Subgroups — C₂₉×#61186 #20356086

Order 7424.

2022 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3486	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#3328	C₂	1	2	yes	maximal, complemented
4	C₂₉×#3327	C₂	1	2	yes	maximal, complemented
5	C₂₉×#3316	C₂	1	2	yes	maximal, complemented
6	C₂₉×#3313	C₂	1	2	yes	maximal, complemented
7	C₂₉×#3312	C₂	1	2	yes	maximal, complemented
8	C₂₉×#3312	C₂	1	2	yes	maximal, complemented
9	C₂₉×#3300	C₂	1	2	yes	maximal, complemented
10	C₂₉×#3299	C₂	1	2	yes	maximal, complemented
11	C₂₉×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#3091	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#3059	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#3056	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₉×#3044	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₉×#3011	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₂₉×#451	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₉×#2950	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×#419	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂³×Q₈×C₂₉	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×#137	C₂²	1	1	yes	characteristic
27	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
28	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
31	C₂₉×#556	C₂²	1	2	yes	—
32	C₂₉×#554	C₂²	1	2	yes	—
33	C₂₉×#552	—	2	2	no	—
34	C₂₉×#552	C₂²	1	2	yes	—
35	C₂₉×#552	C₂²	1	2	yes	—
36	C₂₉×#551	—	2	2	no	—
37	D₄×Q₈×C₂₉	—	2	1	no	—
38	D₄×Q₈×C₂₉	—	2	1	no	—
39	D₄×Q₈×C₂₉	C₂²	1	2	yes	—
40	D₄×Q₈×C₂₉	C₂²	1	2	yes	—
41	C₂₉×#548	—	2	1	no	—
42	C₂₉×#548	—	2	1	no	—
43	C₂₉×#548	C₂²	1	2	yes	—
44	C₂₉×#548	C₂²	1	2	yes	—
45	C₂₉×#544	C₂²	1	1	yes	characteristic
46	C₂₉×#542	—	2	1	no	—
47	C₂₉×#541	—	2	1	no	—
48	C₂₉×#536	—	2	2	no	—
49	C₂₉×#536	C₂²	1	1	yes	characteristic
50	C₂₉×#536	C₂²	1	1	yes	characteristic
51	C₂₉×#536	C₂²	1	1	yes	characteristic
52	C₂₉×#533	—	2	1	no	—
53	C₂₉×#529	—	2	1	no	—
54	C₂₉×#525	—	2	2	no	—
55	C₂₉×#525	C₂²	1	1	yes	characteristic
56	C₂₉×#525	C₂²	1	1	yes	characteristic
57	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₂₉×#520	C₂²	1	1	yes	characteristic
59	C₂₉×#519	C₂²	1	1	yes	characteristic
60	C₂₉×#519	C₂²	1	1	yes	characteristic
61	C₂×C₂₉×#117	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	1	yes	characteristic
67	C₂₉×#485	C₂²	1	1	yes	characteristic
68	C₂₉×#485	C₂²	1	2	yes	complemented
69	C₂₉×#485	C₂²	1	2	yes	complemented
70	C₂₉×#484	C₂²	1	1	yes	characteristic
71	C₂₉×#484	C₂²	1	2	yes	complemented
72	C₂₉×#483	C₂²	1	1	yes	characteristic
73	C₂₉×#483	C₂²	1	2	yes	complemented
74	C₂₉×#482	C₂²	1	1	yes	characteristic
75	C₂₉×#482	C₂²	1	1	yes	characteristic
76	C₂₉×#481	C₂²	1	1	yes	characteristic
77	C₂₉×#480	C₂²	1	1	yes	characteristic
78	C₂₉×#479	C₂²	1	2	yes	complemented
79	C₂₉×#479	C₂²	1	2	yes	complemented
80	C₂₉×#477	C₂²	1	2	yes	complemented
81	C₂₉×#475	C₂²	1	2	yes	complemented
82	C₂₉×#470	C₂²	1	2	yes	—
83	C₂₉×#470	C₂²	1	2	yes	complemented
84	C₂₉×#470	C₂²	1	2	yes	complemented
85	C₂₉×#468	C₂²	1	2	yes	—
86	C₂₉×#467	C₂²	1	2	yes	—
87	C₂₉×#467	C₂²	1	2	yes	complemented
88	C₂₉×#467	C₂²	1	2	yes	complemented
89	C₂₉×#465	C₂²	1	2	yes	—
90	C₂₉×#464	C₂²	1	2	yes	complemented
91	C₂₉×#464	C₂²	1	2	yes	complemented
92	C₂₉×#462	C₂²	1	2	yes	complemented
93	C₂₉×#462	C₂²	1	2	yes	complemented
94	C₂₉×#452	C₂²	1	2	yes	complemented
95	C₂₉×#452	C₂²	1	2	yes	complemented
96	C₂₉×#451	C₂²	1	2	yes	—
97	C₂₉×#451	C₂²	1	2	yes	—
98	C₂₉×#451	C₂²	1	2	yes	—
99	C₂₉×#451	C₂²	1	2	yes	—
100	C₂₉×#451	C₂²	1	2	yes	complemented
101	C₂₉×#451	C₂²	1	2	yes	complemented
102	C₂₉×#441	C₂²	1	2	yes	complemented
103	C₂₉×#441	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₂₉	C₂²	1	2	yes	complemented
105	C₄×Q₁₆×C₂₉	C₂²	1	2	yes	complemented
106	C₂₉×#436	C₂²	1	2	yes	—
107	C₂₉×#435	C₂²	1	2	yes	—
108	C₂₉×#435	C₂²	1	2	yes	—
109	C₈×D₄×C₂₉	C₂²	1	2	yes	—
110	C₂₉×#428	C₂²	1	1	yes	characteristic
111	C₂₉×#427	C₂²	1	1	yes	characteristic
112	C₂₉×#427	C₂²	1	1	yes	characteristic
113	C₂₉×#424	C₂²	1	1	yes	characteristic
114	C₂₉×#419	C₂²	1	1	yes	characteristic
115	C₂₉×#419	C₂²	1	1	yes	characteristic
116	C₂₉×#419	C₂²	1	1	yes	characteristic
117	C₂₉×#419	C₂²	1	1	yes	characteristic
118	C₂₉×#419	C₂²	1	2	yes	—
119	C₂₉×#419	C₂²	1	2	yes	—
120	C₂₉×#419	C₂²	1	1	yes	characteristic
121	C₂₉×#419	C₂²	1	2	yes	complemented
122	C₂₉×#417	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
128	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
129	C₂×C₂₉×#103	C₂²	1	2	yes	—
130	C₂×C₂₉×#103	C₂²	1	2	yes	—
131	C₂×C₂₉×#103	C₂²	1	2	yes	complemented
132	C₂₉×#408	C₂²	1	1	yes	characteristic
133	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
134	C₂₉×#405	C₂²	1	1	yes	characteristic
135	C₂₉×2₋¹⁺⁴	—	2	4	no	—
136	C₂₉×2₋¹⁺⁴	—	4	2	no	—
137	C₂×#41×C₂₉	—	2	2	no	—
138	C₂×#41×C₂₉	—	2	1	no	—
139	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
140	C₂×#41×C₂₉	C₂³	1	2	yes	—
141	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₂₉	—	2	1	no	—
143	C₂²×Q₈×C₂₉	—	2	1	no	—
144	C₂²×Q₈×C₂₉	—	2	1	no	—
145	C₂²×Q₈×C₂₉	—	2	1	no	—
146	C₂²×Q₈×C₂₉	—	2	4	no	—
147	C₂²×Q₈×C₂₉	—	4	2	no	—
148	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
151	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
152	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
153	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₂₉	—	2	1	no	—
155	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
156	C₂₉×#137	—	4	2	no	—
157	C₂×Q₁₆×C₂₉	—	2	4	no	—
158	C₂×Q₁₆×C₂₉	—	4	2	no	—
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×Q₁₆×C₂₉	C₂³	1	2	yes	—
163	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
165	C₂₉×#131	—	4	2	no	—
166	C₂×M₁₆×C₂₉	—	4	2	no	—
167	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
168	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
169	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
170	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
171	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
172	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
173	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
174	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
175	C₂₉×C₄⋊Q₈	—	2	1	no	—
176	C₂₉×C₄⋊Q₈	—	2	1	no	—
177	C₂₉×C₄⋊Q₈	—	2	1	no	—
178	C₂₉×C₄⋊Q₈	—	2	2	no	—
179	C₂₉×C₄⋊Q₈	—	2	2	no	—
180	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
181	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
182	C₂₉×#126	—	2	2	no	—
183	C₂₉×#126	—	2	2	no	—
184	C₂₉×#126	—	2	2	no	—
185	C₂₉×#126	—	2	2	no	—
186	C₂₉×#125	—	2	1	no	—
187	C₂₉×#125	—	2	2	no	—
188	C₂₉×#125	—	2	2	no	—
189	C₂₉×#125	—	2	2	no	—
190	C₂₉×#125	C₂³	1	2	yes	—
191	C₂₉×#124	—	2	1	no	—
192	C₂₉×#124	—	2	1	no	—
193	C₂₉×#124	—	2	2	no	—
194	C₂₉×#124	—	2	2	no	—
195	C₂₉×#124	—	2	2	no	—
196	C₂₉×#124	C₂³	1	2	yes	—
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	1	no	—
202	C₂₉×#123	—	2	2	no	—
203	C₂₉×#123	D₄	1	2	yes	—
204	C₂₉×C₂²⋊Q₈	—	2	1	no	—
205	C₂₉×C₂²⋊Q₈	—	2	1	no	—
206	C₂₉×C₂²⋊Q₈	—	2	2	no	—
207	C₂₉×C₂²⋊Q₈	—	2	2	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	2	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	D₄	1	1	yes	characteristic
218	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
219	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₂₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
225	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
226	C₂₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
227	C₂₉×#121	—	2	2	no	—
228	C₂₉×#121	—	2	2	no	—
229	C₂₉×#121	D₄	1	1	yes	characteristic
230	C₂₉×#121	D₄	1	1	yes	characteristic
231	C₂₉×#121	C₂³	1	1	yes	characteristic
232	C₂₉×#121	C₂³	1	1	yes	characteristic
233	C₂₉×#120	—	2	1	no	—
234	C₂₉×#120	D₄	1	2	yes	—
235	C₄×Q₈×C₂₉	—	2	1	no	—
236	C₄×Q₈×C₂₉	—	2	1	no	—
237	C₄×Q₈×C₂₉	—	2	1	no	—
238	C₄×Q₈×C₂₉	—	2	1	no	—
239	C₄×Q₈×C₂₉	—	2	1	no	—
240	C₄×Q₈×C₂₉	—	2	2	no	—
241	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
242	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
243	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
244	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
245	C₄×D₄×C₂₉	—	2	1	no	—
246	C₄×D₄×C₂₉	—	2	2	no	—
247	C₄×D₄×C₂₉	—	2	2	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	C₂³	1	2	yes	—
255	C₄×D₄×C₂₉	C₂³	1	2	yes	—
256	C₂₉×#117	—	2	1	no	—
257	C₂₉×#117	—	2	1	no	—
258	C₂₉×#117	—	2	2	no	—
259	C₂₉×#117	—	2	2	no	—
260	C₂₉×#117	—	2	2	no	—
261	C₂₉×#117	—	2	2	no	—
262	C₂₉×#117	C₂³	1	1	yes	characteristic
263	C₂₉×#117	C₂³	1	1	yes	characteristic
264	C₂₉×#117	C₂³	1	1	yes	characteristic
265	C₂₉×#117	C₂³	1	1	yes	characteristic
266	C₂₉×#117	C₂³	1	1	yes	characteristic
267	C₂₉×#117	C₂³	1	2	yes	—
268	C₂₉×#117	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
270	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
274	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
275	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
276	C₂×C₄²×C₂₉	—	2	1	no	—
277	C₂₉×#107	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	1	yes	characteristic
281	C₂₉×#107	C₂³	1	2	yes	—
282	C₂₉×#106	C₂³	1	1	yes	characteristic
283	C₂₉×#106	C₂³	1	1	yes	characteristic
284	C₂₉×#106	C₂³	1	1	yes	characteristic
285	C₂₉×#106	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
298	C₂₉×#103	C₂³	1	1	yes	characteristic
299	C₂₉×#103	C₂³	1	2	yes	—
300	C₂₉×#103	C₂³	1	2	yes	—
301	C₂₉×#103	C₂³	1	1	yes	characteristic
302	C₂₉×#103	C₂³	1	1	yes	characteristic
303	C₂₉×#103	C₂³	1	2	yes	—
304	C₂₉×#103	C₂³	1	2	yes	—
305	C₂₉×#103	C₂³	1	2	yes	—
306	C₂₉×#103	C₂³	1	2	yes	—
307	C₂₉×#103	C₂³	1	2	yes	—
308	C₂₉×#102	C₂³	1	1	yes	characteristic
309	C₂₉×#102	C₂³	1	1	yes	characteristic
310	C₂₉×#102	C₂³	1	1	yes	characteristic
311	C₂₉×#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
317	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
322	#41×C₂₉	—	2	2	no	—
323	#41×C₂₉	—	2	2	no	—
324	#41×C₂₉	—	2	4	no	—
325	#41×C₂₉	—	2	2	no	—
326	#41×C₂₉	—	2	2	no	—
327	#41×C₂₉	—	4	2	no	—
328	#41×C₂₉	—	4	8	no	—
329	#41×C₂₉	—	4	4	no	—
330	C₂×Q₈×C₂₉	—	2	1	no	—
331	C₂×Q₈×C₂₉	—	2	1	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	2	no	—
337	C₂×Q₈×C₂₉	—	2	2	no	—
338	C₂×Q₈×C₂₉	—	2	4	no	—
339	C₂×Q₈×C₂₉	—	2	4	no	—
340	C₂×Q₈×C₂₉	—	2	4	no	—
341	C₂×Q₈×C₂₉	—	2	2	no	—
342	C₂×Q₈×C₂₉	—	2	2	no	—
343	C₂×Q₈×C₂₉	—	2	2	no	—
344	C₂×Q₈×C₂₉	—	2	2	no	—
345	C₂×Q₈×C₂₉	—	4	4	no	—
346	C₂×Q₈×C₂₉	—	4	2	no	—
347	C₂×Q₈×C₂₉	—	4	2	no	—
348	C₂×Q₈×C₂₉	—	4	2	no	—
349	C₂×Q₈×C₂₉	—	4	4	no	—
350	C₂×Q₈×C₂₉	—	4	4	no	—
351	C₂×Q₈×C₂₉	—	4	4	no	—
352	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
353	C₂×Q₈×C₂₉	#41	1	4	yes	—
354	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
355	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
356	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
357	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
358	C₂×D₄×C₂₉	—	2	1	no	—
359	C₂×D₄×C₂₉	—	2	1	no	—
360	C₂×D₄×C₂₉	—	2	1	no	—
361	C₂×D₄×C₂₉	—	2	2	no	—
362	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
363	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
364	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
365	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
366	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₂₉	—	2	1	no	—
368	C₂²×C₄×C₂₉	—	2	2	no	—
369	C₂²×C₄×C₂₉	—	2	2	no	—
370	C₂²×C₄×C₂₉	—	2	1	no	—
371	C₂²×C₄×C₂₉	—	2	1	no	—
372	C₂²×C₄×C₂₉	—	2	2	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	1	no	—
377	C₂²×C₄×C₂₉	—	2	1	no	—
378	C₂²×C₄×C₂₉	—	2	2	no	—
379	C₂²×C₄×C₂₉	—	2	2	no	—
380	C₂²×C₄×C₂₉	—	2	1	no	—
381	C₂²×C₄×C₂₉	—	4	4	no	—
382	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
387	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
389	Q₁₆×C₂₉	—	2	4	no	—
390	Q₁₆×C₂₉	—	2	4	no	—
391	Q₁₆×C₂₉	—	4	2	no	—
392	Q₁₆×C₂₉	—	4	2	no	—
393	Q₁₆×C₂₉	—	4	2	no	—
394	SD₁₆×C₂₉	—	4	2	no	—
395	M₁₆×C₂₉	—	2	2	no	—
396	M₁₆×C₂₉	—	2	2	no	—
397	M₁₆×C₂₉	—	4	2	no	—
398	M₁₆×C₂₉	—	4	2	no	—
399	C₂×C₈×C₂₉	—	2	2	no	—
400	C₂×C₈×C₂₉	—	2	2	no	—
401	C₂×C₈×C₂₉	—	4	2	no	—
402	C₂×C₈×C₂₉	—	4	2	no	—
403	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
404	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
405	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
406	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
407	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
413	C₄⋊C₄×C₂₉	—	2	1	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	2	no	—
420	C₄⋊C₄×C₂₉	—	2	2	no	—
421	C₄⋊C₄×C₂₉	—	2	2	no	—
422	C₄⋊C₄×C₂₉	—	2	2	no	—
423	C₄⋊C₄×C₂₉	—	2	2	no	—
424	C₄⋊C₄×C₂₉	—	2	2	no	—
425	C₄⋊C₄×C₂₉	—	2	2	no	—
426	C₄⋊C₄×C₂₉	—	2	1	no	—
427	C₄⋊C₄×C₂₉	—	2	1	no	—
428	C₄⋊C₄×C₂₉	—	2	2	no	—
429	C₄⋊C₄×C₂₉	—	2	2	no	—
430	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
431	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
432	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
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	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
440	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
441	C₂²⋊C₄×C₂₉	—	2	1	no	—
442	C₂²⋊C₄×C₂₉	—	2	1	no	—
443	C₂²⋊C₄×C₂₉	—	2	1	no	—
444	C₂²⋊C₄×C₂₉	—	2	1	no	—
445	C₂²⋊C₄×C₂₉	—	2	2	no	—
446	C₂²⋊C₄×C₂₉	—	2	2	no	—
447	C₂²⋊C₄×C₂₉	—	2	1	no	—
448	C₂²⋊C₄×C₂₉	—	2	2	no	—
449	C₂²⋊C₄×C₂₉	—	2	2	no	—
450	C₂²⋊C₄×C₂₉	—	2	1	no	—
451	C₂²⋊C₄×C₂₉	—	2	1	no	—
452	C₂²⋊C₄×C₂₉	—	2	2	no	—
453	C₂²⋊C₄×C₂₉	—	2	2	no	—
454	C₂²⋊C₄×C₂₉	—	2	2	no	—
455	C₂²⋊C₄×C₂₉	—	2	2	no	—
456	C₂²⋊C₄×C₂₉	—	2	2	no	—
457	C₂²⋊C₄×C₂₉	—	2	1	no	—
458	C₂²⋊C₄×C₂₉	—	2	1	no	—
459	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
460	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
461	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
463	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
464	C₄²×C₂₉	—	2	1	no	—
465	C₄²×C₂₉	—	2	1	no	—
466	C₄²×C₂₉	—	2	1	no	—
467	C₄²×C₂₉	—	2	1	no	—
468	C₄²×C₂₉	—	2	2	no	—
469	C₄²×C₂₉	—	2	2	no	—
470	C₄²×C₂₉	—	2	2	no	—
471	C₄²×C₂₉	—	2	2	no	—
472	C₄²×C₂₉	—	2	2	no	—
473	C₄²×C₂₉	—	2	1	no	—
474	C₄²×C₂₉	C₂⁴	1	2	yes	—
475	#61186	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
476	C₂³×C₂₉	—	2	2	no	—
477	C₂³×C₂₉	—	2	2	no	—
478	C₂³×C₂₉	—	2	1	no	—
479	C₂³×C₂₉	—	4	1	no	—
480	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
481	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
482	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
483	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
484	Q₈×C₂₉	—	2	4	no	—
485	Q₈×C₂₉	—	2	2	no	—
486	Q₈×C₂₉	—	2	2	no	—
487	Q₈×C₂₉	—	2	2	no	—
488	Q₈×C₂₉	—	2	2	no	—
489	Q₈×C₂₉	—	2	1	no	—
490	Q₈×C₂₉	—	2	2	no	—
491	Q₈×C₂₉	—	2	2	no	—
492	Q₈×C₂₉	—	2	1	no	—
493	Q₈×C₂₉	—	4	4	no	—
494	Q₈×C₂₉	—	4	4	no	—
495	Q₈×C₂₉	—	4	4	no	—
496	Q₈×C₂₉	—	4	2	no	—
497	Q₈×C₂₉	—	4	2	no	—
498	Q₈×C₂₉	—	8	2	no	—
499	Q₈×C₂₉	C₂×#41	1	4	yes	—
500	D₄×C₂₉	—	2	4	no	—
501	D₄×C₂₉	—	2	4	no	—
502	D₄×C₂₉	—	2	2	no	—
503	D₄×C₂₉	—	2	1	no	—
504	D₄×C₂₉	—	2	1	no	—
505	D₄×C₂₉	—	4	2	no	—
506	D₄×C₂₉	—	4	4	no	—
507	D₄×C₂₉	—	4	2	no	—
508	D₄×C₂₉	—	4	2	no	—
509	D₄×C₂₉	—	4	2	no	—
510	C₂×C₄×C₂₉	—	2	2	no	—
511	C₂×C₄×C₂₉	—	2	4	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	1	no	—
516	C₂×C₄×C₂₉	—	2	1	no	—
517	C₂×C₄×C₂₉	—	2	2	no	—
518	C₂×C₄×C₂₉	—	2	1	no	—
519	C₂×C₄×C₂₉	—	2	2	no	—
520	C₂×C₄×C₂₉	—	2	1	no	—
521	C₂×C₄×C₂₉	—	2	1	no	—
522	C₂×C₄×C₂₉	—	2	1	no	—
523	C₂×C₄×C₂₉	—	2	1	no	—
524	C₂×C₄×C₂₉	—	2	1	no	—
525	C₂×C₄×C₂₉	—	2	1	no	—
526	C₂×C₄×C₂₉	—	2	2	no	—
527	C₂×C₄×C₂₉	—	2	1	no	—
528	C₂×C₄×C₂₉	—	2	2	no	—
529	C₂×C₄×C₂₉	—	2	2	no	—
530	C₂×C₄×C₂₉	—	2	1	no	—
531	C₂×C₄×C₂₉	—	4	4	no	—
532	C₂×C₄×C₂₉	—	4	4	no	—
533	C₂×C₄×C₂₉	—	4	4	no	—
534	C₂×C₄×C₂₉	—	4	4	no	—
535	C₂×C₄×C₂₉	—	4	2	no	—
536	C₂×C₄×C₂₉	—	4	2	no	—
537	C₂×C₄×C₂₉	—	4	2	no	—
538	C₂×C₄×C₂₉	—	4	2	no	—
539	C₂×C₄×C₂₉	—	8	2	no	—
540	C₂×C₄×C₂₉	—	8	1	no	—
541	C₂×C₄×C₂₉	—	8	1	no	—
542	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
543	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
544	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
546	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
549	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
550	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
551	C₈×C₂₉	—	2	1	no	—
552	C₈×C₂₉	—	2	1	no	—
553	C₈×C₂₉	—	2	1	no	—
554	C₈×C₂₉	—	2	1	no	—
555	C₈×C₂₉	—	2	2	no	—
556	C₈×C₂₉	—	2	2	no	—
557	#3495	C₂×C₂₉	1	1	yes	characteristic, complemented
558	#3486	C₂×C₂₉	1	1	yes	characteristic
559	#3328	C₂×C₂₉	1	2	yes	complemented
560	#3327	C₂×C₂₉	1	2	yes	complemented
561	#3316	C₂×C₂₉	1	2	yes	complemented
562	#3313	C₂×C₂₉	1	2	yes	complemented
563	#3312	C₂×C₂₉	1	2	yes	complemented
564	#3312	C₂×C₂₉	1	2	yes	complemented
565	#3300	C₂×C₂₉	1	2	yes	complemented
566	#3299	C₂×C₂₉	1	2	yes	complemented
567	#3137	C₂×C₂₉	1	1	yes	characteristic, complemented
568	#3097	C₂×C₂₉	1	1	yes	characteristic, complemented
569	#3091	C₂×C₂₉	1	1	yes	characteristic, complemented
570	#3082	C₂×C₂₉	1	1	yes	characteristic, complemented
571	#3059	C₂×C₂₉	1	1	yes	characteristic, complemented
572	#3056	C₂×C₂₉	1	1	yes	characteristic, complemented
573	#3044	C₂×C₂₉	1	1	yes	characteristic, complemented
574	#3011	C₂×C₂₉	1	1	yes	characteristic, complemented
575	C₂×#451	C₂×C₂₉	1	1	yes	characteristic, complemented
576	#2950	C₂×C₂₉	1	1	yes	characteristic, complemented
577	#2933	C₂×C₂₉	1	1	yes	characteristic, complemented
578	#2898	C₂×C₂₉	1	1	yes	characteristic, complemented
579	C₂×#419	C₂×C₂₉	1	1	yes	characteristic, complemented
580	C₂²×C₂₉	—	2	1	no	—
581	C₂²×C₂₉	—	2	1	no	—
582	C₂²×C₂₉	—	2	1	no	—
583	C₂²×C₂₉	—	2	1	no	—
584	C₂²×C₂₉	—	2	2	no	—
585	C₂²×C₂₉	—	2	1	no	—
586	C₂²×C₂₉	—	2	1	no	—
587	C₂²×C₂₉	—	2	2	no	—
588	C₂²×C₂₉	—	2	2	no	—
589	C₂²×C₂₉	—	2	1	no	—
590	C₂²×C₂₉	—	4	4	no	—
591	C₂²×C₂₉	—	4	1	no	—
592	C₂²×C₂₉	—	4	1	no	—
593	C₂²×C₂₉	—	4	1	no	—
594	C₂²×C₂₉	#546	1	2	yes	—
595	C₂²×C₂₉	#578	1	2	yes	—
596	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
597	C₄×C₂₉	—	2	2	no	—
598	C₄×C₂₉	—	2	1	no	—
599	C₄×C₂₉	—	2	1	no	—
600	C₄×C₂₉	—	2	4	no	—
601	C₄×C₂₉	—	2	2	no	—
602	C₄×C₂₉	—	2	2	no	—
603	C₄×C₂₉	—	4	1	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	—	4	2	no	—
609	C₄×C₂₉	—	4	2	no	—
610	C₄×C₂₉	—	4	1	no	—
611	C₄×C₂₉	—	4	1	no	—
612	C₄×C₂₉	—	4	1	no	—
613	C₄×C₂₉	#546	1	2	yes	—
614	C₄×C₂₉	C₂²×#41	1	1	yes	characteristic
615	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
616	C₂×2₋¹⁺⁴	C₂²×C₂₉	1	1	yes	characteristic
617	C₂³×Q₈	C₂²×C₂₉	1	1	yes	characteristic
618	C₂×#137	C₂²×C₂₉	1	1	yes	characteristic
619	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
620	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
621	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
622	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
623	#556	C₂²×C₂₉	1	2	yes	—
624	#554	C₂²×C₂₉	1	2	yes	—
625	#552	—	2	2	no	—
626	#552	C₂²×C₂₉	1	2	yes	—
627	#552	C₂²×C₂₉	1	2	yes	—
628	#551	—	2	2	no	—
629	D₄×Q₈	—	2	1	no	—
630	D₄×Q₈	—	2	1	no	—
631	D₄×Q₈	C₂²×C₂₉	1	2	yes	—
632	D₄×Q₈	C₂²×C₂₉	1	2	yes	—
633	#548	—	2	1	no	—
634	#548	—	2	1	no	—
635	#548	C₂²×C₂₉	1	2	yes	—
636	#548	C₂²×C₂₉	1	2	yes	—
637	#544	C₂²×C₂₉	1	1	yes	characteristic
638	#542	—	2	1	no	—
639	#541	—	2	1	no	—
640	#536	—	2	2	no	—
641	#536	C₂²×C₂₉	1	1	yes	characteristic
642	#536	C₂²×C₂₉	1	1	yes	characteristic
643	#536	C₂²×C₂₉	1	1	yes	characteristic
644	#533	—	2	1	no	—
645	#529	—	2	1	no	—
646	#525	—	2	2	no	—
647	#525	C₂²×C₂₉	1	1	yes	characteristic
648	#525	C₂²×C₂₉	1	1	yes	characteristic
649	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
650	#520	C₂²×C₂₉	1	1	yes	characteristic
651	#519	C₂²×C₂₉	1	1	yes	characteristic
652	#519	C₂²×C₂₉	1	1	yes	characteristic
653	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
654	#491	C₂²×C₂₉	1	2	yes	complemented
655	#489	C₂²×C₂₉	1	2	yes	complemented
656	#488	C₂²×C₂₉	1	2	yes	complemented
657	#487	C₂²×C₂₉	1	2	yes	complemented
658	#485	C₂²×C₂₉	1	1	yes	characteristic
659	#485	C₂²×C₂₉	1	1	yes	characteristic
660	#485	C₂²×C₂₉	1	2	yes	complemented
661	#485	C₂²×C₂₉	1	2	yes	complemented
662	#484	C₂²×C₂₉	1	1	yes	characteristic
663	#484	C₂²×C₂₉	1	2	yes	complemented
664	#483	C₂²×C₂₉	1	1	yes	characteristic
665	#483	C₂²×C₂₉	1	2	yes	complemented
666	#482	C₂²×C₂₉	1	1	yes	characteristic
667	#482	C₂²×C₂₉	1	1	yes	characteristic
668	#481	C₂²×C₂₉	1	1	yes	characteristic
669	#480	C₂²×C₂₉	1	1	yes	characteristic
670	#479	C₂²×C₂₉	1	2	yes	complemented
671	#479	C₂²×C₂₉	1	2	yes	complemented
672	#477	C₂²×C₂₉	1	2	yes	complemented
673	#475	C₂²×C₂₉	1	2	yes	complemented
674	#470	C₂²×C₂₉	1	2	yes	—
675	#470	C₂²×C₂₉	1	2	yes	complemented
676	#470	C₂²×C₂₉	1	2	yes	complemented
677	#468	C₂²×C₂₉	1	2	yes	—
678	#467	C₂²×C₂₉	1	2	yes	—
679	#467	C₂²×C₂₉	1	2	yes	complemented
680	#467	C₂²×C₂₉	1	2	yes	complemented
681	#465	C₂²×C₂₉	1	2	yes	—
682	#464	C₂²×C₂₉	1	2	yes	complemented
683	#464	C₂²×C₂₉	1	2	yes	complemented
684	#462	C₂²×C₂₉	1	2	yes	complemented
685	#462	C₂²×C₂₉	1	2	yes	complemented
686	#452	C₂²×C₂₉	1	2	yes	complemented
687	#452	C₂²×C₂₉	1	2	yes	complemented
688	#451	C₂²×C₂₉	1	2	yes	—
689	#451	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	complemented
693	#451	C₂²×C₂₉	1	2	yes	complemented
694	#441	C₂²×C₂₉	1	2	yes	complemented
695	#441	C₂²×C₂₉	1	2	yes	complemented
696	C₄×Q₁₆	C₂²×C₂₉	1	2	yes	complemented
697	C₄×Q₁₆	C₂²×C₂₉	1	2	yes	complemented
698	#436	C₂²×C₂₉	1	2	yes	—
699	#435	C₂²×C₂₉	1	2	yes	—
700	#435	C₂²×C₂₉	1	2	yes	—
701	C₈×D₄	C₂²×C₂₉	1	2	yes	—
702	#428	C₂²×C₂₉	1	1	yes	characteristic
703	#427	C₂²×C₂₉	1	1	yes	characteristic
704	#427	C₂²×C₂₉	1	1	yes	characteristic
705	#424	C₂²×C₂₉	1	1	yes	characteristic
706	#419	C₂²×C₂₉	1	2	yes	—
707	#419	C₂²×C₂₉	1	1	yes	characteristic
708	#419	C₂²×C₂₉	1	1	yes	characteristic
709	#419	C₂²×C₂₉	1	1	yes	characteristic
710	#419	C₂²×C₂₉	1	1	yes	characteristic
711	#419	C₂²×C₂₉	1	2	yes	—
712	#419	C₂²×C₂₉	1	1	yes	characteristic
713	#419	C₂²×C₂₉	1	2	yes	complemented
714	#417	C₂²×C₂₉	1	1	yes	characteristic
715	#417	C₂²×C₂₉	1	2	yes	complemented
716	#416	C₂²×C₂₉	1	1	yes	characteristic
717	#416	C₂²×C₂₉	1	1	yes	characteristic
718	#416	C₂²×C₂₉	1	2	yes	complemented
719	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
720	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
721	C₂×#103	C₂²×C₂₉	1	2	yes	—
722	C₂×#103	C₂²×C₂₉	1	2	yes	—
723	C₂×#103	C₂²×C₂₉	1	2	yes	complemented
724	#408	C₂²×C₂₉	1	1	yes	characteristic
725	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
726	#405	C₂²×C₂₉	1	1	yes	characteristic
727	C₂×C₂₉	—	2	2	no	—
728	C₂×C₂₉	—	2	2	no	—
729	C₂×C₂₉	—	4	2	no	—
730	C₂×C₂₉	—	4	1	no	—
731	C₂×C₂₉	—	8	1	no	—
732	C₂×C₂₉	C₂×#546	1	1	yes	characteristic
733	C₂×C₂₉	C₂×#578	1	1	yes	characteristic
734	C₂×C₂₉	#3586	1	1	yes	characteristic
735	2₋¹⁺⁴	—	2	4	no	—
736	2₋¹⁺⁴	—	4	2	no	—
737	C₂×#41	—	2	2	no	—
738	C₂×#41	—	2	1	no	—
739	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
740	C₂×#41	C₂³×C₂₉	1	2	yes	—
741	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
742	C₂²×Q₈	—	2	1	no	—
743	C₂²×Q₈	—	2	1	no	—
744	C₂²×Q₈	—	2	1	no	—
745	C₂²×Q₈	—	2	1	no	—
746	C₂²×Q₈	—	2	4	no	—
747	C₂²×Q₈	—	4	2	no	—
748	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
749	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
750	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
751	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
752	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
753	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
754	C₂³×C₄	—	2	1	no	—
755	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
756	#137	—	4	2	no	—
757	C₂×Q₁₆	—	2	4	no	—
758	C₂×Q₁₆	—	4	2	no	—
759	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
760	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
761	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
762	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
763	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
764	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
765	#131	—	4	2	no	—
766	C₂×M₁₆	—	4	2	no	—
767	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
768	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
769	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
770	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
771	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
772	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
773	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
774	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
775	C₄⋊Q₈	—	2	1	no	—
776	C₄⋊Q₈	—	2	1	no	—
777	C₄⋊Q₈	—	2	1	no	—
778	C₄⋊Q₈	—	2	2	no	—
779	C₄⋊Q₈	—	2	2	no	—
780	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
781	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
782	#126	—	2	2	no	—
783	#126	—	2	2	no	—
784	#126	—	2	2	no	—
785	#126	—	2	2	no	—
786	#125	—	2	1	no	—
787	#125	—	2	2	no	—
788	#125	—	2	2	no	—
789	#125	—	2	2	no	—
790	#125	C₂³×C₂₉	1	2	yes	—
791	#124	—	2	1	no	—
792	#124	—	2	1	no	—
793	#124	—	2	2	no	—
794	#124	—	2	2	no	—
795	#124	—	2	2	no	—
796	#124	C₂³×C₂₉	1	2	yes	—
797	#123	—	2	2	no	—
798	#123	—	2	2	no	—
799	#123	—	2	2	no	—
800	#123	—	2	2	no	—
801	#123	—	2	1	no	—
802	#123	—	2	2	no	—
803	#123	D₄×C₂₉	1	2	yes	—
804	C₂²⋊Q₈	—	2	1	no	—
805	C₂²⋊Q₈	—	2	1	no	—
806	C₂²⋊Q₈	—	2	2	no	—
807	C₂²⋊Q₈	—	2	2	no	—
808	C₂²⋊Q₈	—	2	1	no	—
809	C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
815	C₂²⋊Q₈	—	2	2	no	—
816	C₂²⋊Q₈	—	2	2	no	—
817	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
818	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
819	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
820	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
821	C₂²⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
822	C₂²⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
823	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
824	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
825	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
826	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
827	#121	—	2	2	no	—
828	#121	—	2	2	no	—
829	#121	D₄×C₂₉	1	1	yes	characteristic
830	#121	D₄×C₂₉	1	1	yes	characteristic
831	#121	C₂³×C₂₉	1	1	yes	characteristic
832	#121	C₂³×C₂₉	1	1	yes	characteristic
833	#120	—	2	1	no	—
834	#120	D₄×C₂₉	1	2	yes	—
835	C₄×Q₈	—	2	1	no	—
836	C₄×Q₈	—	2	1	no	—
837	C₄×Q₈	—	2	1	no	—
838	C₄×Q₈	—	2	1	no	—
839	C₄×Q₈	—	2	1	no	—
840	C₄×Q₈	—	2	2	no	—
841	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
842	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
843	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
844	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
845	C₄×D₄	—	2	1	no	—
846	C₄×D₄	—	2	2	no	—
847	C₄×D₄	—	2	2	no	—
848	C₄×D₄	—	2	2	no	—
849	C₄×D₄	—	2	2	no	—
850	C₄×D₄	—	2	1	no	—
851	C₄×D₄	—	2	1	no	—
852	C₄×D₄	—	2	2	no	—
853	C₄×D₄	—	2	2	no	—
854	C₄×D₄	C₂³×C₂₉	1	2	yes	—
855	C₄×D₄	C₂³×C₂₉	1	2	yes	—
856	#117	—	2	1	no	—
857	#117	—	2	1	no	—
858	#117	—	2	2	no	—
859	#117	—	2	2	no	—
860	#117	—	2	2	no	—
861	#117	—	2	2	no	—
862	#117	C₂³×C₂₉	1	1	yes	characteristic
863	#117	C₂³×C₂₉	1	1	yes	characteristic
864	#117	C₂³×C₂₉	1	1	yes	characteristic
865	#117	C₂³×C₂₉	1	1	yes	characteristic
866	#117	C₂³×C₂₉	1	1	yes	characteristic
867	#117	C₂³×C₂₉	1	2	yes	—
868	#117	C₂³×C₂₉	1	1	yes	characteristic
869	C₂×C₄⋊C₄	—	2	1	no	—
870	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
871	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
872	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
873	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
874	C₂×C₂²⋊C₄	—	2	1	no	—
875	C₂×C₂²⋊C₄	—	2	1	no	—
876	C₂×C₄²	—	2	1	no	—
877	#107	C₂³×C₂₉	1	1	yes	characteristic
878	#107	C₂³×C₂₉	1	1	yes	characteristic
879	#107	C₂³×C₂₉	1	1	yes	characteristic
880	#107	C₂³×C₂₉	1	1	yes	characteristic
881	#107	C₂³×C₂₉	1	2	yes	—
882	#106	C₂³×C₂₉	1	1	yes	characteristic
883	#106	C₂³×C₂₉	1	1	yes	characteristic
884	#106	C₂³×C₂₉	1	1	yes	characteristic
885	#106	C₂³×C₂₉	1	1	yes	characteristic
886	#106	C₂³×C₂₉	1	2	yes	—
887	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
888	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
889	#103	C₂³×C₂₉	1	2	yes	—
890	#103	C₂³×C₂₉	1	2	yes	—
891	#103	C₂³×C₂₉	1	2	yes	—
892	#103	C₂³×C₂₉	1	2	yes	—
893	#103	C₂³×C₂₉	1	2	yes	—
894	#103	C₂³×C₂₉	1	2	yes	—
895	#103	C₂³×C₂₉	1	2	yes	—
896	#103	C₂³×C₂₉	1	2	yes	—
897	#103	C₂³×C₂₉	1	2	yes	—
898	#103	C₂³×C₂₉	1	2	yes	—
899	#103	C₂³×C₂₉	1	2	yes	—
900	#103	C₂³×C₂₉	1	2	yes	—
901	#103	C₂³×C₂₉	1	1	yes	characteristic
902	#103	C₂³×C₂₉	1	2	yes	—
903	#103	C₂³×C₂₉	1	1	yes	characteristic
904	#103	C₂³×C₂₉	1	1	yes	characteristic
905	#103	C₂³×C₂₉	1	1	yes	characteristic
906	#103	C₂³×C₂₉	1	2	yes	—
907	#103	C₂³×C₂₉	1	2	yes	—
908	#102	C₂³×C₂₉	1	1	yes	characteristic
909	#102	C₂³×C₂₉	1	1	yes	characteristic
910	#102	C₂³×C₂₉	1	1	yes	characteristic
911	#102	C₂³×C₂₉	1	1	yes	characteristic
912	#102	C₂³×C₂₉	1	2	yes	—
913	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
914	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
915	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
916	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
917	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
918	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
919	#97	C₂³×C₂₉	1	2	yes	—
920	C₄×C₈	C₂³×C₂₉	1	2	yes	—
921	C₂₉	#61186	1	1	yes	characteristic, direct product factor, Sylow
922	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
923	#41	—	2	2	no	—
924	#41	—	2	2	no	—
925	#41	—	2	4	no	—
926	#41	—	2	2	no	—
927	#41	—	2	2	no	—
928	#41	—	4	2	no	—
929	#41	—	4	8	no	—
930	#41	—	4	4	no	—
931	C₂×Q₈	—	2	1	no	—
932	C₂×Q₈	—	2	1	no	—
933	C₂×Q₈	—	2	2	no	—
934	C₂×Q₈	—	2	2	no	—
935	C₂×Q₈	—	2	1	no	—
936	C₂×Q₈	—	2	2	no	—
937	C₂×Q₈	—	2	2	no	—
938	C₂×Q₈	—	2	2	no	—
939	C₂×Q₈	—	2	4	no	—
940	C₂×Q₈	—	2	4	no	—
941	C₂×Q₈	—	2	4	no	—
942	C₂×Q₈	—	2	2	no	—
943	C₂×Q₈	—	2	2	no	—
944	C₂×Q₈	—	2	2	no	—
945	C₂×Q₈	—	2	2	no	—
946	C₂×Q₈	—	4	4	no	—
947	C₂×Q₈	—	4	2	no	—
948	C₂×Q₈	—	4	2	no	—
949	C₂×Q₈	—	4	2	no	—
950	C₂×Q₈	—	4	4	no	—
951	C₂×Q₈	—	4	4	no	—
952	C₂×Q₈	—	4	4	no	—
953	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
954	C₂×Q₈	#41×C₂₉	1	4	yes	—
955	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
956	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
957	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
958	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	—	2	1	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
964	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
965	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
966	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
967	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
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	1	no	—
973	C₂²×C₄	—	2	2	no	—
974	C₂²×C₄	—	2	2	no	—
975	C₂²×C₄	—	2	2	no	—
976	C₂²×C₄	—	2	1	no	—
977	C₂²×C₄	—	2	1	no	—
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	2	no	—
980	C₂²×C₄	—	2	2	no	—
981	C₂²×C₄	—	2	1	no	—
982	C₂²×C₄	—	4	4	no	—
983	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
984	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
985	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
986	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
987	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
988	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
989	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
990	Q₁₆	—	2	4	no	—
991	Q₁₆	—	2	4	no	—
992	Q₁₆	—	4	2	no	—
993	Q₁₆	—	4	2	no	—
994	Q₁₆	—	4	2	no	—
995	SD₁₆	—	4	2	no	—
996	M₁₆	—	2	2	no	—
997	M₁₆	—	2	2	no	—
998	M₁₆	—	4	2	no	—
999	M₁₆	—	4	2	no	—
1000	C₂×C₈	—	2	2	no	—
1001	C₂×C₈	—	2	2	no	—
1002	C₂×C₈	—	4	2	no	—
1003	C₂×C₈	—	4	2	no	—
1004	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1005	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
1006	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1007	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1008	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1009	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	—	2	2	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	1	no	—
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	—	2	2	no	—
1020	C₄⋊C₄	—	2	2	no	—
1021	C₄⋊C₄	—	2	2	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	2	no	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1032	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1033	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1034	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1035	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1036	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
1037	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1038	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1039	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1040	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1041	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1042	C₂²⋊C₄	—	2	1	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	1	no	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	1	no	—
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	1	no	—
1060	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1061	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1062	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1063	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1064	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1065	C₄²	—	2	1	no	—
1066	C₄²	—	2	1	no	—
1067	C₄²	—	2	1	no	—
1068	C₄²	—	2	1	no	—
1069	C₄²	—	2	2	no	—
1070	C₄²	—	2	2	no	—
1071	C₄²	—	2	2	no	—
1072	C₄²	—	2	2	no	—
1073	C₄²	—	2	2	no	—
1074	C₄²	—	2	1	no	—
1075	C₄²	C₂⁴×C₂₉	1	2	yes	—
1076	C₂³	—	2	2	no	—
1077	C₂³	—	2	2	no	—
1078	C₂³	—	2	1	no	—
1079	C₂³	—	4	1	no	—
1080	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1081	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
1082	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1083	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1084	Q₈	—	2	4	no	—
1085	Q₈	—	2	2	no	—
1086	Q₈	—	2	2	no	—
1087	Q₈	—	2	2	no	—
1088	Q₈	—	2	2	no	—
1089	Q₈	—	2	1	no	—
1090	Q₈	—	2	2	no	—
1091	Q₈	—	2	2	no	—
1092	Q₈	—	2	1	no	—
1093	Q₈	—	4	4	no	—
1094	Q₈	—	4	4	no	—
1095	Q₈	—	4	4	no	—
1096	Q₈	—	4	2	no	—
1097	Q₈	—	4	2	no	—
1098	Q₈	—	8	2	no	—
1099	Q₈	C₂×#41×C₂₉	1	4	yes	—
1100	D₄	—	2	4	no	—
1101	D₄	—	2	4	no	—
1102	D₄	—	2	2	no	—
1103	D₄	—	2	1	no	—
1104	D₄	—	2	1	no	—
1105	D₄	—	4	2	no	—
1106	D₄	—	4	4	no	—
1107	D₄	—	4	2	no	—
1108	D₄	—	4	2	no	—
1109	D₄	—	4	2	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	4	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	2	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	4	4	no	—
1132	C₂×C₄	—	4	4	no	—
1133	C₂×C₄	—	4	4	no	—
1134	C₂×C₄	—	4	4	no	—
1135	C₂×C₄	—	4	2	no	—
1136	C₂×C₄	—	4	2	no	—
1137	C₂×C₄	—	4	2	no	—
1138	C₂×C₄	—	4	2	no	—
1139	C₂×C₄	—	8	2	no	—
1140	C₂×C₄	—	8	1	no	—
1141	C₂×C₄	—	8	1	no	—
1142	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1143	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1144	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1145	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1146	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1147	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1148	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
1149	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
1150	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1151	C₈	—	2	1	no	—
1152	C₈	—	2	1	no	—
1153	C₈	—	2	1	no	—
1154	C₈	—	2	1	no	—
1155	C₈	—	2	2	no	—
1156	C₈	—	2	2	no	—
1157	C₂²	—	2	1	no	—
1158	C₂²	—	2	1	no	—
1159	C₂²	—	2	1	no	—
1160	C₂²	—	2	1	no	—
1161	C₂²	—	2	1	no	—
1162	C₂²	—	2	2	no	—
1163	C₂²	—	2	2	no	—
1164	C₂²	—	2	1	no	—
1165	C₂²	—	2	2	no	—
1166	C₂²	—	2	1	no	—
1167	C₂²	—	4	4	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	C₂₉×#546	1	2	yes	—
1172	C₂²	C₂₉×#578	1	2	yes	—
1173	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
1174	C₄	—	2	1	no	—
1175	C₄	—	2	1	no	—
1176	C₄	—	2	4	no	—
1177	C₄	—	2	2	no	—
1178	C₄	—	2	2	no	—
1179	C₄	—	2	2	no	—
1180	C₄	—	4	1	no	—
1181	C₄	—	4	2	no	—
1182	C₄	—	4	2	no	—
1183	C₄	—	4	1	no	—
1184	C₄	—	4	1	no	—
1185	C₄	—	4	1	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	2	no	—
1188	C₄	—	4	1	no	—
1189	C₄	—	4	1	no	—
1190	C₄	C₂₉×#546	1	2	yes	—
1191	C₄	C₂²×#41×C₂₉	1	1	yes	characteristic
1192	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
1193	C₂	—	2	2	no	—
1194	C₂	—	2	2	no	—
1195	C₂	—	4	1	no	—
1196	C₂	—	4	2	no	—
1197	C₂	—	8	1	no	—
1198	C₂	C₂×C₂₉×#546	1	1	yes	characteristic
1199	C₂	C₂×C₂₉×#578	1	1	yes	characteristic
1200	C₂	C₂₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
prime radical	C₂₉×#3486	C₂
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×#3495	C₂	semidirect
3. C₂₉×#3328	C₂	semidirect
4. C₂₉×#3327	C₂	semidirect
5. C₂₉×#3316	C₂	semidirect
6. C₂₉×#3313	C₂	semidirect
7. C₂₉×#3312	C₂	semidirect
8. C₂₉×#3312	C₂	semidirect
9. C₂₉×#3300	C₂	semidirect
10. C₂₉×#3299	C₂	semidirect
11. C₂₉×#3137	C₂	semidirect
12. C₂₉×#3097	C₂	semidirect
13. C₂₉×#3091	C₂	semidirect
14. C₂₉×#3082	C₂	semidirect
15. C₂₉×#3059	C₂	semidirect
16. C₂₉×#3056	C₂	semidirect
17. C₂₉×#3044	C₂	semidirect
18. C₂₉×#3011	C₂	semidirect
19. C₂×C₂₉×#451	C₂	semidirect
20. C₂₉×#2950	C₂	semidirect
21. C₂₉×#2933	C₂	semidirect
22. C₂₉×#2898	C₂	semidirect
23. C₂×C₂₉×#419	C₂	semidirect
62. C₂₉×#491	C₂²	semidirect
63. C₂₉×#489	C₂²	semidirect
64. C₂₉×#488	C₂²	semidirect
65. C₂₉×#487	C₂²	semidirect
68. C₂₉×#485	C₂²	semidirect
69. C₂₉×#485	C₂²	semidirect
71. C₂₉×#484	C₂²	semidirect
73. C₂₉×#483	C₂²	semidirect
78. C₂₉×#479	C₂²	semidirect
79. C₂₉×#479	C₂²	semidirect
80. C₂₉×#477	C₂²	semidirect
81. C₂₉×#475	C₂²	semidirect
83. C₂₉×#470	C₂²	semidirect
84. C₂₉×#470	C₂²	semidirect
87. C₂₉×#467	C₂²	semidirect
88. C₂₉×#467	C₂²	semidirect
90. C₂₉×#464	C₂²	semidirect
91. C₂₉×#464	C₂²	semidirect
92. C₂₉×#462	C₂²	semidirect
93. C₂₉×#462	C₂²	semidirect
94. C₂₉×#452	C₂²	semidirect
95. C₂₉×#452	C₂²	semidirect
100. C₂₉×#451	C₂²	semidirect
101. C₂₉×#451	C₂²	semidirect
102. C₂₉×#441	C₂²	semidirect
103. C₂₉×#441	C₂²	semidirect
104. C₄×Q₁₆×C₂₉	C₂²	semidirect
105. C₄×Q₁₆×C₂₉	C₂²	semidirect
121. C₂₉×#419	C₂²	semidirect
123. C₂₉×#417	C₂²	semidirect
126. C₂₉×#416	C₂²	semidirect
131. C₂×C₂₉×#103	C₂²	semidirect
475. #61186	C₂₉	direct (N × H)
557. #3495	C₂×C₂₉	semidirect
559. #3328	C₂×C₂₉	semidirect
560. #3327	C₂×C₂₉	semidirect
561. #3316	C₂×C₂₉	semidirect
562. #3313	C₂×C₂₉	semidirect
563. #3312	C₂×C₂₉	semidirect
564. #3312	C₂×C₂₉	semidirect
565. #3300	C₂×C₂₉	semidirect
566. #3299	C₂×C₂₉	semidirect
567. #3137	C₂×C₂₉	semidirect
568. #3097	C₂×C₂₉	semidirect
569. #3091	C₂×C₂₉	semidirect
570. #3082	C₂×C₂₉	semidirect
571. #3059	C₂×C₂₉	semidirect
572. #3056	C₂×C₂₉	semidirect
573. #3044	C₂×C₂₉	semidirect
574. #3011	C₂×C₂₉	semidirect
575. C₂×#451	C₂×C₂₉	semidirect
576. #2950	C₂×C₂₉	semidirect
577. #2933	C₂×C₂₉	semidirect
578. #2898	C₂×C₂₉	semidirect
579. C₂×#419	C₂×C₂₉	semidirect
654. #491	C₂²×C₂₉	semidirect
655. #489	C₂²×C₂₉	semidirect
656. #488	C₂²×C₂₉	semidirect
657. #487	C₂²×C₂₉	semidirect
660. #485	C₂²×C₂₉	semidirect
661. #485	C₂²×C₂₉	semidirect
663. #484	C₂²×C₂₉	semidirect
665. #483	C₂²×C₂₉	semidirect
670. #479	C₂²×C₂₉	semidirect
671. #479	C₂²×C₂₉	semidirect
672. #477	C₂²×C₂₉	semidirect
673. #475	C₂²×C₂₉	semidirect
675. #470	C₂²×C₂₉	semidirect
676. #470	C₂²×C₂₉	semidirect
679. #467	C₂²×C₂₉	semidirect
680. #467	C₂²×C₂₉	semidirect
682. #464	C₂²×C₂₉	semidirect
683. #464	C₂²×C₂₉	semidirect
684. #462	C₂²×C₂₉	semidirect
685. #462	C₂²×C₂₉	semidirect
686. #452	C₂²×C₂₉	semidirect
687. #452	C₂²×C₂₉	semidirect
692. #451	C₂²×C₂₉	semidirect
693. #451	C₂²×C₂₉	semidirect
694. #441	C₂²×C₂₉	semidirect
695. #441	C₂²×C₂₉	semidirect
696. C₄×Q₁₆	C₂²×C₂₉	semidirect
697. C₄×Q₁₆	C₂²×C₂₉	semidirect
713. #419	C₂²×C₂₉	semidirect
715. #417	C₂²×C₂₉	semidirect
718. #416	C₂²×C₂₉	semidirect
723. C₂×#103	C₂²×C₂₉	semidirect
921. C₂₉	#61186	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×#3495	2
C₂₉×#3486	2
C₂₉×#3328	2
C₂₉×#3327	2
C₂₉×#3316	2
C₂₉×#3313	2
C₂₉×#3312	2
C₂₉×#3300	2
C₂₉×#3299	2
C₂₉×#3137	2
C₂₉×#3097	2
C₂₉×#3091	2
C₂₉×#3082	2
C₂₉×#3059	2
C₂₉×#3056	2
C₂₉×#3044	2
C₂₉×#3011	2
C₂×C₂₉×#451	2
C₂₉×#2950	2
C₂₉×#2933	2
C₂₉×#2898	2
C₂×C₂₉×#419	2
#61186	29

Subgroups — C29×#61186 #20356086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#61186 #20356086