Subgroups — C₂₉×#61991 #20356891

Order 7424.

1848 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3514	C₂	1	1	yes	maximal, characteristic
2	Q₈×#41×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#3369	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#3316	C₂	1	2	yes	maximal, complemented
8	C₂₉×#3314	C₂	1	2	yes	maximal, complemented
9	C₂₉×#3299	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#3295	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×Q₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×SD₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#3270	C₂	1	2	yes	maximal, complemented
14	C₂₉×#3266	C₂	1	2	yes	maximal, complemented
15	C₂₉×#3252	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#3248	C₂	1	2	yes	maximal, complemented
17	C₂₉×#3215	C₂	1	2	yes	maximal, complemented
18	C₂₉×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₉×#3117	C₂	1	2	yes	maximal, complemented
20	C₂₉×#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₉×#3037	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₂₉×#464	C₂	1	2	yes	maximal, complemented
23	C₂₉×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₉×#137	C₂²	1	2	yes	complemented
25	C₂²×Q₁₆×C₂₉	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₂₉	C₂²	1	2	yes	—
27	C₂₉×#559	C₂²	1	1	yes	characteristic
28	Q₈²×C₂₉	C₂²	1	1	yes	characteristic, complemented
29	C₂₉×#557	—	2	1	no	—
30	C₂₉×#557	C₂²	1	1	yes	characteristic, complemented
31	C₂₉×#556	C₂²	1	1	yes	characteristic
32	C₂₉×#555	—	2	1	no	—
33	C₂₉×#554	—	2	1	no	—
34	C₂₉×#554	—	2	2	no	—
35	C₂₉×#554	C₂²	1	1	yes	characteristic
36	C₂₉×#554	C₂²	1	2	yes	complemented
37	C₂₉×#551	—	2	2	no	—
38	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
40	D₄×Q₈×C₂₉	C₂²	1	2	yes	complemented
41	C₂₉×#548	C₂²	1	2	yes	—
42	C₂₉×#546	—	2	1	no	—
43	C₂₉×#546	C₂²	1	2	yes	—
44	D₄²×C₂₉	C₂²	1	1	yes	characteristic
45	C₂₉×#542	—	2	1	no	—
46	C₂₉×#538	—	2	2	no	—
47	C₂₉×#533	—	2	2	no	—
48	C₂₉×#533	—	2	1	no	—
49	C₂₉×#533	C₂²	1	1	yes	characteristic, complemented
50	C₂₉×#533	C₂²	1	2	yes	complemented
51	C₂₉×#532	C₂²	1	1	yes	characteristic
52	C₂₉×#529	C₂²	1	2	yes	—
53	C₂₉×#529	C₂²	1	1	yes	characteristic
54	C₂×C₂₉×#124	C₂²	1	2	yes	—
55	C₂₉×#518	—	2	1	no	—
56	C₄×#41×C₂₉	—	2	1	no	—
57	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
58	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	complemented
59	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
60	C₂₉×#497	C₂²	1	2	yes	—
61	C₂₉×#497	C₂²	1	2	yes	complemented
62	C₂₉×#494	C₂²	1	1	yes	characteristic, complemented
63	C₂₉×#492	C₂²	1	1	yes	characteristic
64	C₂₉×#489	C₂²	1	2	yes	—
65	C₂₉×#489	C₂²	1	2	yes	complemented
66	C₂₉×#487	C₂²	1	1	yes	characteristic, complemented
67	C₂₉×#486	C₂²	1	1	yes	characteristic
68	C₂₉×#484	C₂²	1	2	yes	complemented
69	C₂₉×#483	C₂²	1	1	yes	characteristic, complemented
70	C₂₉×#481	C₂²	1	2	yes	—
71	C₂₉×#480	C₂²	1	1	yes	characteristic
72	C₂₉×#479	C₂²	1	1	yes	characteristic, complemented
73	C₂₉×#479	C₂²	1	2	yes	complemented
74	C₂₉×#479	C₂²	1	1	yes	characteristic, complemented
75	C₂₉×#477	C₂²	1	1	yes	characteristic, complemented
76	C₂₉×#476	C₂²	1	1	yes	characteristic
77	C₂₉×#475	C₂²	1	2	yes	complemented
78	C₂₉×#474	C₂²	1	2	yes	complemented
79	C₂₉×#470	C₂²	1	2	yes	complemented
80	C₂₉×#468	C₂²	1	2	yes	—
81	C₂₉×#467	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×#464	C₂²	1	1	yes	characteristic
86	C₂₉×#464	C₂²	1	2	yes	—
87	C₂₉×#464	C₂²	1	2	yes	—
88	C₂₉×#464	C₂²	1	1	yes	characteristic
89	C₂₉×#464	C₂²	1	2	yes	—
90	C₂₉×#464	C₂²	1	2	yes	complemented
91	C₂₉×#464	C₂²	1	2	yes	complemented
92	C₂₉×#464	C₂²	1	2	yes	complemented
93	C₂₉×#464	C₂²	1	2	yes	complemented
94	C₂₉×#464	C₂²	1	2	yes	complemented
95	C₂₉×#464	C₂²	1	2	yes	complemented
96	C₂₉×#462	C₂²	1	2	yes	complemented
97	C₂₉×#462	C₂²	1	1	yes	characteristic, complemented
98	C₂₉×#462	C₂²	1	1	yes	characteristic, complemented
99	C₂₉×#462	C₂²	1	1	yes	characteristic, complemented
100	C₂₉×#461	C₂²	1	1	yes	characteristic
101	C₂₉×#461	C₂²	1	2	yes	complemented
102	C₂₉×#460	C₂²	1	1	yes	characteristic
103	C₂₉×#460	C₂²	1	1	yes	characteristic
104	C₂₉×#452	C₂²	1	2	yes	complemented
105	C₂₉×#452	C₂²	1	2	yes	complemented
106	C₂₉×#451	C₂²	1	2	yes	complemented
107	C₂₉×#451	C₂²	1	2	yes	complemented
108	C₂₉×#451	C₂²	1	2	yes	complemented
109	C₂₉×#451	C₂²	1	1	yes	characteristic, complemented
110	C₂₉×#450	C₂²	1	2	yes	—
111	C₂₉×#450	C₂²	1	2	yes	—
112	C₂₉×#448	C₂²	1	1	yes	characteristic
113	C₂₉×#448	C₂²	1	2	yes	—
114	C₂₉×#446	C₂²	1	1	yes	characteristic, complemented
115	C₂₉×#446	C₂²	1	1	yes	characteristic, complemented
116	C₂₉×#441	C₂²	1	2	yes	complemented
117	C₂₉×#441	C₂²	1	2	yes	complemented
118	C₂₉×#440	C₂²	1	2	yes	complemented
119	C₂₉×#440	C₂²	1	2	yes	complemented
120	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
122	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
123	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
124	C₂₉×#435	C₂²	1	2	yes	complemented
125	C₂₉×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
127	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
128	C₂₉×#432	C₂²	1	2	yes	complemented
129	C₂₉×#431	C₂²	1	1	yes	characteristic, complemented
130	C₂₉×#423	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	complemented
132	C₂₉×#417	C₂²	1	2	yes	complemented
133	C₂×C₂₉×#103	C₂²	1	2	yes	complemented
134	C₂×C₂₉×#102	C₂²	1	2	yes	—
135	C₂×#41×C₂₉	D₄	1	1	yes	characteristic
136	C₂×#41×C₂₉	C₂³	1	2	yes	—
137	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
138	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
140	C₂²×D₄×C₂₉	—	2	1	no	—
141	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
142	C₂₉×#137	—	4	4	no	—
143	C₂×Q₁₆×C₂₉	—	4	4	no	—
144	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
150	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₂₉	—	4	4	no	—
152	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
153	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
155	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
159	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
160	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
161	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
162	C₂₉×C₄⋊Q₈	—	2	1	no	—
163	C₂₉×C₄⋊Q₈	—	2	2	no	—
164	C₂₉×C₄⋊Q₈	—	2	1	no	—
165	C₂₉×C₄⋊Q₈	—	2	2	no	—
166	C₂₉×C₄⋊Q₈	—	2	1	no	—
167	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
169	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
171	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₂₉×#127	C₂³	1	1	yes	characteristic
173	C₂₉×#126	—	2	2	no	—
174	C₂₉×#126	—	2	2	no	—
175	C₂₉×#126	—	2	1	no	—
176	C₂₉×#125	—	2	1	no	—
177	C₂₉×#125	—	2	2	no	—
178	C₂₉×#125	—	2	1	no	—
179	C₂₉×#125	—	2	2	no	—
180	C₂₉×#125	—	2	1	no	—
181	C₂₉×#125	—	2	2	no	—
182	C₂₉×#125	C₂³	1	1	yes	characteristic
183	C₂₉×#124	—	2	1	no	—
184	C₂₉×#124	—	2	2	no	—
185	C₂₉×#124	—	2	2	no	—
186	C₂₉×#124	—	2	2	no	—
187	C₂₉×#124	C₂³	1	1	yes	characteristic
188	C₂₉×#124	C₂³	1	2	yes	—
189	C₂₉×#124	C₂³	1	2	yes	—
190	C₂₉×#124	C₂³	1	2	yes	—
191	C₂₉×#123	—	2	1	no	—
192	C₂₉×#123	—	2	2	no	—
193	C₂₉×#123	—	2	2	no	—
194	C₂₉×#123	—	2	2	no	—
195	C₂₉×C₂²⋊Q₈	—	2	1	no	—
196	C₂₉×C₂²⋊Q₈	—	2	2	no	—
197	C₂₉×C₂²⋊Q₈	—	2	1	no	—
198	C₂₉×C₂²⋊Q₈	—	2	2	no	—
199	C₂₉×C₂²⋊Q₈	—	2	2	no	—
200	C₂₉×C₂²⋊Q₈	—	2	2	no	—
201	C₂₉×C₂²⋊Q₈	—	2	2	no	—
202	C₂₉×C₂²⋊Q₈	—	2	2	no	—
203	C₂₉×C₂²⋊Q₈	—	2	2	no	—
204	C₂₉×C₂²⋊Q₈	—	2	2	no	—
205	C₂₉×C₂²⋊Q₈	—	2	2	no	—
206	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₂₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₂₉×#121	—	2	2	no	—
212	C₂₉×#121	—	2	1	no	—
213	C₂₉×#121	—	2	1	no	—
214	C₂₉×#121	—	2	1	no	—
215	C₂₉×#121	—	2	2	no	—
216	C₂₉×#121	C₂³	1	2	yes	—
217	C₂₉×#121	C₂³	1	1	yes	characteristic
218	C₂₉×#120	—	2	2	no	—
219	C₂₉×#120	—	2	2	no	—
220	C₄×Q₈×C₂₉	—	2	1	no	—
221	C₄×Q₈×C₂₉	—	2	1	no	—
222	C₄×Q₈×C₂₉	—	2	2	no	—
223	C₄×Q₈×C₂₉	—	2	1	no	—
224	C₄×Q₈×C₂₉	—	2	1	no	—
225	C₄×Q₈×C₂₉	—	2	2	no	—
226	C₄×Q₈×C₂₉	—	2	2	no	—
227	C₄×Q₈×C₂₉	—	2	1	no	—
228	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
229	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
233	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
234	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
235	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
238	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₂₉	—	2	1	no	—
240	C₄×D₄×C₂₉	—	2	2	no	—
241	C₄×D₄×C₂₉	—	2	1	no	—
242	C₄×D₄×C₂₉	—	2	2	no	—
243	C₄×D₄×C₂₉	—	2	1	no	—
244	C₄×D₄×C₂₉	—	2	2	no	—
245	C₄×D₄×C₂₉	—	2	1	no	—
246	C₄×D₄×C₂₉	—	2	1	no	—
247	C₄×D₄×C₂₉	—	2	2	no	—
248	C₄×D₄×C₂₉	—	2	1	no	—
249	C₄×D₄×C₂₉	—	2	1	no	—
250	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
251	C₄×D₄×C₂₉	D₄	1	2	yes	—
252	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₂₉	C₂³	1	2	yes	—
254	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₂₉	C₂³	1	2	yes	—
256	C₂₉×#117	—	2	2	no	—
257	C₂₉×#117	—	2	1	no	—
258	C₂₉×#117	—	2	1	no	—
259	C₂₉×#117	—	2	1	no	—
260	C₂₉×#117	—	2	2	no	—
261	C₂₉×#117	D₄	1	2	yes	—
262	C₂₉×#117	D₄	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
264	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
265	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
267	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
268	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
269	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
270	C₂×C₄²×C₂₉	—	2	2	no	—
271	C₂×C₄²×C₂₉	—	2	1	no	—
272	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
274	C₂₉×#107	C₂³	1	1	yes	characteristic
275	C₂₉×#107	C₂³	1	1	yes	characteristic
276	C₂₉×#107	C₂³	1	2	yes	—
277	C₂₉×#106	C₂³	1	1	yes	characteristic
278	C₂₉×#106	C₂³	1	1	yes	characteristic
279	C₂₉×#106	C₂³	1	2	yes	—
280	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
283	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
286	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
287	C₂₉×#103	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	1	yes	characteristic
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×#102	C₂³	1	1	yes	characteristic
301	C₂₉×#102	C₂³	1	1	yes	characteristic
302	C₂₉×#102	C₂³	1	2	yes	—
303	C₂₉×#102	C₂³	1	2	yes	—
304	C₂₉×#102	C₂³	1	2	yes	—
305	C₂₉×#102	C₂³	1	2	yes	—
306	C₂₉×#102	C₂³	1	2	yes	—
307	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₂₉×#97	C₂³	1	2	yes	—
312	C₂₉×#97	C₂³	1	2	yes	—
313	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
315	C₂⁴×C₂₉	—	2	2	no	—
316	#41×C₂₉	—	2	4	no	—
317	#41×C₂₉	—	4	2	no	—
318	#41×C₂₉	—	4	2	no	—
319	C₂×Q₈×C₂₉	—	2	1	no	—
320	C₂×Q₈×C₂₉	—	2	2	no	—
321	C₂×Q₈×C₂₉	—	2	2	no	—
322	C₂×Q₈×C₂₉	—	2	1	no	—
323	C₂×Q₈×C₂₉	—	2	2	no	—
324	C₂×Q₈×C₂₉	—	2	4	no	—
325	C₂×Q₈×C₂₉	—	2	2	no	—
326	C₂×Q₈×C₂₉	—	4	2	no	—
327	C₂×Q₈×C₂₉	—	4	1	no	—
328	C₂×Q₈×C₂₉	—	4	2	no	—
329	C₂×Q₈×C₂₉	—	4	2	no	—
330	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
335	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₂₉	—	2	2	no	—
337	C₂×D₄×C₂₉	—	2	1	no	—
338	C₂×D₄×C₂₉	—	2	2	no	—
339	C₂×D₄×C₂₉	—	2	1	no	—
340	C₂×D₄×C₂₉	—	2	1	no	—
341	C₂×D₄×C₂₉	—	2	2	no	—
342	C₂×D₄×C₂₉	—	4	2	no	—
343	C₂×D₄×C₂₉	—	4	2	no	—
344	C₂×D₄×C₂₉	—	4	4	no	—
345	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
346	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₂₉	—	2	1	no	—
350	C₂²×C₄×C₂₉	—	2	2	no	—
351	C₂²×C₄×C₂₉	—	2	1	no	—
352	C₂²×C₄×C₂₉	—	2	2	no	—
353	C₂²×C₄×C₂₉	—	2	2	no	—
354	C₂²×C₄×C₂₉	—	2	1	no	—
355	C₂²×C₄×C₂₉	—	2	2	no	—
356	C₂²×C₄×C₂₉	—	2	2	no	—
357	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
358	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
360	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
362	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
363	Q₁₆×C₂₉	—	2	2	no	—
364	Q₁₆×C₂₉	—	2	4	no	—
365	Q₁₆×C₂₉	—	4	2	no	—
366	Q₁₆×C₂₉	—	4	2	no	—
367	Q₁₆×C₂₉	—	4	1	no	—
368	Q₁₆×C₂₉	—	4	2	no	—
369	Q₁₆×C₂₉	—	4	2	no	—
370	SD₁₆×C₂₉	—	2	2	no	—
371	SD₁₆×C₂₉	—	2	4	no	—
372	SD₁₆×C₂₉	—	4	2	no	—
373	SD₁₆×C₂₉	—	4	2	no	—
374	SD₁₆×C₂₉	—	4	2	no	—
375	SD₁₆×C₂₉	—	4	1	no	—
376	SD₁₆×C₂₉	—	4	2	no	—
377	M₁₆×C₂₉	—	4	2	no	—
378	C₂×C₈×C₂₉	—	4	2	no	—
379	C₂×C₈×C₂₉	—	4	2	no	—
380	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
383	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
384	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
386	C₄⋊C₄×C₂₉	—	2	1	no	—
387	C₄⋊C₄×C₂₉	—	2	2	no	—
388	C₄⋊C₄×C₂₉	—	2	1	no	—
389	C₄⋊C₄×C₂₉	—	2	2	no	—
390	C₄⋊C₄×C₂₉	—	2	1	no	—
391	C₄⋊C₄×C₂₉	—	2	2	no	—
392	C₄⋊C₄×C₂₉	—	2	1	no	—
393	C₄⋊C₄×C₂₉	—	2	1	no	—
394	C₄⋊C₄×C₂₉	—	2	2	no	—
395	C₄⋊C₄×C₂₉	—	2	1	no	—
396	C₄⋊C₄×C₂₉	—	2	1	no	—
397	C₄⋊C₄×C₂₉	—	2	1	no	—
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	2	no	—
402	C₄⋊C₄×C₂₉	—	2	1	no	—
403	C₄⋊C₄×C₂₉	—	2	2	no	—
404	C₄⋊C₄×C₂₉	—	2	1	no	—
405	C₄⋊C₄×C₂₉	—	2	2	no	—
406	C₄⋊C₄×C₂₉	—	2	1	no	—
407	C₄⋊C₄×C₂₉	—	2	2	no	—
408	C₄⋊C₄×C₂₉	—	2	2	no	—
409	C₄⋊C₄×C₂₉	—	2	2	no	—
410	C₄⋊C₄×C₂₉	—	2	2	no	—
411	C₄⋊C₄×C₂₉	—	2	1	no	—
412	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
413	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
414	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
415	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
419	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
421	C₂²⋊C₄×C₂₉	—	2	2	no	—
422	C₂²⋊C₄×C₂₉	—	2	2	no	—
423	C₂²⋊C₄×C₂₉	—	2	2	no	—
424	C₂²⋊C₄×C₂₉	—	2	2	no	—
425	C₂²⋊C₄×C₂₉	—	2	1	no	—
426	C₂²⋊C₄×C₂₉	—	2	2	no	—
427	C₂²⋊C₄×C₂₉	—	2	1	no	—
428	C₂²⋊C₄×C₂₉	—	2	1	no	—
429	C₂²⋊C₄×C₂₉	—	2	1	no	—
430	C₂²⋊C₄×C₂₉	—	2	2	no	—
431	C₂²⋊C₄×C₂₉	—	2	2	no	—
432	C₂²⋊C₄×C₂₉	—	2	2	no	—
433	C₂²⋊C₄×C₂₉	—	2	2	no	—
434	C₂²⋊C₄×C₂₉	—	2	2	no	—
435	C₂²⋊C₄×C₂₉	—	2	2	no	—
436	C₂²⋊C₄×C₂₉	—	2	1	no	—
437	C₂²⋊C₄×C₂₉	—	2	2	no	—
438	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
441	C₄²×C₂₉	—	2	1	no	—
442	C₄²×C₂₉	—	2	2	no	—
443	C₄²×C₂₉	—	2	1	no	—
444	C₄²×C₂₉	—	2	2	no	—
445	C₄²×C₂₉	—	2	1	no	—
446	C₄²×C₂₉	—	2	2	no	—
447	C₄²×C₂₉	—	2	1	no	—
448	C₄²×C₂₉	—	2	2	no	—
449	C₄²×C₂₉	—	2	1	no	—
450	C₄²×C₂₉	C₂×D₄	1	2	yes	—
451	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₂₉	C₂×D₄	1	2	yes	—
454	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
455	C₄²×C₂₉	C₂⁴	1	2	yes	—
456	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
457	#61991	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
458	C₂³×C₂₉	—	2	1	no	—
459	C₂³×C₂₉	—	2	2	no	—
460	C₂³×C₂₉	—	4	4	no	—
461	C₂³×C₂₉	—	8	2	no	—
462	C₂³×C₂₉	—	8	2	no	—
463	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
464	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
465	Q₈×C₂₉	—	2	2	no	—
466	Q₈×C₂₉	—	2	1	no	—
467	Q₈×C₂₉	—	2	2	no	—
468	Q₈×C₂₉	—	2	1	no	—
469	Q₈×C₂₉	—	2	1	no	—
470	Q₈×C₂₉	—	2	2	no	—
471	Q₈×C₂₉	—	2	2	no	—
472	Q₈×C₂₉	—	2	1	no	—
473	Q₈×C₂₉	—	2	1	no	—
474	Q₈×C₂₉	—	2	2	no	—
475	Q₈×C₂₉	—	4	2	no	—
476	Q₈×C₂₉	—	4	4	no	—
477	Q₈×C₂₉	—	8	2	no	—
478	Q₈×C₂₉	—	8	1	no	—
479	Q₈×C₂₉	—	8	2	no	—
480	Q₈×C₂₉	H(5,𝔽₂)	1	2	yes	—
481	D₄×C₂₉	—	2	4	no	—
482	D₄×C₂₉	—	2	1	no	—
483	D₄×C₂₉	—	2	2	no	—
484	D₄×C₂₉	—	2	1	no	—
485	D₄×C₂₉	—	2	2	no	—
486	D₄×C₂₉	—	4	4	no	—
487	D₄×C₂₉	—	4	2	no	—
488	D₄×C₂₉	—	8	1	no	—
489	D₄×C₂₉	—	8	2	no	—
490	D₄×C₂₉	—	8	1	no	—
491	D₄×C₂₉	—	8	2	no	—
492	D₄×C₂₉	#137	1	4	yes	complemented
493	C₂×C₄×C₂₉	—	2	4	no	—
494	C₂×C₄×C₂₉	—	2	1	no	—
495	C₂×C₄×C₂₉	—	2	2	no	—
496	C₂×C₄×C₂₉	—	2	2	no	—
497	C₂×C₄×C₂₉	—	2	1	no	—
498	C₂×C₄×C₂₉	—	2	2	no	—
499	C₂×C₄×C₂₉	—	2	1	no	—
500	C₂×C₄×C₂₉	—	2	1	no	—
501	C₂×C₄×C₂₉	—	2	1	no	—
502	C₂×C₄×C₂₉	—	2	2	no	—
503	C₂×C₄×C₂₉	—	2	1	no	—
504	C₂×C₄×C₂₉	—	2	2	no	—
505	C₂×C₄×C₂₉	—	2	1	no	—
506	C₂×C₄×C₂₉	—	2	1	no	—
507	C₂×C₄×C₂₉	—	2	1	no	—
508	C₂×C₄×C₂₉	—	2	2	no	—
509	C₂×C₄×C₂₉	—	4	2	no	—
510	C₂×C₄×C₂₉	—	4	1	no	—
511	C₂×C₄×C₂₉	—	4	4	no	—
512	C₂×C₄×C₂₉	—	4	2	no	—
513	C₂×C₄×C₂₉	—	4	2	no	—
514	C₂×C₄×C₂₉	—	8	2	no	—
515	C₂×C₄×C₂₉	—	8	2	no	—
516	C₂×C₄×C₂₉	—	8	2	no	—
517	C₂×C₄×C₂₉	—	8	1	no	—
518	C₂×C₄×C₂₉	—	8	2	no	—
519	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
528	C₈×C₂₉	—	2	1	no	—
529	C₈×C₂₉	—	2	1	no	—
530	C₈×C₂₉	—	2	2	no	—
531	C₈×C₂₉	—	2	2	no	—
532	C₈×C₂₉	—	2	1	no	—
533	C₈×C₂₉	—	2	1	no	—
534	#3514	C₂×C₂₉	1	1	yes	characteristic
535	Q₈×#41	C₂×C₂₉	1	1	yes	characteristic, complemented
536	#3400	C₂×C₂₉	1	1	yes	characteristic, complemented
537	#3398	C₂×C₂₉	1	1	yes	characteristic, complemented
538	#3375	C₂×C₂₉	1	1	yes	characteristic, complemented
539	#3369	C₂×C₂₉	1	1	yes	characteristic, complemented
540	#3316	C₂×C₂₉	1	2	yes	complemented
541	#3314	C₂×C₂₉	1	2	yes	complemented
542	#3299	C₂×C₂₉	1	1	yes	characteristic, complemented
543	#3295	C₂×C₂₉	1	1	yes	characteristic, complemented
544	D₄×Q₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
545	D₄×SD₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
546	#3270	C₂×C₂₉	1	2	yes	complemented
547	#3266	C₂×C₂₉	1	2	yes	complemented
548	#3252	C₂×C₂₉	1	1	yes	characteristic, complemented
549	#3248	C₂×C₂₉	1	2	yes	complemented
550	#3215	C₂×C₂₉	1	2	yes	complemented
551	#3210	C₂×C₂₉	1	1	yes	characteristic, complemented
552	#3117	C₂×C₂₉	1	2	yes	complemented
553	#3108	C₂×C₂₉	1	1	yes	characteristic, complemented
554	#3037	C₂×C₂₉	1	1	yes	characteristic, complemented
555	C₂×#464	C₂×C₂₉	1	2	yes	complemented
556	#2990	C₂×C₂₉	1	1	yes	characteristic, complemented
557	C₂²×C₂₉	—	2	2	no	—
558	C₂²×C₂₉	—	2	2	no	—
559	C₂²×C₂₉	—	2	1	no	—
560	C₂²×C₂₉	—	2	1	no	—
561	C₂²×C₂₉	—	2	1	no	—
562	C₂²×C₂₉	—	4	2	no	—
563	C₂²×C₂₉	—	4	1	no	—
564	C₂²×C₂₉	—	4	2	no	—
565	C₂²×C₂₉	—	4	1	no	—
566	C₂²×C₂₉	—	4	1	no	—
567	C₂²×C₂₉	—	4	2	no	—
568	C₂²×C₂₉	—	16	4	no	—
569	C₂²×C₂₉	C₂×#137	1	4	yes	—
570	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
571	C₄×C₂₉	—	2	1	no	—
572	C₄×C₂₉	—	2	2	no	—
573	C₄×C₂₉	—	2	1	no	—
574	C₄×C₂₉	—	2	1	no	—
575	C₄×C₂₉	—	2	2	no	—
576	C₄×C₂₉	—	2	2	no	—
577	C₄×C₂₉	—	2	1	no	—
578	C₄×C₂₉	—	2	2	no	—
579	C₄×C₂₉	—	4	1	no	—
580	C₄×C₂₉	—	4	1	no	—
581	C₄×C₂₉	—	4	2	no	—
582	C₄×C₂₉	—	4	1	no	—
583	C₄×C₂₉	—	4	2	no	—
584	C₄×C₂₉	—	4	1	no	—
585	C₄×C₂₉	—	4	2	no	—
586	C₄×C₂₉	—	4	1	no	—
587	C₄×C₂₉	—	4	1	no	—
588	C₄×C₂₉	C₂×#137	1	2	yes	—
589	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
590	C₄×C₂₉	#585	1	1	yes	characteristic
591	C₂×#137	C₂²×C₂₉	1	2	yes	complemented
592	C₂²×Q₁₆	C₂²×C₂₉	1	2	yes	complemented
593	C₂²×SD₁₆	C₂²×C₂₉	1	2	yes	—
594	#559	C₂²×C₂₉	1	1	yes	characteristic
595	Q₈²	C₂²×C₂₉	1	1	yes	characteristic, complemented
596	#557	—	2	1	no	—
597	#557	C₂²×C₂₉	1	1	yes	characteristic, complemented
598	#556	C₂²×C₂₉	1	1	yes	characteristic
599	#555	—	2	1	no	—
600	#554	—	2	1	no	—
601	#554	—	2	2	no	—
602	#554	C₂²×C₂₉	1	1	yes	characteristic
603	#554	C₂²×C₂₉	1	2	yes	complemented
604	#551	—	2	2	no	—
605	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
606	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
607	D₄×Q₈	C₂²×C₂₉	1	2	yes	complemented
608	#548	C₂²×C₂₉	1	2	yes	—
609	#546	—	2	1	no	—
610	#546	C₂²×C₂₉	1	2	yes	—
611	D₄²	C₂²×C₂₉	1	1	yes	characteristic
612	#542	—	2	1	no	—
613	#538	—	2	2	no	—
614	#533	—	2	2	no	—
615	#533	—	2	1	no	—
616	#533	C₂²×C₂₉	1	1	yes	characteristic, complemented
617	#533	C₂²×C₂₉	1	2	yes	complemented
618	#532	C₂²×C₂₉	1	1	yes	characteristic
619	#529	C₂²×C₂₉	1	1	yes	characteristic
620	#529	C₂²×C₂₉	1	2	yes	—
621	C₂×#124	C₂²×C₂₉	1	2	yes	—
622	#518	—	2	1	no	—
623	C₄×#41	—	2	1	no	—
624	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
625	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
626	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	complemented
627	#497	C₂²×C₂₉	1	2	yes	—
628	#497	C₂²×C₂₉	1	2	yes	complemented
629	#494	C₂²×C₂₉	1	1	yes	characteristic, complemented
630	#492	C₂²×C₂₉	1	1	yes	characteristic
631	#489	C₂²×C₂₉	1	2	yes	—
632	#489	C₂²×C₂₉	1	2	yes	complemented
633	#487	C₂²×C₂₉	1	1	yes	characteristic, complemented
634	#486	C₂²×C₂₉	1	1	yes	characteristic
635	#484	C₂²×C₂₉	1	2	yes	complemented
636	#483	C₂²×C₂₉	1	1	yes	characteristic, complemented
637	#481	C₂²×C₂₉	1	2	yes	—
638	#480	C₂²×C₂₉	1	1	yes	characteristic
639	#479	C₂²×C₂₉	1	1	yes	characteristic, complemented
640	#479	C₂²×C₂₉	1	1	yes	characteristic, complemented
641	#479	C₂²×C₂₉	1	2	yes	complemented
642	#477	C₂²×C₂₉	1	1	yes	characteristic, complemented
643	#476	C₂²×C₂₉	1	1	yes	characteristic
644	#475	C₂²×C₂₉	1	2	yes	complemented
645	#474	C₂²×C₂₉	1	2	yes	complemented
646	#470	C₂²×C₂₉	1	2	yes	complemented
647	#468	C₂²×C₂₉	1	2	yes	—
648	#467	C₂²×C₂₉	1	2	yes	complemented
649	#467	C₂²×C₂₉	1	2	yes	complemented
650	#465	C₂²×C₂₉	1	2	yes	—
651	#465	C₂²×C₂₉	1	2	yes	—
652	#464	C₂²×C₂₉	1	1	yes	characteristic
653	#464	C₂²×C₂₉	1	1	yes	characteristic
654	#464	C₂²×C₂₉	1	2	yes	—
655	#464	C₂²×C₂₉	1	2	yes	—
656	#464	C₂²×C₂₉	1	2	yes	—
657	#464	C₂²×C₂₉	1	2	yes	complemented
658	#464	C₂²×C₂₉	1	2	yes	complemented
659	#464	C₂²×C₂₉	1	2	yes	complemented
660	#464	C₂²×C₂₉	1	2	yes	complemented
661	#464	C₂²×C₂₉	1	2	yes	complemented
662	#464	C₂²×C₂₉	1	2	yes	complemented
663	#462	C₂²×C₂₉	1	1	yes	characteristic, complemented
664	#462	C₂²×C₂₉	1	2	yes	complemented
665	#462	C₂²×C₂₉	1	1	yes	characteristic, complemented
666	#462	C₂²×C₂₉	1	1	yes	characteristic, complemented
667	#461	C₂²×C₂₉	1	1	yes	characteristic
668	#461	C₂²×C₂₉	1	2	yes	complemented
669	#460	C₂²×C₂₉	1	1	yes	characteristic
670	#460	C₂²×C₂₉	1	1	yes	characteristic
671	#452	C₂²×C₂₉	1	2	yes	complemented
672	#452	C₂²×C₂₉	1	2	yes	complemented
673	#451	C₂²×C₂₉	1	1	yes	characteristic, complemented
674	#451	C₂²×C₂₉	1	2	yes	complemented
675	#451	C₂²×C₂₉	1	2	yes	complemented
676	#451	C₂²×C₂₉	1	2	yes	complemented
677	#450	C₂²×C₂₉	1	2	yes	—
678	#450	C₂²×C₂₉	1	2	yes	—
679	#448	C₂²×C₂₉	1	1	yes	characteristic
680	#448	C₂²×C₂₉	1	2	yes	—
681	#446	C₂²×C₂₉	1	1	yes	characteristic, complemented
682	#446	C₂²×C₂₉	1	1	yes	characteristic, complemented
683	#441	C₂²×C₂₉	1	2	yes	complemented
684	#441	C₂²×C₂₉	1	2	yes	complemented
685	#440	C₂²×C₂₉	1	2	yes	complemented
686	#440	C₂²×C₂₉	1	2	yes	complemented
687	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
688	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
689	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
690	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
691	#435	C₂²×C₂₉	1	2	yes	complemented
692	#435	C₂²×C₂₉	1	2	yes	complemented
693	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
694	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
695	#432	C₂²×C₂₉	1	2	yes	complemented
696	#431	C₂²×C₂₉	1	1	yes	characteristic, complemented
697	#423	C₂²×C₂₉	1	1	yes	characteristic, complemented
698	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	complemented
699	#417	C₂²×C₂₉	1	2	yes	complemented
700	C₂×#103	C₂²×C₂₉	1	2	yes	complemented
701	C₂×#102	C₂²×C₂₉	1	2	yes	—
702	C₂×C₂₉	—	2	4	no	—
703	C₂×C₂₉	—	4	1	no	—
704	C₂×C₂₉	—	8	2	no	—
705	C₂×C₂₉	—	8	1	no	—
706	C₂×C₂₉	#3488	1	1	yes	characteristic
707	C₂×C₂₉	C₂²×#137	1	1	yes	characteristic
708	C₂×C₂₉	#3584	1	1	yes	characteristic
709	C₂×#41	D₄×C₂₉	1	1	yes	characteristic
710	C₂×#41	C₂³×C₂₉	1	2	yes	—
711	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
712	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
713	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
714	C₂²×D₄	—	2	1	no	—
715	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
716	#137	—	4	4	no	—
717	C₂×Q₁₆	—	4	4	no	—
718	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
719	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
720	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
721	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
722	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
723	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
724	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
725	C₂×SD₁₆	—	4	4	no	—
726	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
727	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
728	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
729	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
730	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
732	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
733	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
734	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
735	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
736	C₄⋊Q₈	—	2	1	no	—
737	C₄⋊Q₈	—	2	2	no	—
738	C₄⋊Q₈	—	2	1	no	—
739	C₄⋊Q₈	—	2	2	no	—
740	C₄⋊Q₈	—	2	1	no	—
741	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
742	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
743	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
744	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
745	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
746	#127	C₂³×C₂₉	1	1	yes	characteristic
747	#126	—	2	2	no	—
748	#126	—	2	2	no	—
749	#126	—	2	1	no	—
750	#125	—	2	1	no	—
751	#125	—	2	2	no	—
752	#125	—	2	1	no	—
753	#125	—	2	2	no	—
754	#125	—	2	1	no	—
755	#125	—	2	2	no	—
756	#125	C₂³×C₂₉	1	1	yes	characteristic
757	#124	—	2	1	no	—
758	#124	—	2	2	no	—
759	#124	—	2	2	no	—
760	#124	—	2	2	no	—
761	#124	C₂³×C₂₉	1	1	yes	characteristic
762	#124	C₂³×C₂₉	1	2	yes	—
763	#124	C₂³×C₂₉	1	2	yes	—
764	#124	C₂³×C₂₉	1	2	yes	—
765	#123	—	2	1	no	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	1	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
781	C₂²⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
782	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
783	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
784	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
785	#121	—	2	2	no	—
786	#121	—	2	1	no	—
787	#121	—	2	1	no	—
788	#121	—	2	1	no	—
789	#121	—	2	2	no	—
790	#121	C₂³×C₂₉	1	2	yes	—
791	#121	C₂³×C₂₉	1	1	yes	characteristic
792	#120	—	2	2	no	—
793	#120	—	2	2	no	—
794	C₄×Q₈	—	2	1	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	—	2	2	no	—
797	C₄×Q₈	—	2	1	no	—
798	C₄×Q₈	—	2	1	no	—
799	C₄×Q₈	—	2	2	no	—
800	C₄×Q₈	—	2	2	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
803	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
804	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
805	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
806	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
807	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
808	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
810	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
811	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
812	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
825	C₄×D₄	D₄×C₂₉	1	2	yes	—
826	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
827	C₄×D₄	C₂³×C₂₉	1	2	yes	—
828	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₂₉	1	2	yes	—
830	#117	—	2	2	no	—
831	#117	—	2	1	no	—
832	#117	—	2	1	no	—
833	#117	—	2	1	no	—
834	#117	—	2	2	no	—
835	#117	D₄×C₂₉	1	2	yes	—
836	#117	D₄×C₂₉	1	1	yes	characteristic
837	C₂×C₄⋊C₄	—	2	2	no	—
838	C₂×C₄⋊C₄	—	2	1	no	—
839	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
840	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
841	C₂×C₂²⋊C₄	—	2	2	no	—
842	C₂×C₂²⋊C₄	—	2	2	no	—
843	C₂×C₂²⋊C₄	—	2	2	no	—
844	C₂×C₄²	—	2	2	no	—
845	C₂×C₄²	—	2	1	no	—
846	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
847	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
848	#107	C₂³×C₂₉	1	1	yes	characteristic
849	#107	C₂³×C₂₉	1	1	yes	characteristic
850	#107	C₂³×C₂₉	1	2	yes	—
851	#106	C₂³×C₂₉	1	1	yes	characteristic
852	#106	C₂³×C₂₉	1	1	yes	characteristic
853	#106	C₂³×C₂₉	1	2	yes	—
854	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
855	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
856	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
857	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
858	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
861	#103	C₂³×C₂₉	1	1	yes	characteristic
862	#103	C₂³×C₂₉	1	2	yes	—
863	#103	C₂³×C₂₉	1	2	yes	—
864	#103	C₂³×C₂₉	1	2	yes	—
865	#103	C₂³×C₂₉	1	2	yes	—
866	#103	C₂³×C₂₉	1	1	yes	characteristic
867	#103	C₂³×C₂₉	1	1	yes	characteristic
868	#103	C₂³×C₂₉	1	1	yes	characteristic
869	#103	C₂³×C₂₉	1	1	yes	characteristic
870	#103	C₂³×C₂₉	1	1	yes	characteristic
871	#103	C₂³×C₂₉	1	2	yes	—
872	#103	C₂³×C₂₉	1	2	yes	—
873	#103	C₂³×C₂₉	1	2	yes	—
874	#102	C₂³×C₂₉	1	1	yes	characteristic
875	#102	C₂³×C₂₉	1	2	yes	—
876	#102	C₂³×C₂₉	1	2	yes	—
877	#102	C₂³×C₂₉	1	2	yes	—
878	#102	C₂³×C₂₉	1	2	yes	—
879	#102	C₂³×C₂₉	1	1	yes	characteristic
880	#102	C₂³×C₂₉	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
882	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
883	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
884	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
885	#97	C₂³×C₂₉	1	2	yes	—
886	#97	C₂³×C₂₉	1	2	yes	—
887	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
888	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
889	C₂₉	#61991	1	1	yes	characteristic, direct product factor, Sylow
890	C₂⁴	—	2	2	no	—
891	#41	—	2	4	no	—
892	#41	—	4	2	no	—
893	#41	—	4	2	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	2	no	—
896	C₂×Q₈	—	2	2	no	—
897	C₂×Q₈	—	2	1	no	—
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	2	4	no	—
900	C₂×Q₈	—	2	2	no	—
901	C₂×Q₈	—	4	2	no	—
902	C₂×Q₈	—	4	1	no	—
903	C₂×Q₈	—	4	2	no	—
904	C₂×Q₈	—	4	2	no	—
905	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
906	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
907	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
908	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
909	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
910	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	4	2	no	—
918	C₂×D₄	—	4	2	no	—
919	C₂×D₄	—	4	4	no	—
920	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
921	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
922	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
923	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
933	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
934	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
935	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
936	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
937	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
938	Q₁₆	—	2	2	no	—
939	Q₁₆	—	2	4	no	—
940	Q₁₆	—	4	2	no	—
941	Q₁₆	—	4	2	no	—
942	Q₁₆	—	4	2	no	—
943	Q₁₆	—	4	1	no	—
944	Q₁₆	—	4	2	no	—
945	SD₁₆	—	2	2	no	—
946	SD₁₆	—	2	4	no	—
947	SD₁₆	—	4	2	no	—
948	SD₁₆	—	4	2	no	—
949	SD₁₆	—	4	2	no	—
950	SD₁₆	—	4	2	no	—
951	SD₁₆	—	4	1	no	—
952	M₁₆	—	4	2	no	—
953	C₂×C₈	—	4	2	no	—
954	C₂×C₈	—	4	2	no	—
955	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
956	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
957	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
958	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
959	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
960	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
988	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
989	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
990	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
991	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
992	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
993	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
995	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1014	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1015	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	2	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	C₂×D₄×C₂₉	1	2	yes	—
1026	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1027	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1028	C₄²	C₂×D₄×C₂₉	1	2	yes	—
1029	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1030	C₄²	C₂⁴×C₂₉	1	2	yes	—
1031	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1032	C₂³	—	2	1	no	—
1033	C₂³	—	2	2	no	—
1034	C₂³	—	4	4	no	—
1035	C₂³	—	8	2	no	—
1036	C₂³	—	8	2	no	—
1037	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1038	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
1039	Q₈	—	2	2	no	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	2	2	no	—
1042	Q₈	—	2	1	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	2	2	no	—
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	4	2	no	—
1050	Q₈	—	4	4	no	—
1051	Q₈	—	8	2	no	—
1052	Q₈	—	8	2	no	—
1053	Q₈	—	8	1	no	—
1054	Q₈	C₂₉×H(5,𝔽₂)	1	2	yes	—
1055	D₄	—	2	4	no	—
1056	D₄	—	2	1	no	—
1057	D₄	—	2	2	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	4	4	no	—
1061	D₄	—	4	2	no	—
1062	D₄	—	8	2	no	—
1063	D₄	—	8	1	no	—
1064	D₄	—	8	2	no	—
1065	D₄	—	8	1	no	—
1066	D₄	C₂₉×#137	1	4	yes	complemented
1067	C₂×C₄	—	2	4	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	1	no	—
1085	C₂×C₄	—	4	4	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	8	2	no	—
1089	C₂×C₄	—	8	2	no	—
1090	C₂×C₄	—	8	2	no	—
1091	C₂×C₄	—	8	2	no	—
1092	C₂×C₄	—	8	1	no	—
1093	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1094	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1095	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1096	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1097	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1098	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1099	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1100	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1101	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1102	C₈	—	2	1	no	—
1103	C₈	—	2	1	no	—
1104	C₈	—	2	2	no	—
1105	C₈	—	2	2	no	—
1106	C₈	—	2	1	no	—
1107	C₈	—	2	1	no	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	2	2	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	2	1	no	—
1112	C₂²	—	2	1	no	—
1113	C₂²	—	4	2	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	2	no	—
1117	C₂²	—	4	2	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	16	4	no	—
1120	C₂²	C₂×C₂₉×#137	1	4	yes	—
1121	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
1122	C₄	—	2	1	no	—
1123	C₄	—	2	2	no	—
1124	C₄	—	2	2	no	—
1125	C₄	—	2	1	no	—
1126	C₄	—	2	2	no	—
1127	C₄	—	2	1	no	—
1128	C₄	—	2	2	no	—
1129	C₄	—	2	1	no	—
1130	C₄	—	4	2	no	—
1131	C₄	—	4	1	no	—
1132	C₄	—	4	2	no	—
1133	C₄	—	4	1	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	2	no	—
1138	C₄	—	4	1	no	—
1139	C₄	C₂×C₂₉×#137	1	2	yes	—
1140	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
1141	C₄	C₂₉×#585	1	1	yes	characteristic
1142	C₂	—	2	4	no	—
1143	C₂	—	4	1	no	—
1144	C₂	—	8	1	no	—
1145	C₂	—	8	2	no	—
1146	C₂	C₂₉×#3488	1	1	yes	characteristic
1147	C₂	C₂²×C₂₉×#137	1	1	yes	characteristic
1148	C₂	C₂₉×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
prime radical	C₂₉×#3514	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄×#41×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×#41×C₂₉	C₂	semidirect
3. C₂₉×#3400	C₂	semidirect
4. C₂₉×#3398	C₂	semidirect
5. C₂₉×#3375	C₂	semidirect
6. C₂₉×#3369	C₂	semidirect
7. C₂₉×#3316	C₂	semidirect
8. C₂₉×#3314	C₂	semidirect
9. C₂₉×#3299	C₂	semidirect
10. C₂₉×#3295	C₂	semidirect
11. D₄×Q₁₆×C₂₉	C₂	semidirect
12. D₄×SD₁₆×C₂₉	C₂	semidirect
13. C₂₉×#3270	C₂	semidirect
14. C₂₉×#3266	C₂	semidirect
15. C₂₉×#3252	C₂	semidirect
16. C₂₉×#3248	C₂	semidirect
17. C₂₉×#3215	C₂	semidirect
18. C₂₉×#3210	C₂	semidirect
19. C₂₉×#3117	C₂	semidirect
20. C₂₉×#3108	C₂	semidirect
21. C₂₉×#3037	C₂	semidirect
22. C₂×C₂₉×#464	C₂	semidirect
23. C₂₉×#2990	C₂	semidirect
24. C₂×C₂₉×#137	C₂²	semidirect
25. C₂²×Q₁₆×C₂₉	C₂²	semidirect
28. Q₈²×C₂₉	C₂²	semidirect
30. C₂₉×#557	C₂²	semidirect
36. C₂₉×#554	C₂²	semidirect
40. D₄×Q₈×C₂₉	C₂²	semidirect
49. C₂₉×#533	C₂²	semidirect
50. C₂₉×#533	C₂²	semidirect
58. C₂×C₄×Q₈×C₂₉	C₂²	semidirect
59. C₂×C₄×Q₈×C₂₉	C₂²	semidirect
61. C₂₉×#497	C₂²	semidirect
62. C₂₉×#494	C₂²	semidirect
65. C₂₉×#489	C₂²	semidirect
66. C₂₉×#487	C₂²	semidirect
68. C₂₉×#484	C₂²	semidirect
69. C₂₉×#483	C₂²	semidirect
72. C₂₉×#479	C₂²	semidirect
73. C₂₉×#479	C₂²	semidirect
74. C₂₉×#479	C₂²	semidirect
75. C₂₉×#477	C₂²	semidirect
77. C₂₉×#475	C₂²	semidirect
78. C₂₉×#474	C₂²	semidirect
79. C₂₉×#470	C₂²	semidirect
81. C₂₉×#467	C₂²	semidirect
82. C₂₉×#467	C₂²	semidirect
90. C₂₉×#464	C₂²	semidirect
91. C₂₉×#464	C₂²	semidirect
92. C₂₉×#464	C₂²	semidirect
93. C₂₉×#464	C₂²	semidirect
94. C₂₉×#464	C₂²	semidirect
95. C₂₉×#464	C₂²	semidirect
96. C₂₉×#462	C₂²	semidirect
97. C₂₉×#462	C₂²	semidirect
98. C₂₉×#462	C₂²	semidirect
99. C₂₉×#462	C₂²	semidirect
101. C₂₉×#461	C₂²	semidirect
104. C₂₉×#452	C₂²	semidirect
105. C₂₉×#452	C₂²	semidirect
106. C₂₉×#451	C₂²	semidirect
107. C₂₉×#451	C₂²	semidirect
108. C₂₉×#451	C₂²	semidirect
109. C₂₉×#451	C₂²	semidirect
114. C₂₉×#446	C₂²	semidirect
115. C₂₉×#446	C₂²	semidirect
116. C₂₉×#441	C₂²	semidirect
117. C₂₉×#441	C₂²	semidirect
118. C₂₉×#440	C₂²	semidirect
119. C₂₉×#440	C₂²	semidirect
120. C₄×Q₁₆×C₂₉	C₂²	semidirect
121. C₄×Q₁₆×C₂₉	C₂²	semidirect
124. C₂₉×#435	C₂²	semidirect
125. C₂₉×#435	C₂²	semidirect
128. C₂₉×#432	C₂²	semidirect
129. C₂₉×#431	C₂²	semidirect
130. C₂₉×#423	C₂²	semidirect
131. C₂×C₂₉×C₄⋊C₈	C₂²	semidirect
132. C₂₉×#417	C₂²	semidirect
133. C₂×C₂₉×#103	C₂²	semidirect
457. #61991	C₂₉	direct (N × H)
492. D₄×C₂₉	#137	semidirect
535. Q₈×#41	C₂×C₂₉	semidirect
536. #3400	C₂×C₂₉	semidirect
537. #3398	C₂×C₂₉	semidirect
538. #3375	C₂×C₂₉	semidirect
539. #3369	C₂×C₂₉	semidirect
540. #3316	C₂×C₂₉	semidirect
541. #3314	C₂×C₂₉	semidirect
542. #3299	C₂×C₂₉	semidirect
543. #3295	C₂×C₂₉	semidirect
544. D₄×Q₁₆	C₂×C₂₉	semidirect
545. D₄×SD₁₆	C₂×C₂₉	semidirect
546. #3270	C₂×C₂₉	semidirect
547. #3266	C₂×C₂₉	semidirect
548. #3252	C₂×C₂₉	semidirect
549. #3248	C₂×C₂₉	semidirect
550. #3215	C₂×C₂₉	semidirect
551. #3210	C₂×C₂₉	semidirect
552. #3117	C₂×C₂₉	semidirect
553. #3108	C₂×C₂₉	semidirect
554. #3037	C₂×C₂₉	semidirect
555. C₂×#464	C₂×C₂₉	semidirect
556. #2990	C₂×C₂₉	semidirect
591. C₂×#137	C₂²×C₂₉	semidirect
592. C₂²×Q₁₆	C₂²×C₂₉	semidirect
595. Q₈²	C₂²×C₂₉	semidirect
597. #557	C₂²×C₂₉	semidirect
603. #554	C₂²×C₂₉	semidirect
607. D₄×Q₈	C₂²×C₂₉	semidirect
616. #533	C₂²×C₂₉	semidirect
617. #533	C₂²×C₂₉	semidirect
625. C₂×C₄×Q₈	C₂²×C₂₉	semidirect
626. C₂×C₄×Q₈	C₂²×C₂₉	semidirect
628. #497	C₂²×C₂₉	semidirect
629. #494	C₂²×C₂₉	semidirect
632. #489	C₂²×C₂₉	semidirect
633. #487	C₂²×C₂₉	semidirect
635. #484	C₂²×C₂₉	semidirect
636. #483	C₂²×C₂₉	semidirect
639. #479	C₂²×C₂₉	semidirect
640. #479	C₂²×C₂₉	semidirect
641. #479	C₂²×C₂₉	semidirect
642. #477	C₂²×C₂₉	semidirect
644. #475	C₂²×C₂₉	semidirect
645. #474	C₂²×C₂₉	semidirect
646. #470	C₂²×C₂₉	semidirect
648. #467	C₂²×C₂₉	semidirect
649. #467	C₂²×C₂₉	semidirect
657. #464	C₂²×C₂₉	semidirect
658. #464	C₂²×C₂₉	semidirect
659. #464	C₂²×C₂₉	semidirect
660. #464	C₂²×C₂₉	semidirect
661. #464	C₂²×C₂₉	semidirect
662. #464	C₂²×C₂₉	semidirect
663. #462	C₂²×C₂₉	semidirect
664. #462	C₂²×C₂₉	semidirect
665. #462	C₂²×C₂₉	semidirect
666. #462	C₂²×C₂₉	semidirect
668. #461	C₂²×C₂₉	semidirect
671. #452	C₂²×C₂₉	semidirect
672. #452	C₂²×C₂₉	semidirect
673. #451	C₂²×C₂₉	semidirect
674. #451	C₂²×C₂₉	semidirect
675. #451	C₂²×C₂₉	semidirect
676. #451	C₂²×C₂₉	semidirect
681. #446	C₂²×C₂₉	semidirect
682. #446	C₂²×C₂₉	semidirect
683. #441	C₂²×C₂₉	semidirect
684. #441	C₂²×C₂₉	semidirect
685. #440	C₂²×C₂₉	semidirect
686. #440	C₂²×C₂₉	semidirect
687. C₄×Q₁₆	C₂²×C₂₉	semidirect
688. C₄×Q₁₆	C₂²×C₂₉	semidirect
691. #435	C₂²×C₂₉	semidirect
692. #435	C₂²×C₂₉	semidirect
695. #432	C₂²×C₂₉	semidirect
696. #431	C₂²×C₂₉	semidirect
697. #423	C₂²×C₂₉	semidirect
698. C₂×C₄⋊C₈	C₂²×C₂₉	semidirect
699. #417	C₂²×C₂₉	semidirect
700. C₂×#103	C₂²×C₂₉	semidirect
889. C₂₉	#61991	direct (N × H)
1066. D₄	C₂₉×#137	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₉×#3514	2
Q₈×#41×C₂₉	2
C₂₉×#3400	2
C₂₉×#3398	2
C₂₉×#3375	2
C₂₉×#3369	2
C₂₉×#3316	2
C₂₉×#3314	2
C₂₉×#3299	2
C₂₉×#3295	2
D₄×Q₁₆×C₂₉	2
D₄×SD₁₆×C₂₉	2
C₂₉×#3270	2
C₂₉×#3266	2
C₂₉×#3252	2
C₂₉×#3248	2
C₂₉×#3215	2
C₂₉×#3210	2
C₂₉×#3117	2
C₂₉×#3108	2
C₂₉×#3037	2
C₂×C₂₉×#464	2
C₂₉×#2990	2
#61991	29

Subgroups — C29×#61991 #20356891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#61991 #20356891