Subgroups — C₂₉×#62103 #20357003

Order 7424.

1804 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3381	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3380	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#3339	C₂	1	2	yes	maximal, complemented
8	C₂₉×#3338	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#3337	C₂	1	2	yes	maximal, complemented
10	C₂₉×#3335	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#3297	C₂	1	2	yes	maximal, complemented
12	C₂₉×#3296	C₂	1	2	yes	maximal, complemented
13	C₂₉×#3295	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#3250	C₂	1	2	yes	maximal, complemented
16	C₂₉×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₉×#3232	C₂	1	2	yes	maximal, complemented
18	C₂₉×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₉×#3105	C₂	1	2	yes	maximal, complemented
20	C₂₉×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₉×#3076	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₂₉×#478	C₂	1	2	yes	maximal, complemented
23	C₂₉×#2988	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₉×#559	C₂²	1	1	yes	characteristic
25	C₂₉×#557	C₂²	1	1	yes	characteristic, complemented
26	C₂₉×#554	C₂²	1	1	yes	characteristic
27	C₂₉×#554	C₂²	1	1	yes	characteristic
28	C₂₉×#554	C₂²	1	1	yes	characteristic
29	C₂₉×#554	C₂²	1	1	yes	characteristic, complemented
30	C₂₉×#553	—	2	1	no	—
31	C₂₉×#553	C₂²	1	2	yes	—
32	C₂₉×#553	C₂²	1	2	yes	complemented
33	C₂₉×#552	—	2	2	no	—
34	C₂₉×#552	—	2	1	no	—
35	C₂₉×#552	C₂²	1	2	yes	complemented
36	C₂₉×#551	—	2	2	no	—
37	C₂₉×#547	—	2	1	no	—
38	C₂₉×#547	C₂²	1	1	yes	characteristic
39	C₂₉×#546	—	2	1	no	—
40	C₂₉×#546	C₂²	1	2	yes	—
41	D₄²×C₂₉	C₂²	1	1	yes	characteristic
42	C₂₉×#541	—	2	1	no	—
43	C₂₉×#539	—	2	2	no	—
44	C₂₉×#533	C₂²	1	1	yes	characteristic, complemented
45	C₂₉×#532	C₂²	1	1	yes	characteristic
46	C₂₉×#529	—	2	1	no	—
47	C₂₉×#529	C₂²	1	2	yes	—
48	C₂₉×#529	C₂²	1	1	yes	characteristic, complemented
49	C₂₉×#529	C₂²	1	2	yes	complemented
50	C₂×C₂₉×#125	C₂²	1	2	yes	complemented
51	C₂₉×#525	—	2	2	no	—
52	C₂₉×#520	—	2	1	no	—
53	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
54	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₂₉	—	2	1	no	—
56	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	—
57	C₂₉×#500	C₂²	1	1	yes	characteristic, complemented
58	C₂₉×#499	C₂²	1	2	yes	complemented
59	C₂₉×#499	C₂²	1	2	yes	complemented
60	C₂₉×#498	C₂²	1	1	yes	characteristic, complemented
61	C₂₉×#488	C₂²	1	2	yes	complemented
62	C₂₉×#488	C₂²	1	2	yes	complemented
63	C₂₉×#486	C₂²	1	1	yes	characteristic
64	C₂₉×#486	C₂²	1	1	yes	characteristic
65	C₂₉×#485	C₂²	1	1	yes	characteristic, complemented
66	C₂₉×#484	C₂²	1	2	yes	complemented
67	C₂₉×#484	C₂²	1	2	yes	complemented
68	C₂₉×#483	C₂²	1	2	yes	complemented
69	C₂₉×#482	C₂²	1	2	yes	complemented
70	C₂₉×#482	C₂²	1	2	yes	complemented
71	C₂₉×#482	C₂²	1	1	yes	characteristic, complemented
72	C₂₉×#481	C₂²	1	2	yes	—
73	C₂₉×#481	C₂²	1	2	yes	complemented
74	C₂₉×#480	C₂²	1	2	yes	—
75	C₂₉×#479	C₂²	1	1	yes	characteristic, complemented
76	C₂₉×#479	C₂²	1	2	yes	complemented
77	C₂₉×#479	C₂²	1	2	yes	complemented
78	C₂₉×#478	C₂²	1	2	yes	—
79	C₂₉×#478	C₂²	1	2	yes	—
80	C₂₉×#478	C₂²	1	1	yes	characteristic
81	C₂₉×#478	C₂²	1	2	yes	—
82	C₂₉×#478	C₂²	1	2	yes	complemented
83	C₂₉×#478	C₂²	1	2	yes	complemented
84	C₂₉×#478	C₂²	1	2	yes	complemented
85	C₂₉×#478	C₂²	1	2	yes	complemented
86	C₂₉×#478	C₂²	1	2	yes	complemented
87	C₂₉×#478	C₂²	1	2	yes	complemented
88	C₂₉×#477	C₂²	1	1	yes	characteristic, complemented
89	C₂₉×#477	C₂²	1	1	yes	characteristic, complemented
90	C₂₉×#476	C₂²	1	1	yes	characteristic
91	C₂₉×#476	C₂²	1	1	yes	characteristic, complemented
92	C₂₉×#475	C₂²	1	1	yes	characteristic, complemented
93	C₂₉×#474	C₂²	1	1	yes	characteristic
94	C₂₉×#467	C₂²	1	2	yes	complemented
95	C₂₉×#466	C₂²	1	2	yes	—
96	C₂₉×#466	C₂²	1	2	yes	complemented
97	C₂₉×#465	C₂²	1	2	yes	—
98	C₂₉×#465	C₂²	1	2	yes	complemented
99	C₂₉×#465	C₂²	1	2	yes	complemented
100	C₂₉×#464	C₂²	1	1	yes	characteristic, complemented
101	C₂₉×#464	C₂²	1	2	yes	complemented
102	C₂₉×#463	C₂²	1	1	yes	characteristic
103	C₂₉×#463	C₂²	1	2	yes	complemented
104	C₂₉×#463	C₂²	1	2	yes	complemented
105	C₂₉×#460	C₂²	1	1	yes	characteristic
106	C₂₉×#459	C₂²	1	1	yes	characteristic
107	C₂₉×#452	C₂²	1	1	yes	characteristic
108	C₂₉×#450	C₂²	1	2	yes	—
109	C₂₉×#449	C₂²	1	1	yes	characteristic
110	C₂₉×#447	C₂²	1	2	yes	—
111	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
113	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
115	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	—
116	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	complemented
118	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₂₉	C₂²	1	2	yes	—
120	C₄×D₈×C₂₉	C₂²	1	2	yes	complemented
121	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
123	C₈×D₄×C₂₉	C₂²	1	2	yes	complemented
124	C₈×D₄×C₂₉	C₂²	1	2	yes	complemented
125	C₂₉×#431	C₂²	1	1	yes	characteristic, complemented
126	C₂₉×#431	C₂²	1	2	yes	complemented
127	C₂₉×#427	C₂²	1	2	yes	complemented
128	C₂×C₂₉×#107	C₂²	1	2	yes	complemented
129	C₂×C₂₉×#106	C₂²	1	2	yes	complemented
130	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	complemented
132	C₂₉×#416	C₂²	1	2	yes	—
133	C₂×C₂₉×#102	C₂²	1	2	yes	—
134	C₂×C₂₉×#102	C₂²	1	2	yes	—
135	C₂×#41×C₂₉	—	2	1	no	—
136	C₂×#41×C₂₉	—	2	1	no	—
137	C₂×#41×C₂₉	D₄	1	1	yes	characteristic
138	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₂₉	—	2	1	no	—
140	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
141	C₂³×C₄×C₂₉	—	2	2	no	—
142	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
146	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₂₉	C₂³	1	2	yes	—
148	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
149	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
150	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
151	C₂₉×C₄⋊Q₈	—	2	1	no	—
152	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₂₉×#127	C₂³	1	1	yes	characteristic
156	C₂₉×#126	—	2	2	no	—
157	C₂₉×#126	—	2	2	no	—
158	C₂₉×#126	—	2	2	no	—
159	C₂₉×#126	—	2	2	no	—
160	C₂₉×#126	—	2	2	no	—
161	C₂₉×#126	—	2	1	no	—
162	C₂₉×#125	—	2	1	no	—
163	C₂₉×#125	—	2	2	no	—
164	C₂₉×#125	—	2	2	no	—
165	C₂₉×#125	—	2	1	no	—
166	C₂₉×#125	—	2	2	no	—
167	C₂₉×#125	—	2	2	no	—
168	C₂₉×#125	C₂³	1	1	yes	characteristic
169	C₂₉×#125	C₂³	1	2	yes	—
170	C₂₉×#125	C₂³	1	2	yes	—
171	C₂₉×#125	C₂³	1	2	yes	—
172	C₂₉×#125	C₂³	1	2	yes	—
173	C₂₉×#124	—	2	1	no	—
174	C₂₉×#124	—	2	1	no	—
175	C₂₉×#124	C₂³	1	1	yes	characteristic
176	C₂₉×#124	C₂³	1	2	yes	—
177	C₂₉×#123	—	2	2	no	—
178	C₂₉×#123	—	2	2	no	—
179	C₂₉×#123	—	2	1	no	—
180	C₂₉×#123	—	2	2	no	—
181	C₂₉×#123	—	2	2	no	—
182	C₂₉×#123	—	2	2	no	—
183	C₂₉×#123	—	2	2	no	—
184	C₂₉×#123	—	2	2	no	—
185	C₂₉×#123	—	2	2	no	—
186	C₂₉×C₂²⋊Q₈	—	2	1	no	—
187	C₂₉×C₂²⋊Q₈	—	2	1	no	—
188	C₂₉×C₂²⋊Q₈	—	2	1	no	—
189	C₂₉×C₂²⋊Q₈	—	2	1	no	—
190	C₂₉×C₂²⋊Q₈	—	2	2	no	—
191	C₂₉×C₂²⋊Q₈	—	2	2	no	—
192	C₂₉×C₂²⋊Q₈	—	2	1	no	—
193	C₂₉×C₂²⋊Q₈	—	2	2	no	—
194	C₂₉×C₂²⋊Q₈	—	2	2	no	—
195	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₂₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
197	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₂₉×#121	—	2	2	no	—
199	C₂₉×#121	—	2	2	no	—
200	C₂₉×#121	—	2	1	no	—
201	C₂₉×#121	—	2	1	no	—
202	C₂₉×#121	—	2	2	no	—
203	C₂₉×#121	C₂³	1	2	yes	—
204	C₂₉×#121	C₂³	1	1	yes	characteristic
205	C₂₉×#121	C₂³	1	2	yes	—
206	C₂₉×#121	C₂³	1	2	yes	—
207	C₂₉×#120	—	2	2	no	—
208	C₂₉×#120	—	2	2	no	—
209	C₄×Q₈×C₂₉	—	2	1	no	—
210	C₄×Q₈×C₂₉	—	2	1	no	—
211	C₄×Q₈×C₂₉	—	2	1	no	—
212	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
213	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
214	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
218	C₄×D₄×C₂₉	—	2	1	no	—
219	C₄×D₄×C₂₉	—	2	1	no	—
220	C₄×D₄×C₂₉	—	2	2	no	—
221	C₄×D₄×C₂₉	—	2	1	no	—
222	C₄×D₄×C₂₉	—	2	1	no	—
223	C₄×D₄×C₂₉	—	2	2	no	—
224	C₄×D₄×C₂₉	—	2	1	no	—
225	C₄×D₄×C₂₉	—	2	1	no	—
226	C₄×D₄×C₂₉	—	2	2	no	—
227	C₄×D₄×C₂₉	—	2	2	no	—
228	C₄×D₄×C₂₉	—	2	1	no	—
229	C₄×D₄×C₂₉	—	2	2	no	—
230	C₄×D₄×C₂₉	—	2	2	no	—
231	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
232	C₄×D₄×C₂₉	D₄	1	2	yes	—
233	C₄×D₄×C₂₉	C₂³	1	2	yes	—
234	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₂₉	C₂³	1	2	yes	—
236	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₂₉	C₂³	1	2	yes	—
238	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₂₉	C₂³	1	2	yes	—
240	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₂₉	C₂³	1	2	yes	—
242	C₂₉×#117	—	2	2	no	—
243	C₂₉×#117	—	2	1	no	—
244	C₂₉×#117	—	2	1	no	—
245	C₂₉×#117	—	2	2	no	—
246	C₂₉×#117	—	2	2	no	—
247	C₂₉×#117	D₄	1	2	yes	—
248	C₂₉×#117	D₄	1	1	yes	characteristic
249	C₂₉×#117	C₂³	1	1	yes	characteristic
250	C₂₉×#117	C₂³	1	2	yes	—
251	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
252	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
253	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
254	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
255	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
259	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
260	C₂×C₄²×C₂₉	—	2	1	no	—
261	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
262	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
263	C₂₉×#107	C₂³	1	1	yes	characteristic
264	C₂₉×#107	C₂³	1	2	yes	—
265	C₂₉×#107	C₂³	1	2	yes	—
266	C₂₉×#107	C₂³	1	2	yes	—
267	C₂₉×#107	C₂³	1	2	yes	—
268	C₂₉×#107	C₂³	1	2	yes	—
269	C₂₉×#107	C₂³	1	1	yes	characteristic
270	C₂₉×#106	C₂³	1	1	yes	characteristic
271	C₂₉×#106	C₂³	1	2	yes	—
272	C₂₉×#106	C₂³	1	2	yes	—
273	C₂₉×#106	C₂³	1	2	yes	—
274	C₂₉×#106	C₂³	1	2	yes	—
275	C₂₉×#106	C₂³	1	2	yes	—
276	C₂₉×#106	C₂³	1	1	yes	characteristic
277	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
279	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
283	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
284	C₂₉×#103	C₂³	1	2	yes	—
285	C₂₉×#103	C₂³	1	1	yes	characteristic
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×#102	C₂³	1	2	yes	—
292	C₂₉×#102	C₂³	1	1	yes	characteristic
293	C₂₉×#102	C₂³	1	2	yes	—
294	C₂₉×#102	C₂³	1	1	yes	characteristic
295	C₂₉×#102	C₂³	1	1	yes	characteristic
296	C₂₉×#102	C₂³	1	2	yes	—
297	C₂₉×#102	C₂³	1	2	yes	—
298	C₂₉×#102	C₂³	1	1	yes	characteristic
299	C₂₉×#102	C₂³	1	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	1	yes	characteristic
307	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₂₉	C₂³	1	2	yes	—
311	C₄×C₈×C₂₉	C₂³	1	2	yes	—
312	C₂⁴×C₂₉	—	2	2	no	—
313	#41×C₂₉	—	2	4	no	—
314	#41×C₂₉	—	2	2	no	—
315	#41×C₂₉	—	4	1	no	—
316	#41×C₂₉	—	4	4	no	—
317	#41×C₂₉	—	8	2	no	—
318	C₂×Q₈×C₂₉	—	2	1	no	—
319	C₂×Q₈×C₂₉	—	2	1	no	—
320	C₂×Q₈×C₂₉	—	2	1	no	—
321	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
323	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
324	C₂×D₄×C₂₉	—	2	4	no	—
325	C₂×D₄×C₂₉	—	2	1	no	—
326	C₂×D₄×C₂₉	—	2	2	no	—
327	C₂×D₄×C₂₉	—	2	2	no	—
328	C₂×D₄×C₂₉	—	2	1	no	—
329	C₂×D₄×C₂₉	—	2	2	no	—
330	C₂×D₄×C₂₉	—	2	2	no	—
331	C₂×D₄×C₂₉	—	2	1	no	—
332	C₂×D₄×C₂₉	—	2	1	no	—
333	C₂×D₄×C₂₉	—	4	2	no	—
334	C₂×D₄×C₂₉	—	4	4	no	—
335	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
338	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
339	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₂₉	—	2	2	no	—
341	C₂²×C₄×C₂₉	—	2	2	no	—
342	C₂²×C₄×C₂₉	—	2	2	no	—
343	C₂²×C₄×C₂₉	—	2	1	no	—
344	C₂²×C₄×C₂₉	—	2	1	no	—
345	C₂²×C₄×C₂₉	—	2	1	no	—
346	C₂²×C₄×C₂₉	—	2	1	no	—
347	C₂²×C₄×C₂₉	—	2	2	no	—
348	C₂²×C₄×C₂₉	—	2	2	no	—
349	C₂²×C₄×C₂₉	—	2	2	no	—
350	C₂²×C₄×C₂₉	—	2	2	no	—
351	C₂²×C₄×C₂₉	—	8	4	no	—
352	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
353	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
355	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
357	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
358	Q₁₆×C₂₉	—	4	1	no	—
359	SD₁₆×C₂₉	—	2	2	no	—
360	SD₁₆×C₂₉	—	4	1	no	—
361	SD₁₆×C₂₉	—	4	2	no	—
362	D₈×C₂₉	—	2	2	no	—
363	D₈×C₂₉	—	4	2	no	—
364	C₂×C₈×C₂₉	—	4	2	no	—
365	C₂×C₈×C₂₉	—	4	2	no	—
366	C₂×C₈×C₂₉	—	4	2	no	—
367	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
368	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
370	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
373	C₄⋊C₄×C₂₉	—	2	2	no	—
374	C₄⋊C₄×C₂₉	—	2	1	no	—
375	C₄⋊C₄×C₂₉	—	2	1	no	—
376	C₄⋊C₄×C₂₉	—	2	2	no	—
377	C₄⋊C₄×C₂₉	—	2	1	no	—
378	C₄⋊C₄×C₂₉	—	2	2	no	—
379	C₄⋊C₄×C₂₉	—	2	1	no	—
380	C₄⋊C₄×C₂₉	—	2	2	no	—
381	C₄⋊C₄×C₂₉	—	2	2	no	—
382	C₄⋊C₄×C₂₉	—	2	2	no	—
383	C₄⋊C₄×C₂₉	—	2	2	no	—
384	C₄⋊C₄×C₂₉	—	2	2	no	—
385	C₄⋊C₄×C₂₉	—	2	2	no	—
386	C₄⋊C₄×C₂₉	—	2	2	no	—
387	C₄⋊C₄×C₂₉	—	2	1	no	—
388	C₄⋊C₄×C₂₉	—	2	1	no	—
389	C₄⋊C₄×C₂₉	—	2	1	no	—
390	C₄⋊C₄×C₂₉	—	2	2	no	—
391	C₄⋊C₄×C₂₉	—	2	2	no	—
392	C₄⋊C₄×C₂₉	—	2	2	no	—
393	C₄⋊C₄×C₂₉	—	2	1	no	—
394	C₄⋊C₄×C₂₉	—	2	1	no	—
395	C₄⋊C₄×C₂₉	—	2	2	no	—
396	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
397	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
407	C₂²⋊C₄×C₂₉	—	2	2	no	—
408	C₂²⋊C₄×C₂₉	—	2	2	no	—
409	C₂²⋊C₄×C₂₉	—	2	1	no	—
410	C₂²⋊C₄×C₂₉	—	2	2	no	—
411	C₂²⋊C₄×C₂₉	—	2	1	no	—
412	C₂²⋊C₄×C₂₉	—	2	1	no	—
413	C₂²⋊C₄×C₂₉	—	2	2	no	—
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	1	no	—
420	C₂²⋊C₄×C₂₉	—	2	1	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	1	no	—
427	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
428	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
430	C₄²×C₂₉	—	2	1	no	—
431	C₄²×C₂₉	—	2	1	no	—
432	C₄²×C₂₉	—	2	1	no	—
433	C₄²×C₂₉	—	2	2	no	—
434	C₄²×C₂₉	—	2	2	no	—
435	C₄²×C₂₉	—	2	1	no	—
436	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₂₉	C₂×D₄	1	2	yes	—
438	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₂₉	C₂×D₄	1	2	yes	—
440	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
441	C₄²×C₂₉	C₂⁴	1	2	yes	—
442	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
443	#62103	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
444	C₂³×C₂₉	—	2	1	no	—
445	C₂³×C₂₉	—	2	1	no	—
446	C₂³×C₂₉	—	2	2	no	—
447	C₂³×C₂₉	—	4	4	no	—
448	C₂³×C₂₉	—	4	4	no	—
449	C₂³×C₂₉	—	8	2	no	—
450	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
451	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
452	Q₈×C₂₉	—	2	2	no	—
453	Q₈×C₂₉	—	2	1	no	—
454	Q₈×C₂₉	—	2	1	no	—
455	Q₈×C₂₉	—	2	1	no	—
456	Q₈×C₂₉	—	2	1	no	—
457	Q₈×C₂₉	—	4	2	no	—
458	Q₈×C₂₉	—	8	1	no	—
459	Q₈×C₂₉	—	8	1	no	—
460	D₄×C₂₉	—	2	4	no	—
461	D₄×C₂₉	—	2	1	no	—
462	D₄×C₂₉	—	2	2	no	—
463	D₄×C₂₉	—	2	1	no	—
464	D₄×C₂₉	—	2	1	no	—
465	D₄×C₂₉	—	2	2	no	—
466	D₄×C₂₉	—	4	4	no	—
467	D₄×C₂₉	—	4	2	no	—
468	D₄×C₂₉	—	4	4	no	—
469	D₄×C₂₉	—	4	4	no	—
470	D₄×C₂₉	—	4	2	no	—
471	D₄×C₂₉	—	8	1	no	—
472	D₄×C₂₉	—	8	1	no	—
473	D₄×C₂₉	—	8	2	no	—
474	D₄×C₂₉	#135	1	4	yes	—
475	D₄×C₂₉	2₋¹⁺⁴	1	2	yes	—
476	C₂×C₄×C₂₉	—	2	4	no	—
477	C₂×C₄×C₂₉	—	2	2	no	—
478	C₂×C₄×C₂₉	—	2	2	no	—
479	C₂×C₄×C₂₉	—	2	1	no	—
480	C₂×C₄×C₂₉	—	2	2	no	—
481	C₂×C₄×C₂₉	—	2	1	no	—
482	C₂×C₄×C₂₉	—	2	1	no	—
483	C₂×C₄×C₂₉	—	2	1	no	—
484	C₂×C₄×C₂₉	—	2	1	no	—
485	C₂×C₄×C₂₉	—	2	1	no	—
486	C₂×C₄×C₂₉	—	2	2	no	—
487	C₂×C₄×C₂₉	—	2	2	no	—
488	C₂×C₄×C₂₉	—	2	1	no	—
489	C₂×C₄×C₂₉	—	2	2	no	—
490	C₂×C₄×C₂₉	—	2	1	no	—
491	C₂×C₄×C₂₉	—	4	2	no	—
492	C₂×C₄×C₂₉	—	4	1	no	—
493	C₂×C₄×C₂₉	—	4	2	no	—
494	C₂×C₄×C₂₉	—	4	2	no	—
495	C₂×C₄×C₂₉	—	4	4	no	—
496	C₂×C₄×C₂₉	—	4	4	no	—
497	C₂×C₄×C₂₉	—	4	2	no	—
498	C₂×C₄×C₂₉	—	4	2	no	—
499	C₂×C₄×C₂₉	—	8	2	no	—
500	C₂×C₄×C₂₉	—	8	2	no	—
501	C₂×C₄×C₂₉	—	8	2	no	—
502	C₂×C₄×C₂₉	—	8	2	no	—
503	C₂×C₄×C₂₉	—	8	2	no	—
504	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
513	C₈×C₂₉	—	2	1	no	—
514	C₈×C₂₉	—	2	1	no	—
515	C₈×C₂₉	—	2	2	no	—
516	C₈×C₂₉	—	2	2	no	—
517	C₈×C₂₉	—	2	1	no	—
518	C₈×C₂₉	—	2	1	no	—
519	#3515	C₂×C₂₉	1	1	yes	characteristic, complemented
520	#3481	C₂×C₂₉	1	1	yes	characteristic, complemented
521	#3381	C₂×C₂₉	1	1	yes	characteristic, complemented
522	#3380	C₂×C₂₉	1	1	yes	characteristic, complemented
523	#3365	C₂×C₂₉	1	1	yes	characteristic, complemented
524	#3361	C₂×C₂₉	1	1	yes	characteristic, complemented
525	#3339	C₂×C₂₉	1	2	yes	complemented
526	#3338	C₂×C₂₉	1	1	yes	characteristic, complemented
527	#3337	C₂×C₂₉	1	2	yes	complemented
528	#3335	C₂×C₂₉	1	1	yes	characteristic, complemented
529	#3297	C₂×C₂₉	1	2	yes	complemented
530	#3296	C₂×C₂₉	1	2	yes	complemented
531	#3295	C₂×C₂₉	1	1	yes	characteristic, complemented
532	#3294	C₂×C₂₉	1	1	yes	characteristic, complemented
533	#3250	C₂×C₂₉	1	2	yes	complemented
534	#3247	C₂×C₂₉	1	1	yes	characteristic, complemented
535	#3232	C₂×C₂₉	1	2	yes	complemented
536	#3228	C₂×C₂₉	1	1	yes	characteristic, complemented
537	#3105	C₂×C₂₉	1	2	yes	complemented
538	#3102	C₂×C₂₉	1	1	yes	characteristic, complemented
539	#3076	C₂×C₂₉	1	1	yes	characteristic, complemented
540	C₂×#478	C₂×C₂₉	1	2	yes	complemented
541	#2988	C₂×C₂₉	1	1	yes	characteristic, complemented
542	C₂²×C₂₉	—	2	2	no	—
543	C₂²×C₂₉	—	2	2	no	—
544	C₂²×C₂₉	—	2	1	no	—
545	C₂²×C₂₉	—	2	1	no	—
546	C₂²×C₂₉	—	2	2	no	—
547	C₂²×C₂₉	—	2	1	no	—
548	C₂²×C₂₉	—	4	1	no	—
549	C₂²×C₂₉	—	4	1	no	—
550	C₂²×C₂₉	—	4	2	no	—
551	C₂²×C₂₉	—	4	1	no	—
552	C₂²×C₂₉	—	4	2	no	—
553	C₂²×C₂₉	—	4	1	no	—
554	C₂²×C₂₉	—	4	1	no	—
555	C₂²×C₂₉	—	4	2	no	—
556	C₂²×C₂₉	—	8	8	no	—
557	C₂²×C₂₉	C₂×#135	1	4	yes	—
558	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
559	C₄×C₂₉	—	2	1	no	—
560	C₄×C₂₉	—	2	2	no	—
561	C₄×C₂₉	—	2	1	no	—
562	C₄×C₂₉	—	2	1	no	—
563	C₄×C₂₉	—	2	2	no	—
564	C₄×C₂₉	—	2	1	no	—
565	C₄×C₂₉	—	2	2	no	—
566	C₄×C₂₉	—	4	1	no	—
567	C₄×C₂₉	—	4	2	no	—
568	C₄×C₂₉	—	4	1	no	—
569	C₄×C₂₉	—	4	2	no	—
570	C₄×C₂₉	—	4	1	no	—
571	C₄×C₂₉	—	4	1	no	—
572	C₄×C₂₉	—	4	1	no	—
573	C₄×C₂₉	—	4	1	no	—
574	C₄×C₂₉	—	4	2	no	—
575	C₄×C₂₉	C₂×#135	1	2	yes	—
576	C₄×C₂₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
577	C₄×C₂₉	#585	1	1	yes	characteristic
578	#559	C₂²×C₂₉	1	1	yes	characteristic
579	#557	C₂²×C₂₉	1	1	yes	characteristic, complemented
580	#554	C₂²×C₂₉	1	1	yes	characteristic
581	#554	C₂²×C₂₉	1	1	yes	characteristic
582	#554	C₂²×C₂₉	1	1	yes	characteristic
583	#554	C₂²×C₂₉	1	1	yes	characteristic, complemented
584	#553	—	2	1	no	—
585	#553	C₂²×C₂₉	1	2	yes	—
586	#553	C₂²×C₂₉	1	2	yes	complemented
587	#552	—	2	2	no	—
588	#552	—	2	1	no	—
589	#552	C₂²×C₂₉	1	2	yes	complemented
590	#551	—	2	2	no	—
591	#547	—	2	1	no	—
592	#547	C₂²×C₂₉	1	1	yes	characteristic
593	#546	—	2	1	no	—
594	#546	C₂²×C₂₉	1	2	yes	—
595	D₄²	C₂²×C₂₉	1	1	yes	characteristic
596	#541	—	2	1	no	—
597	#539	—	2	2	no	—
598	#533	C₂²×C₂₉	1	1	yes	characteristic, complemented
599	#532	C₂²×C₂₉	1	1	yes	characteristic
600	#529	—	2	1	no	—
601	#529	C₂²×C₂₉	1	2	yes	—
602	#529	C₂²×C₂₉	1	1	yes	characteristic, complemented
603	#529	C₂²×C₂₉	1	2	yes	complemented
604	C₂×#125	C₂²×C₂₉	1	2	yes	complemented
605	#525	—	2	2	no	—
606	#520	—	2	1	no	—
607	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
608	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
609	C₂×C₄×D₄	—	2	1	no	—
610	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	—
611	#500	C₂²×C₂₉	1	1	yes	characteristic, complemented
612	#499	C₂²×C₂₉	1	2	yes	complemented
613	#499	C₂²×C₂₉	1	2	yes	complemented
614	#498	C₂²×C₂₉	1	1	yes	characteristic, complemented
615	#488	C₂²×C₂₉	1	2	yes	complemented
616	#488	C₂²×C₂₉	1	2	yes	complemented
617	#486	C₂²×C₂₉	1	1	yes	characteristic
618	#486	C₂²×C₂₉	1	1	yes	characteristic
619	#485	C₂²×C₂₉	1	1	yes	characteristic, complemented
620	#484	C₂²×C₂₉	1	2	yes	complemented
621	#484	C₂²×C₂₉	1	2	yes	complemented
622	#483	C₂²×C₂₉	1	2	yes	complemented
623	#482	C₂²×C₂₉	1	2	yes	complemented
624	#482	C₂²×C₂₉	1	1	yes	characteristic, complemented
625	#482	C₂²×C₂₉	1	2	yes	complemented
626	#481	C₂²×C₂₉	1	2	yes	—
627	#481	C₂²×C₂₉	1	2	yes	complemented
628	#480	C₂²×C₂₉	1	2	yes	—
629	#479	C₂²×C₂₉	1	2	yes	complemented
630	#479	C₂²×C₂₉	1	2	yes	complemented
631	#479	C₂²×C₂₉	1	1	yes	characteristic, complemented
632	#478	C₂²×C₂₉	1	1	yes	characteristic
633	#478	C₂²×C₂₉	1	2	yes	—
634	#478	C₂²×C₂₉	1	2	yes	—
635	#478	C₂²×C₂₉	1	2	yes	—
636	#478	C₂²×C₂₉	1	2	yes	complemented
637	#478	C₂²×C₂₉	1	2	yes	complemented
638	#478	C₂²×C₂₉	1	2	yes	complemented
639	#478	C₂²×C₂₉	1	2	yes	complemented
640	#478	C₂²×C₂₉	1	2	yes	complemented
641	#478	C₂²×C₂₉	1	2	yes	complemented
642	#477	C₂²×C₂₉	1	1	yes	characteristic, complemented
643	#477	C₂²×C₂₉	1	1	yes	characteristic, complemented
644	#476	C₂²×C₂₉	1	1	yes	characteristic
645	#476	C₂²×C₂₉	1	1	yes	characteristic, complemented
646	#475	C₂²×C₂₉	1	1	yes	characteristic, complemented
647	#474	C₂²×C₂₉	1	1	yes	characteristic
648	#467	C₂²×C₂₉	1	2	yes	complemented
649	#466	C₂²×C₂₉	1	2	yes	—
650	#466	C₂²×C₂₉	1	2	yes	complemented
651	#465	C₂²×C₂₉	1	2	yes	—
652	#465	C₂²×C₂₉	1	2	yes	complemented
653	#465	C₂²×C₂₉	1	2	yes	complemented
654	#464	C₂²×C₂₉	1	1	yes	characteristic, complemented
655	#464	C₂²×C₂₉	1	2	yes	complemented
656	#463	C₂²×C₂₉	1	1	yes	characteristic
657	#463	C₂²×C₂₉	1	2	yes	complemented
658	#463	C₂²×C₂₉	1	2	yes	complemented
659	#460	C₂²×C₂₉	1	1	yes	characteristic
660	#459	C₂²×C₂₉	1	1	yes	characteristic
661	#452	C₂²×C₂₉	1	1	yes	characteristic
662	#450	C₂²×C₂₉	1	2	yes	—
663	#449	C₂²×C₂₉	1	1	yes	characteristic
664	#447	C₂²×C₂₉	1	2	yes	—
665	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
666	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
667	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
668	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
669	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	—
670	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
671	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
672	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
673	C₄×D₈	C₂²×C₂₉	1	2	yes	—
674	C₄×D₈	C₂²×C₂₉	1	2	yes	complemented
675	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
676	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
677	C₈×D₄	C₂²×C₂₉	1	2	yes	complemented
678	C₈×D₄	C₂²×C₂₉	1	2	yes	complemented
679	#431	C₂²×C₂₉	1	1	yes	characteristic, complemented
680	#431	C₂²×C₂₉	1	2	yes	complemented
681	#427	C₂²×C₂₉	1	2	yes	complemented
682	C₂×#107	C₂²×C₂₉	1	2	yes	complemented
683	C₂×#106	C₂²×C₂₉	1	2	yes	complemented
684	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	complemented
685	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
686	#416	C₂²×C₂₉	1	2	yes	—
687	C₂×#102	C₂²×C₂₉	1	2	yes	—
688	C₂×#102	C₂²×C₂₉	1	2	yes	—
689	C₂×C₂₉	—	2	4	no	—
690	C₂×C₂₉	—	4	1	no	—
691	C₂×C₂₉	—	4	2	no	—
692	C₂×C₂₉	—	8	1	no	—
693	C₂×C₂₉	—	8	2	no	—
694	C₂×C₂₉	#3489	1	1	yes	characteristic
695	C₂×C₂₉	C₂²×#135	1	1	yes	characteristic
696	C₂×C₂₉	#3585	1	1	yes	characteristic
697	C₂×#41	—	2	1	no	—
698	C₂×#41	—	2	1	no	—
699	C₂×#41	D₄×C₂₉	1	1	yes	characteristic
700	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
701	C₂²×D₄	—	2	1	no	—
702	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
703	C₂³×C₄	—	2	2	no	—
704	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
705	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
706	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
707	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
708	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
709	C₂×D₈	C₂³×C₂₉	1	2	yes	—
710	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
711	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
712	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
713	C₄⋊Q₈	—	2	1	no	—
714	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
715	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
716	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
717	#127	C₂³×C₂₉	1	1	yes	characteristic
718	#126	—	2	2	no	—
719	#126	—	2	2	no	—
720	#126	—	2	2	no	—
721	#126	—	2	2	no	—
722	#126	—	2	2	no	—
723	#126	—	2	1	no	—
724	#125	—	2	1	no	—
725	#125	—	2	2	no	—
726	#125	—	2	2	no	—
727	#125	—	2	1	no	—
728	#125	—	2	2	no	—
729	#125	—	2	2	no	—
730	#125	C₂³×C₂₉	1	1	yes	characteristic
731	#125	C₂³×C₂₉	1	2	yes	—
732	#125	C₂³×C₂₉	1	2	yes	—
733	#125	C₂³×C₂₉	1	2	yes	—
734	#125	C₂³×C₂₉	1	2	yes	—
735	#124	—	2	1	no	—
736	#124	—	2	1	no	—
737	#124	C₂³×C₂₉	1	2	yes	—
738	#124	C₂³×C₂₉	1	1	yes	characteristic
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	1	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	1	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
758	C₂²⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
759	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
760	#121	—	2	2	no	—
761	#121	—	2	2	no	—
762	#121	—	2	1	no	—
763	#121	—	2	1	no	—
764	#121	—	2	2	no	—
765	#121	C₂³×C₂₉	1	2	yes	—
766	#121	C₂³×C₂₉	1	2	yes	—
767	#121	C₂³×C₂₉	1	1	yes	characteristic
768	#121	C₂³×C₂₉	1	2	yes	—
769	#120	—	2	2	no	—
770	#120	—	2	2	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
775	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
776	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
777	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
778	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
779	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
780	C₄×D₄	—	2	1	no	—
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	2	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	—	2	2	no	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
794	C₄×D₄	D₄×C₂₉	1	2	yes	—
795	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
796	C₄×D₄	C₂³×C₂₉	1	2	yes	—
797	C₄×D₄	C₂³×C₂₉	1	2	yes	—
798	C₄×D₄	C₂³×C₂₉	1	2	yes	—
799	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
801	C₄×D₄	C₂³×C₂₉	1	2	yes	—
802	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
803	C₄×D₄	C₂³×C₂₉	1	2	yes	—
804	#117	—	2	2	no	—
805	#117	—	2	1	no	—
806	#117	—	2	1	no	—
807	#117	—	2	2	no	—
808	#117	—	2	2	no	—
809	#117	D₄×C₂₉	1	2	yes	—
810	#117	D₄×C₂₉	1	1	yes	characteristic
811	#117	C₂³×C₂₉	1	1	yes	characteristic
812	#117	C₂³×C₂₉	1	2	yes	—
813	C₂×C₄⋊C₄	—	2	2	no	—
814	C₂×C₄⋊C₄	—	2	2	no	—
815	C₂×C₄⋊C₄	—	2	1	no	—
816	C₂×C₄⋊C₄	—	2	1	no	—
817	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
818	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
819	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
820	C₂×C₂²⋊C₄	—	2	2	no	—
821	C₂×C₂²⋊C₄	—	2	2	no	—
822	C₂×C₄²	—	2	1	no	—
823	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
824	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
825	#107	C₂³×C₂₉	1	1	yes	characteristic
826	#107	C₂³×C₂₉	1	2	yes	—
827	#107	C₂³×C₂₉	1	2	yes	—
828	#107	C₂³×C₂₉	1	2	yes	—
829	#107	C₂³×C₂₉	1	2	yes	—
830	#107	C₂³×C₂₉	1	2	yes	—
831	#107	C₂³×C₂₉	1	1	yes	characteristic
832	#106	C₂³×C₂₉	1	1	yes	characteristic
833	#106	C₂³×C₂₉	1	2	yes	—
834	#106	C₂³×C₂₉	1	2	yes	—
835	#106	C₂³×C₂₉	1	2	yes	—
836	#106	C₂³×C₂₉	1	2	yes	—
837	#106	C₂³×C₂₉	1	2	yes	—
838	#106	C₂³×C₂₉	1	1	yes	characteristic
839	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
840	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
841	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
842	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
843	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
844	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
845	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
846	#103	C₂³×C₂₉	1	2	yes	—
847	#103	C₂³×C₂₉	1	2	yes	—
848	#103	C₂³×C₂₉	1	2	yes	—
849	#103	C₂³×C₂₉	1	1	yes	characteristic
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	#102	C₂³×C₂₉	1	1	yes	characteristic
854	#102	C₂³×C₂₉	1	1	yes	characteristic
855	#102	C₂³×C₂₉	1	2	yes	—
856	#102	C₂³×C₂₉	1	2	yes	—
857	#102	C₂³×C₂₉	1	2	yes	—
858	#102	C₂³×C₂₉	1	2	yes	—
859	#102	C₂³×C₂₉	1	2	yes	—
860	#102	C₂³×C₂₉	1	2	yes	—
861	#102	C₂³×C₂₉	1	2	yes	—
862	#102	C₂³×C₂₉	1	1	yes	characteristic
863	#102	C₂³×C₂₉	1	1	yes	characteristic
864	#102	C₂³×C₂₉	1	2	yes	—
865	#102	C₂³×C₂₉	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
869	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
870	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
871	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
872	C₄×C₈	C₂³×C₂₉	1	2	yes	—
873	C₄×C₈	C₂³×C₂₉	1	2	yes	—
874	C₂₉	#62103	1	1	yes	characteristic, direct product factor, Sylow
875	C₂⁴	—	2	2	no	—
876	#41	—	2	4	no	—
877	#41	—	2	2	no	—
878	#41	—	4	1	no	—
879	#41	—	4	4	no	—
880	#41	—	8	2	no	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	1	no	—
884	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
885	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
886	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
887	C₂×D₄	—	2	4	no	—
888	C₂×D₄	—	2	1	no	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	4	2	no	—
897	C₂×D₄	—	4	4	no	—
898	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
899	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
900	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
901	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
902	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	2	no	—
914	C₂²×C₄	—	8	4	no	—
915	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
916	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
917	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
918	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
919	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
920	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
921	Q₁₆	—	4	1	no	—
922	SD₁₆	—	2	2	no	—
923	SD₁₆	—	4	1	no	—
924	SD₁₆	—	4	2	no	—
925	D₈	—	2	2	no	—
926	D₈	—	4	2	no	—
927	C₂×C₈	—	4	2	no	—
928	C₂×C₈	—	4	2	no	—
929	C₂×C₈	—	4	2	no	—
930	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
935	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	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	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
960	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
961	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
962	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
963	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
964	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
965	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
966	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
967	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
968	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
969	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
991	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
992	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	2	no	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	1	no	—
999	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1000	C₄²	C₂×D₄×C₂₉	1	2	yes	—
1001	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1002	C₄²	C₂×D₄×C₂₉	1	2	yes	—
1003	C₄²	C₂⁴×C₂₉	1	2	yes	—
1004	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1005	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1006	C₂³	—	2	1	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	2	2	no	—
1009	C₂³	—	4	4	no	—
1010	C₂³	—	4	4	no	—
1011	C₂³	—	8	2	no	—
1012	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1013	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
1014	Q₈	—	2	2	no	—
1015	Q₈	—	2	1	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	1	no	—
1018	Q₈	—	2	1	no	—
1019	Q₈	—	4	2	no	—
1020	Q₈	—	8	1	no	—
1021	Q₈	—	8	1	no	—
1022	D₄	—	2	4	no	—
1023	D₄	—	2	1	no	—
1024	D₄	—	2	2	no	—
1025	D₄	—	2	1	no	—
1026	D₄	—	2	1	no	—
1027	D₄	—	2	2	no	—
1028	D₄	—	4	4	no	—
1029	D₄	—	4	2	no	—
1030	D₄	—	4	4	no	—
1031	D₄	—	4	4	no	—
1032	D₄	—	4	2	no	—
1033	D₄	—	8	1	no	—
1034	D₄	—	8	2	no	—
1035	D₄	—	8	1	no	—
1036	D₄	C₂₉×#135	1	4	yes	—
1037	D₄	C₂₉×2₋¹⁺⁴	1	2	yes	—
1038	C₂×C₄	—	2	4	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	4	2	no	—
1054	C₂×C₄	—	4	1	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	4	2	no	—
1057	C₂×C₄	—	4	4	no	—
1058	C₂×C₄	—	4	4	no	—
1059	C₂×C₄	—	4	2	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	8	2	no	—
1062	C₂×C₄	—	8	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	2	no	—
1066	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1067	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1068	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1069	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1070	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1071	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1072	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1073	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1074	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1075	C₈	—	2	1	no	—
1076	C₈	—	2	1	no	—
1077	C₈	—	2	2	no	—
1078	C₈	—	2	2	no	—
1079	C₈	—	2	1	no	—
1080	C₈	—	2	1	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	2	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	2	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	2	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	8	8	no	—
1096	C₂²	C₂×C₂₉×#135	1	4	yes	—
1097	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
1098	C₄	—	2	1	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	2	1	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	2	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	2	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	2	no	—
1114	C₄	C₂×C₂₉×#135	1	2	yes	—
1115	C₄	C₂×C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
1116	C₄	C₂₉×#585	1	1	yes	characteristic
1117	C₂	—	2	4	no	—
1118	C₂	—	4	1	no	—
1119	C₂	—	4	2	no	—
1120	C₂	—	8	2	no	—
1121	C₂	—	8	1	no	—
1122	C₂	C₂₉×#3489	1	1	yes	characteristic
1123	C₂	C₂²×C₂₉×#135	1	1	yes	characteristic
1124	C₂	C₂₉×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3515	C₂	semidirect
2. C₂₉×#3481	C₂	semidirect
3. C₂₉×#3381	C₂	semidirect
4. C₂₉×#3380	C₂	semidirect
5. C₂₉×#3365	C₂	semidirect
6. C₂₉×#3361	C₂	semidirect
7. C₂₉×#3339	C₂	semidirect
8. C₂₉×#3338	C₂	semidirect
9. C₂₉×#3337	C₂	semidirect
10. C₂₉×#3335	C₂	semidirect
11. C₂₉×#3297	C₂	semidirect
12. C₂₉×#3296	C₂	semidirect
13. C₂₉×#3295	C₂	semidirect
14. C₂₉×#3294	C₂	semidirect
15. C₂₉×#3250	C₂	semidirect
16. C₂₉×#3247	C₂	semidirect
17. C₂₉×#3232	C₂	semidirect
18. C₂₉×#3228	C₂	semidirect
19. C₂₉×#3105	C₂	semidirect
20. C₂₉×#3102	C₂	semidirect
21. C₂₉×#3076	C₂	semidirect
22. C₂×C₂₉×#478	C₂	semidirect
23. C₂₉×#2988	C₂	semidirect
25. C₂₉×#557	C₂²	semidirect
29. C₂₉×#554	C₂²	semidirect
32. C₂₉×#553	C₂²	semidirect
35. C₂₉×#552	C₂²	semidirect
44. C₂₉×#533	C₂²	semidirect
48. C₂₉×#529	C₂²	semidirect
49. C₂₉×#529	C₂²	semidirect
50. C₂×C₂₉×#125	C₂²	semidirect
57. C₂₉×#500	C₂²	semidirect
58. C₂₉×#499	C₂²	semidirect
59. C₂₉×#499	C₂²	semidirect
60. C₂₉×#498	C₂²	semidirect
61. C₂₉×#488	C₂²	semidirect
62. C₂₉×#488	C₂²	semidirect
65. C₂₉×#485	C₂²	semidirect
66. C₂₉×#484	C₂²	semidirect
67. C₂₉×#484	C₂²	semidirect
68. C₂₉×#483	C₂²	semidirect
69. C₂₉×#482	C₂²	semidirect
70. C₂₉×#482	C₂²	semidirect
71. C₂₉×#482	C₂²	semidirect
73. C₂₉×#481	C₂²	semidirect
75. C₂₉×#479	C₂²	semidirect
76. C₂₉×#479	C₂²	semidirect
77. C₂₉×#479	C₂²	semidirect
82. C₂₉×#478	C₂²	semidirect
83. C₂₉×#478	C₂²	semidirect
84. C₂₉×#478	C₂²	semidirect
85. C₂₉×#478	C₂²	semidirect
86. C₂₉×#478	C₂²	semidirect
87. C₂₉×#478	C₂²	semidirect
88. C₂₉×#477	C₂²	semidirect
89. C₂₉×#477	C₂²	semidirect
91. C₂₉×#476	C₂²	semidirect
92. C₂₉×#475	C₂²	semidirect
94. C₂₉×#467	C₂²	semidirect
96. C₂₉×#466	C₂²	semidirect
98. C₂₉×#465	C₂²	semidirect
99. C₂₉×#465	C₂²	semidirect
100. C₂₉×#464	C₂²	semidirect
101. C₂₉×#464	C₂²	semidirect
103. C₂₉×#463	C₂²	semidirect
104. C₂₉×#463	C₂²	semidirect
111. C₈×Q₈×C₂₉	C₂²	semidirect
112. C₈×Q₈×C₂₉	C₂²	semidirect
113. C₄×Q₁₆×C₂₉	C₂²	semidirect
116. C₄×SD₁₆×C₂₉	C₂²	semidirect
117. C₄×SD₁₆×C₂₉	C₂²	semidirect
120. C₄×D₈×C₂₉	C₂²	semidirect
123. C₈×D₄×C₂₉	C₂²	semidirect
124. C₈×D₄×C₂₉	C₂²	semidirect
125. C₂₉×#431	C₂²	semidirect
126. C₂₉×#431	C₂²	semidirect
127. C₂₉×#427	C₂²	semidirect
128. C₂×C₂₉×#107	C₂²	semidirect
129. C₂×C₂₉×#106	C₂²	semidirect
130. C₂×C₂₉×C₄⋊C₈	C₂²	semidirect
131. C₂×C₂₉×C₄⋊C₈	C₂²	semidirect
443. #62103	C₂₉	direct (N × H)
519. #3515	C₂×C₂₉	semidirect
520. #3481	C₂×C₂₉	semidirect
521. #3381	C₂×C₂₉	semidirect
522. #3380	C₂×C₂₉	semidirect
523. #3365	C₂×C₂₉	semidirect
524. #3361	C₂×C₂₉	semidirect
525. #3339	C₂×C₂₉	semidirect
526. #3338	C₂×C₂₉	semidirect
527. #3337	C₂×C₂₉	semidirect
528. #3335	C₂×C₂₉	semidirect
529. #3297	C₂×C₂₉	semidirect
530. #3296	C₂×C₂₉	semidirect
531. #3295	C₂×C₂₉	semidirect
532. #3294	C₂×C₂₉	semidirect
533. #3250	C₂×C₂₉	semidirect
534. #3247	C₂×C₂₉	semidirect
535. #3232	C₂×C₂₉	semidirect
536. #3228	C₂×C₂₉	semidirect
537. #3105	C₂×C₂₉	semidirect
538. #3102	C₂×C₂₉	semidirect
539. #3076	C₂×C₂₉	semidirect
540. C₂×#478	C₂×C₂₉	semidirect
541. #2988	C₂×C₂₉	semidirect
579. #557	C₂²×C₂₉	semidirect
583. #554	C₂²×C₂₉	semidirect
586. #553	C₂²×C₂₉	semidirect
589. #552	C₂²×C₂₉	semidirect
598. #533	C₂²×C₂₉	semidirect
602. #529	C₂²×C₂₉	semidirect
603. #529	C₂²×C₂₉	semidirect
604. C₂×#125	C₂²×C₂₉	semidirect
611. #500	C₂²×C₂₉	semidirect
612. #499	C₂²×C₂₉	semidirect
613. #499	C₂²×C₂₉	semidirect
614. #498	C₂²×C₂₉	semidirect
615. #488	C₂²×C₂₉	semidirect
616. #488	C₂²×C₂₉	semidirect
619. #485	C₂²×C₂₉	semidirect
620. #484	C₂²×C₂₉	semidirect
621. #484	C₂²×C₂₉	semidirect
622. #483	C₂²×C₂₉	semidirect
623. #482	C₂²×C₂₉	semidirect
624. #482	C₂²×C₂₉	semidirect
625. #482	C₂²×C₂₉	semidirect
627. #481	C₂²×C₂₉	semidirect
629. #479	C₂²×C₂₉	semidirect
630. #479	C₂²×C₂₉	semidirect
631. #479	C₂²×C₂₉	semidirect
636. #478	C₂²×C₂₉	semidirect
637. #478	C₂²×C₂₉	semidirect
638. #478	C₂²×C₂₉	semidirect
639. #478	C₂²×C₂₉	semidirect
640. #478	C₂²×C₂₉	semidirect
641. #478	C₂²×C₂₉	semidirect
642. #477	C₂²×C₂₉	semidirect
643. #477	C₂²×C₂₉	semidirect
645. #476	C₂²×C₂₉	semidirect
646. #475	C₂²×C₂₉	semidirect
648. #467	C₂²×C₂₉	semidirect
650. #466	C₂²×C₂₉	semidirect
652. #465	C₂²×C₂₉	semidirect
653. #465	C₂²×C₂₉	semidirect
654. #464	C₂²×C₂₉	semidirect
655. #464	C₂²×C₂₉	semidirect
657. #463	C₂²×C₂₉	semidirect
658. #463	C₂²×C₂₉	semidirect
665. C₈×Q₈	C₂²×C₂₉	semidirect
666. C₈×Q₈	C₂²×C₂₉	semidirect
667. C₄×Q₁₆	C₂²×C₂₉	semidirect
670. C₄×SD₁₆	C₂²×C₂₉	semidirect
671. C₄×SD₁₆	C₂²×C₂₉	semidirect
674. C₄×D₈	C₂²×C₂₉	semidirect
677. C₈×D₄	C₂²×C₂₉	semidirect
678. C₈×D₄	C₂²×C₂₉	semidirect
679. #431	C₂²×C₂₉	semidirect
680. #431	C₂²×C₂₉	semidirect
681. #427	C₂²×C₂₉	semidirect
682. C₂×#107	C₂²×C₂₉	semidirect
683. C₂×#106	C₂²×C₂₉	semidirect
684. C₂×C₄⋊C₈	C₂²×C₂₉	semidirect
685. C₂×C₄⋊C₈	C₂²×C₂₉	semidirect
874. C₂₉	#62103	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×#3515	2
C₂₉×#3481	2
C₂₉×#3381	2
C₂₉×#3380	2
C₂₉×#3365	2
C₂₉×#3361	2
C₂₉×#3339	2
C₂₉×#3338	2
C₂₉×#3337	2
C₂₉×#3335	2
C₂₉×#3297	2
C₂₉×#3296	2
C₂₉×#3295	2
C₂₉×#3294	2
C₂₉×#3250	2
C₂₉×#3247	2
C₂₉×#3232	2
C₂₉×#3228	2
C₂₉×#3105	2
C₂₉×#3102	2
C₂₉×#3076	2
C₂×C₂₉×#478	2
C₂₉×#2988	2
#62103	29

Subgroups — C29×#62103 #20357003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#62103 #20357003