Subgroups — C₂₉×#62164 #20357064

Order 7424.

1758 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3519	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#3388	C₂	1	2	yes	maximal, complemented
4	C₂₉×#3368	C₂	1	2	yes	maximal, complemented
5	C₂₉×#3348	C₂	1	2	yes	maximal, complemented
6	C₂₉×#3346	C₂	1	2	yes	maximal, complemented
7	C₂₉×#3337	C₂	1	2	yes	maximal, complemented
8	C₂₉×#3310	C₂	1	2	yes	maximal, complemented
9	C₂₉×#3310	C₂	1	2	yes	maximal, complemented
10	C₂₉×#3295	C₂	1	2	yes	maximal, complemented
11	C₂₉×#3260	C₂	1	2	yes	maximal, complemented
12	C₂₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#3241	C₂	1	2	yes	maximal, complemented
14	C₂₉×#3234	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#3123	C₂	1	2	yes	maximal, complemented
16	C₂₉×#3110	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₉×#3081	C₂	1	2	yes	maximal, complemented
18	C₂×C₂₉×#478	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₉×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₉×#564	—	2	1	no	—
21	C₂₉×#563	—	2	1	no	—
22	C₂₉×#557	C₂²	1	2	yes	complemented
23	C₂₉×#555	C₂²	1	1	yes	characteristic
24	C₂₉×#554	C₂²	1	1	yes	characteristic
25	C₂₉×#554	C₂²	1	2	yes	complemented
26	C₂₉×#553	—	2	1	no	—
27	C₂₉×#553	C₂²	1	2	yes	—
28	C₂₉×#552	—	2	2	no	—
29	C₂₉×#552	C₂²	1	2	yes	complemented
30	C₂₉×#552	C₂²	1	2	yes	complemented
31	C₂₉×#550	C₂²	1	1	yes	characteristic
32	C₂₉×#546	—	2	1	no	—
33	C₂₉×#546	—	2	2	no	—
34	D₄²×C₂₉	C₂²	1	2	yes	—
35	D₄²×C₂₉	C₂²	1	1	yes	characteristic
36	C₂₉×#544	—	2	1	no	—
37	C₂₉×#544	C₂²	1	2	yes	complemented
38	C₂₉×#541	—	2	2	no	—
39	C₂₉×#541	C₂²	1	2	yes	complemented
40	C₂₉×#540	C₂²	1	2	yes	—
41	C₂₉×#539	—	2	1	no	—
42	C₂₉×#538	—	2	2	no	—
43	C₂₉×#533	C₂²	1	1	yes	characteristic, complemented
44	C₂₉×#532	C₂²	1	1	yes	characteristic
45	C₂₉×#529	C₂²	1	1	yes	characteristic
46	C₂×C₂₉×#125	C₂²	1	1	yes	characteristic, complemented
47	C₂₉×#525	—	2	1	no	—
48	C₂×C₂₉×#121	—	2	1	no	—
49	C₂₉×#518	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
51	C₂₉×#501	C₂²	1	2	yes	complemented
52	C₂₉×#501	C₂²	1	2	yes	complemented
53	C₂₉×#499	C₂²	1	2	yes	complemented
54	C₂₉×#490	C₂²	1	2	yes	complemented
55	C₂₉×#490	C₂²	1	2	yes	complemented
56	C₂₉×#486	C₂²	1	2	yes	complemented
57	C₂₉×#485	C₂²	1	2	yes	complemented
58	C₂₉×#485	C₂²	1	2	yes	complemented
59	C₂₉×#484	C₂²	1	2	yes	complemented
60	C₂₉×#482	C₂²	1	2	yes	complemented
61	C₂₉×#482	C₂²	1	2	yes	complemented
62	C₂₉×#481	C₂²	1	2	yes	complemented
63	C₂₉×#481	C₂²	1	2	yes	complemented
64	C₂₉×#480	C₂²	1	2	yes	complemented
65	C₂₉×#480	C₂²	1	2	yes	complemented
66	C₂₉×#479	C₂²	1	2	yes	complemented
67	C₂₉×#479	C₂²	1	2	yes	complemented
68	C₂₉×#478	C₂²	1	2	yes	—
69	C₂₉×#478	C₂²	1	2	yes	—
70	C₂₉×#478	C₂²	1	2	yes	—
71	C₂₉×#478	C₂²	1	2	yes	complemented
72	C₂₉×#478	C₂²	1	2	yes	complemented
73	C₂₉×#478	C₂²	1	2	yes	complemented
74	C₂₉×#478	C₂²	1	2	yes	complemented
75	C₂₉×#478	C₂²	1	2	yes	complemented
76	C₂₉×#476	C₂²	1	2	yes	—
77	C₂₉×#476	C₂²	1	2	yes	complemented
78	C₂₉×#475	C₂²	1	2	yes	complemented
79	C₂₉×#474	C₂²	1	1	yes	characteristic
80	C₂₉×#474	C₂²	1	1	yes	characteristic, complemented
81	C₂₉×#474	C₂²	1	2	yes	complemented
82	C₂₉×#468	C₂²	1	2	yes	complemented
83	C₂₉×#468	C₂²	1	2	yes	complemented
84	C₂₉×#465	C₂²	1	2	yes	complemented
85	C₂₉×#465	C₂²	1	2	yes	complemented
86	C₂₉×#465	C₂²	1	2	yes	complemented
87	C₂₉×#465	C₂²	1	2	yes	complemented
88	C₂₉×#461	C₂²	1	1	yes	characteristic
89	C₂₉×#461	C₂²	1	2	yes	complemented
90	C₂₉×#461	C₂²	1	1	yes	characteristic, complemented
91	C₂₉×#460	C₂²	1	2	yes	complemented
92	C₂₉×#460	C₂²	1	2	yes	complemented
93	C₂₉×#460	C₂²	1	2	yes	complemented
94	C₂₉×#450	C₂²	1	2	yes	—
95	C₂₉×#450	C₂²	1	2	yes	—
96	C₂₉×#450	C₂²	1	2	yes	—
97	C₂₉×#446	C₂²	1	2	yes	complemented
98	C₂₉×#440	C₂²	1	2	yes	—
99	C₂₉×#440	C₂²	1	2	yes	—
100	C₂₉×#440	C₂²	1	2	yes	complemented
101	C₂₉×#440	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	—
103	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	complemented
104	C₂₉×#435	C₂²	1	2	yes	complemented
105	C₂₉×#435	C₂²	1	2	yes	complemented
106	C₈×D₄×C₂₉	C₂²	1	2	yes	complemented
107	C₂₉×#433	C₂²	1	2	yes	complemented
108	C₂₉×#432	C₂²	1	1	yes	characteristic, complemented
109	C₂₉×#428	C₂²	1	2	yes	complemented
110	C₂₉×#427	C₂²	1	2	yes	complemented
111	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic, complemented
112	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic, complemented
113	C₂₉×#424	C₂²	1	2	yes	complemented
114	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
115	C₂₉×#418	C₂²	1	2	yes	—
116	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
117	C₂×C₂₉×#102	C₂²	1	2	yes	—
118	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
119	C₂×#41×C₂₉	—	2	1	no	—
120	C₂×#41×C₂₉	—	2	1	no	—
121	C₂²×D₄×C₂₉	—	2	1	no	—
122	C₂²×D₄×C₂₉	—	2	2	no	—
123	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
125	C₂³×C₄×C₂₉	—	2	1	no	—
126	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
130	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
131	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
134	C₂₉×C₄⋊Q₈	—	2	2	no	—
135	C₂₉×C₄⋊Q₈	—	2	2	no	—
136	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
137	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₂₉×#127	C₂³	1	2	yes	—
141	C₂₉×#127	C₂³	1	1	yes	characteristic
142	C₂₉×#126	—	2	2	no	—
143	C₂₉×#126	—	2	2	no	—
144	C₂₉×#126	—	2	2	no	—
145	C₂₉×#126	—	2	2	no	—
146	C₂₉×#126	—	2	2	no	—
147	C₂₉×#126	D₄	1	2	yes	—
148	C₂₉×#125	—	2	2	no	—
149	C₂₉×#125	—	2	2	no	—
150	C₂₉×#125	—	2	2	no	—
151	C₂₉×#125	—	2	2	no	—
152	C₂₉×#125	—	2	2	no	—
153	C₂₉×#125	—	2	2	no	—
154	C₂₉×#125	—	2	2	no	—
155	C₂₉×#125	—	2	2	no	—
156	C₂₉×#125	—	2	1	no	—
157	C₂₉×#125	—	2	1	no	—
158	C₂₉×#125	—	2	1	no	—
159	C₂₉×#125	D₄	1	1	yes	characteristic
160	C₂₉×#125	C₂³	1	2	yes	—
161	C₂₉×#125	C₂³	1	2	yes	—
162	C₂₉×#125	C₂³	1	2	yes	—
163	C₂₉×#125	C₂³	1	2	yes	—
164	C₂₉×#124	—	2	2	no	—
165	C₂₉×#124	—	2	1	no	—
166	C₂₉×#124	D₄	1	1	yes	characteristic
167	C₂₉×#123	—	2	2	no	—
168	C₂₉×#123	—	2	2	no	—
169	C₂₉×#123	—	2	2	no	—
170	C₂₉×#123	—	2	2	no	—
171	C₂₉×#123	—	2	2	no	—
172	C₂₉×#123	D₄	1	2	yes	—
173	C₂₉×C₂²⋊Q₈	—	2	1	no	—
174	C₂₉×C₂²⋊Q₈	—	2	1	no	—
175	C₂₉×C₂²⋊Q₈	—	2	2	no	—
176	C₂₉×C₂²⋊Q₈	—	2	2	no	—
177	C₂₉×C₂²⋊Q₈	—	2	2	no	—
178	C₂₉×C₂²⋊Q₈	—	2	2	no	—
179	C₂₉×C₂²⋊Q₈	—	2	2	no	—
180	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
181	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
182	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
183	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
184	C₂₉×#121	—	2	2	no	—
185	C₂₉×#121	—	2	1	no	—
186	C₂₉×#121	—	2	1	no	—
187	C₂₉×#121	—	2	1	no	—
188	C₂₉×#121	—	2	1	no	—
189	C₂₉×#121	—	2	2	no	—
190	C₂₉×#121	—	2	2	no	—
191	C₂₉×#121	—	2	2	no	—
192	C₂₉×#121	—	2	2	no	—
193	C₂₉×#121	D₄	1	1	yes	characteristic
194	C₂₉×#121	C₂³	1	2	yes	—
195	C₂₉×#121	C₂³	1	2	yes	—
196	C₂₉×#121	C₂³	1	2	yes	—
197	C₂₉×#120	—	2	2	no	—
198	C₂₉×#120	—	2	2	no	—
199	C₂₉×#120	—	2	2	no	—
200	C₄×Q₈×C₂₉	—	2	2	no	—
201	C₄×Q₈×C₂₉	—	2	1	no	—
202	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
203	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
204	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
205	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
206	C₄×D₄×C₂₉	—	2	2	no	—
207	C₄×D₄×C₂₉	—	2	2	no	—
208	C₄×D₄×C₂₉	—	2	2	no	—
209	C₄×D₄×C₂₉	—	2	2	no	—
210	C₄×D₄×C₂₉	—	2	1	no	—
211	C₄×D₄×C₂₉	—	2	1	no	—
212	C₄×D₄×C₂₉	—	2	1	no	—
213	C₄×D₄×C₂₉	C₂³	1	2	yes	—
214	C₄×D₄×C₂₉	C₂³	1	2	yes	—
215	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
216	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
218	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₂₉	C₂³	1	2	yes	—
220	C₄×D₄×C₂₉	C₂³	1	2	yes	—
221	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
222	C₂₉×#117	—	2	1	no	—
223	C₂₉×#117	—	2	1	no	—
224	C₂₉×#117	—	2	2	no	—
225	C₂₉×#117	—	2	2	no	—
226	C₂₉×#117	C₂³	1	2	yes	—
227	C₂₉×#117	C₂³	1	2	yes	—
228	C₂₉×#117	C₂³	1	2	yes	—
229	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
230	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
231	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
232	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
236	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
237	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
238	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
239	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
240	C₂₉×#107	C₂³	1	2	yes	—
241	C₂₉×#107	C₂³	1	2	yes	—
242	C₂₉×#107	C₂³	1	2	yes	—
243	C₂₉×#107	C₂³	1	2	yes	—
244	C₂₉×#107	C₂³	1	2	yes	—
245	C₂₉×#107	C₂³	1	2	yes	—
246	C₂₉×#106	C₂³	1	2	yes	—
247	C₂₉×#106	C₂³	1	2	yes	—
248	C₂₉×#106	C₂³	1	2	yes	—
249	C₂₉×#106	C₂³	1	2	yes	—
250	C₂₉×#106	C₂³	1	2	yes	—
251	C₂₉×#106	C₂³	1	2	yes	—
252	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
253	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
254	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
255	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
256	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
257	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
258	C₂₉×#103	C₂³	1	2	yes	—
259	C₂₉×#103	C₂³	1	2	yes	—
260	C₂₉×#103	C₂³	1	2	yes	—
261	C₂₉×#103	C₂³	1	2	yes	—
262	C₂₉×#102	C₂³	1	2	yes	—
263	C₂₉×#102	C₂³	1	2	yes	—
264	C₂₉×#102	C₂³	1	2	yes	—
265	C₂₉×#102	C₂³	1	2	yes	—
266	C₂₉×#102	C₂³	1	2	yes	—
267	C₂₉×#102	C₂³	1	2	yes	—
268	C₂₉×#102	C₂³	1	2	yes	—
269	C₂₉×#102	C₂³	1	2	yes	—
270	C₂₉×#102	C₂³	1	2	yes	—
271	C₂₉×#102	C₂³	1	2	yes	—
272	C₂₉×#102	C₂³	1	2	yes	—
273	C₂₉×#102	C₂³	1	2	yes	—
274	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
275	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
276	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₂₉×#97	C₂³	1	2	yes	—
278	C₂₉×#97	C₂³	1	2	yes	—
279	C₄×C₈×C₂₉	C₂³	1	2	yes	—
280	C₂⁴×C₂₉	—	2	1	no	—
281	C₂⁴×C₂₉	—	2	2	no	—
282	#41×C₂₉	—	8	2	no	—
283	#41×C₂₉	—	8	2	no	—
284	C₂×Q₈×C₂₉	—	2	1	no	—
285	C₂×Q₈×C₂₉	—	2	2	no	—
286	C₂×Q₈×C₂₉	—	2	1	no	—
287	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
288	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
289	C₂×D₄×C₂₉	—	2	2	no	—
290	C₂×D₄×C₂₉	—	2	4	no	—
291	C₂×D₄×C₂₉	—	2	2	no	—
292	C₂×D₄×C₂₉	—	2	2	no	—
293	C₂×D₄×C₂₉	—	2	2	no	—
294	C₂×D₄×C₂₉	—	2	2	no	—
295	C₂×D₄×C₂₉	—	2	1	no	—
296	C₂×D₄×C₂₉	—	2	1	no	—
297	C₂×D₄×C₂₉	—	2	2	no	—
298	C₂×D₄×C₂₉	—	2	1	no	—
299	C₂×D₄×C₂₉	—	2	2	no	—
300	C₂×D₄×C₂₉	—	4	1	no	—
301	C₂×D₄×C₂₉	—	4	2	no	—
302	C₂×D₄×C₂₉	—	8	2	no	—
303	C₂×D₄×C₂₉	—	8	4	no	—
304	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
305	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
306	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
307	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
308	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₂₉	—	2	1	no	—
310	C₂²×C₄×C₂₉	—	2	1	no	—
311	C₂²×C₄×C₂₉	—	2	1	no	—
312	C₂²×C₄×C₂₉	—	2	2	no	—
313	C₂²×C₄×C₂₉	—	2	1	no	—
314	C₂²×C₄×C₂₉	—	2	1	no	—
315	C₂²×C₄×C₂₉	—	2	1	no	—
316	C₂²×C₄×C₂₉	—	2	2	no	—
317	C₂²×C₄×C₂₉	—	2	2	no	—
318	C₂²×C₄×C₂₉	—	2	2	no	—
319	C₂²×C₄×C₂₉	—	2	1	no	—
320	C₂²×C₄×C₂₉	—	8	2	no	—
321	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
322	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
323	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
325	SD₁₆×C₂₉	—	2	4	no	—
326	SD₁₆×C₂₉	—	4	2	no	—
327	SD₁₆×C₂₉	—	4	2	no	—
328	SD₁₆×C₂₉	—	4	2	no	—
329	M₁₆×C₂₉	—	4	2	no	—
330	C₂×C₈×C₂₉	—	4	1	no	—
331	C₂×C₈×C₂₉	—	4	2	no	—
332	C₂×C₈×C₂₉	—	4	1	no	—
333	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
334	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
335	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
336	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
337	C₄⋊C₄×C₂₉	—	2	1	no	—
338	C₄⋊C₄×C₂₉	—	2	2	no	—
339	C₄⋊C₄×C₂₉	—	2	2	no	—
340	C₄⋊C₄×C₂₉	—	2	2	no	—
341	C₄⋊C₄×C₂₉	—	2	2	no	—
342	C₄⋊C₄×C₂₉	—	2	2	no	—
343	C₄⋊C₄×C₂₉	—	2	1	no	—
344	C₄⋊C₄×C₂₉	—	2	1	no	—
345	C₄⋊C₄×C₂₉	—	2	2	no	—
346	C₄⋊C₄×C₂₉	—	2	1	no	—
347	C₄⋊C₄×C₂₉	—	2	1	no	—
348	C₄⋊C₄×C₂₉	—	2	2	no	—
349	C₄⋊C₄×C₂₉	—	2	2	no	—
350	C₄⋊C₄×C₂₉	—	2	2	no	—
351	C₄⋊C₄×C₂₉	—	2	1	no	—
352	C₄⋊C₄×C₂₉	—	2	2	no	—
353	C₄⋊C₄×C₂₉	—	2	2	no	—
354	C₄⋊C₄×C₂₉	—	2	2	no	—
355	C₄⋊C₄×C₂₉	—	2	2	no	—
356	C₄⋊C₄×C₂₉	—	2	1	no	—
357	C₄⋊C₄×C₂₉	—	2	2	no	—
358	C₄⋊C₄×C₂₉	—	2	2	no	—
359	C₄⋊C₄×C₂₉	—	2	2	no	—
360	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
365	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
366	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
369	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
370	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
371	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
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	—	2	1	no	—
378	C₂²⋊C₄×C₂₉	—	2	2	no	—
379	C₂²⋊C₄×C₂₉	—	2	1	no	—
380	C₂²⋊C₄×C₂₉	—	2	2	no	—
381	C₂²⋊C₄×C₂₉	—	2	1	no	—
382	C₂²⋊C₄×C₂₉	—	2	2	no	—
383	C₂²⋊C₄×C₂₉	—	2	1	no	—
384	C₂²⋊C₄×C₂₉	—	2	2	no	—
385	C₂²⋊C₄×C₂₉	—	2	2	no	—
386	C₂²⋊C₄×C₂₉	—	2	2	no	—
387	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
389	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
390	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
392	C₄²×C₂₉	—	2	2	no	—
393	C₄²×C₂₉	—	2	2	no	—
394	C₄²×C₂₉	—	2	2	no	—
395	C₄²×C₂₉	—	2	2	no	—
396	C₄²×C₂₉	—	2	2	no	—
397	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
400	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
401	C₄²×C₂₉	C₂⁴	1	2	yes	—
402	#62164	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
403	C₂³×C₂₉	—	2	1	no	—
404	C₂³×C₂₉	—	2	1	no	—
405	C₂³×C₂₉	—	2	2	no	—
406	C₂³×C₂₉	—	4	2	no	—
407	C₂³×C₂₉	—	4	4	no	—
408	C₂³×C₂₉	—	4	2	no	—
409	C₂³×C₂₉	—	8	1	no	—
410	C₂³×C₂₉	—	8	2	no	—
411	C₂³×C₂₉	—	8	2	no	—
412	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
413	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
414	Q₈×C₂₉	—	2	2	no	—
415	Q₈×C₂₉	—	2	2	no	—
416	Q₈×C₂₉	—	4	1	no	—
417	Q₈×C₂₉	—	8	1	no	—
418	Q₈×C₂₉	—	8	2	no	—
419	Q₈×C₂₉	—	8	1	no	—
420	D₄×C₂₉	—	2	4	no	—
421	D₄×C₂₉	—	2	1	no	—
422	D₄×C₂₉	—	2	2	no	—
423	D₄×C₂₉	—	2	1	no	—
424	D₄×C₂₉	—	2	1	no	—
425	D₄×C₂₉	—	2	2	no	—
426	D₄×C₂₉	—	4	1	no	—
427	D₄×C₂₉	—	4	2	no	—
428	D₄×C₂₉	—	4	4	no	—
429	D₄×C₂₉	—	4	2	no	—
430	D₄×C₂₉	—	4	4	no	—
431	D₄×C₂₉	—	8	2	no	—
432	D₄×C₂₉	—	8	2	no	—
433	D₄×C₂₉	—	8	1	no	—
434	D₄×C₂₉	—	8	2	no	—
435	D₄×C₂₉	—	8	2	no	—
436	D₄×C₂₉	2₋¹⁺⁴	1	2	yes	—
437	C₂×C₄×C₂₉	—	2	2	no	—
438	C₂×C₄×C₂₉	—	2	1	no	—
439	C₂×C₄×C₂₉	—	2	2	no	—
440	C₂×C₄×C₂₉	—	2	1	no	—
441	C₂×C₄×C₂₉	—	2	2	no	—
442	C₂×C₄×C₂₉	—	2	2	no	—
443	C₂×C₄×C₂₉	—	2	1	no	—
444	C₂×C₄×C₂₉	—	2	2	no	—
445	C₂×C₄×C₂₉	—	2	2	no	—
446	C₂×C₄×C₂₉	—	2	2	no	—
447	C₂×C₄×C₂₉	—	2	2	no	—
448	C₂×C₄×C₂₉	—	2	1	no	—
449	C₂×C₄×C₂₉	—	4	1	no	—
450	C₂×C₄×C₂₉	—	4	2	no	—
451	C₂×C₄×C₂₉	—	4	2	no	—
452	C₂×C₄×C₂₉	—	4	2	no	—
453	C₂×C₄×C₂₉	—	8	1	no	—
454	C₂×C₄×C₂₉	—	8	1	no	—
455	C₂×C₄×C₂₉	—	8	2	no	—
456	C₂×C₄×C₂₉	—	8	2	no	—
457	C₂×C₄×C₂₉	—	8	2	no	—
458	C₂×C₄×C₂₉	—	8	1	no	—
459	C₂×C₄×C₂₉	—	8	2	no	—
460	C₂×C₄×C₂₉	—	8	1	no	—
461	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
463	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
464	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
465	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
470	C₈×C₂₉	—	2	2	no	—
471	C₈×C₂₉	—	2	2	no	—
472	C₈×C₂₉	—	2	2	no	—
473	C₈×C₂₉	—	2	2	no	—
474	#3563	C₂×C₂₉	1	1	yes	characteristic, complemented
475	#3519	C₂×C₂₉	1	1	yes	characteristic
476	#3388	C₂×C₂₉	1	2	yes	complemented
477	#3368	C₂×C₂₉	1	2	yes	complemented
478	#3348	C₂×C₂₉	1	2	yes	complemented
479	#3346	C₂×C₂₉	1	2	yes	complemented
480	#3337	C₂×C₂₉	1	2	yes	complemented
481	#3310	C₂×C₂₉	1	2	yes	complemented
482	#3310	C₂×C₂₉	1	2	yes	complemented
483	#3295	C₂×C₂₉	1	2	yes	complemented
484	#3260	C₂×C₂₉	1	2	yes	complemented
485	#3246	C₂×C₂₉	1	1	yes	characteristic, complemented
486	#3241	C₂×C₂₉	1	2	yes	complemented
487	#3234	C₂×C₂₉	1	1	yes	characteristic, complemented
488	#3123	C₂×C₂₉	1	2	yes	complemented
489	#3110	C₂×C₂₉	1	1	yes	characteristic, complemented
490	#3081	C₂×C₂₉	1	2	yes	complemented
491	C₂×#478	C₂×C₂₉	1	1	yes	characteristic, complemented
492	#2992	C₂×C₂₉	1	1	yes	characteristic, complemented
493	C₂²×C₂₉	—	2	1	no	—
494	C₂²×C₂₉	—	2	1	no	—
495	C₂²×C₂₉	—	2	2	no	—
496	C₂²×C₂₉	—	2	2	no	—
497	C₂²×C₂₉	—	2	2	no	—
498	C₂²×C₂₉	—	2	2	no	—
499	C₂²×C₂₉	—	4	1	no	—
500	C₂²×C₂₉	—	4	1	no	—
501	C₂²×C₂₉	—	4	1	no	—
502	C₂²×C₂₉	—	4	2	no	—
503	C₂²×C₂₉	—	4	1	no	—
504	C₂²×C₂₉	—	4	2	no	—
505	C₂²×C₂₉	—	4	2	no	—
506	C₂²×C₂₉	—	4	1	no	—
507	C₂²×C₂₉	—	8	4	no	—
508	C₂²×C₂₉	—	16	4	no	—
509	C₂²×C₂₉	#577	1	2	yes	—
510	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
511	C₄×C₂₉	—	2	1	no	—
512	C₄×C₂₉	—	2	1	no	—
513	C₄×C₂₉	—	2	2	no	—
514	C₄×C₂₉	—	2	1	no	—
515	C₄×C₂₉	—	2	2	no	—
516	C₄×C₂₉	—	2	1	no	—
517	C₄×C₂₉	—	2	1	no	—
518	C₄×C₂₉	—	2	2	no	—
519	C₄×C₂₉	—	4	1	no	—
520	C₄×C₂₉	—	4	1	no	—
521	C₄×C₂₉	—	4	2	no	—
522	C₄×C₂₉	—	4	2	no	—
523	C₄×C₂₉	—	4	2	no	—
524	C₄×C₂₉	—	4	2	no	—
525	C₄×C₂₉	—	4	2	no	—
526	C₄×C₂₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
527	C₄×C₂₉	#585	1	1	yes	characteristic
528	#564	—	2	1	no	—
529	#563	—	2	1	no	—
530	#557	C₂²×C₂₉	1	2	yes	complemented
531	#555	C₂²×C₂₉	1	1	yes	characteristic
532	#554	C₂²×C₂₉	1	1	yes	characteristic
533	#554	C₂²×C₂₉	1	2	yes	complemented
534	#553	—	2	1	no	—
535	#553	C₂²×C₂₉	1	2	yes	—
536	#552	—	2	2	no	—
537	#552	C₂²×C₂₉	1	2	yes	complemented
538	#552	C₂²×C₂₉	1	2	yes	complemented
539	#550	C₂²×C₂₉	1	1	yes	characteristic
540	#546	—	2	1	no	—
541	#546	—	2	2	no	—
542	D₄²	C₂²×C₂₉	1	2	yes	—
543	D₄²	C₂²×C₂₉	1	1	yes	characteristic
544	#544	—	2	1	no	—
545	#544	C₂²×C₂₉	1	2	yes	complemented
546	#541	—	2	2	no	—
547	#541	C₂²×C₂₉	1	2	yes	complemented
548	#540	C₂²×C₂₉	1	2	yes	—
549	#539	—	2	1	no	—
550	#538	—	2	2	no	—
551	#533	C₂²×C₂₉	1	1	yes	characteristic, complemented
552	#532	C₂²×C₂₉	1	1	yes	characteristic
553	#529	C₂²×C₂₉	1	1	yes	characteristic
554	C₂×#125	C₂²×C₂₉	1	1	yes	characteristic, complemented
555	#525	—	2	1	no	—
556	C₂×#121	—	2	1	no	—
557	#518	C₂²×C₂₉	1	2	yes	—
558	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
559	#501	C₂²×C₂₉	1	2	yes	complemented
560	#501	C₂²×C₂₉	1	2	yes	complemented
561	#499	C₂²×C₂₉	1	2	yes	complemented
562	#490	C₂²×C₂₉	1	2	yes	complemented
563	#490	C₂²×C₂₉	1	2	yes	complemented
564	#486	C₂²×C₂₉	1	2	yes	complemented
565	#485	C₂²×C₂₉	1	2	yes	complemented
566	#485	C₂²×C₂₉	1	2	yes	complemented
567	#484	C₂²×C₂₉	1	2	yes	complemented
568	#482	C₂²×C₂₉	1	2	yes	complemented
569	#482	C₂²×C₂₉	1	2	yes	complemented
570	#481	C₂²×C₂₉	1	2	yes	complemented
571	#481	C₂²×C₂₉	1	2	yes	complemented
572	#480	C₂²×C₂₉	1	2	yes	complemented
573	#480	C₂²×C₂₉	1	2	yes	complemented
574	#479	C₂²×C₂₉	1	2	yes	complemented
575	#479	C₂²×C₂₉	1	2	yes	complemented
576	#478	C₂²×C₂₉	1	2	yes	—
577	#478	C₂²×C₂₉	1	2	yes	—
578	#478	C₂²×C₂₉	1	2	yes	—
579	#478	C₂²×C₂₉	1	2	yes	complemented
580	#478	C₂²×C₂₉	1	2	yes	complemented
581	#478	C₂²×C₂₉	1	2	yes	complemented
582	#478	C₂²×C₂₉	1	2	yes	complemented
583	#478	C₂²×C₂₉	1	2	yes	complemented
584	#476	C₂²×C₂₉	1	2	yes	—
585	#476	C₂²×C₂₉	1	2	yes	complemented
586	#475	C₂²×C₂₉	1	2	yes	complemented
587	#474	C₂²×C₂₉	1	1	yes	characteristic
588	#474	C₂²×C₂₉	1	2	yes	complemented
589	#474	C₂²×C₂₉	1	1	yes	characteristic, complemented
590	#468	C₂²×C₂₉	1	2	yes	complemented
591	#468	C₂²×C₂₉	1	2	yes	complemented
592	#465	C₂²×C₂₉	1	2	yes	complemented
593	#465	C₂²×C₂₉	1	2	yes	complemented
594	#465	C₂²×C₂₉	1	2	yes	complemented
595	#465	C₂²×C₂₉	1	2	yes	complemented
596	#461	C₂²×C₂₉	1	1	yes	characteristic
597	#461	C₂²×C₂₉	1	1	yes	characteristic, complemented
598	#461	C₂²×C₂₉	1	2	yes	complemented
599	#460	C₂²×C₂₉	1	2	yes	complemented
600	#460	C₂²×C₂₉	1	2	yes	complemented
601	#460	C₂²×C₂₉	1	2	yes	complemented
602	#450	C₂²×C₂₉	1	2	yes	—
603	#450	C₂²×C₂₉	1	2	yes	—
604	#450	C₂²×C₂₉	1	2	yes	—
605	#446	C₂²×C₂₉	1	2	yes	complemented
606	#440	C₂²×C₂₉	1	2	yes	—
607	#440	C₂²×C₂₉	1	2	yes	—
608	#440	C₂²×C₂₉	1	2	yes	complemented
609	#440	C₂²×C₂₉	1	2	yes	complemented
610	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	—
611	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
612	#435	C₂²×C₂₉	1	2	yes	complemented
613	#435	C₂²×C₂₉	1	2	yes	complemented
614	C₈×D₄	C₂²×C₂₉	1	2	yes	complemented
615	#433	C₂²×C₂₉	1	2	yes	complemented
616	#432	C₂²×C₂₉	1	1	yes	characteristic, complemented
617	#428	C₂²×C₂₉	1	2	yes	complemented
618	#427	C₂²×C₂₉	1	2	yes	complemented
619	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic, complemented
620	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic, complemented
621	#424	C₂²×C₂₉	1	2	yes	complemented
622	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
623	#418	C₂²×C₂₉	1	2	yes	—
624	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
625	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
626	C₂×#102	C₂²×C₂₉	1	2	yes	—
627	C₂×C₂₉	—	2	2	no	—
628	C₂×C₂₉	—	4	2	no	—
629	C₂×C₂₉	—	4	2	no	—
630	C₂×C₂₉	—	8	1	no	—
631	C₂×C₂₉	—	8	2	no	—
632	C₂×C₂₉	#3489	1	1	yes	characteristic
633	C₂×C₂₉	C₂×#577	1	1	yes	characteristic
634	C₂×C₂₉	#3585	1	1	yes	characteristic
635	C₂×#41	—	2	1	no	—
636	C₂×#41	—	2	1	no	—
637	C₂²×D₄	—	2	1	no	—
638	C₂²×D₄	—	2	2	no	—
639	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
640	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
641	C₂³×C₄	—	2	1	no	—
642	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
643	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
644	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
645	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
646	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
647	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
648	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
649	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
650	C₄⋊Q₈	—	2	2	no	—
651	C₄⋊Q₈	—	2	2	no	—
652	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
653	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
654	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
655	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
656	#127	C₂³×C₂₉	1	1	yes	characteristic
657	#127	C₂³×C₂₉	1	2	yes	—
658	#126	—	2	2	no	—
659	#126	—	2	2	no	—
660	#126	—	2	2	no	—
661	#126	—	2	2	no	—
662	#126	—	2	2	no	—
663	#126	D₄×C₂₉	1	2	yes	—
664	#125	—	2	2	no	—
665	#125	—	2	2	no	—
666	#125	—	2	2	no	—
667	#125	—	2	2	no	—
668	#125	—	2	2	no	—
669	#125	—	2	2	no	—
670	#125	—	2	2	no	—
671	#125	—	2	2	no	—
672	#125	—	2	1	no	—
673	#125	—	2	1	no	—
674	#125	—	2	1	no	—
675	#125	D₄×C₂₉	1	1	yes	characteristic
676	#125	C₂³×C₂₉	1	2	yes	—
677	#125	C₂³×C₂₉	1	2	yes	—
678	#125	C₂³×C₂₉	1	2	yes	—
679	#125	C₂³×C₂₉	1	2	yes	—
680	#124	—	2	2	no	—
681	#124	—	2	1	no	—
682	#124	D₄×C₂₉	1	1	yes	characteristic
683	#123	—	2	2	no	—
684	#123	—	2	2	no	—
685	#123	—	2	2	no	—
686	#123	—	2	2	no	—
687	#123	—	2	2	no	—
688	#123	D₄×C₂₉	1	2	yes	—
689	C₂²⋊Q₈	—	2	1	no	—
690	C₂²⋊Q₈	—	2	1	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	—	2	2	no	—
696	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
697	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
698	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
699	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
700	#121	—	2	2	no	—
701	#121	—	2	1	no	—
702	#121	—	2	1	no	—
703	#121	—	2	1	no	—
704	#121	—	2	1	no	—
705	#121	—	2	2	no	—
706	#121	—	2	2	no	—
707	#121	—	2	2	no	—
708	#121	—	2	2	no	—
709	#121	D₄×C₂₉	1	1	yes	characteristic
710	#121	C₂³×C₂₉	1	2	yes	—
711	#121	C₂³×C₂₉	1	2	yes	—
712	#121	C₂³×C₂₉	1	2	yes	—
713	#120	—	2	2	no	—
714	#120	—	2	2	no	—
715	#120	—	2	2	no	—
716	C₄×Q₈	—	2	2	no	—
717	C₄×Q₈	—	2	1	no	—
718	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
719	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
720	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
721	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	—	2	2	no	—
724	C₄×D₄	—	2	2	no	—
725	C₄×D₄	—	2	2	no	—
726	C₄×D₄	—	2	1	no	—
727	C₄×D₄	—	2	1	no	—
728	C₄×D₄	—	2	1	no	—
729	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
730	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
731	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
732	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
733	C₄×D₄	C₂³×C₂₉	1	2	yes	—
734	C₄×D₄	C₂³×C₂₉	1	2	yes	—
735	C₄×D₄	C₂³×C₂₉	1	2	yes	—
736	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
737	C₄×D₄	C₂³×C₂₉	1	2	yes	—
738	#117	—	2	1	no	—
739	#117	—	2	1	no	—
740	#117	—	2	2	no	—
741	#117	—	2	2	no	—
742	#117	C₂³×C₂₉	1	2	yes	—
743	#117	C₂³×C₂₉	1	2	yes	—
744	#117	C₂³×C₂₉	1	2	yes	—
745	C₂×C₄⋊C₄	—	2	1	no	—
746	C₂×C₄⋊C₄	—	2	1	no	—
747	C₂×C₄⋊C₄	—	2	1	no	—
748	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
749	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
750	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
751	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
752	C₂×C₂²⋊C₄	—	2	1	no	—
753	C₂×C₂²⋊C₄	—	2	2	no	—
754	C₂×C₂²⋊C₄	—	2	2	no	—
755	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
756	#107	C₂³×C₂₉	1	2	yes	—
757	#107	C₂³×C₂₉	1	2	yes	—
758	#107	C₂³×C₂₉	1	2	yes	—
759	#107	C₂³×C₂₉	1	2	yes	—
760	#107	C₂³×C₂₉	1	2	yes	—
761	#107	C₂³×C₂₉	1	2	yes	—
762	#106	C₂³×C₂₉	1	2	yes	—
763	#106	C₂³×C₂₉	1	2	yes	—
764	#106	C₂³×C₂₉	1	2	yes	—
765	#106	C₂³×C₂₉	1	2	yes	—
766	#106	C₂³×C₂₉	1	2	yes	—
767	#106	C₂³×C₂₉	1	2	yes	—
768	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
769	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
770	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
771	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
772	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
773	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
774	#103	C₂³×C₂₉	1	2	yes	—
775	#103	C₂³×C₂₉	1	2	yes	—
776	#103	C₂³×C₂₉	1	2	yes	—
777	#103	C₂³×C₂₉	1	2	yes	—
778	#102	C₂³×C₂₉	1	2	yes	—
779	#102	C₂³×C₂₉	1	2	yes	—
780	#102	C₂³×C₂₉	1	2	yes	—
781	#102	C₂³×C₂₉	1	2	yes	—
782	#102	C₂³×C₂₉	1	2	yes	—
783	#102	C₂³×C₂₉	1	2	yes	—
784	#102	C₂³×C₂₉	1	2	yes	—
785	#102	C₂³×C₂₉	1	2	yes	—
786	#102	C₂³×C₂₉	1	2	yes	—
787	#102	C₂³×C₂₉	1	2	yes	—
788	#102	C₂³×C₂₉	1	2	yes	—
789	#102	C₂³×C₂₉	1	2	yes	—
790	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
791	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
792	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
793	#97	C₂³×C₂₉	1	2	yes	—
794	#97	C₂³×C₂₉	1	2	yes	—
795	C₄×C₈	C₂³×C₂₉	1	2	yes	—
796	C₂₉	#62164	1	1	yes	characteristic, direct product factor, Sylow
797	C₂⁴	—	2	1	no	—
798	C₂⁴	—	2	2	no	—
799	#41	—	8	2	no	—
800	#41	—	8	2	no	—
801	C₂×Q₈	—	2	1	no	—
802	C₂×Q₈	—	2	2	no	—
803	C₂×Q₈	—	2	1	no	—
804	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
805	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	2	4	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	2	2	no	—
812	C₂×D₄	—	2	1	no	—
813	C₂×D₄	—	2	1	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	4	1	no	—
818	C₂×D₄	—	4	2	no	—
819	C₂×D₄	—	8	2	no	—
820	C₂×D₄	—	8	4	no	—
821	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
822	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
823	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
824	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
825	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
826	C₂²×C₄	—	2	1	no	—
827	C₂²×C₄	—	2	1	no	—
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	1	no	—
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	1	no	—
837	C₂²×C₄	—	8	2	no	—
838	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
839	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
842	SD₁₆	—	2	4	no	—
843	SD₁₆	—	4	2	no	—
844	SD₁₆	—	4	2	no	—
845	SD₁₆	—	4	2	no	—
846	M₁₆	—	4	2	no	—
847	C₂×C₈	—	4	1	no	—
848	C₂×C₈	—	4	2	no	—
849	C₂×C₈	—	4	1	no	—
850	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
851	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
852	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
853	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
854	C₄⋊C₄	—	2	1	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	1	no	—
861	C₄⋊C₄	—	2	1	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	—	2	1	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	1	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	1	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
878	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
879	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
880	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
881	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
882	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
883	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
884	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
885	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
886	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
887	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
888	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	1	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	1	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	1	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	1	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
905	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
906	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
907	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
908	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
909	C₄²	—	2	2	no	—
910	C₄²	—	2	2	no	—
911	C₄²	—	2	2	no	—
912	C₄²	—	2	2	no	—
913	C₄²	—	2	2	no	—
914	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
915	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
916	C₄²	C₂⁴×C₂₉	1	2	yes	—
917	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
918	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
919	C₂³	—	2	1	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	1	no	—
922	C₂³	—	4	2	no	—
923	C₂³	—	4	4	no	—
924	C₂³	—	4	2	no	—
925	C₂³	—	8	1	no	—
926	C₂³	—	8	2	no	—
927	C₂³	—	8	2	no	—
928	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
929	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
930	Q₈	—	2	2	no	—
931	Q₈	—	2	2	no	—
932	Q₈	—	4	1	no	—
933	Q₈	—	8	1	no	—
934	Q₈	—	8	1	no	—
935	Q₈	—	8	2	no	—
936	D₄	—	2	4	no	—
937	D₄	—	2	1	no	—
938	D₄	—	2	2	no	—
939	D₄	—	2	1	no	—
940	D₄	—	2	1	no	—
941	D₄	—	2	2	no	—
942	D₄	—	4	1	no	—
943	D₄	—	4	2	no	—
944	D₄	—	4	4	no	—
945	D₄	—	4	2	no	—
946	D₄	—	4	4	no	—
947	D₄	—	8	2	no	—
948	D₄	—	8	1	no	—
949	D₄	—	8	2	no	—
950	D₄	—	8	2	no	—
951	D₄	—	8	2	no	—
952	D₄	C₂₉×2₋¹⁺⁴	1	2	yes	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	4	1	no	—
966	C₂×C₄	—	4	2	no	—
967	C₂×C₄	—	4	2	no	—
968	C₂×C₄	—	4	2	no	—
969	C₂×C₄	—	8	1	no	—
970	C₂×C₄	—	8	1	no	—
971	C₂×C₄	—	8	2	no	—
972	C₂×C₄	—	8	2	no	—
973	C₂×C₄	—	8	2	no	—
974	C₂×C₄	—	8	1	no	—
975	C₂×C₄	—	8	1	no	—
976	C₂×C₄	—	8	2	no	—
977	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
978	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
979	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
980	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
981	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
982	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
983	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
984	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
985	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
986	C₈	—	2	2	no	—
987	C₈	—	2	2	no	—
988	C₈	—	2	2	no	—
989	C₈	—	2	2	no	—
990	C₂²	—	2	1	no	—
991	C₂²	—	2	1	no	—
992	C₂²	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	2	2	no	—
996	C₂²	—	4	1	no	—
997	C₂²	—	4	1	no	—
998	C₂²	—	4	1	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	1	no	—
1002	C₂²	—	4	1	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	8	4	no	—
1005	C₂²	—	16	4	no	—
1006	C₂²	C₂₉×#577	1	2	yes	—
1007	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
1008	C₄	—	2	1	no	—
1009	C₄	—	2	2	no	—
1010	C₄	—	2	1	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	2	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	1	no	—
1015	C₄	—	2	2	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	2	no	—
1018	C₄	—	4	2	no	—
1019	C₄	—	4	1	no	—
1020	C₄	—	4	1	no	—
1021	C₄	—	4	2	no	—
1022	C₄	—	4	2	no	—
1023	C₄	C₂×C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
1024	C₄	C₂₉×#585	1	1	yes	characteristic
1025	C₂	—	2	2	no	—
1026	C₂	—	4	2	no	—
1027	C₂	—	4	2	no	—
1028	C₂	—	8	1	no	—
1029	C₂	—	8	2	no	—
1030	C₂	C₂₉×#3489	1	1	yes	characteristic
1031	C₂	C₂×C₂₉×#577	1	1	yes	characteristic
1032	C₂	C₂₉×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
prime radical	C₂₉×#3519	C₂
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×#3563	C₂	semidirect
3. C₂₉×#3388	C₂	semidirect
4. C₂₉×#3368	C₂	semidirect
5. C₂₉×#3348	C₂	semidirect
6. C₂₉×#3346	C₂	semidirect
7. C₂₉×#3337	C₂	semidirect
8. C₂₉×#3310	C₂	semidirect
9. C₂₉×#3310	C₂	semidirect
10. C₂₉×#3295	C₂	semidirect
11. C₂₉×#3260	C₂	semidirect
12. C₂₉×#3246	C₂	semidirect
13. C₂₉×#3241	C₂	semidirect
14. C₂₉×#3234	C₂	semidirect
15. C₂₉×#3123	C₂	semidirect
16. C₂₉×#3110	C₂	semidirect
17. C₂₉×#3081	C₂	semidirect
18. C₂×C₂₉×#478	C₂	semidirect
19. C₂₉×#2992	C₂	semidirect
22. C₂₉×#557	C₂²	semidirect
25. C₂₉×#554	C₂²	semidirect
29. C₂₉×#552	C₂²	semidirect
30. C₂₉×#552	C₂²	semidirect
37. C₂₉×#544	C₂²	semidirect
39. C₂₉×#541	C₂²	semidirect
43. C₂₉×#533	C₂²	semidirect
46. C₂×C₂₉×#125	C₂²	semidirect
51. C₂₉×#501	C₂²	semidirect
52. C₂₉×#501	C₂²	semidirect
53. C₂₉×#499	C₂²	semidirect
54. C₂₉×#490	C₂²	semidirect
55. C₂₉×#490	C₂²	semidirect
56. C₂₉×#486	C₂²	semidirect
57. C₂₉×#485	C₂²	semidirect
58. C₂₉×#485	C₂²	semidirect
59. C₂₉×#484	C₂²	semidirect
60. C₂₉×#482	C₂²	semidirect
61. C₂₉×#482	C₂²	semidirect
62. C₂₉×#481	C₂²	semidirect
63. C₂₉×#481	C₂²	semidirect
64. C₂₉×#480	C₂²	semidirect
65. C₂₉×#480	C₂²	semidirect
66. C₂₉×#479	C₂²	semidirect
67. C₂₉×#479	C₂²	semidirect
71. C₂₉×#478	C₂²	semidirect
72. C₂₉×#478	C₂²	semidirect
73. C₂₉×#478	C₂²	semidirect
74. C₂₉×#478	C₂²	semidirect
75. C₂₉×#478	C₂²	semidirect
77. C₂₉×#476	C₂²	semidirect
78. C₂₉×#475	C₂²	semidirect
80. C₂₉×#474	C₂²	semidirect
81. C₂₉×#474	C₂²	semidirect
82. C₂₉×#468	C₂²	semidirect
83. C₂₉×#468	C₂²	semidirect
84. C₂₉×#465	C₂²	semidirect
85. C₂₉×#465	C₂²	semidirect
86. C₂₉×#465	C₂²	semidirect
87. C₂₉×#465	C₂²	semidirect
89. C₂₉×#461	C₂²	semidirect
90. C₂₉×#461	C₂²	semidirect
91. C₂₉×#460	C₂²	semidirect
92. C₂₉×#460	C₂²	semidirect
93. C₂₉×#460	C₂²	semidirect
97. C₂₉×#446	C₂²	semidirect
100. C₂₉×#440	C₂²	semidirect
101. C₂₉×#440	C₂²	semidirect
103. C₄×SD₁₆×C₂₉	C₂²	semidirect
104. C₂₉×#435	C₂²	semidirect
105. C₂₉×#435	C₂²	semidirect
106. C₈×D₄×C₂₉	C₂²	semidirect
107. C₂₉×#433	C₂²	semidirect
108. C₂₉×#432	C₂²	semidirect
109. C₂₉×#428	C₂²	semidirect
110. C₂₉×#427	C₂²	semidirect
111. C₂×C₂₉×#107	C₂²	semidirect
112. C₂×C₂₉×#106	C₂²	semidirect
113. C₂₉×#424	C₂²	semidirect
114. C₂×C₂₉×C₄⋊C₈	C₂²	semidirect
402. #62164	C₂₉	direct (N × H)
474. #3563	C₂×C₂₉	semidirect
476. #3388	C₂×C₂₉	semidirect
477. #3368	C₂×C₂₉	semidirect
478. #3348	C₂×C₂₉	semidirect
479. #3346	C₂×C₂₉	semidirect
480. #3337	C₂×C₂₉	semidirect
481. #3310	C₂×C₂₉	semidirect
482. #3310	C₂×C₂₉	semidirect
483. #3295	C₂×C₂₉	semidirect
484. #3260	C₂×C₂₉	semidirect
485. #3246	C₂×C₂₉	semidirect
486. #3241	C₂×C₂₉	semidirect
487. #3234	C₂×C₂₉	semidirect
488. #3123	C₂×C₂₉	semidirect
489. #3110	C₂×C₂₉	semidirect
490. #3081	C₂×C₂₉	semidirect
491. C₂×#478	C₂×C₂₉	semidirect
492. #2992	C₂×C₂₉	semidirect
530. #557	C₂²×C₂₉	semidirect
533. #554	C₂²×C₂₉	semidirect
537. #552	C₂²×C₂₉	semidirect
538. #552	C₂²×C₂₉	semidirect
545. #544	C₂²×C₂₉	semidirect
547. #541	C₂²×C₂₉	semidirect
551. #533	C₂²×C₂₉	semidirect
554. C₂×#125	C₂²×C₂₉	semidirect
559. #501	C₂²×C₂₉	semidirect
560. #501	C₂²×C₂₉	semidirect
561. #499	C₂²×C₂₉	semidirect
562. #490	C₂²×C₂₉	semidirect
563. #490	C₂²×C₂₉	semidirect
564. #486	C₂²×C₂₉	semidirect
565. #485	C₂²×C₂₉	semidirect
566. #485	C₂²×C₂₉	semidirect
567. #484	C₂²×C₂₉	semidirect
568. #482	C₂²×C₂₉	semidirect
569. #482	C₂²×C₂₉	semidirect
570. #481	C₂²×C₂₉	semidirect
571. #481	C₂²×C₂₉	semidirect
572. #480	C₂²×C₂₉	semidirect
573. #480	C₂²×C₂₉	semidirect
574. #479	C₂²×C₂₉	semidirect
575. #479	C₂²×C₂₉	semidirect
579. #478	C₂²×C₂₉	semidirect
580. #478	C₂²×C₂₉	semidirect
581. #478	C₂²×C₂₉	semidirect
582. #478	C₂²×C₂₉	semidirect
583. #478	C₂²×C₂₉	semidirect
585. #476	C₂²×C₂₉	semidirect
586. #475	C₂²×C₂₉	semidirect
588. #474	C₂²×C₂₉	semidirect
589. #474	C₂²×C₂₉	semidirect
590. #468	C₂²×C₂₉	semidirect
591. #468	C₂²×C₂₉	semidirect
592. #465	C₂²×C₂₉	semidirect
593. #465	C₂²×C₂₉	semidirect
594. #465	C₂²×C₂₉	semidirect
595. #465	C₂²×C₂₉	semidirect
597. #461	C₂²×C₂₉	semidirect
598. #461	C₂²×C₂₉	semidirect
599. #460	C₂²×C₂₉	semidirect
600. #460	C₂²×C₂₉	semidirect
601. #460	C₂²×C₂₉	semidirect
605. #446	C₂²×C₂₉	semidirect
608. #440	C₂²×C₂₉	semidirect
609. #440	C₂²×C₂₉	semidirect
611. C₄×SD₁₆	C₂²×C₂₉	semidirect
612. #435	C₂²×C₂₉	semidirect
613. #435	C₂²×C₂₉	semidirect
614. C₈×D₄	C₂²×C₂₉	semidirect
615. #433	C₂²×C₂₉	semidirect
616. #432	C₂²×C₂₉	semidirect
617. #428	C₂²×C₂₉	semidirect
618. #427	C₂²×C₂₉	semidirect
619. C₂×#107	C₂²×C₂₉	semidirect
620. C₂×#106	C₂²×C₂₉	semidirect
621. #424	C₂²×C₂₉	semidirect
622. C₂×C₄⋊C₈	C₂²×C₂₉	semidirect
796. C₂₉	#62164	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×#3563	2
C₂₉×#3519	2
C₂₉×#3388	2
C₂₉×#3368	2
C₂₉×#3348	2
C₂₉×#3346	2
C₂₉×#3337	2
C₂₉×#3310	2
C₂₉×#3295	2
C₂₉×#3260	2
C₂₉×#3246	2
C₂₉×#3241	2
C₂₉×#3234	2
C₂₉×#3123	2
C₂₉×#3110	2
C₂₉×#3081	2
C₂×C₂₉×#478	2
C₂₉×#2992	2
#62164	29

Subgroups — C29×#62164 #20357064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#62164 #20357064