Subgroups — C₂₉×#61194 #20356094

Order 7424.

2088 conjugacy classes of subgroups.

The subgroup lattice has 1268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3489	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3330	C₂	1	2	yes	maximal, complemented
4	C₂₉×#3327	C₂	1	2	yes	maximal, complemented
5	C₂₉×#3320	C₂	1	2	yes	maximal, complemented
6	C₂₉×#3315	C₂	1	2	yes	maximal, complemented
7	C₂₉×#3314	C₂	1	2	yes	maximal, complemented
8	C₂₉×#3308	C₂	1	2	yes	maximal, complemented
9	C₂₉×#3299	C₂	1	2	yes	maximal, complemented
10	C₂₉×#3297	C₂	1	2	yes	maximal, complemented
11	C₂₉×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₉×#484	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#3083	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#3061	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#3056	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₉×#3046	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₉×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₉×#3002	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₉×#2951	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₉×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₉×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₂₉×#417	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₂₉	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×#137	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic, complemented
30	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
31	C₂₉×#554	—	2	1	no	—
32	C₂₉×#554	C₂²	1	2	yes	—
33	C₂₉×#553	—	2	1	no	—
34	C₂₉×#553	C₂²	1	2	yes	—
35	C₂₉×#552	—	2	1	no	—
36	C₂₉×#552	C₂²	1	2	yes	complemented
37	D₄×Q₈×C₂₉	C₂²	1	2	yes	—
38	C₂₉×#548	C₂²	1	2	yes	—
39	C₂₉×#547	—	2	2	no	—
40	C₂₉×#547	—	2	1	no	—
41	C₂₉×#547	C₂²	1	2	yes	—
42	C₂₉×#547	C₂²	1	2	yes	complemented
43	C₂₉×#546	—	2	2	no	—
44	C₂₉×#546	C₂²	1	2	yes	—
45	C₂₉×#544	C₂²	1	1	yes	characteristic, complemented
46	C₂₉×#539	—	2	2	no	—
47	C₂₉×#537	—	2	1	no	—
48	C₂₉×#537	C₂²	1	1	yes	characteristic
49	C₂₉×#537	C₂²	1	1	yes	characteristic, complemented
50	C₂₉×#536	—	2	1	no	—
51	C₂₉×#536	C₂²	1	1	yes	characteristic
52	C₂₉×#525	—	2	1	no	—
53	C₂₉×#525	—	2	2	no	—
54	C₂₉×#525	C₂²	1	1	yes	characteristic
55	C₂₉×#525	C₂²	1	1	yes	characteristic
56	C₂×C₂₉×C₂²⋊Q₈	—	2	1	no	—
57	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₂₉×#520	C₂²	1	1	yes	characteristic
59	C₂₉×#520	C₂²	1	1	yes	characteristic, complemented
60	C₂₉×#520	C₂²	1	1	yes	characteristic, complemented
61	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
62	C₂₉×#491	C₂²	1	2	yes	complemented
63	C₂₉×#489	C₂²	1	2	yes	complemented
64	C₂₉×#488	C₂²	1	2	yes	complemented
65	C₂₉×#487	C₂²	1	2	yes	complemented
66	C₂₉×#485	C₂²	1	2	yes	complemented
67	C₂₉×#484	C₂²	1	2	yes	—
68	C₂₉×#484	C₂²	1	2	yes	—
69	C₂₉×#484	C₂²	1	2	yes	complemented
70	C₂₉×#484	C₂²	1	2	yes	complemented
71	C₂₉×#484	C₂²	1	2	yes	complemented
72	C₂₉×#482	C₂²	1	2	yes	complemented
73	C₂₉×#480	C₂²	1	2	yes	complemented
74	C₂₉×#479	C₂²	1	2	yes	complemented
75	C₂₉×#478	C₂²	1	2	yes	complemented
76	C₂₉×#477	C₂²	1	2	yes	complemented
77	C₂₉×#474	C₂²	1	2	yes	complemented
78	C₂₉×#470	C₂²	1	2	yes	complemented
79	C₂₉×#468	C₂²	1	2	yes	complemented
80	C₂₉×#468	C₂²	1	2	yes	complemented
81	C₂₉×#468	C₂²	1	2	yes	complemented
82	C₂₉×#467	C₂²	1	2	yes	—
83	C₂₉×#467	C₂²	1	2	yes	complemented
84	C₂₉×#466	C₂²	1	2	yes	complemented
85	C₂₉×#465	C₂²	1	2	yes	—
86	C₂₉×#464	C₂²	1	2	yes	complemented
87	C₂₉×#463	C₂²	1	2	yes	complemented
88	C₂₉×#462	C₂²	1	2	yes	complemented
89	C₂₉×#461	C₂²	1	2	yes	complemented
90	C₂₉×#452	C₂²	1	1	yes	characteristic
91	C₂₉×#452	C₂²	1	1	yes	characteristic
92	C₂₉×#452	C₂²	1	2	yes	complemented
93	C₂₉×#451	C₂²	1	1	yes	characteristic
94	C₂₉×#451	C₂²	1	2	yes	complemented
95	C₂₉×#450	C₂²	1	1	yes	characteristic
96	C₂₉×#449	C₂²	1	1	yes	characteristic
97	C₂₉×#449	C₂²	1	1	yes	characteristic
98	C₂₉×#449	C₂²	1	2	yes	complemented
99	C₂₉×#448	C₂²	1	1	yes	characteristic
100	C₂₉×#448	C₂²	1	2	yes	complemented
101	C₂₉×#447	C₂²	1	1	yes	characteristic
102	C₂₉×#440	C₂²	1	2	yes	complemented
103	C₂₉×#440	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₂₉	C₂²	1	2	yes	complemented
105	C₄×D₈×C₂₉	C₂²	1	2	yes	complemented
106	C₂₉×#436	C₂²	1	2	yes	complemented
107	C₂₉×#435	C₂²	1	2	yes	—
108	C₂₉×#435	C₂²	1	2	yes	complemented
109	C₈×D₄×C₂₉	C₂²	1	2	yes	—
110	C₂₉×#428	C₂²	1	1	yes	characteristic, complemented
111	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic, complemented
112	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic, complemented
113	C₂₉×#424	C₂²	1	1	yes	characteristic, complemented
114	C₂₉×#419	C₂²	1	1	yes	characteristic, complemented
115	C₂₉×#419	C₂²	1	2	yes	complemented
116	C₂₉×#417	C₂²	1	1	yes	characteristic
117	C₂₉×#417	C₂²	1	1	yes	characteristic
118	C₂₉×#417	C₂²	1	1	yes	characteristic
119	C₂₉×#417	C₂²	1	2	yes	—
120	C₂₉×#417	C₂²	1	2	yes	—
121	C₂₉×#417	C₂²	1	1	yes	characteristic
122	C₂₉×#417	C₂²	1	1	yes	characteristic, complemented
123	C₂₉×#417	C₂²	1	2	yes	complemented
124	C₂₉×#416	C₂²	1	1	yes	characteristic
125	C₂₉×#416	C₂²	1	1	yes	characteristic
126	C₂₉×#416	C₂²	1	2	yes	complemented
127	C₂×C₂₉×#103	C₂²	1	2	yes	—
128	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₂₉×#103	C₂²	1	2	yes	complemented
130	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₂₉×#102	C₂²	1	2	yes	—
132	C₂₉×#408	C₂²	1	1	yes	characteristic, complemented
133	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
134	C₂₉×#405	C₂²	1	1	yes	characteristic, complemented
135	C₂₉×2₋¹⁺⁴	—	2	4	no	—
136	C₂₉×2₋¹⁺⁴	—	4	2	no	—
137	C₂×#41×C₂₉	—	2	1	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	—	2	4	no	—
143	C₂×#41×C₂₉	—	4	2	no	—
144	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
145	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
146	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
147	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
148	C₂×#41×C₂₉	C₂³	1	2	yes	—
149	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
150	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
151	C₂²×Q₈×C₂₉	—	2	1	no	—
152	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
153	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
154	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
155	C₂²×D₄×C₂₉	—	2	1	no	—
156	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
157	C₂³×C₄×C₂₉	—	2	1	no	—
158	C₂³×C₄×C₂₉	—	2	1	no	—
159	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
160	C₂₉×#137	—	4	2	no	—
161	C₂₉×#135	—	2	4	no	—
162	C₂₉×#135	—	4	2	no	—
163	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
164	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
165	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
167	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
168	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
169	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
170	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
171	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
172	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
173	C₂₉×#131	—	4	2	no	—
174	C₂×M₁₆×C₂₉	—	4	2	no	—
175	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
176	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
177	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
178	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
179	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
180	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
181	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
182	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
183	C₂₉×C₄⋊Q₈	—	2	2	no	—
184	C₂₉×C₄⋊Q₈	—	2	1	no	—
185	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
186	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
187	C₂₉×#126	—	2	2	no	—
188	C₂₉×#126	—	2	2	no	—
189	C₂₉×#125	—	2	2	no	—
190	C₂₉×#125	—	2	2	no	—
191	C₂₉×#125	—	2	1	no	—
192	C₂₉×#125	C₂³	1	2	yes	—
193	C₂₉×#124	—	2	2	no	—
194	C₂₉×#124	C₂³	1	2	yes	—
195	C₂₉×#123	—	2	2	no	—
196	C₂₉×#123	—	2	1	no	—
197	C₂₉×#123	—	2	2	no	—
198	C₂₉×#123	—	2	2	no	—
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	D₄	1	2	yes	—
205	C₂₉×C₂²⋊Q₈	—	2	1	no	—
206	C₂₉×C₂²⋊Q₈	—	2	1	no	—
207	C₂₉×C₂²⋊Q₈	—	2	1	no	—
208	C₂₉×C₂²⋊Q₈	—	2	1	no	—
209	C₂₉×C₂²⋊Q₈	—	2	1	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	D₄	1	1	yes	characteristic
219	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
220	C₂₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₂₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
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×#121	—	2	1	no	—
227	C₂₉×#121	—	2	2	no	—
228	C₂₉×#121	—	2	2	no	—
229	C₂₉×#121	—	2	2	no	—
230	C₂₉×#121	—	2	2	no	—
231	C₂₉×#121	—	2	2	no	—
232	C₂₉×#121	—	2	1	no	—
233	C₂₉×#121	—	2	2	no	—
234	C₂₉×#121	D₄	1	1	yes	characteristic
235	C₂₉×#121	D₄	1	1	yes	characteristic
236	C₂₉×#121	C₂³	1	1	yes	characteristic
237	C₂₉×#121	C₂³	1	2	yes	—
238	C₂₉×#121	C₂³	1	1	yes	characteristic
239	C₂₉×#121	C₂³	1	2	yes	—
240	C₂₉×#120	—	2	1	no	—
241	C₂₉×#120	—	2	2	no	—
242	C₂₉×#120	D₄	1	2	yes	—
243	C₄×Q₈×C₂₉	—	2	1	no	—
244	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
245	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
246	C₄×D₄×C₂₉	—	2	2	no	—
247	C₄×D₄×C₂₉	—	2	1	no	—
248	C₄×D₄×C₂₉	—	2	2	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	2	no	—
253	C₄×D₄×C₂₉	—	2	2	no	—
254	C₄×D₄×C₂₉	—	2	2	no	—
255	C₄×D₄×C₂₉	—	2	2	no	—
256	C₄×D₄×C₂₉	C₂³	1	2	yes	—
257	C₄×D₄×C₂₉	C₂³	1	2	yes	—
258	C₄×D₄×C₂₉	C₂³	1	2	yes	—
259	C₄×D₄×C₂₉	C₂³	1	2	yes	—
260	C₂₉×#117	—	2	1	no	—
261	C₂₉×#117	—	2	1	no	—
262	C₂₉×#117	—	2	2	no	—
263	C₂₉×#117	C₂³	1	1	yes	characteristic
264	C₂₉×#117	C₂³	1	2	yes	—
265	C₂₉×#117	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
267	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
268	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
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	2	no	—
273	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
277	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
278	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
279	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
280	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
281	C₂₉×#107	C₂³	1	2	yes	—
282	C₂₉×#107	C₂³	1	2	yes	—
283	C₂₉×#107	C₂³	1	2	yes	—
284	C₂₉×#107	C₂³	1	2	yes	—
285	C₂₉×#107	C₂³	1	2	yes	—
286	C₂₉×#106	C₂³	1	2	yes	—
287	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
288	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
289	C₂₉×#103	C₂³	1	2	yes	—
290	C₂₉×#103	C₂³	1	2	yes	—
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	1	yes	characteristic
296	C₂₉×#103	C₂³	1	1	yes	characteristic
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×#103	C₂³	1	2	yes	—
304	C₂₉×#102	C₂³	1	2	yes	—
305	C₂₉×#102	C₂³	1	2	yes	—
306	C₂₉×#102	C₂³	1	1	yes	characteristic
307	C₂₉×#102	C₂³	1	1	yes	characteristic
308	C₂₉×#102	C₂³	1	1	yes	characteristic
309	C₂₉×#102	C₂³	1	1	yes	characteristic
310	C₂₉×#102	C₂³	1	2	yes	—
311	C₂₉×#102	C₂³	1	2	yes	—
312	C₂₉×#102	C₂³	1	2	yes	—
313	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
314	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
316	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
318	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
319	C₂₉×#97	C₂³	1	2	yes	—
320	C₄×C₈×C₂₉	C₂³	1	2	yes	—
321	C₂⁴×C₂₉	—	2	1	no	—
322	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
323	#41×C₂₉	—	2	2	no	—
324	#41×C₂₉	—	2	2	no	—
325	#41×C₂₉	—	2	2	no	—
326	#41×C₂₉	—	2	2	no	—
327	#41×C₂₉	—	2	2	no	—
328	#41×C₂₉	—	2	4	no	—
329	#41×C₂₉	—	2	2	no	—
330	#41×C₂₉	—	2	2	no	—
331	#41×C₂₉	—	2	2	no	—
332	#41×C₂₉	—	2	2	no	—
333	#41×C₂₉	—	4	4	no	—
334	#41×C₂₉	—	4	1	no	—
335	#41×C₂₉	—	4	1	no	—
336	#41×C₂₉	—	4	2	no	—
337	#41×C₂₉	—	4	4	no	—
338	#41×C₂₉	—	4	4	no	—
339	#41×C₂₉	—	4	8	no	—
340	#41×C₂₉	—	8	4	no	—
341	#41×C₂₉	#41	1	4	yes	complemented
342	C₂×Q₈×C₂₉	—	2	1	no	—
343	C₂×Q₈×C₂₉	—	2	2	no	—
344	C₂×Q₈×C₂₉	—	2	1	no	—
345	C₂×Q₈×C₂₉	—	2	2	no	—
346	C₂×Q₈×C₂₉	—	2	2	no	—
347	C₂×Q₈×C₂₉	—	2	4	no	—
348	C₂×Q₈×C₂₉	—	2	2	no	—
349	C₂×Q₈×C₂₉	—	2	2	no	—
350	C₂×Q₈×C₂₉	—	4	1	no	—
351	C₂×Q₈×C₂₉	—	4	2	no	—
352	C₂×Q₈×C₂₉	—	4	4	no	—
353	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
354	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
355	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
356	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
357	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₂₉	—	2	1	no	—
359	C₂×D₄×C₂₉	—	2	2	no	—
360	C₂×D₄×C₂₉	—	2	1	no	—
361	C₂×D₄×C₂₉	—	2	1	no	—
362	C₂×D₄×C₂₉	—	2	1	no	—
363	C₂×D₄×C₂₉	—	2	2	no	—
364	C₂×D₄×C₂₉	—	2	1	no	—
365	C₂×D₄×C₂₉	—	2	1	no	—
366	C₂×D₄×C₂₉	—	2	1	no	—
367	C₂×D₄×C₂₉	—	2	2	no	—
368	C₂×D₄×C₂₉	—	2	2	no	—
369	C₂×D₄×C₂₉	—	2	1	no	—
370	C₂×D₄×C₂₉	—	4	1	no	—
371	C₂×D₄×C₂₉	—	4	4	no	—
372	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
373	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
374	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
375	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
376	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
377	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
378	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₂₉	—	2	1	no	—
380	C₂²×C₄×C₂₉	—	2	2	no	—
381	C₂²×C₄×C₂₉	—	2	2	no	—
382	C₂²×C₄×C₂₉	—	2	1	no	—
383	C₂²×C₄×C₂₉	—	2	2	no	—
384	C₂²×C₄×C₂₉	—	2	2	no	—
385	C₂²×C₄×C₂₉	—	2	1	no	—
386	C₂²×C₄×C₂₉	—	2	1	no	—
387	C₂²×C₄×C₂₉	—	2	1	no	—
388	C₂²×C₄×C₂₉	—	2	2	no	—
389	C₂²×C₄×C₂₉	—	2	1	no	—
390	C₂²×C₄×C₂₉	—	2	2	no	—
391	C₂²×C₄×C₂₉	—	2	2	no	—
392	C₂²×C₄×C₂₉	—	2	1	no	—
393	C₂²×C₄×C₂₉	—	2	1	no	—
394	C₂²×C₄×C₂₉	—	2	1	no	—
395	C₂²×C₄×C₂₉	—	2	1	no	—
396	C₂²×C₄×C₂₉	—	2	2	no	—
397	C₂²×C₄×C₂₉	—	2	2	no	—
398	C₂²×C₄×C₂₉	—	4	4	no	—
399	C₂²×C₄×C₂₉	—	8	2	no	—
400	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
402	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
403	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
406	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
407	Q₁₆×C₂₉	—	2	2	no	—
408	Q₁₆×C₂₉	—	4	1	no	—
409	Q₁₆×C₂₉	—	4	2	no	—
410	SD₁₆×C₂₉	—	2	2	no	—
411	SD₁₆×C₂₉	—	2	2	no	—
412	SD₁₆×C₂₉	—	4	1	no	—
413	SD₁₆×C₂₉	—	4	1	no	—
414	SD₁₆×C₂₉	—	4	2	no	—
415	D₈×C₂₉	—	2	2	no	—
416	D₈×C₂₉	—	4	1	no	—
417	M₁₆×C₂₉	—	2	2	no	—
418	M₁₆×C₂₉	—	2	2	no	—
419	M₁₆×C₂₉	—	4	2	no	—
420	M₁₆×C₂₉	—	4	2	no	—
421	C₂×C₈×C₂₉	—	2	2	no	—
422	C₂×C₈×C₂₉	—	2	2	no	—
423	C₂×C₈×C₂₉	—	4	2	no	—
424	C₂×C₈×C₂₉	—	4	2	no	—
425	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
426	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
427	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
428	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
429	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
430	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
431	C₄⋊C₄×C₂₉	—	2	1	no	—
432	C₄⋊C₄×C₂₉	—	2	1	no	—
433	C₄⋊C₄×C₂₉	—	2	2	no	—
434	C₄⋊C₄×C₂₉	—	2	2	no	—
435	C₄⋊C₄×C₂₉	—	2	2	no	—
436	C₄⋊C₄×C₂₉	—	2	1	no	—
437	C₄⋊C₄×C₂₉	—	2	2	no	—
438	C₄⋊C₄×C₂₉	—	2	2	no	—
439	C₄⋊C₄×C₂₉	—	2	2	no	—
440	C₄⋊C₄×C₂₉	—	2	2	no	—
441	C₄⋊C₄×C₂₉	—	2	2	no	—
442	C₄⋊C₄×C₂₉	—	2	2	no	—
443	C₄⋊C₄×C₂₉	—	2	2	no	—
444	C₄⋊C₄×C₂₉	—	2	2	no	—
445	C₄⋊C₄×C₂₉	—	2	1	no	—
446	C₄⋊C₄×C₂₉	—	2	2	no	—
447	C₄⋊C₄×C₂₉	—	2	2	no	—
448	C₄⋊C₄×C₂₉	—	2	2	no	—
449	C₄⋊C₄×C₂₉	—	2	1	no	—
450	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
451	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
452	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
453	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
454	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
455	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
456	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
457	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
458	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
459	C₂²⋊C₄×C₂₉	—	2	2	no	—
460	C₂²⋊C₄×C₂₉	—	2	2	no	—
461	C₂²⋊C₄×C₂₉	—	2	1	no	—
462	C₂²⋊C₄×C₂₉	—	2	1	no	—
463	C₂²⋊C₄×C₂₉	—	2	2	no	—
464	C₂²⋊C₄×C₂₉	—	2	1	no	—
465	C₂²⋊C₄×C₂₉	—	2	2	no	—
466	C₂²⋊C₄×C₂₉	—	2	2	no	—
467	C₂²⋊C₄×C₂₉	—	2	2	no	—
468	C₂²⋊C₄×C₂₉	—	2	2	no	—
469	C₂²⋊C₄×C₂₉	—	2	2	no	—
470	C₂²⋊C₄×C₂₉	—	2	2	no	—
471	C₂²⋊C₄×C₂₉	—	2	2	no	—
472	C₂²⋊C₄×C₂₉	—	2	2	no	—
473	C₂²⋊C₄×C₂₉	—	2	1	no	—
474	C₂²⋊C₄×C₂₉	—	2	1	no	—
475	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
476	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
477	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
478	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
479	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
480	C₄²×C₂₉	—	2	2	no	—
481	C₄²×C₂₉	—	2	2	no	—
482	C₄²×C₂₉	—	2	2	no	—
483	C₄²×C₂₉	—	2	1	no	—
484	C₄²×C₂₉	C₂⁴	1	2	yes	—
485	#61194	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
486	C₂³×C₂₉	—	2	2	no	—
487	C₂³×C₂₉	—	2	2	no	—
488	C₂³×C₂₉	—	2	1	no	—
489	C₂³×C₂₉	—	2	1	no	—
490	C₂³×C₂₉	—	2	1	no	—
491	C₂³×C₂₉	—	4	1	no	—
492	C₂³×C₂₉	—	4	2	no	—
493	C₂³×C₂₉	—	4	2	no	—
494	C₂³×C₂₉	—	8	1	no	—
495	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
496	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
497	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
498	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
499	Q₈×C₂₉	—	2	2	no	—
500	Q₈×C₂₉	—	2	1	no	—
501	Q₈×C₂₉	—	2	1	no	—
502	Q₈×C₂₉	—	2	2	no	—
503	Q₈×C₂₉	—	2	1	no	—
504	Q₈×C₂₉	—	2	1	no	—
505	Q₈×C₂₉	—	2	2	no	—
506	Q₈×C₂₉	—	2	1	no	—
507	Q₈×C₂₉	—	4	4	no	—
508	Q₈×C₂₉	—	4	2	no	—
509	Q₈×C₂₉	—	4	2	no	—
510	Q₈×C₂₉	—	8	2	no	—
511	Q₈×C₂₉	C₂×#41	1	2	yes	—
512	D₄×C₂₉	—	2	4	no	—
513	D₄×C₂₉	—	2	4	no	—
514	D₄×C₂₉	—	2	4	no	—
515	D₄×C₂₉	—	2	2	no	—
516	D₄×C₂₉	—	2	1	no	—
517	D₄×C₂₉	—	2	1	no	—
518	D₄×C₂₉	—	2	1	no	—
519	D₄×C₂₉	—	2	1	no	—
520	D₄×C₂₉	—	2	1	no	—
521	D₄×C₂₉	—	4	2	no	—
522	D₄×C₂₉	—	4	2	no	—
523	D₄×C₂₉	—	4	2	no	—
524	D₄×C₂₉	—	4	2	no	—
525	D₄×C₂₉	—	4	4	no	—
526	D₄×C₂₉	—	4	2	no	—
527	D₄×C₂₉	—	4	2	no	—
528	D₄×C₂₉	—	4	2	no	—
529	D₄×C₂₉	—	4	2	no	—
530	D₄×C₂₉	—	8	2	no	—
531	D₄×C₂₉	—	8	2	no	—
532	D₄×C₂₉	C₂×#41	1	2	yes	—
533	C₂×C₄×C₂₉	—	2	2	no	—
534	C₂×C₄×C₂₉	—	2	1	no	—
535	C₂×C₄×C₂₉	—	2	2	no	—
536	C₂×C₄×C₂₉	—	2	2	no	—
537	C₂×C₄×C₂₉	—	2	4	no	—
538	C₂×C₄×C₂₉	—	2	1	no	—
539	C₂×C₄×C₂₉	—	2	1	no	—
540	C₂×C₄×C₂₉	—	2	2	no	—
541	C₂×C₄×C₂₉	—	2	1	no	—
542	C₂×C₄×C₂₉	—	2	2	no	—
543	C₂×C₄×C₂₉	—	2	1	no	—
544	C₂×C₄×C₂₉	—	2	1	no	—
545	C₂×C₄×C₂₉	—	2	1	no	—
546	C₂×C₄×C₂₉	—	2	2	no	—
547	C₂×C₄×C₂₉	—	2	2	no	—
548	C₂×C₄×C₂₉	—	2	1	no	—
549	C₂×C₄×C₂₉	—	2	2	no	—
550	C₂×C₄×C₂₉	—	2	2	no	—
551	C₂×C₄×C₂₉	—	2	1	no	—
552	C₂×C₄×C₂₉	—	4	2	no	—
553	C₂×C₄×C₂₉	—	4	2	no	—
554	C₂×C₄×C₂₉	—	4	2	no	—
555	C₂×C₄×C₂₉	—	4	4	no	—
556	C₂×C₄×C₂₉	—	4	4	no	—
557	C₂×C₄×C₂₉	—	4	4	no	—
558	C₂×C₄×C₂₉	—	4	2	no	—
559	C₂×C₄×C₂₉	—	4	2	no	—
560	C₂×C₄×C₂₉	—	4	2	no	—
561	C₂×C₄×C₂₉	—	8	2	no	—
562	C₂×C₄×C₂₉	—	8	2	no	—
563	C₂×C₄×C₂₉	—	8	1	no	—
564	C₂×C₄×C₂₉	—	8	1	no	—
565	C₂×C₄×C₂₉	—	8	2	no	—
566	C₂×C₄×C₂₉	—	8	1	no	—
567	C₂×C₄×C₂₉	—	8	2	no	—
568	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
569	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
570	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
571	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
572	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
573	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
575	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
576	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
577	C₈×C₂₉	—	2	1	no	—
578	C₈×C₂₉	—	2	1	no	—
579	C₈×C₂₉	—	2	1	no	—
580	C₈×C₂₉	—	2	1	no	—
581	C₈×C₂₉	—	2	2	no	—
582	C₈×C₂₉	—	2	2	no	—
583	#3492	C₂×C₂₉	1	1	yes	characteristic, complemented
584	#3489	C₂×C₂₉	1	1	yes	characteristic, complemented
585	#3330	C₂×C₂₉	1	2	yes	complemented
586	#3327	C₂×C₂₉	1	2	yes	complemented
587	#3320	C₂×C₂₉	1	2	yes	complemented
588	#3315	C₂×C₂₉	1	2	yes	complemented
589	#3314	C₂×C₂₉	1	2	yes	complemented
590	#3308	C₂×C₂₉	1	2	yes	complemented
591	#3299	C₂×C₂₉	1	2	yes	complemented
592	#3297	C₂×C₂₉	1	2	yes	complemented
593	#3137	C₂×C₂₉	1	1	yes	characteristic, complemented
594	#3098	C₂×C₂₉	1	1	yes	characteristic, complemented
595	C₂×#484	C₂×C₂₉	1	1	yes	characteristic, complemented
596	#3083	C₂×C₂₉	1	1	yes	characteristic, complemented
597	#3061	C₂×C₂₉	1	1	yes	characteristic, complemented
598	#3056	C₂×C₂₉	1	1	yes	characteristic, complemented
599	#3046	C₂×C₂₉	1	1	yes	characteristic, complemented
600	#3013	C₂×C₂₉	1	1	yes	characteristic, complemented
601	#3002	C₂×C₂₉	1	1	yes	characteristic, complemented
602	#2951	C₂×C₂₉	1	1	yes	characteristic, complemented
603	#2933	C₂×C₂₉	1	1	yes	characteristic, complemented
604	#2898	C₂×C₂₉	1	1	yes	characteristic, complemented
605	C₂×#417	C₂×C₂₉	1	1	yes	characteristic, complemented
606	C₂²×C₂₉	—	2	1	no	—
607	C₂²×C₂₉	—	2	1	no	—
608	C₂²×C₂₉	—	2	1	no	—
609	C₂²×C₂₉	—	2	1	no	—
610	C₂²×C₂₉	—	2	1	no	—
611	C₂²×C₂₉	—	2	2	no	—
612	C₂²×C₂₉	—	2	1	no	—
613	C₂²×C₂₉	—	2	2	no	—
614	C₂²×C₂₉	—	2	2	no	—
615	C₂²×C₂₉	—	2	2	no	—
616	C₂²×C₂₉	—	2	1	no	—
617	C₂²×C₂₉	—	4	4	no	—
618	C₂²×C₂₉	—	4	1	no	—
619	C₂²×C₂₉	—	4	1	no	—
620	C₂²×C₂₉	—	4	1	no	—
621	C₂²×C₂₉	—	4	1	no	—
622	C₂²×C₂₉	—	4	1	no	—
623	C₂²×C₂₉	—	4	1	no	—
624	C₂²×C₂₉	—	4	1	no	—
625	C₂²×C₂₉	—	4	1	no	—
626	C₂²×C₂₉	—	8	4	no	—
627	C₂²×C₂₉	#546	1	2	yes	—
628	C₂²×C₂₉	#578	1	2	yes	—
629	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
630	C₄×C₂₉	—	2	2	no	—
631	C₄×C₂₉	—	2	1	no	—
632	C₄×C₂₉	—	2	1	no	—
633	C₄×C₂₉	—	2	2	no	—
634	C₄×C₂₉	—	2	2	no	—
635	C₄×C₂₉	—	2	2	no	—
636	C₄×C₂₉	—	4	2	no	—
637	C₄×C₂₉	—	4	2	no	—
638	C₄×C₂₉	—	4	1	no	—
639	C₄×C₂₉	—	4	2	no	—
640	C₄×C₂₉	—	4	1	no	—
641	C₄×C₂₉	—	4	2	no	—
642	C₄×C₂₉	—	4	1	no	—
643	C₄×C₂₉	—	4	1	no	—
644	C₄×C₂₉	#546	1	2	yes	—
645	C₄×C₂₉	C₂²×#41	1	1	yes	characteristic
646	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
647	C₂×2₋¹⁺⁴	C₂²×C₂₉	1	1	yes	characteristic
648	C₂²×#41	C₂²×C₂₉	1	1	yes	characteristic
649	C₂×#137	C₂²×C₂₉	1	1	yes	characteristic, complemented
650	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
651	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
652	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic, complemented
653	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
654	#554	—	2	1	no	—
655	#554	C₂²×C₂₉	1	2	yes	—
656	#553	—	2	1	no	—
657	#553	C₂²×C₂₉	1	2	yes	—
658	#552	—	2	1	no	—
659	#552	C₂²×C₂₉	1	2	yes	complemented
660	D₄×Q₈	C₂²×C₂₉	1	2	yes	—
661	#548	C₂²×C₂₉	1	2	yes	—
662	#547	—	2	2	no	—
663	#547	—	2	1	no	—
664	#547	C₂²×C₂₉	1	2	yes	—
665	#547	C₂²×C₂₉	1	2	yes	complemented
666	#546	—	2	2	no	—
667	#546	C₂²×C₂₉	1	2	yes	—
668	#544	C₂²×C₂₉	1	1	yes	characteristic, complemented
669	#539	—	2	2	no	—
670	#537	—	2	1	no	—
671	#537	C₂²×C₂₉	1	1	yes	characteristic
672	#537	C₂²×C₂₉	1	1	yes	characteristic, complemented
673	#536	—	2	1	no	—
674	#536	C₂²×C₂₉	1	1	yes	characteristic
675	#525	—	2	1	no	—
676	#525	—	2	2	no	—
677	#525	C₂²×C₂₉	1	1	yes	characteristic
678	#525	C₂²×C₂₉	1	1	yes	characteristic
679	C₂×C₂²⋊Q₈	—	2	1	no	—
680	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
681	#520	C₂²×C₂₉	1	1	yes	characteristic
682	#520	C₂²×C₂₉	1	1	yes	characteristic, complemented
683	#520	C₂²×C₂₉	1	1	yes	characteristic, complemented
684	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
685	#491	C₂²×C₂₉	1	2	yes	complemented
686	#489	C₂²×C₂₉	1	2	yes	complemented
687	#488	C₂²×C₂₉	1	2	yes	complemented
688	#487	C₂²×C₂₉	1	2	yes	complemented
689	#485	C₂²×C₂₉	1	2	yes	complemented
690	#484	C₂²×C₂₉	1	2	yes	—
691	#484	C₂²×C₂₉	1	2	yes	—
692	#484	C₂²×C₂₉	1	2	yes	complemented
693	#484	C₂²×C₂₉	1	2	yes	complemented
694	#484	C₂²×C₂₉	1	2	yes	complemented
695	#482	C₂²×C₂₉	1	2	yes	complemented
696	#480	C₂²×C₂₉	1	2	yes	complemented
697	#479	C₂²×C₂₉	1	2	yes	complemented
698	#478	C₂²×C₂₉	1	2	yes	complemented
699	#477	C₂²×C₂₉	1	2	yes	complemented
700	#474	C₂²×C₂₉	1	2	yes	complemented
701	#470	C₂²×C₂₉	1	2	yes	complemented
702	#468	C₂²×C₂₉	1	2	yes	complemented
703	#468	C₂²×C₂₉	1	2	yes	complemented
704	#468	C₂²×C₂₉	1	2	yes	complemented
705	#467	C₂²×C₂₉	1	2	yes	—
706	#467	C₂²×C₂₉	1	2	yes	complemented
707	#466	C₂²×C₂₉	1	2	yes	complemented
708	#465	C₂²×C₂₉	1	2	yes	—
709	#464	C₂²×C₂₉	1	2	yes	complemented
710	#463	C₂²×C₂₉	1	2	yes	complemented
711	#462	C₂²×C₂₉	1	2	yes	complemented
712	#461	C₂²×C₂₉	1	2	yes	complemented
713	#452	C₂²×C₂₉	1	1	yes	characteristic
714	#452	C₂²×C₂₉	1	1	yes	characteristic
715	#452	C₂²×C₂₉	1	2	yes	complemented
716	#451	C₂²×C₂₉	1	1	yes	characteristic
717	#451	C₂²×C₂₉	1	2	yes	complemented
718	#450	C₂²×C₂₉	1	1	yes	characteristic
719	#449	C₂²×C₂₉	1	1	yes	characteristic
720	#449	C₂²×C₂₉	1	1	yes	characteristic
721	#449	C₂²×C₂₉	1	2	yes	complemented
722	#448	C₂²×C₂₉	1	1	yes	characteristic
723	#448	C₂²×C₂₉	1	2	yes	complemented
724	#447	C₂²×C₂₉	1	1	yes	characteristic
725	#440	C₂²×C₂₉	1	2	yes	complemented
726	#440	C₂²×C₂₉	1	2	yes	complemented
727	C₄×Q₁₆	C₂²×C₂₉	1	2	yes	complemented
728	C₄×D₈	C₂²×C₂₉	1	2	yes	complemented
729	#436	C₂²×C₂₉	1	2	yes	complemented
730	#435	C₂²×C₂₉	1	2	yes	—
731	#435	C₂²×C₂₉	1	2	yes	complemented
732	C₈×D₄	C₂²×C₂₉	1	2	yes	—
733	#428	C₂²×C₂₉	1	1	yes	characteristic, complemented
734	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic, complemented
735	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic, complemented
736	#424	C₂²×C₂₉	1	1	yes	characteristic, complemented
737	#419	C₂²×C₂₉	1	1	yes	characteristic, complemented
738	#419	C₂²×C₂₉	1	2	yes	complemented
739	#417	C₂²×C₂₉	1	2	yes	—
740	#417	C₂²×C₂₉	1	1	yes	characteristic
741	#417	C₂²×C₂₉	1	1	yes	characteristic
742	#417	C₂²×C₂₉	1	1	yes	characteristic
743	#417	C₂²×C₂₉	1	1	yes	characteristic
744	#417	C₂²×C₂₉	1	2	yes	—
745	#417	C₂²×C₂₉	1	2	yes	complemented
746	#417	C₂²×C₂₉	1	1	yes	characteristic, complemented
747	#416	C₂²×C₂₉	1	1	yes	characteristic
748	#416	C₂²×C₂₉	1	1	yes	characteristic
749	#416	C₂²×C₂₉	1	2	yes	complemented
750	C₂×#103	C₂²×C₂₉	1	2	yes	—
751	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic, complemented
752	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic, complemented
753	C₂×#103	C₂²×C₂₉	1	2	yes	complemented
754	C₂×#102	C₂²×C₂₉	1	2	yes	—
755	#408	C₂²×C₂₉	1	1	yes	characteristic, complemented
756	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
757	#405	C₂²×C₂₉	1	1	yes	characteristic, complemented
758	C₂×C₂₉	—	2	2	no	—
759	C₂×C₂₉	—	2	2	no	—
760	C₂×C₂₉	—	4	2	no	—
761	C₂×C₂₉	—	4	1	no	—
762	C₂×C₂₉	—	4	2	no	—
763	C₂×C₂₉	—	8	1	no	—
764	C₂×C₂₉	—	8	1	no	—
765	C₂×C₂₉	C₂×#546	1	1	yes	characteristic
766	C₂×C₂₉	C₂×#578	1	1	yes	characteristic
767	C₂×C₂₉	#3585	1	1	yes	characteristic
768	2₋¹⁺⁴	—	2	4	no	—
769	2₋¹⁺⁴	—	4	2	no	—
770	C₂×#41	—	2	1	no	—
771	C₂×#41	—	2	2	no	—
772	C₂×#41	—	2	2	no	—
773	C₂×#41	—	2	1	no	—
774	C₂×#41	—	2	1	no	—
775	C₂×#41	—	2	4	no	—
776	C₂×#41	—	4	2	no	—
777	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
778	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
779	C₂×#41	C₂³×C₂₉	1	2	yes	—
780	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
781	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
782	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
783	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
784	C₂²×Q₈	—	2	1	no	—
785	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
786	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
787	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
788	C₂²×D₄	—	2	1	no	—
789	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
790	C₂³×C₄	—	2	1	no	—
791	C₂³×C₄	—	2	1	no	—
792	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
793	#137	—	4	2	no	—
794	#135	—	2	4	no	—
795	#135	—	4	2	no	—
796	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
797	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
798	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
799	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
800	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
801	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
802	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
803	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
804	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
805	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
806	#131	—	4	2	no	—
807	C₂×M₁₆	—	4	2	no	—
808	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
809	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
810	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
811	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
812	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
813	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
814	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
815	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
816	C₄⋊Q₈	—	2	2	no	—
817	C₄⋊Q₈	—	2	1	no	—
818	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
819	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
820	#126	—	2	2	no	—
821	#126	—	2	2	no	—
822	#125	—	2	2	no	—
823	#125	—	2	2	no	—
824	#125	—	2	1	no	—
825	#125	C₂³×C₂₉	1	2	yes	—
826	#124	—	2	2	no	—
827	#124	C₂³×C₂₉	1	2	yes	—
828	#123	—	2	2	no	—
829	#123	—	2	1	no	—
830	#123	—	2	2	no	—
831	#123	—	2	2	no	—
832	#123	—	2	2	no	—
833	#123	—	2	2	no	—
834	#123	—	2	2	no	—
835	#123	—	2	2	no	—
836	#123	—	2	2	no	—
837	#123	D₄×C₂₉	1	2	yes	—
838	C₂²⋊Q₈	—	2	1	no	—
839	C₂²⋊Q₈	—	2	1	no	—
840	C₂²⋊Q₈	—	2	1	no	—
841	C₂²⋊Q₈	—	2	1	no	—
842	C₂²⋊Q₈	—	2	1	no	—
843	C₂²⋊Q₈	—	2	2	no	—
844	C₂²⋊Q₈	—	2	1	no	—
845	C₂²⋊Q₈	—	2	2	no	—
846	C₂²⋊Q₈	—	2	2	no	—
847	C₂²⋊Q₈	—	2	2	no	—
848	C₂²⋊Q₈	—	2	2	no	—
849	C₂²⋊Q₈	—	2	2	no	—
850	C₂²⋊Q₈	—	2	2	no	—
851	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
852	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
853	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
854	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
855	C₂²⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
856	C₂²⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
857	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
858	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
859	#121	—	2	1	no	—
860	#121	—	2	2	no	—
861	#121	—	2	2	no	—
862	#121	—	2	2	no	—
863	#121	—	2	2	no	—
864	#121	—	2	2	no	—
865	#121	—	2	1	no	—
866	#121	—	2	2	no	—
867	#121	D₄×C₂₉	1	1	yes	characteristic
868	#121	D₄×C₂₉	1	1	yes	characteristic
869	#121	C₂³×C₂₉	1	1	yes	characteristic
870	#121	C₂³×C₂₉	1	1	yes	characteristic
871	#121	C₂³×C₂₉	1	2	yes	—
872	#121	C₂³×C₂₉	1	2	yes	—
873	#120	—	2	1	no	—
874	#120	—	2	2	no	—
875	#120	D₄×C₂₉	1	2	yes	—
876	C₄×Q₈	—	2	1	no	—
877	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
878	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
879	C₄×D₄	—	2	2	no	—
880	C₄×D₄	—	2	1	no	—
881	C₄×D₄	—	2	2	no	—
882	C₄×D₄	—	2	2	no	—
883	C₄×D₄	—	2	1	no	—
884	C₄×D₄	—	2	1	no	—
885	C₄×D₄	—	2	2	no	—
886	C₄×D₄	—	2	2	no	—
887	C₄×D₄	—	2	2	no	—
888	C₄×D₄	—	2	2	no	—
889	C₄×D₄	C₂³×C₂₉	1	2	yes	—
890	C₄×D₄	C₂³×C₂₉	1	2	yes	—
891	C₄×D₄	C₂³×C₂₉	1	2	yes	—
892	C₄×D₄	C₂³×C₂₉	1	2	yes	—
893	#117	—	2	1	no	—
894	#117	—	2	1	no	—
895	#117	—	2	2	no	—
896	#117	C₂³×C₂₉	1	1	yes	characteristic
897	#117	C₂³×C₂₉	1	2	yes	—
898	#117	C₂³×C₂₉	1	1	yes	characteristic
899	C₂×C₄⋊C₄	—	2	1	no	—
900	C₂×C₄⋊C₄	—	2	1	no	—
901	C₂×C₄⋊C₄	—	2	1	no	—
902	C₂×C₄⋊C₄	—	2	1	no	—
903	C₂×C₄⋊C₄	—	2	1	no	—
904	C₂×C₄⋊C₄	—	2	1	no	—
905	C₂×C₄⋊C₄	—	2	2	no	—
906	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
907	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
908	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
909	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
910	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
911	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
912	C₂×C₂²⋊C₄	—	2	1	no	—
913	C₂×C₂²⋊C₄	—	2	2	no	—
914	#107	C₂³×C₂₉	1	2	yes	—
915	#107	C₂³×C₂₉	1	2	yes	—
916	#107	C₂³×C₂₉	1	2	yes	—
917	#107	C₂³×C₂₉	1	2	yes	—
918	#107	C₂³×C₂₉	1	2	yes	—
919	#106	C₂³×C₂₉	1	2	yes	—
920	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
921	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
922	#103	C₂³×C₂₉	1	2	yes	—
923	#103	C₂³×C₂₉	1	2	yes	—
924	#103	C₂³×C₂₉	1	2	yes	—
925	#103	C₂³×C₂₉	1	2	yes	—
926	#103	C₂³×C₂₉	1	1	yes	characteristic
927	#103	C₂³×C₂₉	1	2	yes	—
928	#103	C₂³×C₂₉	1	2	yes	—
929	#103	C₂³×C₂₉	1	2	yes	—
930	#103	C₂³×C₂₉	1	2	yes	—
931	#103	C₂³×C₂₉	1	2	yes	—
932	#103	C₂³×C₂₉	1	1	yes	characteristic
933	#103	C₂³×C₂₉	1	1	yes	characteristic
934	#103	C₂³×C₂₉	1	1	yes	characteristic
935	#103	C₂³×C₂₉	1	2	yes	—
936	#103	C₂³×C₂₉	1	2	yes	—
937	#102	C₂³×C₂₉	1	2	yes	—
938	#102	C₂³×C₂₉	1	2	yes	—
939	#102	C₂³×C₂₉	1	2	yes	—
940	#102	C₂³×C₂₉	1	2	yes	—
941	#102	C₂³×C₂₉	1	1	yes	characteristic
942	#102	C₂³×C₂₉	1	1	yes	characteristic
943	#102	C₂³×C₂₉	1	1	yes	characteristic
944	#102	C₂³×C₂₉	1	1	yes	characteristic
945	#102	C₂³×C₂₉	1	2	yes	—
946	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
947	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
948	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
949	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
950	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
951	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
952	#97	C₂³×C₂₉	1	2	yes	—
953	C₄×C₈	C₂³×C₂₉	1	2	yes	—
954	C₂₉	#61194	1	1	yes	characteristic, direct product factor, Sylow
955	C₂⁴	—	2	1	no	—
956	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
957	#41	—	2	2	no	—
958	#41	—	2	2	no	—
959	#41	—	2	2	no	—
960	#41	—	2	2	no	—
961	#41	—	2	2	no	—
962	#41	—	2	4	no	—
963	#41	—	2	2	no	—
964	#41	—	2	2	no	—
965	#41	—	2	2	no	—
966	#41	—	2	2	no	—
967	#41	—	4	4	no	—
968	#41	—	4	1	no	—
969	#41	—	4	1	no	—
970	#41	—	4	2	no	—
971	#41	—	4	4	no	—
972	#41	—	4	4	no	—
973	#41	—	4	8	no	—
974	#41	—	8	4	no	—
975	#41	#41×C₂₉	1	4	yes	complemented
976	C₂×Q₈	—	2	1	no	—
977	C₂×Q₈	—	2	2	no	—
978	C₂×Q₈	—	2	1	no	—
979	C₂×Q₈	—	2	2	no	—
980	C₂×Q₈	—	2	2	no	—
981	C₂×Q₈	—	2	4	no	—
982	C₂×Q₈	—	2	2	no	—
983	C₂×Q₈	—	2	2	no	—
984	C₂×Q₈	—	4	1	no	—
985	C₂×Q₈	—	4	2	no	—
986	C₂×Q₈	—	4	4	no	—
987	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
988	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
989	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
990	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
991	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
992	C₂×D₄	—	2	1	no	—
993	C₂×D₄	—	2	2	no	—
994	C₂×D₄	—	2	1	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	1	no	—
997	C₂×D₄	—	2	2	no	—
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	—	2	1	no	—
1000	C₂×D₄	—	2	1	no	—
1001	C₂×D₄	—	2	2	no	—
1002	C₂×D₄	—	2	2	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	4	1	no	—
1005	C₂×D₄	—	4	4	no	—
1006	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
1007	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
1008	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1009	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
1010	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
1011	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
1012	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
1013	C₂²×C₄	—	2	1	no	—
1014	C₂²×C₄	—	2	2	no	—
1015	C₂²×C₄	—	2	2	no	—
1016	C₂²×C₄	—	2	1	no	—
1017	C₂²×C₄	—	2	2	no	—
1018	C₂²×C₄	—	2	2	no	—
1019	C₂²×C₄	—	2	1	no	—
1020	C₂²×C₄	—	2	1	no	—
1021	C₂²×C₄	—	2	1	no	—
1022	C₂²×C₄	—	2	2	no	—
1023	C₂²×C₄	—	2	1	no	—
1024	C₂²×C₄	—	2	2	no	—
1025	C₂²×C₄	—	2	2	no	—
1026	C₂²×C₄	—	2	1	no	—
1027	C₂²×C₄	—	2	1	no	—
1028	C₂²×C₄	—	2	1	no	—
1029	C₂²×C₄	—	2	1	no	—
1030	C₂²×C₄	—	2	2	no	—
1031	C₂²×C₄	—	2	2	no	—
1032	C₂²×C₄	—	4	4	no	—
1033	C₂²×C₄	—	8	2	no	—
1034	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1035	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1036	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1037	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1038	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1039	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
1040	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1041	Q₁₆	—	2	2	no	—
1042	Q₁₆	—	4	1	no	—
1043	Q₁₆	—	4	2	no	—
1044	SD₁₆	—	2	2	no	—
1045	SD₁₆	—	2	2	no	—
1046	SD₁₆	—	4	1	no	—
1047	SD₁₆	—	4	1	no	—
1048	SD₁₆	—	4	2	no	—
1049	D₈	—	2	2	no	—
1050	D₈	—	4	1	no	—
1051	M₁₆	—	2	2	no	—
1052	M₁₆	—	2	2	no	—
1053	M₁₆	—	4	2	no	—
1054	M₁₆	—	4	2	no	—
1055	C₂×C₈	—	2	2	no	—
1056	C₂×C₈	—	2	2	no	—
1057	C₂×C₈	—	4	2	no	—
1058	C₂×C₈	—	4	2	no	—
1059	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1060	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
1061	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1062	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
1063	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1064	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1065	C₄⋊C₄	—	2	1	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	2	no	—
1068	C₄⋊C₄	—	2	2	no	—
1069	C₄⋊C₄	—	2	2	no	—
1070	C₄⋊C₄	—	2	1	no	—
1071	C₄⋊C₄	—	2	2	no	—
1072	C₄⋊C₄	—	2	2	no	—
1073	C₄⋊C₄	—	2	2	no	—
1074	C₄⋊C₄	—	2	2	no	—
1075	C₄⋊C₄	—	2	2	no	—
1076	C₄⋊C₄	—	2	2	no	—
1077	C₄⋊C₄	—	2	2	no	—
1078	C₄⋊C₄	—	2	2	no	—
1079	C₄⋊C₄	—	2	1	no	—
1080	C₄⋊C₄	—	2	2	no	—
1081	C₄⋊C₄	—	2	2	no	—
1082	C₄⋊C₄	—	2	2	no	—
1083	C₄⋊C₄	—	2	1	no	—
1084	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1085	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1086	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1087	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1088	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1089	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
1090	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
1091	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1092	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
1093	C₂²⋊C₄	—	2	2	no	—
1094	C₂²⋊C₄	—	2	2	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	2	no	—
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	—	2	2	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	—	2	2	no	—
1105	C₂²⋊C₄	—	2	2	no	—
1106	C₂²⋊C₄	—	2	2	no	—
1107	C₂²⋊C₄	—	2	1	no	—
1108	C₂²⋊C₄	—	2	1	no	—
1109	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1110	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1111	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1112	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1113	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1114	C₄²	—	2	2	no	—
1115	C₄²	—	2	2	no	—
1116	C₄²	—	2	2	no	—
1117	C₄²	—	2	1	no	—
1118	C₄²	C₂⁴×C₂₉	1	2	yes	—
1119	C₂³	—	2	2	no	—
1120	C₂³	—	2	2	no	—
1121	C₂³	—	2	1	no	—
1122	C₂³	—	2	1	no	—
1123	C₂³	—	2	1	no	—
1124	C₂³	—	4	1	no	—
1125	C₂³	—	4	2	no	—
1126	C₂³	—	4	2	no	—
1127	C₂³	—	8	1	no	—
1128	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1129	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
1130	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1131	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1132	Q₈	—	2	2	no	—
1133	Q₈	—	2	1	no	—
1134	Q₈	—	2	1	no	—
1135	Q₈	—	2	2	no	—
1136	Q₈	—	2	1	no	—
1137	Q₈	—	2	1	no	—
1138	Q₈	—	2	2	no	—
1139	Q₈	—	2	1	no	—
1140	Q₈	—	4	4	no	—
1141	Q₈	—	4	2	no	—
1142	Q₈	—	4	2	no	—
1143	Q₈	—	8	2	no	—
1144	Q₈	C₂×#41×C₂₉	1	2	yes	—
1145	D₄	—	2	4	no	—
1146	D₄	—	2	4	no	—
1147	D₄	—	2	4	no	—
1148	D₄	—	2	2	no	—
1149	D₄	—	2	1	no	—
1150	D₄	—	2	1	no	—
1151	D₄	—	2	1	no	—
1152	D₄	—	2	1	no	—
1153	D₄	—	2	1	no	—
1154	D₄	—	4	2	no	—
1155	D₄	—	4	2	no	—
1156	D₄	—	4	2	no	—
1157	D₄	—	4	2	no	—
1158	D₄	—	4	4	no	—
1159	D₄	—	4	2	no	—
1160	D₄	—	4	2	no	—
1161	D₄	—	4	2	no	—
1162	D₄	—	4	2	no	—
1163	D₄	—	8	2	no	—
1164	D₄	—	8	2	no	—
1165	D₄	C₂×#41×C₂₉	1	2	yes	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	2	4	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	2	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	2	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	1	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	2	no	—
1180	C₂×C₄	—	2	2	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	2	no	—
1183	C₂×C₄	—	2	2	no	—
1184	C₂×C₄	—	2	1	no	—
1185	C₂×C₄	—	4	2	no	—
1186	C₂×C₄	—	4	2	no	—
1187	C₂×C₄	—	4	2	no	—
1188	C₂×C₄	—	4	4	no	—
1189	C₂×C₄	—	4	4	no	—
1190	C₂×C₄	—	4	4	no	—
1191	C₂×C₄	—	4	2	no	—
1192	C₂×C₄	—	4	2	no	—
1193	C₂×C₄	—	4	2	no	—
1194	C₂×C₄	—	8	2	no	—
1195	C₂×C₄	—	8	2	no	—
1196	C₂×C₄	—	8	1	no	—
1197	C₂×C₄	—	8	2	no	—
1198	C₂×C₄	—	8	1	no	—
1199	C₂×C₄	—	8	2	no	—
1200	C₂×C₄	—	8	1	no	—
1201	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1202	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1203	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1204	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1205	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1206	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1207	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
1208	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
1209	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1210	C₈	—	2	1	no	—
1211	C₈	—	2	1	no	—
1212	C₈	—	2	1	no	—
1213	C₈	—	2	1	no	—
1214	C₈	—	2	2	no	—
1215	C₈	—	2	2	no	—
1216	C₂²	—	2	1	no	—
1217	C₂²	—	2	1	no	—
1218	C₂²	—	2	1	no	—
1219	C₂²	—	2	1	no	—
1220	C₂²	—	2	1	no	—
1221	C₂²	—	2	2	no	—
1222	C₂²	—	2	2	no	—
1223	C₂²	—	2	2	no	—
1224	C₂²	—	2	1	no	—
1225	C₂²	—	2	1	no	—
1226	C₂²	—	2	2	no	—
1227	C₂²	—	4	4	no	—
1228	C₂²	—	4	1	no	—
1229	C₂²	—	4	1	no	—
1230	C₂²	—	4	1	no	—
1231	C₂²	—	4	1	no	—
1232	C₂²	—	4	1	no	—
1233	C₂²	—	4	1	no	—
1234	C₂²	—	4	1	no	—
1235	C₂²	—	4	1	no	—
1236	C₂²	—	8	4	no	—
1237	C₂²	C₂₉×#546	1	2	yes	—
1238	C₂²	C₂₉×#578	1	2	yes	—
1239	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
1240	C₄	—	2	1	no	—
1241	C₄	—	2	1	no	—
1242	C₄	—	2	2	no	—
1243	C₄	—	2	2	no	—
1244	C₄	—	2	2	no	—
1245	C₄	—	2	2	no	—
1246	C₄	—	4	1	no	—
1247	C₄	—	4	2	no	—
1248	C₄	—	4	1	no	—
1249	C₄	—	4	1	no	—
1250	C₄	—	4	2	no	—
1251	C₄	—	4	2	no	—
1252	C₄	—	4	1	no	—
1253	C₄	—	4	2	no	—
1254	C₄	C₂₉×#546	1	2	yes	—
1255	C₄	C₂²×#41×C₂₉	1	1	yes	characteristic
1256	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
1257	C₂	—	2	2	no	—
1258	C₂	—	2	2	no	—
1259	C₂	—	4	1	no	—
1260	C₂	—	4	2	no	—
1261	C₂	—	4	2	no	—
1262	C₂	—	8	1	no	—
1263	C₂	—	8	1	no	—
1264	C₂	C₂×C₂₉×#546	1	1	yes	characteristic
1265	C₂	C₂×C₂₉×#578	1	1	yes	characteristic
1266	C₂	C₂₉×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂₉×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3492	C₂	semidirect
2. C₂₉×#3489	C₂	semidirect
3. C₂₉×#3330	C₂	semidirect
4. C₂₉×#3327	C₂	semidirect
5. C₂₉×#3320	C₂	semidirect
6. C₂₉×#3315	C₂	semidirect
7. C₂₉×#3314	C₂	semidirect
8. C₂₉×#3308	C₂	semidirect
9. C₂₉×#3299	C₂	semidirect
10. C₂₉×#3297	C₂	semidirect
11. C₂₉×#3137	C₂	semidirect
12. C₂₉×#3098	C₂	semidirect
13. C₂×C₂₉×#484	C₂	semidirect
14. C₂₉×#3083	C₂	semidirect
15. C₂₉×#3061	C₂	semidirect
16. C₂₉×#3056	C₂	semidirect
17. C₂₉×#3046	C₂	semidirect
18. C₂₉×#3013	C₂	semidirect
19. C₂₉×#3002	C₂	semidirect
20. C₂₉×#2951	C₂	semidirect
21. C₂₉×#2933	C₂	semidirect
22. C₂₉×#2898	C₂	semidirect
23. C₂×C₂₉×#417	C₂	semidirect
26. C₂×C₂₉×#137	C₂²	semidirect
29. C₂×C₂₉×#131	C₂²	semidirect
36. C₂₉×#552	C₂²	semidirect
42. C₂₉×#547	C₂²	semidirect
45. C₂₉×#544	C₂²	semidirect
49. C₂₉×#537	C₂²	semidirect
59. C₂₉×#520	C₂²	semidirect
60. C₂₉×#520	C₂²	semidirect
62. C₂₉×#491	C₂²	semidirect
63. C₂₉×#489	C₂²	semidirect
64. C₂₉×#488	C₂²	semidirect
65. C₂₉×#487	C₂²	semidirect
66. C₂₉×#485	C₂²	semidirect
69. C₂₉×#484	C₂²	semidirect
70. C₂₉×#484	C₂²	semidirect
71. C₂₉×#484	C₂²	semidirect
72. C₂₉×#482	C₂²	semidirect
73. C₂₉×#480	C₂²	semidirect
74. C₂₉×#479	C₂²	semidirect
75. C₂₉×#478	C₂²	semidirect
76. C₂₉×#477	C₂²	semidirect
77. C₂₉×#474	C₂²	semidirect
78. C₂₉×#470	C₂²	semidirect
79. C₂₉×#468	C₂²	semidirect
80. C₂₉×#468	C₂²	semidirect
81. C₂₉×#468	C₂²	semidirect
83. C₂₉×#467	C₂²	semidirect
84. C₂₉×#466	C₂²	semidirect
86. C₂₉×#464	C₂²	semidirect
87. C₂₉×#463	C₂²	semidirect
88. C₂₉×#462	C₂²	semidirect
89. C₂₉×#461	C₂²	semidirect
92. C₂₉×#452	C₂²	semidirect
94. C₂₉×#451	C₂²	semidirect
98. C₂₉×#449	C₂²	semidirect
100. C₂₉×#448	C₂²	semidirect
102. C₂₉×#440	C₂²	semidirect
103. C₂₉×#440	C₂²	semidirect
104. C₄×Q₁₆×C₂₉	C₂²	semidirect
105. C₄×D₈×C₂₉	C₂²	semidirect
106. C₂₉×#436	C₂²	semidirect
108. C₂₉×#435	C₂²	semidirect
110. C₂₉×#428	C₂²	semidirect
111. C₂×C₂₉×#107	C₂²	semidirect
112. C₂×C₂₉×#107	C₂²	semidirect
113. C₂₉×#424	C₂²	semidirect
114. C₂₉×#419	C₂²	semidirect
115. C₂₉×#419	C₂²	semidirect
122. C₂₉×#417	C₂²	semidirect
123. C₂₉×#417	C₂²	semidirect
126. C₂₉×#416	C₂²	semidirect
128. C₂×C₂₉×#103	C₂²	semidirect
129. C₂×C₂₉×#103	C₂²	semidirect
130. C₂×C₂₉×#103	C₂²	semidirect
132. C₂₉×#408	C₂²	semidirect
134. C₂₉×#405	C₂²	semidirect
341. #41×C₂₉	#41	semidirect
485. #61194	C₂₉	direct (N × H)
583. #3492	C₂×C₂₉	semidirect
584. #3489	C₂×C₂₉	semidirect
585. #3330	C₂×C₂₉	semidirect
586. #3327	C₂×C₂₉	semidirect
587. #3320	C₂×C₂₉	semidirect
588. #3315	C₂×C₂₉	semidirect
589. #3314	C₂×C₂₉	semidirect
590. #3308	C₂×C₂₉	semidirect
591. #3299	C₂×C₂₉	semidirect
592. #3297	C₂×C₂₉	semidirect
593. #3137	C₂×C₂₉	semidirect
594. #3098	C₂×C₂₉	semidirect
595. C₂×#484	C₂×C₂₉	semidirect
596. #3083	C₂×C₂₉	semidirect
597. #3061	C₂×C₂₉	semidirect
598. #3056	C₂×C₂₉	semidirect
599. #3046	C₂×C₂₉	semidirect
600. #3013	C₂×C₂₉	semidirect
601. #3002	C₂×C₂₉	semidirect
602. #2951	C₂×C₂₉	semidirect
603. #2933	C₂×C₂₉	semidirect
604. #2898	C₂×C₂₉	semidirect
605. C₂×#417	C₂×C₂₉	semidirect
649. C₂×#137	C₂²×C₂₉	semidirect
652. C₂×#131	C₂²×C₂₉	semidirect
659. #552	C₂²×C₂₉	semidirect
665. #547	C₂²×C₂₉	semidirect
668. #544	C₂²×C₂₉	semidirect
672. #537	C₂²×C₂₉	semidirect
682. #520	C₂²×C₂₉	semidirect
683. #520	C₂²×C₂₉	semidirect
685. #491	C₂²×C₂₉	semidirect
686. #489	C₂²×C₂₉	semidirect
687. #488	C₂²×C₂₉	semidirect
688. #487	C₂²×C₂₉	semidirect
689. #485	C₂²×C₂₉	semidirect
692. #484	C₂²×C₂₉	semidirect
693. #484	C₂²×C₂₉	semidirect
694. #484	C₂²×C₂₉	semidirect
695. #482	C₂²×C₂₉	semidirect
696. #480	C₂²×C₂₉	semidirect
697. #479	C₂²×C₂₉	semidirect
698. #478	C₂²×C₂₉	semidirect
699. #477	C₂²×C₂₉	semidirect
700. #474	C₂²×C₂₉	semidirect
701. #470	C₂²×C₂₉	semidirect
702. #468	C₂²×C₂₉	semidirect
703. #468	C₂²×C₂₉	semidirect
704. #468	C₂²×C₂₉	semidirect
706. #467	C₂²×C₂₉	semidirect
707. #466	C₂²×C₂₉	semidirect
709. #464	C₂²×C₂₉	semidirect
710. #463	C₂²×C₂₉	semidirect
711. #462	C₂²×C₂₉	semidirect
712. #461	C₂²×C₂₉	semidirect
715. #452	C₂²×C₂₉	semidirect
717. #451	C₂²×C₂₉	semidirect
721. #449	C₂²×C₂₉	semidirect
723. #448	C₂²×C₂₉	semidirect
725. #440	C₂²×C₂₉	semidirect
726. #440	C₂²×C₂₉	semidirect
727. C₄×Q₁₆	C₂²×C₂₉	semidirect
728. C₄×D₈	C₂²×C₂₉	semidirect
729. #436	C₂²×C₂₉	semidirect
731. #435	C₂²×C₂₉	semidirect
733. #428	C₂²×C₂₉	semidirect
734. C₂×#107	C₂²×C₂₉	semidirect
735. C₂×#107	C₂²×C₂₉	semidirect
736. #424	C₂²×C₂₉	semidirect
737. #419	C₂²×C₂₉	semidirect
738. #419	C₂²×C₂₉	semidirect
745. #417	C₂²×C₂₉	semidirect
746. #417	C₂²×C₂₉	semidirect
749. #416	C₂²×C₂₉	semidirect
751. C₂×#103	C₂²×C₂₉	semidirect
752. C₂×#103	C₂²×C₂₉	semidirect
753. C₂×#103	C₂²×C₂₉	semidirect
755. #408	C₂²×C₂₉	semidirect
757. #405	C₂²×C₂₉	semidirect
954. C₂₉	#61194	direct (N × H)
975. #41	#41×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#3492	2
C₂₉×#3489	2
C₂₉×#3330	2
C₂₉×#3327	2
C₂₉×#3320	2
C₂₉×#3315	2
C₂₉×#3314	2
C₂₉×#3308	2
C₂₉×#3299	2
C₂₉×#3297	2
C₂₉×#3137	2
C₂₉×#3098	2
C₂×C₂₉×#484	2
C₂₉×#3083	2
C₂₉×#3061	2
C₂₉×#3056	2
C₂₉×#3046	2
C₂₉×#3013	2
C₂₉×#3002	2
C₂₉×#2951	2
C₂₉×#2933	2
C₂₉×#2898	2
C₂×C₂₉×#417	2
#61194	29

Subgroups — C29×#61194 #20356094

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#61194 #20356094