Subgroups — C₂₉×#61692 #20356592

Order 7424.

2078 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3330	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3328	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#3320	C₂	1	2	yes	maximal, complemented
6	C₂₉×#3307	C₂	1	2	yes	maximal, complemented
7	C₂₉×#3302	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#3298	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#3284	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×SD₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#3278	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#3272	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#3267	C₂	1	2	yes	maximal, complemented
14	C₂₉×#3266	C₂	1	2	yes	maximal, complemented
15	C₂₉×#3218	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#3206	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₉×#3201	C₂	1	2	yes	maximal, complemented
18	C₂₉×#3200	C₂	1	2	yes	maximal, complemented
19	C₂₉×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₉×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₉×#3013	C₂	1	2	yes	maximal, complemented
22	C₂₉×#3010	C₂	1	2	yes	maximal, complemented
23	C₂₉×#2981	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₉×2₋¹⁺⁴	C₂²	1	2	yes	complemented
25	C₂×C₂₉×#137	C₂²	1	2	yes	complemented
26	C₂×C₂₉×AGL(1,ℤ/8)	C₂²	1	2	yes	—
27	C₂×C₂₉×#135	C₂²	1	2	yes	complemented
28	C₂²×SD₁₆×C₂₉	C₂²	1	2	yes	—
29	C₂₉×#560	—	2	2	no	—
30	C₂₉×#556	C₂²	1	1	yes	characteristic
31	C₂₉×#553	C₂²	1	2	yes	—
32	C₂₉×#550	—	2	1	no	—
33	C₂₉×#550	C₂²	1	1	yes	characteristic
34	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₂₉	C₂²	1	2	yes	complemented
36	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
37	C₂₉×#547	—	2	1	no	—
38	C₂₉×#547	—	2	1	no	—
39	C₂₉×#547	—	2	2	no	—
40	C₂₉×#547	C₂²	1	1	yes	characteristic
41	C₂₉×#547	C₂²	1	1	yes	characteristic
42	C₂₉×#547	C₂²	1	2	yes	complemented
43	C₂₉×#547	C₂²	1	1	yes	characteristic, complemented
44	C₂₉×#546	—	2	1	no	—
45	C₂₉×#546	C₂²	1	2	yes	—
46	D₄²×C₂₉	C₂²	1	1	yes	characteristic
47	C₂₉×#542	—	2	1	no	—
48	C₂₉×#538	—	2	2	no	—
49	C₂₉×#537	C₂²	1	2	yes	—
50	C₂₉×#536	—	2	2	no	—
51	C₂₉×#536	C₂²	1	2	yes	complemented
52	C₂₉×#535	—	2	1	no	—
53	C₂₉×#535	C₂²	1	2	yes	—
54	C₂₉×#532	—	2	1	no	—
55	C₂₉×#532	C₂²	1	1	yes	characteristic
56	C₂₉×#532	C₂²	1	1	yes	characteristic
57	C₂×C₂₉×C₄⋊Q₈	—	2	1	no	—
58	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
59	C₂₉×#529	C₂²	1	1	yes	characteristic
60	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic, complemented
61	C₂₉×#497	C₂²	1	2	yes	—
62	C₂₉×#492	C₂²	1	1	yes	characteristic
63	C₂₉×#492	C₂²	1	1	yes	characteristic
64	C₂₉×#491	C₂²	1	2	yes	complemented
65	C₂₉×#487	C₂²	1	1	yes	characteristic, complemented
66	C₂₉×#487	C₂²	1	1	yes	characteristic, complemented
67	C₂₉×#485	C₂²	1	2	yes	complemented
68	C₂₉×#485	C₂²	1	2	yes	complemented
69	C₂₉×#485	C₂²	1	1	yes	characteristic, complemented
70	C₂₉×#484	C₂²	1	2	yes	complemented
71	C₂₉×#483	C₂²	1	2	yes	complemented
72	C₂₉×#482	C₂²	1	1	yes	characteristic
73	C₂₉×#482	C₂²	1	2	yes	complemented
74	C₂₉×#479	C₂²	1	1	yes	characteristic, complemented
75	C₂₉×#478	C₂²	1	1	yes	characteristic, complemented
76	C₂₉×#475	C₂²	1	1	yes	characteristic, complemented
77	C₂₉×#474	C₂²	1	1	yes	characteristic, complemented
78	C₂₉×#470	C₂²	1	2	yes	complemented
79	C₂₉×#468	C₂²	1	2	yes	—
80	C₂₉×#468	C₂²	1	2	yes	—
81	C₂₉×#468	C₂²	1	2	yes	complemented
82	C₂₉×#467	C₂²	1	2	yes	complemented
83	C₂₉×#465	C₂²	1	2	yes	—
84	C₂₉×#465	C₂²	1	2	yes	—
85	C₂₉×#465	C₂²	1	2	yes	complemented
86	C₂₉×#464	C₂²	1	1	yes	characteristic
87	C₂₉×#463	C₂²	1	1	yes	characteristic
88	C₂₉×#462	C₂²	1	1	yes	characteristic, complemented
89	C₂₉×#462	C₂²	1	1	yes	characteristic, complemented
90	C₂₉×#461	C₂²	1	1	yes	characteristic
91	C₂₉×#461	C₂²	1	1	yes	characteristic
92	C₂₉×#461	C₂²	1	2	yes	complemented
93	C₂₉×#461	C₂²	1	2	yes	complemented
94	C₂₉×#460	C₂²	1	1	yes	characteristic
95	C₂₉×#459	C₂²	1	1	yes	characteristic
96	C₂₉×#452	C₂²	1	2	yes	complemented
97	C₂₉×#452	C₂²	1	2	yes	complemented
98	C₂₉×#452	C₂²	1	2	yes	complemented
99	C₂₉×#452	C₂²	1	1	yes	characteristic, complemented
100	C₂₉×#451	C₂²	1	2	yes	complemented
101	C₂₉×#451	C₂²	1	2	yes	complemented
102	C₂₉×#450	C₂²	1	2	yes	—
103	C₂₉×#450	C₂²	1	2	yes	—
104	C₂₉×#449	C₂²	1	1	yes	characteristic
105	C₂₉×#449	C₂²	1	2	yes	—
106	C₂₉×#449	C₂²	1	2	yes	—
107	C₂₉×#449	C₂²	1	2	yes	complemented
108	C₂₉×#449	C₂²	1	2	yes	complemented
109	C₂₉×#448	C₂²	1	2	yes	—
110	C₂₉×#448	C₂²	1	2	yes	—
111	C₂₉×#448	C₂²	1	2	yes	—
112	C₂₉×#448	C₂²	1	2	yes	complemented
113	C₂₉×#448	C₂²	1	2	yes	complemented
114	C₂₉×#448	C₂²	1	2	yes	complemented
115	C₂₉×#442	C₂²	1	2	yes	complemented
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, complemented
123	C₂₉×#435	C₂²	1	2	yes	complemented
124	C₂₉×#435	C₂²	1	2	yes	complemented
125	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
126	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
127	C₂₉×#432	C₂²	1	1	yes	characteristic, complemented
128	C₂₉×#431	C₂²	1	1	yes	characteristic, complemented
129	C₂₉×#419	C₂²	1	2	yes	complemented
130	C₂₉×#417	C₂²	1	2	yes	complemented
131	C₂₉×#416	C₂²	1	2	yes	complemented
132	C₂×C₂₉×#103	C₂²	1	2	yes	complemented
133	C₂₉×#408	C₂²	1	2	yes	complemented
134	C₂₉×#408	C₂²	1	2	yes	complemented
135	C₂₉×2₋¹⁺⁴	—	4	4	no	—
136	C₂₉×2₋¹⁺⁴	—	4	4	no	—
137	C₂×#41×C₂₉	—	2	2	no	—
138	C₂×#41×C₂₉	—	2	2	no	—
139	C₂×#41×C₂₉	—	2	2	no	—
140	C₂×#41×C₂₉	—	2	1	no	—
141	C₂×#41×C₂₉	—	2	1	no	—
142	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
143	C₂×#41×C₂₉	C₂³	1	2	yes	—
144	C₂×#41×C₂₉	C₂³	1	2	yes	—
145	C₂×#41×C₂₉	C₂³	1	2	yes	—
146	C₂×#41×C₂₉	C₂³	1	2	yes	—
147	C₂²×Q₈×C₂₉	—	2	2	no	—
148	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
149	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
150	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
151	C₂²×D₄×C₂₉	—	2	1	no	—
152	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
153	C₂₉×#137	—	4	4	no	—
154	C₂₉×AGL(1,ℤ/8)	—	4	4	no	—
155	C₂₉×#135	—	4	4	no	—
156	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
157	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
158	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₂₉	—	4	4	no	—
160	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
167	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
168	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
169	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
170	C₂×D₈×C₂₉	C₂³	1	2	yes	—
171	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
172	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
173	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
174	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
175	C₂₉×C₄⋊Q₈	—	2	2	no	—
176	C₂₉×C₄⋊Q₈	—	2	1	no	—
177	C₂₉×C₄⋊Q₈	—	2	1	no	—
178	C₂₉×C₄⋊Q₈	—	2	2	no	—
179	C₂₉×C₄⋊Q₈	—	2	1	no	—
180	C₂₉×C₄⋊Q₈	—	2	1	no	—
181	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
182	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
183	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
184	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
185	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
186	C₂₉×#127	—	2	1	no	—
187	C₂₉×#127	—	2	2	no	—
188	C₂₉×#127	D₄	1	1	yes	characteristic
189	C₂₉×#127	C₂³	1	1	yes	characteristic
190	C₂₉×#126	—	2	2	no	—
191	C₂₉×#126	—	2	2	no	—
192	C₂₉×#126	—	2	1	no	—
193	C₂₉×#125	C₂³	1	1	yes	characteristic
194	C₂₉×#124	—	2	2	no	—
195	C₂₉×#124	—	2	2	no	—
196	C₂₉×#124	—	2	1	no	—
197	C₂₉×#124	—	2	1	no	—
198	C₂₉×#124	D₄	1	2	yes	—
199	C₂₉×#124	C₂³	1	1	yes	characteristic
200	C₂₉×#123	—	2	2	no	—
201	C₂₉×#123	—	2	2	no	—
202	C₂₉×#123	—	2	1	no	—
203	C₂₉×#123	—	2	2	no	—
204	C₂₉×#123	—	2	2	no	—
205	C₂₉×#123	—	2	2	no	—
206	C₂₉×#123	—	2	2	no	—
207	C₂₉×#123	—	2	2	no	—
208	C₂₉×#123	—	2	2	no	—
209	C₂₉×#123	—	2	2	no	—
210	C₂₉×C₂²⋊Q₈	—	2	2	no	—
211	C₂₉×C₂²⋊Q₈	—	2	1	no	—
212	C₂₉×C₂²⋊Q₈	—	2	2	no	—
213	C₂₉×C₂²⋊Q₈	—	2	2	no	—
214	C₂₉×C₂²⋊Q₈	—	2	2	no	—
215	C₂₉×C₂²⋊Q₈	—	2	2	no	—
216	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₂₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₂₉×#121	—	2	1	no	—
223	C₂₉×#121	—	2	1	no	—
224	C₂₉×#121	—	2	2	no	—
225	C₂₉×#121	—	2	2	no	—
226	C₂₉×#121	—	2	2	no	—
227	C₂₉×#121	—	2	2	no	—
228	C₂₉×#121	—	2	2	no	—
229	C₂₉×#121	—	2	1	no	—
230	C₂₉×#121	—	2	1	no	—
231	C₂₉×#121	—	2	2	no	—
232	C₂₉×#121	—	2	2	no	—
233	C₂₉×#121	D₄	1	1	yes	characteristic
234	C₂₉×#121	D₄	1	1	yes	characteristic
235	C₂₉×#121	D₄	1	2	yes	—
236	C₂₉×#121	C₂³	1	1	yes	characteristic
237	C₂₉×#121	C₂³	1	2	yes	—
238	C₂₉×#121	C₂³	1	2	yes	—
239	C₂₉×#121	C₂³	1	2	yes	—
240	C₂₉×#121	C₂³	1	2	yes	—
241	C₂₉×#120	—	2	2	no	—
242	C₂₉×#120	—	2	2	no	—
243	C₂₉×#120	—	2	2	no	—
244	C₂₉×#120	—	2	2	no	—
245	C₄×Q₈×C₂₉	—	2	1	no	—
246	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
247	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₂₉	—	2	1	no	—
250	C₄×D₄×C₂₉	—	2	1	no	—
251	C₄×D₄×C₂₉	—	2	2	no	—
252	C₄×D₄×C₂₉	—	2	1	no	—
253	C₄×D₄×C₂₉	—	2	1	no	—
254	C₄×D₄×C₂₉	—	2	1	no	—
255	C₄×D₄×C₂₉	—	2	1	no	—
256	C₄×D₄×C₂₉	—	2	2	no	—
257	C₄×D₄×C₂₉	—	2	1	no	—
258	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₂₉	C₂³	1	2	yes	—
261	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₂₉	C₂³	1	2	yes	—
265	C₂₉×#117	—	2	1	no	—
266	C₂₉×#117	—	2	1	no	—
267	C₂₉×#117	C₂³	1	1	yes	characteristic
268	C₂₉×#117	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
270	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
271	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
272	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
273	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
274	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
275	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
276	C₂×C₄²×C₂₉	—	2	1	no	—
277	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
278	C₂₉×#107	C₂³	1	1	yes	characteristic
279	C₂₉×#107	C₂³	1	1	yes	characteristic
280	C₂₉×#107	C₂³	1	2	yes	—
281	C₂₉×#106	C₂³	1	1	yes	characteristic
282	C₂₉×#106	C₂³	1	1	yes	characteristic
283	C₂₉×#106	C₂³	1	2	yes	—
284	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₂₉×#103	C₂³	1	1	yes	characteristic
289	C₂₉×#103	C₂³	1	1	yes	characteristic
290	C₂₉×#103	C₂³	1	1	yes	characteristic
291	C₂₉×#103	C₂³	1	1	yes	characteristic
292	C₂₉×#103	C₂³	1	2	yes	—
293	C₂₉×#103	C₂³	1	2	yes	—
294	C₂₉×#103	C₂³	1	2	yes	—
295	C₂₉×#103	C₂³	1	2	yes	—
296	C₂₉×#103	C₂³	1	2	yes	—
297	C₂₉×#103	C₂³	1	2	yes	—
298	C₂₉×#103	C₂³	1	2	yes	—
299	C₂₉×#103	C₂³	1	2	yes	—
300	C₂₉×#103	C₂³	1	2	yes	—
301	C₂₉×#102	C₂³	1	1	yes	characteristic
302	C₂₉×#102	C₂³	1	1	yes	characteristic
303	C₂₉×#102	C₂³	1	1	yes	characteristic
304	C₂₉×#102	C₂³	1	1	yes	characteristic
305	C₂₉×#102	C₂³	1	2	yes	—
306	C₂₉×#102	C₂³	1	2	yes	—
307	C₂₉×#102	C₂³	1	2	yes	—
308	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₂₉×#97	C₂³	1	2	yes	—
316	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
318	C₂⁴×C₂₉	—	2	2	no	—
319	#41×C₂₉	—	2	2	no	—
320	#41×C₂₉	—	2	2	no	—
321	#41×C₂₉	—	2	4	no	—
322	#41×C₂₉	—	2	4	no	—
323	#41×C₂₉	—	4	2	no	—
324	#41×C₂₉	—	4	2	no	—
325	#41×C₂₉	—	4	2	no	—
326	#41×C₂₉	—	4	2	no	—
327	#41×C₂₉	—	4	8	no	—
328	#41×C₂₉	—	4	2	no	—
329	#41×C₂₉	—	4	2	no	—
330	#41×C₂₉	—	4	8	no	—
331	#41×C₂₉	—	4	8	no	—
332	#41×C₂₉	—	8	2	no	—
333	#41×C₂₉	—	8	2	no	—
334	C₂×Q₈×C₂₉	—	2	1	no	—
335	C₂×Q₈×C₂₉	—	2	2	no	—
336	C₂×Q₈×C₂₉	—	2	2	no	—
337	C₂×Q₈×C₂₉	—	2	2	no	—
338	C₂×Q₈×C₂₉	—	2	4	no	—
339	C₂×Q₈×C₂₉	—	2	4	no	—
340	C₂×Q₈×C₂₉	—	4	2	no	—
341	C₂×Q₈×C₂₉	—	4	2	no	—
342	C₂×Q₈×C₂₉	—	4	2	no	—
343	C₂×Q₈×C₂₉	—	4	2	no	—
344	C₂×Q₈×C₂₉	—	4	8	no	—
345	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
346	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
347	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
348	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
349	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₂₉	—	2	1	no	—
351	C₂×D₄×C₂₉	—	2	2	no	—
352	C₂×D₄×C₂₉	—	2	2	no	—
353	C₂×D₄×C₂₉	—	2	1	no	—
354	C₂×D₄×C₂₉	—	2	2	no	—
355	C₂×D₄×C₂₉	—	2	2	no	—
356	C₂×D₄×C₂₉	—	2	2	no	—
357	C₂×D₄×C₂₉	—	2	2	no	—
358	C₂×D₄×C₂₉	—	2	2	no	—
359	C₂×D₄×C₂₉	—	2	1	no	—
360	C₂×D₄×C₂₉	—	2	1	no	—
361	C₂×D₄×C₂₉	—	2	2	no	—
362	C₂×D₄×C₂₉	—	4	2	no	—
363	C₂×D₄×C₂₉	—	4	2	no	—
364	C₂×D₄×C₂₉	—	8	2	no	—
365	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
366	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
367	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
368	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
369	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
370	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
371	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
372	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
373	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₂₉	—	2	1	no	—
375	C₂²×C₄×C₂₉	—	2	2	no	—
376	C₂²×C₄×C₂₉	—	2	2	no	—
377	C₂²×C₄×C₂₉	—	2	2	no	—
378	C₂²×C₄×C₂₉	—	2	2	no	—
379	C₂²×C₄×C₂₉	—	2	1	no	—
380	C₂²×C₄×C₂₉	—	2	1	no	—
381	C₂²×C₄×C₂₉	—	2	2	no	—
382	C₂²×C₄×C₂₉	—	2	2	no	—
383	C₂²×C₄×C₂₉	—	2	1	no	—
384	C₂²×C₄×C₂₉	—	2	2	no	—
385	C₂²×C₄×C₂₉	—	2	2	no	—
386	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
387	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
388	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
390	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
391	Q₁₆×C₂₉	—	2	2	no	—
392	Q₁₆×C₂₉	—	4	2	no	—
393	Q₁₆×C₂₉	—	4	2	no	—
394	SD₁₆×C₂₉	—	2	2	no	—
395	SD₁₆×C₂₉	—	2	4	no	—
396	SD₁₆×C₂₉	—	2	2	no	—
397	SD₁₆×C₂₉	—	4	2	no	—
398	SD₁₆×C₂₉	—	4	2	no	—
399	SD₁₆×C₂₉	—	4	2	no	—
400	SD₁₆×C₂₉	—	4	2	no	—
401	SD₁₆×C₂₉	—	4	2	no	—
402	SD₁₆×C₂₉	—	4	2	no	—
403	D₈×C₂₉	—	2	4	no	—
404	D₈×C₂₉	—	2	2	no	—
405	M₁₆×C₂₉	—	4	2	no	—
406	M₁₆×C₂₉	—	4	2	no	—
407	C₂×C₈×C₂₉	—	4	2	no	—
408	C₂×C₈×C₂₉	—	4	2	no	—
409	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
410	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
411	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
412	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
413	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
414	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₂₉	—	2	2	no	—
416	C₄⋊C₄×C₂₉	—	2	1	no	—
417	C₄⋊C₄×C₂₉	—	2	1	no	—
418	C₄⋊C₄×C₂₉	—	2	1	no	—
419	C₄⋊C₄×C₂₉	—	2	1	no	—
420	C₄⋊C₄×C₂₉	—	2	2	no	—
421	C₄⋊C₄×C₂₉	—	2	2	no	—
422	C₄⋊C₄×C₂₉	—	2	2	no	—
423	C₄⋊C₄×C₂₉	—	2	2	no	—
424	C₄⋊C₄×C₂₉	—	2	2	no	—
425	C₄⋊C₄×C₂₉	—	2	2	no	—
426	C₄⋊C₄×C₂₉	—	2	1	no	—
427	C₄⋊C₄×C₂₉	—	2	1	no	—
428	C₄⋊C₄×C₂₉	—	2	1	no	—
429	C₄⋊C₄×C₂₉	—	2	1	no	—
430	C₄⋊C₄×C₂₉	—	2	1	no	—
431	C₄⋊C₄×C₂₉	—	2	1	no	—
432	C₄⋊C₄×C₂₉	—	2	2	no	—
433	C₄⋊C₄×C₂₉	—	2	1	no	—
434	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
435	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
437	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
439	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
440	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
442	C₂²⋊C₄×C₂₉	—	2	2	no	—
443	C₂²⋊C₄×C₂₉	—	2	1	no	—
444	C₂²⋊C₄×C₂₉	—	2	2	no	—
445	C₂²⋊C₄×C₂₉	—	2	1	no	—
446	C₂²⋊C₄×C₂₉	—	2	2	no	—
447	C₂²⋊C₄×C₂₉	—	2	2	no	—
448	C₂²⋊C₄×C₂₉	—	2	2	no	—
449	C₂²⋊C₄×C₂₉	—	2	2	no	—
450	C₂²⋊C₄×C₂₉	—	2	1	no	—
451	C₂²⋊C₄×C₂₉	—	2	2	no	—
452	C₂²⋊C₄×C₂₉	—	2	1	no	—
453	C₂²⋊C₄×C₂₉	—	2	1	no	—
454	C₂²⋊C₄×C₂₉	—	2	1	no	—
455	C₂²⋊C₄×C₂₉	—	2	1	no	—
456	C₂²⋊C₄×C₂₉	—	2	2	no	—
457	C₂²⋊C₄×C₂₉	—	2	2	no	—
458	C₂²⋊C₄×C₂₉	—	2	2	no	—
459	C₂²⋊C₄×C₂₉	—	2	1	no	—
460	C₂²⋊C₄×C₂₉	—	2	2	no	—
461	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
463	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
464	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
465	C₄²×C₂₉	—	2	1	no	—
466	C₄²×C₂₉	—	2	1	no	—
467	C₄²×C₂₉	—	2	1	no	—
468	C₄²×C₂₉	—	2	1	no	—
469	C₄²×C₂₉	—	2	2	no	—
470	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
471	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
472	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
473	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
474	#61692	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
475	C₂³×C₂₉	—	2	1	no	—
476	C₂³×C₂₉	—	2	1	no	—
477	C₂³×C₂₉	—	2	2	no	—
478	C₂³×C₂₉	—	8	2	no	—
479	C₂³×C₂₉	—	8	2	no	—
480	C₂³×C₂₉	—	8	2	no	—
481	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
482	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
483	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
484	Q₈×C₂₉	—	2	1	no	—
485	Q₈×C₂₉	—	2	1	no	—
486	Q₈×C₂₉	—	2	2	no	—
487	Q₈×C₂₉	—	2	2	no	—
488	Q₈×C₂₉	—	2	2	no	—
489	Q₈×C₂₉	—	2	2	no	—
490	Q₈×C₂₉	—	2	1	no	—
491	Q₈×C₂₉	—	4	2	no	—
492	Q₈×C₂₉	—	4	4	no	—
493	Q₈×C₂₉	—	4	4	no	—
494	Q₈×C₂₉	—	4	4	no	—
495	Q₈×C₂₉	—	4	2	no	—
496	Q₈×C₂₉	H(5,𝔽₂)	1	2	yes	—
497	D₄×C₂₉	—	2	4	no	—
498	D₄×C₂₉	—	2	2	no	—
499	D₄×C₂₉	—	2	2	no	—
500	D₄×C₂₉	—	2	1	no	—
501	D₄×C₂₉	—	2	1	no	—
502	D₄×C₂₉	—	2	2	no	—
503	D₄×C₂₉	—	2	1	no	—
504	D₄×C₂₉	—	2	2	no	—
505	D₄×C₂₉	—	4	2	no	—
506	D₄×C₂₉	—	4	2	no	—
507	D₄×C₂₉	—	4	2	no	—
508	D₄×C₂₉	—	4	2	no	—
509	D₄×C₂₉	—	4	4	no	—
510	D₄×C₂₉	—	4	4	no	—
511	D₄×C₂₉	—	4	2	no	—
512	D₄×C₂₉	—	8	1	no	—
513	D₄×C₂₉	—	8	2	no	—
514	D₄×C₂₉	—	8	1	no	—
515	D₄×C₂₉	—	8	2	no	—
516	D₄×C₂₉	—	8	2	no	—
517	D₄×C₂₉	—	8	2	no	—
518	D₄×C₂₉	—	8	2	no	—
519	D₄×C₂₉	—	8	2	no	—
520	D₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
521	C₂×C₄×C₂₉	—	2	4	no	—
522	C₂×C₄×C₂₉	—	2	1	no	—
523	C₂×C₄×C₂₉	—	2	2	no	—
524	C₂×C₄×C₂₉	—	2	2	no	—
525	C₂×C₄×C₂₉	—	2	2	no	—
526	C₂×C₄×C₂₉	—	2	2	no	—
527	C₂×C₄×C₂₉	—	2	2	no	—
528	C₂×C₄×C₂₉	—	2	1	no	—
529	C₂×C₄×C₂₉	—	2	1	no	—
530	C₂×C₄×C₂₉	—	2	1	no	—
531	C₂×C₄×C₂₉	—	2	1	no	—
532	C₂×C₄×C₂₉	—	2	1	no	—
533	C₂×C₄×C₂₉	—	2	1	no	—
534	C₂×C₄×C₂₉	—	2	2	no	—
535	C₂×C₄×C₂₉	—	2	1	no	—
536	C₂×C₄×C₂₉	—	2	2	no	—
537	C₂×C₄×C₂₉	—	2	2	no	—
538	C₂×C₄×C₂₉	—	4	1	no	—
539	C₂×C₄×C₂₉	—	4	4	no	—
540	C₂×C₄×C₂₉	—	4	4	no	—
541	C₂×C₄×C₂₉	—	4	4	no	—
542	C₂×C₄×C₂₉	—	4	4	no	—
543	C₂×C₄×C₂₉	—	4	2	no	—
544	C₂×C₄×C₂₉	—	4	4	no	—
545	C₂×C₄×C₂₉	—	4	2	no	—
546	C₂×C₄×C₂₉	—	4	2	no	—
547	C₂×C₄×C₂₉	—	8	2	no	—
548	C₂×C₄×C₂₉	—	8	2	no	—
549	C₂×C₄×C₂₉	—	8	2	no	—
550	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
553	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
556	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
558	C₈×C₂₉	—	2	1	no	—
559	C₈×C₂₉	—	2	1	no	—
560	C₈×C₂₉	—	2	2	no	—
561	C₈×C₂₉	—	2	2	no	—
562	C₈×C₂₉	—	2	1	no	—
563	C₈×C₂₉	—	2	1	no	—
564	#3546	C₂×C₂₉	1	1	yes	characteristic, complemented
565	#3499	C₂×C₂₉	1	1	yes	characteristic, complemented
566	#3330	C₂×C₂₉	1	1	yes	characteristic, complemented
567	#3328	C₂×C₂₉	1	1	yes	characteristic, complemented
568	#3320	C₂×C₂₉	1	2	yes	complemented
569	#3307	C₂×C₂₉	1	2	yes	complemented
570	#3302	C₂×C₂₉	1	1	yes	characteristic, complemented
571	#3298	C₂×C₂₉	1	1	yes	characteristic, complemented
572	#3284	C₂×C₂₉	1	1	yes	characteristic, complemented
573	D₄×SD₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
574	#3278	C₂×C₂₉	1	1	yes	characteristic, complemented
575	#3272	C₂×C₂₉	1	1	yes	characteristic, complemented
576	#3267	C₂×C₂₉	1	2	yes	complemented
577	#3266	C₂×C₂₉	1	2	yes	complemented
578	#3218	C₂×C₂₉	1	1	yes	characteristic, complemented
579	#3206	C₂×C₂₉	1	1	yes	characteristic, complemented
580	#3201	C₂×C₂₉	1	2	yes	complemented
581	#3200	C₂×C₂₉	1	2	yes	complemented
582	#3115	C₂×C₂₉	1	1	yes	characteristic, complemented
583	#3102	C₂×C₂₉	1	1	yes	characteristic, complemented
584	#3013	C₂×C₂₉	1	2	yes	complemented
585	#3010	C₂×C₂₉	1	2	yes	complemented
586	#2981	C₂×C₂₉	1	1	yes	characteristic, complemented
587	C₂²×C₂₉	—	2	1	no	—
588	C₂²×C₂₉	—	2	2	no	—
589	C₂²×C₂₉	—	2	2	no	—
590	C₂²×C₂₉	—	2	1	no	—
591	C₂²×C₂₉	—	2	2	no	—
592	C₂²×C₂₉	—	2	2	no	—
593	C₂²×C₂₉	—	2	2	no	—
594	C₂²×C₂₉	—	2	1	no	—
595	C₂²×C₂₉	—	2	2	no	—
596	C₂²×C₂₉	—	2	2	no	—
597	C₂²×C₂₉	—	4	1	no	—
598	C₂²×C₂₉	—	4	1	no	—
599	C₂²×C₂₉	—	4	2	no	—
600	C₂²×C₂₉	—	4	1	no	—
601	C₂²×C₂₉	—	4	2	no	—
602	C₂²×C₂₉	—	4	1	no	—
603	C₂²×C₂₉	—	4	1	no	—
604	C₂²×C₂₉	—	4	2	no	—
605	C₂²×C₂₉	—	16	4	no	—
606	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
607	C₄×C₂₉	—	2	1	no	—
608	C₄×C₂₉	—	2	1	no	—
609	C₄×C₂₉	—	2	1	no	—
610	C₄×C₂₉	—	2	2	no	—
611	C₄×C₂₉	—	2	2	no	—
612	C₄×C₂₉	—	2	2	no	—
613	C₄×C₂₉	—	2	1	no	—
614	C₄×C₂₉	—	4	1	no	—
615	C₄×C₂₉	—	4	1	no	—
616	C₄×C₂₉	—	4	2	no	—
617	C₄×C₂₉	—	4	2	no	—
618	C₄×C₂₉	—	4	1	no	—
619	C₄×C₂₉	—	4	1	no	—
620	C₄×C₂₉	—	4	1	no	—
621	C₄×C₂₉	—	4	2	no	—
622	C₄×C₂₉	#577	1	2	yes	—
623	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
624	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
625	C₂×2₋¹⁺⁴	C₂²×C₂₉	1	2	yes	complemented
626	C₂×#137	C₂²×C₂₉	1	2	yes	complemented
627	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	2	yes	—
628	C₂×#135	C₂²×C₂₉	1	2	yes	complemented
629	C₂²×SD₁₆	C₂²×C₂₉	1	2	yes	—
630	#560	—	2	2	no	—
631	#556	C₂²×C₂₉	1	1	yes	characteristic
632	#553	C₂²×C₂₉	1	2	yes	—
633	#550	—	2	1	no	—
634	#550	C₂²×C₂₉	1	1	yes	characteristic
635	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
636	D₄×Q₈	C₂²×C₂₉	1	2	yes	complemented
637	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
638	#547	—	2	1	no	—
639	#547	—	2	1	no	—
640	#547	—	2	2	no	—
641	#547	C₂²×C₂₉	1	1	yes	characteristic
642	#547	C₂²×C₂₉	1	1	yes	characteristic
643	#547	C₂²×C₂₉	1	1	yes	characteristic, complemented
644	#547	C₂²×C₂₉	1	2	yes	complemented
645	#546	—	2	1	no	—
646	#546	C₂²×C₂₉	1	2	yes	—
647	D₄²	C₂²×C₂₉	1	1	yes	characteristic
648	#542	—	2	1	no	—
649	#538	—	2	2	no	—
650	#537	C₂²×C₂₉	1	2	yes	—
651	#536	—	2	2	no	—
652	#536	C₂²×C₂₉	1	2	yes	complemented
653	#535	—	2	1	no	—
654	#535	C₂²×C₂₉	1	2	yes	—
655	#532	—	2	1	no	—
656	#532	C₂²×C₂₉	1	1	yes	characteristic
657	#532	C₂²×C₂₉	1	1	yes	characteristic
658	C₂×C₄⋊Q₈	—	2	1	no	—
659	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
660	#529	C₂²×C₂₉	1	1	yes	characteristic
661	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic, complemented
662	#497	C₂²×C₂₉	1	2	yes	—
663	#492	C₂²×C₂₉	1	1	yes	characteristic
664	#492	C₂²×C₂₉	1	1	yes	characteristic
665	#491	C₂²×C₂₉	1	2	yes	complemented
666	#487	C₂²×C₂₉	1	1	yes	characteristic, complemented
667	#487	C₂²×C₂₉	1	1	yes	characteristic, complemented
668	#485	C₂²×C₂₉	1	2	yes	complemented
669	#485	C₂²×C₂₉	1	1	yes	characteristic, complemented
670	#485	C₂²×C₂₉	1	2	yes	complemented
671	#484	C₂²×C₂₉	1	2	yes	complemented
672	#483	C₂²×C₂₉	1	2	yes	complemented
673	#482	C₂²×C₂₉	1	1	yes	characteristic
674	#482	C₂²×C₂₉	1	2	yes	complemented
675	#479	C₂²×C₂₉	1	1	yes	characteristic, complemented
676	#478	C₂²×C₂₉	1	1	yes	characteristic, complemented
677	#475	C₂²×C₂₉	1	1	yes	characteristic, complemented
678	#474	C₂²×C₂₉	1	1	yes	characteristic, complemented
679	#470	C₂²×C₂₉	1	2	yes	complemented
680	#468	C₂²×C₂₉	1	2	yes	—
681	#468	C₂²×C₂₉	1	2	yes	—
682	#468	C₂²×C₂₉	1	2	yes	complemented
683	#467	C₂²×C₂₉	1	2	yes	complemented
684	#465	C₂²×C₂₉	1	2	yes	—
685	#465	C₂²×C₂₉	1	2	yes	—
686	#465	C₂²×C₂₉	1	2	yes	complemented
687	#464	C₂²×C₂₉	1	1	yes	characteristic
688	#463	C₂²×C₂₉	1	1	yes	characteristic
689	#462	C₂²×C₂₉	1	1	yes	characteristic, complemented
690	#462	C₂²×C₂₉	1	1	yes	characteristic, complemented
691	#461	C₂²×C₂₉	1	1	yes	characteristic
692	#461	C₂²×C₂₉	1	1	yes	characteristic
693	#461	C₂²×C₂₉	1	2	yes	complemented
694	#461	C₂²×C₂₉	1	2	yes	complemented
695	#460	C₂²×C₂₉	1	1	yes	characteristic
696	#459	C₂²×C₂₉	1	1	yes	characteristic
697	#452	C₂²×C₂₉	1	1	yes	characteristic, complemented
698	#452	C₂²×C₂₉	1	2	yes	complemented
699	#452	C₂²×C₂₉	1	2	yes	complemented
700	#452	C₂²×C₂₉	1	2	yes	complemented
701	#451	C₂²×C₂₉	1	2	yes	complemented
702	#451	C₂²×C₂₉	1	2	yes	complemented
703	#450	C₂²×C₂₉	1	2	yes	—
704	#450	C₂²×C₂₉	1	2	yes	—
705	#449	C₂²×C₂₉	1	2	yes	—
706	#449	C₂²×C₂₉	1	1	yes	characteristic
707	#449	C₂²×C₂₉	1	2	yes	—
708	#449	C₂²×C₂₉	1	2	yes	complemented
709	#449	C₂²×C₂₉	1	2	yes	complemented
710	#448	C₂²×C₂₉	1	2	yes	—
711	#448	C₂²×C₂₉	1	2	yes	—
712	#448	C₂²×C₂₉	1	2	yes	—
713	#448	C₂²×C₂₉	1	2	yes	complemented
714	#448	C₂²×C₂₉	1	2	yes	complemented
715	#448	C₂²×C₂₉	1	2	yes	complemented
716	#442	C₂²×C₂₉	1	2	yes	complemented
717	#440	C₂²×C₂₉	1	2	yes	complemented
718	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
719	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
720	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
721	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
722	#436	C₂²×C₂₉	1	1	yes	characteristic
723	#436	C₂²×C₂₉	1	1	yes	characteristic, complemented
724	#435	C₂²×C₂₉	1	2	yes	complemented
725	#435	C₂²×C₂₉	1	2	yes	complemented
726	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
727	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
728	#432	C₂²×C₂₉	1	1	yes	characteristic, complemented
729	#431	C₂²×C₂₉	1	1	yes	characteristic, complemented
730	#419	C₂²×C₂₉	1	2	yes	complemented
731	#417	C₂²×C₂₉	1	2	yes	complemented
732	#416	C₂²×C₂₉	1	2	yes	complemented
733	C₂×#103	C₂²×C₂₉	1	2	yes	complemented
734	#408	C₂²×C₂₉	1	2	yes	complemented
735	#408	C₂²×C₂₉	1	2	yes	complemented
736	C₂×C₂₉	—	4	1	no	—
737	C₂×C₂₉	—	4	2	no	—
738	C₂×C₂₉	—	4	2	no	—
739	C₂×C₂₉	—	4	2	no	—
740	C₂×C₂₉	—	8	2	no	—
741	C₂×C₂₉	—	8	1	no	—
742	C₂×C₂₉	#3484	1	1	yes	characteristic
743	C₂×C₂₉	C₂×#577	1	1	yes	characteristic
744	C₂×C₂₉	#3586	1	1	yes	characteristic
745	2₋¹⁺⁴	—	4	4	no	—
746	2₋¹⁺⁴	—	4	4	no	—
747	C₂×#41	—	2	2	no	—
748	C₂×#41	—	2	2	no	—
749	C₂×#41	—	2	2	no	—
750	C₂×#41	—	2	1	no	—
751	C₂×#41	—	2	1	no	—
752	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
753	C₂×#41	C₂³×C₂₉	1	2	yes	—
754	C₂×#41	C₂³×C₂₉	1	2	yes	—
755	C₂×#41	C₂³×C₂₉	1	2	yes	—
756	C₂×#41	C₂³×C₂₉	1	2	yes	—
757	C₂²×Q₈	—	2	2	no	—
758	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
759	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
760	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
761	C₂²×D₄	—	2	1	no	—
762	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
763	#137	—	4	4	no	—
764	AGL(1,ℤ/8)	—	4	4	no	—
765	#135	—	4	4	no	—
766	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
767	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
768	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
769	C₂×SD₁₆	—	4	4	no	—
770	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
771	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
772	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
773	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
774	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
776	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
777	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
778	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
779	C₂×D₈	C₂³×C₂₉	1	2	yes	—
780	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
781	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
782	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
783	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
784	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
785	C₄⋊Q₈	—	2	2	no	—
786	C₄⋊Q₈	—	2	1	no	—
787	C₄⋊Q₈	—	2	1	no	—
788	C₄⋊Q₈	—	2	2	no	—
789	C₄⋊Q₈	—	2	1	no	—
790	C₄⋊Q₈	—	2	1	no	—
791	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
792	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
793	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
794	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
795	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
796	#127	—	2	1	no	—
797	#127	—	2	2	no	—
798	#127	D₄×C₂₉	1	1	yes	characteristic
799	#127	C₂³×C₂₉	1	1	yes	characteristic
800	#126	—	2	2	no	—
801	#126	—	2	2	no	—
802	#126	—	2	1	no	—
803	#125	C₂³×C₂₉	1	1	yes	characteristic
804	#124	—	2	2	no	—
805	#124	—	2	2	no	—
806	#124	—	2	1	no	—
807	#124	—	2	1	no	—
808	#124	D₄×C₂₉	1	2	yes	—
809	#124	C₂³×C₂₉	1	1	yes	characteristic
810	#123	—	2	2	no	—
811	#123	—	2	2	no	—
812	#123	—	2	1	no	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	#123	—	2	2	no	—
817	#123	—	2	2	no	—
818	#123	—	2	2	no	—
819	#123	—	2	2	no	—
820	C₂²⋊Q₈	—	2	2	no	—
821	C₂²⋊Q₈	—	2	1	no	—
822	C₂²⋊Q₈	—	2	2	no	—
823	C₂²⋊Q₈	—	2	2	no	—
824	C₂²⋊Q₈	—	2	2	no	—
825	C₂²⋊Q₈	—	2	2	no	—
826	C₂²⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
827	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
828	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
829	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
830	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
831	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
832	#121	—	2	1	no	—
833	#121	—	2	1	no	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	—	2	2	no	—
837	#121	—	2	2	no	—
838	#121	—	2	2	no	—
839	#121	—	2	1	no	—
840	#121	—	2	1	no	—
841	#121	—	2	2	no	—
842	#121	—	2	2	no	—
843	#121	D₄×C₂₉	1	1	yes	characteristic
844	#121	D₄×C₂₉	1	1	yes	characteristic
845	#121	D₄×C₂₉	1	2	yes	—
846	#121	C₂³×C₂₉	1	1	yes	characteristic
847	#121	C₂³×C₂₉	1	2	yes	—
848	#121	C₂³×C₂₉	1	2	yes	—
849	#121	C₂³×C₂₉	1	2	yes	—
850	#121	C₂³×C₂₉	1	2	yes	—
851	#120	—	2	2	no	—
852	#120	—	2	2	no	—
853	#120	—	2	2	no	—
854	#120	—	2	2	no	—
855	C₄×Q₈	—	2	1	no	—
856	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
857	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
858	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
859	C₄×D₄	—	2	1	no	—
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	—	2	2	no	—
862	C₄×D₄	—	2	1	no	—
863	C₄×D₄	—	2	1	no	—
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	2	1	no	—
866	C₄×D₄	—	2	2	no	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
869	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
870	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
871	C₄×D₄	C₂³×C₂₉	1	2	yes	—
872	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
873	C₄×D₄	C₂³×C₂₉	1	2	yes	—
874	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
875	#117	—	2	1	no	—
876	#117	—	2	1	no	—
877	#117	C₂³×C₂₉	1	1	yes	characteristic
878	#117	C₂³×C₂₉	1	2	yes	—
879	C₂×C₄⋊C₄	—	2	1	no	—
880	C₂×C₄⋊C₄	—	2	1	no	—
881	C₂×C₄⋊C₄	—	2	1	no	—
882	C₂×C₄⋊C₄	—	2	1	no	—
883	C₂×C₄⋊C₄	—	2	2	no	—
884	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
885	C₂×C₂²⋊C₄	—	2	2	no	—
886	C₂×C₄²	—	2	1	no	—
887	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
888	#107	C₂³×C₂₉	1	1	yes	characteristic
889	#107	C₂³×C₂₉	1	1	yes	characteristic
890	#107	C₂³×C₂₉	1	2	yes	—
891	#106	C₂³×C₂₉	1	1	yes	characteristic
892	#106	C₂³×C₂₉	1	1	yes	characteristic
893	#106	C₂³×C₂₉	1	2	yes	—
894	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
895	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
896	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
897	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
898	#103	C₂³×C₂₉	1	1	yes	characteristic
899	#103	C₂³×C₂₉	1	2	yes	—
900	#103	C₂³×C₂₉	1	2	yes	—
901	#103	C₂³×C₂₉	1	2	yes	—
902	#103	C₂³×C₂₉	1	2	yes	—
903	#103	C₂³×C₂₉	1	2	yes	—
904	#103	C₂³×C₂₉	1	2	yes	—
905	#103	C₂³×C₂₉	1	2	yes	—
906	#103	C₂³×C₂₉	1	1	yes	characteristic
907	#103	C₂³×C₂₉	1	2	yes	—
908	#103	C₂³×C₂₉	1	2	yes	—
909	#103	C₂³×C₂₉	1	1	yes	characteristic
910	#103	C₂³×C₂₉	1	1	yes	characteristic
911	#102	C₂³×C₂₉	1	1	yes	characteristic
912	#102	C₂³×C₂₉	1	2	yes	—
913	#102	C₂³×C₂₉	1	1	yes	characteristic
914	#102	C₂³×C₂₉	1	1	yes	characteristic
915	#102	C₂³×C₂₉	1	1	yes	characteristic
916	#102	C₂³×C₂₉	1	2	yes	—
917	#102	C₂³×C₂₉	1	2	yes	—
918	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
919	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
920	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
921	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
922	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
923	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
924	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
925	#97	C₂³×C₂₉	1	2	yes	—
926	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
927	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
928	C₂₉	#61692	1	1	yes	characteristic, direct product factor, Sylow
929	C₂⁴	—	2	2	no	—
930	#41	—	2	2	no	—
931	#41	—	2	2	no	—
932	#41	—	2	4	no	—
933	#41	—	2	4	no	—
934	#41	—	4	2	no	—
935	#41	—	4	2	no	—
936	#41	—	4	2	no	—
937	#41	—	4	2	no	—
938	#41	—	4	8	no	—
939	#41	—	4	2	no	—
940	#41	—	4	2	no	—
941	#41	—	4	8	no	—
942	#41	—	4	8	no	—
943	#41	—	8	2	no	—
944	#41	—	8	2	no	—
945	C₂×Q₈	—	2	1	no	—
946	C₂×Q₈	—	2	2	no	—
947	C₂×Q₈	—	2	2	no	—
948	C₂×Q₈	—	2	2	no	—
949	C₂×Q₈	—	2	4	no	—
950	C₂×Q₈	—	2	4	no	—
951	C₂×Q₈	—	4	2	no	—
952	C₂×Q₈	—	4	2	no	—
953	C₂×Q₈	—	4	2	no	—
954	C₂×Q₈	—	4	2	no	—
955	C₂×Q₈	—	4	8	no	—
956	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
957	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
958	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
959	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
960	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	1	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	2	no	—
967	C₂×D₄	—	2	2	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	1	no	—
971	C₂×D₄	—	2	1	no	—
972	C₂×D₄	—	2	2	no	—
973	C₂×D₄	—	4	2	no	—
974	C₂×D₄	—	4	2	no	—
975	C₂×D₄	—	8	2	no	—
976	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
977	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
978	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
979	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
980	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
981	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
982	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
983	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
984	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
985	C₂²×C₄	—	2	1	no	—
986	C₂²×C₄	—	2	2	no	—
987	C₂²×C₄	—	2	2	no	—
988	C₂²×C₄	—	2	2	no	—
989	C₂²×C₄	—	2	2	no	—
990	C₂²×C₄	—	2	1	no	—
991	C₂²×C₄	—	2	1	no	—
992	C₂²×C₄	—	2	2	no	—
993	C₂²×C₄	—	2	2	no	—
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	2	no	—
997	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
998	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
999	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1000	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
1001	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
1002	Q₁₆	—	2	2	no	—
1003	Q₁₆	—	4	2	no	—
1004	Q₁₆	—	4	2	no	—
1005	SD₁₆	—	2	2	no	—
1006	SD₁₆	—	2	4	no	—
1007	SD₁₆	—	2	2	no	—
1008	SD₁₆	—	4	2	no	—
1009	SD₁₆	—	4	2	no	—
1010	SD₁₆	—	4	2	no	—
1011	SD₁₆	—	4	2	no	—
1012	SD₁₆	—	4	2	no	—
1013	SD₁₆	—	4	2	no	—
1014	D₈	—	2	4	no	—
1015	D₈	—	2	2	no	—
1016	M₁₆	—	4	2	no	—
1017	M₁₆	—	4	2	no	—
1018	C₂×C₈	—	4	2	no	—
1019	C₂×C₈	—	4	2	no	—
1020	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1021	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1022	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1023	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1024	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
1025	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	2	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	2	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1046	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1047	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1048	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1049	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1050	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1051	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
1052	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	1	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	1	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	1	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	2	1	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1073	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1074	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1075	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1076	C₄²	—	2	1	no	—
1077	C₄²	—	2	1	no	—
1078	C₄²	—	2	1	no	—
1079	C₄²	—	2	1	no	—
1080	C₄²	—	2	2	no	—
1081	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1082	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1083	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1084	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1085	C₂³	—	2	1	no	—
1086	C₂³	—	2	1	no	—
1087	C₂³	—	2	2	no	—
1088	C₂³	—	8	2	no	—
1089	C₂³	—	8	2	no	—
1090	C₂³	—	8	2	no	—
1091	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
1092	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
1093	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1094	Q₈	—	2	1	no	—
1095	Q₈	—	2	1	no	—
1096	Q₈	—	2	2	no	—
1097	Q₈	—	2	2	no	—
1098	Q₈	—	2	2	no	—
1099	Q₈	—	2	2	no	—
1100	Q₈	—	2	1	no	—
1101	Q₈	—	4	2	no	—
1102	Q₈	—	4	4	no	—
1103	Q₈	—	4	4	no	—
1104	Q₈	—	4	4	no	—
1105	Q₈	—	4	2	no	—
1106	Q₈	C₂₉×H(5,𝔽₂)	1	2	yes	—
1107	D₄	—	2	4	no	—
1108	D₄	—	2	2	no	—
1109	D₄	—	2	2	no	—
1110	D₄	—	2	1	no	—
1111	D₄	—	2	1	no	—
1112	D₄	—	2	2	no	—
1113	D₄	—	2	1	no	—
1114	D₄	—	2	2	no	—
1115	D₄	—	4	2	no	—
1116	D₄	—	4	2	no	—
1117	D₄	—	4	2	no	—
1118	D₄	—	4	2	no	—
1119	D₄	—	4	4	no	—
1120	D₄	—	4	4	no	—
1121	D₄	—	4	2	no	—
1122	D₄	—	8	2	no	—
1123	D₄	—	8	1	no	—
1124	D₄	—	8	2	no	—
1125	D₄	—	8	2	no	—
1126	D₄	—	8	2	no	—
1127	D₄	—	8	2	no	—
1128	D₄	—	8	1	no	—
1129	D₄	—	8	2	no	—
1130	D₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
1131	C₂×C₄	—	2	4	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	2	no	—
1147	C₂×C₄	—	2	2	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	4	no	—
1150	C₂×C₄	—	4	4	no	—
1151	C₂×C₄	—	4	4	no	—
1152	C₂×C₄	—	4	4	no	—
1153	C₂×C₄	—	4	2	no	—
1154	C₂×C₄	—	4	4	no	—
1155	C₂×C₄	—	4	2	no	—
1156	C₂×C₄	—	4	2	no	—
1157	C₂×C₄	—	8	2	no	—
1158	C₂×C₄	—	8	2	no	—
1159	C₂×C₄	—	8	2	no	—
1160	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1161	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1162	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1163	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1164	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1165	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1166	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1167	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1168	C₈	—	2	1	no	—
1169	C₈	—	2	1	no	—
1170	C₈	—	2	2	no	—
1171	C₈	—	2	2	no	—
1172	C₈	—	2	1	no	—
1173	C₈	—	2	1	no	—
1174	C₂²	—	2	1	no	—
1175	C₂²	—	2	2	no	—
1176	C₂²	—	2	2	no	—
1177	C₂²	—	2	2	no	—
1178	C₂²	—	2	1	no	—
1179	C₂²	—	2	2	no	—
1180	C₂²	—	2	2	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	1	no	—
1186	C₂²	—	4	2	no	—
1187	C₂²	—	4	1	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	2	no	—
1190	C₂²	—	4	2	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	16	4	no	—
1193	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
1194	C₄	—	2	1	no	—
1195	C₄	—	2	2	no	—
1196	C₄	—	2	2	no	—
1197	C₄	—	2	2	no	—
1198	C₄	—	2	1	no	—
1199	C₄	—	2	1	no	—
1200	C₄	—	2	1	no	—
1201	C₄	—	4	2	no	—
1202	C₄	—	4	2	no	—
1203	C₄	—	4	1	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	2	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	1	no	—
1209	C₄	C₂₉×#577	1	2	yes	—
1210	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
1211	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
1212	C₂	—	4	2	no	—
1213	C₂	—	4	1	no	—
1214	C₂	—	4	2	no	—
1215	C₂	—	4	2	no	—
1216	C₂	—	8	1	no	—
1217	C₂	—	8	2	no	—
1218	C₂	C₂₉×#3484	1	1	yes	characteristic
1219	C₂	C₂×C₂₉×#577	1	1	yes	characteristic
1220	C₂	C₂₉×#3586	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3546	C₂	semidirect
2. C₂₉×#3499	C₂	semidirect
3. C₂₉×#3330	C₂	semidirect
4. C₂₉×#3328	C₂	semidirect
5. C₂₉×#3320	C₂	semidirect
6. C₂₉×#3307	C₂	semidirect
7. C₂₉×#3302	C₂	semidirect
8. C₂₉×#3298	C₂	semidirect
9. C₂₉×#3284	C₂	semidirect
10. D₄×SD₁₆×C₂₉	C₂	semidirect
11. C₂₉×#3278	C₂	semidirect
12. C₂₉×#3272	C₂	semidirect
13. C₂₉×#3267	C₂	semidirect
14. C₂₉×#3266	C₂	semidirect
15. C₂₉×#3218	C₂	semidirect
16. C₂₉×#3206	C₂	semidirect
17. C₂₉×#3201	C₂	semidirect
18. C₂₉×#3200	C₂	semidirect
19. C₂₉×#3115	C₂	semidirect
20. C₂₉×#3102	C₂	semidirect
21. C₂₉×#3013	C₂	semidirect
22. C₂₉×#3010	C₂	semidirect
23. C₂₉×#2981	C₂	semidirect
24. C₂×C₂₉×2₋¹⁺⁴	C₂²	semidirect
25. C₂×C₂₉×#137	C₂²	semidirect
27. C₂×C₂₉×#135	C₂²	semidirect
35. D₄×Q₈×C₂₉	C₂²	semidirect
36. D₄×Q₈×C₂₉	C₂²	semidirect
42. C₂₉×#547	C₂²	semidirect
43. C₂₉×#547	C₂²	semidirect
51. C₂₉×#536	C₂²	semidirect
58. C₂×C₂₉×C₄⋊Q₈	C₂²	semidirect
60. C₄×#41×C₂₉	C₂²	semidirect
64. C₂₉×#491	C₂²	semidirect
65. C₂₉×#487	C₂²	semidirect
66. C₂₉×#487	C₂²	semidirect
67. C₂₉×#485	C₂²	semidirect
68. C₂₉×#485	C₂²	semidirect
69. C₂₉×#485	C₂²	semidirect
70. C₂₉×#484	C₂²	semidirect
71. C₂₉×#483	C₂²	semidirect
73. C₂₉×#482	C₂²	semidirect
74. C₂₉×#479	C₂²	semidirect
75. C₂₉×#478	C₂²	semidirect
76. C₂₉×#475	C₂²	semidirect
77. C₂₉×#474	C₂²	semidirect
78. C₂₉×#470	C₂²	semidirect
81. C₂₉×#468	C₂²	semidirect
82. C₂₉×#467	C₂²	semidirect
85. C₂₉×#465	C₂²	semidirect
88. C₂₉×#462	C₂²	semidirect
89. C₂₉×#462	C₂²	semidirect
92. C₂₉×#461	C₂²	semidirect
93. C₂₉×#461	C₂²	semidirect
96. C₂₉×#452	C₂²	semidirect
97. C₂₉×#452	C₂²	semidirect
98. C₂₉×#452	C₂²	semidirect
99. C₂₉×#452	C₂²	semidirect
100. C₂₉×#451	C₂²	semidirect
101. C₂₉×#451	C₂²	semidirect
107. C₂₉×#449	C₂²	semidirect
108. C₂₉×#449	C₂²	semidirect
112. C₂₉×#448	C₂²	semidirect
113. C₂₉×#448	C₂²	semidirect
114. C₂₉×#448	C₂²	semidirect
115. C₂₉×#442	C₂²	semidirect
116. C₂₉×#440	C₂²	semidirect
117. C₄×Q₁₆×C₂₉	C₂²	semidirect
119. C₄×SD₁₆×C₂₉	C₂²	semidirect
122. C₂₉×#436	C₂²	semidirect
123. C₂₉×#435	C₂²	semidirect
124. C₂₉×#435	C₂²	semidirect
126. C₈×D₄×C₂₉	C₂²	semidirect
127. C₂₉×#432	C₂²	semidirect
128. C₂₉×#431	C₂²	semidirect
129. C₂₉×#419	C₂²	semidirect
130. C₂₉×#417	C₂²	semidirect
131. C₂₉×#416	C₂²	semidirect
132. C₂×C₂₉×#103	C₂²	semidirect
133. C₂₉×#408	C₂²	semidirect
134. C₂₉×#408	C₂²	semidirect
474. #61692	C₂₉	direct (N × H)
564. #3546	C₂×C₂₉	semidirect
565. #3499	C₂×C₂₉	semidirect
566. #3330	C₂×C₂₉	semidirect
567. #3328	C₂×C₂₉	semidirect
568. #3320	C₂×C₂₉	semidirect
569. #3307	C₂×C₂₉	semidirect
570. #3302	C₂×C₂₉	semidirect
571. #3298	C₂×C₂₉	semidirect
572. #3284	C₂×C₂₉	semidirect
573. D₄×SD₁₆	C₂×C₂₉	semidirect
574. #3278	C₂×C₂₉	semidirect
575. #3272	C₂×C₂₉	semidirect
576. #3267	C₂×C₂₉	semidirect
577. #3266	C₂×C₂₉	semidirect
578. #3218	C₂×C₂₉	semidirect
579. #3206	C₂×C₂₉	semidirect
580. #3201	C₂×C₂₉	semidirect
581. #3200	C₂×C₂₉	semidirect
582. #3115	C₂×C₂₉	semidirect
583. #3102	C₂×C₂₉	semidirect
584. #3013	C₂×C₂₉	semidirect
585. #3010	C₂×C₂₉	semidirect
586. #2981	C₂×C₂₉	semidirect
625. C₂×2₋¹⁺⁴	C₂²×C₂₉	semidirect
626. C₂×#137	C₂²×C₂₉	semidirect
628. C₂×#135	C₂²×C₂₉	semidirect
636. D₄×Q₈	C₂²×C₂₉	semidirect
637. D₄×Q₈	C₂²×C₂₉	semidirect
643. #547	C₂²×C₂₉	semidirect
644. #547	C₂²×C₂₉	semidirect
652. #536	C₂²×C₂₉	semidirect
659. C₂×C₄⋊Q₈	C₂²×C₂₉	semidirect
661. C₄×#41	C₂²×C₂₉	semidirect
665. #491	C₂²×C₂₉	semidirect
666. #487	C₂²×C₂₉	semidirect
667. #487	C₂²×C₂₉	semidirect
668. #485	C₂²×C₂₉	semidirect
669. #485	C₂²×C₂₉	semidirect
670. #485	C₂²×C₂₉	semidirect
671. #484	C₂²×C₂₉	semidirect
672. #483	C₂²×C₂₉	semidirect
674. #482	C₂²×C₂₉	semidirect
675. #479	C₂²×C₂₉	semidirect
676. #478	C₂²×C₂₉	semidirect
677. #475	C₂²×C₂₉	semidirect
678. #474	C₂²×C₂₉	semidirect
679. #470	C₂²×C₂₉	semidirect
682. #468	C₂²×C₂₉	semidirect
683. #467	C₂²×C₂₉	semidirect
686. #465	C₂²×C₂₉	semidirect
689. #462	C₂²×C₂₉	semidirect
690. #462	C₂²×C₂₉	semidirect
693. #461	C₂²×C₂₉	semidirect
694. #461	C₂²×C₂₉	semidirect
697. #452	C₂²×C₂₉	semidirect
698. #452	C₂²×C₂₉	semidirect
699. #452	C₂²×C₂₉	semidirect
700. #452	C₂²×C₂₉	semidirect
701. #451	C₂²×C₂₉	semidirect
702. #451	C₂²×C₂₉	semidirect
708. #449	C₂²×C₂₉	semidirect
709. #449	C₂²×C₂₉	semidirect
713. #448	C₂²×C₂₉	semidirect
714. #448	C₂²×C₂₉	semidirect
715. #448	C₂²×C₂₉	semidirect
716. #442	C₂²×C₂₉	semidirect
717. #440	C₂²×C₂₉	semidirect
718. C₄×Q₁₆	C₂²×C₂₉	semidirect
720. C₄×SD₁₆	C₂²×C₂₉	semidirect
723. #436	C₂²×C₂₉	semidirect
724. #435	C₂²×C₂₉	semidirect
725. #435	C₂²×C₂₉	semidirect
727. C₈×D₄	C₂²×C₂₉	semidirect
728. #432	C₂²×C₂₉	semidirect
729. #431	C₂²×C₂₉	semidirect
730. #419	C₂²×C₂₉	semidirect
731. #417	C₂²×C₂₉	semidirect
732. #416	C₂²×C₂₉	semidirect
733. C₂×#103	C₂²×C₂₉	semidirect
734. #408	C₂²×C₂₉	semidirect
735. #408	C₂²×C₂₉	semidirect
928. C₂₉	#61692	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×#3546	2
C₂₉×#3499	2
C₂₉×#3330	2
C₂₉×#3328	2
C₂₉×#3320	2
C₂₉×#3307	2
C₂₉×#3302	2
C₂₉×#3298	2
C₂₉×#3284	2
D₄×SD₁₆×C₂₉	2
C₂₉×#3278	2
C₂₉×#3272	2
C₂₉×#3267	2
C₂₉×#3266	2
C₂₉×#3218	2
C₂₉×#3206	2
C₂₉×#3201	2
C₂₉×#3200	2
C₂₉×#3115	2
C₂₉×#3102	2
C₂₉×#3013	2
C₂₉×#3010	2
C₂₉×#2981	2
#61692	29

Subgroups — C29×#61692 #20356592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#61692 #20356592