Subgroups — C₂₉×#62126 #20357026

Order 7424.

1776 conjugacy classes of subgroups.

The subgroup lattice has 1284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3481	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#3388	C₂	1	2	yes	maximal, complemented
4	C₂₉×#3371	C₂	1	2	yes	maximal, complemented
5	C₂₉×#3350	C₂	1	2	yes	maximal, complemented
6	C₂₉×#3344	C₂	1	2	yes	maximal, complemented
7	C₂₉×#3337	C₂	1	2	yes	maximal, complemented
8	C₂₉×#3311	C₂	1	2	yes	maximal, complemented
9	C₂₉×#3310	C₂	1	2	yes	maximal, complemented
10	C₂₉×#3296	C₂	1	2	yes	maximal, complemented
11	C₂₉×#3252	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#3248	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#3238	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#3235	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#3233	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₉×#3116	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₉×#3110	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₉×#3101	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₉×#3077	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₉×#3076	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₂₉×#476	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₉×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₉×#559	C₂²	1	1	yes	characteristic
25	C₂₉×#557	—	2	1	no	—
26	C₂₉×#557	C₂²	1	2	yes	complemented
27	C₂₉×#556	—	2	1	no	—
28	C₂₉×#556	C₂²	1	2	yes	complemented
29	C₂₉×#554	C₂²	1	1	yes	characteristic
30	C₂₉×#554	C₂²	1	1	yes	characteristic
31	C₂₉×#553	—	2	1	no	—
32	C₂₉×#553	C₂²	1	1	yes	characteristic
33	C₂₉×#553	C₂²	1	1	yes	characteristic
34	C₂₉×#552	—	2	1	no	—
35	C₂₉×#552	—	2	1	no	—
36	C₂₉×#552	C₂²	1	2	yes	—
37	C₂₉×#552	C₂²	1	2	yes	complemented
38	C₂₉×#551	—	2	1	no	—
39	C₂₉×#551	—	2	1	no	—
40	C₂₉×#546	—	2	1	no	—
41	C₂₉×#546	C₂²	1	1	yes	characteristic
42	C₂₉×#546	C₂²	1	1	yes	characteristic
43	D₄²×C₂₉	C₂²	1	1	yes	characteristic
44	C₂₉×#541	—	2	1	no	—
45	C₂₉×#541	—	2	1	no	—
46	C₂₉×#536	—	2	1	no	—
47	C₂₉×#533	C₂²	1	1	yes	characteristic, complemented
48	C₂₉×#533	C₂²	1	1	yes	characteristic, complemented
49	C₂₉×#533	C₂²	1	1	yes	characteristic, complemented
50	C₂₉×#533	C₂²	1	1	yes	characteristic, complemented
51	C₂₉×#533	C₂²	1	1	yes	characteristic, complemented
52	C₂₉×#532	C₂²	1	1	yes	characteristic
53	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
54	C₂₉×#529	—	2	1	no	—
55	C₂₉×#529	C₂²	1	1	yes	characteristic
56	C₂₉×#529	C₂²	1	1	yes	characteristic
57	C₂₉×#525	—	2	1	no	—
58	C₂₉×#525	—	2	1	no	—
59	C₂₉×#519	—	2	1	no	—
60	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
61	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
62	C₂×C₄×D₄×C₂₉	—	2	1	no	—
63	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
64	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
65	C₂₉×#501	C₂²	1	2	yes	complemented
66	C₂₉×#501	C₂²	1	2	yes	complemented
67	C₂₉×#499	C₂²	1	2	yes	complemented
68	C₂₉×#490	C₂²	1	2	yes	—
69	C₂₉×#489	C₂²	1	2	yes	complemented
70	C₂₉×#488	C₂²	1	2	yes	complemented
71	C₂₉×#485	C₂²	1	2	yes	complemented
72	C₂₉×#485	C₂²	1	2	yes	complemented
73	C₂₉×#484	C₂²	1	2	yes	complemented
74	C₂₉×#483	C₂²	1	2	yes	complemented
75	C₂₉×#483	C₂²	1	2	yes	complemented
76	C₂₉×#482	C₂²	1	2	yes	—
77	C₂₉×#482	C₂²	1	2	yes	complemented
78	C₂₉×#482	C₂²	1	2	yes	complemented
79	C₂₉×#480	C₂²	1	2	yes	—
80	C₂₉×#479	C₂²	1	2	yes	complemented
81	C₂₉×#479	C₂²	1	2	yes	complemented
82	C₂₉×#479	C₂²	1	2	yes	complemented
83	C₂₉×#478	C₂²	1	2	yes	—
84	C₂₉×#478	C₂²	1	2	yes	—
85	C₂₉×#478	C₂²	1	2	yes	complemented
86	C₂₉×#477	C₂²	1	1	yes	characteristic, complemented
87	C₂₉×#477	C₂²	1	1	yes	characteristic, complemented
88	C₂₉×#476	C₂²	1	2	yes	—
89	C₂₉×#476	C₂²	1	1	yes	characteristic
90	C₂₉×#476	C₂²	1	1	yes	characteristic
91	C₂₉×#476	C₂²	1	1	yes	characteristic, complemented
92	C₂₉×#476	C₂²	1	1	yes	characteristic, complemented
93	C₂₉×#476	C₂²	1	1	yes	characteristic, complemented
94	C₂₉×#476	C₂²	1	1	yes	characteristic, complemented
95	C₂₉×#476	C₂²	1	2	yes	complemented
96	C₂₉×#475	C₂²	1	1	yes	characteristic, complemented
97	C₂₉×#475	C₂²	1	2	yes	complemented
98	C₂₉×#474	C₂²	1	1	yes	characteristic
99	C₂₉×#474	C₂²	1	1	yes	characteristic, complemented
100	C₂₉×#474	C₂²	1	1	yes	characteristic, complemented
101	C₂₉×#470	C₂²	1	2	yes	complemented
102	C₂₉×#468	C₂²	1	2	yes	—
103	C₂₉×#467	C₂²	1	2	yes	complemented
104	C₂₉×#465	C₂²	1	2	yes	—
105	C₂₉×#465	C₂²	1	2	yes	complemented
106	C₂₉×#465	C₂²	1	2	yes	complemented
107	C₂₉×#464	C₂²	1	2	yes	complemented
108	C₂₉×#464	C₂²	1	2	yes	complemented
109	C₂₉×#462	C₂²	1	1	yes	characteristic, complemented
110	C₂₉×#461	C₂²	1	1	yes	characteristic
111	C₂₉×#461	C₂²	1	1	yes	characteristic, complemented
112	C₂₉×#461	C₂²	1	1	yes	characteristic, complemented
113	C₂₉×#460	C₂²	1	2	yes	—
114	C₂₉×#452	C₂²	1	2	yes	—
115	C₂₉×#450	C₂²	1	2	yes	—
116	C₂₉×#450	C₂²	1	2	yes	—
117	C₂₉×#446	C₂²	1	2	yes	complemented
118	C₂₉×#441	C₂²	1	2	yes	complemented
119	C₂₉×#440	C₂²	1	2	yes	—
120	C₂₉×#440	C₂²	1	2	yes	—
121	C₂₉×#440	C₂²	1	2	yes	complemented
122	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	—
123	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	complemented
124	C₂₉×#435	C₂²	1	2	yes	—
125	C₂₉×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₂₉	C₂²	1	2	yes	complemented
127	C₂₉×#432	C₂²	1	1	yes	characteristic, complemented
128	C₂₉×#432	C₂²	1	1	yes	characteristic, complemented
129	C₂₉×#431	C₂²	1	1	yes	characteristic, complemented
130	C₂₉×#428	C₂²	1	2	yes	complemented
131	C₂₉×#427	C₂²	1	2	yes	complemented
132	C₂×C₂₉×#106	C₂²	1	2	yes	complemented
133	C₂₉×#423	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
136	C₂₉×#418	C₂²	1	2	yes	—
137	C₂₉×#416	C₂²	1	2	yes	—
138	C₂×C₂₉×#102	C₂²	1	2	yes	—
139	C₂×#41×C₂₉	—	2	1	no	—
140	C₂×#41×C₂₉	D₄	1	1	yes	characteristic
141	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₂₉	—	2	1	no	—
143	C₂²×D₄×C₂₉	—	2	1	no	—
144	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
145	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₂₉	—	2	1	no	—
147	C₂³×C₄×C₂₉	—	2	1	no	—
148	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
152	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
153	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
154	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
155	C₂₉×C₄⋊Q₈	—	2	2	no	—
156	C₂₉×C₄⋊Q₈	—	2	1	no	—
157	C₂₉×C₄⋊Q₈	—	2	1	no	—
158	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₂₉×#127	C₂³	1	1	yes	characteristic
165	C₂₉×#126	—	2	1	no	—
166	C₂₉×#126	—	2	1	no	—
167	C₂₉×#126	—	2	2	no	—
168	C₂₉×#126	—	2	2	no	—
169	C₂₉×#126	—	2	2	no	—
170	C₂₉×#126	—	2	2	no	—
171	C₂₉×#126	—	2	1	no	—
172	C₂₉×#126	—	2	1	no	—
173	C₂₉×#125	—	2	1	no	—
174	C₂₉×#125	—	2	2	no	—
175	C₂₉×#125	—	2	2	no	—
176	C₂₉×#125	—	2	2	no	—
177	C₂₉×#125	—	2	2	no	—
178	C₂₉×#125	—	2	1	no	—
179	C₂₉×#125	—	2	1	no	—
180	C₂₉×#125	—	2	1	no	—
181	C₂₉×#125	C₂³	1	2	yes	—
182	C₂₉×#125	C₂³	1	2	yes	—
183	C₂₉×#125	C₂³	1	1	yes	characteristic
184	C₂₉×#125	C₂³	1	1	yes	characteristic
185	C₂₉×#124	—	2	1	no	—
186	C₂₉×#124	—	2	2	no	—
187	C₂₉×#124	—	2	1	no	—
188	C₂₉×#124	C₂³	1	1	yes	characteristic
189	C₂₉×#124	C₂³	1	1	yes	characteristic
190	C₂₉×#123	—	2	2	no	—
191	C₂₉×#123	—	2	2	no	—
192	C₂₉×#123	—	2	1	no	—
193	C₂₉×#123	—	2	1	no	—
194	C₂₉×#123	—	2	1	no	—
195	C₂₉×#123	—	2	1	no	—
196	C₂₉×#123	—	2	1	no	—
197	C₂₉×#123	—	2	1	no	—
198	C₂₉×#123	—	2	1	no	—
199	C₂₉×#123	—	2	1	no	—
200	C₂₉×C₂²⋊Q₈	—	2	1	no	—
201	C₂₉×C₂²⋊Q₈	—	2	1	no	—
202	C₂₉×C₂²⋊Q₈	—	2	1	no	—
203	C₂₉×C₂²⋊Q₈	—	2	1	no	—
204	C₂₉×C₂²⋊Q₈	—	2	1	no	—
205	C₂₉×C₂²⋊Q₈	—	2	1	no	—
206	C₂₉×C₂²⋊Q₈	—	2	1	no	—
207	C₂₉×C₂²⋊Q₈	—	2	1	no	—
208	C₂₉×C₂²⋊Q₈	—	2	1	no	—
209	C₂₉×C₂²⋊Q₈	—	2	1	no	—
210	C₂₉×C₂²⋊Q₈	—	2	1	no	—
211	C₂₉×C₂²⋊Q₈	—	2	1	no	—
212	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₂₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
216	C₂₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
217	C₂₉×#121	—	2	1	no	—
218	C₂₉×#121	—	2	1	no	—
219	C₂₉×#121	—	2	1	no	—
220	C₂₉×#121	—	2	1	no	—
221	C₂₉×#121	—	2	1	no	—
222	C₂₉×#121	—	2	1	no	—
223	C₂₉×#121	C₂³	1	1	yes	characteristic
224	C₂₉×#121	C₂³	1	1	yes	characteristic
225	C₂₉×#121	C₂³	1	1	yes	characteristic
226	C₂₉×#121	C₂³	1	1	yes	characteristic
227	C₂₉×#120	—	2	1	no	—
228	C₂₉×#120	—	2	1	no	—
229	C₂₉×#120	—	2	1	no	—
230	C₂₉×#120	—	2	1	no	—
231	C₄×Q₈×C₂₉	—	2	2	no	—
232	C₄×Q₈×C₂₉	—	2	2	no	—
233	C₄×Q₈×C₂₉	—	2	1	no	—
234	C₄×Q₈×C₂₉	—	2	1	no	—
235	C₄×Q₈×C₂₉	—	2	1	no	—
236	C₄×Q₈×C₂₉	—	2	1	no	—
237	C₄×Q₈×C₂₉	—	2	1	no	—
238	C₄×Q₈×C₂₉	—	2	1	no	—
239	C₄×Q₈×C₂₉	—	2	1	no	—
240	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
241	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
242	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
243	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
244	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
245	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
246	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₂₉	—	2	1	no	—
248	C₄×D₄×C₂₉	—	2	1	no	—
249	C₄×D₄×C₂₉	—	2	1	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	—	2	1	no	—
255	C₄×D₄×C₂₉	—	2	1	no	—
256	C₄×D₄×C₂₉	—	2	1	no	—
257	C₄×D₄×C₂₉	—	2	1	no	—
258	C₄×D₄×C₂₉	—	2	1	no	—
259	C₄×D₄×C₂₉	—	2	1	no	—
260	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
261	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
262	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
263	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
266	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
267	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
268	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
269	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
270	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
271	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
272	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
273	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
274	C₂₉×#117	—	2	1	no	—
275	C₂₉×#117	—	2	1	no	—
276	C₂₉×#117	—	2	1	no	—
277	C₂₉×#117	—	2	2	no	—
278	C₂₉×#117	—	2	2	no	—
279	C₂₉×#117	—	2	1	no	—
280	C₂₉×#117	—	2	1	no	—
281	C₂₉×#117	—	2	1	no	—
282	C₂₉×#117	D₄	1	1	yes	characteristic
283	C₂₉×#117	D₄	1	1	yes	characteristic
284	C₂₉×#117	D₄	1	1	yes	characteristic
285	C₂₉×#117	C₂³	1	1	yes	characteristic
286	C₂₉×#117	C₂³	1	2	yes	—
287	C₂₉×#117	C₂³	1	2	yes	—
288	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
289	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
290	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
292	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
294	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
295	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
296	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
297	C₂×C₄²×C₂₉	—	2	1	no	—
298	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
300	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
301	C₂₉×#107	C₂³	1	2	yes	—
302	C₂₉×#107	C₂³	1	2	yes	—
303	C₂₉×#107	C₂³	1	2	yes	—
304	C₂₉×#107	C₂³	1	2	yes	—
305	C₂₉×#107	C₂³	1	2	yes	—
306	C₂₉×#106	C₂³	1	2	yes	—
307	C₂₉×#106	C₂³	1	2	yes	—
308	C₂₉×#106	C₂³	1	2	yes	—
309	C₂₉×#106	C₂³	1	2	yes	—
310	C₂₉×#106	C₂³	1	2	yes	—
311	C₂₉×#106	C₂³	1	2	yes	—
312	C₂₉×#106	C₂³	1	2	yes	—
313	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
314	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
315	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
316	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
317	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
318	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
319	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
320	C₂₉×#103	C₂³	1	2	yes	—
321	C₂₉×#103	C₂³	1	2	yes	—
322	C₂₉×#103	C₂³	1	2	yes	—
323	C₂₉×#103	C₂³	1	2	yes	—
324	C₂₉×#103	C₂³	1	2	yes	—
325	C₂₉×#103	C₂³	1	2	yes	—
326	C₂₉×#103	C₂³	1	2	yes	—
327	C₂₉×#102	C₂³	1	2	yes	—
328	C₂₉×#102	C₂³	1	2	yes	—
329	C₂₉×#102	C₂³	1	2	yes	—
330	C₂₉×#102	C₂³	1	2	yes	—
331	C₂₉×#102	C₂³	1	2	yes	—
332	C₂₉×#102	C₂³	1	2	yes	—
333	C₂₉×#102	C₂³	1	2	yes	—
334	C₂₉×#102	C₂³	1	2	yes	—
335	C₂₉×#102	C₂³	1	2	yes	—
336	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
337	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
338	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
339	C₂₉×#97	C₂³	1	2	yes	—
340	C₂₉×#97	C₂³	1	2	yes	—
341	C₄×C₈×C₂₉	C₂³	1	2	yes	—
342	C₂⁴×C₂₉	—	2	1	no	—
343	C₂⁴×C₂₉	—	2	1	no	—
344	#41×C₂₉	—	2	2	no	—
345	#41×C₂₉	—	4	2	no	—
346	#41×C₂₉	—	4	1	no	—
347	#41×C₂₉	—	8	2	no	—
348	C₂×Q₈×C₂₉	—	2	1	no	—
349	C₂×Q₈×C₂₉	—	2	1	no	—
350	C₂×Q₈×C₂₉	—	2	1	no	—
351	C₂×Q₈×C₂₉	—	2	2	no	—
352	C₂×Q₈×C₂₉	—	2	1	no	—
353	C₂×Q₈×C₂₉	—	4	4	no	—
354	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
355	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
356	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₂₉	—	2	2	no	—
358	C₂×D₄×C₂₉	—	2	2	no	—
359	C₂×D₄×C₂₉	—	2	1	no	—
360	C₂×D₄×C₂₉	—	2	1	no	—
361	C₂×D₄×C₂₉	—	2	1	no	—
362	C₂×D₄×C₂₉	—	2	1	no	—
363	C₂×D₄×C₂₉	—	2	1	no	—
364	C₂×D₄×C₂₉	—	2	1	no	—
365	C₂×D₄×C₂₉	—	2	1	no	—
366	C₂×D₄×C₂₉	—	2	1	no	—
367	C₂×D₄×C₂₉	—	2	1	no	—
368	C₂×D₄×C₂₉	—	4	1	no	—
369	C₂×D₄×C₂₉	—	4	1	no	—
370	C₂×D₄×C₂₉	—	4	4	no	—
371	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
372	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
373	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
374	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
375	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
376	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₂₉	—	2	2	no	—
378	C₂²×C₄×C₂₉	—	2	1	no	—
379	C₂²×C₄×C₂₉	—	2	1	no	—
380	C₂²×C₄×C₂₉	—	2	1	no	—
381	C₂²×C₄×C₂₉	—	2	1	no	—
382	C₂²×C₄×C₂₉	—	2	1	no	—
383	C₂²×C₄×C₂₉	—	2	1	no	—
384	C₂²×C₄×C₂₉	—	2	1	no	—
385	C₂²×C₄×C₂₉	—	2	1	no	—
386	C₂²×C₄×C₂₉	—	2	1	no	—
387	C₂²×C₄×C₂₉	—	2	1	no	—
388	C₂²×C₄×C₂₉	—	2	1	no	—
389	C₂²×C₄×C₂₉	—	8	2	no	—
390	C₂²×C₄×C₂₉	—	8	2	no	—
391	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
400	Q₁₆×C₂₉	—	4	2	no	—
401	SD₁₆×C₂₉	—	2	4	no	—
402	SD₁₆×C₂₉	—	4	2	no	—
403	SD₁₆×C₂₉	—	4	2	no	—
404	M₁₆×C₂₉	—	4	2	no	—
405	C₂×C₈×C₂₉	—	4	2	no	—
406	C₂×C₈×C₂₉	—	4	2	no	—
407	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
408	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
409	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
410	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₂₉	—	2	1	no	—
412	C₄⋊C₄×C₂₉	—	2	1	no	—
413	C₄⋊C₄×C₂₉	—	2	1	no	—
414	C₄⋊C₄×C₂₉	—	2	1	no	—
415	C₄⋊C₄×C₂₉	—	2	1	no	—
416	C₄⋊C₄×C₂₉	—	2	2	no	—
417	C₄⋊C₄×C₂₉	—	2	1	no	—
418	C₄⋊C₄×C₂₉	—	2	1	no	—
419	C₄⋊C₄×C₂₉	—	2	2	no	—
420	C₄⋊C₄×C₂₉	—	2	1	no	—
421	C₄⋊C₄×C₂₉	—	2	1	no	—
422	C₄⋊C₄×C₂₉	—	2	1	no	—
423	C₄⋊C₄×C₂₉	—	2	1	no	—
424	C₄⋊C₄×C₂₉	—	2	1	no	—
425	C₄⋊C₄×C₂₉	—	2	2	no	—
426	C₄⋊C₄×C₂₉	—	2	2	no	—
427	C₄⋊C₄×C₂₉	—	2	2	no	—
428	C₄⋊C₄×C₂₉	—	2	2	no	—
429	C₄⋊C₄×C₂₉	—	2	1	no	—
430	C₄⋊C₄×C₂₉	—	2	1	no	—
431	C₄⋊C₄×C₂₉	—	2	1	no	—
432	C₄⋊C₄×C₂₉	—	2	1	no	—
433	C₄⋊C₄×C₂₉	—	2	2	no	—
434	C₄⋊C₄×C₂₉	—	2	2	no	—
435	C₄⋊C₄×C₂₉	—	2	2	no	—
436	C₄⋊C₄×C₂₉	—	2	2	no	—
437	C₄⋊C₄×C₂₉	—	2	2	no	—
438	C₄⋊C₄×C₂₉	—	2	2	no	—
439	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
441	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
446	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
447	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
448	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
451	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
452	C₂²⋊C₄×C₂₉	—	2	1	no	—
453	C₂²⋊C₄×C₂₉	—	2	1	no	—
454	C₂²⋊C₄×C₂₉	—	2	2	no	—
455	C₂²⋊C₄×C₂₉	—	2	2	no	—
456	C₂²⋊C₄×C₂₉	—	2	2	no	—
457	C₂²⋊C₄×C₂₉	—	2	1	no	—
458	C₂²⋊C₄×C₂₉	—	2	2	no	—
459	C₂²⋊C₄×C₂₉	—	2	2	no	—
460	C₂²⋊C₄×C₂₉	—	2	1	no	—
461	C₂²⋊C₄×C₂₉	—	2	1	no	—
462	C₂²⋊C₄×C₂₉	—	2	1	no	—
463	C₂²⋊C₄×C₂₉	—	2	1	no	—
464	C₂²⋊C₄×C₂₉	—	2	1	no	—
465	C₂²⋊C₄×C₂₉	—	2	1	no	—
466	C₂²⋊C₄×C₂₉	—	2	1	no	—
467	C₂²⋊C₄×C₂₉	—	2	1	no	—
468	C₂²⋊C₄×C₂₉	—	2	1	no	—
469	C₂²⋊C₄×C₂₉	—	2	1	no	—
470	C₂²⋊C₄×C₂₉	—	2	1	no	—
471	C₂²⋊C₄×C₂₉	—	2	1	no	—
472	C₂²⋊C₄×C₂₉	—	2	1	no	—
473	C₂²⋊C₄×C₂₉	—	2	1	no	—
474	C₂²⋊C₄×C₂₉	—	2	1	no	—
475	C₂²⋊C₄×C₂₉	—	2	1	no	—
476	C₂²⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
477	C₂²⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
478	C₂²⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
479	C₂²⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
480	C₂²⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
481	C₂²⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
482	C₄²×C₂₉	—	2	1	no	—
483	C₄²×C₂₉	—	2	1	no	—
484	C₄²×C₂₉	—	2	1	no	—
485	C₄²×C₂₉	—	2	2	no	—
486	C₄²×C₂₉	—	2	2	no	—
487	C₄²×C₂₉	—	2	2	no	—
488	C₄²×C₂₉	—	2	2	no	—
489	C₄²×C₂₉	—	2	2	no	—
490	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
491	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
492	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
493	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
494	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
495	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
496	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
497	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
498	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
499	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
500	#62126	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
501	C₂³×C₂₉	—	2	1	no	—
502	C₂³×C₂₉	—	2	1	no	—
503	C₂³×C₂₉	—	2	1	no	—
504	C₂³×C₂₉	—	4	2	no	—
505	C₂³×C₂₉	—	4	2	no	—
506	C₂³×C₂₉	—	4	2	no	—
507	C₂³×C₂₉	—	4	2	no	—
508	C₂³×C₂₉	—	8	1	no	—
509	C₂³×C₂₉	—	8	1	no	—
510	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
511	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
512	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
513	Q₈×C₂₉	—	2	2	no	—
514	Q₈×C₂₉	—	2	1	no	—
515	Q₈×C₂₉	—	2	2	no	—
516	Q₈×C₂₉	—	2	1	no	—
517	Q₈×C₂₉	—	4	1	no	—
518	Q₈×C₂₉	—	4	2	no	—
519	Q₈×C₂₉	—	4	2	no	—
520	Q₈×C₂₉	—	4	4	no	—
521	Q₈×C₂₉	—	4	2	no	—
522	Q₈×C₂₉	—	8	1	no	—
523	D₄×C₂₉	—	2	2	no	—
524	D₄×C₂₉	—	2	2	no	—
525	D₄×C₂₉	—	2	1	no	—
526	D₄×C₂₉	—	2	1	no	—
527	D₄×C₂₉	—	2	1	no	—
528	D₄×C₂₉	—	2	1	no	—
529	D₄×C₂₉	—	2	1	no	—
530	D₄×C₂₉	—	4	1	no	—
531	D₄×C₂₉	—	4	2	no	—
532	D₄×C₂₉	—	4	2	no	—
533	D₄×C₂₉	—	4	2	no	—
534	D₄×C₂₉	—	4	2	no	—
535	D₄×C₂₉	—	4	2	no	—
536	D₄×C₂₉	—	4	2	no	—
537	D₄×C₂₉	—	8	1	no	—
538	D₄×C₂₉	—	8	1	no	—
539	D₄×C₂₉	—	8	1	no	—
540	D₄×C₂₉	2₋¹⁺⁴	1	2	yes	—
541	C₂×C₄×C₂₉	—	2	2	no	—
542	C₂×C₄×C₂₉	—	2	2	no	—
543	C₂×C₄×C₂₉	—	2	2	no	—
544	C₂×C₄×C₂₉	—	2	2	no	—
545	C₂×C₄×C₂₉	—	2	1	no	—
546	C₂×C₄×C₂₉	—	2	1	no	—
547	C₂×C₄×C₂₉	—	2	1	no	—
548	C₂×C₄×C₂₉	—	2	1	no	—
549	C₂×C₄×C₂₉	—	2	1	no	—
550	C₂×C₄×C₂₉	—	2	1	no	—
551	C₂×C₄×C₂₉	—	2	2	no	—
552	C₂×C₄×C₂₉	—	2	2	no	—
553	C₂×C₄×C₂₉	—	2	1	no	—
554	C₂×C₄×C₂₉	—	2	1	no	—
555	C₂×C₄×C₂₉	—	2	1	no	—
556	C₂×C₄×C₂₉	—	2	2	no	—
557	C₂×C₄×C₂₉	—	2	2	no	—
558	C₂×C₄×C₂₉	—	2	1	no	—
559	C₂×C₄×C₂₉	—	2	1	no	—
560	C₂×C₄×C₂₉	—	4	1	no	—
561	C₂×C₄×C₂₉	—	4	1	no	—
562	C₂×C₄×C₂₉	—	4	2	no	—
563	C₂×C₄×C₂₉	—	4	2	no	—
564	C₂×C₄×C₂₉	—	4	4	no	—
565	C₂×C₄×C₂₉	—	4	2	no	—
566	C₂×C₄×C₂₉	—	4	2	no	—
567	C₂×C₄×C₂₉	—	4	2	no	—
568	C₂×C₄×C₂₉	—	8	1	no	—
569	C₂×C₄×C₂₉	—	8	1	no	—
570	C₂×C₄×C₂₉	—	8	1	no	—
571	C₂×C₄×C₂₉	—	8	1	no	—
572	C₂×C₄×C₂₉	—	8	1	no	—
573	C₂×C₄×C₂₉	—	8	1	no	—
574	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
575	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
576	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
578	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
579	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
584	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
585	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
586	C₈×C₂₉	—	2	2	no	—
587	C₈×C₂₉	—	2	2	no	—
588	C₈×C₂₉	—	2	2	no	—
589	C₈×C₂₉	—	2	2	no	—
590	#3509	C₂×C₂₉	1	1	yes	characteristic, complemented
591	#3481	C₂×C₂₉	1	1	yes	characteristic
592	#3388	C₂×C₂₉	1	2	yes	complemented
593	#3371	C₂×C₂₉	1	2	yes	complemented
594	#3350	C₂×C₂₉	1	2	yes	complemented
595	#3344	C₂×C₂₉	1	2	yes	complemented
596	#3337	C₂×C₂₉	1	2	yes	complemented
597	#3311	C₂×C₂₉	1	2	yes	complemented
598	#3310	C₂×C₂₉	1	2	yes	complemented
599	#3296	C₂×C₂₉	1	2	yes	complemented
600	#3252	C₂×C₂₉	1	1	yes	characteristic, complemented
601	#3248	C₂×C₂₉	1	1	yes	characteristic, complemented
602	#3246	C₂×C₂₉	1	1	yes	characteristic, complemented
603	#3238	C₂×C₂₉	1	1	yes	characteristic, complemented
604	#3235	C₂×C₂₉	1	1	yes	characteristic, complemented
605	#3233	C₂×C₂₉	1	1	yes	characteristic, complemented
606	#3116	C₂×C₂₉	1	1	yes	characteristic, complemented
607	#3110	C₂×C₂₉	1	1	yes	characteristic, complemented
608	#3101	C₂×C₂₉	1	1	yes	characteristic, complemented
609	#3077	C₂×C₂₉	1	1	yes	characteristic, complemented
610	#3076	C₂×C₂₉	1	1	yes	characteristic, complemented
611	C₂×#476	C₂×C₂₉	1	1	yes	characteristic, complemented
612	#2990	C₂×C₂₉	1	1	yes	characteristic, complemented
613	C₂²×C₂₉	—	2	1	no	—
614	C₂²×C₂₉	—	2	1	no	—
615	C₂²×C₂₉	—	2	1	no	—
616	C₂²×C₂₉	—	2	1	no	—
617	C₂²×C₂₉	—	2	2	no	—
618	C₂²×C₂₉	—	2	1	no	—
619	C₂²×C₂₉	—	2	1	no	—
620	C₂²×C₂₉	—	2	1	no	—
621	C₂²×C₂₉	—	2	1	no	—
622	C₂²×C₂₉	—	4	1	no	—
623	C₂²×C₂₉	—	4	1	no	—
624	C₂²×C₂₉	—	4	1	no	—
625	C₂²×C₂₉	—	4	1	no	—
626	C₂²×C₂₉	—	4	1	no	—
627	C₂²×C₂₉	—	4	1	no	—
628	C₂²×C₂₉	—	4	1	no	—
629	C₂²×C₂₉	—	4	1	no	—
630	C₂²×C₂₉	—	8	4	no	—
631	C₂²×C₂₉	—	8	4	no	—
632	C₂²×C₂₉	#575	1	2	yes	—
633	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
634	C₄×C₂₉	—	2	1	no	—
635	C₄×C₂₉	—	2	1	no	—
636	C₄×C₂₉	—	2	1	no	—
637	C₄×C₂₉	—	2	1	no	—
638	C₄×C₂₉	—	2	1	no	—
639	C₄×C₂₉	—	2	1	no	—
640	C₄×C₂₉	—	2	1	no	—
641	C₄×C₂₉	—	2	1	no	—
642	C₄×C₂₉	—	2	1	no	—
643	C₄×C₂₉	—	2	1	no	—
644	C₄×C₂₉	—	4	1	no	—
645	C₄×C₂₉	—	4	2	no	—
646	C₄×C₂₉	—	4	1	no	—
647	C₄×C₂₉	—	4	2	no	—
648	C₄×C₂₉	—	4	2	no	—
649	C₄×C₂₉	—	4	1	no	—
650	C₄×C₂₉	—	4	1	no	—
651	C₄×C₂₉	—	4	1	no	—
652	C₄×C₂₉	—	4	2	no	—
653	C₄×C₂₉	#577	1	2	yes	—
654	C₄×C₂₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
655	C₄×C₂₉	#585	1	1	yes	characteristic
656	#559	C₂²×C₂₉	1	1	yes	characteristic
657	#557	—	2	1	no	—
658	#557	C₂²×C₂₉	1	2	yes	complemented
659	#556	—	2	1	no	—
660	#556	C₂²×C₂₉	1	2	yes	complemented
661	#554	C₂²×C₂₉	1	1	yes	characteristic
662	#554	C₂²×C₂₉	1	1	yes	characteristic
663	#553	—	2	1	no	—
664	#553	C₂²×C₂₉	1	1	yes	characteristic
665	#553	C₂²×C₂₉	1	1	yes	characteristic
666	#552	—	2	1	no	—
667	#552	—	2	1	no	—
668	#552	C₂²×C₂₉	1	2	yes	—
669	#552	C₂²×C₂₉	1	2	yes	complemented
670	#551	—	2	1	no	—
671	#551	—	2	1	no	—
672	#546	—	2	1	no	—
673	#546	C₂²×C₂₉	1	1	yes	characteristic
674	#546	C₂²×C₂₉	1	1	yes	characteristic
675	D₄²	C₂²×C₂₉	1	1	yes	characteristic
676	#541	—	2	1	no	—
677	#541	—	2	1	no	—
678	#536	—	2	1	no	—
679	#533	C₂²×C₂₉	1	1	yes	characteristic, complemented
680	#533	C₂²×C₂₉	1	1	yes	characteristic, complemented
681	#533	C₂²×C₂₉	1	1	yes	characteristic, complemented
682	#533	C₂²×C₂₉	1	1	yes	characteristic, complemented
683	#533	C₂²×C₂₉	1	1	yes	characteristic, complemented
684	#532	C₂²×C₂₉	1	1	yes	characteristic
685	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
686	#529	—	2	1	no	—
687	#529	C₂²×C₂₉	1	1	yes	characteristic
688	#529	C₂²×C₂₉	1	1	yes	characteristic
689	#525	—	2	1	no	—
690	#525	—	2	1	no	—
691	#519	—	2	1	no	—
692	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
693	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
694	C₂×C₄×D₄	—	2	1	no	—
695	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
696	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
697	#501	C₂²×C₂₉	1	2	yes	complemented
698	#501	C₂²×C₂₉	1	2	yes	complemented
699	#499	C₂²×C₂₉	1	2	yes	complemented
700	#490	C₂²×C₂₉	1	2	yes	—
701	#489	C₂²×C₂₉	1	2	yes	complemented
702	#488	C₂²×C₂₉	1	2	yes	complemented
703	#485	C₂²×C₂₉	1	2	yes	complemented
704	#485	C₂²×C₂₉	1	2	yes	complemented
705	#484	C₂²×C₂₉	1	2	yes	complemented
706	#483	C₂²×C₂₉	1	2	yes	complemented
707	#483	C₂²×C₂₉	1	2	yes	complemented
708	#482	C₂²×C₂₉	1	2	yes	—
709	#482	C₂²×C₂₉	1	2	yes	complemented
710	#482	C₂²×C₂₉	1	2	yes	complemented
711	#480	C₂²×C₂₉	1	2	yes	—
712	#479	C₂²×C₂₉	1	2	yes	complemented
713	#479	C₂²×C₂₉	1	2	yes	complemented
714	#479	C₂²×C₂₉	1	2	yes	complemented
715	#478	C₂²×C₂₉	1	2	yes	—
716	#478	C₂²×C₂₉	1	2	yes	—
717	#478	C₂²×C₂₉	1	2	yes	complemented
718	#477	C₂²×C₂₉	1	1	yes	characteristic, complemented
719	#477	C₂²×C₂₉	1	1	yes	characteristic, complemented
720	#476	C₂²×C₂₉	1	1	yes	characteristic
721	#476	C₂²×C₂₉	1	1	yes	characteristic
722	#476	C₂²×C₂₉	1	2	yes	—
723	#476	C₂²×C₂₉	1	1	yes	characteristic, complemented
724	#476	C₂²×C₂₉	1	2	yes	complemented
725	#476	C₂²×C₂₉	1	1	yes	characteristic, complemented
726	#476	C₂²×C₂₉	1	1	yes	characteristic, complemented
727	#476	C₂²×C₂₉	1	1	yes	characteristic, complemented
728	#475	C₂²×C₂₉	1	1	yes	characteristic, complemented
729	#475	C₂²×C₂₉	1	2	yes	complemented
730	#474	C₂²×C₂₉	1	1	yes	characteristic
731	#474	C₂²×C₂₉	1	1	yes	characteristic, complemented
732	#474	C₂²×C₂₉	1	1	yes	characteristic, complemented
733	#470	C₂²×C₂₉	1	2	yes	complemented
734	#468	C₂²×C₂₉	1	2	yes	—
735	#467	C₂²×C₂₉	1	2	yes	complemented
736	#465	C₂²×C₂₉	1	2	yes	—
737	#465	C₂²×C₂₉	1	2	yes	complemented
738	#465	C₂²×C₂₉	1	2	yes	complemented
739	#464	C₂²×C₂₉	1	2	yes	complemented
740	#464	C₂²×C₂₉	1	2	yes	complemented
741	#462	C₂²×C₂₉	1	1	yes	characteristic, complemented
742	#461	C₂²×C₂₉	1	1	yes	characteristic
743	#461	C₂²×C₂₉	1	1	yes	characteristic, complemented
744	#461	C₂²×C₂₉	1	1	yes	characteristic, complemented
745	#460	C₂²×C₂₉	1	2	yes	—
746	#452	C₂²×C₂₉	1	2	yes	—
747	#450	C₂²×C₂₉	1	2	yes	—
748	#450	C₂²×C₂₉	1	2	yes	—
749	#446	C₂²×C₂₉	1	2	yes	complemented
750	#441	C₂²×C₂₉	1	2	yes	complemented
751	#440	C₂²×C₂₉	1	2	yes	—
752	#440	C₂²×C₂₉	1	2	yes	—
753	#440	C₂²×C₂₉	1	2	yes	complemented
754	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	—
755	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
756	#435	C₂²×C₂₉	1	2	yes	—
757	#435	C₂²×C₂₉	1	2	yes	complemented
758	C₈×D₄	C₂²×C₂₉	1	2	yes	complemented
759	#432	C₂²×C₂₉	1	1	yes	characteristic, complemented
760	#432	C₂²×C₂₉	1	1	yes	characteristic, complemented
761	#431	C₂²×C₂₉	1	1	yes	characteristic, complemented
762	#428	C₂²×C₂₉	1	2	yes	complemented
763	#427	C₂²×C₂₉	1	2	yes	complemented
764	C₂×#106	C₂²×C₂₉	1	2	yes	complemented
765	#423	C₂²×C₂₉	1	1	yes	characteristic, complemented
766	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
767	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
768	#418	C₂²×C₂₉	1	2	yes	—
769	#416	C₂²×C₂₉	1	2	yes	—
770	C₂×#102	C₂²×C₂₉	1	2	yes	—
771	C₂×C₂₉	—	2	2	no	—
772	C₂×C₂₉	—	4	1	no	—
773	C₂×C₂₉	—	4	1	no	—
774	C₂×C₂₉	—	4	2	no	—
775	C₂×C₂₉	—	8	1	no	—
776	C₂×C₂₉	—	8	1	no	—
777	C₂×C₂₉	#3489	1	1	yes	characteristic
778	C₂×C₂₉	C₂×#575	1	1	yes	characteristic
779	C₂×C₂₉	C₂×#577	1	1	yes	characteristic
780	C₂×#41	—	2	1	no	—
781	C₂×#41	D₄×C₂₉	1	1	yes	characteristic
782	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
783	C₂²×Q₈	—	2	1	no	—
784	C₂²×D₄	—	2	1	no	—
785	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
786	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
787	C₂³×C₄	—	2	1	no	—
788	C₂³×C₄	—	2	1	no	—
789	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
790	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
791	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
792	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
793	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
794	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
795	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
796	C₄⋊Q₈	—	2	2	no	—
797	C₄⋊Q₈	—	2	1	no	—
798	C₄⋊Q₈	—	2	1	no	—
799	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
800	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
801	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
802	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
803	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
804	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
805	#127	C₂³×C₂₉	1	1	yes	characteristic
806	#126	—	2	1	no	—
807	#126	—	2	1	no	—
808	#126	—	2	2	no	—
809	#126	—	2	2	no	—
810	#126	—	2	2	no	—
811	#126	—	2	2	no	—
812	#126	—	2	1	no	—
813	#126	—	2	1	no	—
814	#125	—	2	1	no	—
815	#125	—	2	2	no	—
816	#125	—	2	2	no	—
817	#125	—	2	2	no	—
818	#125	—	2	2	no	—
819	#125	—	2	1	no	—
820	#125	—	2	1	no	—
821	#125	—	2	1	no	—
822	#125	C₂³×C₂₉	1	1	yes	characteristic
823	#125	C₂³×C₂₉	1	1	yes	characteristic
824	#125	C₂³×C₂₉	1	2	yes	—
825	#125	C₂³×C₂₉	1	2	yes	—
826	#124	—	2	1	no	—
827	#124	—	2	2	no	—
828	#124	—	2	1	no	—
829	#124	C₂³×C₂₉	1	1	yes	characteristic
830	#124	C₂³×C₂₉	1	1	yes	characteristic
831	#123	—	2	2	no	—
832	#123	—	2	2	no	—
833	#123	—	2	1	no	—
834	#123	—	2	1	no	—
835	#123	—	2	1	no	—
836	#123	—	2	1	no	—
837	#123	—	2	1	no	—
838	#123	—	2	1	no	—
839	#123	—	2	1	no	—
840	#123	—	2	1	no	—
841	C₂²⋊Q₈	—	2	1	no	—
842	C₂²⋊Q₈	—	2	1	no	—
843	C₂²⋊Q₈	—	2	1	no	—
844	C₂²⋊Q₈	—	2	1	no	—
845	C₂²⋊Q₈	—	2	1	no	—
846	C₂²⋊Q₈	—	2	1	no	—
847	C₂²⋊Q₈	—	2	1	no	—
848	C₂²⋊Q₈	—	2	1	no	—
849	C₂²⋊Q₈	—	2	1	no	—
850	C₂²⋊Q₈	—	2	1	no	—
851	C₂²⋊Q₈	—	2	1	no	—
852	C₂²⋊Q₈	—	2	1	no	—
853	C₂²⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
854	C₂²⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
855	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
856	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
857	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
858	#121	—	2	1	no	—
859	#121	—	2	1	no	—
860	#121	—	2	1	no	—
861	#121	—	2	1	no	—
862	#121	—	2	1	no	—
863	#121	—	2	1	no	—
864	#121	C₂³×C₂₉	1	1	yes	characteristic
865	#121	C₂³×C₂₉	1	1	yes	characteristic
866	#121	C₂³×C₂₉	1	1	yes	characteristic
867	#121	C₂³×C₂₉	1	1	yes	characteristic
868	#120	—	2	1	no	—
869	#120	—	2	1	no	—
870	#120	—	2	1	no	—
871	#120	—	2	1	no	—
872	C₄×Q₈	—	2	2	no	—
873	C₄×Q₈	—	2	2	no	—
874	C₄×Q₈	—	2	1	no	—
875	C₄×Q₈	—	2	1	no	—
876	C₄×Q₈	—	2	1	no	—
877	C₄×Q₈	—	2	1	no	—
878	C₄×Q₈	—	2	1	no	—
879	C₄×Q₈	—	2	1	no	—
880	C₄×Q₈	—	2	1	no	—
881	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
882	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
883	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
884	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
885	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
886	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
887	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
888	C₄×D₄	—	2	1	no	—
889	C₄×D₄	—	2	1	no	—
890	C₄×D₄	—	2	1	no	—
891	C₄×D₄	—	2	1	no	—
892	C₄×D₄	—	2	1	no	—
893	C₄×D₄	—	2	1	no	—
894	C₄×D₄	—	2	1	no	—
895	C₄×D₄	—	2	1	no	—
896	C₄×D₄	—	2	1	no	—
897	C₄×D₄	—	2	1	no	—
898	C₄×D₄	—	2	1	no	—
899	C₄×D₄	—	2	1	no	—
900	C₄×D₄	—	2	1	no	—
901	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
902	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
903	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
904	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
905	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
906	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
907	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
908	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
909	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
910	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
911	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
912	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
913	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
914	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
915	#117	—	2	1	no	—
916	#117	—	2	1	no	—
917	#117	—	2	1	no	—
918	#117	—	2	2	no	—
919	#117	—	2	2	no	—
920	#117	—	2	1	no	—
921	#117	—	2	1	no	—
922	#117	—	2	1	no	—
923	#117	D₄×C₂₉	1	1	yes	characteristic
924	#117	D₄×C₂₉	1	1	yes	characteristic
925	#117	D₄×C₂₉	1	1	yes	characteristic
926	#117	C₂³×C₂₉	1	1	yes	characteristic
927	#117	C₂³×C₂₉	1	2	yes	—
928	#117	C₂³×C₂₉	1	2	yes	—
929	C₂×C₄⋊C₄	—	2	1	no	—
930	C₂×C₄⋊C₄	—	2	1	no	—
931	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
932	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
933	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
934	C₂×C₂²⋊C₄	—	2	1	no	—
935	C₂×C₂²⋊C₄	—	2	1	no	—
936	C₂×C₂²⋊C₄	—	2	1	no	—
937	C₂×C₂²⋊C₄	—	2	1	no	—
938	C₂×C₄²	—	2	1	no	—
939	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
940	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
941	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
942	#107	C₂³×C₂₉	1	2	yes	—
943	#107	C₂³×C₂₉	1	2	yes	—
944	#107	C₂³×C₂₉	1	2	yes	—
945	#107	C₂³×C₂₉	1	2	yes	—
946	#107	C₂³×C₂₉	1	2	yes	—
947	#106	C₂³×C₂₉	1	2	yes	—
948	#106	C₂³×C₂₉	1	2	yes	—
949	#106	C₂³×C₂₉	1	2	yes	—
950	#106	C₂³×C₂₉	1	2	yes	—
951	#106	C₂³×C₂₉	1	2	yes	—
952	#106	C₂³×C₂₉	1	2	yes	—
953	#106	C₂³×C₂₉	1	2	yes	—
954	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
955	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
956	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
957	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
958	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
959	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
960	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
961	#103	C₂³×C₂₉	1	2	yes	—
962	#103	C₂³×C₂₉	1	2	yes	—
963	#103	C₂³×C₂₉	1	2	yes	—
964	#103	C₂³×C₂₉	1	2	yes	—
965	#103	C₂³×C₂₉	1	2	yes	—
966	#103	C₂³×C₂₉	1	2	yes	—
967	#103	C₂³×C₂₉	1	2	yes	—
968	#102	C₂³×C₂₉	1	2	yes	—
969	#102	C₂³×C₂₉	1	2	yes	—
970	#102	C₂³×C₂₉	1	2	yes	—
971	#102	C₂³×C₂₉	1	2	yes	—
972	#102	C₂³×C₂₉	1	2	yes	—
973	#102	C₂³×C₂₉	1	2	yes	—
974	#102	C₂³×C₂₉	1	2	yes	—
975	#102	C₂³×C₂₉	1	2	yes	—
976	#102	C₂³×C₂₉	1	2	yes	—
977	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
978	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
979	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
980	#97	C₂³×C₂₉	1	2	yes	—
981	#97	C₂³×C₂₉	1	2	yes	—
982	C₄×C₈	C₂³×C₂₉	1	2	yes	—
983	C₂₉	#62126	1	1	yes	characteristic, direct product factor, Sylow
984	C₂⁴	—	2	1	no	—
985	C₂⁴	—	2	1	no	—
986	#41	—	2	2	no	—
987	#41	—	4	2	no	—
988	#41	—	4	1	no	—
989	#41	—	8	2	no	—
990	C₂×Q₈	—	2	1	no	—
991	C₂×Q₈	—	2	1	no	—
992	C₂×Q₈	—	2	1	no	—
993	C₂×Q₈	—	2	2	no	—
994	C₂×Q₈	—	2	1	no	—
995	C₂×Q₈	—	4	4	no	—
996	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
997	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
998	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	2	1	no	—
1002	C₂×D₄	—	2	1	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	2	1	no	—
1005	C₂×D₄	—	2	1	no	—
1006	C₂×D₄	—	2	1	no	—
1007	C₂×D₄	—	2	1	no	—
1008	C₂×D₄	—	2	1	no	—
1009	C₂×D₄	—	2	1	no	—
1010	C₂×D₄	—	4	1	no	—
1011	C₂×D₄	—	4	1	no	—
1012	C₂×D₄	—	4	4	no	—
1013	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1014	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1015	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1016	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
1017	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
1018	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
1019	C₂²×C₄	—	2	2	no	—
1020	C₂²×C₄	—	2	1	no	—
1021	C₂²×C₄	—	2	1	no	—
1022	C₂²×C₄	—	2	1	no	—
1023	C₂²×C₄	—	2	1	no	—
1024	C₂²×C₄	—	2	1	no	—
1025	C₂²×C₄	—	2	1	no	—
1026	C₂²×C₄	—	2	1	no	—
1027	C₂²×C₄	—	2	1	no	—
1028	C₂²×C₄	—	2	1	no	—
1029	C₂²×C₄	—	2	1	no	—
1030	C₂²×C₄	—	2	1	no	—
1031	C₂²×C₄	—	8	2	no	—
1032	C₂²×C₄	—	8	2	no	—
1033	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1034	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1035	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1036	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1037	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1038	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1039	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1040	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1041	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1042	Q₁₆	—	4	2	no	—
1043	SD₁₆	—	2	4	no	—
1044	SD₁₆	—	4	2	no	—
1045	SD₁₆	—	4	2	no	—
1046	M₁₆	—	4	2	no	—
1047	C₂×C₈	—	4	2	no	—
1048	C₂×C₈	—	4	2	no	—
1049	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
1050	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
1051	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
1052	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	1	no	—
1060	C₄⋊C₄	—	2	1	no	—
1061	C₄⋊C₄	—	2	2	no	—
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	—	2	1	no	—
1064	C₄⋊C₄	—	2	1	no	—
1065	C₄⋊C₄	—	2	1	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	2	no	—
1068	C₄⋊C₄	—	2	2	no	—
1069	C₄⋊C₄	—	2	2	no	—
1070	C₄⋊C₄	—	2	2	no	—
1071	C₄⋊C₄	—	2	1	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	—	2	1	no	—
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	2	no	—
1076	C₄⋊C₄	—	2	2	no	—
1077	C₄⋊C₄	—	2	2	no	—
1078	C₄⋊C₄	—	2	2	no	—
1079	C₄⋊C₄	—	2	2	no	—
1080	C₄⋊C₄	—	2	2	no	—
1081	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1082	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1083	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1084	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1085	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1086	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1087	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
1088	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
1089	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
1090	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1091	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1092	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1093	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	2	no	—
1097	C₂²⋊C₄	—	2	2	no	—
1098	C₂²⋊C₄	—	2	2	no	—
1099	C₂²⋊C₄	—	2	1	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	—	2	1	no	—
1103	C₂²⋊C₄	—	2	1	no	—
1104	C₂²⋊C₄	—	2	1	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	1	no	—
1108	C₂²⋊C₄	—	2	1	no	—
1109	C₂²⋊C₄	—	2	1	no	—
1110	C₂²⋊C₄	—	2	1	no	—
1111	C₂²⋊C₄	—	2	1	no	—
1112	C₂²⋊C₄	—	2	1	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	—	2	1	no	—
1115	C₂²⋊C₄	—	2	1	no	—
1116	C₂²⋊C₄	—	2	1	no	—
1117	C₂²⋊C₄	—	2	1	no	—
1118	C₂²⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1119	C₂²⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1120	C₂²⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1121	C₂²⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1122	C₂²⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1123	C₂²⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1124	C₄²	—	2	1	no	—
1125	C₄²	—	2	1	no	—
1126	C₄²	—	2	1	no	—
1127	C₄²	—	2	2	no	—
1128	C₄²	—	2	2	no	—
1129	C₄²	—	2	2	no	—
1130	C₄²	—	2	2	no	—
1131	C₄²	—	2	2	no	—
1132	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1133	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1134	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1135	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1136	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1137	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1138	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1139	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1140	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1141	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1142	C₂³	—	2	1	no	—
1143	C₂³	—	2	1	no	—
1144	C₂³	—	2	1	no	—
1145	C₂³	—	4	2	no	—
1146	C₂³	—	4	2	no	—
1147	C₂³	—	4	2	no	—
1148	C₂³	—	4	2	no	—
1149	C₂³	—	8	1	no	—
1150	C₂³	—	8	1	no	—
1151	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1152	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1153	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1154	Q₈	—	2	2	no	—
1155	Q₈	—	2	1	no	—
1156	Q₈	—	2	2	no	—
1157	Q₈	—	2	1	no	—
1158	Q₈	—	4	1	no	—
1159	Q₈	—	4	2	no	—
1160	Q₈	—	4	2	no	—
1161	Q₈	—	4	4	no	—
1162	Q₈	—	4	2	no	—
1163	Q₈	—	8	1	no	—
1164	D₄	—	2	2	no	—
1165	D₄	—	2	2	no	—
1166	D₄	—	2	1	no	—
1167	D₄	—	2	1	no	—
1168	D₄	—	2	1	no	—
1169	D₄	—	2	1	no	—
1170	D₄	—	2	1	no	—
1171	D₄	—	4	1	no	—
1172	D₄	—	4	2	no	—
1173	D₄	—	4	2	no	—
1174	D₄	—	4	2	no	—
1175	D₄	—	4	2	no	—
1176	D₄	—	4	2	no	—
1177	D₄	—	4	2	no	—
1178	D₄	—	8	1	no	—
1179	D₄	—	8	1	no	—
1180	D₄	—	8	1	no	—
1181	D₄	C₂₉×2₋¹⁺⁴	1	2	yes	—
1182	C₂×C₄	—	2	2	no	—
1183	C₂×C₄	—	2	2	no	—
1184	C₂×C₄	—	2	2	no	—
1185	C₂×C₄	—	2	2	no	—
1186	C₂×C₄	—	2	1	no	—
1187	C₂×C₄	—	2	1	no	—
1188	C₂×C₄	—	2	1	no	—
1189	C₂×C₄	—	2	1	no	—
1190	C₂×C₄	—	2	1	no	—
1191	C₂×C₄	—	2	1	no	—
1192	C₂×C₄	—	2	2	no	—
1193	C₂×C₄	—	2	2	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	4	1	no	—
1202	C₂×C₄	—	4	1	no	—
1203	C₂×C₄	—	4	2	no	—
1204	C₂×C₄	—	4	2	no	—
1205	C₂×C₄	—	4	4	no	—
1206	C₂×C₄	—	4	2	no	—
1207	C₂×C₄	—	4	2	no	—
1208	C₂×C₄	—	4	2	no	—
1209	C₂×C₄	—	8	1	no	—
1210	C₂×C₄	—	8	1	no	—
1211	C₂×C₄	—	8	1	no	—
1212	C₂×C₄	—	8	1	no	—
1213	C₂×C₄	—	8	1	no	—
1214	C₂×C₄	—	8	1	no	—
1215	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1216	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1217	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1218	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1219	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1220	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1221	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1222	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1223	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1224	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1225	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1226	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1227	C₈	—	2	2	no	—
1228	C₈	—	2	2	no	—
1229	C₈	—	2	2	no	—
1230	C₈	—	2	2	no	—
1231	C₂²	—	2	1	no	—
1232	C₂²	—	2	1	no	—
1233	C₂²	—	2	1	no	—
1234	C₂²	—	2	1	no	—
1235	C₂²	—	2	2	no	—
1236	C₂²	—	2	1	no	—
1237	C₂²	—	2	1	no	—
1238	C₂²	—	2	1	no	—
1239	C₂²	—	2	1	no	—
1240	C₂²	—	4	1	no	—
1241	C₂²	—	4	1	no	—
1242	C₂²	—	4	1	no	—
1243	C₂²	—	4	1	no	—
1244	C₂²	—	4	1	no	—
1245	C₂²	—	4	1	no	—
1246	C₂²	—	4	1	no	—
1247	C₂²	—	4	1	no	—
1248	C₂²	—	8	4	no	—
1249	C₂²	—	8	4	no	—
1250	C₂²	C₂₉×#575	1	2	yes	—
1251	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
1252	C₄	—	2	1	no	—
1253	C₄	—	2	1	no	—
1254	C₄	—	2	1	no	—
1255	C₄	—	2	1	no	—
1256	C₄	—	2	1	no	—
1257	C₄	—	2	1	no	—
1258	C₄	—	2	1	no	—
1259	C₄	—	2	1	no	—
1260	C₄	—	2	1	no	—
1261	C₄	—	2	1	no	—
1262	C₄	—	4	1	no	—
1263	C₄	—	4	2	no	—
1264	C₄	—	4	1	no	—
1265	C₄	—	4	2	no	—
1266	C₄	—	4	2	no	—
1267	C₄	—	4	1	no	—
1268	C₄	—	4	1	no	—
1269	C₄	—	4	1	no	—
1270	C₄	—	4	2	no	—
1271	C₄	C₂₉×#577	1	2	yes	—
1272	C₄	C₂×C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
1273	C₄	C₂₉×#585	1	1	yes	characteristic
1274	C₂	—	2	2	no	—
1275	C₂	—	4	1	no	—
1276	C₂	—	4	1	no	—
1277	C₂	—	4	2	no	—
1278	C₂	—	8	1	no	—
1279	C₂	—	8	1	no	—
1280	C₂	C₂₉×#3489	1	1	yes	characteristic
1281	C₂	C₂×C₂₉×#575	1	1	yes	characteristic
1282	C₂	C₂×C₂₉×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
prime radical	C₂₉×#3481	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄×#41×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3509	C₂	semidirect
3. C₂₉×#3388	C₂	semidirect
4. C₂₉×#3371	C₂	semidirect
5. C₂₉×#3350	C₂	semidirect
6. C₂₉×#3344	C₂	semidirect
7. C₂₉×#3337	C₂	semidirect
8. C₂₉×#3311	C₂	semidirect
9. C₂₉×#3310	C₂	semidirect
10. C₂₉×#3296	C₂	semidirect
11. C₂₉×#3252	C₂	semidirect
12. C₂₉×#3248	C₂	semidirect
13. C₂₉×#3246	C₂	semidirect
14. C₂₉×#3238	C₂	semidirect
15. C₂₉×#3235	C₂	semidirect
16. C₂₉×#3233	C₂	semidirect
17. C₂₉×#3116	C₂	semidirect
18. C₂₉×#3110	C₂	semidirect
19. C₂₉×#3101	C₂	semidirect
20. C₂₉×#3077	C₂	semidirect
21. C₂₉×#3076	C₂	semidirect
22. C₂×C₂₉×#476	C₂	semidirect
23. C₂₉×#2990	C₂	semidirect
26. C₂₉×#557	C₂²	semidirect
28. C₂₉×#556	C₂²	semidirect
37. C₂₉×#552	C₂²	semidirect
47. C₂₉×#533	C₂²	semidirect
48. C₂₉×#533	C₂²	semidirect
49. C₂₉×#533	C₂²	semidirect
50. C₂₉×#533	C₂²	semidirect
51. C₂₉×#533	C₂²	semidirect
53. C₂×C₂₉×C₄⋊Q₈	C₂²	semidirect
65. C₂₉×#501	C₂²	semidirect
66. C₂₉×#501	C₂²	semidirect
67. C₂₉×#499	C₂²	semidirect
69. C₂₉×#489	C₂²	semidirect
70. C₂₉×#488	C₂²	semidirect
71. C₂₉×#485	C₂²	semidirect
72. C₂₉×#485	C₂²	semidirect
73. C₂₉×#484	C₂²	semidirect
74. C₂₉×#483	C₂²	semidirect
75. C₂₉×#483	C₂²	semidirect
77. C₂₉×#482	C₂²	semidirect
78. C₂₉×#482	C₂²	semidirect
80. C₂₉×#479	C₂²	semidirect
81. C₂₉×#479	C₂²	semidirect
82. C₂₉×#479	C₂²	semidirect
85. C₂₉×#478	C₂²	semidirect
86. C₂₉×#477	C₂²	semidirect
87. C₂₉×#477	C₂²	semidirect
91. C₂₉×#476	C₂²	semidirect
92. C₂₉×#476	C₂²	semidirect
93. C₂₉×#476	C₂²	semidirect
94. C₂₉×#476	C₂²	semidirect
95. C₂₉×#476	C₂²	semidirect
96. C₂₉×#475	C₂²	semidirect
97. C₂₉×#475	C₂²	semidirect
99. C₂₉×#474	C₂²	semidirect
100. C₂₉×#474	C₂²	semidirect
101. C₂₉×#470	C₂²	semidirect
103. C₂₉×#467	C₂²	semidirect
105. C₂₉×#465	C₂²	semidirect
106. C₂₉×#465	C₂²	semidirect
107. C₂₉×#464	C₂²	semidirect
108. C₂₉×#464	C₂²	semidirect
109. C₂₉×#462	C₂²	semidirect
111. C₂₉×#461	C₂²	semidirect
112. C₂₉×#461	C₂²	semidirect
117. C₂₉×#446	C₂²	semidirect
118. C₂₉×#441	C₂²	semidirect
121. C₂₉×#440	C₂²	semidirect
123. C₄×SD₁₆×C₂₉	C₂²	semidirect
125. C₂₉×#435	C₂²	semidirect
126. C₈×D₄×C₂₉	C₂²	semidirect
127. C₂₉×#432	C₂²	semidirect
128. C₂₉×#432	C₂²	semidirect
129. C₂₉×#431	C₂²	semidirect
130. C₂₉×#428	C₂²	semidirect
131. C₂₉×#427	C₂²	semidirect
132. C₂×C₂₉×#106	C₂²	semidirect
133. C₂₉×#423	C₂²	semidirect
134. C₂×C₂₉×C₄⋊C₈	C₂²	semidirect
135. C₂×C₂₉×C₄⋊C₈	C₂²	semidirect
500. #62126	C₂₉	direct (N × H)
590. #3509	C₂×C₂₉	semidirect
592. #3388	C₂×C₂₉	semidirect
593. #3371	C₂×C₂₉	semidirect
594. #3350	C₂×C₂₉	semidirect
595. #3344	C₂×C₂₉	semidirect
596. #3337	C₂×C₂₉	semidirect
597. #3311	C₂×C₂₉	semidirect
598. #3310	C₂×C₂₉	semidirect
599. #3296	C₂×C₂₉	semidirect
600. #3252	C₂×C₂₉	semidirect
601. #3248	C₂×C₂₉	semidirect
602. #3246	C₂×C₂₉	semidirect
603. #3238	C₂×C₂₉	semidirect
604. #3235	C₂×C₂₉	semidirect
605. #3233	C₂×C₂₉	semidirect
606. #3116	C₂×C₂₉	semidirect
607. #3110	C₂×C₂₉	semidirect
608. #3101	C₂×C₂₉	semidirect
609. #3077	C₂×C₂₉	semidirect
610. #3076	C₂×C₂₉	semidirect
611. C₂×#476	C₂×C₂₉	semidirect
612. #2990	C₂×C₂₉	semidirect
658. #557	C₂²×C₂₉	semidirect
660. #556	C₂²×C₂₉	semidirect
669. #552	C₂²×C₂₉	semidirect
679. #533	C₂²×C₂₉	semidirect
680. #533	C₂²×C₂₉	semidirect
681. #533	C₂²×C₂₉	semidirect
682. #533	C₂²×C₂₉	semidirect
683. #533	C₂²×C₂₉	semidirect
685. C₂×C₄⋊Q₈	C₂²×C₂₉	semidirect
697. #501	C₂²×C₂₉	semidirect
698. #501	C₂²×C₂₉	semidirect
699. #499	C₂²×C₂₉	semidirect
701. #489	C₂²×C₂₉	semidirect
702. #488	C₂²×C₂₉	semidirect
703. #485	C₂²×C₂₉	semidirect
704. #485	C₂²×C₂₉	semidirect
705. #484	C₂²×C₂₉	semidirect
706. #483	C₂²×C₂₉	semidirect
707. #483	C₂²×C₂₉	semidirect
709. #482	C₂²×C₂₉	semidirect
710. #482	C₂²×C₂₉	semidirect
712. #479	C₂²×C₂₉	semidirect
713. #479	C₂²×C₂₉	semidirect
714. #479	C₂²×C₂₉	semidirect
717. #478	C₂²×C₂₉	semidirect
718. #477	C₂²×C₂₉	semidirect
719. #477	C₂²×C₂₉	semidirect
723. #476	C₂²×C₂₉	semidirect
724. #476	C₂²×C₂₉	semidirect
725. #476	C₂²×C₂₉	semidirect
726. #476	C₂²×C₂₉	semidirect
727. #476	C₂²×C₂₉	semidirect
728. #475	C₂²×C₂₉	semidirect
729. #475	C₂²×C₂₉	semidirect
731. #474	C₂²×C₂₉	semidirect
732. #474	C₂²×C₂₉	semidirect
733. #470	C₂²×C₂₉	semidirect
735. #467	C₂²×C₂₉	semidirect
737. #465	C₂²×C₂₉	semidirect
738. #465	C₂²×C₂₉	semidirect
739. #464	C₂²×C₂₉	semidirect
740. #464	C₂²×C₂₉	semidirect
741. #462	C₂²×C₂₉	semidirect
743. #461	C₂²×C₂₉	semidirect
744. #461	C₂²×C₂₉	semidirect
749. #446	C₂²×C₂₉	semidirect
750. #441	C₂²×C₂₉	semidirect
753. #440	C₂²×C₂₉	semidirect
755. C₄×SD₁₆	C₂²×C₂₉	semidirect
757. #435	C₂²×C₂₉	semidirect
758. C₈×D₄	C₂²×C₂₉	semidirect
759. #432	C₂²×C₂₉	semidirect
760. #432	C₂²×C₂₉	semidirect
761. #431	C₂²×C₂₉	semidirect
762. #428	C₂²×C₂₉	semidirect
763. #427	C₂²×C₂₉	semidirect
764. C₂×#106	C₂²×C₂₉	semidirect
765. #423	C₂²×C₂₉	semidirect
766. C₂×C₄⋊C₈	C₂²×C₂₉	semidirect
767. C₂×C₄⋊C₈	C₂²×C₂₉	semidirect
983. C₂₉	#62126	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×#3509	2
C₂₉×#3481	2
C₂₉×#3388	2
C₂₉×#3371	2
C₂₉×#3350	2
C₂₉×#3344	2
C₂₉×#3337	2
C₂₉×#3311	2
C₂₉×#3310	2
C₂₉×#3296	2
C₂₉×#3252	2
C₂₉×#3248	2
C₂₉×#3246	2
C₂₉×#3238	2
C₂₉×#3235	2
C₂₉×#3233	2
C₂₉×#3116	2
C₂₉×#3110	2
C₂₉×#3101	2
C₂₉×#3077	2
C₂₉×#3076	2
C₂×C₂₉×#476	2
C₂₉×#2990	2
#62126	29

Subgroups — C29×#62126 #20357026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#62126 #20357026