₂³×C₂₉	1	8	yes	—
874	C₄×D₄	C₂³×C₂₉	1	8	yes	—
875	C₄×D₄	C₂³×C₂₉	1	8	yes	—
876	C₄×D₄	C₂³×C₂₉	1	8	yes	—
877	C₄×D₄	C₂³×C₂₉	1	8	yes	—
878	C₄×D₄	C₂³×C₂₉	1	8	yes	—
879	C₄×D₄	C₂³×C₂₉	1	4	yes	—
880	C₄×D₄	C₂³×C₂₉	1	8	yes	—
881	C₄×D₄	C₂³×C₂₉	1	8	yes	—
882	C₄×D₄	C₂³×C₂₉	1	4	yes	—
883	C₄×D₄	C₂³×C₂₉	1	4	yes	—
884	C₄×D₄	C₂³×C₂₉	1	8	yes	—
885	C₄×D₄	C₂³×C₂₉	1	8	yes	—
886	C₄×D₄	C₂³×C₂₉	1	8	yes	—
887	C₄×D₄	C₂³×C₂₉	1	8	yes	—
888	C₄×D₄	C₂³×C₂₉	1	8	yes	—
889	C₄×D₄	C₂³×C₂₉	1	8	yes	—
890	#117	C₂³×C₂₉	1	8	yes	—
891	#117	C₂³×C₂₉	1	8	yes	—
892	#117	C₂³×C₂₉	1	8	yes	—
893	#117	C₂³×C₂₉	1	8	yes	—
894	#117	C₂³×C₂₉	1	8	yes	—
895	#117	C₂³×C₂₉	1	8	yes	—
896	#117	C₂³×C₂₉	1	8	yes	—
897	#117	C₂³×C₂₉	1	4	yes	—
898	#117	C₂³×C₂₉	1	2	yes	—
899	#117	C₂³×C₂₉	1	4	yes	—
900	#117	C₂³×C₂₉	1	4	yes	—
901	#117	C₂³×C₂₉	1	8	yes	—
902	#117	C₂³×C₂₉	1	8	yes	—
903	#117	C₂³×C₂₉	1	8	yes	—
904	#117	C₂³×C₂₉	1	8	yes	—
905	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
906	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
907	C₂×C₄⋊C₄	C₂³×C₂₉	1	8	yes	—
908	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
909	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
910	C₂×C₄⋊C₄	C₂³×C₂₉	1	8	yes	—
911	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
912	C₂×C₄⋊C₄	C₂³×C₂₉	1	4	yes	—
913	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
914	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
915	C₂×C₂²⋊C₄	C₂³×C₂₉	1	8	yes	—
916	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
917	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
918	C₂×C₂²⋊C₄	C₂³×C₂₉	1	4	yes	—
919	C₂×C₂²⋊C₄	C₂³×C₂₉	1	8	yes	—
920	C₂×C₂²⋊C₄	C₂³×C₂₉	1	8	yes	—
921	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
922	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
923	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
924	C₂×C₄²	C₂³×C₂₉	1	4	yes	—
925	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
926	C₂×C₄²	C₂³×C₂₉	1	8	yes	—
927	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
928	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
929	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
930	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
931	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
932	C₂₉	#62755	1	1	yes	characteristic, direct product factor, Sylow
933	C₂⁴	C₂⁴×C₂₉	1	1	yes	characteristic
934	C₂⁴	C₂⁴×C₂₉	1	4	yes	—
935	C₂⁴	C₂⁴×C₂₉	1	4	yes	—
936	#41	—	4	8	no	—
937	#41	—	4	4	no	—
938	#41	—	4	8	no	—
939	#41	—	4	16	no	—
940	C₂×Q₈	—	4	4	no	—
941	C₂×Q₈	C₂⁴×C₂₉	1	4	yes	—
942	C₂×Q₈	C₂⁴×C₂₉	1	4	yes	—
943	C₂×Q₈	C₂⁴×C₂₉	1	4	yes	—
944	C₂×Q₈	C₂⁴×C₂₉	1	8	yes	—
945	C₂×Q₈	C₂⁴×C₂₉	1	4	yes	—
946	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
947	C₂×D₄	—	4	4	no	—
948	C₂×D₄	—	4	8	no	—
949	C₂×D₄	—	4	16	no	—
950	C₂×D₄	C₂⁴×C₂₉	1	8	yes	—
951	C₂×D₄	C₂⁴×C₂₉	1	8	yes	—
952	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
953	C₂×D₄	C₂⁴×C₂₉	1	8	yes	—
954	C₂×D₄	C₂⁴×C₂₉	1	8	yes	—
955	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
956	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
957	C₂×D₄	C₂⁴×C₂₉	1	8	yes	—
958	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
959	C₂×D₄	C₂⁴×C₂₉	1	4	yes	—
960	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
961	C₂×D₄	C₂⁴×C₂₉	1	8	yes	—
962	C₂×D₄	C₂⁴×C₂₉	1	8	yes	—
963	C₂²×C₄	—	4	2	no	—
964	C₂²×C₄	—	4	8	no	—
965	C₂²×C₄	—	4	8	no	—
966	C₂²×C₄	—	4	4	no	—
967	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
968	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
969	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
970	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
971	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
972	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
973	C₂²×C₄	C₂⁴×C₂₉	1	8	yes	—
974	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
975	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
976	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
977	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
978	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
979	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
980	C₂²×C₄	C₂⁴×C₂₉	1	8	yes	—
981	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
982	C₂²×C₄	C₂⁴×C₂₉	1	8	yes	—
983	C₂²×C₄	C₂⁴×C₂₉	1	8	yes	—
984	C₂²×C₄	C₂⁴×C₂₉	1	8	yes	—
985	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
986	C₂²×C₄	C₂⁴×C₂₉	1	8	yes	—
987	C₂²×C₄	C₂⁴×C₂₉	1	8	yes	—
988	C₂²×C₄	C₂⁴×C₂₉	1	4	yes	—
989	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
990	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
991	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
992	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
993	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
994	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
995	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
996	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
997	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
998	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
999	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
1000	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
1001	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1002	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
1003	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
1004	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1005	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1006	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1007	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1008	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1009	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1010	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
1011	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
1012	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
1013	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1014	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1015	C₄⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1016	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1017	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1018	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1019	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1020	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1021	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1022	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1023	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1024	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1025	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1026	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1027	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1028	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1029	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1030	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1031	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1032	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1033	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1034	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1035	C₂²⋊C₄	C₂⁴×C₂₉	1	4	yes	—
1036	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1037	C₂²⋊C₄	C₂⁴×C₂₉	1	4	yes	—
1038	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1039	C₂²⋊C₄	C₂⁴×C₂₉	1	8	yes	—
1040	C₂²⋊C₄	C₂⁴×C₂₉	1	4	yes	—
1041	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1042	C₄²	C₂⁴×C₂₉	1	2	yes	—
1043	C₄²	C₂⁴×C₂₉	1	8	yes	—
1044	C₄²	C₂⁴×C₂₉	1	2	yes	—
1045	C₄²	C₂⁴×C₂₉	1	4	yes	—
1046	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1047	C₄²	C₂⁴×C₂₉	1	2	yes	—
1048	C₄²	C₂⁴×C₂₉	1	2	yes	—
1049	C₄²	C₂⁴×C₂₉	1	2	yes	—
1050	C₄²	C₂⁴×C₂₉	1	2	yes	—
1051	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1052	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1053	C₄²	C₂⁴×C₂₉	1	4	yes	—
1054	C₄²	C₂⁴×C₂₉	1	8	yes	—
1055	C₄²	C₂⁴×C₂₉	1	8	yes	—
1056	C₄²	C₂⁴×C₂₉	1	8	yes	—
1057	C₄²	C₂⁴×C₂₉	1	4	yes	—
1058	C₄²	C₂⁴×C₂₉	1	8	yes	—
1059	C₂³	—	2	4	no	—
1060	C₂³	—	2	8	no	—
1061	C₂³	—	4	1	no	—
1062	C₂³	—	4	4	no	—
1063	C₂³	—	4	4	no	—
1064	C₂³	—	4	4	no	—
1065	C₂³	—	4	8	no	—
1066	C₂³	C₂⁵×C₂₉	1	8	yes	—
1067	C₂³	C₂⁵×C₂₉	1	4	yes	—
1068	C₂³	C₂⁵×C₂₉	1	1	yes	characteristic
1069	C₂³	C₂⁵×C₂₉	1	2	yes	—
1070	Q₈	—	4	4	no	—
1071	Q₈	—	4	4	no	—
1072	Q₈	—	4	4	no	—
1073	Q₈	—	4	2	no	—
1074	Q₈	—	4	4	no	—
1075	Q₈	—	4	8	no	—
1076	D₄	—	2	16	no	—
1077	D₄	—	2	16	no	—
1078	D₄	—	4	4	no	—
1079	D₄	—	4	4	no	—
1080	D₄	—	4	8	no	—
1081	D₄	—	4	8	no	—
1082	D₄	—	4	8	no	—
1083	D₄	—	4	8	no	—
1084	D₄	—	4	4	no	—
1085	D₄	—	4	4	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	4	4	no	—
1088	D₄	—	4	8	no	—
1089	C₂×C₄	—	2	4	no	—
1090	C₂×C₄	—	2	4	no	—
1091	C₂×C₄	—	2	8	no	—
1092	C₂×C₄	—	2	4	no	—
1093	C₂×C₄	—	2	16	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	8	no	—
1096	C₂×C₄	—	4	1	no	—
1097	C₂×C₄	—	4	8	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	4	no	—
1102	C₂×C₄	—	4	4	no	—
1103	C₂×C₄	—	4	8	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	4	2	no	—
1106	C₂×C₄	—	4	4	no	—
1107	C₂×C₄	—	4	8	no	—
1108	C₂×C₄	—	4	8	no	—
1109	C₂×C₄	—	4	8	no	—
1110	C₂×C₄	—	4	8	no	—
1111	C₂×C₄	C₂⁵×C₂₉	1	2	yes	—
1112	C₂×C₄	C₂⁵×C₂₉	1	2	yes	—
1113	C₂×C₄	C₂⁵×C₂₉	1	8	yes	—
1114	C₂×C₄	C₂⁵×C₂₉	1	2	yes	—
1115	C₂×C₄	C₂⁵×C₂₉	1	2	yes	—
1116	C₂×C₄	C₂⁵×C₂₉	1	2	yes	—
1117	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1118	C₂×C₄	C₂⁵×C₂₉	1	4	yes	—
1119	C₂×C₄	C₂⁵×C₂₉	1	8	yes	—
1120	C₂×C₄	C₂⁵×C₂₉	1	8	yes	—
1121	C₂×C₄	C₂⁵×C₂₉	1	8	yes	—
1122	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1123	C₂²	—	2	2	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	8	no	—
1126	C₂²	—	2	1	no	—
1127	C₂²	—	2	4	no	—
1128	C₂²	—	2	8	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	2	8	no	—
1131	C₂²	—	2	8	no	—
1132	C₂²	—	4	4	no	—
1133	C₂²	—	8	8	no	—
1134	C₂²	—	8	8	no	—
1135	C₂²	C₂₉×#585	1	4	yes	—
1136	C₂²	C₂⁶×C₂₉	1	1	yes	characteristic
1137	C₄	—	2	2	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	2	8	no	—
1140	C₄	—	2	2	no	—
1141	C₄	—	2	2	no	—
1142	C₄	—	2	2	no	—
1143	C₄	—	2	1	no	—
1144	C₄	—	2	4	no	—
1145	C₄	—	2	8	no	—
1146	C₄	—	2	8	no	—
1147	C₄	—	2	8	no	—
1148	C₄	C₂₉×#585	1	2	yes	—
1149	C₂	—	2	4	no	—
1150	C₂	—	4	1	no	—
1151	C₂	—	4	8	no	—
1152	C₂	—	4	4	no	—
1153	C₂	C₂×C₂₉×#585	1	2	yes	—
1154	C₂	C₂×C₂₉×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₂₉
socle	C₂²×C₂₉	C₂⁶
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
1. C₂₉×#3566	C₂	semidirect
2. C₂₉×#3564	C₂	semidirect
3. C₂₉×#3560	C₂	semidirect
4. C₂₉×#3553	C₂	semidirect
5. C₂₉×#3545	C₂	semidirect
6. C₂₉×#3535	C₂	semidirect
7. C₂₉×#3534	C₂	semidirect
8. C₂₉×#3531	C₂	semidirect
9. C₂₉×#3529	C₂	semidirect
10. C₂₉×#3481	C₂	semidirect
11. C₂₉×#3475	C₂	semidirect
12. C₂₉×#3461	C₂	semidirect
13. C₂₉×#3459	C₂	semidirect
14. C₂₉×#3455	C₂	semidirect
15. C₂₉×#3444	C₂	semidirect
16. C₂×C₂₉×#529	C₂	semidirect
17. C₂₉×#564	C₂²	semidirect
18. C₂₉×#563	C₂²	semidirect
19. C₂₉×#563	C₂²	semidirect
20. C₂₉×#563	C₂²	semidirect
21. C₂₉×#563	C₂²	semidirect
22. C₂₉×#563	C₂²	semidirect
23. C₂₉×#562	C₂²	semidirect
24. C₂₉×#562	C₂²	semidirect
25. C₂₉×#562	C₂²	semidirect
26. C₂₉×#562	C₂²	semidirect
27. C₂₉×H(3,𝔽₄)	C₂²	semidirect
28. C₂₉×#560	C₂²	semidirect
29. C₂₉×#560	C₂²	semidirect
30. C₂₉×#559	C₂²	semidirect
31. C₂₉×#556	C₂²	semidirect
32. C₂₉×#555	C₂²	semidirect
33. C₂₉×#554	C₂²	semidirect
34. C₂₉×#554	C₂²	semidirect
35. C₂₉×#553	C₂²	semidirect
36. C₂₉×#553	C₂²	semidirect
37. C₂₉×#553	C₂²	semidirect
38. C₂₉×#553	C₂²	semidirect
39. C₂₉×#552	C₂²	semidirect
40. C₂₉×#552	C₂²	semidirect
41. C₂₉×#552	C₂²	semidirect
42. C₂₉×#552	C₂²	semidirect
43. C₂₉×#551	C₂²	semidirect
44. C₂₉×#551	C₂²	semidirect
45. C₂₉×#551	C₂²	semidirect
46. C₂₉×#551	C₂²	semidirect
47. C₂₉×#551	C₂²	semidirect
48. C₂₉×#551	C₂²	semidirect
49. C₂₉×#551	C₂²	semidirect
50. C₂₉×#547	C₂²	semidirect
51. C₂₉×#546	C₂²	semidirect
52. C₂₉×#546	C₂²	semidirect
53. C₂₉×#546	C₂²	semidirect
54. C₂₉×#546	C₂²	semidirect
55. D₄²×C₂₉	C₂²	semidirect
56. C₂₉×#544	C₂²	semidirect
57. C₂₉×#543	C₂²	semidirect
58. C₂₉×#542	C₂²	semidirect
59. C₂₉×#542	C₂²	semidirect
60. C₂₉×#542	C₂²	semidirect
61. C₂₉×#542	C₂²	semidirect
62. C₂₉×#541	C₂²	semidirect
63. C₂₉×#541	C₂²	semidirect
64. C₂₉×#541	C₂²	semidirect
65. C₂₉×#540	C₂²	semidirect
66. C₂₉×#539	C₂²	semidirect
67. C₂₉×#539	C₂²	semidirect
68. C₂₉×#539	C₂²	semidirect
69. C₂₉×#539	C₂²	semidirect
70. C₂₉×#539	C₂²	semidirect
71. C₂₉×#539	C₂²	semidirect
72. C₂₉×#539	C₂²	semidirect
73. C₂₉×#539	C₂²	semidirect
75. C₂₉×#538	C₂²	semidirect
76. C₂₉×#538	C₂²	semidirect
77. C₂₉×#538	C₂²	semidirect
78. C₂₉×#538	C₂²	semidirect
79. C₂₉×#538	C₂²	semidirect
81. C₂₉×#536	C₂²	semidirect
82. C₂₉×#534	C₂²	semidirect
83. C₂₉×#534	C₂²	semidirect
84. C₂₉×#533	C₂²	semidirect
85. C₂₉×#533	C₂²	semidirect
86. C₂₉×#533	C₂²	semidirect
87. C₂₉×#533	C₂²	semidirect
88. C₂₉×#532	C₂²	semidirect
89. C₂₉×#532	C₂²	semidirect
90. C₂₉×#532	C₂²	semidirect
91. C₂₉×#529	C₂²	semidirect
92. C₂₉×#529	C₂²	semidirect
93. C₂₉×#529	C₂²	semidirect
94. C₂₉×#529	C₂²	semidirect
95. C₂₉×#529	C₂²	semidirect
96. C₂₉×#529	C₂²	semidirect
97. C₂₉×#529	C₂²	semidirect
98. C₂₉×#529	C₂²	semidirect
99. C₂₉×#529	C₂²	semidirect
100. C₂₉×#529	C₂²	semidirect
101. C₂₉×#529	C₂²	semidirect
102. C₂₉×#529	C₂²	semidirect
103. C₂₉×#529	C₂²	semidirect
104. C₂₉×#529	C₂²	semidirect
105. C₂₉×#529	C₂²	semidirect
106. C₂₉×#529	C₂²	semidirect
107. C₂₉×#529	C₂²	semidirect
108. C₂×C₂₉×#126	C₂²	semidirect
109. C₂×C₂₉×#125	C₂²	semidirect
110. C₂×C₂₉×#124	C₂²	semidirect
111. C₂₉×#525	C₂²	semidirect
112. C₂₉×#525	C₂²	semidirect
113. C₂₉×#525	C₂²	semidirect
114. C₂₉×#525	C₂²	semidirect
115. C₂₉×#525	C₂²	semidirect
116. C₂₉×#525	C₂²	semidirect
117. C₂×C₂₉×#123	C₂²	semidirect
118. C₂×C₂₉×C₂²⋊Q₈	C₂²	semidirect
120. C₄×#41×C₂₉	C₂²	semidirect
121. C₄×#41×C₂₉	C₂²	semidirect
122. C₄×#41×C₂₉	C₂²	semidirect
123. C₄×#41×C₂₉	C₂²	semidirect
124. C₂×C₄×Q₈×C₂₉	C₂²	semidirect
125. C₂×C₄×D₄×C₂₉	C₂²	semidirect
126. C₂×C₄×D₄×C₂₉	C₂²	semidirect
127. C₂×C₄×D₄×C₂₉	C₂²	semidirect
128. C₂×C₂₉×#117	C₂²	semidirect
129. C₂×C₂₉×#117	C₂²	semidirect
130. C₂²×C₄²×C₂₉	C₂²	semidirect
481. #62755	C₂₉	direct (N × H)
546. #3566	C₂×C₂₉	semidirect
547. #3564	C₂×C₂₉	semidirect
548. #3560	C₂×C₂₉	semidirect
549. #3553	C₂×C₂₉	semidirect
550. #3545	C₂×C₂₉	semidirect
551. #3535	C₂×C₂₉	semidirect
552. #3534	C₂×C₂₉	semidirect
553. #3531	C₂×C₂₉	semidirect
554. #3529	C₂×C₂₉	semidirect
555. #3481	C₂×C₂₉	semidirect
556. #3475	C₂×C₂₉	semidirect
557. #3461	C₂×C₂₉	semidirect
558. #3459	C₂×C₂₉	semidirect
559. #3455	C₂×C₂₉	semidirect
560. #3444	C₂×C₂₉	semidirect
561. C₂×#529	C₂×C₂₉	semidirect
588. #564	C₂²×C₂₉	semidirect
589. #563	C₂²×C₂₉	semidirect
590. #563	C₂²×C₂₉	semidirect
591. #563	C₂²×C₂₉	semidirect
592. #563	C₂²×C₂₉	semidirect
593. #563	C₂²×C₂₉	semidirect
594. #562	C₂²×C₂₉	semidirect
595. #562	C₂²×C₂₉	semidirect
596. #562	C₂²×C₂₉	semidirect
597. #562	C₂²×C₂₉	semidirect
598. H(3,𝔽₄)	C₂²×C₂₉	semidirect
599. #560	C₂²×C₂₉	semidirect
600. #560	C₂²×C₂₉	semidirect
601. #559	C₂²×C₂₉	semidirect
602. #556	C₂²×C₂₉	semidirect
603. #555	C₂²×C₂₉	semidirect
604. #554	C₂²×C₂₉	semidirect
605. #554	C₂²×C₂₉	semidirect
606. #553	C₂²×C₂₉	semidirect
607. #553	C₂²×C₂₉	semidirect
608. #553	C₂²×C₂₉	semidirect
609. #553	C₂²×C₂₉	semidirect
610. #552	C₂²×C₂₉	semidirect
611. #552	C₂²×C₂₉	semidirect
612. #552	C₂²×C₂₉	semidirect
613. #552	C₂²×C₂₉	semidirect
614. #551	C₂²×C₂₉	semidirect
615. #551	C₂²×C₂₉	semidirect
616. #551	C₂²×C₂₉	semidirect
617. #551	C₂²×C₂₉	semidirect
618. #551	C₂²×C₂₉	semidirect
619. #551	C₂²×C₂₉	semidirect
620. #551	C₂²×C₂₉	semidirect
621. #547	C₂²×C₂₉	semidirect
622. #546	C₂²×C₂₉	semidirect
623. #546	C₂²×C₂₉	semidirect
624. #546	C₂²×C₂₉	semidirect
625. #546	C₂²×C₂₉	semidirect
626. D₄²	C₂²×C₂₉	semidirect
627. #544	C₂²×C₂₉	semidirect
628. #543	C₂²×C₂₉	semidirect
629. #542	C₂²×C₂₉	semidirect
630. #542	C₂²×C₂₉	semidirect
631. #542	C₂²×C₂₉	semidirect
632. #542	C₂²×C₂₉	semidirect
633. #541	C₂²×C₂₉	semidirect
634. #541	C₂²×C₂₉	semidirect
635. #541	C₂²×C₂₉	semidirect
636. #540	C₂²×C₂₉	semidirect
637. #539	C₂²×C₂₉	semidirect
638. #539	C₂²×C₂₉	semidirect
639. #539	C₂²×C₂₉	semidirect
640. #539	C₂²×C₂₉	semidirect
641. #539	C₂²×C₂₉	semidirect
642. #539	C₂²×C₂₉	semidirect
643. #539	C₂²×C₂₉	semidirect
644. #539	C₂²×C₂₉	semidirect
646. #538	C₂²×C₂₉	semidirect
647. #538	C₂²×C₂₉	semidirect
648. #538	C₂²×C₂₉	semidirect
649. #538	C₂²×C₂₉	semidirect
650. #538	C₂²×C₂₉	semidirect
652. #536	C₂²×C₂₉	semidirect
653. #534	C₂²×C₂₉	semidirect
654. #534	C₂²×C₂₉	semidirect
655. #533	C₂²×C₂₉	semidirect
656. #533	C₂²×C₂₉	semidirect
657. #533	C₂²×C₂₉	semidirect
658. #533	C₂²×C₂₉	semidirect
659. #532	C₂²×C₂₉	semidirect
660. #532	C₂²×C₂₉	semidirect
661. #532	C₂²×C₂₉	semidirect
662. #529	C₂²×C₂₉	semidirect
663. #529	C₂²×C₂₉	semidirect
664. #529	C₂²×C₂₉	semidirect
665. #529	C₂²×C₂₉	semidirect
666. #529	C₂²×C₂₉	semidirect
667. #529	C₂²×C₂₉	semidirect
668. #529	C₂²×C₂₉	semidirect
669. #529	C₂²×C₂₉	semidirect
670. #529	C₂²×C₂₉	semidirect
671. #529	C₂²×C₂₉	semidirect
672. #529	C₂²×C₂₉	semidirect
673. #529	C₂²×C₂₉	semidirect
674. #529	C₂²×C₂₉	semidirect
675. #529	C₂²×C₂₉	semidirect
676. #529	C₂²×C₂₉	semidirect
677. #529	C₂²×C₂₉	semidirect
678. #529	C₂²×C₂₉	semidirect
679. C₂×#126	C₂²×C₂₉	semidirect
680. C₂×#125	C₂²×C₂₉	semidirect
681. C₂×#124	C₂²×C₂₉	semidirect
682. #525	C₂²×C₂₉	semidirect
683. #525	C₂²×C₂₉	semidirect
684. #525	C₂²×C₂₉	semidirect
685. #525	C₂²×C₂₉	semidirect
686. #525	C₂²×C₂₉	semidirect
687. #525	C₂²×C₂₉	semidirect
688. C₂×#123	C₂²×C₂₉	semidirect
689. C₂×C₂²⋊Q₈	C₂²×C₂₉	semidirect
691. C₄×#41	C₂²×C₂₉	semidirect
692. C₄×#41	C₂²×C₂₉	semidirect
693. C₄×#41	C₂²×C₂₉	semidirect
694. C₄×#41	C₂²×C₂₉	semidirect
695. C₂×C₄×Q₈	C₂²×C₂₉	semidirect
696. C₂×C₄×D₄	C₂²×C₂₉	semidirect
697. C₂×C₄×D₄	C₂²×C₂₉	semidirect
698. C₂×C₄×D₄	C₂²×C₂₉	semidirect
699. C₂×#117	C₂²×C₂₉	semidirect
700. C₂×#117	C₂²×C₂₉	semidirect
701. C₂²×C₄²	C₂²×C₂₉	semidirect
932. C₂₉	#62755	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×#3566	2
C₂₉×#3564	2
C₂₉×#3560	2
C₂₉×#3553	2
C₂₉×#3545	2
C₂₉×#3535	2
C₂₉×#3534	2
C₂₉×#3531	2
C₂₉×#3529	2
C₂₉×#3481	2
C₂₉×#3475	2
C₂₉×#3461	2
C₂₉×#3459	2
C₂₉×#3455	2
C₂₉×#3444	2
C₂×C₂₉×#529	2
#62755	29

Subgroups — C29×#62755 #20357655

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#62755 #20357655