Subgroups — C₂₉×#62122 #20357022

Order 7424.

1780 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×#3518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3385	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#3373	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#3356	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#3350	C₂	1	2	yes	maximal, complemented
10	C₂₉×#3347	C₂	1	2	yes	maximal, complemented
11	C₂₉×#3325	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#3324	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#3319	C₂	1	2	yes	maximal, complemented
14	C₂₉×#3311	C₂	1	2	yes	maximal, complemented
15	C₂₉×#3256	C₂	1	2	yes	maximal, complemented
16	C₂₉×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₉×#3240	C₂	1	2	yes	maximal, complemented
18	C₂₉×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₉×#3114	C₂	1	2	yes	maximal, complemented
20	C₂₉×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₉×#3077	C₂	1	2	yes	maximal, complemented
22	C₂₉×#3076	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₉×#2989	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₉×#559	C₂²	1	1	yes	characteristic
25	Q₈²×C₂₉	C₂²	1	1	yes	characteristic, complemented
26	C₂₉×#556	—	2	1	no	—
27	C₂₉×#556	—	2	2	no	—
28	C₂₉×#556	C₂²	1	1	yes	characteristic
29	C₂₉×#556	C₂²	1	2	yes	complemented
30	C₂₉×#555	C₂²	1	1	yes	characteristic
31	C₂₉×#555	C₂²	1	2	yes	complemented
32	C₂₉×#554	C₂²	1	1	yes	characteristic
33	C₂₉×#554	C₂²	1	1	yes	characteristic
34	C₂₉×#553	—	2	1	no	—
35	C₂₉×#553	C₂²	1	2	yes	—
36	C₂₉×#551	—	2	2	no	—
37	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
38	C₂₉×#548	—	2	1	no	—
39	C₂₉×#546	—	2	1	no	—
40	C₂₉×#546	C₂²	1	2	yes	—
41	D₄²×C₂₉	C₂²	1	1	yes	characteristic
42	C₂₉×#542	—	2	1	no	—
43	C₂₉×#542	—	2	2	no	—
44	C₂₉×#533	C₂²	1	1	yes	characteristic, complemented
45	C₂₉×#533	C₂²	1	2	yes	complemented
46	C₂₉×#532	C₂²	1	1	yes	characteristic
47	C₂₉×#529	—	2	1	no	—
48	C₂₉×#529	C₂²	1	2	yes	—
49	C₂₉×#529	C₂²	1	1	yes	characteristic, complemented
50	C₂₉×#529	C₂²	1	2	yes	complemented
51	C₂₉×#525	—	2	2	no	—
52	C₂₉×#519	—	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×#501	C₂²	1	2	yes	complemented
58	C₂₉×#501	C₂²	1	2	yes	complemented
59	C₂₉×#500	C₂²	1	1	yes	characteristic, complemented
60	C₂₉×#498	C₂²	1	1	yes	characteristic, complemented
61	C₂₉×#489	C₂²	1	2	yes	complemented
62	C₂₉×#489	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	2	yes	complemented
66	C₂₉×#485	C₂²	1	2	yes	complemented
67	C₂₉×#485	C₂²	1	1	yes	characteristic, complemented
68	C₂₉×#483	C₂²	1	2	yes	complemented
69	C₂₉×#482	C₂²	1	2	yes	—
70	C₂₉×#482	C₂²	1	2	yes	—
71	C₂₉×#482	C₂²	1	2	yes	complemented
72	C₂₉×#482	C₂²	1	2	yes	complemented
73	C₂₉×#482	C₂²	1	1	yes	characteristic, complemented
74	C₂₉×#480	C₂²	1	2	yes	complemented
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	1	yes	characteristic
80	C₂₉×#478	C₂²	1	2	yes	complemented
81	C₂₉×#478	C₂²	1	2	yes	complemented
82	C₂₉×#478	C₂²	1	2	yes	complemented
83	C₂₉×#478	C₂²	1	2	yes	complemented
84	C₂₉×#477	C₂²	1	1	yes	characteristic, complemented
85	C₂₉×#477	C₂²	1	1	yes	characteristic, complemented
86	C₂₉×#476	C₂²	1	2	yes	—
87	C₂₉×#476	C₂²	1	1	yes	characteristic
88	C₂₉×#476	C₂²	1	1	yes	characteristic, complemented
89	C₂₉×#476	C₂²	1	2	yes	complemented
90	C₂₉×#475	C₂²	1	1	yes	characteristic, complemented
91	C₂₉×#474	C₂²	1	2	yes	—
92	C₂₉×#474	C₂²	1	1	yes	characteristic
93	C₂₉×#474	C₂²	1	2	yes	complemented
94	C₂₉×#470	C₂²	1	2	yes	complemented
95	C₂₉×#469	C₂²	1	2	yes	—
96	C₂₉×#468	C₂²	1	2	yes	—
97	C₂₉×#468	C₂²	1	2	yes	complemented
98	C₂₉×#466	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	C₂₉×#446	C₂²	1	1	yes	characteristic, complemented
112	C₂₉×#446	C₂²	1	1	yes	characteristic, complemented
113	C₂₉×#442	C₂²	1	2	yes	—
114	C₂₉×#442	C₂²	1	2	yes	complemented
115	C₂₉×#440	C₂²	1	2	yes	—
116	C₂₉×#440	C₂²	1	2	yes	complemented
117	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
121	C₂₉×#436	C₂²	1	1	yes	characteristic
122	C₂₉×#436	C₂²	1	1	yes	characteristic
123	C₂₉×#435	C₂²	1	2	yes	complemented
124	C₂₉×#435	C₂²	1	2	yes	complemented
125	C₂₉×#432	C₂²	1	2	yes	complemented
126	C₂₉×#431	C₂²	1	1	yes	characteristic, complemented
127	C₂₉×#428	C₂²	1	2	yes	complemented
128	C₂₉×#428	C₂²	1	2	yes	complemented
129	C₂₉×#427	C₂²	1	2	yes	complemented
130	C₂₉×#423	C₂²	1	2	yes	complemented
131	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
132	C₂₉×#418	C₂²	1	2	yes	—
133	C₂₉×#418	C₂²	1	2	yes	—
134	C₂₉×#416	C₂²	1	2	yes	—
135	C₂×#41×C₂₉	—	2	1	no	—
136	C₂×#41×C₂₉	D₄	1	1	yes	characteristic
137	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₂₉	—	2	1	no	—
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	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
149	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
150	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
151	C₂₉×C₄⋊Q₈	—	2	1	no	—
152	C₂₉×C₄⋊Q₈	—	2	2	no	—
153	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
154	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
156	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₂₉×#127	C₂³	1	1	yes	characteristic
159	C₂₉×#126	—	2	2	no	—
160	C₂₉×#126	—	2	2	no	—
161	C₂₉×#126	—	2	2	no	—
162	C₂₉×#126	—	2	2	no	—
163	C₂₉×#126	—	2	2	no	—
164	C₂₉×#126	—	2	1	no	—
165	C₂₉×#126	—	2	2	no	—
166	C₂₉×#125	—	2	1	no	—
167	C₂₉×#125	C₂³	1	2	yes	—
168	C₂₉×#125	C₂³	1	1	yes	characteristic
169	C₂₉×#125	C₂³	1	2	yes	—
170	C₂₉×#124	—	2	1	no	—
171	C₂₉×#124	—	2	1	no	—
172	C₂₉×#124	—	2	2	no	—
173	C₂₉×#124	—	2	2	no	—
174	C₂₉×#124	—	2	2	no	—
175	C₂₉×#124	—	2	2	no	—
176	C₂₉×#124	—	2	1	no	—
177	C₂₉×#124	C₂³	1	1	yes	characteristic
178	C₂₉×#124	C₂³	1	2	yes	—
179	C₂₉×#123	—	2	2	no	—
180	C₂₉×#123	—	2	2	no	—
181	C₂₉×#123	—	2	1	no	—
182	C₂₉×#123	—	2	2	no	—
183	C₂₉×#123	—	2	2	no	—
184	C₂₉×#123	—	2	2	no	—
185	C₂₉×C₂²⋊Q₈	—	2	1	no	—
186	C₂₉×C₂²⋊Q₈	—	2	2	no	—
187	C₂₉×C₂²⋊Q₈	—	2	1	no	—
188	C₂₉×C₂²⋊Q₈	—	2	1	no	—
189	C₂₉×C₂²⋊Q₈	—	2	2	no	—
190	C₂₉×C₂²⋊Q₈	—	2	2	no	—
191	C₂₉×C₂²⋊Q₈	—	2	1	no	—
192	C₂₉×C₂²⋊Q₈	—	2	2	no	—
193	C₂₉×C₂²⋊Q₈	—	2	2	no	—
194	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₂₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
196	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₂₉×#121	—	2	2	no	—
198	C₂₉×#121	—	2	1	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	2	no	—
212	C₄×Q₈×C₂₉	—	2	1	no	—
213	C₄×Q₈×C₂₉	—	2	2	no	—
214	C₄×Q₈×C₂₉	—	2	1	no	—
215	C₄×Q₈×C₂₉	—	2	2	no	—
216	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
217	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
220	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
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	1	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	1	no	—
231	C₄×D₄×C₂₉	—	2	2	no	—
232	C₄×D₄×C₂₉	—	2	2	no	—
233	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
234	C₄×D₄×C₂₉	D₄	1	2	yes	—
235	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₂₉	C₂³	1	2	yes	—
238	C₄×D₄×C₂₉	C₂³	1	2	yes	—
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	C₄×D₄×C₂₉	C₂³	1	2	yes	—
243	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
244	C₂₉×#117	—	2	1	no	—
245	C₂₉×#117	—	2	2	no	—
246	C₂₉×#117	—	2	1	no	—
247	C₂₉×#117	—	2	1	no	—
248	C₂₉×#117	—	2	2	no	—
249	C₂₉×#117	—	2	2	no	—
250	C₂₉×#117	D₄	1	2	yes	—
251	C₂₉×#117	D₄	1	1	yes	characteristic
252	C₂₉×#117	C₂³	1	1	yes	characteristic
253	C₂₉×#117	C₂³	1	2	yes	—
254	C₂₉×#117	C₂³	1	2	yes	—
255	C₂₉×#117	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
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	1	yes	characteristic
262	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
263	C₂₉×#107	C₂³	1	2	yes	—
264	C₂₉×#107	C₂³	1	2	yes	—
265	C₂₉×#107	C₂³	1	1	yes	characteristic
266	C₂₉×#107	C₂³	1	2	yes	—
267	C₂₉×#107	C₂³	1	2	yes	—
268	C₂₉×#107	C₂³	1	1	yes	characteristic
269	C₂₉×#107	C₂³	1	2	yes	—
270	C₂₉×#106	C₂³	1	2	yes	—
271	C₂₉×#106	C₂³	1	2	yes	—
272	C₂₉×#106	C₂³	1	1	yes	characteristic
273	C₂₉×#106	C₂³	1	2	yes	—
274	C₂₉×#106	C₂³	1	2	yes	—
275	C₂₉×#106	C₂³	1	1	yes	characteristic
276	C₂₉×#106	C₂³	1	2	yes	—
277	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
280	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
281	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
282	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₂₉×#103	C₂³	1	1	yes	characteristic
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	2	yes	—
289	C₂₉×#103	C₂³	1	2	yes	—
290	C₂₉×#103	C₂³	1	2	yes	—
291	C₂₉×#102	C₂³	1	1	yes	characteristic
292	C₂₉×#102	C₂³	1	1	yes	characteristic
293	C₂₉×#102	C₂³	1	1	yes	characteristic
294	C₂₉×#102	C₂³	1	1	yes	characteristic
295	C₂₉×#102	C₂³	1	2	yes	—
296	C₂₉×#102	C₂³	1	2	yes	—
297	C₂₉×#102	C₂³	1	2	yes	—
298	C₂₉×#102	C₂³	1	2	yes	—
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	1	yes	characteristic
305	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₂₉×#97	C₂³	1	2	yes	—
309	C₂₉×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
312	C₂⁴×C₂₉	—	2	2	no	—
313	#41×C₂₉	—	2	2	no	—
314	#41×C₂₉	—	4	2	no	—
315	#41×C₂₉	—	4	1	no	—
316	#41×C₂₉	—	8	2	no	—
317	C₂×Q₈×C₂₉	—	2	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	—	4	4	no	—
323	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₂₉	—	2	4	no	—
327	C₂×D₄×C₂₉	—	2	1	no	—
328	C₂×D₄×C₂₉	—	2	2	no	—
329	C₂×D₄×C₂₉	—	2	2	no	—
330	C₂×D₄×C₂₉	—	2	1	no	—
331	C₂×D₄×C₂₉	—	2	2	no	—
332	C₂×D₄×C₂₉	—	2	2	no	—
333	C₂×D₄×C₂₉	—	2	1	no	—
334	C₂×D₄×C₂₉	—	2	1	no	—
335	C₂×D₄×C₂₉	—	4	2	no	—
336	C₂×D₄×C₂₉	—	4	4	no	—
337	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
338	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
340	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
341	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
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	2	no	—
347	C₂²×C₄×C₂₉	—	2	1	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	1	yes	characteristic
353	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
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	2	no	—
361	SD₁₆×C₂₉	—	4	1	no	—
362	D₈×C₂₉	—	2	2	no	—
363	D₈×C₂₉	—	4	2	no	—
364	M₁₆×C₂₉	—	4	2	no	—
365	M₁₆×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	2	yes	—
369	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
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	1	no	—
374	C₄⋊C₄×C₂₉	—	2	2	no	—
375	C₄⋊C₄×C₂₉	—	2	2	no	—
376	C₄⋊C₄×C₂₉	—	2	1	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	1	no	—
381	C₄⋊C₄×C₂₉	—	2	2	no	—
382	C₄⋊C₄×C₂₉	—	2	1	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	1	no	—
387	C₄⋊C₄×C₂₉	—	2	2	no	—
388	C₄⋊C₄×C₂₉	—	2	2	no	—
389	C₄⋊C₄×C₂₉	—	2	1	no	—
390	C₄⋊C₄×C₂₉	—	2	2	no	—
391	C₄⋊C₄×C₂₉	—	2	1	no	—
392	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
393	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
403	C₂²⋊C₄×C₂₉	—	2	2	no	—
404	C₂²⋊C₄×C₂₉	—	2	1	no	—
405	C₂²⋊C₄×C₂₉	—	2	2	no	—
406	C₂²⋊C₄×C₂₉	—	2	2	no	—
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	1	no	—
411	C₂²⋊C₄×C₂₉	—	2	2	no	—
412	C₂²⋊C₄×C₂₉	—	2	2	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	1	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	2	no	—
421	C₂²⋊C₄×C₂₉	—	2	2	no	—
422	C₂²⋊C₄×C₂₉	—	2	1	no	—
423	C₂²⋊C₄×C₂₉	—	2	2	no	—
424	C₂²⋊C₄×C₂₉	—	2	1	no	—
425	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
428	C₄²×C₂₉	—	2	1	no	—
429	C₄²×C₂₉	—	2	1	no	—
430	C₄²×C₂₉	—	2	1	no	—
431	C₄²×C₂₉	—	2	2	no	—
432	C₄²×C₂₉	—	2	2	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	#62122	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	2	yes	—
451	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
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	4	no	—
458	Q₈×C₂₉	—	4	2	no	—
459	Q₈×C₂₉	—	8	2	no	—
460	Q₈×C₂₉	—	8	1	no	—
461	Q₈×C₂₉	—	8	1	no	—
462	D₄×C₂₉	—	2	2	no	—
463	D₄×C₂₉	—	2	1	no	—
464	D₄×C₂₉	—	2	2	no	—
465	D₄×C₂₉	—	2	1	no	—
466	D₄×C₂₉	—	2	1	no	—
467	D₄×C₂₉	—	2	2	no	—
468	D₄×C₂₉	—	4	2	no	—
469	D₄×C₂₉	—	4	4	no	—
470	D₄×C₂₉	—	4	2	no	—
471	D₄×C₂₉	—	4	4	no	—
472	D₄×C₂₉	—	4	2	no	—
473	D₄×C₂₉	—	8	1	no	—
474	D₄×C₂₉	—	8	2	no	—
475	D₄×C₂₉	—	8	1	no	—
476	D₄×C₂₉	—	8	2	no	—
477	D₄×C₂₉	2₋¹⁺⁴	1	2	yes	—
478	C₂×C₄×C₂₉	—	2	2	no	—
479	C₂×C₄×C₂₉	—	2	2	no	—
480	C₂×C₄×C₂₉	—	2	1	no	—
481	C₂×C₄×C₂₉	—	2	1	no	—
482	C₂×C₄×C₂₉	—	2	2	no	—
483	C₂×C₄×C₂₉	—	2	1	no	—
484	C₂×C₄×C₂₉	—	2	2	no	—
485	C₂×C₄×C₂₉	—	2	1	no	—
486	C₂×C₄×C₂₉	—	2	1	no	—
487	C₂×C₄×C₂₉	—	2	1	no	—
488	C₂×C₄×C₂₉	—	2	2	no	—
489	C₂×C₄×C₂₉	—	2	1	no	—
490	C₂×C₄×C₂₉	—	2	1	no	—
491	C₂×C₄×C₂₉	—	2	2	no	—
492	C₂×C₄×C₂₉	—	4	2	no	—
493	C₂×C₄×C₂₉	—	4	2	no	—
494	C₂×C₄×C₂₉	—	4	1	no	—
495	C₂×C₄×C₂₉	—	4	2	no	—
496	C₂×C₄×C₂₉	—	4	2	no	—
497	C₂×C₄×C₂₉	—	4	4	no	—
498	C₂×C₄×C₂₉	—	4	4	no	—
499	C₂×C₄×C₂₉	—	4	2	no	—
500	C₂×C₄×C₂₉	—	4	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	2	yes	—
506	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
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	#3518	C₂×C₂₉	1	1	yes	characteristic, complemented
520	#3481	C₂×C₂₉	1	1	yes	characteristic, complemented
521	#3385	C₂×C₂₉	1	1	yes	characteristic, complemented
522	#3384	C₂×C₂₉	1	1	yes	characteristic, complemented
523	#3375	C₂×C₂₉	1	1	yes	characteristic, complemented
524	#3373	C₂×C₂₉	1	1	yes	characteristic, complemented
525	#3357	C₂×C₂₉	1	1	yes	characteristic, complemented
526	#3356	C₂×C₂₉	1	1	yes	characteristic, complemented
527	#3350	C₂×C₂₉	1	2	yes	complemented
528	#3347	C₂×C₂₉	1	2	yes	complemented
529	#3325	C₂×C₂₉	1	1	yes	characteristic, complemented
530	#3324	C₂×C₂₉	1	1	yes	characteristic, complemented
531	#3319	C₂×C₂₉	1	2	yes	complemented
532	#3311	C₂×C₂₉	1	2	yes	complemented
533	#3256	C₂×C₂₉	1	2	yes	complemented
534	#3247	C₂×C₂₉	1	1	yes	characteristic, complemented
535	#3240	C₂×C₂₉	1	2	yes	complemented
536	#3228	C₂×C₂₉	1	1	yes	characteristic, complemented
537	#3114	C₂×C₂₉	1	2	yes	complemented
538	#3102	C₂×C₂₉	1	1	yes	characteristic, complemented
539	#3077	C₂×C₂₉	1	2	yes	complemented
540	#3076	C₂×C₂₉	1	1	yes	characteristic, complemented
541	#2989	C₂×C₂₉	1	1	yes	characteristic, complemented
542	C₂²×C₂₉	—	2	2	no	—
543	C₂²×C₂₉	—	2	1	no	—
544	C₂²×C₂₉	—	2	1	no	—
545	C₂²×C₂₉	—	2	2	no	—
546	C₂²×C₂₉	—	2	2	no	—
547	C₂²×C₂₉	—	2	1	no	—
548	C₂²×C₂₉	—	2	2	no	—
549	C₂²×C₂₉	—	4	1	no	—
550	C₂²×C₂₉	—	4	1	no	—
551	C₂²×C₂₉	—	4	2	no	—
552	C₂²×C₂₉	—	4	1	no	—
553	C₂²×C₂₉	—	4	2	no	—
554	C₂²×C₂₉	—	4	1	no	—
555	C₂²×C₂₉	—	4	1	no	—
556	C₂²×C₂₉	—	4	2	no	—
557	C₂²×C₂₉	—	8	8	no	—
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	2	no	—
569	C₄×C₂₉	—	4	1	no	—
570	C₄×C₂₉	—	4	1	no	—
571	C₄×C₂₉	—	4	1	no	—
572	C₄×C₂₉	—	4	1	no	—
573	C₄×C₂₉	—	4	2	no	—
574	C₄×C₂₉	—	4	1	no	—
575	C₄×C₂₉	#575	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	Q₈²	C₂²×C₂₉	1	1	yes	characteristic, complemented
580	#556	—	2	1	no	—
581	#556	—	2	2	no	—
582	#556	C₂²×C₂₉	1	1	yes	characteristic
583	#556	C₂²×C₂₉	1	2	yes	complemented
584	#555	C₂²×C₂₉	1	1	yes	characteristic
585	#555	C₂²×C₂₉	1	2	yes	complemented
586	#554	C₂²×C₂₉	1	1	yes	characteristic
587	#554	C₂²×C₂₉	1	1	yes	characteristic
588	#553	—	2	1	no	—
589	#553	C₂²×C₂₉	1	2	yes	—
590	#551	—	2	2	no	—
591	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
592	#548	—	2	1	no	—
593	#546	—	2	1	no	—
594	#546	C₂²×C₂₉	1	2	yes	—
595	D₄²	C₂²×C₂₉	1	1	yes	characteristic
596	#542	—	2	1	no	—
597	#542	—	2	2	no	—
598	#533	C₂²×C₂₉	1	1	yes	characteristic, complemented
599	#533	C₂²×C₂₉	1	2	yes	complemented
600	#532	C₂²×C₂₉	1	1	yes	characteristic
601	#529	—	2	1	no	—
602	#529	C₂²×C₂₉	1	2	yes	—
603	#529	C₂²×C₂₉	1	1	yes	characteristic, complemented
604	#529	C₂²×C₂₉	1	2	yes	complemented
605	#525	—	2	2	no	—
606	#519	—	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	#501	C₂²×C₂₉	1	2	yes	complemented
612	#501	C₂²×C₂₉	1	2	yes	complemented
613	#500	C₂²×C₂₉	1	1	yes	characteristic, complemented
614	#498	C₂²×C₂₉	1	1	yes	characteristic, complemented
615	#489	C₂²×C₂₉	1	2	yes	complemented
616	#489	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	#485	C₂²×C₂₉	1	2	yes	complemented
621	#485	C₂²×C₂₉	1	2	yes	complemented
622	#483	C₂²×C₂₉	1	2	yes	complemented
623	#482	C₂²×C₂₉	1	2	yes	—
624	#482	C₂²×C₂₉	1	2	yes	—
625	#482	C₂²×C₂₉	1	1	yes	characteristic, complemented
626	#482	C₂²×C₂₉	1	2	yes	complemented
627	#482	C₂²×C₂₉	1	2	yes	complemented
628	#480	C₂²×C₂₉	1	2	yes	complemented
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	2	yes	—
633	#478	C₂²×C₂₉	1	1	yes	characteristic
634	#478	C₂²×C₂₉	1	2	yes	complemented
635	#478	C₂²×C₂₉	1	2	yes	complemented
636	#478	C₂²×C₂₉	1	2	yes	complemented
637	#478	C₂²×C₂₉	1	2	yes	complemented
638	#477	C₂²×C₂₉	1	1	yes	characteristic, complemented
639	#477	C₂²×C₂₉	1	1	yes	characteristic, complemented
640	#476	C₂²×C₂₉	1	1	yes	characteristic
641	#476	C₂²×C₂₉	1	2	yes	—
642	#476	C₂²×C₂₉	1	2	yes	complemented
643	#476	C₂²×C₂₉	1	1	yes	characteristic, complemented
644	#475	C₂²×C₂₉	1	1	yes	characteristic, complemented
645	#474	C₂²×C₂₉	1	1	yes	characteristic
646	#474	C₂²×C₂₉	1	2	yes	—
647	#474	C₂²×C₂₉	1	2	yes	complemented
648	#470	C₂²×C₂₉	1	2	yes	complemented
649	#469	C₂²×C₂₉	1	2	yes	—
650	#468	C₂²×C₂₉	1	2	yes	—
651	#468	C₂²×C₂₉	1	2	yes	complemented
652	#466	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	#446	C₂²×C₂₉	1	1	yes	characteristic, complemented
666	#446	C₂²×C₂₉	1	1	yes	characteristic, complemented
667	#442	C₂²×C₂₉	1	2	yes	—
668	#442	C₂²×C₂₉	1	2	yes	complemented
669	#440	C₂²×C₂₉	1	2	yes	—
670	#440	C₂²×C₂₉	1	2	yes	complemented
671	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
672	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
673	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
674	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
675	#436	C₂²×C₂₉	1	1	yes	characteristic
676	#436	C₂²×C₂₉	1	1	yes	characteristic
677	#435	C₂²×C₂₉	1	2	yes	complemented
678	#435	C₂²×C₂₉	1	2	yes	complemented
679	#432	C₂²×C₂₉	1	2	yes	complemented
680	#431	C₂²×C₂₉	1	1	yes	characteristic, complemented
681	#428	C₂²×C₂₉	1	2	yes	complemented
682	#428	C₂²×C₂₉	1	2	yes	complemented
683	#427	C₂²×C₂₉	1	2	yes	complemented
684	#423	C₂²×C₂₉	1	2	yes	complemented
685	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
686	#418	C₂²×C₂₉	1	2	yes	—
687	#418	C₂²×C₂₉	1	2	yes	—
688	#416	C₂²×C₂₉	1	2	yes	—
689	C₂×C₂₉	—	4	1	no	—
690	C₂×C₂₉	—	4	2	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	C₂×#575	1	1	yes	characteristic
696	C₂×C₂₉	#3585	1	1	yes	characteristic
697	C₂×#41	—	2	1	no	—
698	C₂×#41	D₄×C₂₉	1	1	yes	characteristic
699	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
700	C₂²×Q₈	—	2	1	no	—
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	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
711	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
712	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
713	C₄⋊Q₈	—	2	1	no	—
714	C₄⋊Q₈	—	2	2	no	—
715	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
716	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
717	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
718	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
719	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
720	#127	C₂³×C₂₉	1	1	yes	characteristic
721	#126	—	2	2	no	—
722	#126	—	2	2	no	—
723	#126	—	2	2	no	—
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#126	—	2	1	no	—
727	#126	—	2	2	no	—
728	#125	—	2	1	no	—
729	#125	C₂³×C₂₉	1	2	yes	—
730	#125	C₂³×C₂₉	1	1	yes	characteristic
731	#125	C₂³×C₂₉	1	2	yes	—
732	#124	—	2	1	no	—
733	#124	—	2	1	no	—
734	#124	—	2	2	no	—
735	#124	—	2	2	no	—
736	#124	—	2	2	no	—
737	#124	—	2	2	no	—
738	#124	—	2	1	no	—
739	#124	C₂³×C₂₉	1	2	yes	—
740	#124	C₂³×C₂₉	1	1	yes	characteristic
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	1	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
757	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
758	C₂²⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
759	#121	—	2	2	no	—
760	#121	—	2	1	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	2	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	2	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	2	no	—
778	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
779	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
783	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
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	1	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
796	C₄×D₄	D₄×C₂₉	1	2	yes	—
797	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
798	C₄×D₄	C₂³×C₂₉	1	2	yes	—
799	C₄×D₄	C₂³×C₂₉	1	2	yes	—
800	C₄×D₄	C₂³×C₂₉	1	2	yes	—
801	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
802	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
803	C₄×D₄	C₂³×C₂₉	1	2	yes	—
804	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
805	C₄×D₄	C₂³×C₂₉	1	2	yes	—
806	#117	—	2	1	no	—
807	#117	—	2	2	no	—
808	#117	—	2	1	no	—
809	#117	—	2	1	no	—
810	#117	—	2	2	no	—
811	#117	—	2	2	no	—
812	#117	D₄×C₂₉	1	2	yes	—
813	#117	D₄×C₂₉	1	1	yes	characteristic
814	#117	C₂³×C₂₉	1	1	yes	characteristic
815	#117	C₂³×C₂₉	1	2	yes	—
816	#117	C₂³×C₂₉	1	2	yes	—
817	#117	C₂³×C₂₉	1	2	yes	—
818	C₂×C₄⋊C₄	—	2	1	no	—
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	2	yes	—
826	#107	C₂³×C₂₉	1	2	yes	—
827	#107	C₂³×C₂₉	1	1	yes	characteristic
828	#107	C₂³×C₂₉	1	2	yes	—
829	#107	C₂³×C₂₉	1	2	yes	—
830	#107	C₂³×C₂₉	1	1	yes	characteristic
831	#107	C₂³×C₂₉	1	2	yes	—
832	#106	C₂³×C₂₉	1	2	yes	—
833	#106	C₂³×C₂₉	1	2	yes	—
834	#106	C₂³×C₂₉	1	1	yes	characteristic
835	#106	C₂³×C₂₉	1	2	yes	—
836	#106	C₂³×C₂₉	1	2	yes	—
837	#106	C₂³×C₂₉	1	1	yes	characteristic
838	#106	C₂³×C₂₉	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
853	#102	C₂³×C₂₉	1	2	yes	—
854	#102	C₂³×C₂₉	1	2	yes	—
855	#102	C₂³×C₂₉	1	1	yes	characteristic
856	#102	C₂³×C₂₉	1	1	yes	characteristic
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	1	yes	characteristic
862	#102	C₂³×C₂₉	1	1	yes	characteristic
863	#102	C₂³×C₂₉	1	2	yes	—
864	#102	C₂³×C₂₉	1	2	yes	—
865	#102	C₂³×C₂₉	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
867	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
868	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
870	#97	C₂³×C₂₉	1	2	yes	—
871	#97	C₂³×C₂₉	1	2	yes	—
872	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
873	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
874	C₂₉	#62122	1	1	yes	characteristic, direct product factor, Sylow
875	C₂⁴	—	2	2	no	—
876	#41	—	2	2	no	—
877	#41	—	4	2	no	—
878	#41	—	4	1	no	—
879	#41	—	8	2	no	—
880	C₂×Q₈	—	2	2	no	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	2	2	no	—
883	C₂×Q₈	—	2	1	no	—
884	C₂×Q₈	—	2	1	no	—
885	C₂×Q₈	—	4	4	no	—
886	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
887	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
888	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
889	C₂×D₄	—	2	4	no	—
890	C₂×D₄	—	2	1	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	2	no	—
893	C₂×D₄	—	2	1	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	4	2	no	—
899	C₂×D₄	—	4	4	no	—
900	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
901	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
902	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
903	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
904	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
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	2	no	—
910	C₂²×C₄	—	2	1	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	1	yes	characteristic
916	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
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	2	no	—
924	SD₁₆	—	4	1	no	—
925	D₈	—	2	2	no	—
926	D₈	—	4	2	no	—
927	M₁₆	—	4	2	no	—
928	M₁₆	—	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	1	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
956	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
957	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
958	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
959	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
960	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
961	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
962	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
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	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	1	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	1	no	—
988	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
989	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
990	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	1	no	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	2	no	—
995	C₄²	—	2	2	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	1	yes	characteristic
1004	C₄²	C₂⁴×C₂₉	1	2	yes	—
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	2	yes	—
1013	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
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	4	no	—
1020	Q₈	—	4	2	no	—
1021	Q₈	—	8	1	no	—
1022	Q₈	—	8	2	no	—
1023	Q₈	—	8	1	no	—
1024	D₄	—	2	2	no	—
1025	D₄	—	2	1	no	—
1026	D₄	—	2	2	no	—
1027	D₄	—	2	1	no	—
1028	D₄	—	2	1	no	—
1029	D₄	—	2	2	no	—
1030	D₄	—	4	2	no	—
1031	D₄	—	4	4	no	—
1032	D₄	—	4	2	no	—
1033	D₄	—	4	4	no	—
1034	D₄	—	4	2	no	—
1035	D₄	—	8	1	no	—
1036	D₄	—	8	2	no	—
1037	D₄	—	8	2	no	—
1038	D₄	—	8	1	no	—
1039	D₄	C₂₉×2₋¹⁺⁴	1	2	yes	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	4	2	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	4	1	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	4	4	no	—
1060	C₂×C₄	—	4	4	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	4	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	2	yes	—
1068	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1069	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1070	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
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	1	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	2	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	2	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	8	8	no	—
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	2	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	2	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	C₂₉×#575	1	2	yes	—
1115	C₄	C₂×C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
1116	C₄	C₂₉×#585	1	1	yes	characteristic
1117	C₂	—	4	2	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	C₂×C₂₉×#575	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×#3518	C₂	semidirect
2. C₂₉×#3481	C₂	semidirect
3. C₂₉×#3385	C₂	semidirect
4. C₂₉×#3384	C₂	semidirect
5. C₂₉×#3375	C₂	semidirect
6. C₂₉×#3373	C₂	semidirect
7. C₂₉×#3357	C₂	semidirect
8. C₂₉×#3356	C₂	semidirect
9. C₂₉×#3350	C₂	semidirect
10. C₂₉×#3347	C₂	semidirect
11. C₂₉×#3325	C₂	semidirect
12. C₂₉×#3324	C₂	semidirect
13. C₂₉×#3319	C₂	semidirect
14. C₂₉×#3311	C₂	semidirect
15. C₂₉×#3256	C₂	semidirect
16. C₂₉×#3247	C₂	semidirect
17. C₂₉×#3240	C₂	semidirect
18. C₂₉×#3228	C₂	semidirect
19. C₂₉×#3114	C₂	semidirect
20. C₂₉×#3102	C₂	semidirect
21. C₂₉×#3077	C₂	semidirect
22. C₂₉×#3076	C₂	semidirect
23. C₂₉×#2989	C₂	semidirect
25. Q₈²×C₂₉	C₂²	semidirect
29. C₂₉×#556	C₂²	semidirect
31. C₂₉×#555	C₂²	semidirect
37. D₄×Q₈×C₂₉	C₂²	semidirect
44. C₂₉×#533	C₂²	semidirect
45. C₂₉×#533	C₂²	semidirect
49. C₂₉×#529	C₂²	semidirect
50. C₂₉×#529	C₂²	semidirect
57. C₂₉×#501	C₂²	semidirect
58. C₂₉×#501	C₂²	semidirect
59. C₂₉×#500	C₂²	semidirect
60. C₂₉×#498	C₂²	semidirect
61. C₂₉×#489	C₂²	semidirect
62. C₂₉×#489	C₂²	semidirect
65. C₂₉×#485	C₂²	semidirect
66. C₂₉×#485	C₂²	semidirect
67. C₂₉×#485	C₂²	semidirect
68. C₂₉×#483	C₂²	semidirect
71. C₂₉×#482	C₂²	semidirect
72. C₂₉×#482	C₂²	semidirect
73. C₂₉×#482	C₂²	semidirect
74. C₂₉×#480	C₂²	semidirect
75. C₂₉×#479	C₂²	semidirect
76. C₂₉×#479	C₂²	semidirect
77. C₂₉×#479	C₂²	semidirect
80. C₂₉×#478	C₂²	semidirect
81. C₂₉×#478	C₂²	semidirect
82. C₂₉×#478	C₂²	semidirect
83. C₂₉×#478	C₂²	semidirect
84. C₂₉×#477	C₂²	semidirect
85. C₂₉×#477	C₂²	semidirect
88. C₂₉×#476	C₂²	semidirect
89. C₂₉×#476	C₂²	semidirect
90. C₂₉×#475	C₂²	semidirect
93. C₂₉×#474	C₂²	semidirect
94. C₂₉×#470	C₂²	semidirect
97. C₂₉×#468	C₂²	semidirect
98. C₂₉×#466	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. C₂₉×#446	C₂²	semidirect
112. C₂₉×#446	C₂²	semidirect
114. C₂₉×#442	C₂²	semidirect
116. C₂₉×#440	C₂²	semidirect
117. C₄×Q₁₆×C₂₉	C₂²	semidirect
119. C₄×SD₁₆×C₂₉	C₂²	semidirect
123. C₂₉×#435	C₂²	semidirect
124. C₂₉×#435	C₂²	semidirect
125. C₂₉×#432	C₂²	semidirect
126. C₂₉×#431	C₂²	semidirect
127. C₂₉×#428	C₂²	semidirect
128. C₂₉×#428	C₂²	semidirect
129. C₂₉×#427	C₂²	semidirect
130. C₂₉×#423	C₂²	semidirect
131. C₂×C₂₉×C₄⋊C₈	C₂²	semidirect
443. #62122	C₂₉	direct (N × H)
519. #3518	C₂×C₂₉	semidirect
520. #3481	C₂×C₂₉	semidirect
521. #3385	C₂×C₂₉	semidirect
522. #3384	C₂×C₂₉	semidirect
523. #3375	C₂×C₂₉	semidirect
524. #3373	C₂×C₂₉	semidirect
525. #3357	C₂×C₂₉	semidirect
526. #3356	C₂×C₂₉	semidirect
527. #3350	C₂×C₂₉	semidirect
528. #3347	C₂×C₂₉	semidirect
529. #3325	C₂×C₂₉	semidirect
530. #3324	C₂×C₂₉	semidirect
531. #3319	C₂×C₂₉	semidirect
532. #3311	C₂×C₂₉	semidirect
533. #3256	C₂×C₂₉	semidirect
534. #3247	C₂×C₂₉	semidirect
535. #3240	C₂×C₂₉	semidirect
536. #3228	C₂×C₂₉	semidirect
537. #3114	C₂×C₂₉	semidirect
538. #3102	C₂×C₂₉	semidirect
539. #3077	C₂×C₂₉	semidirect
540. #3076	C₂×C₂₉	semidirect
541. #2989	C₂×C₂₉	semidirect
579. Q₈²	C₂²×C₂₉	semidirect
583. #556	C₂²×C₂₉	semidirect
585. #555	C₂²×C₂₉	semidirect
591. D₄×Q₈	C₂²×C₂₉	semidirect
598. #533	C₂²×C₂₉	semidirect
599. #533	C₂²×C₂₉	semidirect
603. #529	C₂²×C₂₉	semidirect
604. #529	C₂²×C₂₉	semidirect
611. #501	C₂²×C₂₉	semidirect
612. #501	C₂²×C₂₉	semidirect
613. #500	C₂²×C₂₉	semidirect
614. #498	C₂²×C₂₉	semidirect
615. #489	C₂²×C₂₉	semidirect
616. #489	C₂²×C₂₉	semidirect
619. #485	C₂²×C₂₉	semidirect
620. #485	C₂²×C₂₉	semidirect
621. #485	C₂²×C₂₉	semidirect
622. #483	C₂²×C₂₉	semidirect
625. #482	C₂²×C₂₉	semidirect
626. #482	C₂²×C₂₉	semidirect
627. #482	C₂²×C₂₉	semidirect
628. #480	C₂²×C₂₉	semidirect
629. #479	C₂²×C₂₉	semidirect
630. #479	C₂²×C₂₉	semidirect
631. #479	C₂²×C₂₉	semidirect
634. #478	C₂²×C₂₉	semidirect
635. #478	C₂²×C₂₉	semidirect
636. #478	C₂²×C₂₉	semidirect
637. #478	C₂²×C₂₉	semidirect
638. #477	C₂²×C₂₉	semidirect
639. #477	C₂²×C₂₉	semidirect
642. #476	C₂²×C₂₉	semidirect
643. #476	C₂²×C₂₉	semidirect
644. #475	C₂²×C₂₉	semidirect
647. #474	C₂²×C₂₉	semidirect
648. #470	C₂²×C₂₉	semidirect
651. #468	C₂²×C₂₉	semidirect
652. #466	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. #446	C₂²×C₂₉	semidirect
666. #446	C₂²×C₂₉	semidirect
668. #442	C₂²×C₂₉	semidirect
670. #440	C₂²×C₂₉	semidirect
671. C₄×Q₁₆	C₂²×C₂₉	semidirect
673. C₄×SD₁₆	C₂²×C₂₉	semidirect
677. #435	C₂²×C₂₉	semidirect
678. #435	C₂²×C₂₉	semidirect
679. #432	C₂²×C₂₉	semidirect
680. #431	C₂²×C₂₉	semidirect
681. #428	C₂²×C₂₉	semidirect
682. #428	C₂²×C₂₉	semidirect
683. #427	C₂²×C₂₉	semidirect
684. #423	C₂²×C₂₉	semidirect
685. C₂×C₄⋊C₈	C₂²×C₂₉	semidirect
874. C₂₉	#62122	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×#3518	2
C₂₉×#3481	2
C₂₉×#3385	2
C₂₉×#3384	2
C₂₉×#3375	2
C₂₉×#3373	2
C₂₉×#3357	2
C₂₉×#3356	2
C₂₉×#3350	2
C₂₉×#3347	2
C₂₉×#3325	2
C₂₉×#3324	2
C₂₉×#3319	2
C₂₉×#3311	2
C₂₉×#3256	2
C₂₉×#3247	2
C₂₉×#3240	2
C₂₉×#3228	2
C₂₉×#3114	2
C₂₉×#3102	2
C₂₉×#3077	2
C₂₉×#3076	2
C₂₉×#2989	2
#62122	29

Subgroups — C29×#62122 #20357022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#62122 #20357022