Subgroups — C₂₉×#61540 #20356440

Order 7424.

1820 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3514	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3386	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#3348	C₂	1	2	yes	maximal, complemented
8	C₂₉×#3342	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#3329	C₂	1	2	yes	maximal, complemented
10	C₂₉×#3328	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#3324	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#3323	C₂	1	2	yes	maximal, complemented
13	D₄×SD₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#3266	C₂	1	2	yes	maximal, complemented
15	C₂₉×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#3178	C₂	1	2	yes	maximal, complemented
17	C₂₉×#3123	C₂	1	2	yes	maximal, complemented
18	C₂₉×#3121	C₂	1	2	yes	maximal, complemented
19	C₂₉×#3107	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₉×#3103	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₉×#2969	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₉×#2949	C₂	1	2	yes	maximal, complemented
23	C₄×C₂₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₉×#137	C₂²	1	1	yes	characteristic
25	C₂²×SD₁₆×C₂₉	C₂²	1	2	yes	—
26	C₂₉×#559	C₂²	1	1	yes	characteristic
27	C₂₉×#557	—	2	1	no	—
28	C₂₉×#557	C₂²	1	1	yes	characteristic, complemented
29	C₂₉×#557	C₂²	1	1	yes	characteristic, complemented
30	C₂₉×#556	—	2	1	no	—
31	C₂₉×#556	C₂²	1	1	yes	characteristic
32	C₂₉×#556	C₂²	1	1	yes	characteristic
33	C₂₉×#555	C₂²	1	2	yes	—
34	C₂₉×#552	—	2	2	no	—
35	C₂₉×#552	C₂²	1	2	yes	complemented
36	C₂₉×#551	—	2	2	no	—
37	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₂₉	C₂²	1	2	yes	complemented
40	C₂₉×#548	—	2	1	no	—
41	C₂₉×#546	—	2	1	no	—
42	C₂₉×#546	C₂²	1	2	yes	—
43	D₄²×C₂₉	C₂²	1	1	yes	characteristic
44	C₂₉×#542	C₂²	1	2	yes	—
45	C₂₉×#541	—	2	2	no	—
46	C₂₉×#541	C₂²	1	2	yes	complemented
47	C₂₉×#538	—	2	2	no	—
48	C₂₉×#533	—	2	1	no	—
49	C₂₉×#533	C₂²	1	1	yes	characteristic, complemented
50	C₂₉×#532	C₂²	1	1	yes	characteristic
51	C₂₉×#529	—	2	1	no	—
52	C₂₉×#529	—	2	1	no	—
53	C₂₉×#529	C₂²	1	1	yes	characteristic
54	C₂×C₂₉×#124	—	2	1	no	—
55	C₂₉×#519	C₂²	1	2	yes	complemented
56	C₂₉×#518	C₂²	1	2	yes	—
57	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
58	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
59	C₂₉×#501	C₂²	1	2	yes	complemented
60	C₂₉×#500	C₂²	1	1	yes	characteristic, complemented
61	C₂₉×#497	C₂²	1	2	yes	complemented
62	C₂₉×#492	C₂²	1	1	yes	characteristic
63	C₂₉×#488	C₂²	1	2	yes	complemented
64	C₂₉×#487	C₂²	1	1	yes	characteristic, complemented
65	C₂₉×#487	C₂²	1	2	yes	complemented
66	C₂₉×#486	C₂²	1	1	yes	characteristic
67	C₂₉×#485	C₂²	1	2	yes	complemented
68	C₂₉×#485	C₂²	1	2	yes	complemented
69	C₂₉×#485	C₂²	1	2	yes	complemented
70	C₂₉×#485	C₂²	1	2	yes	complemented
71	C₂₉×#482	C₂²	1	2	yes	—
72	C₂₉×#481	C₂²	1	2	yes	complemented
73	C₂₉×#478	C₂²	1	2	yes	—
74	C₂₉×#478	C₂²	1	2	yes	complemented
75	C₂₉×#477	C₂²	1	2	yes	complemented
76	C₂₉×#475	C₂²	1	1	yes	characteristic, complemented
77	C₂₉×#475	C₂²	1	1	yes	characteristic, complemented
78	C₂₉×#475	C₂²	1	1	yes	characteristic, complemented
79	C₂₉×#475	C₂²	1	2	yes	complemented
80	C₂₉×#474	C₂²	1	1	yes	characteristic
81	C₂₉×#470	C₂²	1	2	yes	complemented
82	C₂₉×#468	C₂²	1	2	yes	—
83	C₂₉×#468	C₂²	1	2	yes	complemented
84	C₂₉×#468	C₂²	1	2	yes	complemented
85	C₂₉×#467	C₂²	1	2	yes	complemented
86	C₂₉×#465	C₂²	1	2	yes	—
87	C₂₉×#464	C₂²	1	2	yes	complemented
88	C₂₉×#464	C₂²	1	2	yes	complemented
89	C₂₉×#462	C₂²	1	1	yes	characteristic, complemented
90	C₂₉×#461	C₂²	1	2	yes	—
91	C₂₉×#461	C₂²	1	1	yes	characteristic
92	C₂₉×#461	C₂²	1	2	yes	complemented
93	C₂₉×#460	C₂²	1	1	yes	characteristic
94	C₂₉×#460	C₂²	1	1	yes	characteristic
95	C₂₉×#452	C₂²	1	2	yes	—
96	C₂₉×#451	C₂²	1	2	yes	complemented
97	C₂₉×#450	C₂²	1	2	yes	—
98	C₂₉×#450	C₂²	1	2	yes	—
99	C₂₉×#448	C₂²	1	2	yes	—
100	C₂₉×#448	C₂²	1	2	yes	complemented
101	C₂₉×#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
103	C₂₉×#441	C₂²	1	1	yes	characteristic, complemented
104	C₂₉×#441	C₂²	1	1	yes	characteristic, complemented
105	C₂₉×#440	C₂²	1	1	yes	characteristic
106	C₂₉×#440	C₂²	1	1	yes	characteristic
107	C₂₉×#440	C₂²	1	2	yes	—
108	C₂₉×#440	C₂²	1	2	yes	complemented
109	C₂₉×#440	C₂²	1	2	yes	complemented
110	C₂₉×#440	C₂²	1	2	yes	complemented
111	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
112	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
113	C₄×Q₁₆×C₂₉	C₂²	1	2	yes	complemented
114	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
115	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	—
117	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	—
118	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	complemented
119	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	complemented
121	C₂₉×#436	C₂²	1	1	yes	characteristic
122	C₂₉×#436	C₂²	1	2	yes	complemented
123	C₂₉×#435	C₂²	1	2	yes	complemented
124	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
125	C₂₉×#433	C₂²	1	2	yes	complemented
126	C₂₉×#431	C₂²	1	1	yes	characteristic, complemented
127	C₂₉×#428	C₂²	1	1	yes	characteristic, complemented
128	C₂₉×#427	C₂²	1	2	yes	complemented
129	C₂₉×#419	C₂²	1	1	yes	characteristic, complemented
130	C₂₉×#419	C₂²	1	2	yes	complemented
131	C₂₉×#418	C₂²	1	2	yes	—
132	C₂₉×#417	C₂²	1	1	yes	characteristic
133	C₂₉×#405	C₂²	1	2	yes	complemented
134	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₂₉	—	2	1	no	—
136	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₂₉	—	2	1	no	—
138	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
139	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₂₉	—	2	1	no	—
141	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
142	C₂₉×#137	—	2	4	no	—
143	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
144	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₂₉	—	2	8	no	—
147	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
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×SD₁₆×C₂₉	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
155	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
156	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
158	C₂₉×C₄⋊Q₈	—	2	1	no	—
159	C₂₉×C₄⋊Q₈	—	2	1	no	—
160	C₂₉×C₄⋊Q₈	—	2	2	no	—
161	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₂₉×#127	C₂³	1	1	yes	characteristic
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	2	no	—
172	C₂₉×#126	—	2	2	no	—
173	C₂₉×#126	D₄	1	2	yes	—
174	C₂₉×#125	—	2	1	no	—
175	C₂₉×#125	—	2	2	no	—
176	C₂₉×#125	—	2	2	no	—
177	C₂₉×#125	—	2	2	no	—
178	C₂₉×#125	—	2	2	no	—
179	C₂₉×#125	—	2	2	no	—
180	C₂₉×#125	—	2	1	no	—
181	C₂₉×#125	D₄	1	1	yes	characteristic
182	C₂₉×#125	C₂³	1	2	yes	—
183	C₂₉×#124	—	2	1	no	—
184	C₂₉×#124	—	2	1	no	—
185	C₂₉×#124	—	2	1	no	—
186	C₂₉×#124	—	2	2	no	—
187	C₂₉×#124	—	2	2	no	—
188	C₂₉×#124	—	2	2	no	—
189	C₂₉×#124	—	2	1	no	—
190	C₂₉×#124	D₄	1	1	yes	characteristic
191	C₂₉×#124	C₂³	1	2	yes	—
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	D₄	1	2	yes	—
197	C₂₉×C₂²⋊Q₈	—	2	1	no	—
198	C₂₉×C₂²⋊Q₈	—	2	1	no	—
199	C₂₉×C₂²⋊Q₈	—	2	2	no	—
200	C₂₉×C₂²⋊Q₈	—	2	2	no	—
201	C₂₉×C₂²⋊Q₈	—	2	2	no	—
202	C₂₉×C₂²⋊Q₈	—	2	2	no	—
203	C₂₉×C₂²⋊Q₈	—	2	2	no	—
204	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
205	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₂₉×#121	—	2	2	no	—
210	C₂₉×#121	—	2	1	no	—
211	C₂₉×#121	—	2	1	no	—
212	C₂₉×#121	—	2	2	no	—
213	C₂₉×#121	D₄	1	1	yes	characteristic
214	C₂₉×#121	C₂³	1	2	yes	—
215	C₂₉×#121	C₂³	1	2	yes	—
216	C₂₉×#120	—	2	2	no	—
217	C₂₉×#120	—	2	2	no	—
218	C₄×Q₈×C₂₉	—	2	1	no	—
219	C₄×Q₈×C₂₉	—	2	2	no	—
220	C₄×Q₈×C₂₉	—	2	2	no	—
221	C₄×Q₈×C₂₉	—	2	1	no	—
222	C₄×Q₈×C₂₉	—	2	1	no	—
223	C₄×Q₈×C₂₉	—	2	1	no	—
224	C₄×Q₈×C₂₉	—	2	1	no	—
225	C₄×Q₈×C₂₉	—	2	1	no	—
226	C₄×Q₈×C₂₉	—	2	1	no	—
227	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
228	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
231	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
234	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
235	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₂₉	—	2	1	no	—
238	C₄×D₄×C₂₉	—	2	2	no	—
239	C₄×D₄×C₂₉	—	2	1	no	—
240	C₄×D₄×C₂₉	—	2	1	no	—
241	C₄×D₄×C₂₉	—	2	2	no	—
242	C₄×D₄×C₂₉	—	2	2	no	—
243	C₄×D₄×C₂₉	—	2	1	no	—
244	C₄×D₄×C₂₉	—	2	1	no	—
245	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₂₉	C₂³	1	2	yes	—
248	C₄×D₄×C₂₉	C₂³	1	2	yes	—
249	C₄×D₄×C₂₉	C₂³	1	2	yes	—
250	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₂₉	C₂³	1	2	yes	—
252	C₂₉×#117	—	2	1	no	—
253	C₂₉×#117	—	2	2	no	—
254	C₂₉×#117	—	2	2	no	—
255	C₂₉×#117	—	2	2	no	—
256	C₂₉×#117	—	2	2	no	—
257	C₂₉×#117	—	2	1	no	—
258	C₂₉×#117	C₂³	1	2	yes	—
259	C₂₉×#117	C₂³	1	2	yes	—
260	C₂₉×#117	C₂³	1	1	yes	characteristic
261	C₂₉×#117	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
263	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
266	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
267	C₂×C₄²×C₂₉	—	2	1	no	—
268	C₂×C₄²×C₂₉	—	2	1	no	—
269	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
270	C₂₉×#107	C₂³	1	1	yes	characteristic
271	C₂₉×#107	C₂³	1	2	yes	—
272	C₂₉×#107	C₂³	1	1	yes	characteristic
273	C₂₉×#107	C₂³	1	2	yes	—
274	C₂₉×#107	C₂³	1	2	yes	—
275	C₂₉×#106	C₂³	1	2	yes	—
276	C₂₉×#106	C₂³	1	2	yes	—
277	C₂₉×#106	C₂³	1	1	yes	characteristic
278	C₂₉×#106	C₂³	1	1	yes	characteristic
279	C₂₉×#106	C₂³	1	2	yes	—
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	2	yes	—
284	C₂₉×#103	C₂³	1	2	yes	—
285	C₂₉×#103	C₂³	1	2	yes	—
286	C₂₉×#103	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	1	yes	characteristic
292	C₂₉×#103	C₂³	1	1	yes	characteristic
293	C₂₉×#103	C₂³	1	1	yes	characteristic
294	C₂₉×#103	C₂³	1	2	yes	—
295	C₂₉×#103	C₂³	1	2	yes	—
296	C₂₉×#103	C₂³	1	2	yes	—
297	C₂₉×#102	C₂³	1	1	yes	characteristic
298	C₂₉×#102	C₂³	1	1	yes	characteristic
299	C₂₉×#102	C₂³	1	2	yes	—
300	C₂₉×#102	C₂³	1	2	yes	—
301	C₂₉×#102	C₂³	1	2	yes	—
302	C₂₉×#102	C₂³	1	2	yes	—
303	C₂₉×#102	C₂³	1	2	yes	—
304	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂₉×#97	C₂³	1	1	yes	characteristic
308	C₂₉×#97	C₂³	1	2	yes	—
309	C₂₉×#97	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₂₉	C₂³	1	2	yes	—
311	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₂₉	C₂³	1	2	yes	—
314	C₂⁴×C₂₉	—	2	2	no	—
315	#41×C₂₉	—	2	2	no	—
316	#41×C₂₉	—	4	1	no	—
317	#41×C₂₉	—	8	2	no	—
318	C₂×Q₈×C₂₉	—	2	1	no	—
319	C₂×Q₈×C₂₉	—	2	2	no	—
320	C₂×Q₈×C₂₉	—	2	1	no	—
321	C₂×Q₈×C₂₉	—	2	1	no	—
322	C₂×Q₈×C₂₉	—	2	2	no	—
323	C₂×Q₈×C₂₉	—	2	4	no	—
324	C₂×Q₈×C₂₉	—	2	2	no	—
325	C₂×Q₈×C₂₉	—	4	2	no	—
326	C₂×Q₈×C₂₉	—	4	1	no	—
327	C₂×Q₈×C₂₉	—	8	2	no	—
328	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₂₉	—	2	4	no	—
334	C₂×D₄×C₂₉	—	2	1	no	—
335	C₂×D₄×C₂₉	—	2	2	no	—
336	C₂×D₄×C₂₉	—	2	2	no	—
337	C₂×D₄×C₂₉	—	2	2	no	—
338	C₂×D₄×C₂₉	—	2	1	no	—
339	C₂×D₄×C₂₉	—	2	1	no	—
340	C₂×D₄×C₂₉	—	4	2	no	—
341	C₂×D₄×C₂₉	—	8	2	no	—
342	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
343	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
345	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
346	C₂²×C₄×C₂₉	—	2	1	no	—
347	C₂²×C₄×C₂₉	—	2	1	no	—
348	C₂²×C₄×C₂₉	—	2	2	no	—
349	C₂²×C₄×C₂₉	—	2	1	no	—
350	C₂²×C₄×C₂₉	—	2	1	no	—
351	C₂²×C₄×C₂₉	—	2	1	no	—
352	C₂²×C₄×C₂₉	—	2	2	no	—
353	C₂²×C₄×C₂₉	—	2	2	no	—
354	C₂²×C₄×C₂₉	—	2	2	no	—
355	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
359	Q₁₆×C₂₉	—	2	2	no	—
360	Q₁₆×C₂₉	—	2	2	no	—
361	Q₁₆×C₂₉	—	4	2	no	—
362	SD₁₆×C₂₉	—	2	4	no	—
363	SD₁₆×C₂₉	—	2	4	no	—
364	SD₁₆×C₂₉	—	2	2	no	—
365	SD₁₆×C₂₉	—	2	4	no	—
366	SD₁₆×C₂₉	—	4	2	no	—
367	SD₁₆×C₂₉	—	4	2	no	—
368	SD₁₆×C₂₉	#41	1	4	yes	complemented
369	M₁₆×C₂₉	—	2	2	no	—
370	M₁₆×C₂₉	—	4	1	no	—
371	M₁₆×C₂₉	—	4	2	no	—
372	C₂×C₈×C₂₉	—	2	4	no	—
373	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
374	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
378	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
379	C₄⋊C₄×C₂₉	—	2	1	no	—
380	C₄⋊C₄×C₂₉	—	2	1	no	—
381	C₄⋊C₄×C₂₉	—	2	1	no	—
382	C₄⋊C₄×C₂₉	—	2	1	no	—
383	C₄⋊C₄×C₂₉	—	2	1	no	—
384	C₄⋊C₄×C₂₉	—	2	1	no	—
385	C₄⋊C₄×C₂₉	—	2	1	no	—
386	C₄⋊C₄×C₂₉	—	2	2	no	—
387	C₄⋊C₄×C₂₉	—	2	2	no	—
388	C₄⋊C₄×C₂₉	—	2	2	no	—
389	C₄⋊C₄×C₂₉	—	2	2	no	—
390	C₄⋊C₄×C₂₉	—	2	1	no	—
391	C₄⋊C₄×C₂₉	—	2	2	no	—
392	C₄⋊C₄×C₂₉	—	2	1	no	—
393	C₄⋊C₄×C₂₉	—	2	2	no	—
394	C₄⋊C₄×C₂₉	—	2	1	no	—
395	C₄⋊C₄×C₂₉	—	2	1	no	—
396	C₄⋊C₄×C₂₉	—	2	2	no	—
397	C₄⋊C₄×C₂₉	—	2	2	no	—
398	C₄⋊C₄×C₂₉	—	2	2	no	—
399	C₄⋊C₄×C₂₉	—	2	2	no	—
400	C₄⋊C₄×C₂₉	—	2	2	no	—
401	C₄⋊C₄×C₂₉	—	2	2	no	—
402	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
412	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
414	C₂²⋊C₄×C₂₉	—	2	2	no	—
415	C₂²⋊C₄×C₂₉	—	2	2	no	—
416	C₂²⋊C₄×C₂₉	—	2	2	no	—
417	C₂²⋊C₄×C₂₉	—	2	2	no	—
418	C₂²⋊C₄×C₂₉	—	2	1	no	—
419	C₂²⋊C₄×C₂₉	—	2	2	no	—
420	C₂²⋊C₄×C₂₉	—	2	2	no	—
421	C₂²⋊C₄×C₂₉	—	2	1	no	—
422	C₂²⋊C₄×C₂₉	—	2	2	no	—
423	C₂²⋊C₄×C₂₉	—	2	2	no	—
424	C₂²⋊C₄×C₂₉	—	2	2	no	—
425	C₂²⋊C₄×C₂₉	—	2	2	no	—
426	C₂²⋊C₄×C₂₉	—	2	2	no	—
427	C₂²⋊C₄×C₂₉	—	2	1	no	—
428	C₂²⋊C₄×C₂₉	—	2	2	no	—
429	C₂²⋊C₄×C₂₉	—	2	2	no	—
430	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
435	C₄²×C₂₉	—	2	1	no	—
436	C₄²×C₂₉	—	2	1	no	—
437	C₄²×C₂₉	—	2	1	no	—
438	C₄²×C₂₉	—	2	1	no	—
439	C₄²×C₂₉	—	2	1	no	—
440	C₄²×C₂₉	—	2	1	no	—
441	C₄²×C₂₉	—	2	1	no	—
442	C₄²×C₂₉	—	2	2	no	—
443	C₄²×C₂₉	—	2	2	no	—
444	C₄²×C₂₉	—	2	2	no	—
445	C₄²×C₂₉	—	2	2	no	—
446	C₄²×C₂₉	—	2	2	no	—
447	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
450	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
451	C₄²×C₂₉	C₂⁴	1	2	yes	—
452	#61540	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
453	C₂³×C₂₉	—	2	1	no	—
454	C₂³×C₂₉	—	2	2	no	—
455	C₂³×C₂₉	—	4	4	no	—
456	C₂³×C₂₉	—	8	2	no	—
457	C₂³×C₂₉	—	8	2	no	—
458	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
459	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
460	Q₈×C₂₉	—	2	2	no	—
461	Q₈×C₂₉	—	2	1	no	—
462	Q₈×C₂₉	—	2	2	no	—
463	Q₈×C₂₉	—	2	1	no	—
464	Q₈×C₂₉	—	2	1	no	—
465	Q₈×C₂₉	—	2	1	no	—
466	Q₈×C₂₉	—	2	2	no	—
467	Q₈×C₂₉	—	2	1	no	—
468	Q₈×C₂₉	—	4	2	no	—
469	Q₈×C₂₉	—	4	4	no	—
470	Q₈×C₂₉	—	4	2	no	—
471	Q₈×C₂₉	—	4	2	no	—
472	Q₈×C₂₉	—	8	2	no	—
473	Q₈×C₂₉	C₂×#41	1	2	yes	—
474	D₄×C₂₉	—	2	2	no	—
475	D₄×C₂₉	—	2	2	no	—
476	D₄×C₂₉	—	2	1	no	—
477	D₄×C₂₉	—	2	2	no	—
478	D₄×C₂₉	—	4	2	no	—
479	D₄×C₂₉	—	4	4	no	—
480	D₄×C₂₉	—	4	2	no	—
481	D₄×C₂₉	—	4	2	no	—
482	D₄×C₂₉	—	8	1	no	—
483	D₄×C₂₉	—	8	2	no	—
484	D₄×C₂₉	—	8	2	no	—
485	D₄×C₂₉	C₂×#41	1	2	yes	—
486	C₂×C₄×C₂₉	—	2	1	no	—
487	C₂×C₄×C₂₉	—	2	2	no	—
488	C₂×C₄×C₂₉	—	2	2	no	—
489	C₂×C₄×C₂₉	—	2	1	no	—
490	C₂×C₄×C₂₉	—	2	2	no	—
491	C₂×C₄×C₂₉	—	2	1	no	—
492	C₂×C₄×C₂₉	—	2	1	no	—
493	C₂×C₄×C₂₉	—	2	1	no	—
494	C₂×C₄×C₂₉	—	2	2	no	—
495	C₂×C₄×C₂₉	—	2	1	no	—
496	C₂×C₄×C₂₉	—	2	1	no	—
497	C₂×C₄×C₂₉	—	2	1	no	—
498	C₂×C₄×C₂₉	—	2	1	no	—
499	C₂×C₄×C₂₉	—	2	2	no	—
500	C₂×C₄×C₂₉	—	2	2	no	—
501	C₂×C₄×C₂₉	—	4	1	no	—
502	C₂×C₄×C₂₉	—	4	2	no	—
503	C₂×C₄×C₂₉	—	4	4	no	—
504	C₂×C₄×C₂₉	—	4	2	no	—
505	C₂×C₄×C₂₉	—	4	2	no	—
506	C₂×C₄×C₂₉	—	4	2	no	—
507	C₂×C₄×C₂₉	—	8	1	no	—
508	C₂×C₄×C₂₉	—	8	2	no	—
509	C₂×C₄×C₂₉	—	8	2	no	—
510	C₂×C₄×C₂₉	—	8	2	no	—
511	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
520	C₈×C₂₉	—	2	2	no	—
521	C₈×C₂₉	—	2	1	no	—
522	C₈×C₂₉	—	2	1	no	—
523	C₈×C₂₉	—	2	1	no	—
524	C₈×C₂₉	—	2	2	no	—
525	C₈×C₂₉	C₂×#41	1	2	yes	—
526	#3523	C₂×C₂₉	1	1	yes	characteristic, complemented
527	#3514	C₂×C₂₉	1	1	yes	characteristic
528	#3400	C₂×C₂₉	1	1	yes	characteristic, complemented
529	#3386	C₂×C₂₉	1	1	yes	characteristic, complemented
530	#3365	C₂×C₂₉	1	1	yes	characteristic, complemented
531	#3359	C₂×C₂₉	1	1	yes	characteristic, complemented
532	#3348	C₂×C₂₉	1	2	yes	complemented
533	#3342	C₂×C₂₉	1	1	yes	characteristic, complemented
534	#3329	C₂×C₂₉	1	2	yes	complemented
535	#3328	C₂×C₂₉	1	1	yes	characteristic, complemented
536	#3324	C₂×C₂₉	1	1	yes	characteristic, complemented
537	#3323	C₂×C₂₉	1	2	yes	complemented
538	D₄×SD₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
539	#3266	C₂×C₂₉	1	2	yes	complemented
540	#3182	C₂×C₂₉	1	1	yes	characteristic, complemented
541	#3178	C₂×C₂₉	1	2	yes	complemented
542	#3123	C₂×C₂₉	1	2	yes	complemented
543	#3121	C₂×C₂₉	1	2	yes	complemented
544	#3107	C₂×C₂₉	1	1	yes	characteristic, complemented
545	#3103	C₂×C₂₉	1	1	yes	characteristic, complemented
546	#2969	C₂×C₂₉	1	1	yes	characteristic, complemented
547	#2949	C₂×C₂₉	1	2	yes	complemented
548	C₄×#137	C₂×C₂₉	1	1	yes	characteristic, complemented
549	C₂²×C₂₉	—	2	1	no	—
550	C₂²×C₂₉	—	2	2	no	—
551	C₂²×C₂₉	—	2	1	no	—
552	C₂²×C₂₉	—	2	2	no	—
553	C₂²×C₂₉	—	2	2	no	—
554	C₂²×C₂₉	—	2	1	no	—
555	C₂²×C₂₉	—	2	2	no	—
556	C₂²×C₂₉	—	4	1	no	—
557	C₂²×C₂₉	—	4	1	no	—
558	C₂²×C₂₉	—	4	2	no	—
559	C₂²×C₂₉	—	4	2	no	—
560	C₂²×C₂₉	—	4	2	no	—
561	C₂²×C₂₉	—	16	4	no	—
562	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
563	C₄×C₂₉	—	2	1	no	—
564	C₄×C₂₉	—	2	1	no	—
565	C₄×C₂₉	—	2	2	no	—
566	C₄×C₂₉	—	2	1	no	—
567	C₄×C₂₉	—	2	2	no	—
568	C₄×C₂₉	—	2	2	no	—
569	C₄×C₂₉	—	2	1	no	—
570	C₄×C₂₉	—	2	2	no	—
571	C₄×C₂₉	—	4	1	no	—
572	C₄×C₂₉	—	4	1	no	—
573	C₄×C₂₉	—	4	1	no	—
574	C₄×C₂₉	—	4	1	no	—
575	C₄×C₂₉	—	4	2	no	—
576	C₄×C₂₉	—	4	1	no	—
577	C₄×C₂₉	—	4	1	no	—
578	C₄×C₂₉	—	4	2	no	—
579	C₄×C₂₉	—	4	2	no	—
580	C₄×C₂₉	#577	1	2	yes	—
581	C₄×C₂₉	C₂²×#41	1	1	yes	characteristic
582	C₄×C₂₉	#585	1	1	yes	characteristic
583	C₂×#137	C₂²×C₂₉	1	1	yes	characteristic
584	C₂²×SD₁₆	C₂²×C₂₉	1	2	yes	—
585	#559	C₂²×C₂₉	1	1	yes	characteristic
586	#557	—	2	1	no	—
587	#557	C₂²×C₂₉	1	1	yes	characteristic, complemented
588	#557	C₂²×C₂₉	1	1	yes	characteristic, complemented
589	#556	—	2	1	no	—
590	#556	C₂²×C₂₉	1	1	yes	characteristic
591	#556	C₂²×C₂₉	1	1	yes	characteristic
592	#555	C₂²×C₂₉	1	2	yes	—
593	#552	—	2	2	no	—
594	#552	C₂²×C₂₉	1	2	yes	complemented
595	#551	—	2	2	no	—
596	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
597	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
598	D₄×Q₈	C₂²×C₂₉	1	2	yes	complemented
599	#548	—	2	1	no	—
600	#546	—	2	1	no	—
601	#546	C₂²×C₂₉	1	2	yes	—
602	D₄²	C₂²×C₂₉	1	1	yes	characteristic
603	#542	C₂²×C₂₉	1	2	yes	—
604	#541	—	2	2	no	—
605	#541	C₂²×C₂₉	1	2	yes	complemented
606	#538	—	2	2	no	—
607	#533	—	2	1	no	—
608	#533	C₂²×C₂₉	1	1	yes	characteristic, complemented
609	#532	C₂²×C₂₉	1	1	yes	characteristic
610	#529	—	2	1	no	—
611	#529	—	2	1	no	—
612	#529	C₂²×C₂₉	1	1	yes	characteristic
613	C₂×#124	—	2	1	no	—
614	#519	C₂²×C₂₉	1	2	yes	complemented
615	#518	C₂²×C₂₉	1	2	yes	—
616	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
617	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
618	#501	C₂²×C₂₉	1	2	yes	complemented
619	#500	C₂²×C₂₉	1	1	yes	characteristic, complemented
620	#497	C₂²×C₂₉	1	2	yes	complemented
621	#492	C₂²×C₂₉	1	1	yes	characteristic
622	#488	C₂²×C₂₉	1	2	yes	complemented
623	#487	C₂²×C₂₉	1	1	yes	characteristic, complemented
624	#487	C₂²×C₂₉	1	2	yes	complemented
625	#486	C₂²×C₂₉	1	1	yes	characteristic
626	#485	C₂²×C₂₉	1	2	yes	complemented
627	#485	C₂²×C₂₉	1	2	yes	complemented
628	#485	C₂²×C₂₉	1	2	yes	complemented
629	#485	C₂²×C₂₉	1	2	yes	complemented
630	#482	C₂²×C₂₉	1	2	yes	—
631	#481	C₂²×C₂₉	1	2	yes	complemented
632	#478	C₂²×C₂₉	1	2	yes	—
633	#478	C₂²×C₂₉	1	2	yes	complemented
634	#477	C₂²×C₂₉	1	2	yes	complemented
635	#475	C₂²×C₂₉	1	1	yes	characteristic, complemented
636	#475	C₂²×C₂₉	1	1	yes	characteristic, complemented
637	#475	C₂²×C₂₉	1	1	yes	characteristic, complemented
638	#475	C₂²×C₂₉	1	2	yes	complemented
639	#474	C₂²×C₂₉	1	1	yes	characteristic
640	#470	C₂²×C₂₉	1	2	yes	complemented
641	#468	C₂²×C₂₉	1	2	yes	—
642	#468	C₂²×C₂₉	1	2	yes	complemented
643	#468	C₂²×C₂₉	1	2	yes	complemented
644	#467	C₂²×C₂₉	1	2	yes	complemented
645	#465	C₂²×C₂₉	1	2	yes	—
646	#464	C₂²×C₂₉	1	2	yes	complemented
647	#464	C₂²×C₂₉	1	2	yes	complemented
648	#462	C₂²×C₂₉	1	1	yes	characteristic, complemented
649	#461	C₂²×C₂₉	1	1	yes	characteristic
650	#461	C₂²×C₂₉	1	2	yes	—
651	#461	C₂²×C₂₉	1	2	yes	complemented
652	#460	C₂²×C₂₉	1	1	yes	characteristic
653	#460	C₂²×C₂₉	1	1	yes	characteristic
654	#452	C₂²×C₂₉	1	2	yes	—
655	#451	C₂²×C₂₉	1	2	yes	complemented
656	#450	C₂²×C₂₉	1	2	yes	—
657	#450	C₂²×C₂₉	1	2	yes	—
658	#448	C₂²×C₂₉	1	2	yes	—
659	#448	C₂²×C₂₉	1	2	yes	complemented
660	#446	C₂²×C₂₉	1	1	yes	characteristic, complemented
661	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
662	#441	C₂²×C₂₉	1	1	yes	characteristic, complemented
663	#441	C₂²×C₂₉	1	1	yes	characteristic, complemented
664	#440	C₂²×C₂₉	1	1	yes	characteristic
665	#440	C₂²×C₂₉	1	2	yes	—
666	#440	C₂²×C₂₉	1	1	yes	characteristic
667	#440	C₂²×C₂₉	1	2	yes	complemented
668	#440	C₂²×C₂₉	1	2	yes	complemented
669	#440	C₂²×C₂₉	1	2	yes	complemented
670	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
671	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
672	C₄×Q₁₆	C₂²×C₂₉	1	2	yes	complemented
673	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
674	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	—
675	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	—
676	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
677	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
678	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
679	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
680	#436	C₂²×C₂₉	1	1	yes	characteristic
681	#436	C₂²×C₂₉	1	2	yes	complemented
682	#435	C₂²×C₂₉	1	2	yes	complemented
683	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
684	#433	C₂²×C₂₉	1	2	yes	complemented
685	#431	C₂²×C₂₉	1	1	yes	characteristic, complemented
686	#428	C₂²×C₂₉	1	1	yes	characteristic, complemented
687	#427	C₂²×C₂₉	1	2	yes	complemented
688	#419	C₂²×C₂₉	1	2	yes	complemented
689	#419	C₂²×C₂₉	1	1	yes	characteristic, complemented
690	#418	C₂²×C₂₉	1	2	yes	—
691	#417	C₂²×C₂₉	1	1	yes	characteristic
692	#405	C₂²×C₂₉	1	2	yes	complemented
693	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
694	C₂×C₂₉	—	4	1	no	—
695	C₂×C₂₉	—	4	2	no	—
696	C₂×C₂₉	—	4	2	no	—
697	C₂×C₂₉	—	8	2	no	—
698	C₂×C₂₉	D₄×#41	1	1	yes	characteristic
699	C₂×C₂₉	C₂×#577	1	1	yes	characteristic
700	C₂×C₂₉	#3586	1	1	yes	characteristic
701	C₂×#41	—	2	1	no	—
702	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
703	C₂²×Q₈	—	2	1	no	—
704	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
705	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
706	C₂²×D₄	—	2	1	no	—
707	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
708	#137	—	2	4	no	—
709	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
710	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
711	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
712	C₂×SD₁₆	—	2	8	no	—
713	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
714	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
715	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
716	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
717	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
719	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
720	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
721	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
722	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
723	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
724	C₄⋊Q₈	—	2	1	no	—
725	C₄⋊Q₈	—	2	1	no	—
726	C₄⋊Q₈	—	2	2	no	—
727	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
729	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
730	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
731	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
732	#127	C₂³×C₂₉	1	1	yes	characteristic
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	D₄×C₂₉	1	2	yes	—
740	#125	—	2	1	no	—
741	#125	—	2	2	no	—
742	#125	—	2	2	no	—
743	#125	—	2	2	no	—
744	#125	—	2	2	no	—
745	#125	—	2	2	no	—
746	#125	—	2	1	no	—
747	#125	D₄×C₂₉	1	1	yes	characteristic
748	#125	C₂³×C₂₉	1	2	yes	—
749	#124	—	2	1	no	—
750	#124	—	2	1	no	—
751	#124	—	2	1	no	—
752	#124	—	2	2	no	—
753	#124	—	2	2	no	—
754	#124	—	2	2	no	—
755	#124	—	2	1	no	—
756	#124	D₄×C₂₉	1	1	yes	characteristic
757	#124	C₂³×C₂₉	1	2	yes	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	D₄×C₂₉	1	2	yes	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
771	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
772	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
773	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
774	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
775	#121	—	2	2	no	—
776	#121	—	2	1	no	—
777	#121	—	2	1	no	—
778	#121	—	2	2	no	—
779	#121	D₄×C₂₉	1	1	yes	characteristic
780	#121	C₂³×C₂₉	1	2	yes	—
781	#121	C₂³×C₂₉	1	2	yes	—
782	#120	—	2	2	no	—
783	#120	—	2	2	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	—	2	2	no	—
786	C₄×Q₈	—	2	2	no	—
787	C₄×Q₈	—	2	1	no	—
788	C₄×Q₈	—	2	1	no	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
794	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
795	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
799	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
800	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
801	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
802	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
812	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₂₉	1	2	yes	—
814	C₄×D₄	C₂³×C₂₉	1	2	yes	—
815	C₄×D₄	C₂³×C₂₉	1	2	yes	—
816	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
817	C₄×D₄	C₂³×C₂₉	1	2	yes	—
818	#117	—	2	1	no	—
819	#117	—	2	2	no	—
820	#117	—	2	2	no	—
821	#117	—	2	2	no	—
822	#117	—	2	2	no	—
823	#117	—	2	1	no	—
824	#117	C₂³×C₂₉	1	1	yes	characteristic
825	#117	C₂³×C₂₉	1	2	yes	—
826	#117	C₂³×C₂₉	1	2	yes	—
827	#117	C₂³×C₂₉	1	2	yes	—
828	C₂×C₄⋊C₄	—	2	1	no	—
829	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
830	C₂×C₂²⋊C₄	—	2	2	no	—
831	C₂×C₂²⋊C₄	—	2	2	no	—
832	C₂×C₂²⋊C₄	—	2	2	no	—
833	C₂×C₄²	—	2	1	no	—
834	C₂×C₄²	—	2	1	no	—
835	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
836	#107	C₂³×C₂₉	1	1	yes	characteristic
837	#107	C₂³×C₂₉	1	2	yes	—
838	#107	C₂³×C₂₉	1	1	yes	characteristic
839	#107	C₂³×C₂₉	1	2	yes	—
840	#107	C₂³×C₂₉	1	2	yes	—
841	#106	C₂³×C₂₉	1	2	yes	—
842	#106	C₂³×C₂₉	1	2	yes	—
843	#106	C₂³×C₂₉	1	1	yes	characteristic
844	#106	C₂³×C₂₉	1	1	yes	characteristic
845	#106	C₂³×C₂₉	1	2	yes	—
846	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
848	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
849	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
850	#103	C₂³×C₂₉	1	1	yes	characteristic
851	#103	C₂³×C₂₉	1	1	yes	characteristic
852	#103	C₂³×C₂₉	1	1	yes	characteristic
853	#103	C₂³×C₂₉	1	2	yes	—
854	#103	C₂³×C₂₉	1	2	yes	—
855	#103	C₂³×C₂₉	1	1	yes	characteristic
856	#103	C₂³×C₂₉	1	1	yes	characteristic
857	#103	C₂³×C₂₉	1	2	yes	—
858	#103	C₂³×C₂₉	1	1	yes	characteristic
859	#103	C₂³×C₂₉	1	2	yes	—
860	#103	C₂³×C₂₉	1	2	yes	—
861	#103	C₂³×C₂₉	1	2	yes	—
862	#103	C₂³×C₂₉	1	2	yes	—
863	#102	C₂³×C₂₉	1	1	yes	characteristic
864	#102	C₂³×C₂₉	1	1	yes	characteristic
865	#102	C₂³×C₂₉	1	2	yes	—
866	#102	C₂³×C₂₉	1	2	yes	—
867	#102	C₂³×C₂₉	1	2	yes	—
868	#102	C₂³×C₂₉	1	2	yes	—
869	#102	C₂³×C₂₉	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
873	#97	C₂³×C₂₉	1	1	yes	characteristic
874	#97	C₂³×C₂₉	1	1	yes	characteristic
875	#97	C₂³×C₂₉	1	2	yes	—
876	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
877	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
878	C₄×C₈	C₂³×C₂₉	1	2	yes	—
879	C₄×C₈	C₂³×C₂₉	1	2	yes	—
880	C₂₉	#61540	1	1	yes	characteristic, direct product factor, Sylow
881	C₂⁴	—	2	2	no	—
882	#41	—	2	2	no	—
883	#41	—	4	1	no	—
884	#41	—	8	2	no	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	—	2	2	no	—
887	C₂×Q₈	—	2	1	no	—
888	C₂×Q₈	—	2	1	no	—
889	C₂×Q₈	—	2	2	no	—
890	C₂×Q₈	—	2	4	no	—
891	C₂×Q₈	—	2	2	no	—
892	C₂×Q₈	—	4	2	no	—
893	C₂×Q₈	—	4	1	no	—
894	C₂×Q₈	—	8	2	no	—
895	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
896	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
897	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
898	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
899	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
900	C₂×D₄	—	2	4	no	—
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	4	2	no	—
908	C₂×D₄	—	8	2	no	—
909	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
910	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
911	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
912	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
923	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
924	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
925	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
926	Q₁₆	—	2	2	no	—
927	Q₁₆	—	2	2	no	—
928	Q₁₆	—	4	2	no	—
929	SD₁₆	—	2	4	no	—
930	SD₁₆	—	2	4	no	—
931	SD₁₆	—	2	2	no	—
932	SD₁₆	—	2	4	no	—
933	SD₁₆	—	4	2	no	—
934	SD₁₆	—	4	2	no	—
935	SD₁₆	#41×C₂₉	1	4	yes	complemented
936	M₁₆	—	2	2	no	—
937	M₁₆	—	4	1	no	—
938	M₁₆	—	4	2	no	—
939	C₂×C₈	—	2	4	no	—
940	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
941	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
942	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
943	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
944	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
945	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
970	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
971	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
972	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
973	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
974	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
977	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
978	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
979	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
998	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
999	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1000	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1001	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	2	no	—
1011	C₄²	—	2	2	no	—
1012	C₄²	—	2	2	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1015	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1016	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1017	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1018	C₄²	C₂⁴×C₂₉	1	2	yes	—
1019	C₂³	—	2	1	no	—
1020	C₂³	—	2	2	no	—
1021	C₂³	—	4	4	no	—
1022	C₂³	—	8	2	no	—
1023	C₂³	—	8	2	no	—
1024	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
1025	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1026	Q₈	—	2	2	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	2	2	no	—
1029	Q₈	—	2	1	no	—
1030	Q₈	—	2	1	no	—
1031	Q₈	—	2	1	no	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	2	1	no	—
1034	Q₈	—	4	2	no	—
1035	Q₈	—	4	4	no	—
1036	Q₈	—	4	2	no	—
1037	Q₈	—	4	2	no	—
1038	Q₈	—	8	2	no	—
1039	Q₈	C₂×#41×C₂₉	1	2	yes	—
1040	D₄	—	2	2	no	—
1041	D₄	—	2	2	no	—
1042	D₄	—	2	1	no	—
1043	D₄	—	2	2	no	—
1044	D₄	—	4	2	no	—
1045	D₄	—	4	4	no	—
1046	D₄	—	4	2	no	—
1047	D₄	—	4	2	no	—
1048	D₄	—	8	1	no	—
1049	D₄	—	8	2	no	—
1050	D₄	—	8	2	no	—
1051	D₄	C₂×#41×C₂₉	1	2	yes	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	4	1	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	4	4	no	—
1070	C₂×C₄	—	4	2	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	8	2	no	—
1074	C₂×C₄	—	8	2	no	—
1075	C₂×C₄	—	8	1	no	—
1076	C₂×C₄	—	8	2	no	—
1077	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1078	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1079	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1080	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1081	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1082	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1083	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1084	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1085	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1086	C₈	—	2	2	no	—
1087	C₈	—	2	1	no	—
1088	C₈	—	2	1	no	—
1089	C₈	—	2	1	no	—
1090	C₈	—	2	2	no	—
1091	C₈	C₂×#41×C₂₉	1	2	yes	—
1092	C₂²	—	2	1	no	—
1093	C₂²	—	2	2	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	2	no	—
1097	C₂²	—	2	1	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	—	4	2	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	—	4	2	no	—
1104	C₂²	—	16	4	no	—
1105	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
1106	C₄	—	2	1	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	1	no	—
1110	C₄	—	2	2	no	—
1111	C₄	—	2	1	no	—
1112	C₄	—	2	1	no	—
1113	C₄	—	2	2	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	2	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	2	no	—
1120	C₄	—	4	1	no	—
1121	C₄	—	4	1	no	—
1122	C₄	—	4	1	no	—
1123	C₄	C₂₉×#577	1	2	yes	—
1124	C₄	C₂²×#41×C₂₉	1	1	yes	characteristic
1125	C₄	C₂₉×#585	1	1	yes	characteristic
1126	C₂	—	4	2	no	—
1127	C₂	—	4	1	no	—
1128	C₂	—	4	2	no	—
1129	C₂	—	8	2	no	—
1130	C₂	D₄×#41×C₂₉	1	1	yes	characteristic
1131	C₂	C₂×C₂₉×#577	1	1	yes	characteristic
1132	C₂	C₂₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
prime radical	C₂₉×#3514	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×#3523	C₂	semidirect
3. C₂₉×#3400	C₂	semidirect
4. C₂₉×#3386	C₂	semidirect
5. C₂₉×#3365	C₂	semidirect
6. C₂₉×#3359	C₂	semidirect
7. C₂₉×#3348	C₂	semidirect
8. C₂₉×#3342	C₂	semidirect
9. C₂₉×#3329	C₂	semidirect
10. C₂₉×#3328	C₂	semidirect
11. C₂₉×#3324	C₂	semidirect
12. C₂₉×#3323	C₂	semidirect
13. D₄×SD₁₆×C₂₉	C₂	semidirect
14. C₂₉×#3266	C₂	semidirect
15. C₂₉×#3182	C₂	semidirect
16. C₂₉×#3178	C₂	semidirect
17. C₂₉×#3123	C₂	semidirect
18. C₂₉×#3121	C₂	semidirect
19. C₂₉×#3107	C₂	semidirect
20. C₂₉×#3103	C₂	semidirect
21. C₂₉×#2969	C₂	semidirect
22. C₂₉×#2949	C₂	semidirect
23. C₄×C₂₉×#137	C₂	semidirect
28. C₂₉×#557	C₂²	semidirect
29. C₂₉×#557	C₂²	semidirect
35. C₂₉×#552	C₂²	semidirect
39. D₄×Q₈×C₂₉	C₂²	semidirect
46. C₂₉×#541	C₂²	semidirect
49. C₂₉×#533	C₂²	semidirect
55. C₂₉×#519	C₂²	semidirect
58. C₂×C₄×Q₈×C₂₉	C₂²	semidirect
59. C₂₉×#501	C₂²	semidirect
60. C₂₉×#500	C₂²	semidirect
61. C₂₉×#497	C₂²	semidirect
63. C₂₉×#488	C₂²	semidirect
64. C₂₉×#487	C₂²	semidirect
65. C₂₉×#487	C₂²	semidirect
67. C₂₉×#485	C₂²	semidirect
68. C₂₉×#485	C₂²	semidirect
69. C₂₉×#485	C₂²	semidirect
70. C₂₉×#485	C₂²	semidirect
72. C₂₉×#481	C₂²	semidirect
74. C₂₉×#478	C₂²	semidirect
75. C₂₉×#477	C₂²	semidirect
76. C₂₉×#475	C₂²	semidirect
77. C₂₉×#475	C₂²	semidirect
78. C₂₉×#475	C₂²	semidirect
79. C₂₉×#475	C₂²	semidirect
81. C₂₉×#470	C₂²	semidirect
83. C₂₉×#468	C₂²	semidirect
84. C₂₉×#468	C₂²	semidirect
85. C₂₉×#467	C₂²	semidirect
87. C₂₉×#464	C₂²	semidirect
88. C₂₉×#464	C₂²	semidirect
89. C₂₉×#462	C₂²	semidirect
92. C₂₉×#461	C₂²	semidirect
96. C₂₉×#451	C₂²	semidirect
100. C₂₉×#448	C₂²	semidirect
101. C₂₉×#446	C₂²	semidirect
102. C₈×Q₈×C₂₉	C₂²	semidirect
103. C₂₉×#441	C₂²	semidirect
104. C₂₉×#441	C₂²	semidirect
108. C₂₉×#440	C₂²	semidirect
109. C₂₉×#440	C₂²	semidirect
110. C₂₉×#440	C₂²	semidirect
111. C₄×Q₁₆×C₂₉	C₂²	semidirect
112. C₄×Q₁₆×C₂₉	C₂²	semidirect
113. C₄×Q₁₆×C₂₉	C₂²	semidirect
118. C₄×SD₁₆×C₂₉	C₂²	semidirect
119. C₄×SD₁₆×C₂₉	C₂²	semidirect
120. C₄×SD₁₆×C₂₉	C₂²	semidirect
122. C₂₉×#436	C₂²	semidirect
123. C₂₉×#435	C₂²	semidirect
125. C₂₉×#433	C₂²	semidirect
126. C₂₉×#431	C₂²	semidirect
127. C₂₉×#428	C₂²	semidirect
128. C₂₉×#427	C₂²	semidirect
129. C₂₉×#419	C₂²	semidirect
130. C₂₉×#419	C₂²	semidirect
133. C₂₉×#405	C₂²	semidirect
134. C₄×M₁₆×C₂₉	C₂²	semidirect
368. SD₁₆×C₂₉	#41	semidirect
452. #61540	C₂₉	direct (N × H)
526. #3523	C₂×C₂₉	semidirect
528. #3400	C₂×C₂₉	semidirect
529. #3386	C₂×C₂₉	semidirect
530. #3365	C₂×C₂₉	semidirect
531. #3359	C₂×C₂₉	semidirect
532. #3348	C₂×C₂₉	semidirect
533. #3342	C₂×C₂₉	semidirect
534. #3329	C₂×C₂₉	semidirect
535. #3328	C₂×C₂₉	semidirect
536. #3324	C₂×C₂₉	semidirect
537. #3323	C₂×C₂₉	semidirect
538. D₄×SD₁₆	C₂×C₂₉	semidirect
539. #3266	C₂×C₂₉	semidirect
540. #3182	C₂×C₂₉	semidirect
541. #3178	C₂×C₂₉	semidirect
542. #3123	C₂×C₂₉	semidirect
543. #3121	C₂×C₂₉	semidirect
544. #3107	C₂×C₂₉	semidirect
545. #3103	C₂×C₂₉	semidirect
546. #2969	C₂×C₂₉	semidirect
547. #2949	C₂×C₂₉	semidirect
548. C₄×#137	C₂×C₂₉	semidirect
587. #557	C₂²×C₂₉	semidirect
588. #557	C₂²×C₂₉	semidirect
594. #552	C₂²×C₂₉	semidirect
598. D₄×Q₈	C₂²×C₂₉	semidirect
605. #541	C₂²×C₂₉	semidirect
608. #533	C₂²×C₂₉	semidirect
614. #519	C₂²×C₂₉	semidirect
617. C₂×C₄×Q₈	C₂²×C₂₉	semidirect
618. #501	C₂²×C₂₉	semidirect
619. #500	C₂²×C₂₉	semidirect
620. #497	C₂²×C₂₉	semidirect
622. #488	C₂²×C₂₉	semidirect
623. #487	C₂²×C₂₉	semidirect
624. #487	C₂²×C₂₉	semidirect
626. #485	C₂²×C₂₉	semidirect
627. #485	C₂²×C₂₉	semidirect
628. #485	C₂²×C₂₉	semidirect
629. #485	C₂²×C₂₉	semidirect
631. #481	C₂²×C₂₉	semidirect
633. #478	C₂²×C₂₉	semidirect
634. #477	C₂²×C₂₉	semidirect
635. #475	C₂²×C₂₉	semidirect
636. #475	C₂²×C₂₉	semidirect
637. #475	C₂²×C₂₉	semidirect
638. #475	C₂²×C₂₉	semidirect
640. #470	C₂²×C₂₉	semidirect
642. #468	C₂²×C₂₉	semidirect
643. #468	C₂²×C₂₉	semidirect
644. #467	C₂²×C₂₉	semidirect
646. #464	C₂²×C₂₉	semidirect
647. #464	C₂²×C₂₉	semidirect
648. #462	C₂²×C₂₉	semidirect
651. #461	C₂²×C₂₉	semidirect
655. #451	C₂²×C₂₉	semidirect
659. #448	C₂²×C₂₉	semidirect
660. #446	C₂²×C₂₉	semidirect
661. C₈×Q₈	C₂²×C₂₉	semidirect
662. #441	C₂²×C₂₉	semidirect
663. #441	C₂²×C₂₉	semidirect
667. #440	C₂²×C₂₉	semidirect
668. #440	C₂²×C₂₉	semidirect
669. #440	C₂²×C₂₉	semidirect
670. C₄×Q₁₆	C₂²×C₂₉	semidirect
671. C₄×Q₁₆	C₂²×C₂₉	semidirect
672. C₄×Q₁₆	C₂²×C₂₉	semidirect
677. C₄×SD₁₆	C₂²×C₂₉	semidirect
678. C₄×SD₁₆	C₂²×C₂₉	semidirect
679. C₄×SD₁₆	C₂²×C₂₉	semidirect
681. #436	C₂²×C₂₉	semidirect
682. #435	C₂²×C₂₉	semidirect
684. #433	C₂²×C₂₉	semidirect
685. #431	C₂²×C₂₉	semidirect
686. #428	C₂²×C₂₉	semidirect
687. #427	C₂²×C₂₉	semidirect
688. #419	C₂²×C₂₉	semidirect
689. #419	C₂²×C₂₉	semidirect
692. #405	C₂²×C₂₉	semidirect
693. C₄×M₁₆	C₂²×C₂₉	semidirect
880. C₂₉	#61540	direct (N × H)
935. SD₁₆	#41×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#3523	2
C₂₉×#3514	2
C₂₉×#3400	2
C₂₉×#3386	2
C₂₉×#3365	2
C₂₉×#3359	2
C₂₉×#3348	2
C₂₉×#3342	2
C₂₉×#3329	2
C₂₉×#3328	2
C₂₉×#3324	2
C₂₉×#3323	2
D₄×SD₁₆×C₂₉	2
C₂₉×#3266	2
C₂₉×#3182	2
C₂₉×#3178	2
C₂₉×#3123	2
C₂₉×#3121	2
C₂₉×#3107	2
C₂₉×#3103	2
C₂₉×#2969	2
C₂₉×#2949	2
C₄×C₂₉×#137	2
#61540	29

Subgroups — C29×#61540 #20356440

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#61540 #20356440