Subgroups — C₂₉×#61693 #20356593

Order 7424.

2014 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3331	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3329	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#3315	C₂	1	2	yes	maximal, complemented
6	C₂₉×#3312	C₂	1	2	yes	maximal, complemented
7	C₂₉×#3303	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#3299	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×Q₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#3283	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#3276	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#3276	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#3270	C₂	1	2	yes	maximal, complemented
14	C₂₉×#3269	C₂	1	2	yes	maximal, complemented
15	C₂₉×#3218	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₉×#3202	C₂	1	2	yes	maximal, complemented
18	C₂₉×#3201	C₂	1	2	yes	maximal, complemented
19	C₂₉×#3116	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×#3011	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	—
25	C₂×C₂₉×#137	C₂²	1	2	yes	—
26	C₂×C₂₉×#137	C₂²	1	2	yes	—
27	C₂×C₂₉×#135	C₂²	1	2	yes	—
28	C₂²×Q₁₆×C₂₉	C₂²	1	2	yes	—
29	C₂₉×#562	—	2	2	no	—
30	C₂₉×#555	—	2	1	no	—
31	C₂₉×#555	C₂²	1	1	yes	characteristic
32	C₂₉×#554	C₂²	1	1	yes	characteristic
33	C₂₉×#553	—	2	1	no	—
34	C₂₉×#552	C₂²	1	2	yes	—
35	D₄×Q₈×C₂₉	C₂²	1	2	yes	—
36	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
37	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
39	C₂₉×#548	C₂²	1	2	yes	—
40	C₂₉×#547	—	2	1	no	—
41	C₂₉×#547	—	2	1	no	—
42	C₂₉×#547	—	2	2	no	—
43	C₂₉×#547	C₂²	1	2	yes	—
44	C₂₉×#547	C₂²	1	1	yes	characteristic
45	C₂₉×#547	C₂²	1	1	yes	characteristic
46	C₂₉×#547	C₂²	1	1	yes	characteristic
47	C₂₉×#544	—	2	1	no	—
48	C₂₉×#542	—	2	2	no	—
49	C₂₉×#540	—	2	1	no	—
50	C₂₉×#537	C₂²	1	2	yes	—
51	C₂₉×#536	—	2	2	no	—
52	C₂₉×#536	C₂²	1	2	yes	—
53	C₂₉×#536	C₂²	1	2	yes	—
54	C₂₉×#533	C₂²	1	1	yes	characteristic
55	C₂₉×#532	—	2	1	no	—
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
59	C₂₉×#529	C₂²	1	1	yes	characteristic
60	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
61	C₂₉×#497	C₂²	1	2	yes	—
62	C₂₉×#494	C₂²	1	1	yes	characteristic
63	C₂₉×#494	C₂²	1	1	yes	characteristic
64	C₂₉×#491	C₂²	1	2	yes	—
65	C₂₉×#487	C₂²	1	1	yes	characteristic
66	C₂₉×#487	C₂²	1	1	yes	characteristic
67	C₂₉×#485	C₂²	1	2	yes	—
68	C₂₉×#485	C₂²	1	1	yes	characteristic
69	C₂₉×#485	C₂²	1	2	yes	—
70	C₂₉×#485	C₂²	1	2	yes	—
71	C₂₉×#484	C₂²	1	2	yes	—
72	C₂₉×#483	C₂²	1	2	yes	—
73	C₂₉×#482	C₂²	1	1	yes	characteristic
74	C₂₉×#479	C₂²	1	1	yes	characteristic
75	C₂₉×#478	C₂²	1	1	yes	characteristic
76	C₂₉×#477	C₂²	1	1	yes	characteristic
77	C₂₉×#476	C₂²	1	1	yes	characteristic
78	C₂₉×#470	C₂²	1	2	yes	—
79	C₂₉×#470	C₂²	1	2	yes	—
80	C₂₉×#470	C₂²	1	2	yes	—
81	C₂₉×#468	C₂²	1	2	yes	—
82	C₂₉×#467	C₂²	1	2	yes	—
83	C₂₉×#467	C₂²	1	2	yes	—
84	C₂₉×#467	C₂²	1	2	yes	—
85	C₂₉×#465	C₂²	1	2	yes	—
86	C₂₉×#464	C₂²	1	1	yes	characteristic
87	C₂₉×#463	C₂²	1	1	yes	characteristic
88	C₂₉×#462	C₂²	1	2	yes	—
89	C₂₉×#462	C₂²	1	2	yes	—
90	C₂₉×#462	C₂²	1	1	yes	characteristic
91	C₂₉×#462	C₂²	1	1	yes	characteristic
92	C₂₉×#462	C₂²	1	1	yes	characteristic
93	C₂₉×#461	C₂²	1	1	yes	characteristic
94	C₂₉×#461	C₂²	1	1	yes	characteristic
95	C₂₉×#461	C₂²	1	1	yes	characteristic
96	C₂₉×#452	C₂²	1	2	yes	—
97	C₂₉×#452	C₂²	1	2	yes	—
98	C₂₉×#452	C₂²	1	1	yes	characteristic
99	C₂₉×#452	C₂²	1	2	yes	—
100	C₂₉×#452	C₂²	1	2	yes	—
101	C₂₉×#452	C₂²	1	2	yes	—
102	C₂₉×#452	C₂²	1	2	yes	—
103	C₂₉×#451	C₂²	1	2	yes	—
104	C₂₉×#451	C₂²	1	2	yes	—
105	C₂₉×#451	C₂²	1	2	yes	—
106	C₂₉×#451	C₂²	1	2	yes	—
107	C₂₉×#451	C₂²	1	2	yes	—
108	C₂₉×#451	C₂²	1	2	yes	—
109	C₂₉×#451	C₂²	1	2	yes	—
110	C₂₉×#451	C₂²	1	2	yes	—
111	C₂₉×#449	C₂²	1	1	yes	characteristic
112	C₂₉×#449	C₂²	1	2	yes	—
113	C₂₉×#448	C₂²	1	2	yes	—
114	C₂₉×#448	C₂²	1	2	yes	—
115	C₂₉×#441	C₂²	1	2	yes	—
116	C₂₉×#440	C₂²	1	2	yes	—
117	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
121	C₂₉×#436	C₂²	1	1	yes	characteristic
122	C₂₉×#436	C₂²	1	1	yes	characteristic
123	C₂₉×#435	C₂²	1	2	yes	—
124	C₂₉×#435	C₂²	1	2	yes	—
125	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
126	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
127	C₂₉×#432	C₂²	1	1	yes	characteristic
128	C₂₉×#431	C₂²	1	1	yes	characteristic
129	C₂₉×#419	C₂²	1	2	yes	—
130	C₂₉×#417	C₂²	1	2	yes	—
131	C₂₉×#416	C₂²	1	2	yes	—
132	C₂×C₂₉×#103	C₂²	1	2	yes	—
133	C₂₉×#408	C₂²	1	2	yes	—
134	C₂₉×#408	C₂²	1	2	yes	—
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	C₂³	1	1	yes	characteristic
141	C₂×#41×C₂₉	C₂³	1	2	yes	—
142	C₂×#41×C₂₉	C₂³	1	2	yes	—
143	C₂×#41×C₂₉	C₂³	1	2	yes	—
144	C₂×#41×C₂₉	C₂³	1	2	yes	—
145	C₂²×Q₈×C₂₉	—	2	2	no	—
146	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
147	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
148	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
149	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
150	C₂₉×#137	—	4	4	no	—
151	C₂₉×#137	—	4	4	no	—
152	C₂₉×#135	—	4	4	no	—
153	C₂×Q₁₆×C₂₉	—	4	4	no	—
154	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
155	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
156	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
157	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
158	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
159	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
160	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
161	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
163	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
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×D₈×C₂₉	C₂³	1	1	yes	characteristic
168	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
169	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
170	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
171	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
172	C₂₉×C₄⋊Q₈	—	2	2	no	—
173	C₂₉×C₄⋊Q₈	—	2	2	no	—
174	C₂₉×C₄⋊Q₈	—	2	1	no	—
175	C₂₉×C₄⋊Q₈	—	2	1	no	—
176	C₂₉×C₄⋊Q₈	—	2	2	no	—
177	C₂₉×C₄⋊Q₈	—	2	1	no	—
178	C₂₉×C₄⋊Q₈	—	2	1	no	—
179	C₂₉×C₄⋊Q₈	—	2	1	no	—
180	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
181	C₂₉×C₄⋊Q₈	C₂³	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	D₄	1	1	yes	characteristic
187	C₂₉×#126	—	2	2	no	—
188	C₂₉×#126	—	2	1	no	—
189	C₂₉×#125	—	2	2	no	—
190	C₂₉×#125	—	2	1	no	—
191	C₂₉×#125	—	2	1	no	—
192	C₂₉×#125	C₂³	1	1	yes	characteristic
193	C₂₉×#124	—	2	2	no	—
194	C₂₉×#124	—	2	2	no	—
195	C₂₉×#124	—	2	2	no	—
196	C₂₉×#124	—	2	2	no	—
197	C₂₉×#124	D₄	1	2	yes	—
198	C₂₉×#124	C₂³	1	1	yes	characteristic
199	C₂₉×#123	—	2	2	no	—
200	C₂₉×#123	—	2	2	no	—
201	C₂₉×#123	—	2	2	no	—
202	C₂₉×#123	—	2	2	no	—
203	C₂₉×#123	—	2	2	no	—
204	C₂₉×#123	—	2	1	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	—	2	2	no	—
217	C₂₉×C₂²⋊Q₈	—	2	2	no	—
218	C₂₉×C₂²⋊Q₈	—	2	2	no	—
219	C₂₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
220	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
224	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
225	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
226	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
227	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
228	C₂₉×#121	—	2	1	no	—
229	C₂₉×#121	—	2	1	no	—
230	C₂₉×#121	—	2	2	no	—
231	C₂₉×#121	—	2	2	no	—
232	C₂₉×#121	—	2	2	no	—
233	C₂₉×#121	—	2	2	no	—
234	C₂₉×#121	—	2	1	no	—
235	C₂₉×#121	—	2	2	no	—
236	C₂₉×#121	—	2	1	no	—
237	C₂₉×#121	D₄	1	1	yes	characteristic
238	C₂₉×#121	D₄	1	1	yes	characteristic
239	C₂₉×#121	D₄	1	2	yes	—
240	C₂₉×#121	C₂³	1	1	yes	characteristic
241	C₂₉×#121	C₂³	1	2	yes	—
242	C₄×Q₈×C₂₉	—	2	1	no	—
243	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
245	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
246	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₂₉	—	2	1	no	—
248	C₄×D₄×C₂₉	—	2	1	no	—
249	C₄×D₄×C₂₉	—	2	2	no	—
250	C₄×D₄×C₂₉	—	2	1	no	—
251	C₄×D₄×C₂₉	—	2	1	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	2	no	—
256	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₂₉	C₂³	1	2	yes	—
262	C₂₉×#117	—	2	1	no	—
263	C₂₉×#117	—	2	1	no	—
264	C₂₉×#117	—	2	2	no	—
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	—	2	1	no	—
275	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
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×#103	C₂³	1	2	yes	—
302	C₂₉×#103	C₂³	1	2	yes	—
303	C₂₉×#102	C₂³	1	1	yes	characteristic
304	C₂₉×#102	C₂³	1	1	yes	characteristic
305	C₂₉×#102	C₂³	1	1	yes	characteristic
306	C₂₉×#102	C₂³	1	1	yes	characteristic
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	#41×C₂₉	—	2	2	no	—
319	#41×C₂₉	—	2	2	no	—
320	#41×C₂₉	—	2	4	no	—
321	#41×C₂₉	—	2	4	no	—
322	#41×C₂₉	—	4	2	no	—
323	#41×C₂₉	—	4	2	no	—
324	#41×C₂₉	—	4	2	no	—
325	#41×C₂₉	—	4	2	no	—
326	#41×C₂₉	—	4	8	no	—
327	#41×C₂₉	—	4	2	no	—
328	#41×C₂₉	—	4	2	no	—
329	#41×C₂₉	—	4	8	no	—
330	#41×C₂₉	—	4	8	no	—
331	C₂×Q₈×C₂₉	—	2	2	no	—
332	C₂×Q₈×C₂₉	—	2	2	no	—
333	C₂×Q₈×C₂₉	—	2	2	no	—
334	C₂×Q₈×C₂₉	—	2	1	no	—
335	C₂×Q₈×C₂₉	—	2	2	no	—
336	C₂×Q₈×C₂₉	—	2	4	no	—
337	C₂×Q₈×C₂₉	—	2	4	no	—
338	C₂×Q₈×C₂₉	—	4	2	no	—
339	C₂×Q₈×C₂₉	—	4	2	no	—
340	C₂×Q₈×C₂₉	—	4	2	no	—
341	C₂×Q₈×C₂₉	—	4	2	no	—
342	C₂×Q₈×C₂₉	—	4	8	no	—
343	C₂×Q₈×C₂₉	—	4	2	no	—
344	C₂×Q₈×C₂₉	—	4	2	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	2	yes	—
350	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₂₉	—	2	1	no	—
352	C₂×D₄×C₂₉	—	2	2	no	—
353	C₂×D₄×C₂₉	—	2	2	no	—
354	C₂×D₄×C₂₉	—	2	1	no	—
355	C₂×D₄×C₂₉	—	2	2	no	—
356	C₂×D₄×C₂₉	—	2	2	no	—
357	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
358	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
359	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
360	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
361	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
362	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
363	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
364	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
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	1	no	—
372	C₂²×C₄×C₂₉	—	2	1	no	—
373	C₂²×C₄×C₂₉	—	2	2	no	—
374	C₂²×C₄×C₂₉	—	2	2	no	—
375	C₂²×C₄×C₂₉	—	2	1	no	—
376	C₂²×C₄×C₂₉	—	2	2	no	—
377	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
378	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
379	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
381	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
382	Q₁₆×C₂₉	—	2	2	no	—
383	Q₁₆×C₂₉	—	2	4	no	—
384	Q₁₆×C₂₉	—	4	2	no	—
385	Q₁₆×C₂₉	—	4	2	no	—
386	Q₁₆×C₂₉	—	4	2	no	—
387	Q₁₆×C₂₉	—	4	2	no	—
388	Q₁₆×C₂₉	—	4	2	no	—
389	Q₁₆×C₂₉	—	4	2	no	—
390	SD₁₆×C₂₉	—	2	2	no	—
391	SD₁₆×C₂₉	—	2	4	no	—
392	SD₁₆×C₂₉	—	2	2	no	—
393	SD₁₆×C₂₉	—	4	2	no	—
394	SD₁₆×C₂₉	—	4	2	no	—
395	D₈×C₂₉	—	2	2	no	—
396	M₁₆×C₂₉	—	4	2	no	—
397	M₁₆×C₂₉	—	4	2	no	—
398	C₂×C₈×C₂₉	—	4	2	no	—
399	C₂×C₈×C₂₉	—	4	2	no	—
400	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
401	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
402	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
403	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
404	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₂₉	—	2	2	no	—
407	C₄⋊C₄×C₂₉	—	2	1	no	—
408	C₄⋊C₄×C₂₉	—	2	1	no	—
409	C₄⋊C₄×C₂₉	—	2	1	no	—
410	C₄⋊C₄×C₂₉	—	2	2	no	—
411	C₄⋊C₄×C₂₉	—	2	1	no	—
412	C₄⋊C₄×C₂₉	—	2	1	no	—
413	C₄⋊C₄×C₂₉	—	2	2	no	—
414	C₄⋊C₄×C₂₉	—	2	2	no	—
415	C₄⋊C₄×C₂₉	—	2	2	no	—
416	C₄⋊C₄×C₂₉	—	2	2	no	—
417	C₄⋊C₄×C₂₉	—	2	2	no	—
418	C₄⋊C₄×C₂₉	—	2	2	no	—
419	C₄⋊C₄×C₂₉	—	2	1	no	—
420	C₄⋊C₄×C₂₉	—	2	1	no	—
421	C₄⋊C₄×C₂₉	—	2	1	no	—
422	C₄⋊C₄×C₂₉	—	2	1	no	—
423	C₄⋊C₄×C₂₉	—	2	2	no	—
424	C₄⋊C₄×C₂₉	—	2	1	no	—
425	C₄⋊C₄×C₂₉	—	2	1	no	—
426	C₄⋊C₄×C₂₉	—	2	2	no	—
427	C₄⋊C₄×C₂₉	—	2	2	no	—
428	C₄⋊C₄×C₂₉	—	2	1	no	—
429	C₄⋊C₄×C₂₉	—	2	2	no	—
430	C₄⋊C₄×C₂₉	—	2	1	no	—
431	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
432	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
433	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
434	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
435	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
436	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
439	C₂²⋊C₄×C₂₉	—	2	2	no	—
440	C₂²⋊C₄×C₂₉	—	2	2	no	—
441	C₂²⋊C₄×C₂₉	—	2	1	no	—
442	C₂²⋊C₄×C₂₉	—	2	2	no	—
443	C₂²⋊C₄×C₂₉	—	2	2	no	—
444	C₂²⋊C₄×C₂₉	—	2	2	no	—
445	C₂²⋊C₄×C₂₉	—	2	2	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	1	no	—
450	C₂²⋊C₄×C₂₉	—	2	1	no	—
451	C₂²⋊C₄×C₂₉	—	2	1	no	—
452	C₂²⋊C₄×C₂₉	—	2	1	no	—
453	C₂²⋊C₄×C₂₉	—	2	1	no	—
454	C₂²⋊C₄×C₂₉	—	2	2	no	—
455	C₂²⋊C₄×C₂₉	—	2	1	no	—
456	C₂²⋊C₄×C₂₉	—	2	1	no	—
457	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
458	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
459	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
460	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
461	C₄²×C₂₉	—	2	1	no	—
462	C₄²×C₂₉	—	2	1	no	—
463	C₄²×C₂₉	—	2	1	no	—
464	C₄²×C₂₉	—	2	2	no	—
465	C₄²×C₂₉	—	2	2	no	—
466	C₄²×C₂₉	—	2	1	no	—
467	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
468	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
469	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
470	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
471	#61693	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
472	C₂³×C₂₉	—	2	1	no	—
473	C₂³×C₂₉	—	2	1	no	—
474	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
475	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
476	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
477	Q₈×C₂₉	—	2	1	no	—
478	Q₈×C₂₉	—	2	1	no	—
479	Q₈×C₂₉	—	2	2	no	—
480	Q₈×C₂₉	—	2	2	no	—
481	Q₈×C₂₉	—	2	2	no	—
482	Q₈×C₂₉	—	2	1	no	—
483	Q₈×C₂₉	—	2	2	no	—
484	Q₈×C₂₉	—	2	2	no	—
485	Q₈×C₂₉	—	2	2	no	—
486	Q₈×C₂₉	—	4	2	no	—
487	Q₈×C₂₉	—	4	4	no	—
488	Q₈×C₂₉	—	4	4	no	—
489	Q₈×C₂₉	—	4	4	no	—
490	Q₈×C₂₉	—	8	1	no	—
491	Q₈×C₂₉	—	8	2	no	—
492	Q₈×C₂₉	H(5,𝔽₂)	1	2	yes	—
493	D₄×C₂₉	—	2	4	no	—
494	D₄×C₂₉	—	2	2	no	—
495	D₄×C₂₉	—	2	2	no	—
496	D₄×C₂₉	—	2	1	no	—
497	D₄×C₂₉	—	2	1	no	—
498	D₄×C₂₉	—	2	1	no	—
499	D₄×C₂₉	—	4	2	no	—
500	D₄×C₂₉	—	4	2	no	—
501	D₄×C₂₉	—	4	2	no	—
502	D₄×C₂₉	—	4	2	no	—
503	D₄×C₂₉	—	4	4	no	—
504	D₄×C₂₉	—	4	4	no	—
505	D₄×C₂₉	—	8	1	no	—
506	D₄×C₂₉	—	8	2	no	—
507	D₄×C₂₉	—	8	2	no	—
508	D₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
509	C₂×C₄×C₂₉	—	2	4	no	—
510	C₂×C₄×C₂₉	—	2	1	no	—
511	C₂×C₄×C₂₉	—	2	2	no	—
512	C₂×C₄×C₂₉	—	2	2	no	—
513	C₂×C₄×C₂₉	—	2	2	no	—
514	C₂×C₄×C₂₉	—	2	2	no	—
515	C₂×C₄×C₂₉	—	2	2	no	—
516	C₂×C₄×C₂₉	—	2	1	no	—
517	C₂×C₄×C₂₉	—	2	1	no	—
518	C₂×C₄×C₂₉	—	2	1	no	—
519	C₂×C₄×C₂₉	—	2	1	no	—
520	C₂×C₄×C₂₉	—	2	1	no	—
521	C₂×C₄×C₂₉	—	2	2	no	—
522	C₂×C₄×C₂₉	—	2	1	no	—
523	C₂×C₄×C₂₉	—	2	1	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	—	4	1	no	—
528	C₂×C₄×C₂₉	—	4	4	no	—
529	C₂×C₄×C₂₉	—	4	4	no	—
530	C₂×C₄×C₂₉	—	4	4	no	—
531	C₂×C₄×C₂₉	—	4	4	no	—
532	C₂×C₄×C₂₉	—	4	2	no	—
533	C₂×C₄×C₂₉	—	4	4	no	—
534	C₂×C₄×C₂₉	—	4	2	no	—
535	C₂×C₄×C₂₉	—	4	2	no	—
536	C₂×C₄×C₂₉	—	8	2	no	—
537	C₂×C₄×C₂₉	—	8	2	no	—
538	C₂×C₄×C₂₉	—	8	2	no	—
539	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
543	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
545	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
547	C₈×C₂₉	—	2	1	no	—
548	C₈×C₂₉	—	2	1	no	—
549	C₈×C₂₉	—	2	2	no	—
550	C₈×C₂₉	—	2	2	no	—
551	C₈×C₂₉	—	2	1	no	—
552	C₈×C₂₉	—	2	1	no	—
553	#3547	C₂×C₂₉	1	1	yes	characteristic, complemented
554	#3499	C₂×C₂₉	1	1	yes	characteristic, complemented
555	#3331	C₂×C₂₉	1	1	yes	characteristic, complemented
556	#3329	C₂×C₂₉	1	1	yes	characteristic, complemented
557	#3315	C₂×C₂₉	1	2	yes	complemented
558	#3312	C₂×C₂₉	1	2	yes	complemented
559	#3303	C₂×C₂₉	1	1	yes	characteristic, complemented
560	#3299	C₂×C₂₉	1	1	yes	characteristic, complemented
561	D₄×Q₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
562	#3283	C₂×C₂₉	1	1	yes	characteristic, complemented
563	#3276	C₂×C₂₉	1	1	yes	characteristic, complemented
564	#3276	C₂×C₂₉	1	1	yes	characteristic, complemented
565	#3270	C₂×C₂₉	1	2	yes	complemented
566	#3269	C₂×C₂₉	1	2	yes	complemented
567	#3218	C₂×C₂₉	1	1	yes	characteristic, complemented
568	#3209	C₂×C₂₉	1	1	yes	characteristic, complemented
569	#3202	C₂×C₂₉	1	2	yes	complemented
570	#3201	C₂×C₂₉	1	2	yes	complemented
571	#3116	C₂×C₂₉	1	1	yes	characteristic, complemented
572	#3102	C₂×C₂₉	1	1	yes	characteristic, complemented
573	#3013	C₂×C₂₉	1	2	yes	complemented
574	#3011	C₂×C₂₉	1	2	yes	complemented
575	#2981	C₂×C₂₉	1	1	yes	characteristic, complemented
576	C₂²×C₂₉	—	2	1	no	—
577	C₂²×C₂₉	—	2	2	no	—
578	C₂²×C₂₉	—	2	2	no	—
579	C₂²×C₂₉	—	2	1	no	—
580	C₂²×C₂₉	—	2	2	no	—
581	C₂²×C₂₉	—	2	2	no	—
582	C₂²×C₂₉	—	2	2	no	—
583	C₂²×C₂₉	—	2	1	no	—
584	C₂²×C₂₉	—	2	2	no	—
585	C₂²×C₂₉	—	2	2	no	—
586	C₂²×C₂₉	—	4	1	no	—
587	C₂²×C₂₉	—	4	1	no	—
588	C₂²×C₂₉	—	4	1	no	—
589	C₂²×C₂₉	—	4	1	no	—
590	C₂²×C₂₉	—	4	1	no	—
591	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
592	C₄×C₂₉	—	2	1	no	—
593	C₄×C₂₉	—	2	1	no	—
594	C₄×C₂₉	—	2	1	no	—
595	C₄×C₂₉	—	2	2	no	—
596	C₄×C₂₉	—	2	2	no	—
597	C₄×C₂₉	—	2	2	no	—
598	C₄×C₂₉	—	2	1	no	—
599	C₄×C₂₉	—	4	1	no	—
600	C₄×C₂₉	—	4	1	no	—
601	C₄×C₂₉	—	4	2	no	—
602	C₄×C₂₉	—	4	2	no	—
603	C₄×C₂₉	—	4	2	no	—
604	C₄×C₂₉	—	4	2	no	—
605	C₄×C₂₉	—	4	1	no	—
606	C₄×C₂₉	—	4	1	no	—
607	C₄×C₂₉	—	4	1	no	—
608	C₄×C₂₉	#578	1	2	yes	—
609	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
610	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
611	C₂×2₋¹⁺⁴	C₂²×C₂₉	1	2	yes	—
612	C₂×#137	C₂²×C₂₉	1	2	yes	—
613	C₂×#137	C₂²×C₂₉	1	2	yes	—
614	C₂×#135	C₂²×C₂₉	1	2	yes	—
615	C₂²×Q₁₆	C₂²×C₂₉	1	2	yes	—
616	#562	—	2	2	no	—
617	#555	—	2	1	no	—
618	#555	C₂²×C₂₉	1	1	yes	characteristic
619	#554	C₂²×C₂₉	1	1	yes	characteristic
620	#553	—	2	1	no	—
621	#552	C₂²×C₂₉	1	2	yes	—
622	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
623	D₄×Q₈	C₂²×C₂₉	1	2	yes	—
624	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
625	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
626	#548	C₂²×C₂₉	1	2	yes	—
627	#547	—	2	1	no	—
628	#547	—	2	1	no	—
629	#547	—	2	2	no	—
630	#547	C₂²×C₂₉	1	1	yes	characteristic
631	#547	C₂²×C₂₉	1	2	yes	—
632	#547	C₂²×C₂₉	1	1	yes	characteristic
633	#547	C₂²×C₂₉	1	1	yes	characteristic
634	#544	—	2	1	no	—
635	#542	—	2	2	no	—
636	#540	—	2	1	no	—
637	#537	C₂²×C₂₉	1	2	yes	—
638	#536	—	2	2	no	—
639	#536	C₂²×C₂₉	1	2	yes	—
640	#536	C₂²×C₂₉	1	2	yes	—
641	#533	C₂²×C₂₉	1	1	yes	characteristic
642	#532	—	2	1	no	—
643	#532	C₂²×C₂₉	1	1	yes	characteristic
644	C₂×C₄⋊Q₈	—	2	1	no	—
645	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
646	#529	C₂²×C₂₉	1	1	yes	characteristic
647	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
648	#497	C₂²×C₂₉	1	2	yes	—
649	#494	C₂²×C₂₉	1	1	yes	characteristic
650	#494	C₂²×C₂₉	1	1	yes	characteristic
651	#491	C₂²×C₂₉	1	2	yes	—
652	#487	C₂²×C₂₉	1	1	yes	characteristic
653	#487	C₂²×C₂₉	1	1	yes	characteristic
654	#485	C₂²×C₂₉	1	2	yes	—
655	#485	C₂²×C₂₉	1	1	yes	characteristic
656	#485	C₂²×C₂₉	1	2	yes	—
657	#485	C₂²×C₂₉	1	2	yes	—
658	#484	C₂²×C₂₉	1	2	yes	—
659	#483	C₂²×C₂₉	1	2	yes	—
660	#482	C₂²×C₂₉	1	1	yes	characteristic
661	#479	C₂²×C₂₉	1	1	yes	characteristic
662	#478	C₂²×C₂₉	1	1	yes	characteristic
663	#477	C₂²×C₂₉	1	1	yes	characteristic
664	#476	C₂²×C₂₉	1	1	yes	characteristic
665	#470	C₂²×C₂₉	1	2	yes	—
666	#470	C₂²×C₂₉	1	2	yes	—
667	#470	C₂²×C₂₉	1	2	yes	—
668	#468	C₂²×C₂₉	1	2	yes	—
669	#467	C₂²×C₂₉	1	2	yes	—
670	#467	C₂²×C₂₉	1	2	yes	—
671	#467	C₂²×C₂₉	1	2	yes	—
672	#465	C₂²×C₂₉	1	2	yes	—
673	#464	C₂²×C₂₉	1	1	yes	characteristic
674	#463	C₂²×C₂₉	1	1	yes	characteristic
675	#462	C₂²×C₂₉	1	1	yes	characteristic
676	#462	C₂²×C₂₉	1	1	yes	characteristic
677	#462	C₂²×C₂₉	1	2	yes	—
678	#462	C₂²×C₂₉	1	2	yes	—
679	#462	C₂²×C₂₉	1	1	yes	characteristic
680	#461	C₂²×C₂₉	1	1	yes	characteristic
681	#461	C₂²×C₂₉	1	1	yes	characteristic
682	#461	C₂²×C₂₉	1	1	yes	characteristic
683	#452	C₂²×C₂₉	1	2	yes	—
684	#452	C₂²×C₂₉	1	1	yes	characteristic
685	#452	C₂²×C₂₉	1	2	yes	—
686	#452	C₂²×C₂₉	1	2	yes	—
687	#452	C₂²×C₂₉	1	2	yes	—
688	#452	C₂²×C₂₉	1	2	yes	—
689	#452	C₂²×C₂₉	1	2	yes	—
690	#451	C₂²×C₂₉	1	2	yes	—
691	#451	C₂²×C₂₉	1	2	yes	—
692	#451	C₂²×C₂₉	1	2	yes	—
693	#451	C₂²×C₂₉	1	2	yes	—
694	#451	C₂²×C₂₉	1	2	yes	—
695	#451	C₂²×C₂₉	1	2	yes	—
696	#451	C₂²×C₂₉	1	2	yes	—
697	#451	C₂²×C₂₉	1	2	yes	—
698	#449	C₂²×C₂₉	1	1	yes	characteristic
699	#449	C₂²×C₂₉	1	2	yes	—
700	#448	C₂²×C₂₉	1	2	yes	—
701	#448	C₂²×C₂₉	1	2	yes	—
702	#441	C₂²×C₂₉	1	2	yes	—
703	#440	C₂²×C₂₉	1	2	yes	—
704	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
705	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
706	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
707	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
708	#436	C₂²×C₂₉	1	1	yes	characteristic
709	#436	C₂²×C₂₉	1	1	yes	characteristic
710	#435	C₂²×C₂₉	1	2	yes	—
711	#435	C₂²×C₂₉	1	2	yes	—
712	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
713	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
714	#432	C₂²×C₂₉	1	1	yes	characteristic
715	#431	C₂²×C₂₉	1	1	yes	characteristic
716	#419	C₂²×C₂₉	1	2	yes	—
717	#417	C₂²×C₂₉	1	2	yes	—
718	#416	C₂²×C₂₉	1	2	yes	—
719	C₂×#103	C₂²×C₂₉	1	2	yes	—
720	#408	C₂²×C₂₉	1	2	yes	—
721	#408	C₂²×C₂₉	1	2	yes	—
722	C₂×C₂₉	—	4	1	no	—
723	C₂×C₂₉	—	4	2	no	—
724	C₂×C₂₉	—	4	2	no	—
725	C₂×C₂₉	—	4	2	no	—
726	C₂×C₂₉	—	8	1	no	—
727	C₂×C₂₉	#3484	1	1	yes	characteristic
728	C₂×C₂₉	C₂×#578	1	1	yes	characteristic
729	C₂×C₂₉	#3586	1	1	yes	characteristic
730	2₋¹⁺⁴	—	4	4	no	—
731	2₋¹⁺⁴	—	4	4	no	—
732	C₂×#41	—	2	2	no	—
733	C₂×#41	—	2	2	no	—
734	C₂×#41	—	2	2	no	—
735	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
736	C₂×#41	C₂³×C₂₉	1	2	yes	—
737	C₂×#41	C₂³×C₂₉	1	2	yes	—
738	C₂×#41	C₂³×C₂₉	1	2	yes	—
739	C₂×#41	C₂³×C₂₉	1	2	yes	—
740	C₂²×Q₈	—	2	2	no	—
741	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
742	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
743	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
744	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
745	#137	—	4	4	no	—
746	#137	—	4	4	no	—
747	#135	—	4	4	no	—
748	C₂×Q₁₆	—	4	4	no	—
749	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
750	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
751	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
752	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
753	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
754	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
755	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
756	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
757	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
758	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
759	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
760	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
761	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
762	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
763	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
764	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
765	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
766	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
767	C₄⋊Q₈	—	2	2	no	—
768	C₄⋊Q₈	—	2	2	no	—
769	C₄⋊Q₈	—	2	1	no	—
770	C₄⋊Q₈	—	2	1	no	—
771	C₄⋊Q₈	—	2	2	no	—
772	C₄⋊Q₈	—	2	1	no	—
773	C₄⋊Q₈	—	2	1	no	—
774	C₄⋊Q₈	—	2	1	no	—
775	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
776	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
777	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
778	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
779	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
780	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
781	#127	D₄×C₂₉	1	1	yes	characteristic
782	#126	—	2	2	no	—
783	#126	—	2	1	no	—
784	#125	—	2	2	no	—
785	#125	—	2	1	no	—
786	#125	—	2	1	no	—
787	#125	C₂³×C₂₉	1	1	yes	characteristic
788	#124	—	2	2	no	—
789	#124	—	2	2	no	—
790	#124	—	2	2	no	—
791	#124	—	2	2	no	—
792	#124	D₄×C₂₉	1	2	yes	—
793	#124	C₂³×C₂₉	1	1	yes	characteristic
794	#123	—	2	2	no	—
795	#123	—	2	2	no	—
796	#123	—	2	2	no	—
797	#123	—	2	2	no	—
798	#123	—	2	2	no	—
799	#123	—	2	1	no	—
800	#123	—	2	2	no	—
801	#123	—	2	2	no	—
802	#123	—	2	2	no	—
803	#123	—	2	2	no	—
804	#123	—	2	2	no	—
805	C₂²⋊Q₈	—	2	2	no	—
806	C₂²⋊Q₈	—	2	1	no	—
807	C₂²⋊Q₈	—	2	2	no	—
808	C₂²⋊Q₈	—	2	2	no	—
809	C₂²⋊Q₈	—	2	2	no	—
810	C₂²⋊Q₈	—	2	2	no	—
811	C₂²⋊Q₈	—	2	2	no	—
812	C₂²⋊Q₈	—	2	2	no	—
813	C₂²⋊Q₈	—	2	2	no	—
814	C₂²⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
815	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
816	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
817	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
818	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
819	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
820	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
821	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
822	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
823	#121	—	2	1	no	—
824	#121	—	2	1	no	—
825	#121	—	2	2	no	—
826	#121	—	2	2	no	—
827	#121	—	2	2	no	—
828	#121	—	2	2	no	—
829	#121	—	2	1	no	—
830	#121	—	2	2	no	—
831	#121	—	2	1	no	—
832	#121	D₄×C₂₉	1	1	yes	characteristic
833	#121	D₄×C₂₉	1	1	yes	characteristic
834	#121	D₄×C₂₉	1	2	yes	—
835	#121	C₂³×C₂₉	1	1	yes	characteristic
836	#121	C₂³×C₂₉	1	2	yes	—
837	C₄×Q₈	—	2	1	no	—
838	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
839	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
840	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
841	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
842	C₄×D₄	—	2	1	no	—
843	C₄×D₄	—	2	1	no	—
844	C₄×D₄	—	2	2	no	—
845	C₄×D₄	—	2	1	no	—
846	C₄×D₄	—	2	1	no	—
847	C₄×D₄	—	2	1	no	—
848	C₄×D₄	—	2	1	no	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	2	no	—
851	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
852	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
853	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
854	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
855	C₄×D₄	C₂³×C₂₉	1	2	yes	—
856	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
857	#117	—	2	1	no	—
858	#117	—	2	1	no	—
859	#117	—	2	2	no	—
860	#117	—	2	1	no	—
861	#117	—	2	1	no	—
862	#117	C₂³×C₂₉	1	1	yes	characteristic
863	#117	C₂³×C₂₉	1	2	yes	—
864	C₂×C₄⋊C₄	—	2	1	no	—
865	C₂×C₄⋊C₄	—	2	1	no	—
866	C₂×C₄⋊C₄	—	2	1	no	—
867	C₂×C₄⋊C₄	—	2	1	no	—
868	C₂×C₄⋊C₄	—	2	2	no	—
869	C₂×C₄⋊C₄	—	2	1	no	—
870	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
871	C₂×C₄²	—	2	1	no	—
872	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
873	#107	C₂³×C₂₉	1	1	yes	characteristic
874	#107	C₂³×C₂₉	1	1	yes	characteristic
875	#107	C₂³×C₂₉	1	2	yes	—
876	#106	C₂³×C₂₉	1	1	yes	characteristic
877	#106	C₂³×C₂₉	1	1	yes	characteristic
878	#106	C₂³×C₂₉	1	2	yes	—
879	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
880	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
881	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
882	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
883	#103	C₂³×C₂₉	1	1	yes	characteristic
884	#103	C₂³×C₂₉	1	2	yes	—
885	#103	C₂³×C₂₉	1	2	yes	—
886	#103	C₂³×C₂₉	1	2	yes	—
887	#103	C₂³×C₂₉	1	2	yes	—
888	#103	C₂³×C₂₉	1	2	yes	—
889	#103	C₂³×C₂₉	1	2	yes	—
890	#103	C₂³×C₂₉	1	2	yes	—
891	#103	C₂³×C₂₉	1	1	yes	characteristic
892	#103	C₂³×C₂₉	1	2	yes	—
893	#103	C₂³×C₂₉	1	2	yes	—
894	#103	C₂³×C₂₉	1	1	yes	characteristic
895	#103	C₂³×C₂₉	1	1	yes	characteristic
896	#103	C₂³×C₂₉	1	2	yes	—
897	#103	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	1	yes	characteristic
901	#102	C₂³×C₂₉	1	1	yes	characteristic
902	#102	C₂³×C₂₉	1	1	yes	characteristic
903	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
904	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
905	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
906	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
907	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
908	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
909	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
910	#97	C₂³×C₂₉	1	2	yes	—
911	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
912	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
913	C₂₉	#61693	1	1	yes	characteristic, direct product factor, Sylow
914	#41	—	2	2	no	—
915	#41	—	2	2	no	—
916	#41	—	2	4	no	—
917	#41	—	2	4	no	—
918	#41	—	4	2	no	—
919	#41	—	4	2	no	—
920	#41	—	4	2	no	—
921	#41	—	4	2	no	—
922	#41	—	4	8	no	—
923	#41	—	4	2	no	—
924	#41	—	4	2	no	—
925	#41	—	4	8	no	—
926	#41	—	4	8	no	—
927	C₂×Q₈	—	2	2	no	—
928	C₂×Q₈	—	2	2	no	—
929	C₂×Q₈	—	2	2	no	—
930	C₂×Q₈	—	2	1	no	—
931	C₂×Q₈	—	2	2	no	—
932	C₂×Q₈	—	2	4	no	—
933	C₂×Q₈	—	2	4	no	—
934	C₂×Q₈	—	4	2	no	—
935	C₂×Q₈	—	4	2	no	—
936	C₂×Q₈	—	4	2	no	—
937	C₂×Q₈	—	4	2	no	—
938	C₂×Q₈	—	4	8	no	—
939	C₂×Q₈	—	4	2	no	—
940	C₂×Q₈	—	4	2	no	—
941	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
942	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
943	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
944	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
945	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
946	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
947	C₂×D₄	—	2	1	no	—
948	C₂×D₄	—	2	2	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	1	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
954	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
955	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
956	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
957	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
958	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
959	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
960	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
961	C₂²×C₄	—	2	1	no	—
962	C₂²×C₄	—	2	2	no	—
963	C₂²×C₄	—	2	2	no	—
964	C₂²×C₄	—	2	2	no	—
965	C₂²×C₄	—	2	2	no	—
966	C₂²×C₄	—	2	2	no	—
967	C₂²×C₄	—	2	1	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	2	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	2	no	—
973	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
974	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
975	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
976	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
977	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
978	Q₁₆	—	2	2	no	—
979	Q₁₆	—	2	4	no	—
980	Q₁₆	—	4	2	no	—
981	Q₁₆	—	4	2	no	—
982	Q₁₆	—	4	2	no	—
983	Q₁₆	—	4	2	no	—
984	Q₁₆	—	4	2	no	—
985	Q₁₆	—	4	2	no	—
986	SD₁₆	—	2	2	no	—
987	SD₁₆	—	2	4	no	—
988	SD₁₆	—	2	2	no	—
989	SD₁₆	—	4	2	no	—
990	SD₁₆	—	4	2	no	—
991	D₈	—	2	2	no	—
992	M₁₆	—	4	2	no	—
993	M₁₆	—	4	2	no	—
994	C₂×C₈	—	4	2	no	—
995	C₂×C₈	—	4	2	no	—
996	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
997	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
998	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
999	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1000	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
1001	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	1	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	—	2	2	no	—
1012	C₄⋊C₄	—	2	2	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	1	no	—
1018	C₄⋊C₄	—	2	1	no	—
1019	C₄⋊C₄	—	2	2	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	1	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	1	no	—
1027	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1028	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1029	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1030	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1031	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
1032	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1033	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1034	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
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	—	2	2	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	1	no	—
1047	C₂²⋊C₄	—	2	1	no	—
1048	C₂²⋊C₄	—	2	1	no	—
1049	C₂²⋊C₄	—	2	1	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	1	no	—
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1054	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1055	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1056	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1057	C₄²	—	2	1	no	—
1058	C₄²	—	2	1	no	—
1059	C₄²	—	2	1	no	—
1060	C₄²	—	2	2	no	—
1061	C₄²	—	2	2	no	—
1062	C₄²	—	2	1	no	—
1063	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1064	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1065	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1066	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1067	C₂³	—	2	1	no	—
1068	C₂³	—	2	1	no	—
1069	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
1070	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
1071	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1072	Q₈	—	2	1	no	—
1073	Q₈	—	2	1	no	—
1074	Q₈	—	2	2	no	—
1075	Q₈	—	2	2	no	—
1076	Q₈	—	2	2	no	—
1077	Q₈	—	2	1	no	—
1078	Q₈	—	2	2	no	—
1079	Q₈	—	2	2	no	—
1080	Q₈	—	2	2	no	—
1081	Q₈	—	4	2	no	—
1082	Q₈	—	4	4	no	—
1083	Q₈	—	4	4	no	—
1084	Q₈	—	4	4	no	—
1085	Q₈	—	8	2	no	—
1086	Q₈	—	8	1	no	—
1087	Q₈	C₂₉×H(5,𝔽₂)	1	2	yes	—
1088	D₄	—	2	4	no	—
1089	D₄	—	2	2	no	—
1090	D₄	—	2	2	no	—
1091	D₄	—	2	1	no	—
1092	D₄	—	2	1	no	—
1093	D₄	—	2	1	no	—
1094	D₄	—	4	2	no	—
1095	D₄	—	4	2	no	—
1096	D₄	—	4	2	no	—
1097	D₄	—	4	2	no	—
1098	D₄	—	4	4	no	—
1099	D₄	—	4	4	no	—
1100	D₄	—	8	2	no	—
1101	D₄	—	8	1	no	—
1102	D₄	—	8	2	no	—
1103	D₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
1104	C₂×C₄	—	2	4	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	2	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	1	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	2	no	—
1121	C₂×C₄	—	2	2	no	—
1122	C₂×C₄	—	4	1	no	—
1123	C₂×C₄	—	4	4	no	—
1124	C₂×C₄	—	4	4	no	—
1125	C₂×C₄	—	4	4	no	—
1126	C₂×C₄	—	4	4	no	—
1127	C₂×C₄	—	4	2	no	—
1128	C₂×C₄	—	4	4	no	—
1129	C₂×C₄	—	4	2	no	—
1130	C₂×C₄	—	4	2	no	—
1131	C₂×C₄	—	8	2	no	—
1132	C₂×C₄	—	8	2	no	—
1133	C₂×C₄	—	8	2	no	—
1134	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
1141	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1142	C₈	—	2	1	no	—
1143	C₈	—	2	1	no	—
1144	C₈	—	2	2	no	—
1145	C₈	—	2	2	no	—
1146	C₈	—	2	1	no	—
1147	C₈	—	2	1	no	—
1148	C₂²	—	2	1	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	2	1	no	—
1153	C₂²	—	2	2	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	1	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	2	2	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
1164	C₄	—	2	1	no	—
1165	C₄	—	2	2	no	—
1166	C₄	—	2	2	no	—
1167	C₄	—	2	2	no	—
1168	C₄	—	2	1	no	—
1169	C₄	—	2	1	no	—
1170	C₄	—	2	1	no	—
1171	C₄	—	4	2	no	—
1172	C₄	—	4	2	no	—
1173	C₄	—	4	2	no	—
1174	C₄	—	4	1	no	—
1175	C₄	—	4	1	no	—
1176	C₄	—	4	1	no	—
1177	C₄	—	4	1	no	—
1178	C₄	—	4	1	no	—
1179	C₄	—	4	2	no	—
1180	C₄	C₂₉×#578	1	2	yes	—
1181	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
1182	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
1183	C₂	—	4	1	no	—
1184	C₂	—	4	2	no	—
1185	C₂	—	4	2	no	—
1186	C₂	—	4	2	no	—
1187	C₂	—	8	1	no	—
1188	C₂	C₂₉×#3484	1	1	yes	characteristic
1189	C₂	C₂×C₂₉×#578	1	1	yes	characteristic
1190	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×#3547	C₂	semidirect
2. C₂₉×#3499	C₂	semidirect
3. C₂₉×#3331	C₂	semidirect
4. C₂₉×#3329	C₂	semidirect
5. C₂₉×#3315	C₂	semidirect
6. C₂₉×#3312	C₂	semidirect
7. C₂₉×#3303	C₂	semidirect
8. C₂₉×#3299	C₂	semidirect
9. D₄×Q₁₆×C₂₉	C₂	semidirect
10. C₂₉×#3283	C₂	semidirect
11. C₂₉×#3276	C₂	semidirect
12. C₂₉×#3276	C₂	semidirect
13. C₂₉×#3270	C₂	semidirect
14. C₂₉×#3269	C₂	semidirect
15. C₂₉×#3218	C₂	semidirect
16. C₂₉×#3209	C₂	semidirect
17. C₂₉×#3202	C₂	semidirect
18. C₂₉×#3201	C₂	semidirect
19. C₂₉×#3116	C₂	semidirect
20. C₂₉×#3102	C₂	semidirect
21. C₂₉×#3013	C₂	semidirect
22. C₂₉×#3011	C₂	semidirect
23. C₂₉×#2981	C₂	semidirect
471. #61693	C₂₉	direct (N × H)
553. #3547	C₂×C₂₉	semidirect
554. #3499	C₂×C₂₉	semidirect
555. #3331	C₂×C₂₉	semidirect
556. #3329	C₂×C₂₉	semidirect
557. #3315	C₂×C₂₉	semidirect
558. #3312	C₂×C₂₉	semidirect
559. #3303	C₂×C₂₉	semidirect
560. #3299	C₂×C₂₉	semidirect
561. D₄×Q₁₆	C₂×C₂₉	semidirect
562. #3283	C₂×C₂₉	semidirect
563. #3276	C₂×C₂₉	semidirect
564. #3276	C₂×C₂₉	semidirect
565. #3270	C₂×C₂₉	semidirect
566. #3269	C₂×C₂₉	semidirect
567. #3218	C₂×C₂₉	semidirect
568. #3209	C₂×C₂₉	semidirect
569. #3202	C₂×C₂₉	semidirect
570. #3201	C₂×C₂₉	semidirect
571. #3116	C₂×C₂₉	semidirect
572. #3102	C₂×C₂₉	semidirect
573. #3013	C₂×C₂₉	semidirect
574. #3011	C₂×C₂₉	semidirect
575. #2981	C₂×C₂₉	semidirect
913. C₂₉	#61693	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×#3547	2
C₂₉×#3499	2
C₂₉×#3331	2
C₂₉×#3329	2
C₂₉×#3315	2
C₂₉×#3312	2
C₂₉×#3303	2
C₂₉×#3299	2
D₄×Q₁₆×C₂₉	2
C₂₉×#3283	2
C₂₉×#3276	2
C₂₉×#3270	2
C₂₉×#3269	2
C₂₉×#3218	2
C₂₉×#3209	2
C₂₉×#3202	2
C₂₉×#3201	2
C₂₉×#3116	2
C₂₉×#3102	2
C₂₉×#3013	2
C₂₉×#3011	2
C₂₉×#2981	2
#61693	29

Subgroups — C29×#61693 #20356593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#61693 #20356593