Subgroups — C₂₉×#61543 #20356443

Order 7424.

1884 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#3362	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#3350	C₂	1	2	yes	maximal, complemented
8	C₂₉×#3341	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#3329	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#3326	C₂	1	2	yes	maximal, complemented
11	C₂₉×#3325	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#3324	C₂	1	2	yes	maximal, complemented
13	D₄×SD₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#3265	C₂	1	2	yes	maximal, complemented
15	C₂₉×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#3179	C₂	1	2	yes	maximal, complemented
17	C₂₉×#3126	C₂	1	2	yes	maximal, complemented
18	C₂₉×#3118	C₂	1	2	yes	maximal, complemented
19	C₂₉×#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₉×#3101	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×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂²×SD₁₆×C₂₉	C₂²	1	2	yes	—
26	Q₈²×C₂₉	C₂²	1	1	yes	characteristic, complemented
27	C₂₉×#556	—	2	2	no	—
28	C₂₉×#556	—	2	1	no	—
29	C₂₉×#556	C₂²	1	1	yes	characteristic, complemented
30	C₂₉×#556	C₂²	1	2	yes	complemented
31	C₂₉×#555	—	2	1	no	—
32	C₂₉×#555	C₂²	1	1	yes	characteristic
33	C₂₉×#555	C₂²	1	1	yes	characteristic, complemented
34	C₂₉×#554	C₂²	1	1	yes	characteristic
35	C₂₉×#553	—	2	1	no	—
36	C₂₉×#553	C₂²	1	2	yes	—
37	C₂₉×#550	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
39	C₂₉×#548	C₂²	1	2	yes	complemented
40	C₂₉×#546	—	2	1	no	—
41	C₂₉×#546	—	2	2	no	—
42	D₄²×C₂₉	C₂²	1	2	yes	—
43	D₄²×C₂₉	C₂²	1	1	yes	characteristic
44	C₂₉×#542	—	2	2	no	—
45	C₂₉×#542	C₂²	1	2	yes	complemented
46	C₂₉×#540	C₂²	1	2	yes	—
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	C₂²	1	1	yes	characteristic
53	C₂₉×#525	—	2	1	no	—
54	C₂×C₂₉×#121	—	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, complemented
58	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
59	C₂₉×#501	C₂²	1	2	yes	complemented
60	C₂₉×#500	C₂²	1	1	yes	characteristic, complemented
61	C₂₉×#496	C₂²	1	2	yes	complemented
62	C₂₉×#492	C₂²	1	1	yes	characteristic, complemented
63	C₂₉×#488	C₂²	1	2	yes	complemented
64	C₂₉×#487	C₂²	1	1	yes	characteristic, complemented
65	C₂₉×#486	C₂²	1	1	yes	characteristic, complemented
66	C₂₉×#486	C₂²	1	2	yes	complemented
67	C₂₉×#485	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	2	yes	complemented
72	C₂₉×#482	C₂²	1	2	yes	complemented
73	C₂₉×#479	C₂²	1	2	yes	complemented
74	C₂₉×#479	C₂²	1	2	yes	complemented
75	C₂₉×#477	C₂²	1	1	yes	characteristic, complemented
76	C₂₉×#476	C₂²	1	1	yes	characteristic
77	C₂₉×#476	C₂²	1	1	yes	characteristic, complemented
78	C₂₉×#476	C₂²	1	1	yes	characteristic, complemented
79	C₂₉×#476	C₂²	1	2	yes	complemented
80	C₂₉×#474	C₂²	1	2	yes	—
81	C₂₉×#469	C₂²	1	2	yes	complemented
82	C₂₉×#468	C₂²	1	2	yes	complemented
83	C₂₉×#468	C₂²	1	2	yes	complemented
84	C₂₉×#468	C₂²	1	2	yes	complemented
85	C₂₉×#466	C₂²	1	2	yes	complemented
86	C₂₉×#465	C₂²	1	2	yes	complemented
87	C₂₉×#463	C₂²	1	2	yes	—
88	C₂₉×#463	C₂²	1	2	yes	complemented
89	C₂₉×#461	C₂²	1	1	yes	characteristic
90	C₂₉×#461	C₂²	1	1	yes	characteristic, complemented
91	C₂₉×#460	C₂²	1	2	yes	complemented
92	C₂₉×#460	C₂²	1	1	yes	characteristic, complemented
93	C₂₉×#460	C₂²	1	2	yes	complemented
94	C₂₉×#459	C₂²	1	1	yes	characteristic, complemented
95	C₂₉×#450	C₂²	1	2	yes	—
96	C₂₉×#450	C₂²	1	2	yes	—
97	C₂₉×#449	C₂²	1	2	yes	complemented
98	C₂₉×#448	C₂²	1	2	yes	complemented
99	C₂₉×#448	C₂²	1	2	yes	complemented
100	C₂₉×#447	C₂²	1	2	yes	—
101	C₂₉×#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
103	C₂₉×#442	C₂²	1	1	yes	characteristic
104	C₂₉×#442	C₂²	1	1	yes	characteristic, complemented
105	C₂₉×#440	C₂²	1	1	yes	characteristic
106	C₂₉×#440	C₂²	1	2	yes	—
107	C₂₉×#440	C₂²	1	2	yes	complemented
108	C₂₉×#440	C₂²	1	2	yes	complemented
109	C₂₉×#440	C₂²	1	1	yes	characteristic, complemented
110	C₂₉×#440	C₂²	1	2	yes	complemented
111	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	—
114	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	complemented
116	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	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	1	yes	characteristic, complemented
120	C₄×D₈×C₂₉	C₂²	1	2	yes	complemented
121	C₂₉×#436	C₂²	1	2	yes	complemented
122	C₂₉×#436	C₂²	1	1	yes	characteristic, complemented
123	C₂₉×#435	C₂²	1	2	yes	complemented
124	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
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	2	yes	complemented
130	C₂₉×#418	C₂²	1	1	yes	characteristic
131	C₂₉×#418	C₂²	1	2	yes	—
132	C₂₉×#417	C₂²	1	1	yes	characteristic, complemented
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	—	2	1	no	—
137	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
139	C₂²×D₄×C₂₉	—	2	1	no	—
140	C₂²×D₄×C₂₉	—	2	2	no	—
141	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
142	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₂₉	—	2	1	no	—
144	C₂₉×AGL(1,ℤ/8)	—	2	4	no	—
145	C₂×SD₁₆×C₂₉	—	2	8	no	—
146	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
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	1	yes	characteristic
153	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
155	C₂×D₈×C₂₉	C₂³	1	2	yes	—
156	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
157	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
158	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
159	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
160	C₂₉×C₄⋊Q₈	—	2	1	no	—
161	C₂₉×C₄⋊Q₈	—	2	1	no	—
162	C₂₉×C₄⋊Q₈	—	2	2	no	—
163	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₂₉×#127	C₂³	1	1	yes	characteristic
168	C₂₉×#127	C₂³	1	2	yes	—
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	—	2	2	no	—
174	C₂₉×#126	D₄	1	2	yes	—
175	C₂₉×#125	—	2	1	no	—
176	C₂₉×#125	D₄	1	1	yes	characteristic
177	C₂₉×#125	C₂³	1	2	yes	—
178	C₂₉×#124	—	2	2	no	—
179	C₂₉×#124	—	2	2	no	—
180	C₂₉×#124	—	2	2	no	—
181	C₂₉×#124	—	2	2	no	—
182	C₂₉×#124	—	2	2	no	—
183	C₂₉×#124	—	2	1	no	—
184	C₂₉×#124	D₄	1	1	yes	characteristic
185	C₂₉×#124	C₂³	1	2	yes	—
186	C₂₉×#123	—	2	2	no	—
187	C₂₉×#123	—	2	2	no	—
188	C₂₉×#123	—	2	2	no	—
189	C₂₉×#123	—	2	2	no	—
190	C₂₉×#123	D₄	1	2	yes	—
191	C₂₉×C₂²⋊Q₈	—	2	1	no	—
192	C₂₉×C₂²⋊Q₈	—	2	1	no	—
193	C₂₉×C₂²⋊Q₈	—	2	1	no	—
194	C₂₉×C₂²⋊Q₈	—	2	2	no	—
195	C₂₉×C₂²⋊Q₈	—	2	2	no	—
196	C₂₉×C₂²⋊Q₈	—	2	2	no	—
197	C₂₉×C₂²⋊Q₈	—	2	2	no	—
198	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
199	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₂₉×#121	—	2	2	no	—
202	C₂₉×#121	—	2	1	no	—
203	C₂₉×#121	—	2	1	no	—
204	C₂₉×#121	—	2	2	no	—
205	C₂₉×#121	—	2	1	no	—
206	C₂₉×#121	—	2	1	no	—
207	C₂₉×#121	—	2	1	no	—
208	C₂₉×#121	—	2	2	no	—
209	C₂₉×#121	—	2	2	no	—
210	C₂₉×#121	—	2	2	no	—
211	C₂₉×#121	—	2	2	no	—
212	C₂₉×#121	D₄	1	1	yes	characteristic
213	C₂₉×#121	C₂³	1	2	yes	—
214	C₂₉×#121	C₂³	1	2	yes	—
215	C₂₉×#121	C₂³	1	2	yes	—
216	C₂₉×#121	C₂³	1	2	yes	—
217	C₂₉×#120	—	2	2	no	—
218	C₂₉×#120	—	2	2	no	—
219	C₂₉×#120	—	2	2	no	—
220	C₄×Q₈×C₂₉	—	2	1	no	—
221	C₄×Q₈×C₂₉	—	2	2	no	—
222	C₄×Q₈×C₂₉	—	2	2	no	—
223	C₄×Q₈×C₂₉	—	2	2	no	—
224	C₄×Q₈×C₂₉	—	2	1	no	—
225	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
226	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
228	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
230	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
231	C₄×D₄×C₂₉	—	2	1	no	—
232	C₄×D₄×C₂₉	—	2	1	no	—
233	C₄×D₄×C₂₉	—	2	1	no	—
234	C₄×D₄×C₂₉	—	2	2	no	—
235	C₄×D₄×C₂₉	—	2	2	no	—
236	C₄×D₄×C₂₉	—	2	2	no	—
237	C₄×D₄×C₂₉	—	2	2	no	—
238	C₄×D₄×C₂₉	—	2	1	no	—
239	C₄×D₄×C₂₉	—	2	1	no	—
240	C₄×D₄×C₂₉	—	2	1	no	—
241	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₂₉	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	no	—
254	C₂₉×#117	—	2	1	no	—
255	C₂₉×#117	—	2	1	no	—
256	C₂₉×#117	—	2	2	no	—
257	C₂₉×#117	—	2	2	no	—
258	C₂₉×#117	—	2	1	no	—
259	C₂₉×#117	C₂³	1	2	yes	—
260	C₂₉×#117	C₂³	1	2	yes	—
261	C₂₉×#117	C₂³	1	1	yes	characteristic
262	C₂₉×#117	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
264	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
266	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₂₉	—	2	2	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	1	yes	characteristic
285	C₂₉×#103	C₂³	1	2	yes	—
286	C₂₉×#103	C₂³	1	2	yes	—
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	1	yes	characteristic
299	C₂₉×#102	C₂³	1	2	yes	—
300	C₂₉×#102	C₂³	1	2	yes	—
301	C₂₉×#102	C₂³	1	1	yes	characteristic
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	1	no	—
315	C₂⁴×C₂₉	—	2	2	no	—
316	#41×C₂₉	—	2	2	no	—
317	#41×C₂₉	—	4	1	no	—
318	#41×C₂₉	—	8	2	no	—
319	#41×C₂₉	—	8	2	no	—
320	C₂×Q₈×C₂₉	—	2	2	no	—
321	C₂×Q₈×C₂₉	—	2	1	no	—
322	C₂×Q₈×C₂₉	—	2	2	no	—
323	C₂×Q₈×C₂₉	—	2	1	no	—
324	C₂×Q₈×C₂₉	—	2	4	no	—
325	C₂×Q₈×C₂₉	—	4	2	no	—
326	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₂₉	—	2	4	no	—
330	C₂×D₄×C₂₉	—	2	2	no	—
331	C₂×D₄×C₂₉	—	2	1	no	—
332	C₂×D₄×C₂₉	—	2	2	no	—
333	C₂×D₄×C₂₉	—	2	2	no	—
334	C₂×D₄×C₂₉	—	2	2	no	—
335	C₂×D₄×C₂₉	—	2	2	no	—
336	C₂×D₄×C₂₉	—	2	2	no	—
337	C₂×D₄×C₂₉	—	2	1	no	—
338	C₂×D₄×C₂₉	—	2	1	no	—
339	C₂×D₄×C₂₉	—	2	2	no	—
340	C₂×D₄×C₂₉	—	2	1	no	—
341	C₂×D₄×C₂₉	—	2	2	no	—
342	C₂×D₄×C₂₉	—	4	2	no	—
343	C₂×D₄×C₂₉	—	4	1	no	—
344	C₂×D₄×C₂₉	—	8	2	no	—
345	C₂×D₄×C₂₉	—	8	4	no	—
346	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
348	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
349	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
351	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₂₉	—	2	2	no	—
353	C₂²×C₄×C₂₉	—	2	1	no	—
354	C₂²×C₄×C₂₉	—	2	1	no	—
355	C₂²×C₄×C₂₉	—	2	1	no	—
356	C₂²×C₄×C₂₉	—	2	1	no	—
357	C₂²×C₄×C₂₉	—	2	1	no	—
358	C₂²×C₄×C₂₉	—	2	1	no	—
359	C₂²×C₄×C₂₉	—	2	1	no	—
360	C₂²×C₄×C₂₉	—	2	2	no	—
361	C₂²×C₄×C₂₉	—	2	2	no	—
362	C₂²×C₄×C₂₉	—	2	2	no	—
363	C₂²×C₄×C₂₉	—	2	1	no	—
364	C₂²×C₄×C₂₉	—	8	2	no	—
365	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
369	SD₁₆×C₂₉	—	2	4	no	—
370	SD₁₆×C₂₉	—	2	2	no	—
371	SD₁₆×C₂₉	—	2	4	no	—
372	SD₁₆×C₂₉	—	2	4	no	—
373	SD₁₆×C₂₉	—	4	2	no	—
374	SD₁₆×C₂₉	—	4	2	no	—
375	SD₁₆×C₂₉	#41	1	4	yes	complemented
376	D₈×C₂₉	—	2	2	no	—
377	D₈×C₂₉	—	2	2	no	—
378	D₈×C₂₉	—	4	2	no	—
379	M₁₆×C₂₉	—	2	2	no	—
380	M₁₆×C₂₉	—	4	2	no	—
381	M₁₆×C₂₉	—	4	1	no	—
382	C₂×C₈×C₂₉	—	2	4	no	—
383	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
384	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
387	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
393	C₄⋊C₄×C₂₉	—	2	1	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	1	no	—
402	C₄⋊C₄×C₂₉	—	2	2	no	—
403	C₄⋊C₄×C₂₉	—	2	2	no	—
404	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
416	C₂²⋊C₄×C₂₉	—	2	2	no	—
417	C₂²⋊C₄×C₂₉	—	2	2	no	—
418	C₂²⋊C₄×C₂₉	—	2	2	no	—
419	C₂²⋊C₄×C₂₉	—	2	1	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	1	no	—
424	C₂²⋊C₄×C₂₉	—	2	2	no	—
425	C₂²⋊C₄×C₂₉	—	2	1	no	—
426	C₂²⋊C₄×C₂₉	—	2	2	no	—
427	C₂²⋊C₄×C₂₉	—	2	1	no	—
428	C₂²⋊C₄×C₂₉	—	2	1	no	—
429	C₂²⋊C₄×C₂₉	—	2	1	no	—
430	C₂²⋊C₄×C₂₉	—	2	2	no	—
431	C₂²⋊C₄×C₂₉	—	2	2	no	—
432	C₂²⋊C₄×C₂₉	—	2	2	no	—
433	C₂²⋊C₄×C₂₉	—	2	2	no	—
434	C₂²⋊C₄×C₂₉	—	2	2	no	—
435	C₂²⋊C₄×C₂₉	—	2	2	no	—
436	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
441	C₄²×C₂₉	—	2	1	no	—
442	C₄²×C₂₉	—	2	1	no	—
443	C₄²×C₂₉	—	2	1	no	—
444	C₄²×C₂₉	—	2	2	no	—
445	C₄²×C₂₉	—	2	2	no	—
446	C₄²×C₂₉	—	2	2	no	—
447	C₄²×C₂₉	—	2	2	no	—
448	C₄²×C₂₉	—	2	2	no	—
449	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
452	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
453	C₄²×C₂₉	C₂⁴	1	2	yes	—
454	#61543	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
455	C₂³×C₂₉	—	2	1	no	—
456	C₂³×C₂₉	—	2	1	no	—
457	C₂³×C₂₉	—	2	2	no	—
458	C₂³×C₂₉	—	2	1	no	—
459	C₂³×C₂₉	—	4	2	no	—
460	C₂³×C₂₉	—	4	4	no	—
461	C₂³×C₂₉	—	4	2	no	—
462	C₂³×C₂₉	—	8	1	no	—
463	C₂³×C₂₉	—	8	2	no	—
464	C₂³×C₂₉	—	8	2	no	—
465	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
466	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
467	Q₈×C₂₉	—	2	2	no	—
468	Q₈×C₂₉	—	2	1	no	—
469	Q₈×C₂₉	—	2	2	no	—
470	Q₈×C₂₉	—	2	2	no	—
471	Q₈×C₂₉	—	4	4	no	—
472	Q₈×C₂₉	—	8	1	no	—
473	Q₈×C₂₉	—	8	2	no	—
474	Q₈×C₂₉	—	8	1	no	—
475	Q₈×C₂₉	C₂×#41	1	2	yes	—
476	D₄×C₂₉	—	2	2	no	—
477	D₄×C₂₉	—	2	1	no	—
478	D₄×C₂₉	—	2	1	no	—
479	D₄×C₂₉	—	2	2	no	—
480	D₄×C₂₉	—	2	1	no	—
481	D₄×C₂₉	—	2	1	no	—
482	D₄×C₂₉	—	2	2	no	—
483	D₄×C₂₉	—	2	1	no	—
484	D₄×C₂₉	—	4	2	no	—
485	D₄×C₂₉	—	4	2	no	—
486	D₄×C₂₉	—	4	4	no	—
487	D₄×C₂₉	—	4	2	no	—
488	D₄×C₂₉	—	4	4	no	—
489	D₄×C₂₉	—	4	2	no	—
490	D₄×C₂₉	—	8	2	no	—
491	D₄×C₂₉	—	8	1	no	—
492	D₄×C₂₉	—	8	2	no	—
493	D₄×C₂₉	—	8	2	no	—
494	D₄×C₂₉	—	8	2	no	—
495	D₄×C₂₉	—	8	2	no	—
496	D₄×C₂₉	C₂×#41	1	2	yes	—
497	C₂×C₄×C₂₉	—	2	1	no	—
498	C₂×C₄×C₂₉	—	2	2	no	—
499	C₂×C₄×C₂₉	—	2	2	no	—
500	C₂×C₄×C₂₉	—	2	1	no	—
501	C₂×C₄×C₂₉	—	2	2	no	—
502	C₂×C₄×C₂₉	—	2	1	no	—
503	C₂×C₄×C₂₉	—	2	1	no	—
504	C₂×C₄×C₂₉	—	2	2	no	—
505	C₂×C₄×C₂₉	—	2	1	no	—
506	C₂×C₄×C₂₉	—	2	2	no	—
507	C₂×C₄×C₂₉	—	2	1	no	—
508	C₂×C₄×C₂₉	—	2	2	no	—
509	C₂×C₄×C₂₉	—	2	1	no	—
510	C₂×C₄×C₂₉	—	4	1	no	—
511	C₂×C₄×C₂₉	—	4	2	no	—
512	C₂×C₄×C₂₉	—	4	4	no	—
513	C₂×C₄×C₂₉	—	4	2	no	—
514	C₂×C₄×C₂₉	—	4	2	no	—
515	C₂×C₄×C₂₉	—	4	2	no	—
516	C₂×C₄×C₂₉	—	8	1	no	—
517	C₂×C₄×C₂₉	—	8	1	no	—
518	C₂×C₄×C₂₉	—	8	1	no	—
519	C₂×C₄×C₂₉	—	8	2	no	—
520	C₂×C₄×C₂₉	—	8	2	no	—
521	C₂×C₄×C₂₉	—	8	2	no	—
522	C₂×C₄×C₂₉	—	8	1	no	—
523	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
532	C₈×C₂₉	—	2	2	no	—
533	C₈×C₂₉	—	2	1	no	—
534	C₈×C₂₉	—	2	1	no	—
535	C₈×C₂₉	—	2	2	no	—
536	C₈×C₂₉	—	2	1	no	—
537	C₈×C₂₉	C₂×#41	1	2	yes	—
538	#3519	C₂×C₂₉	1	1	yes	characteristic, complemented
539	#3518	C₂×C₂₉	1	1	yes	characteristic, complemented
540	#3397	C₂×C₂₉	1	1	yes	characteristic, complemented
541	#3385	C₂×C₂₉	1	1	yes	characteristic, complemented
542	#3362	C₂×C₂₉	1	1	yes	characteristic, complemented
543	#3360	C₂×C₂₉	1	1	yes	characteristic, complemented
544	#3350	C₂×C₂₉	1	2	yes	complemented
545	#3341	C₂×C₂₉	1	1	yes	characteristic, complemented
546	#3329	C₂×C₂₉	1	1	yes	characteristic, complemented
547	#3326	C₂×C₂₉	1	2	yes	complemented
548	#3325	C₂×C₂₉	1	1	yes	characteristic, complemented
549	#3324	C₂×C₂₉	1	2	yes	complemented
550	D₄×SD₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
551	#3265	C₂×C₂₉	1	2	yes	complemented
552	#3182	C₂×C₂₉	1	1	yes	characteristic, complemented
553	#3179	C₂×C₂₉	1	2	yes	complemented
554	#3126	C₂×C₂₉	1	2	yes	complemented
555	#3118	C₂×C₂₉	1	2	yes	complemented
556	#3106	C₂×C₂₉	1	1	yes	characteristic, complemented
557	#3101	C₂×C₂₉	1	1	yes	characteristic, complemented
558	#2969	C₂×C₂₉	1	1	yes	characteristic, complemented
559	#2949	C₂×C₂₉	1	2	yes	complemented
560	C₄×AGL(1,ℤ/8)	C₂×C₂₉	1	1	yes	characteristic, complemented
561	C₂²×C₂₉	—	2	1	no	—
562	C₂²×C₂₉	—	2	2	no	—
563	C₂²×C₂₉	—	2	2	no	—
564	C₂²×C₂₉	—	2	1	no	—
565	C₂²×C₂₉	—	2	2	no	—
566	C₂²×C₂₉	—	2	1	no	—
567	C₂²×C₂₉	—	2	2	no	—
568	C₂²×C₂₉	—	4	1	no	—
569	C₂²×C₂₉	—	4	1	no	—
570	C₂²×C₂₉	—	4	2	no	—
571	C₂²×C₂₉	—	4	1	no	—
572	C₂²×C₂₉	—	4	1	no	—
573	C₂²×C₂₉	—	4	1	no	—
574	C₂²×C₂₉	—	4	1	no	—
575	C₂²×C₂₉	—	4	2	no	—
576	C₂²×C₂₉	—	4	1	no	—
577	C₂²×C₂₉	—	4	1	no	—
578	C₂²×C₂₉	—	4	2	no	—
579	C₂²×C₂₉	—	8	4	no	—
580	C₂²×C₂₉	—	16	4	no	—
581	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
582	C₄×C₂₉	—	2	1	no	—
583	C₄×C₂₉	—	2	1	no	—
584	C₄×C₂₉	—	2	2	no	—
585	C₄×C₂₉	—	2	1	no	—
586	C₄×C₂₉	—	2	2	no	—
587	C₄×C₂₉	—	2	2	no	—
588	C₄×C₂₉	—	2	1	no	—
589	C₄×C₂₉	—	2	2	no	—
590	C₄×C₂₉	—	4	2	no	—
591	C₄×C₂₉	—	4	1	no	—
592	C₄×C₂₉	—	4	2	no	—
593	C₄×C₂₉	—	4	2	no	—
594	C₄×C₂₉	—	4	1	no	—
595	C₄×C₂₉	—	4	1	no	—
596	C₄×C₂₉	—	4	1	no	—
597	C₄×C₂₉	#577	1	2	yes	—
598	C₄×C₂₉	C₂²×#41	1	1	yes	characteristic
599	C₄×C₂₉	#585	1	1	yes	characteristic
600	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	1	yes	characteristic
601	C₂²×SD₁₆	C₂²×C₂₉	1	2	yes	—
602	Q₈²	C₂²×C₂₉	1	1	yes	characteristic, complemented
603	#556	—	2	2	no	—
604	#556	—	2	1	no	—
605	#556	C₂²×C₂₉	1	1	yes	characteristic, complemented
606	#556	C₂²×C₂₉	1	2	yes	complemented
607	#555	—	2	1	no	—
608	#555	C₂²×C₂₉	1	1	yes	characteristic
609	#555	C₂²×C₂₉	1	1	yes	characteristic, complemented
610	#554	C₂²×C₂₉	1	1	yes	characteristic
611	#553	—	2	1	no	—
612	#553	C₂²×C₂₉	1	2	yes	—
613	#550	C₂²×C₂₉	1	1	yes	characteristic
614	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
615	#548	C₂²×C₂₉	1	2	yes	complemented
616	#546	—	2	1	no	—
617	#546	—	2	2	no	—
618	D₄²	C₂²×C₂₉	1	2	yes	—
619	D₄²	C₂²×C₂₉	1	1	yes	characteristic
620	#542	—	2	2	no	—
621	#542	C₂²×C₂₉	1	2	yes	complemented
622	#540	C₂²×C₂₉	1	2	yes	—
623	#538	—	2	2	no	—
624	#533	—	2	1	no	—
625	#533	C₂²×C₂₉	1	1	yes	characteristic, complemented
626	#532	C₂²×C₂₉	1	1	yes	characteristic
627	#529	—	2	1	no	—
628	#529	C₂²×C₂₉	1	1	yes	characteristic
629	#525	—	2	1	no	—
630	C₂×#121	—	2	1	no	—
631	#519	C₂²×C₂₉	1	2	yes	complemented
632	#518	C₂²×C₂₉	1	2	yes	—
633	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic, complemented
634	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
635	#501	C₂²×C₂₉	1	2	yes	complemented
636	#500	C₂²×C₂₉	1	1	yes	characteristic, complemented
637	#496	C₂²×C₂₉	1	2	yes	complemented
638	#492	C₂²×C₂₉	1	1	yes	characteristic, complemented
639	#488	C₂²×C₂₉	1	2	yes	complemented
640	#487	C₂²×C₂₉	1	1	yes	characteristic, complemented
641	#486	C₂²×C₂₉	1	2	yes	complemented
642	#486	C₂²×C₂₉	1	1	yes	characteristic, complemented
643	#485	C₂²×C₂₉	1	2	yes	complemented
644	#483	C₂²×C₂₉	1	2	yes	complemented
645	#482	C₂²×C₂₉	1	2	yes	complemented
646	#482	C₂²×C₂₉	1	2	yes	complemented
647	#482	C₂²×C₂₉	1	2	yes	complemented
648	#482	C₂²×C₂₉	1	2	yes	complemented
649	#479	C₂²×C₂₉	1	2	yes	complemented
650	#479	C₂²×C₂₉	1	2	yes	complemented
651	#477	C₂²×C₂₉	1	1	yes	characteristic, complemented
652	#476	C₂²×C₂₉	1	1	yes	characteristic
653	#476	C₂²×C₂₉	1	1	yes	characteristic, complemented
654	#476	C₂²×C₂₉	1	1	yes	characteristic, complemented
655	#476	C₂²×C₂₉	1	2	yes	complemented
656	#474	C₂²×C₂₉	1	2	yes	—
657	#469	C₂²×C₂₉	1	2	yes	complemented
658	#468	C₂²×C₂₉	1	2	yes	complemented
659	#468	C₂²×C₂₉	1	2	yes	complemented
660	#468	C₂²×C₂₉	1	2	yes	complemented
661	#466	C₂²×C₂₉	1	2	yes	complemented
662	#465	C₂²×C₂₉	1	2	yes	complemented
663	#463	C₂²×C₂₉	1	2	yes	—
664	#463	C₂²×C₂₉	1	2	yes	complemented
665	#461	C₂²×C₂₉	1	1	yes	characteristic
666	#461	C₂²×C₂₉	1	1	yes	characteristic, complemented
667	#460	C₂²×C₂₉	1	1	yes	characteristic, complemented
668	#460	C₂²×C₂₉	1	2	yes	complemented
669	#460	C₂²×C₂₉	1	2	yes	complemented
670	#459	C₂²×C₂₉	1	1	yes	characteristic, complemented
671	#450	C₂²×C₂₉	1	2	yes	—
672	#450	C₂²×C₂₉	1	2	yes	—
673	#449	C₂²×C₂₉	1	2	yes	complemented
674	#448	C₂²×C₂₉	1	2	yes	complemented
675	#448	C₂²×C₂₉	1	2	yes	complemented
676	#447	C₂²×C₂₉	1	2	yes	—
677	#446	C₂²×C₂₉	1	1	yes	characteristic, complemented
678	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
679	#442	C₂²×C₂₉	1	1	yes	characteristic
680	#442	C₂²×C₂₉	1	1	yes	characteristic, complemented
681	#440	C₂²×C₂₉	1	2	yes	—
682	#440	C₂²×C₂₉	1	1	yes	characteristic
683	#440	C₂²×C₂₉	1	2	yes	complemented
684	#440	C₂²×C₂₉	1	2	yes	complemented
685	#440	C₂²×C₂₉	1	1	yes	characteristic, complemented
686	#440	C₂²×C₂₉	1	2	yes	complemented
687	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	—
688	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	—
689	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
690	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
691	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
692	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
693	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
694	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
695	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
696	C₄×D₈	C₂²×C₂₉	1	2	yes	complemented
697	#436	C₂²×C₂₉	1	1	yes	characteristic, complemented
698	#436	C₂²×C₂₉	1	2	yes	complemented
699	#435	C₂²×C₂₉	1	2	yes	complemented
700	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
701	#433	C₂²×C₂₉	1	2	yes	complemented
702	#431	C₂²×C₂₉	1	1	yes	characteristic, complemented
703	#428	C₂²×C₂₉	1	1	yes	characteristic, complemented
704	#427	C₂²×C₂₉	1	2	yes	complemented
705	#419	C₂²×C₂₉	1	2	yes	complemented
706	#418	C₂²×C₂₉	1	1	yes	characteristic
707	#418	C₂²×C₂₉	1	2	yes	—
708	#417	C₂²×C₂₉	1	1	yes	characteristic, complemented
709	#405	C₂²×C₂₉	1	2	yes	complemented
710	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
711	C₂×C₂₉	—	4	1	no	—
712	C₂×C₂₉	—	4	2	no	—
713	C₂×C₂₉	—	4	2	no	—
714	C₂×C₂₉	—	8	1	no	—
715	C₂×C₂₉	—	8	1	no	—
716	C₂×C₂₉	—	8	2	no	—
717	C₂×C₂₉	D₄×#41	1	1	yes	characteristic
718	C₂×C₂₉	C₂×#577	1	1	yes	characteristic
719	C₂×C₂₉	#3585	1	1	yes	characteristic
720	C₂×#41	—	2	1	no	—
721	C₂×#41	—	2	1	no	—
722	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
723	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
724	C₂²×D₄	—	2	1	no	—
725	C₂²×D₄	—	2	2	no	—
726	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
727	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
728	C₂³×C₄	—	2	1	no	—
729	AGL(1,ℤ/8)	—	2	4	no	—
730	C₂×SD₁₆	—	2	8	no	—
731	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
735	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
737	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
738	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
739	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
740	C₂×D₈	C₂³×C₂₉	1	2	yes	—
741	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
742	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
743	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
744	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
745	C₄⋊Q₈	—	2	1	no	—
746	C₄⋊Q₈	—	2	1	no	—
747	C₄⋊Q₈	—	2	2	no	—
748	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
749	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
750	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
751	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
752	#127	C₂³×C₂₉	1	1	yes	characteristic
753	#127	C₂³×C₂₉	1	2	yes	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#126	D₄×C₂₉	1	2	yes	—
760	#125	—	2	1	no	—
761	#125	D₄×C₂₉	1	1	yes	characteristic
762	#125	C₂³×C₂₉	1	2	yes	—
763	#124	—	2	2	no	—
764	#124	—	2	2	no	—
765	#124	—	2	2	no	—
766	#124	—	2	2	no	—
767	#124	—	2	2	no	—
768	#124	—	2	1	no	—
769	#124	D₄×C₂₉	1	1	yes	characteristic
770	#124	C₂³×C₂₉	1	2	yes	—
771	#123	—	2	2	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	D₄×C₂₉	1	2	yes	—
776	C₂²⋊Q₈	—	2	1	no	—
777	C₂²⋊Q₈	—	2	1	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
784	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
785	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
786	#121	—	2	2	no	—
787	#121	—	2	1	no	—
788	#121	—	2	1	no	—
789	#121	—	2	2	no	—
790	#121	—	2	1	no	—
791	#121	—	2	1	no	—
792	#121	—	2	1	no	—
793	#121	—	2	2	no	—
794	#121	—	2	2	no	—
795	#121	—	2	2	no	—
796	#121	—	2	2	no	—
797	#121	D₄×C₂₉	1	1	yes	characteristic
798	#121	C₂³×C₂₉	1	2	yes	—
799	#121	C₂³×C₂₉	1	2	yes	—
800	#121	C₂³×C₂₉	1	2	yes	—
801	#121	C₂³×C₂₉	1	2	yes	—
802	#120	—	2	2	no	—
803	#120	—	2	2	no	—
804	#120	—	2	2	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	—	2	2	no	—
807	C₄×Q₈	—	2	2	no	—
808	C₄×Q₈	—	2	2	no	—
809	C₄×Q₈	—	2	1	no	—
810	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
812	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
813	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
814	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
815	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
827	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
830	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₂₉	1	2	yes	—
833	C₄×D₄	C₂³×C₂₉	1	2	yes	—
834	C₄×D₄	C₂³×C₂₉	1	2	yes	—
835	C₄×D₄	C₂³×C₂₉	1	2	yes	—
836	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
837	#117	—	2	1	no	—
838	#117	—	2	1	no	—
839	#117	—	2	1	no	—
840	#117	—	2	1	no	—
841	#117	—	2	2	no	—
842	#117	—	2	2	no	—
843	#117	—	2	1	no	—
844	#117	C₂³×C₂₉	1	1	yes	characteristic
845	#117	C₂³×C₂₉	1	2	yes	—
846	#117	C₂³×C₂₉	1	2	yes	—
847	#117	C₂³×C₂₉	1	2	yes	—
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
850	C₂×C₂²⋊C₄	—	2	1	no	—
851	C₂×C₂²⋊C₄	—	2	2	no	—
852	C₂×C₂²⋊C₄	—	2	2	no	—
853	C₂×C₄²	—	2	1	no	—
854	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
855	#107	C₂³×C₂₉	1	1	yes	characteristic
856	#107	C₂³×C₂₉	1	2	yes	—
857	#107	C₂³×C₂₉	1	1	yes	characteristic
858	#107	C₂³×C₂₉	1	2	yes	—
859	#107	C₂³×C₂₉	1	2	yes	—
860	#106	C₂³×C₂₉	1	2	yes	—
861	#106	C₂³×C₂₉	1	2	yes	—
862	#106	C₂³×C₂₉	1	1	yes	characteristic
863	#106	C₂³×C₂₉	1	1	yes	characteristic
864	#106	C₂³×C₂₉	1	2	yes	—
865	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
866	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
867	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
868	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
869	#103	C₂³×C₂₉	1	1	yes	characteristic
870	#103	C₂³×C₂₉	1	1	yes	characteristic
871	#103	C₂³×C₂₉	1	2	yes	—
872	#103	C₂³×C₂₉	1	2	yes	—
873	#103	C₂³×C₂₉	1	2	yes	—
874	#103	C₂³×C₂₉	1	2	yes	—
875	#103	C₂³×C₂₉	1	2	yes	—
876	#102	C₂³×C₂₉	1	1	yes	characteristic
877	#102	C₂³×C₂₉	1	1	yes	characteristic
878	#102	C₂³×C₂₉	1	1	yes	characteristic
879	#102	C₂³×C₂₉	1	1	yes	characteristic
880	#102	C₂³×C₂₉	1	2	yes	—
881	#102	C₂³×C₂₉	1	1	yes	characteristic
882	#102	C₂³×C₂₉	1	2	yes	—
883	#102	C₂³×C₂₉	1	2	yes	—
884	#102	C₂³×C₂₉	1	1	yes	characteristic
885	#102	C₂³×C₂₉	1	2	yes	—
886	#102	C₂³×C₂₉	1	2	yes	—
887	#102	C₂³×C₂₉	1	2	yes	—
888	#102	C₂³×C₂₉	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
890	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
891	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
892	#97	C₂³×C₂₉	1	1	yes	characteristic
893	#97	C₂³×C₂₉	1	1	yes	characteristic
894	#97	C₂³×C₂₉	1	2	yes	—
895	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
896	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
897	C₄×C₈	C₂³×C₂₉	1	2	yes	—
898	C₄×C₈	C₂³×C₂₉	1	2	yes	—
899	C₂₉	#61543	1	1	yes	characteristic, direct product factor, Sylow
900	C₂⁴	—	2	1	no	—
901	C₂⁴	—	2	2	no	—
902	#41	—	2	2	no	—
903	#41	—	4	1	no	—
904	#41	—	8	2	no	—
905	#41	—	8	2	no	—
906	C₂×Q₈	—	2	2	no	—
907	C₂×Q₈	—	2	1	no	—
908	C₂×Q₈	—	2	2	no	—
909	C₂×Q₈	—	2	1	no	—
910	C₂×Q₈	—	2	4	no	—
911	C₂×Q₈	—	4	2	no	—
912	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
914	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
915	C₂×D₄	—	2	4	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	4	2	no	—
929	C₂×D₄	—	4	1	no	—
930	C₂×D₄	—	8	2	no	—
931	C₂×D₄	—	8	4	no	—
932	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
933	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
934	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
935	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
936	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
937	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	8	2	no	—
951	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
952	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
953	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
954	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
955	SD₁₆	—	2	4	no	—
956	SD₁₆	—	2	2	no	—
957	SD₁₆	—	2	4	no	—
958	SD₁₆	—	2	4	no	—
959	SD₁₆	—	4	2	no	—
960	SD₁₆	—	4	2	no	—
961	SD₁₆	#41×C₂₉	1	4	yes	complemented
962	D₈	—	2	2	no	—
963	D₈	—	2	2	no	—
964	D₈	—	4	2	no	—
965	M₁₆	—	2	2	no	—
966	M₁₆	—	4	2	no	—
967	M₁₆	—	4	1	no	—
968	C₂×C₈	—	2	4	no	—
969	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
971	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
972	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
974	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
991	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
992	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
993	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
994	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
995	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
996	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
999	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1001	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	2	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	—	2	2	no	—
1035	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1036	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1037	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1038	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1039	C₄²	C₂⁴×C₂₉	1	2	yes	—
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	4	2	no	—
1045	C₂³	—	4	4	no	—
1046	C₂³	—	4	2	no	—
1047	C₂³	—	8	1	no	—
1048	C₂³	—	8	2	no	—
1049	C₂³	—	8	2	no	—
1050	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
1051	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1052	Q₈	—	2	2	no	—
1053	Q₈	—	2	1	no	—
1054	Q₈	—	2	2	no	—
1055	Q₈	—	2	2	no	—
1056	Q₈	—	4	4	no	—
1057	Q₈	—	8	1	no	—
1058	Q₈	—	8	1	no	—
1059	Q₈	—	8	2	no	—
1060	Q₈	C₂×#41×C₂₉	1	2	yes	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	2	1	no	—
1067	D₄	—	2	2	no	—
1068	D₄	—	2	1	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	4	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	4	no	—
1074	D₄	—	4	2	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	1	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	2	no	—
1081	D₄	C₂×#41×C₂₉	1	2	yes	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	4	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	8	1	no	—
1102	C₂×C₄	—	8	1	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	2	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	—	8	1	no	—
1107	C₂×C₄	—	8	1	no	—
1108	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1109	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1110	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1112	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1113	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1114	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1115	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1116	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1117	C₈	—	2	2	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	2	no	—
1121	C₈	—	2	1	no	—
1122	C₈	C₂×#41×C₂₉	1	2	yes	—
1123	C₂²	—	2	2	no	—
1124	C₂²	—	2	1	no	—
1125	C₂²	—	2	2	no	—
1126	C₂²	—	2	1	no	—
1127	C₂²	—	2	2	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	4	1	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	8	4	no	—
1142	C₂²	—	16	4	no	—
1143	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	2	2	no	—
1147	C₄	—	2	1	no	—
1148	C₄	—	2	2	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	4	2	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	2	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	2	no	—
1159	C₄	C₂₉×#577	1	2	yes	—
1160	C₄	C₂²×#41×C₂₉	1	1	yes	characteristic
1161	C₄	C₂₉×#585	1	1	yes	characteristic
1162	C₂	—	4	1	no	—
1163	C₂	—	4	2	no	—
1164	C₂	—	4	2	no	—
1165	C₂	—	8	1	no	—
1166	C₂	—	8	2	no	—
1167	C₂	—	8	1	no	—
1168	C₂	D₄×#41×C₂₉	1	1	yes	characteristic
1169	C₂	C₂×C₂₉×#577	1	1	yes	characteristic
1170	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 ◁ C₂₉×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3519	C₂	semidirect
2. C₂₉×#3518	C₂	semidirect
3. C₂₉×#3397	C₂	semidirect
4. C₂₉×#3385	C₂	semidirect
5. C₂₉×#3362	C₂	semidirect
6. C₂₉×#3360	C₂	semidirect
7. C₂₉×#3350	C₂	semidirect
8. C₂₉×#3341	C₂	semidirect
9. C₂₉×#3329	C₂	semidirect
10. C₂₉×#3326	C₂	semidirect
11. C₂₉×#3325	C₂	semidirect
12. C₂₉×#3324	C₂	semidirect
13. D₄×SD₁₆×C₂₉	C₂	semidirect
14. C₂₉×#3265	C₂	semidirect
15. C₂₉×#3182	C₂	semidirect
16. C₂₉×#3179	C₂	semidirect
17. C₂₉×#3126	C₂	semidirect
18. C₂₉×#3118	C₂	semidirect
19. C₂₉×#3106	C₂	semidirect
20. C₂₉×#3101	C₂	semidirect
21. C₂₉×#2969	C₂	semidirect
22. C₂₉×#2949	C₂	semidirect
23. C₄×C₂₉×AGL(1,ℤ/8)	C₂	semidirect
26. Q₈²×C₂₉	C₂²	semidirect
29. C₂₉×#556	C₂²	semidirect
30. C₂₉×#556	C₂²	semidirect
33. C₂₉×#555	C₂²	semidirect
38. D₄×Q₈×C₂₉	C₂²	semidirect
39. C₂₉×#548	C₂²	semidirect
45. C₂₉×#542	C₂²	semidirect
49. C₂₉×#533	C₂²	semidirect
55. C₂₉×#519	C₂²	semidirect
57. C₄×#41×C₂₉	C₂²	semidirect
59. C₂₉×#501	C₂²	semidirect
60. C₂₉×#500	C₂²	semidirect
61. C₂₉×#496	C₂²	semidirect
62. C₂₉×#492	C₂²	semidirect
63. C₂₉×#488	C₂²	semidirect
64. C₂₉×#487	C₂²	semidirect
65. C₂₉×#486	C₂²	semidirect
66. C₂₉×#486	C₂²	semidirect
67. C₂₉×#485	C₂²	semidirect
68. C₂₉×#483	C₂²	semidirect
69. C₂₉×#482	C₂²	semidirect
70. C₂₉×#482	C₂²	semidirect
71. C₂₉×#482	C₂²	semidirect
72. C₂₉×#482	C₂²	semidirect
73. C₂₉×#479	C₂²	semidirect
74. C₂₉×#479	C₂²	semidirect
75. C₂₉×#477	C₂²	semidirect
77. C₂₉×#476	C₂²	semidirect
78. C₂₉×#476	C₂²	semidirect
79. C₂₉×#476	C₂²	semidirect
81. C₂₉×#469	C₂²	semidirect
82. C₂₉×#468	C₂²	semidirect
83. C₂₉×#468	C₂²	semidirect
84. C₂₉×#468	C₂²	semidirect
85. C₂₉×#466	C₂²	semidirect
86. C₂₉×#465	C₂²	semidirect
88. C₂₉×#463	C₂²	semidirect
90. C₂₉×#461	C₂²	semidirect
91. C₂₉×#460	C₂²	semidirect
92. C₂₉×#460	C₂²	semidirect
93. C₂₉×#460	C₂²	semidirect
94. C₂₉×#459	C₂²	semidirect
97. C₂₉×#449	C₂²	semidirect
98. C₂₉×#448	C₂²	semidirect
99. C₂₉×#448	C₂²	semidirect
101. C₂₉×#446	C₂²	semidirect
102. C₈×Q₈×C₂₉	C₂²	semidirect
104. C₂₉×#442	C₂²	semidirect
107. C₂₉×#440	C₂²	semidirect
108. C₂₉×#440	C₂²	semidirect
109. C₂₉×#440	C₂²	semidirect
110. C₂₉×#440	C₂²	semidirect
114. C₄×SD₁₆×C₂₉	C₂²	semidirect
115. C₄×SD₁₆×C₂₉	C₂²	semidirect
116. C₄×SD₁₆×C₂₉	C₂²	semidirect
117. C₄×SD₁₆×C₂₉	C₂²	semidirect
119. C₄×D₈×C₂₉	C₂²	semidirect
120. C₄×D₈×C₂₉	C₂²	semidirect
121. C₂₉×#436	C₂²	semidirect
122. C₂₉×#436	C₂²	semidirect
123. C₂₉×#435	C₂²	semidirect
124. C₈×D₄×C₂₉	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
132. C₂₉×#417	C₂²	semidirect
133. C₂₉×#405	C₂²	semidirect
134. C₄×M₁₆×C₂₉	C₂²	semidirect
375. SD₁₆×C₂₉	#41	semidirect
454. #61543	C₂₉	direct (N × H)
538. #3519	C₂×C₂₉	semidirect
539. #3518	C₂×C₂₉	semidirect
540. #3397	C₂×C₂₉	semidirect
541. #3385	C₂×C₂₉	semidirect
542. #3362	C₂×C₂₉	semidirect
543. #3360	C₂×C₂₉	semidirect
544. #3350	C₂×C₂₉	semidirect
545. #3341	C₂×C₂₉	semidirect
546. #3329	C₂×C₂₉	semidirect
547. #3326	C₂×C₂₉	semidirect
548. #3325	C₂×C₂₉	semidirect
549. #3324	C₂×C₂₉	semidirect
550. D₄×SD₁₆	C₂×C₂₉	semidirect
551. #3265	C₂×C₂₉	semidirect
552. #3182	C₂×C₂₉	semidirect
553. #3179	C₂×C₂₉	semidirect
554. #3126	C₂×C₂₉	semidirect
555. #3118	C₂×C₂₉	semidirect
556. #3106	C₂×C₂₉	semidirect
557. #3101	C₂×C₂₉	semidirect
558. #2969	C₂×C₂₉	semidirect
559. #2949	C₂×C₂₉	semidirect
560. C₄×AGL(1,ℤ/8)	C₂×C₂₉	semidirect
602. Q₈²	C₂²×C₂₉	semidirect
605. #556	C₂²×C₂₉	semidirect
606. #556	C₂²×C₂₉	semidirect
609. #555	C₂²×C₂₉	semidirect
614. D₄×Q₈	C₂²×C₂₉	semidirect
615. #548	C₂²×C₂₉	semidirect
621. #542	C₂²×C₂₉	semidirect
625. #533	C₂²×C₂₉	semidirect
631. #519	C₂²×C₂₉	semidirect
633. C₄×#41	C₂²×C₂₉	semidirect
635. #501	C₂²×C₂₉	semidirect
636. #500	C₂²×C₂₉	semidirect
637. #496	C₂²×C₂₉	semidirect
638. #492	C₂²×C₂₉	semidirect
639. #488	C₂²×C₂₉	semidirect
640. #487	C₂²×C₂₉	semidirect
641. #486	C₂²×C₂₉	semidirect
642. #486	C₂²×C₂₉	semidirect
643. #485	C₂²×C₂₉	semidirect
644. #483	C₂²×C₂₉	semidirect
645. #482	C₂²×C₂₉	semidirect
646. #482	C₂²×C₂₉	semidirect
647. #482	C₂²×C₂₉	semidirect
648. #482	C₂²×C₂₉	semidirect
649. #479	C₂²×C₂₉	semidirect
650. #479	C₂²×C₂₉	semidirect
651. #477	C₂²×C₂₉	semidirect
653. #476	C₂²×C₂₉	semidirect
654. #476	C₂²×C₂₉	semidirect
655. #476	C₂²×C₂₉	semidirect
657. #469	C₂²×C₂₉	semidirect
658. #468	C₂²×C₂₉	semidirect
659. #468	C₂²×C₂₉	semidirect
660. #468	C₂²×C₂₉	semidirect
661. #466	C₂²×C₂₉	semidirect
662. #465	C₂²×C₂₉	semidirect
664. #463	C₂²×C₂₉	semidirect
666. #461	C₂²×C₂₉	semidirect
667. #460	C₂²×C₂₉	semidirect
668. #460	C₂²×C₂₉	semidirect
669. #460	C₂²×C₂₉	semidirect
670. #459	C₂²×C₂₉	semidirect
673. #449	C₂²×C₂₉	semidirect
674. #448	C₂²×C₂₉	semidirect
675. #448	C₂²×C₂₉	semidirect
677. #446	C₂²×C₂₉	semidirect
678. C₈×Q₈	C₂²×C₂₉	semidirect
680. #442	C₂²×C₂₉	semidirect
683. #440	C₂²×C₂₉	semidirect
684. #440	C₂²×C₂₉	semidirect
685. #440	C₂²×C₂₉	semidirect
686. #440	C₂²×C₂₉	semidirect
690. C₄×SD₁₆	C₂²×C₂₉	semidirect
691. C₄×SD₁₆	C₂²×C₂₉	semidirect
692. C₄×SD₁₆	C₂²×C₂₉	semidirect
693. C₄×SD₁₆	C₂²×C₂₉	semidirect
695. C₄×D₈	C₂²×C₂₉	semidirect
696. C₄×D₈	C₂²×C₂₉	semidirect
697. #436	C₂²×C₂₉	semidirect
698. #436	C₂²×C₂₉	semidirect
699. #435	C₂²×C₂₉	semidirect
700. C₈×D₄	C₂²×C₂₉	semidirect
701. #433	C₂²×C₂₉	semidirect
702. #431	C₂²×C₂₉	semidirect
703. #428	C₂²×C₂₉	semidirect
704. #427	C₂²×C₂₉	semidirect
705. #419	C₂²×C₂₉	semidirect
708. #417	C₂²×C₂₉	semidirect
709. #405	C₂²×C₂₉	semidirect
710. C₄×M₁₆	C₂²×C₂₉	semidirect
899. C₂₉	#61543	direct (N × H)
961. 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×#3519	2
C₂₉×#3518	2
C₂₉×#3397	2
C₂₉×#3385	2
C₂₉×#3362	2
C₂₉×#3360	2
C₂₉×#3350	2
C₂₉×#3341	2
C₂₉×#3329	2
C₂₉×#3326	2
C₂₉×#3325	2
C₂₉×#3324	2
D₄×SD₁₆×C₂₉	2
C₂₉×#3265	2
C₂₉×#3182	2
C₂₉×#3179	2
C₂₉×#3126	2
C₂₉×#3118	2
C₂₉×#3106	2
C₂₉×#3101	2
C₂₉×#2969	2
C₂₉×#2949	2
C₄×C₂₉×AGL(1,ℤ/8)	2
#61543	29

Subgroups — C29×#61543 #20356443

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#61543 #20356443