Subgroups — C₂₉×#61539 #20356439

Order 7424.

1950 conjugacy classes of subgroups.

The subgroup lattice has 1202 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×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#3361	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#3347	C₂	1	2	yes	maximal, complemented
8	C₂₉×#3340	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#3325	C₂	1	2	yes	maximal, complemented
10	C₂₉×#3325	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#3324	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#3322	C₂	1	2	yes	maximal, complemented
13	D₄×D₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#3264	C₂	1	2	yes	maximal, complemented
15	C₂₉×#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#3179	C₂	1	2	yes	maximal, complemented
17	C₂₉×#3122	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×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₉×#2969	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₉×#2948	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×D₈×C₂₉	C₂²	1	2	yes	—
26	C₂₉×#559	C₂²	1	1	yes	characteristic, complemented
27	C₂₉×#556	C₂²	1	1	yes	characteristic, complemented
28	C₂₉×#555	C₂²	1	1	yes	characteristic
29	C₂₉×#555	C₂²	1	2	yes	complemented
30	C₂₉×#554	C₂²	1	1	yes	characteristic, complemented
31	C₂₉×#553	—	2	1	no	—
32	C₂₉×#553	C₂²	1	2	yes	complemented
33	C₂₉×#551	—	2	2	no	—
34	C₂₉×#550	C₂²	1	1	yes	characteristic, complemented
35	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
36	C₂₉×#548	—	2	1	no	—
37	C₂₉×#546	—	2	1	no	—
38	C₂₉×#546	—	2	2	no	—
39	C₂₉×#546	—	2	1	no	—
40	C₂₉×#546	C₂²	1	2	yes	complemented
41	D₄²×C₂₉	C₂²	1	1	yes	characteristic
42	D₄²×C₂₉	C₂²	1	1	yes	characteristic, complemented
43	D₄²×C₂₉	C₂²	1	2	yes	complemented
44	C₂₉×#542	C₂²	1	2	yes	complemented
45	C₂₉×#540	C₂²	1	2	yes	complemented
46	C₂₉×#538	—	2	2	no	—
47	C₂₉×#538	—	2	2	no	—
48	C₂₉×#532	C₂²	1	1	yes	characteristic, complemented
49	C₂₉×#532	C₂²	1	1	yes	characteristic, complemented
50	C₂₉×#529	—	2	1	no	—
51	C₂₉×#529	C₂²	1	1	yes	characteristic
52	C₂×C₂₉×#124	—	2	1	no	—
53	C₂₉×#525	—	2	1	no	—
54	C₂×C₂₉×#121	—	2	1	no	—
55	C₂₉×#518	C₂²	1	2	yes	complemented
56	C₂₉×#518	C₂²	1	2	yes	complemented
57	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
59	C₂₉×#501	C₂²	1	2	yes	complemented
60	C₂₉×#498	C₂²	1	1	yes	characteristic, complemented
61	C₂₉×#496	C₂²	1	2	yes	complemented
62	C₂₉×#493	C₂²	1	1	yes	characteristic, complemented
63	C₂₉×#488	C₂²	1	2	yes	complemented
64	C₂₉×#486	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×#482	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×#480	C₂²	1	2	yes	complemented
73	C₂₉×#478	C₂²	1	2	yes	complemented
74	C₂₉×#478	C₂²	1	2	yes	complemented
75	C₂₉×#477	C₂²	1	1	yes	characteristic, complemented
76	C₂₉×#476	C₂²	1	1	yes	characteristic, complemented
77	C₂₉×#476	C₂²	1	2	yes	complemented
78	C₂₉×#474	C₂²	1	1	yes	characteristic, complemented
79	C₂₉×#474	C₂²	1	1	yes	characteristic, complemented
80	C₂₉×#474	C₂²	1	2	yes	complemented
81	C₂₉×#469	C₂²	1	2	yes	complemented
82	C₂₉×#469	C₂²	1	2	yes	complemented
83	C₂₉×#469	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	complemented
88	C₂₉×#463	C₂²	1	2	yes	complemented
89	C₂₉×#460	C₂²	1	1	yes	characteristic, complemented
90	C₂₉×#459	C₂²	1	1	yes	characteristic
91	C₂₉×#459	C₂²	1	2	yes	complemented
92	C₂₉×#459	C₂²	1	1	yes	characteristic, complemented
93	C₂₉×#459	C₂²	1	1	yes	characteristic, complemented
94	C₂₉×#459	C₂²	1	2	yes	complemented
95	C₂₉×#450	C₂²	1	2	yes	complemented
96	C₂₉×#449	C₂²	1	2	yes	complemented
97	C₂₉×#447	C₂²	1	2	yes	—
98	C₂₉×#447	C₂²	1	2	yes	complemented
99	C₂₉×#447	C₂²	1	2	yes	complemented
100	C₂₉×#447	C₂²	1	2	yes	complemented
101	C₂₉×#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
103	C₂₉×#442	C₂²	1	1	yes	characteristic
104	C₂₉×#442	C₂²	1	2	yes	—
105	C₂₉×#442	C₂²	1	2	yes	complemented
106	C₂₉×#442	C₂²	1	2	yes	complemented
107	C₂₉×#442	C₂²	1	1	yes	characteristic, complemented
108	C₂₉×#442	C₂²	1	2	yes	complemented
109	C₂₉×#440	C₂²	1	1	yes	characteristic, complemented
110	C₂₉×#440	C₂²	1	1	yes	characteristic, complemented
111	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
112	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
113	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	complemented
114	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
115	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₈×C₂₉	C₂²	1	2	yes	complemented
117	C₄×D₈×C₂₉	C₂²	1	2	yes	complemented
118	C₄×D₈×C₂₉	C₂²	1	2	yes	complemented
119	C₄×D₈×C₂₉	C₂²	1	2	yes	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×#418	C₂²	1	1	yes	characteristic, complemented
130	C₂₉×#418	C₂²	1	2	yes	complemented
131	C₂₉×#418	C₂²	1	2	yes	complemented
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	—	2	1	no	—
138	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₂₉	—	2	1	no	—
140	C₂²×D₄×C₂₉	—	2	1	no	—
141	C₂²×D₄×C₂₉	—	2	2	no	—
142	C₂²×D₄×C₂₉	—	2	1	no	—
143	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
144	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
145	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
146	C₂³×C₄×C₂₉	—	2	1	no	—
147	C₂₉×AGL(1,ℤ/8)	—	2	4	no	—
148	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
151	C₂×D₈×C₂₉	—	2	8	no	—
152	C₂×D₈×C₂₉	C₂³	1	2	yes	—
153	C₂×D₈×C₂₉	C₂³	1	2	yes	—
154	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
155	C₂×D₈×C₂₉	C₂³	1	2	yes	—
156	C₂×D₈×C₂₉	C₂³	1	2	yes	—
157	C₂×D₈×C₂₉	C₂³	1	2	yes	—
158	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
159	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
160	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
161	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
162	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
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×#127	C₂³	1	1	yes	characteristic
167	C₂₉×#127	C₂³	1	2	yes	—
168	C₂₉×#127	C₂³	1	1	yes	characteristic
169	C₂₉×#126	—	2	2	no	—
170	C₂₉×#126	—	2	2	no	—
171	C₂₉×#126	—	2	2	no	—
172	C₂₉×#126	D₄	1	2	yes	—
173	C₂₉×#125	D₄	1	1	yes	characteristic
174	C₂₉×#125	C₂³	1	2	yes	—
175	C₂₉×#124	—	2	1	no	—
176	C₂₉×#124	—	2	1	no	—
177	C₂₉×#124	—	2	2	no	—
178	C₂₉×#124	—	2	2	no	—
179	C₂₉×#124	—	2	2	no	—
180	C₂₉×#124	—	2	2	no	—
181	C₂₉×#124	—	2	1	no	—
182	C₂₉×#124	—	2	1	no	—
183	C₂₉×#124	D₄	1	1	yes	characteristic
184	C₂₉×#124	C₂³	1	2	yes	—
185	C₂₉×#123	—	2	2	no	—
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	—	2	2	no	—
191	C₂₉×#123	D₄	1	2	yes	—
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	D₄	1	1	yes	characteristic
198	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₂₉×#121	—	2	2	no	—
200	C₂₉×#121	—	2	1	no	—
201	C₂₉×#121	—	2	2	no	—
202	C₂₉×#121	—	2	1	no	—
203	C₂₉×#121	—	2	1	no	—
204	C₂₉×#121	—	2	1	no	—
205	C₂₉×#121	—	2	1	no	—
206	C₂₉×#121	—	2	1	no	—
207	C₂₉×#121	—	2	2	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×#121	C₂³	1	2	yes	—
218	C₂₉×#120	—	2	2	no	—
219	C₂₉×#120	—	2	2	no	—
220	C₂₉×#120	—	2	2	no	—
221	C₂₉×#120	—	2	2	no	—
222	C₂₉×#120	—	2	2	no	—
223	C₄×Q₈×C₂₉	—	2	1	no	—
224	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₂₉	—	2	1	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	—	2	2	no	—
232	C₄×D₄×C₂₉	—	2	2	no	—
233	C₄×D₄×C₂₉	—	2	1	no	—
234	C₄×D₄×C₂₉	—	2	2	no	—
235	C₄×D₄×C₂₉	—	2	1	no	—
236	C₄×D₄×C₂₉	—	2	1	no	—
237	C₄×D₄×C₂₉	—	2	1	no	—
238	C₄×D₄×C₂₉	—	2	1	no	—
239	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
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	2	yes	—
246	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₂₉	C₂³	1	2	yes	—
248	C₄×D₄×C₂₉	C₂³	1	2	yes	—
249	C₄×D₄×C₂₉	C₂³	1	2	yes	—
250	C₄×D₄×C₂₉	C₂³	1	2	yes	—
251	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₂₉	C₂³	1	2	yes	—
253	C₂₉×#117	—	2	1	no	—
254	C₂₉×#117	—	2	2	no	—
255	C₂₉×#117	—	2	1	no	—
256	C₂₉×#117	C₂³	1	2	yes	—
257	C₂₉×#117	C₂³	1	2	yes	—
258	C₂₉×#117	C₂³	1	1	yes	characteristic
259	C₂₉×#117	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
261	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
263	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
264	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
266	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
267	C₂×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	2	yes	—
271	C₂₉×#107	C₂³	1	2	yes	—
272	C₂₉×#107	C₂³	1	1	yes	characteristic
273	C₂₉×#107	C₂³	1	1	yes	characteristic
274	C₂₉×#107	C₂³	1	2	yes	—
275	C₂₉×#106	C₂³	1	1	yes	characteristic
276	C₂₉×#106	C₂³	1	2	yes	—
277	C₂₉×#106	C₂³	1	1	yes	characteristic
278	C₂₉×#106	C₂³	1	2	yes	—
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	1	yes	characteristic
286	C₂₉×#103	C₂³	1	2	yes	—
287	C₂₉×#102	C₂³	1	1	yes	characteristic
288	C₂₉×#102	C₂³	1	1	yes	characteristic
289	C₂₉×#102	C₂³	1	1	yes	characteristic
290	C₂₉×#102	C₂³	1	1	yes	characteristic
291	C₂₉×#102	C₂³	1	1	yes	characteristic
292	C₂₉×#102	C₂³	1	2	yes	—
293	C₂₉×#102	C₂³	1	2	yes	—
294	C₂₉×#102	C₂³	1	2	yes	—
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	1	yes	characteristic
301	C₂₉×#102	C₂³	1	2	yes	—
302	C₂₉×#102	C₂³	1	2	yes	—
303	C₂₉×#102	C₂³	1	2	yes	—
304	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂₉×#97	C₂³	1	1	yes	characteristic
308	C₂₉×#97	C₂³	1	2	yes	—
309	C₂₉×#97	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₂₉	C₂³	1	2	yes	—
311	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₂₉	C₂³	1	2	yes	—
313	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
314	C₂⁴×C₂₉	—	2	1	no	—
315	C₂⁴×C₂₉	—	2	2	no	—
316	C₂⁴×C₂₉	—	2	2	no	—
317	#41×C₂₉	—	2	2	no	—
318	#41×C₂₉	—	4	1	no	—
319	#41×C₂₉	—	8	2	no	—
320	#41×C₂₉	—	8	2	no	—
321	#41×C₂₉	—	8	2	no	—
322	C₂×Q₈×C₂₉	—	2	1	no	—
323	C₂×Q₈×C₂₉	—	2	2	no	—
324	C₂×Q₈×C₂₉	—	2	1	no	—
325	C₂×Q₈×C₂₉	—	8	2	no	—
326	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₂₉	—	2	4	no	—
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	2	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	1	no	—
342	C₂×D₄×C₂₉	—	2	1	no	—
343	C₂×D₄×C₂₉	—	2	2	no	—
344	C₂×D₄×C₂₉	—	2	1	no	—
345	C₂×D₄×C₂₉	—	2	2	no	—
346	C₂×D₄×C₂₉	—	4	2	no	—
347	C₂×D₄×C₂₉	—	4	2	no	—
348	C₂×D₄×C₂₉	—	4	1	no	—
349	C₂×D₄×C₂₉	—	8	2	no	—
350	C₂×D₄×C₂₉	—	8	2	no	—
351	C₂×D₄×C₂₉	—	8	4	no	—
352	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
353	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
354	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
355	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
356	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₂₉	—	2	1	no	—
360	C₂²×C₄×C₂₉	—	2	1	no	—
361	C₂²×C₄×C₂₉	—	2	1	no	—
362	C₂²×C₄×C₂₉	—	2	1	no	—
363	C₂²×C₄×C₂₉	—	2	1	no	—
364	C₂²×C₄×C₂₉	—	2	1	no	—
365	C₂²×C₄×C₂₉	—	2	1	no	—
366	C₂²×C₄×C₂₉	—	2	2	no	—
367	C₂²×C₄×C₂₉	—	2	2	no	—
368	C₂²×C₄×C₂₉	—	2	2	no	—
369	C₂²×C₄×C₂₉	—	2	2	no	—
370	C₂²×C₄×C₂₉	—	2	2	no	—
371	C₂²×C₄×C₂₉	—	2	2	no	—
372	C₂²×C₄×C₂₉	—	2	1	no	—
373	C₂²×C₄×C₂₉	—	8	2	no	—
374	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
376	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
378	SD₁₆×C₂₉	—	2	2	no	—
379	SD₁₆×C₂₉	—	2	2	no	—
380	SD₁₆×C₂₉	—	4	2	no	—
381	D₈×C₂₉	—	2	4	no	—
382	D₈×C₂₉	—	2	4	no	—
383	D₈×C₂₉	—	2	2	no	—
384	D₈×C₂₉	—	2	4	no	—
385	D₈×C₂₉	—	4	2	no	—
386	D₈×C₂₉	—	4	2	no	—
387	D₈×C₂₉	#41	1	4	yes	complemented
388	M₁₆×C₂₉	—	2	2	no	—
389	M₁₆×C₂₉	—	4	1	no	—
390	M₁₆×C₂₉	—	4	2	no	—
391	C₂×C₈×C₂₉	—	2	4	no	—
392	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
393	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
397	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₂₉	—	2	1	no	—
399	C₄⋊C₄×C₂₉	—	2	2	no	—
400	C₄⋊C₄×C₂₉	—	2	1	no	—
401	C₄⋊C₄×C₂₉	—	2	1	no	—
402	C₄⋊C₄×C₂₉	—	2	1	no	—
403	C₄⋊C₄×C₂₉	—	2	2	no	—
404	C₄⋊C₄×C₂₉	—	2	2	no	—
405	C₄⋊C₄×C₂₉	—	2	1	no	—
406	C₄⋊C₄×C₂₉	—	2	2	no	—
407	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
417	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
418	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
419	C₂²⋊C₄×C₂₉	—	2	2	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	1	no	—
424	C₂²⋊C₄×C₂₉	—	2	1	no	—
425	C₂²⋊C₄×C₂₉	—	2	2	no	—
426	C₂²⋊C₄×C₂₉	—	2	2	no	—
427	C₂²⋊C₄×C₂₉	—	2	1	no	—
428	C₂²⋊C₄×C₂₉	—	2	2	no	—
429	C₂²⋊C₄×C₂₉	—	2	2	no	—
430	C₂²⋊C₄×C₂₉	—	2	1	no	—
431	C₂²⋊C₄×C₂₉	—	2	2	no	—
432	C₂²⋊C₄×C₂₉	—	2	1	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	—	2	1	no	—
437	C₂²⋊C₄×C₂₉	—	2	2	no	—
438	C₂²⋊C₄×C₂₉	—	2	2	no	—
439	C₂²⋊C₄×C₂₉	—	2	2	no	—
440	C₂²⋊C₄×C₂₉	—	2	2	no	—
441	C₂²⋊C₄×C₂₉	—	2	2	no	—
442	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
447	C₄²×C₂₉	—	2	1	no	—
448	C₄²×C₂₉	—	2	1	no	—
449	C₄²×C₂₉	—	2	1	no	—
450	C₄²×C₂₉	—	2	2	no	—
451	C₄²×C₂₉	—	2	2	no	—
452	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
455	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
456	C₄²×C₂₉	C₂⁴	1	2	yes	—
457	#61539	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
458	C₂³×C₂₉	—	2	1	no	—
459	C₂³×C₂₉	—	2	1	no	—
460	C₂³×C₂₉	—	2	2	no	—
461	C₂³×C₂₉	—	2	2	no	—
462	C₂³×C₂₉	—	2	1	no	—
463	C₂³×C₂₉	—	4	2	no	—
464	C₂³×C₂₉	—	4	4	no	—
465	C₂³×C₂₉	—	4	4	no	—
466	C₂³×C₂₉	—	4	2	no	—
467	C₂³×C₂₉	—	8	1	no	—
468	C₂³×C₂₉	—	8	2	no	—
469	C₂³×C₂₉	—	8	2	no	—
470	C₂³×C₂₉	—	8	2	no	—
471	C₂³×C₂₉	—	8	2	no	—
472	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
473	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
474	Q₈×C₂₉	—	2	2	no	—
475	Q₈×C₂₉	—	2	1	no	—
476	Q₈×C₂₉	—	2	1	no	—
477	Q₈×C₂₉	—	4	2	no	—
478	Q₈×C₂₉	—	8	2	no	—
479	Q₈×C₂₉	—	8	1	no	—
480	D₄×C₂₉	—	2	2	no	—
481	D₄×C₂₉	—	2	2	no	—
482	D₄×C₂₉	—	2	2	no	—
483	D₄×C₂₉	—	2	1	no	—
484	D₄×C₂₉	—	2	1	no	—
485	D₄×C₂₉	—	2	1	no	—
486	D₄×C₂₉	—	2	2	no	—
487	D₄×C₂₉	—	2	1	no	—
488	D₄×C₂₉	—	2	2	no	—
489	D₄×C₂₉	—	4	2	no	—
490	D₄×C₂₉	—	4	2	no	—
491	D₄×C₂₉	—	4	4	no	—
492	D₄×C₂₉	—	4	4	no	—
493	D₄×C₂₉	—	4	2	no	—
494	D₄×C₂₉	—	4	4	no	—
495	D₄×C₂₉	—	4	2	no	—
496	D₄×C₂₉	—	4	2	no	—
497	D₄×C₂₉	—	8	1	no	—
498	D₄×C₂₉	—	8	2	no	—
499	D₄×C₂₉	—	8	1	no	—
500	D₄×C₂₉	—	8	2	no	—
501	D₄×C₂₉	—	8	2	no	—
502	D₄×C₂₉	—	8	2	no	—
503	D₄×C₂₉	—	8	2	no	—
504	D₄×C₂₉	—	8	2	no	—
505	D₄×C₂₉	C₂×#41	1	2	yes	—
506	D₄×C₂₉	C₂×#41	1	2	yes	—
507	C₂×C₄×C₂₉	—	2	2	no	—
508	C₂×C₄×C₂₉	—	2	2	no	—
509	C₂×C₄×C₂₉	—	2	1	no	—
510	C₂×C₄×C₂₉	—	2	2	no	—
511	C₂×C₄×C₂₉	—	2	1	no	—
512	C₂×C₄×C₂₉	—	2	1	no	—
513	C₂×C₄×C₂₉	—	2	1	no	—
514	C₂×C₄×C₂₉	—	2	1	no	—
515	C₂×C₄×C₂₉	—	2	1	no	—
516	C₂×C₄×C₂₉	—	2	2	no	—
517	C₂×C₄×C₂₉	—	2	2	no	—
518	C₂×C₄×C₂₉	—	2	1	no	—
519	C₂×C₄×C₂₉	—	4	1	no	—
520	C₂×C₄×C₂₉	—	4	2	no	—
521	C₂×C₄×C₂₉	—	4	2	no	—
522	C₂×C₄×C₂₉	—	4	2	no	—
523	C₂×C₄×C₂₉	—	4	2	no	—
524	C₂×C₄×C₂₉	—	8	1	no	—
525	C₂×C₄×C₂₉	—	8	2	no	—
526	C₂×C₄×C₂₉	—	8	1	no	—
527	C₂×C₄×C₂₉	—	8	1	no	—
528	C₂×C₄×C₂₉	—	8	2	no	—
529	C₂×C₄×C₂₉	—	8	2	no	—
530	C₂×C₄×C₂₉	—	8	2	no	—
531	C₂×C₄×C₂₉	—	8	2	no	—
532	C₂×C₄×C₂₉	—	8	2	no	—
533	C₂×C₄×C₂₉	—	8	1	no	—
534	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
535	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
540	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
541	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
543	C₈×C₂₉	—	2	2	no	—
544	C₈×C₂₉	—	2	1	no	—
545	C₈×C₂₉	—	2	1	no	—
546	C₈×C₂₉	—	2	1	no	—
547	C₈×C₂₉	—	2	2	no	—
548	C₈×C₂₉	C₂×#41	1	2	yes	—
549	#3519	C₂×C₂₉	1	1	yes	characteristic, complemented
550	#3514	C₂×C₂₉	1	1	yes	characteristic, complemented
551	#3399	C₂×C₂₉	1	1	yes	characteristic, complemented
552	#3384	C₂×C₂₉	1	1	yes	characteristic, complemented
553	#3361	C₂×C₂₉	1	1	yes	characteristic, complemented
554	#3358	C₂×C₂₉	1	1	yes	characteristic, complemented
555	#3347	C₂×C₂₉	1	2	yes	complemented
556	#3340	C₂×C₂₉	1	1	yes	characteristic, complemented
557	#3325	C₂×C₂₉	1	1	yes	characteristic, complemented
558	#3325	C₂×C₂₉	1	2	yes	complemented
559	#3324	C₂×C₂₉	1	1	yes	characteristic, complemented
560	#3322	C₂×C₂₉	1	2	yes	complemented
561	D₄×D₈	C₂×C₂₉	1	1	yes	characteristic, complemented
562	#3264	C₂×C₂₉	1	2	yes	complemented
563	#3184	C₂×C₂₉	1	1	yes	characteristic, complemented
564	#3179	C₂×C₂₉	1	2	yes	complemented
565	#3122	C₂×C₂₉	1	2	yes	complemented
566	#3118	C₂×C₂₉	1	2	yes	complemented
567	#3106	C₂×C₂₉	1	1	yes	characteristic, complemented
568	#3100	C₂×C₂₉	1	1	yes	characteristic, complemented
569	#2969	C₂×C₂₉	1	1	yes	characteristic, complemented
570	#2948	C₂×C₂₉	1	2	yes	complemented
571	C₄×AGL(1,ℤ/8)	C₂×C₂₉	1	1	yes	characteristic, complemented
572	C₂²×C₂₉	—	2	1	no	—
573	C₂²×C₂₉	—	2	2	no	—
574	C₂²×C₂₉	—	2	1	no	—
575	C₂²×C₂₉	—	2	2	no	—
576	C₂²×C₂₉	—	2	2	no	—
577	C₂²×C₂₉	—	2	2	no	—
578	C₂²×C₂₉	—	2	1	no	—
579	C₂²×C₂₉	—	2	2	no	—
580	C₂²×C₂₉	—	4	1	no	—
581	C₂²×C₂₉	—	4	1	no	—
582	C₂²×C₂₉	—	4	1	no	—
583	C₂²×C₂₉	—	4	1	no	—
584	C₂²×C₂₉	—	4	2	no	—
585	C₂²×C₂₉	—	4	2	no	—
586	C₂²×C₂₉	—	4	1	no	—
587	C₂²×C₂₉	—	4	1	no	—
588	C₂²×C₂₉	—	4	2	no	—
589	C₂²×C₂₉	—	4	2	no	—
590	C₂²×C₂₉	—	4	1	no	—
591	C₂²×C₂₉	—	4	2	no	—
592	C₂²×C₂₉	—	4	2	no	—
593	C₂²×C₂₉	—	8	4	no	—
594	C₂²×C₂₉	—	16	4	no	—
595	C₂²×C₂₉	—	16	4	no	—
596	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
597	C₄×C₂₉	—	2	1	no	—
598	C₄×C₂₉	—	2	1	no	—
599	C₄×C₂₉	—	2	2	no	—
600	C₄×C₂₉	—	2	1	no	—
601	C₄×C₂₉	—	2	2	no	—
602	C₄×C₂₉	—	2	1	no	—
603	C₄×C₂₉	—	2	2	no	—
604	C₄×C₂₉	—	4	1	no	—
605	C₄×C₂₉	—	4	2	no	—
606	C₄×C₂₉	—	4	1	no	—
607	C₄×C₂₉	—	4	1	no	—
608	C₄×C₂₉	—	4	1	no	—
609	C₄×C₂₉	—	4	1	no	—
610	C₄×C₂₉	—	4	2	no	—
611	C₄×C₂₉	#576	1	2	yes	—
612	C₄×C₂₉	C₂²×#41	1	1	yes	characteristic
613	C₄×C₂₉	#585	1	1	yes	characteristic
614	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	1	yes	characteristic
615	C₂²×D₈	C₂²×C₂₉	1	2	yes	—
616	#559	C₂²×C₂₉	1	1	yes	characteristic, complemented
617	#556	C₂²×C₂₉	1	1	yes	characteristic, complemented
618	#555	C₂²×C₂₉	1	1	yes	characteristic
619	#555	C₂²×C₂₉	1	2	yes	complemented
620	#554	C₂²×C₂₉	1	1	yes	characteristic, complemented
621	#553	—	2	1	no	—
622	#553	C₂²×C₂₉	1	2	yes	complemented
623	#551	—	2	2	no	—
624	#550	C₂²×C₂₉	1	1	yes	characteristic, complemented
625	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
626	#548	—	2	1	no	—
627	#546	—	2	1	no	—
628	#546	—	2	2	no	—
629	#546	—	2	1	no	—
630	#546	C₂²×C₂₉	1	2	yes	complemented
631	D₄²	C₂²×C₂₉	1	1	yes	characteristic
632	D₄²	C₂²×C₂₉	1	1	yes	characteristic, complemented
633	D₄²	C₂²×C₂₉	1	2	yes	complemented
634	#542	C₂²×C₂₉	1	2	yes	complemented
635	#540	C₂²×C₂₉	1	2	yes	complemented
636	#538	—	2	2	no	—
637	#538	—	2	2	no	—
638	#532	C₂²×C₂₉	1	1	yes	characteristic, complemented
639	#532	C₂²×C₂₉	1	1	yes	characteristic, complemented
640	#529	—	2	1	no	—
641	#529	C₂²×C₂₉	1	1	yes	characteristic
642	C₂×#124	—	2	1	no	—
643	#525	—	2	1	no	—
644	C₂×#121	—	2	1	no	—
645	#518	C₂²×C₂₉	1	2	yes	complemented
646	#518	C₂²×C₂₉	1	2	yes	complemented
647	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic, complemented
648	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
649	#501	C₂²×C₂₉	1	2	yes	complemented
650	#498	C₂²×C₂₉	1	1	yes	characteristic, complemented
651	#496	C₂²×C₂₉	1	2	yes	complemented
652	#493	C₂²×C₂₉	1	1	yes	characteristic, complemented
653	#488	C₂²×C₂₉	1	2	yes	complemented
654	#486	C₂²×C₂₉	1	2	yes	complemented
655	#486	C₂²×C₂₉	1	1	yes	characteristic, complemented
656	#486	C₂²×C₂₉	1	1	yes	characteristic, complemented
657	#485	C₂²×C₂₉	1	2	yes	complemented
658	#482	C₂²×C₂₉	1	2	yes	complemented
659	#482	C₂²×C₂₉	1	2	yes	complemented
660	#482	C₂²×C₂₉	1	2	yes	complemented
661	#482	C₂²×C₂₉	1	2	yes	complemented
662	#480	C₂²×C₂₉	1	2	yes	complemented
663	#478	C₂²×C₂₉	1	2	yes	complemented
664	#478	C₂²×C₂₉	1	2	yes	complemented
665	#477	C₂²×C₂₉	1	1	yes	characteristic, complemented
666	#476	C₂²×C₂₉	1	1	yes	characteristic, complemented
667	#476	C₂²×C₂₉	1	2	yes	complemented
668	#474	C₂²×C₂₉	1	1	yes	characteristic, complemented
669	#474	C₂²×C₂₉	1	2	yes	complemented
670	#474	C₂²×C₂₉	1	1	yes	characteristic, complemented
671	#469	C₂²×C₂₉	1	2	yes	complemented
672	#469	C₂²×C₂₉	1	2	yes	complemented
673	#469	C₂²×C₂₉	1	2	yes	complemented
674	#468	C₂²×C₂₉	1	2	yes	complemented
675	#466	C₂²×C₂₉	1	2	yes	complemented
676	#465	C₂²×C₂₉	1	2	yes	complemented
677	#463	C₂²×C₂₉	1	2	yes	complemented
678	#463	C₂²×C₂₉	1	2	yes	complemented
679	#460	C₂²×C₂₉	1	1	yes	characteristic, complemented
680	#459	C₂²×C₂₉	1	1	yes	characteristic
681	#459	C₂²×C₂₉	1	1	yes	characteristic, complemented
682	#459	C₂²×C₂₉	1	1	yes	characteristic, complemented
683	#459	C₂²×C₂₉	1	2	yes	complemented
684	#459	C₂²×C₂₉	1	2	yes	complemented
685	#450	C₂²×C₂₉	1	2	yes	complemented
686	#449	C₂²×C₂₉	1	2	yes	complemented
687	#447	C₂²×C₂₉	1	2	yes	—
688	#447	C₂²×C₂₉	1	2	yes	complemented
689	#447	C₂²×C₂₉	1	2	yes	complemented
690	#447	C₂²×C₂₉	1	2	yes	complemented
691	#446	C₂²×C₂₉	1	1	yes	characteristic, complemented
692	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
693	#442	C₂²×C₂₉	1	2	yes	—
694	#442	C₂²×C₂₉	1	1	yes	characteristic
695	#442	C₂²×C₂₉	1	2	yes	complemented
696	#442	C₂²×C₂₉	1	2	yes	complemented
697	#442	C₂²×C₂₉	1	1	yes	characteristic, complemented
698	#442	C₂²×C₂₉	1	2	yes	complemented
699	#440	C₂²×C₂₉	1	1	yes	characteristic, complemented
700	#440	C₂²×C₂₉	1	1	yes	characteristic, complemented
701	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
702	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
703	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
704	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
705	C₄×D₈	C₂²×C₂₉	1	2	yes	complemented
706	C₄×D₈	C₂²×C₂₉	1	2	yes	complemented
707	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
708	C₄×D₈	C₂²×C₂₉	1	2	yes	complemented
709	C₄×D₈	C₂²×C₂₉	1	2	yes	complemented
710	C₄×D₈	C₂²×C₂₉	1	2	yes	complemented
711	#436	C₂²×C₂₉	1	2	yes	complemented
712	#436	C₂²×C₂₉	1	1	yes	characteristic, complemented
713	#435	C₂²×C₂₉	1	2	yes	complemented
714	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
715	#433	C₂²×C₂₉	1	2	yes	complemented
716	#431	C₂²×C₂₉	1	1	yes	characteristic, complemented
717	#428	C₂²×C₂₉	1	1	yes	characteristic, complemented
718	#427	C₂²×C₂₉	1	2	yes	complemented
719	#418	C₂²×C₂₉	1	1	yes	characteristic, complemented
720	#418	C₂²×C₂₉	1	2	yes	complemented
721	#418	C₂²×C₂₉	1	2	yes	complemented
722	#417	C₂²×C₂₉	1	1	yes	characteristic, complemented
723	#405	C₂²×C₂₉	1	2	yes	complemented
724	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
725	C₂×C₂₉	—	4	1	no	—
726	C₂×C₂₉	—	4	2	no	—
727	C₂×C₂₉	—	4	2	no	—
728	C₂×C₂₉	—	4	2	no	—
729	C₂×C₂₉	—	8	1	no	—
730	C₂×C₂₉	—	8	2	no	—
731	C₂×C₂₉	—	8	2	no	—
732	C₂×C₂₉	D₄×#41	1	1	yes	characteristic
733	C₂×C₂₉	C₂×#576	1	1	yes	characteristic
734	C₂×C₂₉	#3585	1	1	yes	characteristic
735	C₂×#41	—	2	1	no	—
736	C₂×#41	—	2	1	no	—
737	C₂×#41	—	2	1	no	—
738	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
739	C₂²×Q₈	—	2	1	no	—
740	C₂²×D₄	—	2	1	no	—
741	C₂²×D₄	—	2	2	no	—
742	C₂²×D₄	—	2	1	no	—
743	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
744	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
745	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
746	C₂³×C₄	—	2	1	no	—
747	AGL(1,ℤ/8)	—	2	4	no	—
748	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
749	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
750	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
751	C₂×D₈	—	2	8	no	—
752	C₂×D₈	C₂³×C₂₉	1	2	yes	—
753	C₂×D₈	C₂³×C₂₉	1	2	yes	—
754	C₂×D₈	C₂³×C₂₉	1	2	yes	—
755	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
756	C₂×D₈	C₂³×C₂₉	1	2	yes	—
757	C₂×D₈	C₂³×C₂₉	1	2	yes	—
758	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
759	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
760	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
761	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
762	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
763	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
764	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
765	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
766	#127	C₂³×C₂₉	1	1	yes	characteristic
767	#127	C₂³×C₂₉	1	1	yes	characteristic
768	#127	C₂³×C₂₉	1	2	yes	—
769	#126	—	2	2	no	—
770	#126	—	2	2	no	—
771	#126	—	2	2	no	—
772	#126	D₄×C₂₉	1	2	yes	—
773	#125	D₄×C₂₉	1	1	yes	characteristic
774	#125	C₂³×C₂₉	1	2	yes	—
775	#124	—	2	1	no	—
776	#124	—	2	1	no	—
777	#124	—	2	2	no	—
778	#124	—	2	2	no	—
779	#124	—	2	2	no	—
780	#124	—	2	2	no	—
781	#124	—	2	1	no	—
782	#124	—	2	1	no	—
783	#124	D₄×C₂₉	1	1	yes	characteristic
784	#124	C₂³×C₂₉	1	2	yes	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	#123	D₄×C₂₉	1	2	yes	—
792	C₂²⋊Q₈	—	2	1	no	—
793	C₂²⋊Q₈	—	2	1	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	—	2	2	no	—
797	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
798	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
799	#121	—	2	2	no	—
800	#121	—	2	1	no	—
801	#121	—	2	2	no	—
802	#121	—	2	1	no	—
803	#121	—	2	1	no	—
804	#121	—	2	1	no	—
805	#121	—	2	1	no	—
806	#121	—	2	1	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	D₄×C₂₉	1	1	yes	characteristic
813	#121	C₂³×C₂₉	1	2	yes	—
814	#121	C₂³×C₂₉	1	2	yes	—
815	#121	C₂³×C₂₉	1	2	yes	—
816	#121	C₂³×C₂₉	1	2	yes	—
817	#121	C₂³×C₂₉	1	2	yes	—
818	#120	—	2	2	no	—
819	#120	—	2	2	no	—
820	#120	—	2	2	no	—
821	#120	—	2	2	no	—
822	#120	—	2	2	no	—
823	C₄×Q₈	—	2	1	no	—
824	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
825	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
826	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
840	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
841	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
842	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
843	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
844	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
845	C₄×D₄	C₂³×C₂₉	1	2	yes	—
846	C₄×D₄	C₂³×C₂₉	1	2	yes	—
847	C₄×D₄	C₂³×C₂₉	1	2	yes	—
848	C₄×D₄	C₂³×C₂₉	1	2	yes	—
849	C₄×D₄	C₂³×C₂₉	1	2	yes	—
850	C₄×D₄	C₂³×C₂₉	1	2	yes	—
851	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
852	C₄×D₄	C₂³×C₂₉	1	2	yes	—
853	#117	—	2	1	no	—
854	#117	—	2	2	no	—
855	#117	—	2	1	no	—
856	#117	C₂³×C₂₉	1	1	yes	characteristic
857	#117	C₂³×C₂₉	1	2	yes	—
858	#117	C₂³×C₂₉	1	2	yes	—
859	#117	C₂³×C₂₉	1	2	yes	—
860	C₂×C₄⋊C₄	—	2	1	no	—
861	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
862	C₂×C₂²⋊C₄	—	2	1	no	—
863	C₂×C₂²⋊C₄	—	2	2	no	—
864	C₂×C₂²⋊C₄	—	2	2	no	—
865	C₂×C₂²⋊C₄	—	2	2	no	—
866	C₂×C₂²⋊C₄	—	2	2	no	—
867	C₂×C₂²⋊C₄	—	2	2	no	—
868	C₂×C₄²	—	2	1	no	—
869	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
870	#107	C₂³×C₂₉	1	2	yes	—
871	#107	C₂³×C₂₉	1	2	yes	—
872	#107	C₂³×C₂₉	1	1	yes	characteristic
873	#107	C₂³×C₂₉	1	1	yes	characteristic
874	#107	C₂³×C₂₉	1	2	yes	—
875	#106	C₂³×C₂₉	1	1	yes	characteristic
876	#106	C₂³×C₂₉	1	2	yes	—
877	#106	C₂³×C₂₉	1	1	yes	characteristic
878	#106	C₂³×C₂₉	1	2	yes	—
879	#106	C₂³×C₂₉	1	2	yes	—
880	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
881	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
882	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
883	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
884	#103	C₂³×C₂₉	1	1	yes	characteristic
885	#103	C₂³×C₂₉	1	1	yes	characteristic
886	#103	C₂³×C₂₉	1	2	yes	—
887	#102	C₂³×C₂₉	1	1	yes	characteristic
888	#102	C₂³×C₂₉	1	1	yes	characteristic
889	#102	C₂³×C₂₉	1	1	yes	characteristic
890	#102	C₂³×C₂₉	1	1	yes	characteristic
891	#102	C₂³×C₂₉	1	1	yes	characteristic
892	#102	C₂³×C₂₉	1	2	yes	—
893	#102	C₂³×C₂₉	1	2	yes	—
894	#102	C₂³×C₂₉	1	2	yes	—
895	#102	C₂³×C₂₉	1	2	yes	—
896	#102	C₂³×C₂₉	1	2	yes	—
897	#102	C₂³×C₂₉	1	2	yes	—
898	#102	C₂³×C₂₉	1	1	yes	characteristic
899	#102	C₂³×C₂₉	1	2	yes	—
900	#102	C₂³×C₂₉	1	2	yes	—
901	#102	C₂³×C₂₉	1	2	yes	—
902	#102	C₂³×C₂₉	1	2	yes	—
903	#102	C₂³×C₂₉	1	2	yes	—
904	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
905	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
906	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
907	#97	C₂³×C₂₉	1	1	yes	characteristic
908	#97	C₂³×C₂₉	1	1	yes	characteristic
909	#97	C₂³×C₂₉	1	2	yes	—
910	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
911	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
912	C₄×C₈	C₂³×C₂₉	1	2	yes	—
913	C₄×C₈	C₂³×C₂₉	1	2	yes	—
914	C₂₉	#61539	1	1	yes	characteristic, direct product factor, Sylow
915	C₂⁴	—	2	1	no	—
916	C₂⁴	—	2	2	no	—
917	C₂⁴	—	2	2	no	—
918	#41	—	2	2	no	—
919	#41	—	4	1	no	—
920	#41	—	8	2	no	—
921	#41	—	8	2	no	—
922	#41	—	8	2	no	—
923	C₂×Q₈	—	2	1	no	—
924	C₂×Q₈	—	2	2	no	—
925	C₂×Q₈	—	2	1	no	—
926	C₂×Q₈	—	8	2	no	—
927	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
928	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
929	C₂×D₄	—	2	4	no	—
930	C₂×D₄	—	2	4	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	1	no	—
942	C₂×D₄	—	2	1	no	—
943	C₂×D₄	—	2	1	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	1	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	4	2	no	—
948	C₂×D₄	—	4	2	no	—
949	C₂×D₄	—	4	1	no	—
950	C₂×D₄	—	8	2	no	—
951	C₂×D₄	—	8	2	no	—
952	C₂×D₄	—	8	4	no	—
953	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
954	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
955	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
956	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
957	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
958	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
959	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
960	C₂²×C₄	—	2	1	no	—
961	C₂²×C₄	—	2	1	no	—
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	1	no	—
964	C₂²×C₄	—	2	1	no	—
965	C₂²×C₄	—	2	1	no	—
966	C₂²×C₄	—	2	1	no	—
967	C₂²×C₄	—	2	2	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	2	no	—
973	C₂²×C₄	—	2	1	no	—
974	C₂²×C₄	—	8	2	no	—
975	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
976	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
977	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
978	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
979	SD₁₆	—	2	2	no	—
980	SD₁₆	—	2	2	no	—
981	SD₁₆	—	4	2	no	—
982	D₈	—	2	4	no	—
983	D₈	—	2	4	no	—
984	D₈	—	2	2	no	—
985	D₈	—	2	4	no	—
986	D₈	—	4	2	no	—
987	D₈	—	4	2	no	—
988	D₈	#41×C₂₉	1	4	yes	complemented
989	M₁₆	—	2	2	no	—
990	M₁₆	—	4	1	no	—
991	M₁₆	—	4	2	no	—
992	C₂×C₈	—	2	4	no	—
993	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
994	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
995	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
996	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
997	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
998	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	1	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1009	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1010	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1011	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1012	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1013	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1014	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1015	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
1016	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1017	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
1018	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1019	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	1	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1044	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1045	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1046	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1047	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1048	C₄²	—	2	1	no	—
1049	C₄²	—	2	1	no	—
1050	C₄²	—	2	1	no	—
1051	C₄²	—	2	2	no	—
1052	C₄²	—	2	2	no	—
1053	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1054	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1055	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1056	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1057	C₄²	C₂⁴×C₂₉	1	2	yes	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	1	no	—
1060	C₂³	—	2	2	no	—
1061	C₂³	—	2	1	no	—
1062	C₂³	—	2	2	no	—
1063	C₂³	—	4	2	no	—
1064	C₂³	—	4	4	no	—
1065	C₂³	—	4	4	no	—
1066	C₂³	—	4	2	no	—
1067	C₂³	—	8	1	no	—
1068	C₂³	—	8	2	no	—
1069	C₂³	—	8	2	no	—
1070	C₂³	—	8	2	no	—
1071	C₂³	—	8	2	no	—
1072	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
1073	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1074	Q₈	—	2	2	no	—
1075	Q₈	—	2	1	no	—
1076	Q₈	—	2	1	no	—
1077	Q₈	—	4	2	no	—
1078	Q₈	—	8	2	no	—
1079	Q₈	—	8	1	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	2	no	—
1082	D₄	—	2	2	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	2	1	no	—
1085	D₄	—	2	1	no	—
1086	D₄	—	2	2	no	—
1087	D₄	—	2	1	no	—
1088	D₄	—	2	2	no	—
1089	D₄	—	4	2	no	—
1090	D₄	—	4	2	no	—
1091	D₄	—	4	4	no	—
1092	D₄	—	4	4	no	—
1093	D₄	—	4	2	no	—
1094	D₄	—	4	4	no	—
1095	D₄	—	4	2	no	—
1096	D₄	—	4	2	no	—
1097	D₄	—	8	2	no	—
1098	D₄	—	8	2	no	—
1099	D₄	—	8	1	no	—
1100	D₄	—	8	1	no	—
1101	D₄	—	8	2	no	—
1102	D₄	—	8	2	no	—
1103	D₄	—	8	2	no	—
1104	D₄	—	8	2	no	—
1105	D₄	C₂×#41×C₂₉	1	2	yes	—
1106	D₄	C₂×#41×C₂₉	1	2	yes	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	4	1	no	—
1120	C₂×C₄	—	4	2	no	—
1121	C₂×C₄	—	4	2	no	—
1122	C₂×C₄	—	4	2	no	—
1123	C₂×C₄	—	4	2	no	—
1124	C₂×C₄	—	8	1	no	—
1125	C₂×C₄	—	8	1	no	—
1126	C₂×C₄	—	8	2	no	—
1127	C₂×C₄	—	8	2	no	—
1128	C₂×C₄	—	8	2	no	—
1129	C₂×C₄	—	8	2	no	—
1130	C₂×C₄	—	8	2	no	—
1131	C₂×C₄	—	8	1	no	—
1132	C₂×C₄	—	8	2	no	—
1133	C₂×C₄	—	8	1	no	—
1134	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1135	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1136	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1137	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1138	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1139	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1140	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1141	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1142	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1143	C₈	—	2	2	no	—
1144	C₈	—	2	1	no	—
1145	C₈	—	2	1	no	—
1146	C₈	—	2	1	no	—
1147	C₈	—	2	2	no	—
1148	C₈	C₂×#41×C₂₉	1	2	yes	—
1149	C₂²	—	2	1	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	2	1	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	1	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	2	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	4	2	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	2	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	8	4	no	—
1171	C₂²	—	16	4	no	—
1172	C₂²	—	16	4	no	—
1173	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
1174	C₄	—	2	1	no	—
1175	C₄	—	2	2	no	—
1176	C₄	—	2	1	no	—
1177	C₄	—	2	2	no	—
1178	C₄	—	2	1	no	—
1179	C₄	—	2	1	no	—
1180	C₄	—	2	2	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	1	no	—
1184	C₄	—	4	1	no	—
1185	C₄	—	4	2	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	2	no	—
1188	C₄	C₂₉×#576	1	2	yes	—
1189	C₄	C₂²×#41×C₂₉	1	1	yes	characteristic
1190	C₄	C₂₉×#585	1	1	yes	characteristic
1191	C₂	—	4	1	no	—
1192	C₂	—	4	2	no	—
1193	C₂	—	4	2	no	—
1194	C₂	—	4	2	no	—
1195	C₂	—	8	1	no	—
1196	C₂	—	8	2	no	—
1197	C₂	—	8	2	no	—
1198	C₂	D₄×#41×C₂₉	1	1	yes	characteristic
1199	C₂	C₂×C₂₉×#576	1	1	yes	characteristic
1200	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×#3514	C₂	semidirect
3. C₂₉×#3399	C₂	semidirect
4. C₂₉×#3384	C₂	semidirect
5. C₂₉×#3361	C₂	semidirect
6. C₂₉×#3358	C₂	semidirect
7. C₂₉×#3347	C₂	semidirect
8. C₂₉×#3340	C₂	semidirect
9. C₂₉×#3325	C₂	semidirect
10. C₂₉×#3325	C₂	semidirect
11. C₂₉×#3324	C₂	semidirect
12. C₂₉×#3322	C₂	semidirect
13. D₄×D₈×C₂₉	C₂	semidirect
14. C₂₉×#3264	C₂	semidirect
15. C₂₉×#3184	C₂	semidirect
16. C₂₉×#3179	C₂	semidirect
17. C₂₉×#3122	C₂	semidirect
18. C₂₉×#3118	C₂	semidirect
19. C₂₉×#3106	C₂	semidirect
20. C₂₉×#3100	C₂	semidirect
21. C₂₉×#2969	C₂	semidirect
22. C₂₉×#2948	C₂	semidirect
23. C₄×C₂₉×AGL(1,ℤ/8)	C₂	semidirect
26. C₂₉×#559	C₂²	semidirect
27. C₂₉×#556	C₂²	semidirect
29. C₂₉×#555	C₂²	semidirect
30. C₂₉×#554	C₂²	semidirect
32. C₂₉×#553	C₂²	semidirect
34. C₂₉×#550	C₂²	semidirect
35. D₄×Q₈×C₂₉	C₂²	semidirect
40. C₂₉×#546	C₂²	semidirect
42. D₄²×C₂₉	C₂²	semidirect
43. D₄²×C₂₉	C₂²	semidirect
44. C₂₉×#542	C₂²	semidirect
45. C₂₉×#540	C₂²	semidirect
48. C₂₉×#532	C₂²	semidirect
49. C₂₉×#532	C₂²	semidirect
55. C₂₉×#518	C₂²	semidirect
56. C₂₉×#518	C₂²	semidirect
57. C₄×#41×C₂₉	C₂²	semidirect
58. C₂×C₄×D₄×C₂₉	C₂²	semidirect
59. C₂₉×#501	C₂²	semidirect
60. C₂₉×#498	C₂²	semidirect
61. C₂₉×#496	C₂²	semidirect
62. C₂₉×#493	C₂²	semidirect
63. C₂₉×#488	C₂²	semidirect
64. C₂₉×#486	C₂²	semidirect
65. C₂₉×#486	C₂²	semidirect
66. C₂₉×#486	C₂²	semidirect
67. C₂₉×#485	C₂²	semidirect
68. C₂₉×#482	C₂²	semidirect
69. C₂₉×#482	C₂²	semidirect
70. C₂₉×#482	C₂²	semidirect
71. C₂₉×#482	C₂²	semidirect
72. C₂₉×#480	C₂²	semidirect
73. C₂₉×#478	C₂²	semidirect
74. C₂₉×#478	C₂²	semidirect
75. C₂₉×#477	C₂²	semidirect
76. C₂₉×#476	C₂²	semidirect
77. C₂₉×#476	C₂²	semidirect
78. C₂₉×#474	C₂²	semidirect
79. C₂₉×#474	C₂²	semidirect
80. C₂₉×#474	C₂²	semidirect
81. C₂₉×#469	C₂²	semidirect
82. C₂₉×#469	C₂²	semidirect
83. C₂₉×#469	C₂²	semidirect
84. C₂₉×#468	C₂²	semidirect
85. C₂₉×#466	C₂²	semidirect
86. C₂₉×#465	C₂²	semidirect
87. C₂₉×#463	C₂²	semidirect
88. C₂₉×#463	C₂²	semidirect
89. C₂₉×#460	C₂²	semidirect
91. C₂₉×#459	C₂²	semidirect
92. C₂₉×#459	C₂²	semidirect
93. C₂₉×#459	C₂²	semidirect
94. C₂₉×#459	C₂²	semidirect
95. C₂₉×#450	C₂²	semidirect
96. C₂₉×#449	C₂²	semidirect
98. C₂₉×#447	C₂²	semidirect
99. C₂₉×#447	C₂²	semidirect
100. C₂₉×#447	C₂²	semidirect
101. C₂₉×#446	C₂²	semidirect
102. C₈×Q₈×C₂₉	C₂²	semidirect
105. C₂₉×#442	C₂²	semidirect
106. C₂₉×#442	C₂²	semidirect
107. C₂₉×#442	C₂²	semidirect
108. C₂₉×#442	C₂²	semidirect
109. C₂₉×#440	C₂²	semidirect
110. C₂₉×#440	C₂²	semidirect
111. C₄×SD₁₆×C₂₉	C₂²	semidirect
112. C₄×SD₁₆×C₂₉	C₂²	semidirect
113. C₄×SD₁₆×C₂₉	C₂²	semidirect
115. C₄×D₈×C₂₉	C₂²	semidirect
116. C₄×D₈×C₂₉	C₂²	semidirect
117. C₄×D₈×C₂₉	C₂²	semidirect
118. C₄×D₈×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×#418	C₂²	semidirect
130. C₂₉×#418	C₂²	semidirect
131. C₂₉×#418	C₂²	semidirect
132. C₂₉×#417	C₂²	semidirect
133. C₂₉×#405	C₂²	semidirect
134. C₄×M₁₆×C₂₉	C₂²	semidirect
387. D₈×C₂₉	#41	semidirect
457. #61539	C₂₉	direct (N × H)
549. #3519	C₂×C₂₉	semidirect
550. #3514	C₂×C₂₉	semidirect
551. #3399	C₂×C₂₉	semidirect
552. #3384	C₂×C₂₉	semidirect
553. #3361	C₂×C₂₉	semidirect
554. #3358	C₂×C₂₉	semidirect
555. #3347	C₂×C₂₉	semidirect
556. #3340	C₂×C₂₉	semidirect
557. #3325	C₂×C₂₉	semidirect
558. #3325	C₂×C₂₉	semidirect
559. #3324	C₂×C₂₉	semidirect
560. #3322	C₂×C₂₉	semidirect
561. D₄×D₈	C₂×C₂₉	semidirect
562. #3264	C₂×C₂₉	semidirect
563. #3184	C₂×C₂₉	semidirect
564. #3179	C₂×C₂₉	semidirect
565. #3122	C₂×C₂₉	semidirect
566. #3118	C₂×C₂₉	semidirect
567. #3106	C₂×C₂₉	semidirect
568. #3100	C₂×C₂₉	semidirect
569. #2969	C₂×C₂₉	semidirect
570. #2948	C₂×C₂₉	semidirect
571. C₄×AGL(1,ℤ/8)	C₂×C₂₉	semidirect
616. #559	C₂²×C₂₉	semidirect
617. #556	C₂²×C₂₉	semidirect
619. #555	C₂²×C₂₉	semidirect
620. #554	C₂²×C₂₉	semidirect
622. #553	C₂²×C₂₉	semidirect
624. #550	C₂²×C₂₉	semidirect
625. D₄×Q₈	C₂²×C₂₉	semidirect
630. #546	C₂²×C₂₉	semidirect
632. D₄²	C₂²×C₂₉	semidirect
633. D₄²	C₂²×C₂₉	semidirect
634. #542	C₂²×C₂₉	semidirect
635. #540	C₂²×C₂₉	semidirect
638. #532	C₂²×C₂₉	semidirect
639. #532	C₂²×C₂₉	semidirect
645. #518	C₂²×C₂₉	semidirect
646. #518	C₂²×C₂₉	semidirect
647. C₄×#41	C₂²×C₂₉	semidirect
648. C₂×C₄×D₄	C₂²×C₂₉	semidirect
649. #501	C₂²×C₂₉	semidirect
650. #498	C₂²×C₂₉	semidirect
651. #496	C₂²×C₂₉	semidirect
652. #493	C₂²×C₂₉	semidirect
653. #488	C₂²×C₂₉	semidirect
654. #486	C₂²×C₂₉	semidirect
655. #486	C₂²×C₂₉	semidirect
656. #486	C₂²×C₂₉	semidirect
657. #485	C₂²×C₂₉	semidirect
658. #482	C₂²×C₂₉	semidirect
659. #482	C₂²×C₂₉	semidirect
660. #482	C₂²×C₂₉	semidirect
661. #482	C₂²×C₂₉	semidirect
662. #480	C₂²×C₂₉	semidirect
663. #478	C₂²×C₂₉	semidirect
664. #478	C₂²×C₂₉	semidirect
665. #477	C₂²×C₂₉	semidirect
666. #476	C₂²×C₂₉	semidirect
667. #476	C₂²×C₂₉	semidirect
668. #474	C₂²×C₂₉	semidirect
669. #474	C₂²×C₂₉	semidirect
670. #474	C₂²×C₂₉	semidirect
671. #469	C₂²×C₂₉	semidirect
672. #469	C₂²×C₂₉	semidirect
673. #469	C₂²×C₂₉	semidirect
674. #468	C₂²×C₂₉	semidirect
675. #466	C₂²×C₂₉	semidirect
676. #465	C₂²×C₂₉	semidirect
677. #463	C₂²×C₂₉	semidirect
678. #463	C₂²×C₂₉	semidirect
679. #460	C₂²×C₂₉	semidirect
681. #459	C₂²×C₂₉	semidirect
682. #459	C₂²×C₂₉	semidirect
683. #459	C₂²×C₂₉	semidirect
684. #459	C₂²×C₂₉	semidirect
685. #450	C₂²×C₂₉	semidirect
686. #449	C₂²×C₂₉	semidirect
688. #447	C₂²×C₂₉	semidirect
689. #447	C₂²×C₂₉	semidirect
690. #447	C₂²×C₂₉	semidirect
691. #446	C₂²×C₂₉	semidirect
692. C₈×Q₈	C₂²×C₂₉	semidirect
695. #442	C₂²×C₂₉	semidirect
696. #442	C₂²×C₂₉	semidirect
697. #442	C₂²×C₂₉	semidirect
698. #442	C₂²×C₂₉	semidirect
699. #440	C₂²×C₂₉	semidirect
700. #440	C₂²×C₂₉	semidirect
701. C₄×SD₁₆	C₂²×C₂₉	semidirect
702. C₄×SD₁₆	C₂²×C₂₉	semidirect
703. C₄×SD₁₆	C₂²×C₂₉	semidirect
705. C₄×D₈	C₂²×C₂₉	semidirect
706. C₄×D₈	C₂²×C₂₉	semidirect
707. C₄×D₈	C₂²×C₂₉	semidirect
708. C₄×D₈	C₂²×C₂₉	semidirect
709. C₄×D₈	C₂²×C₂₉	semidirect
710. C₄×D₈	C₂²×C₂₉	semidirect
711. #436	C₂²×C₂₉	semidirect
712. #436	C₂²×C₂₉	semidirect
713. #435	C₂²×C₂₉	semidirect
714. C₈×D₄	C₂²×C₂₉	semidirect
715. #433	C₂²×C₂₉	semidirect
716. #431	C₂²×C₂₉	semidirect
717. #428	C₂²×C₂₉	semidirect
718. #427	C₂²×C₂₉	semidirect
719. #418	C₂²×C₂₉	semidirect
720. #418	C₂²×C₂₉	semidirect
721. #418	C₂²×C₂₉	semidirect
722. #417	C₂²×C₂₉	semidirect
723. #405	C₂²×C₂₉	semidirect
724. C₄×M₁₆	C₂²×C₂₉	semidirect
914. C₂₉	#61539	direct (N × H)
988. D₈	#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×#3514	2
C₂₉×#3399	2
C₂₉×#3384	2
C₂₉×#3361	2
C₂₉×#3358	2
C₂₉×#3347	2
C₂₉×#3340	2
C₂₉×#3325	2
C₂₉×#3324	2
C₂₉×#3322	2
D₄×D₈×C₂₉	2
C₂₉×#3264	2
C₂₉×#3184	2
C₂₉×#3179	2
C₂₉×#3122	2
C₂₉×#3118	2
C₂₉×#3106	2
C₂₉×#3100	2
C₂₉×#2969	2
C₂₉×#2948	2
C₄×C₂₉×AGL(1,ℤ/8)	2
#61539	29

Subgroups — C29×#61539 #20356439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#61539 #20356439