Subgroups — C₂₉×#62074 #20356974

Order 7424.

1900 conjugacy classes of subgroups.

The subgroup lattice has 1204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3517	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#3330	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#3309	C₂	1	2	yes	maximal, complemented
9	C₂₉×#3297	C₂	1	2	yes	maximal, complemented
10	C₂₉×#3294	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#3287	C₂	1	2	yes	maximal, complemented
12	C₂₉×#3284	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#3274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#3268	C₂	1	2	yes	maximal, complemented
15	C₂₉×#3257	C₂	1	2	yes	maximal, complemented
16	C₂₉×#3245	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₉×#3220	C₂	1	2	yes	maximal, complemented
18	C₂₉×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₉×#3124	C₂	1	2	yes	maximal, complemented
20	C₂₉×#3106	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₉×#3045	C₂	1	2	yes	maximal, complemented
22	C₂₉×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₉×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₉×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂×C₂₉×#135	C₂²	1	2	yes	complemented
26	C₂×C₂₉×#135	C₂²	1	2	yes	complemented
27	C₂₉×#560	—	2	2	no	—
28	C₂₉×#557	C₂²	1	1	yes	characteristic, complemented
29	C₂₉×#556	C₂²	1	1	yes	characteristic
30	C₂₉×#553	—	2	2	no	—
31	C₂₉×#553	—	2	1	no	—
32	C₂₉×#553	C₂²	1	2	yes	complemented
33	C₂₉×#550	—	2	1	no	—
34	C₂₉×#550	C₂²	1	1	yes	characteristic
35	C₂₉×#550	C₂²	1	2	yes	—
36	C₂₉×#550	C₂²	1	1	yes	characteristic
37	C₂₉×#550	C₂²	1	2	yes	complemented
38	C₂₉×#550	C₂²	1	1	yes	characteristic, complemented
39	C₂₉×#547	—	2	1	no	—
40	C₂₉×#547	C₂²	1	1	yes	characteristic
41	C₂₉×#547	C₂²	1	1	yes	characteristic
42	C₂₉×#546	—	2	1	no	—
43	C₂₉×#546	C₂²	1	2	yes	—
44	D₄²×C₂₉	C₂²	1	1	yes	characteristic
45	C₂₉×#542	C₂²	1	2	yes	—
46	C₂₉×#540	—	2	2	no	—
47	C₂₉×#540	C₂²	1	2	yes	complemented
48	C₂₉×#538	—	2	2	no	—
49	C₂₉×#537	—	2	1	no	—
50	C₂₉×#535	—	2	1	no	—
51	C₂₉×#535	C₂²	1	2	yes	—
52	C₂₉×#532	—	2	1	no	—
53	C₂₉×#532	C₂²	1	1	yes	characteristic
54	C₂₉×#532	C₂²	1	1	yes	characteristic
55	C₂₉×#532	C₂²	1	1	yes	characteristic, complemented
56	C₂₉×#529	—	2	1	no	—
57	C₂₉×#529	C₂²	1	1	yes	characteristic
58	C₂₉×#520	C₂²	1	2	yes	complemented
59	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic, complemented
60	C₂₉×#496	C₂²	1	2	yes	—
61	C₂₉×#493	C₂²	1	1	yes	characteristic
62	C₂₉×#493	C₂²	1	2	yes	complemented
63	C₂₉×#492	C₂²	1	1	yes	characteristic, complemented
64	C₂₉×#490	C₂²	1	2	yes	complemented
65	C₂₉×#488	C₂²	1	2	yes	—
66	C₂₉×#487	C₂²	1	1	yes	characteristic, complemented
67	C₂₉×#486	C₂²	1	1	yes	characteristic
68	C₂₉×#484	C₂²	1	2	yes	complemented
69	C₂₉×#482	C₂²	1	1	yes	characteristic
70	C₂₉×#482	C₂²	1	1	yes	characteristic, complemented
71	C₂₉×#480	C₂²	1	2	yes	—
72	C₂₉×#479	C₂²	1	2	yes	complemented
73	C₂₉×#478	C₂²	1	2	yes	complemented
74	C₂₉×#477	C₂²	1	1	yes	characteristic, complemented
75	C₂₉×#476	C₂²	1	1	yes	characteristic, complemented
76	C₂₉×#474	C₂²	1	1	yes	characteristic
77	C₂₉×#474	C₂²	1	2	yes	complemented
78	C₂₉×#474	C₂²	1	1	yes	characteristic, complemented
79	C₂₉×#469	C₂²	1	2	yes	—
80	C₂₉×#468	C₂²	1	2	yes	complemented
81	C₂₉×#466	C₂²	1	2	yes	—
82	C₂₉×#466	C₂²	1	2	yes	—
83	C₂₉×#466	C₂²	1	2	yes	complemented
84	C₂₉×#465	C₂²	1	2	yes	complemented
85	C₂₉×#464	C₂²	1	2	yes	—
86	C₂₉×#464	C₂²	1	2	yes	complemented
87	C₂₉×#463	C₂²	1	2	yes	—
88	C₂₉×#463	C₂²	1	2	yes	complemented
89	C₂₉×#463	C₂²	1	2	yes	complemented
90	C₂₉×#463	C₂²	1	2	yes	complemented
91	C₂₉×#462	C₂²	1	1	yes	characteristic, complemented
92	C₂₉×#461	C₂²	1	1	yes	characteristic, complemented
93	C₂₉×#460	C₂²	1	1	yes	characteristic
94	C₂₉×#460	C₂²	1	1	yes	characteristic
95	C₂₉×#460	C₂²	1	2	yes	complemented
96	C₂₉×#460	C₂²	1	2	yes	complemented
97	C₂₉×#459	C₂²	1	1	yes	characteristic
98	C₂₉×#459	C₂²	1	2	yes	—
99	C₂₉×#459	C₂²	1	1	yes	characteristic
100	C₂₉×#459	C₂²	1	1	yes	characteristic
101	C₂₉×#459	C₂²	1	1	yes	characteristic, complemented
102	C₂₉×#459	C₂²	1	2	yes	complemented
103	C₂₉×#459	C₂²	1	2	yes	complemented
104	C₂₉×#452	C₂²	1	2	yes	complemented
105	C₂₉×#449	C₂²	1	1	yes	characteristic
106	C₂₉×#449	C₂²	1	2	yes	—
107	C₂₉×#449	C₂²	1	2	yes	complemented
108	C₂₉×#449	C₂²	1	2	yes	complemented
109	C₂₉×#449	C₂²	1	2	yes	complemented
110	C₂₉×#449	C₂²	1	2	yes	complemented
111	C₂₉×#449	C₂²	1	1	yes	characteristic, complemented
112	C₂₉×#447	C₂²	1	2	yes	—
113	C₂₉×#447	C₂²	1	2	yes	—
114	C₂₉×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
116	C₂₉×#440	C₂²	1	2	yes	complemented
117	C₂₉×#440	C₂²	1	2	yes	complemented
118	C₄×Q₁₆×C₂₉	C₂²	1	2	yes	complemented
119	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
122	C₄×D₈×C₂₉	C₂²	1	2	yes	complemented
123	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
124	C₂₉×#436	C₂²	1	1	yes	characteristic
125	C₂₉×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
127	C₈×D₄×C₂₉	C₂²	1	2	yes	complemented
128	C₂₉×#433	C₂²	1	2	yes	complemented
129	C₂₉×#431	C₂²	1	1	yes	characteristic, complemented
130	C₂₉×#424	C₂²	1	2	yes	complemented
131	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
132	C₂₉×#417	C₂²	1	2	yes	complemented
133	C₂₉×#416	C₂²	1	2	yes	complemented
134	C₂×C₂₉×#102	C₂²	1	2	yes	—
135	C₂×#41×C₂₉	—	2	1	no	—
136	C₂×#41×C₂₉	—	2	1	no	—
137	C₂×#41×C₂₉	—	2	1	no	—
138	C₂×#41×C₂₉	—	2	1	no	—
139	C₂×#41×C₂₉	—	2	1	no	—
140	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
141	C₂×#41×C₂₉	C₂³	1	2	yes	—
142	C₂×#41×C₂₉	C₂³	1	2	yes	—
143	C₂×#41×C₂₉	C₂³	1	2	yes	—
144	C₂²×D₄×C₂₉	—	2	1	no	—
145	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
146	C₂₉×AGL(1,ℤ/8)	—	4	4	no	—
147	C₂₉×#135	—	4	4	no	—
148	C₂₉×#135	—	4	4	no	—
149	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
156	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
157	C₂×D₈×C₂₉	C₂³	1	2	yes	—
158	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
159	C₂×D₈×C₂₉	C₂³	1	2	yes	—
160	C₂×D₈×C₂₉	C₂³	1	2	yes	—
161	C₂×D₈×C₂₉	C₂³	1	2	yes	—
162	C₂×D₈×C₂₉	C₂³	1	2	yes	—
163	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
164	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
165	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
166	C₂₉×C₄⋊Q₈	—	2	1	no	—
167	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₂₉×#127	—	2	1	no	—
171	C₂₉×#127	—	2	2	no	—
172	C₂₉×#127	—	2	2	no	—
173	C₂₉×#127	C₂³	1	1	yes	characteristic
174	C₂₉×#127	C₂³	1	1	yes	characteristic
175	C₂₉×#127	C₂³	1	1	yes	characteristic
176	C₂₉×#127	C₂³	1	2	yes	—
177	C₂₉×#127	C₂³	1	2	yes	—
178	C₂₉×#126	—	2	2	no	—
179	C₂₉×#126	—	2	2	no	—
180	C₂₉×#126	—	2	2	no	—
181	C₂₉×#126	D₄	1	2	yes	—
182	C₂₉×#125	—	2	2	no	—
183	C₂₉×#125	D₄	1	1	yes	characteristic
184	C₂₉×#125	C₂³	1	2	yes	—
185	C₂₉×#124	—	2	2	no	—
186	C₂₉×#124	—	2	1	no	—
187	C₂₉×#124	—	2	1	no	—
188	C₂₉×#124	D₄	1	1	yes	characteristic
189	C₂₉×#124	C₂³	1	2	yes	—
190	C₂₉×#124	C₂³	1	2	yes	—
191	C₂₉×#123	—	2	2	no	—
192	C₂₉×#123	—	2	2	no	—
193	C₂₉×#123	—	2	2	no	—
194	C₂₉×#123	—	2	2	no	—
195	C₂₉×#123	—	2	2	no	—
196	C₂₉×#123	—	2	2	no	—
197	C₂₉×#123	—	2	2	no	—
198	C₂₉×#123	D₄	1	2	yes	—
199	C₂₉×C₂²⋊Q₈	—	2	1	no	—
200	C₂₉×C₂²⋊Q₈	—	2	1	no	—
201	C₂₉×C₂²⋊Q₈	—	2	2	no	—
202	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
203	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₂₉×#121	—	2	1	no	—
205	C₂₉×#121	—	2	2	no	—
206	C₂₉×#121	—	2	1	no	—
207	C₂₉×#121	—	2	1	no	—
208	C₂₉×#121	—	2	1	no	—
209	C₂₉×#121	—	2	1	no	—
210	C₂₉×#121	—	2	1	no	—
211	C₂₉×#121	—	2	1	no	—
212	C₂₉×#121	—	2	2	no	—
213	C₂₉×#121	—	2	2	no	—
214	C₂₉×#121	—	2	1	no	—
215	C₂₉×#121	—	2	2	no	—
216	C₂₉×#121	—	2	2	no	—
217	C₂₉×#121	—	2	2	no	—
218	C₂₉×#121	—	2	2	no	—
219	C₂₉×#121	—	2	2	no	—
220	C₂₉×#121	—	2	2	no	—
221	C₂₉×#121	—	2	2	no	—
222	C₂₉×#121	—	2	2	no	—
223	C₂₉×#121	—	2	2	no	—
224	C₂₉×#121	—	2	2	no	—
225	C₂₉×#121	D₄	1	1	yes	characteristic
226	C₂₉×#121	C₂³	1	2	yes	—
227	C₂₉×#121	C₂³	1	2	yes	—
228	C₂₉×#121	C₂³	1	1	yes	characteristic
229	C₂₉×#121	C₂³	1	2	yes	—
230	C₂₉×#121	C₂³	1	2	yes	—
231	C₂₉×#121	C₂³	1	1	yes	characteristic
232	C₂₉×#120	—	2	2	no	—
233	C₂₉×#120	—	2	2	no	—
234	C₂₉×#120	—	2	2	no	—
235	C₂₉×#120	—	2	2	no	—
236	C₄×Q₈×C₂₉	—	2	1	no	—
237	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
239	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
240	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₂₉	—	2	1	no	—
243	C₄×D₄×C₂₉	—	2	1	no	—
244	C₄×D₄×C₂₉	—	2	1	no	—
245	C₄×D₄×C₂₉	—	2	2	no	—
246	C₄×D₄×C₂₉	—	2	2	no	—
247	C₄×D₄×C₂₉	—	2	2	no	—
248	C₄×D₄×C₂₉	—	2	2	no	—
249	C₄×D₄×C₂₉	—	2	2	no	—
250	C₄×D₄×C₂₉	—	2	1	no	—
251	C₄×D₄×C₂₉	—	2	1	no	—
252	C₄×D₄×C₂₉	—	2	1	no	—
253	C₄×D₄×C₂₉	—	2	1	no	—
254	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₂₉	C₂³	1	2	yes	—
258	C₄×D₄×C₂₉	C₂³	1	2	yes	—
259	C₄×D₄×C₂₉	C₂³	1	2	yes	—
260	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₂₉	C₂³	1	2	yes	—
263	C₂₉×#117	—	2	2	no	—
264	C₂₉×#117	—	2	1	no	—
265	C₂₉×#117	—	2	1	no	—
266	C₂₉×#117	C₂³	1	1	yes	characteristic
267	C₂₉×#117	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
269	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
270	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
271	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
272	C₂×C₄²×C₂₉	—	2	1	no	—
273	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
274	C₂₉×#107	C₂³	1	1	yes	characteristic
275	C₂₉×#107	C₂³	1	1	yes	characteristic
276	C₂₉×#107	C₂³	1	2	yes	—
277	C₂₉×#107	C₂³	1	2	yes	—
278	C₂₉×#106	C₂³	1	1	yes	characteristic
279	C₂₉×#106	C₂³	1	1	yes	characteristic
280	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
283	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
285	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
286	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₂₉×#103	C₂³	1	1	yes	characteristic
288	C₂₉×#103	C₂³	1	1	yes	characteristic
289	C₂₉×#103	C₂³	1	2	yes	—
290	C₂₉×#103	C₂³	1	2	yes	—
291	C₂₉×#103	C₂³	1	2	yes	—
292	C₂₉×#103	C₂³	1	2	yes	—
293	C₂₉×#102	C₂³	1	1	yes	characteristic
294	C₂₉×#102	C₂³	1	1	yes	characteristic
295	C₂₉×#102	C₂³	1	1	yes	characteristic
296	C₂₉×#102	C₂³	1	2	yes	—
297	C₂₉×#102	C₂³	1	2	yes	—
298	C₂₉×#102	C₂³	1	1	yes	characteristic
299	C₂₉×#102	C₂³	1	1	yes	characteristic
300	C₂₉×#102	C₂³	1	1	yes	characteristic
301	C₂₉×#102	C₂³	1	2	yes	—
302	C₂₉×#102	C₂³	1	2	yes	—
303	C₂₉×#102	C₂³	1	2	yes	—
304	C₂₉×#102	C₂³	1	2	yes	—
305	C₂₉×#102	C₂³	1	2	yes	—
306	C₂₉×#102	C₂³	1	2	yes	—
307	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₂₉×#97	C₂³	1	2	yes	—
312	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₂₉	C₂³	1	2	yes	—
315	C₂⁴×C₂₉	—	2	2	no	—
316	#41×C₂₉	—	2	2	no	—
317	#41×C₂₉	—	2	4	no	—
318	#41×C₂₉	—	4	2	no	—
319	#41×C₂₉	—	4	1	no	—
320	#41×C₂₉	—	4	2	no	—
321	#41×C₂₉	—	4	2	no	—
322	#41×C₂₉	—	4	2	no	—
323	#41×C₂₉	—	4	2	no	—
324	#41×C₂₉	—	8	2	no	—
325	#41×C₂₉	—	8	2	no	—
326	#41×C₂₉	—	8	2	no	—
327	#41×C₂₉	—	8	2	no	—
328	#41×C₂₉	—	8	2	no	—
329	C₂×Q₈×C₂₉	—	2	1	no	—
330	C₂×Q₈×C₂₉	—	2	1	no	—
331	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
332	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₂₉	—	2	2	no	—
335	C₂×D₄×C₂₉	—	2	1	no	—
336	C₂×D₄×C₂₉	—	2	2	no	—
337	C₂×D₄×C₂₉	—	2	1	no	—
338	C₂×D₄×C₂₉	—	2	2	no	—
339	C₂×D₄×C₂₉	—	2	2	no	—
340	C₂×D₄×C₂₉	—	2	2	no	—
341	C₂×D₄×C₂₉	—	2	2	no	—
342	C₂×D₄×C₂₉	—	2	2	no	—
343	C₂×D₄×C₂₉	—	2	1	no	—
344	C₂×D₄×C₂₉	—	2	1	no	—
345	C₂×D₄×C₂₉	—	2	1	no	—
346	C₂×D₄×C₂₉	—	2	1	no	—
347	C₂×D₄×C₂₉	—	2	1	no	—
348	C₂×D₄×C₂₉	—	2	2	no	—
349	C₂×D₄×C₂₉	—	2	1	no	—
350	C₂×D₄×C₂₉	—	2	2	no	—
351	C₂×D₄×C₂₉	—	2	1	no	—
352	C₂×D₄×C₂₉	—	2	2	no	—
353	C₂×D₄×C₂₉	—	2	2	no	—
354	C₂×D₄×C₂₉	—	2	2	no	—
355	C₂×D₄×C₂₉	—	4	2	no	—
356	C₂×D₄×C₂₉	—	4	2	no	—
357	C₂×D₄×C₂₉	—	8	2	no	—
358	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
359	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
360	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
361	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
362	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
363	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
364	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₂₉	—	2	2	no	—
366	C₂²×C₄×C₂₉	—	2	1	no	—
367	C₂²×C₄×C₂₉	—	2	1	no	—
368	C₂²×C₄×C₂₉	—	2	2	no	—
369	C₂²×C₄×C₂₉	—	2	1	no	—
370	C₂²×C₄×C₂₉	—	2	1	no	—
371	C₂²×C₄×C₂₉	—	2	1	no	—
372	C₂²×C₄×C₂₉	—	2	2	no	—
373	C₂²×C₄×C₂₉	—	2	2	no	—
374	C₂²×C₄×C₂₉	—	2	2	no	—
375	C₂²×C₄×C₂₉	—	2	2	no	—
376	C₂²×C₄×C₂₉	—	2	2	no	—
377	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
378	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
379	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
381	Q₁₆×C₂₉	—	2	4	no	—
382	SD₁₆×C₂₉	—	2	2	no	—
383	SD₁₆×C₂₉	—	2	4	no	—
384	SD₁₆×C₂₉	—	2	2	no	—
385	SD₁₆×C₂₉	—	4	2	no	—
386	SD₁₆×C₂₉	—	4	2	no	—
387	SD₁₆×C₂₉	—	4	2	no	—
388	D₈×C₂₉	—	4	1	no	—
389	D₈×C₂₉	—	4	2	no	—
390	D₈×C₂₉	—	4	1	no	—
391	D₈×C₂₉	—	4	2	no	—
392	D₈×C₂₉	—	4	2	no	—
393	D₈×C₂₉	—	4	2	no	—
394	D₈×C₂₉	—	4	2	no	—
395	M₁₆×C₂₉	—	4	2	no	—
396	C₂×C₈×C₂₉	—	4	2	no	—
397	C₂×C₈×C₂₉	—	4	2	no	—
398	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
399	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
400	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
401	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
402	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
403	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₂₉	—	2	1	no	—
405	C₄⋊C₄×C₂₉	—	2	2	no	—
406	C₄⋊C₄×C₂₉	—	2	1	no	—
407	C₄⋊C₄×C₂₉	—	2	2	no	—
408	C₄⋊C₄×C₂₉	—	2	2	no	—
409	C₄⋊C₄×C₂₉	—	2	1	no	—
410	C₄⋊C₄×C₂₉	—	2	1	no	—
411	C₄⋊C₄×C₂₉	—	2	2	no	—
412	C₄⋊C₄×C₂₉	—	2	1	no	—
413	C₄⋊C₄×C₂₉	—	2	1	no	—
414	C₄⋊C₄×C₂₉	—	2	2	no	—
415	C₄⋊C₄×C₂₉	—	2	2	no	—
416	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
420	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
424	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
427	C₂²⋊C₄×C₂₉	—	2	2	no	—
428	C₂²⋊C₄×C₂₉	—	2	1	no	—
429	C₂²⋊C₄×C₂₉	—	2	1	no	—
430	C₂²⋊C₄×C₂₉	—	2	2	no	—
431	C₂²⋊C₄×C₂₉	—	2	2	no	—
432	C₂²⋊C₄×C₂₉	—	2	1	no	—
433	C₂²⋊C₄×C₂₉	—	2	1	no	—
434	C₂²⋊C₄×C₂₉	—	2	2	no	—
435	C₂²⋊C₄×C₂₉	—	2	2	no	—
436	C₂²⋊C₄×C₂₉	—	2	1	no	—
437	C₂²⋊C₄×C₂₉	—	2	2	no	—
438	C₂²⋊C₄×C₂₉	—	2	2	no	—
439	C₂²⋊C₄×C₂₉	—	2	2	no	—
440	C₂²⋊C₄×C₂₉	—	2	2	no	—
441	C₂²⋊C₄×C₂₉	—	2	2	no	—
442	C₂²⋊C₄×C₂₉	—	2	2	no	—
443	C₂²⋊C₄×C₂₉	—	2	1	no	—
444	C₂²⋊C₄×C₂₉	—	2	2	no	—
445	C₂²⋊C₄×C₂₉	—	2	1	no	—
446	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
448	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
451	C₄²×C₂₉	—	2	1	no	—
452	C₄²×C₂₉	—	2	1	no	—
453	C₄²×C₂₉	—	2	1	no	—
454	C₄²×C₂₉	—	2	2	no	—
455	C₄²×C₂₉	—	2	2	no	—
456	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
459	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
460	C₄²×C₂₉	C₂⁴	1	2	yes	—
461	#62074	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
462	C₂³×C₂₉	—	2	1	no	—
463	C₂³×C₂₉	—	2	1	no	—
464	C₂³×C₂₉	—	2	2	no	—
465	C₂³×C₂₉	—	2	2	no	—
466	C₂³×C₂₉	—	2	1	no	—
467	C₂³×C₂₉	—	8	2	no	—
468	C₂³×C₂₉	—	8	2	no	—
469	C₂³×C₂₉	—	8	2	no	—
470	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
471	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
472	Q₈×C₂₉	—	2	2	no	—
473	Q₈×C₂₉	—	2	1	no	—
474	Q₈×C₂₉	—	2	2	no	—
475	Q₈×C₂₉	—	2	2	no	—
476	Q₈×C₂₉	—	4	2	no	—
477	Q₈×C₂₉	—	8	1	no	—
478	Q₈×C₂₉	H(5,𝔽₂)	1	2	yes	—
479	D₄×C₂₉	—	2	2	no	—
480	D₄×C₂₉	—	2	2	no	—
481	D₄×C₂₉	—	2	1	no	—
482	D₄×C₂₉	—	2	2	no	—
483	D₄×C₂₉	—	2	1	no	—
484	D₄×C₂₉	—	2	1	no	—
485	D₄×C₂₉	—	2	1	no	—
486	D₄×C₂₉	—	2	2	no	—
487	D₄×C₂₉	—	2	1	no	—
488	D₄×C₂₉	—	2	2	no	—
489	D₄×C₂₉	—	2	1	no	—
490	D₄×C₂₉	—	4	2	no	—
491	D₄×C₂₉	—	4	2	no	—
492	D₄×C₂₉	—	4	4	no	—
493	D₄×C₂₉	—	4	2	no	—
494	D₄×C₂₉	—	4	2	no	—
495	D₄×C₂₉	—	8	1	no	—
496	D₄×C₂₉	—	8	1	no	—
497	D₄×C₂₉	—	8	1	no	—
498	D₄×C₂₉	—	8	2	no	—
499	D₄×C₂₉	—	8	2	no	—
500	D₄×C₂₉	—	8	2	no	—
501	D₄×C₂₉	—	8	1	no	—
502	D₄×C₂₉	—	8	2	no	—
503	D₄×C₂₉	—	8	2	no	—
504	D₄×C₂₉	—	8	2	no	—
505	D₄×C₂₉	—	8	2	no	—
506	D₄×C₂₉	—	8	2	no	—
507	D₄×C₂₉	—	8	2	no	—
508	D₄×C₂₉	—	8	1	no	—
509	D₄×C₂₉	—	8	1	no	—
510	D₄×C₂₉	—	8	2	no	—
511	D₄×C₂₉	—	8	2	no	—
512	C₂×C₄×C₂₉	—	2	1	no	—
513	C₂×C₄×C₂₉	—	2	2	no	—
514	C₂×C₄×C₂₉	—	2	1	no	—
515	C₂×C₄×C₂₉	—	2	2	no	—
516	C₂×C₄×C₂₉	—	2	2	no	—
517	C₂×C₄×C₂₉	—	2	1	no	—
518	C₂×C₄×C₂₉	—	2	1	no	—
519	C₂×C₄×C₂₉	—	2	1	no	—
520	C₂×C₄×C₂₉	—	2	1	no	—
521	C₂×C₄×C₂₉	—	2	2	no	—
522	C₂×C₄×C₂₉	—	2	2	no	—
523	C₂×C₄×C₂₉	—	2	1	no	—
524	C₂×C₄×C₂₉	—	4	1	no	—
525	C₂×C₄×C₂₉	—	4	2	no	—
526	C₂×C₄×C₂₉	—	4	4	no	—
527	C₂×C₄×C₂₉	—	4	2	no	—
528	C₂×C₄×C₂₉	—	4	2	no	—
529	C₂×C₄×C₂₉	—	4	2	no	—
530	C₂×C₄×C₂₉	—	8	1	no	—
531	C₂×C₄×C₂₉	—	8	2	no	—
532	C₂×C₄×C₂₉	—	8	2	no	—
533	C₂×C₄×C₂₉	—	8	2	no	—
534	C₂×C₄×C₂₉	—	8	2	no	—
535	C₂×C₄×C₂₉	—	8	2	no	—
536	C₂×C₄×C₂₉	—	8	2	no	—
537	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
538	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
543	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
544	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
546	C₈×C₂₉	—	2	2	no	—
547	C₈×C₂₉	—	2	1	no	—
548	C₈×C₂₉	—	2	2	no	—
549	C₈×C₂₉	—	2	1	no	—
550	C₈×C₂₉	—	2	1	no	—
551	C₈×C₂₉	—	2	1	no	—
552	#3546	C₂×C₂₉	1	1	yes	characteristic, complemented
553	#3517	C₂×C₂₉	1	1	yes	characteristic, complemented
554	#3397	C₂×C₂₉	1	1	yes	characteristic, complemented
555	#3391	C₂×C₂₉	1	1	yes	characteristic, complemented
556	#3368	C₂×C₂₉	1	1	yes	characteristic, complemented
557	#3364	C₂×C₂₉	1	1	yes	characteristic, complemented
558	#3330	C₂×C₂₉	1	1	yes	characteristic, complemented
559	#3309	C₂×C₂₉	1	2	yes	complemented
560	#3297	C₂×C₂₉	1	2	yes	complemented
561	#3294	C₂×C₂₉	1	1	yes	characteristic, complemented
562	#3287	C₂×C₂₉	1	2	yes	complemented
563	#3284	C₂×C₂₉	1	1	yes	characteristic, complemented
564	#3274	C₂×C₂₉	1	1	yes	characteristic, complemented
565	#3268	C₂×C₂₉	1	2	yes	complemented
566	#3257	C₂×C₂₉	1	2	yes	complemented
567	#3245	C₂×C₂₉	1	1	yes	characteristic, complemented
568	#3220	C₂×C₂₉	1	2	yes	complemented
569	#3207	C₂×C₂₉	1	1	yes	characteristic, complemented
570	#3124	C₂×C₂₉	1	2	yes	complemented
571	#3106	C₂×C₂₉	1	1	yes	characteristic, complemented
572	#3045	C₂×C₂₉	1	2	yes	complemented
573	#3035	C₂×C₂₉	1	1	yes	characteristic, complemented
574	#2994	C₂×C₂₉	1	1	yes	characteristic, complemented
575	C₂²×C₂₉	—	2	1	no	—
576	C₂²×C₂₉	—	2	2	no	—
577	C₂²×C₂₉	—	2	1	no	—
578	C₂²×C₂₉	—	2	2	no	—
579	C₂²×C₂₉	—	2	1	no	—
580	C₂²×C₂₉	—	2	2	no	—
581	C₂²×C₂₉	—	4	1	no	—
582	C₂²×C₂₉	—	4	1	no	—
583	C₂²×C₂₉	—	4	2	no	—
584	C₂²×C₂₉	—	4	2	no	—
585	C₂²×C₂₉	—	4	1	no	—
586	C₂²×C₂₉	—	4	2	no	—
587	C₂²×C₂₉	—	4	1	no	—
588	C₂²×C₂₉	—	4	1	no	—
589	C₂²×C₂₉	—	4	2	no	—
590	C₂²×C₂₉	—	4	1	no	—
591	C₂²×C₂₉	—	4	1	no	—
592	C₂²×C₂₉	—	4	1	no	—
593	C₂²×C₂₉	—	4	1	no	—
594	C₂²×C₂₉	—	4	2	no	—
595	C₂²×C₂₉	—	4	2	no	—
596	C₂²×C₂₉	—	16	4	no	—
597	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
598	C₄×C₂₉	—	2	1	no	—
599	C₄×C₂₉	—	2	1	no	—
600	C₄×C₂₉	—	2	2	no	—
601	C₄×C₂₉	—	2	1	no	—
602	C₄×C₂₉	—	2	2	no	—
603	C₄×C₂₉	—	2	2	no	—
604	C₄×C₂₉	—	2	1	no	—
605	C₄×C₂₉	—	2	2	no	—
606	C₄×C₂₉	—	4	1	no	—
607	C₄×C₂₉	—	4	2	no	—
608	C₄×C₂₉	—	4	1	no	—
609	C₄×C₂₉	—	4	1	no	—
610	C₄×C₂₉	—	4	1	no	—
611	C₄×C₂₉	—	4	2	no	—
612	C₄×C₂₉	#576	1	2	yes	—
613	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
614	C₄×C₂₉	#585	1	1	yes	characteristic
615	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	2	yes	—
616	C₂×#135	C₂²×C₂₉	1	2	yes	complemented
617	C₂×#135	C₂²×C₂₉	1	2	yes	complemented
618	#560	—	2	2	no	—
619	#557	C₂²×C₂₉	1	1	yes	characteristic, complemented
620	#556	C₂²×C₂₉	1	1	yes	characteristic
621	#553	—	2	2	no	—
622	#553	—	2	1	no	—
623	#553	C₂²×C₂₉	1	2	yes	complemented
624	#550	—	2	1	no	—
625	#550	C₂²×C₂₉	1	1	yes	characteristic
626	#550	C₂²×C₂₉	1	2	yes	—
627	#550	C₂²×C₂₉	1	1	yes	characteristic
628	#550	C₂²×C₂₉	1	2	yes	complemented
629	#550	C₂²×C₂₉	1	1	yes	characteristic, complemented
630	#547	—	2	1	no	—
631	#547	C₂²×C₂₉	1	1	yes	characteristic
632	#547	C₂²×C₂₉	1	1	yes	characteristic
633	#546	—	2	1	no	—
634	#546	C₂²×C₂₉	1	2	yes	—
635	D₄²	C₂²×C₂₉	1	1	yes	characteristic
636	#542	C₂²×C₂₉	1	2	yes	—
637	#540	—	2	2	no	—
638	#540	C₂²×C₂₉	1	2	yes	complemented
639	#538	—	2	2	no	—
640	#537	—	2	1	no	—
641	#535	—	2	1	no	—
642	#535	C₂²×C₂₉	1	2	yes	—
643	#532	—	2	1	no	—
644	#532	C₂²×C₂₉	1	1	yes	characteristic
645	#532	C₂²×C₂₉	1	1	yes	characteristic
646	#532	C₂²×C₂₉	1	1	yes	characteristic, complemented
647	#529	—	2	1	no	—
648	#529	C₂²×C₂₉	1	1	yes	characteristic
649	#520	C₂²×C₂₉	1	2	yes	complemented
650	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic, complemented
651	#496	C₂²×C₂₉	1	2	yes	—
652	#493	C₂²×C₂₉	1	1	yes	characteristic
653	#493	C₂²×C₂₉	1	2	yes	complemented
654	#492	C₂²×C₂₉	1	1	yes	characteristic, complemented
655	#490	C₂²×C₂₉	1	2	yes	complemented
656	#488	C₂²×C₂₉	1	2	yes	—
657	#487	C₂²×C₂₉	1	1	yes	characteristic, complemented
658	#486	C₂²×C₂₉	1	1	yes	characteristic
659	#484	C₂²×C₂₉	1	2	yes	complemented
660	#482	C₂²×C₂₉	1	1	yes	characteristic
661	#482	C₂²×C₂₉	1	1	yes	characteristic, complemented
662	#480	C₂²×C₂₉	1	2	yes	—
663	#479	C₂²×C₂₉	1	2	yes	complemented
664	#478	C₂²×C₂₉	1	2	yes	complemented
665	#477	C₂²×C₂₉	1	1	yes	characteristic, complemented
666	#476	C₂²×C₂₉	1	1	yes	characteristic, complemented
667	#474	C₂²×C₂₉	1	1	yes	characteristic
668	#474	C₂²×C₂₉	1	1	yes	characteristic, complemented
669	#474	C₂²×C₂₉	1	2	yes	complemented
670	#469	C₂²×C₂₉	1	2	yes	—
671	#468	C₂²×C₂₉	1	2	yes	complemented
672	#466	C₂²×C₂₉	1	2	yes	—
673	#466	C₂²×C₂₉	1	2	yes	—
674	#466	C₂²×C₂₉	1	2	yes	complemented
675	#465	C₂²×C₂₉	1	2	yes	complemented
676	#464	C₂²×C₂₉	1	2	yes	—
677	#464	C₂²×C₂₉	1	2	yes	complemented
678	#463	C₂²×C₂₉	1	2	yes	—
679	#463	C₂²×C₂₉	1	2	yes	complemented
680	#463	C₂²×C₂₉	1	2	yes	complemented
681	#463	C₂²×C₂₉	1	2	yes	complemented
682	#462	C₂²×C₂₉	1	1	yes	characteristic, complemented
683	#461	C₂²×C₂₉	1	1	yes	characteristic, complemented
684	#460	C₂²×C₂₉	1	1	yes	characteristic
685	#460	C₂²×C₂₉	1	1	yes	characteristic
686	#460	C₂²×C₂₉	1	2	yes	complemented
687	#460	C₂²×C₂₉	1	2	yes	complemented
688	#459	C₂²×C₂₉	1	1	yes	characteristic
689	#459	C₂²×C₂₉	1	1	yes	characteristic
690	#459	C₂²×C₂₉	1	1	yes	characteristic
691	#459	C₂²×C₂₉	1	2	yes	—
692	#459	C₂²×C₂₉	1	1	yes	characteristic, complemented
693	#459	C₂²×C₂₉	1	2	yes	complemented
694	#459	C₂²×C₂₉	1	2	yes	complemented
695	#452	C₂²×C₂₉	1	2	yes	complemented
696	#449	C₂²×C₂₉	1	1	yes	characteristic
697	#449	C₂²×C₂₉	1	2	yes	—
698	#449	C₂²×C₂₉	1	2	yes	complemented
699	#449	C₂²×C₂₉	1	1	yes	characteristic, complemented
700	#449	C₂²×C₂₉	1	2	yes	complemented
701	#449	C₂²×C₂₉	1	2	yes	complemented
702	#449	C₂²×C₂₉	1	2	yes	complemented
703	#447	C₂²×C₂₉	1	2	yes	—
704	#447	C₂²×C₂₉	1	2	yes	—
705	#446	C₂²×C₂₉	1	1	yes	characteristic, complemented
706	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
707	#440	C₂²×C₂₉	1	2	yes	complemented
708	#440	C₂²×C₂₉	1	2	yes	complemented
709	C₄×Q₁₆	C₂²×C₂₉	1	2	yes	complemented
710	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
711	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
712	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
713	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
714	C₄×D₈	C₂²×C₂₉	1	2	yes	complemented
715	#436	C₂²×C₂₉	1	1	yes	characteristic
716	#435	C₂²×C₂₉	1	2	yes	complemented
717	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
718	C₈×D₄	C₂²×C₂₉	1	2	yes	complemented
719	#433	C₂²×C₂₉	1	2	yes	complemented
720	#431	C₂²×C₂₉	1	1	yes	characteristic, complemented
721	#424	C₂²×C₂₉	1	2	yes	complemented
722	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
723	#417	C₂²×C₂₉	1	2	yes	complemented
724	#416	C₂²×C₂₉	1	2	yes	complemented
725	C₂×#102	C₂²×C₂₉	1	2	yes	—
726	C₂×C₂₉	—	4	1	no	—
727	C₂×C₂₉	—	4	2	no	—
728	C₂×C₂₉	—	8	1	no	—
729	C₂×C₂₉	—	8	2	no	—
730	C₂×C₂₉	—	8	1	no	—
731	C₂×C₂₉	—	8	2	no	—
732	C₂×C₂₉	—	8	1	no	—
733	C₂×C₂₉	#3488	1	1	yes	characteristic
734	C₂×C₂₉	C₂×#576	1	1	yes	characteristic
735	C₂×C₂₉	#3584	1	1	yes	characteristic
736	C₂×#41	—	2	1	no	—
737	C₂×#41	—	2	1	no	—
738	C₂×#41	—	2	1	no	—
739	C₂×#41	—	2	1	no	—
740	C₂×#41	—	2	1	no	—
741	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
742	C₂×#41	C₂³×C₂₉	1	2	yes	—
743	C₂×#41	C₂³×C₂₉	1	2	yes	—
744	C₂×#41	C₂³×C₂₉	1	2	yes	—
745	C₂²×D₄	—	2	1	no	—
746	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
747	AGL(1,ℤ/8)	—	4	4	no	—
748	#135	—	4	4	no	—
749	#135	—	4	4	no	—
750	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
751	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
752	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
753	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
754	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
755	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
756	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
757	C₂×D₈	C₂³×C₂₉	1	2	yes	—
758	C₂×D₈	C₂³×C₂₉	1	2	yes	—
759	C₂×D₈	C₂³×C₂₉	1	2	yes	—
760	C₂×D₈	C₂³×C₂₉	1	2	yes	—
761	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
762	C₂×D₈	C₂³×C₂₉	1	2	yes	—
763	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
764	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
765	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
766	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
767	C₄⋊Q₈	—	2	1	no	—
768	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
769	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
770	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
771	#127	—	2	1	no	—
772	#127	—	2	2	no	—
773	#127	—	2	2	no	—
774	#127	C₂³×C₂₉	1	1	yes	characteristic
775	#127	C₂³×C₂₉	1	1	yes	characteristic
776	#127	C₂³×C₂₉	1	1	yes	characteristic
777	#127	C₂³×C₂₉	1	2	yes	—
778	#127	C₂³×C₂₉	1	2	yes	—
779	#126	—	2	2	no	—
780	#126	—	2	2	no	—
781	#126	—	2	2	no	—
782	#126	D₄×C₂₉	1	2	yes	—
783	#125	—	2	2	no	—
784	#125	D₄×C₂₉	1	1	yes	characteristic
785	#125	C₂³×C₂₉	1	2	yes	—
786	#124	—	2	2	no	—
787	#124	—	2	1	no	—
788	#124	—	2	1	no	—
789	#124	D₄×C₂₉	1	1	yes	characteristic
790	#124	C₂³×C₂₉	1	2	yes	—
791	#124	C₂³×C₂₉	1	2	yes	—
792	#123	—	2	2	no	—
793	#123	—	2	2	no	—
794	#123	—	2	2	no	—
795	#123	—	2	2	no	—
796	#123	—	2	2	no	—
797	#123	—	2	2	no	—
798	#123	—	2	2	no	—
799	#123	D₄×C₂₉	1	2	yes	—
800	C₂²⋊Q₈	—	2	1	no	—
801	C₂²⋊Q₈	—	2	1	no	—
802	C₂²⋊Q₈	—	2	2	no	—
803	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
804	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
805	#121	—	2	1	no	—
806	#121	—	2	2	no	—
807	#121	—	2	1	no	—
808	#121	—	2	1	no	—
809	#121	—	2	1	no	—
810	#121	—	2	1	no	—
811	#121	—	2	1	no	—
812	#121	—	2	1	no	—
813	#121	—	2	2	no	—
814	#121	—	2	2	no	—
815	#121	—	2	1	no	—
816	#121	—	2	2	no	—
817	#121	—	2	2	no	—
818	#121	—	2	2	no	—
819	#121	—	2	2	no	—
820	#121	—	2	2	no	—
821	#121	—	2	2	no	—
822	#121	—	2	2	no	—
823	#121	—	2	2	no	—
824	#121	—	2	2	no	—
825	#121	—	2	2	no	—
826	#121	D₄×C₂₉	1	1	yes	characteristic
827	#121	C₂³×C₂₉	1	1	yes	characteristic
828	#121	C₂³×C₂₉	1	1	yes	characteristic
829	#121	C₂³×C₂₉	1	2	yes	—
830	#121	C₂³×C₂₉	1	2	yes	—
831	#121	C₂³×C₂₉	1	2	yes	—
832	#121	C₂³×C₂₉	1	2	yes	—
833	#120	—	2	2	no	—
834	#120	—	2	2	no	—
835	#120	—	2	2	no	—
836	#120	—	2	2	no	—
837	C₄×Q₈	—	2	1	no	—
838	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
839	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
840	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
841	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
842	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
843	C₄×D₄	—	2	1	no	—
844	C₄×D₄	—	2	1	no	—
845	C₄×D₄	—	2	1	no	—
846	C₄×D₄	—	2	2	no	—
847	C₄×D₄	—	2	2	no	—
848	C₄×D₄	—	2	2	no	—
849	C₄×D₄	—	2	2	no	—
850	C₄×D₄	—	2	2	no	—
851	C₄×D₄	—	2	1	no	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	2	1	no	—
854	C₄×D₄	—	2	1	no	—
855	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
856	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
857	C₄×D₄	C₂³×C₂₉	1	2	yes	—
858	C₄×D₄	C₂³×C₂₉	1	2	yes	—
859	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
860	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
861	C₄×D₄	C₂³×C₂₉	1	2	yes	—
862	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
863	C₄×D₄	C₂³×C₂₉	1	2	yes	—
864	#117	—	2	2	no	—
865	#117	—	2	1	no	—
866	#117	—	2	1	no	—
867	#117	C₂³×C₂₉	1	1	yes	characteristic
868	#117	C₂³×C₂₉	1	2	yes	—
869	C₂×C₄⋊C₄	—	2	2	no	—
870	C₂×C₄⋊C₄	—	2	1	no	—
871	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
872	C₂×C₂²⋊C₄	—	2	2	no	—
873	C₂×C₄²	—	2	1	no	—
874	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
875	#107	C₂³×C₂₉	1	1	yes	characteristic
876	#107	C₂³×C₂₉	1	1	yes	characteristic
877	#107	C₂³×C₂₉	1	2	yes	—
878	#107	C₂³×C₂₉	1	2	yes	—
879	#106	C₂³×C₂₉	1	1	yes	characteristic
880	#106	C₂³×C₂₉	1	1	yes	characteristic
881	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
882	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
883	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
884	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
885	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
886	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
887	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
888	#103	C₂³×C₂₉	1	2	yes	—
889	#103	C₂³×C₂₉	1	2	yes	—
890	#103	C₂³×C₂₉	1	2	yes	—
891	#103	C₂³×C₂₉	1	1	yes	characteristic
892	#103	C₂³×C₂₉	1	1	yes	characteristic
893	#103	C₂³×C₂₉	1	2	yes	—
894	#102	C₂³×C₂₉	1	1	yes	characteristic
895	#102	C₂³×C₂₉	1	2	yes	—
896	#102	C₂³×C₂₉	1	2	yes	—
897	#102	C₂³×C₂₉	1	2	yes	—
898	#102	C₂³×C₂₉	1	2	yes	—
899	#102	C₂³×C₂₉	1	1	yes	characteristic
900	#102	C₂³×C₂₉	1	2	yes	—
901	#102	C₂³×C₂₉	1	1	yes	characteristic
902	#102	C₂³×C₂₉	1	1	yes	characteristic
903	#102	C₂³×C₂₉	1	2	yes	—
904	#102	C₂³×C₂₉	1	1	yes	characteristic
905	#102	C₂³×C₂₉	1	1	yes	characteristic
906	#102	C₂³×C₂₉	1	2	yes	—
907	#102	C₂³×C₂₉	1	2	yes	—
908	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
909	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
910	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
911	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
912	#97	C₂³×C₂₉	1	2	yes	—
913	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
914	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
915	C₄×C₈	C₂³×C₂₉	1	2	yes	—
916	C₂₉	#62074	1	1	yes	characteristic, direct product factor, Sylow
917	C₂⁴	—	2	2	no	—
918	#41	—	2	2	no	—
919	#41	—	2	4	no	—
920	#41	—	4	2	no	—
921	#41	—	4	1	no	—
922	#41	—	4	2	no	—
923	#41	—	4	2	no	—
924	#41	—	4	2	no	—
925	#41	—	4	2	no	—
926	#41	—	8	2	no	—
927	#41	—	8	2	no	—
928	#41	—	8	2	no	—
929	#41	—	8	2	no	—
930	#41	—	8	2	no	—
931	C₂×Q₈	—	2	1	no	—
932	C₂×Q₈	—	2	1	no	—
933	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
934	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
935	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	1	no	—
946	C₂×D₄	—	2	1	no	—
947	C₂×D₄	—	2	1	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	1	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	1	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	1	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	4	2	no	—
958	C₂×D₄	—	4	2	no	—
959	C₂×D₄	—	8	2	no	—
960	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
961	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
962	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
963	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
964	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
965	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
966	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	1	no	—
970	C₂²×C₄	—	2	2	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	2	1	no	—
974	C₂²×C₄	—	2	2	no	—
975	C₂²×C₄	—	2	2	no	—
976	C₂²×C₄	—	2	2	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	2	no	—
979	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
980	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
981	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
982	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
983	Q₁₆	—	2	4	no	—
984	SD₁₆	—	2	2	no	—
985	SD₁₆	—	2	4	no	—
986	SD₁₆	—	2	2	no	—
987	SD₁₆	—	4	2	no	—
988	SD₁₆	—	4	2	no	—
989	SD₁₆	—	4	2	no	—
990	D₈	—	4	2	no	—
991	D₈	—	4	2	no	—
992	D₈	—	4	2	no	—
993	D₈	—	4	2	no	—
994	D₈	—	4	1	no	—
995	D₈	—	4	2	no	—
996	D₈	—	4	1	no	—
997	M₁₆	—	4	2	no	—
998	C₂×C₈	—	4	2	no	—
999	C₂×C₈	—	4	2	no	—
1000	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1001	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1002	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1003	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
1004	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1005	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1019	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1020	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1021	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1022	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1023	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1024	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1025	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1026	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
1027	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1028	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	1	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	1	no	—
1048	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1049	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1050	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1051	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1052	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1053	C₄²	—	2	1	no	—
1054	C₄²	—	2	1	no	—
1055	C₄²	—	2	1	no	—
1056	C₄²	—	2	2	no	—
1057	C₄²	—	2	2	no	—
1058	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1059	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1060	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1061	C₄²	C₂⁴×C₂₉	1	2	yes	—
1062	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1063	C₂³	—	2	1	no	—
1064	C₂³	—	2	1	no	—
1065	C₂³	—	2	2	no	—
1066	C₂³	—	2	2	no	—
1067	C₂³	—	2	1	no	—
1068	C₂³	—	8	2	no	—
1069	C₂³	—	8	2	no	—
1070	C₂³	—	8	2	no	—
1071	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
1072	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1073	Q₈	—	2	2	no	—
1074	Q₈	—	2	1	no	—
1075	Q₈	—	2	2	no	—
1076	Q₈	—	2	2	no	—
1077	Q₈	—	4	2	no	—
1078	Q₈	—	8	1	no	—
1079	Q₈	C₂₉×H(5,𝔽₂)	1	2	yes	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	2	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	2	no	—
1084	D₄	—	2	1	no	—
1085	D₄	—	2	1	no	—
1086	D₄	—	2	1	no	—
1087	D₄	—	2	2	no	—
1088	D₄	—	2	1	no	—
1089	D₄	—	2	2	no	—
1090	D₄	—	2	1	no	—
1091	D₄	—	4	2	no	—
1092	D₄	—	4	2	no	—
1093	D₄	—	4	4	no	—
1094	D₄	—	4	2	no	—
1095	D₄	—	4	2	no	—
1096	D₄	—	8	2	no	—
1097	D₄	—	8	1	no	—
1098	D₄	—	8	2	no	—
1099	D₄	—	8	2	no	—
1100	D₄	—	8	1	no	—
1101	D₄	—	8	1	no	—
1102	D₄	—	8	1	no	—
1103	D₄	—	8	2	no	—
1104	D₄	—	8	2	no	—
1105	D₄	—	8	2	no	—
1106	D₄	—	8	2	no	—
1107	D₄	—	8	2	no	—
1108	D₄	—	8	1	no	—
1109	D₄	—	8	1	no	—
1110	D₄	—	8	2	no	—
1111	D₄	—	8	2	no	—
1112	D₄	—	8	2	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	4	1	no	—
1126	C₂×C₄	—	4	2	no	—
1127	C₂×C₄	—	4	4	no	—
1128	C₂×C₄	—	4	2	no	—
1129	C₂×C₄	—	4	2	no	—
1130	C₂×C₄	—	4	2	no	—
1131	C₂×C₄	—	8	2	no	—
1132	C₂×C₄	—	8	2	no	—
1133	C₂×C₄	—	8	2	no	—
1134	C₂×C₄	—	8	2	no	—
1135	C₂×C₄	—	8	2	no	—
1136	C₂×C₄	—	8	1	no	—
1137	C₂×C₄	—	8	2	no	—
1138	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1139	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1140	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1141	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1142	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1143	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1144	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1145	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1146	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1147	C₈	—	2	2	no	—
1148	C₈	—	2	1	no	—
1149	C₈	—	2	2	no	—
1150	C₈	—	2	1	no	—
1151	C₈	—	2	1	no	—
1152	C₈	—	2	1	no	—
1153	C₂²	—	2	1	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	1	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	2	1	no	—
1158	C₂²	—	2	2	no	—
1159	C₂²	—	4	2	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	1	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	2	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	4	2	no	—
1172	C₂²	—	4	2	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	16	4	no	—
1175	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
1176	C₄	—	2	1	no	—
1177	C₄	—	2	2	no	—
1178	C₄	—	2	2	no	—
1179	C₄	—	2	1	no	—
1180	C₄	—	2	2	no	—
1181	C₄	—	2	1	no	—
1182	C₄	—	2	1	no	—
1183	C₄	—	2	2	no	—
1184	C₄	—	4	2	no	—
1185	C₄	—	4	1	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	1	no	—
1188	C₄	—	4	2	no	—
1189	C₄	—	4	1	no	—
1190	C₄	C₂₉×#576	1	2	yes	—
1191	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
1192	C₄	C₂₉×#585	1	1	yes	characteristic
1193	C₂	—	4	2	no	—
1194	C₂	—	4	1	no	—
1195	C₂	—	8	1	no	—
1196	C₂	—	8	2	no	—
1197	C₂	—	8	1	no	—
1198	C₂	—	8	2	no	—
1199	C₂	—	8	1	no	—
1200	C₂	C₂₉×#3488	1	1	yes	characteristic
1201	C₂	C₂×C₂₉×#576	1	1	yes	characteristic
1202	C₂	C₂₉×#3584	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 ◁ C₂₉×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3546	C₂	semidirect
2. C₂₉×#3517	C₂	semidirect
3. C₂₉×#3397	C₂	semidirect
4. C₂₉×#3391	C₂	semidirect
5. C₂₉×#3368	C₂	semidirect
6. C₂₉×#3364	C₂	semidirect
7. C₂₉×#3330	C₂	semidirect
8. C₂₉×#3309	C₂	semidirect
9. C₂₉×#3297	C₂	semidirect
10. C₂₉×#3294	C₂	semidirect
11. C₂₉×#3287	C₂	semidirect
12. C₂₉×#3284	C₂	semidirect
13. C₂₉×#3274	C₂	semidirect
14. C₂₉×#3268	C₂	semidirect
15. C₂₉×#3257	C₂	semidirect
16. C₂₉×#3245	C₂	semidirect
17. C₂₉×#3220	C₂	semidirect
18. C₂₉×#3207	C₂	semidirect
19. C₂₉×#3124	C₂	semidirect
20. C₂₉×#3106	C₂	semidirect
21. C₂₉×#3045	C₂	semidirect
22. C₂₉×#3035	C₂	semidirect
23. C₂₉×#2994	C₂	semidirect
25. C₂×C₂₉×#135	C₂²	semidirect
26. C₂×C₂₉×#135	C₂²	semidirect
28. C₂₉×#557	C₂²	semidirect
32. C₂₉×#553	C₂²	semidirect
37. C₂₉×#550	C₂²	semidirect
38. C₂₉×#550	C₂²	semidirect
47. C₂₉×#540	C₂²	semidirect
55. C₂₉×#532	C₂²	semidirect
58. C₂₉×#520	C₂²	semidirect
59. C₄×#41×C₂₉	C₂²	semidirect
62. C₂₉×#493	C₂²	semidirect
63. C₂₉×#492	C₂²	semidirect
64. C₂₉×#490	C₂²	semidirect
66. C₂₉×#487	C₂²	semidirect
68. C₂₉×#484	C₂²	semidirect
70. C₂₉×#482	C₂²	semidirect
72. C₂₉×#479	C₂²	semidirect
73. C₂₉×#478	C₂²	semidirect
74. C₂₉×#477	C₂²	semidirect
75. C₂₉×#476	C₂²	semidirect
77. C₂₉×#474	C₂²	semidirect
78. C₂₉×#474	C₂²	semidirect
80. C₂₉×#468	C₂²	semidirect
83. C₂₉×#466	C₂²	semidirect
84. C₂₉×#465	C₂²	semidirect
86. C₂₉×#464	C₂²	semidirect
88. C₂₉×#463	C₂²	semidirect
89. C₂₉×#463	C₂²	semidirect
90. C₂₉×#463	C₂²	semidirect
91. C₂₉×#462	C₂²	semidirect
92. C₂₉×#461	C₂²	semidirect
95. C₂₉×#460	C₂²	semidirect
96. C₂₉×#460	C₂²	semidirect
101. C₂₉×#459	C₂²	semidirect
102. C₂₉×#459	C₂²	semidirect
103. C₂₉×#459	C₂²	semidirect
104. C₂₉×#452	C₂²	semidirect
107. C₂₉×#449	C₂²	semidirect
108. C₂₉×#449	C₂²	semidirect
109. C₂₉×#449	C₂²	semidirect
110. C₂₉×#449	C₂²	semidirect
111. C₂₉×#449	C₂²	semidirect
114. C₂₉×#446	C₂²	semidirect
115. C₈×Q₈×C₂₉	C₂²	semidirect
116. C₂₉×#440	C₂²	semidirect
117. C₂₉×#440	C₂²	semidirect
118. C₄×Q₁₆×C₂₉	C₂²	semidirect
120. C₄×SD₁₆×C₂₉	C₂²	semidirect
122. C₄×D₈×C₂₉	C₂²	semidirect
123. C₄×D₈×C₂₉	C₂²	semidirect
125. C₂₉×#435	C₂²	semidirect
127. C₈×D₄×C₂₉	C₂²	semidirect
128. C₂₉×#433	C₂²	semidirect
129. C₂₉×#431	C₂²	semidirect
130. C₂₉×#424	C₂²	semidirect
131. C₂×C₂₉×C₄⋊C₈	C₂²	semidirect
132. C₂₉×#417	C₂²	semidirect
133. C₂₉×#416	C₂²	semidirect
461. #62074	C₂₉	direct (N × H)
552. #3546	C₂×C₂₉	semidirect
553. #3517	C₂×C₂₉	semidirect
554. #3397	C₂×C₂₉	semidirect
555. #3391	C₂×C₂₉	semidirect
556. #3368	C₂×C₂₉	semidirect
557. #3364	C₂×C₂₉	semidirect
558. #3330	C₂×C₂₉	semidirect
559. #3309	C₂×C₂₉	semidirect
560. #3297	C₂×C₂₉	semidirect
561. #3294	C₂×C₂₉	semidirect
562. #3287	C₂×C₂₉	semidirect
563. #3284	C₂×C₂₉	semidirect
564. #3274	C₂×C₂₉	semidirect
565. #3268	C₂×C₂₉	semidirect
566. #3257	C₂×C₂₉	semidirect
567. #3245	C₂×C₂₉	semidirect
568. #3220	C₂×C₂₉	semidirect
569. #3207	C₂×C₂₉	semidirect
570. #3124	C₂×C₂₉	semidirect
571. #3106	C₂×C₂₉	semidirect
572. #3045	C₂×C₂₉	semidirect
573. #3035	C₂×C₂₉	semidirect
574. #2994	C₂×C₂₉	semidirect
616. C₂×#135	C₂²×C₂₉	semidirect
617. C₂×#135	C₂²×C₂₉	semidirect
619. #557	C₂²×C₂₉	semidirect
623. #553	C₂²×C₂₉	semidirect
628. #550	C₂²×C₂₉	semidirect
629. #550	C₂²×C₂₉	semidirect
638. #540	C₂²×C₂₉	semidirect
646. #532	C₂²×C₂₉	semidirect
649. #520	C₂²×C₂₉	semidirect
650. C₄×#41	C₂²×C₂₉	semidirect
653. #493	C₂²×C₂₉	semidirect
654. #492	C₂²×C₂₉	semidirect
655. #490	C₂²×C₂₉	semidirect
657. #487	C₂²×C₂₉	semidirect
659. #484	C₂²×C₂₉	semidirect
661. #482	C₂²×C₂₉	semidirect
663. #479	C₂²×C₂₉	semidirect
664. #478	C₂²×C₂₉	semidirect
665. #477	C₂²×C₂₉	semidirect
666. #476	C₂²×C₂₉	semidirect
668. #474	C₂²×C₂₉	semidirect
669. #474	C₂²×C₂₉	semidirect
671. #468	C₂²×C₂₉	semidirect
674. #466	C₂²×C₂₉	semidirect
675. #465	C₂²×C₂₉	semidirect
677. #464	C₂²×C₂₉	semidirect
679. #463	C₂²×C₂₉	semidirect
680. #463	C₂²×C₂₉	semidirect
681. #463	C₂²×C₂₉	semidirect
682. #462	C₂²×C₂₉	semidirect
683. #461	C₂²×C₂₉	semidirect
686. #460	C₂²×C₂₉	semidirect
687. #460	C₂²×C₂₉	semidirect
692. #459	C₂²×C₂₉	semidirect
693. #459	C₂²×C₂₉	semidirect
694. #459	C₂²×C₂₉	semidirect
695. #452	C₂²×C₂₉	semidirect
698. #449	C₂²×C₂₉	semidirect
699. #449	C₂²×C₂₉	semidirect
700. #449	C₂²×C₂₉	semidirect
701. #449	C₂²×C₂₉	semidirect
702. #449	C₂²×C₂₉	semidirect
705. #446	C₂²×C₂₉	semidirect
706. C₈×Q₈	C₂²×C₂₉	semidirect
707. #440	C₂²×C₂₉	semidirect
708. #440	C₂²×C₂₉	semidirect
709. C₄×Q₁₆	C₂²×C₂₉	semidirect
711. C₄×SD₁₆	C₂²×C₂₉	semidirect
713. C₄×D₈	C₂²×C₂₉	semidirect
714. C₄×D₈	C₂²×C₂₉	semidirect
716. #435	C₂²×C₂₉	semidirect
718. C₈×D₄	C₂²×C₂₉	semidirect
719. #433	C₂²×C₂₉	semidirect
720. #431	C₂²×C₂₉	semidirect
721. #424	C₂²×C₂₉	semidirect
722. C₂×C₄⋊C₈	C₂²×C₂₉	semidirect
723. #417	C₂²×C₂₉	semidirect
724. #416	C₂²×C₂₉	semidirect
916. C₂₉	#62074	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×#3546	2
C₂₉×#3517	2
C₂₉×#3397	2
C₂₉×#3391	2
C₂₉×#3368	2
C₂₉×#3364	2
C₂₉×#3330	2
C₂₉×#3309	2
C₂₉×#3297	2
C₂₉×#3294	2
C₂₉×#3287	2
C₂₉×#3284	2
C₂₉×#3274	2
C₂₉×#3268	2
C₂₉×#3257	2
C₂₉×#3245	2
C₂₉×#3220	2
C₂₉×#3207	2
C₂₉×#3124	2
C₂₉×#3106	2
C₂₉×#3045	2
C₂₉×#3035	2
C₂₉×#2994	2
#62074	29

Subgroups — C29×#62074 #20356974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#62074 #20356974