Subgroups — C₂₉×#62035 #20356935

Order 7424.

1894 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#3325	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#3324	C₂	1	2	yes	maximal, complemented
9	C₂₉×#3311	C₂	1	2	yes	maximal, complemented
10	C₂₉×#3305	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×SD₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#3278	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#3275	C₂	1	2	yes	maximal, complemented
14	C₂₉×#3265	C₂	1	2	yes	maximal, complemented
15	C₂₉×#3257	C₂	1	2	yes	maximal, complemented
16	C₂₉×#3252	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₉×#3224	C₂	1	2	yes	maximal, complemented
18	C₂₉×#3208	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₉×#3126	C₂	1	2	yes	maximal, complemented
20	C₂₉×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₉×#3043	C₂	1	2	yes	maximal, complemented
22	C₂₉×#3038	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₉×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₉×#137	C₂²	1	2	yes	complemented
25	C₂×C₂₉×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₂₉	C₂²	1	2	yes	complemented
27	C₂₉×#560	—	2	2	no	—
28	C₂₉×#559	C₂²	1	1	yes	characteristic
29	Q₈²×C₂₉	C₂²	1	1	yes	characteristic, complemented
30	C₂₉×#556	—	2	2	no	—
31	C₂₉×#556	—	2	1	no	—
32	C₂₉×#556	C₂²	1	1	yes	characteristic, complemented
33	C₂₉×#556	C₂²	1	2	yes	complemented
34	C₂₉×#555	—	2	1	no	—
35	C₂₉×#555	C₂²	1	1	yes	characteristic, complemented
36	C₂₉×#550	C₂²	1	1	yes	characteristic
37	C₂₉×#550	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
39	C₂₉×#548	C₂²	1	2	yes	complemented
40	C₂₉×#546	—	2	1	no	—
41	C₂₉×#546	C₂²	1	2	yes	—
42	D₄²×C₂₉	—	2	1	no	—
43	D₄²×C₂₉	C₂²	1	2	yes	—
44	D₄²×C₂₉	C₂²	1	1	yes	characteristic
45	C₂₉×#542	—	2	2	no	—
46	C₂₉×#542	C₂²	1	2	yes	complemented
47	C₂₉×#540	—	2	1	no	—
48	C₂₉×#540	C₂²	1	2	yes	—
49	C₂₉×#535	—	2	1	no	—
50	C₂₉×#535	C₂²	1	2	yes	—
51	C₂₉×#534	—	2	2	no	—
52	C₂₉×#533	—	2	1	no	—
53	C₂₉×#533	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
55	C₂₉×#529	—	2	1	no	—
56	C₂₉×#529	C₂²	1	1	yes	characteristic
57	C₂₉×#529	C₂²	1	1	yes	characteristic
58	C₂₉×#519	C₂²	1	2	yes	complemented
59	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic, complemented
60	C₂₉×#496	C₂²	1	2	yes	complemented
61	C₂₉×#495	C₂²	1	2	yes	complemented
62	C₂₉×#492	C₂²	1	1	yes	characteristic
63	C₂₉×#492	C₂²	1	1	yes	characteristic, complemented
64	C₂₉×#489	C₂²	1	2	yes	complemented
65	C₂₉×#486	C₂²	1	1	yes	characteristic
66	C₂₉×#486	C₂²	1	1	yes	characteristic, complemented
67	C₂₉×#486	C₂²	1	2	yes	complemented
68	C₂₉×#485	C₂²	1	1	yes	characteristic, complemented
69	C₂₉×#482	C₂²	1	1	yes	characteristic
70	C₂₉×#482	C₂²	1	2	yes	complemented
71	C₂₉×#482	C₂²	1	2	yes	complemented
72	C₂₉×#479	C₂²	1	2	yes	complemented
73	C₂₉×#479	C₂²	1	1	yes	characteristic, complemented
74	C₂₉×#478	C₂²	1	1	yes	characteristic, complemented
75	C₂₉×#477	C₂²	1	1	yes	characteristic, complemented
76	C₂₉×#476	C₂²	1	1	yes	characteristic, complemented
77	C₂₉×#476	C₂²	1	2	yes	complemented
78	C₂₉×#474	C₂²	1	2	yes	complemented
79	C₂₉×#470	C₂²	1	2	yes	complemented
80	C₂₉×#469	C₂²	1	2	yes	complemented
81	C₂₉×#468	C₂²	1	2	yes	—
82	C₂₉×#468	C₂²	1	2	yes	complemented
83	C₂₉×#466	C₂²	1	2	yes	complemented
84	C₂₉×#465	C₂²	1	2	yes	complemented
85	C₂₉×#464	C₂²	1	2	yes	complemented
86	C₂₉×#464	C₂²	1	2	yes	complemented
87	C₂₉×#464	C₂²	1	1	yes	characteristic, complemented
88	C₂₉×#464	C₂²	1	2	yes	complemented
89	C₂₉×#463	C₂²	1	1	yes	characteristic, complemented
90	C₂₉×#463	C₂²	1	2	yes	complemented
91	C₂₉×#463	C₂²	1	2	yes	complemented
92	C₂₉×#462	C₂²	1	1	yes	characteristic, complemented
93	C₂₉×#461	C₂²	1	1	yes	characteristic, complemented
94	C₂₉×#460	C₂²	1	1	yes	characteristic
95	C₂₉×#460	C₂²	1	2	yes	complemented
96	C₂₉×#460	C₂²	1	2	yes	complemented
97	C₂₉×#460	C₂²	1	2	yes	complemented
98	C₂₉×#460	C₂²	1	1	yes	characteristic, complemented
99	C₂₉×#460	C₂²	1	2	yes	complemented
100	C₂₉×#460	C₂²	1	2	yes	complemented
101	C₂₉×#459	C₂²	1	1	yes	characteristic
102	C₂₉×#459	C₂²	1	2	yes	complemented
103	C₂₉×#459	C₂²	1	1	yes	characteristic, complemented
104	C₂₉×#452	C₂²	1	2	yes	complemented
105	C₂₉×#452	C₂²	1	1	yes	characteristic, complemented
106	C₂₉×#450	C₂²	1	2	yes	complemented
107	C₂₉×#450	C₂²	1	2	yes	complemented
108	C₂₉×#450	C₂²	1	2	yes	complemented
109	C₂₉×#449	C₂²	1	1	yes	characteristic
110	C₂₉×#449	C₂²	1	2	yes	complemented
111	C₂₉×#448	C₂²	1	2	yes	complemented
112	C₂₉×#448	C₂²	1	2	yes	complemented
113	C₂₉×#447	C₂²	1	2	yes	complemented
114	C₂₉×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
116	C₂₉×#440	C₂²	1	2	yes	complemented
117	C₂₉×#440	C₂²	1	2	yes	complemented
118	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
122	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	complemented
123	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
124	C₂₉×#436	C₂²	1	2	yes	complemented
125	C₂₉×#436	C₂²	1	1	yes	characteristic, complemented
126	C₂₉×#435	C₂²	1	2	yes	complemented
127	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
128	C₂₉×#433	C₂²	1	2	yes	complemented
129	C₂₉×#431	C₂²	1	1	yes	characteristic, complemented
130	C₂₉×#424	C₂²	1	2	yes	complemented
131	C₂₉×#423	C₂²	1	1	yes	characteristic, complemented
132	C₂₉×#418	C₂²	1	2	yes	complemented
133	C₂₉×#418	C₂²	1	2	yes	complemented
134	C₂₉×#416	C₂²	1	2	yes	complemented
135	C₂×#41×C₂₉	—	2	1	no	—
136	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
137	C₂×#41×C₂₉	C₂³	1	2	yes	—
138	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
139	C₂²×D₄×C₂₉	—	2	2	no	—
140	C₂²×D₄×C₂₉	—	2	1	no	—
141	C₂²×D₄×C₂₉	—	2	1	no	—
142	C₂²×D₄×C₂₉	—	2	1	no	—
143	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
144	C₂²×D₄×C₂₉	C₂³	1	2	yes	—
145	C₂₉×#137	—	4	4	no	—
146	C₂₉×AGL(1,ℤ/8)	—	4	4	no	—
147	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
148	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₂₉	—	4	4	no	—
150	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
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×D₈×C₂₉	C₂³	1	1	yes	characteristic
160	C₂×D₈×C₂₉	C₂³	1	2	yes	—
161	C₂×D₈×C₂₉	C₂³	1	2	yes	—
162	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
163	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
164	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
165	C₂₉×C₄⋊Q₈	—	2	1	no	—
166	C₂₉×C₄⋊Q₈	—	2	1	no	—
167	C₂₉×C₄⋊Q₈	—	2	2	no	—
168	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
170	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₂₉×#127	—	2	1	no	—
172	C₂₉×#127	—	2	1	no	—
173	C₂₉×#127	—	2	1	no	—
174	C₂₉×#127	C₂³	1	1	yes	characteristic
175	C₂₉×#127	C₂³	1	2	yes	—
176	C₂₉×#127	C₂³	1	1	yes	characteristic
177	C₂₉×#127	C₂³	1	2	yes	—
178	C₂₉×#126	—	2	2	no	—
179	C₂₉×#126	—	2	2	no	—
180	C₂₉×#126	—	2	2	no	—
181	C₂₉×#126	—	2	2	no	—
182	C₂₉×#126	—	2	1	no	—
183	C₂₉×#126	D₄	1	2	yes	—
184	C₂₉×#125	—	2	1	no	—
185	C₂₉×#125	D₄	1	1	yes	characteristic
186	C₂₉×#125	C₂³	1	1	yes	characteristic
187	C₂₉×#124	—	2	1	no	—
188	C₂₉×#124	—	2	2	no	—
189	C₂₉×#124	—	2	2	no	—
190	C₂₉×#124	—	2	2	no	—
191	C₂₉×#124	—	2	2	no	—
192	C₂₉×#124	D₄	1	1	yes	characteristic
193	C₂₉×#124	C₂³	1	2	yes	—
194	C₂₉×#124	C₂³	1	1	yes	characteristic
195	C₂₉×#124	C₂³	1	2	yes	—
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	D₄	1	2	yes	—
203	C₂₉×C₂²⋊Q₈	—	2	1	no	—
204	C₂₉×C₂²⋊Q₈	—	2	1	no	—
205	C₂₉×C₂²⋊Q₈	—	2	2	no	—
206	C₂₉×C₂²⋊Q₈	—	2	2	no	—
207	C₂₉×C₂²⋊Q₈	—	2	2	no	—
208	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₂₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₂₉×#121	—	2	1	no	—
213	C₂₉×#121	—	2	2	no	—
214	C₂₉×#121	—	2	2	no	—
215	C₂₉×#121	—	2	2	no	—
216	C₂₉×#121	—	2	2	no	—
217	C₂₉×#121	—	2	1	no	—
218	C₂₉×#121	—	2	1	no	—
219	C₂₉×#121	—	2	2	no	—
220	C₂₉×#121	—	2	2	no	—
221	C₂₉×#121	—	2	2	no	—
222	C₂₉×#121	—	2	2	no	—
223	C₂₉×#121	—	2	2	no	—
224	C₂₉×#121	D₄	1	1	yes	characteristic
225	C₂₉×#121	C₂³	1	2	yes	—
226	C₂₉×#121	C₂³	1	2	yes	—
227	C₂₉×#121	C₂³	1	2	yes	—
228	C₂₉×#121	C₂³	1	1	yes	characteristic
229	C₂₉×#120	—	2	2	no	—
230	C₂₉×#120	—	2	2	no	—
231	C₂₉×#120	—	2	2	no	—
232	C₂₉×#120	—	2	2	no	—
233	C₂₉×#120	—	2	2	no	—
234	C₂₉×#120	—	2	2	no	—
235	C₄×Q₈×C₂₉	—	2	1	no	—
236	C₄×Q₈×C₂₉	—	2	2	no	—
237	C₄×Q₈×C₂₉	—	2	2	no	—
238	C₄×Q₈×C₂₉	—	2	2	no	—
239	C₄×Q₈×C₂₉	—	2	1	no	—
240	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
243	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
244	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
245	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
246	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₂₉	—	2	1	no	—
248	C₄×D₄×C₂₉	—	2	1	no	—
249	C₄×D₄×C₂₉	—	2	1	no	—
250	C₄×D₄×C₂₉	—	2	1	no	—
251	C₄×D₄×C₂₉	—	2	1	no	—
252	C₄×D₄×C₂₉	—	2	1	no	—
253	C₄×D₄×C₂₉	—	2	2	no	—
254	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₂₉	C₂³	1	2	yes	—
257	C₄×D₄×C₂₉	C₂³	1	2	yes	—
258	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₂₉	C₂³	1	2	yes	—
261	C₂₉×#117	—	2	1	no	—
262	C₂₉×#117	—	2	1	no	—
263	C₂₉×#117	—	2	1	no	—
264	C₂₉×#117	—	2	2	no	—
265	C₂₉×#117	—	2	2	no	—
266	C₂₉×#117	—	2	1	no	—
267	C₂₉×#117	—	2	1	no	—
268	C₂₉×#117	C₂³	1	1	yes	characteristic
269	C₂₉×#117	C₂³	1	2	yes	—
270	C₂₉×#117	C₂³	1	2	yes	—
271	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
272	C₂×C₄²×C₂₉	—	2	1	no	—
273	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
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	2	yes	—
285	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
287	C₂₉×#103	C₂³	1	1	yes	characteristic
288	C₂₉×#103	C₂³	1	2	yes	—
289	C₂₉×#103	C₂³	1	1	yes	characteristic
290	C₂₉×#103	C₂³	1	1	yes	characteristic
291	C₂₉×#103	C₂³	1	1	yes	characteristic
292	C₂₉×#103	C₂³	1	2	yes	—
293	C₂₉×#103	C₂³	1	2	yes	—
294	C₂₉×#102	C₂³	1	1	yes	characteristic
295	C₂₉×#102	C₂³	1	1	yes	characteristic
296	C₂₉×#102	C₂³	1	1	yes	characteristic
297	C₂₉×#102	C₂³	1	2	yes	—
298	C₂₉×#102	C₂³	1	1	yes	characteristic
299	C₂₉×#102	C₂³	1	2	yes	—
300	C₂₉×#102	C₂³	1	2	yes	—
301	C₂₉×#102	C₂³	1	2	yes	—
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	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₂₉	C₂³	1	2	yes	—
315	C₂⁴×C₂₉	—	2	2	no	—
316	C₂⁴×C₂₉	—	2	2	no	—
317	#41×C₂₉	—	2	2	no	—
318	#41×C₂₉	—	4	1	no	—
319	#41×C₂₉	—	4	2	no	—
320	#41×C₂₉	—	4	2	no	—
321	#41×C₂₉	—	8	2	no	—
322	C₂×Q₈×C₂₉	—	2	2	no	—
323	C₂×Q₈×C₂₉	—	2	1	no	—
324	C₂×Q₈×C₂₉	—	2	2	no	—
325	C₂×Q₈×C₂₉	—	2	4	no	—
326	C₂×Q₈×C₂₉	—	4	2	no	—
327	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₂₉	—	2	1	no	—
332	C₂×D₄×C₂₉	—	2	1	no	—
333	C₂×D₄×C₂₉	—	2	2	no	—
334	C₂×D₄×C₂₉	—	2	2	no	—
335	C₂×D₄×C₂₉	—	2	2	no	—
336	C₂×D₄×C₂₉	—	2	2	no	—
337	C₂×D₄×C₂₉	—	2	1	no	—
338	C₂×D₄×C₂₉	—	2	1	no	—
339	C₂×D₄×C₂₉	—	2	2	no	—
340	C₂×D₄×C₂₉	—	2	2	no	—
341	C₂×D₄×C₂₉	—	2	1	no	—
342	C₂×D₄×C₂₉	—	2	2	no	—
343	C₂×D₄×C₂₉	—	2	2	no	—
344	C₂×D₄×C₂₉	—	2	2	no	—
345	C₂×D₄×C₂₉	—	2	2	no	—
346	C₂×D₄×C₂₉	—	2	1	no	—
347	C₂×D₄×C₂₉	—	4	2	no	—
348	C₂×D₄×C₂₉	—	4	2	no	—
349	C₂×D₄×C₂₉	—	4	2	no	—
350	C₂×D₄×C₂₉	—	4	2	no	—
351	C₂×D₄×C₂₉	—	8	2	no	—
352	C₂×D₄×C₂₉	—	8	2	no	—
353	C₂×D₄×C₂₉	—	8	2	no	—
354	C₂×D₄×C₂₉	—	8	4	no	—
355	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
356	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
357	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
359	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
360	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
361	C₂²×C₄×C₂₉	—	2	2	no	—
362	C₂²×C₄×C₂₉	—	2	1	no	—
363	C₂²×C₄×C₂₉	—	2	1	no	—
364	C₂²×C₄×C₂₉	—	2	1	no	—
365	C₂²×C₄×C₂₉	—	2	1	no	—
366	C₂²×C₄×C₂₉	—	2	2	no	—
367	C₂²×C₄×C₂₉	—	2	2	no	—
368	C₂²×C₄×C₂₉	—	2	2	no	—
369	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
373	Q₁₆×C₂₉	—	2	2	no	—
374	Q₁₆×C₂₉	—	4	2	no	—
375	SD₁₆×C₂₉	—	2	2	no	—
376	SD₁₆×C₂₉	—	2	4	no	—
377	SD₁₆×C₂₉	—	2	4	no	—
378	SD₁₆×C₂₉	—	4	2	no	—
379	SD₁₆×C₂₉	—	4	2	no	—
380	SD₁₆×C₂₉	—	4	2	no	—
381	SD₁₆×C₂₉	—	4	1	no	—
382	SD₁₆×C₂₉	—	4	2	no	—
383	SD₁₆×C₂₉	—	4	2	no	—
384	D₈×C₂₉	—	4	1	no	—
385	D₈×C₂₉	—	4	2	no	—
386	D₈×C₂₉	—	4	2	no	—
387	M₁₆×C₂₉	—	4	2	no	—
388	M₁₆×C₂₉	—	4	2	no	—
389	C₂×C₈×C₂₉	—	4	2	no	—
390	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
392	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
393	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
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	1	no	—
400	C₄⋊C₄×C₂₉	—	2	2	no	—
401	C₄⋊C₄×C₂₉	—	2	2	no	—
402	C₄⋊C₄×C₂₉	—	2	2	no	—
403	C₄⋊C₄×C₂₉	—	2	1	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	1	no	—
408	C₄⋊C₄×C₂₉	—	2	2	no	—
409	C₄⋊C₄×C₂₉	—	2	2	no	—
410	C₄⋊C₄×C₂₉	—	2	1	no	—
411	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
415	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
420	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
422	C₂²⋊C₄×C₂₉	—	2	1	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	2	no	—
428	C₂²⋊C₄×C₂₉	—	2	2	no	—
429	C₂²⋊C₄×C₂₉	—	2	1	no	—
430	C₂²⋊C₄×C₂₉	—	2	1	no	—
431	C₂²⋊C₄×C₂₉	—	2	1	no	—
432	C₂²⋊C₄×C₂₉	—	2	1	no	—
433	C₂²⋊C₄×C₂₉	—	2	2	no	—
434	C₂²⋊C₄×C₂₉	—	2	2	no	—
435	C₂²⋊C₄×C₂₉	—	2	1	no	—
436	C₂²⋊C₄×C₂₉	—	2	2	no	—
437	C₂²⋊C₄×C₂₉	—	2	2	no	—
438	C₂²⋊C₄×C₂₉	—	2	2	no	—
439	C₂²⋊C₄×C₂₉	—	2	1	no	—
440	C₂²⋊C₄×C₂₉	—	2	2	no	—
441	C₂²⋊C₄×C₂₉	—	2	2	no	—
442	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
447	C₄²×C₂₉	—	2	1	no	—
448	C₄²×C₂₉	—	2	1	no	—
449	C₄²×C₂₉	—	2	1	no	—
450	C₄²×C₂₉	—	2	2	no	—
451	C₄²×C₂₉	—	2	2	no	—
452	C₄²×C₂₉	—	2	2	no	—
453	C₄²×C₂₉	—	2	1	no	—
454	C₄²×C₂₉	—	2	2	no	—
455	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
456	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
458	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
459	C₄²×C₂₉	C₂⁴	1	2	yes	—
460	#62035	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
461	C₂³×C₂₉	—	2	1	no	—
462	C₂³×C₂₉	—	2	2	no	—
463	C₂³×C₂₉	—	2	1	no	—
464	C₂³×C₂₉	—	2	2	no	—
465	C₂³×C₂₉	—	4	4	no	—
466	C₂³×C₂₉	—	8	2	no	—
467	C₂³×C₂₉	—	8	2	no	—
468	C₂³×C₂₉	—	8	2	no	—
469	C₂³×C₂₉	—	8	2	no	—
470	C₂³×C₂₉	—	8	2	no	—
471	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
472	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
473	Q₈×C₂₉	—	2	2	no	—
474	Q₈×C₂₉	—	2	1	no	—
475	Q₈×C₂₉	—	2	2	no	—
476	Q₈×C₂₉	—	2	1	no	—
477	Q₈×C₂₉	—	2	2	no	—
478	Q₈×C₂₉	—	2	1	no	—
479	Q₈×C₂₉	—	4	4	no	—
480	Q₈×C₂₉	—	8	1	no	—
481	Q₈×C₂₉	—	8	2	no	—
482	Q₈×C₂₉	H(5,𝔽₂)	1	2	yes	—
483	D₄×C₂₉	—	2	2	no	—
484	D₄×C₂₉	—	2	1	no	—
485	D₄×C₂₉	—	2	2	no	—
486	D₄×C₂₉	—	2	2	no	—
487	D₄×C₂₉	—	2	1	no	—
488	D₄×C₂₉	—	2	1	no	—
489	D₄×C₂₉	—	2	1	no	—
490	D₄×C₂₉	—	2	2	no	—
491	D₄×C₂₉	—	2	2	no	—
492	D₄×C₂₉	—	4	2	no	—
493	D₄×C₂₉	—	4	2	no	—
494	D₄×C₂₉	—	4	2	no	—
495	D₄×C₂₉	—	4	2	no	—
496	D₄×C₂₉	—	4	2	no	—
497	D₄×C₂₉	—	8	2	no	—
498	D₄×C₂₉	—	8	2	no	—
499	D₄×C₂₉	—	8	2	no	—
500	D₄×C₂₉	—	8	1	no	—
501	D₄×C₂₉	—	8	1	no	—
502	D₄×C₂₉	—	8	2	no	—
503	D₄×C₂₉	—	8	2	no	—
504	D₄×C₂₉	—	8	2	no	—
505	D₄×C₂₉	—	8	2	no	—
506	D₄×C₂₉	—	8	2	no	—
507	D₄×C₂₉	—	8	2	no	—
508	D₄×C₂₉	—	8	2	no	—
509	C₂×C₄×C₂₉	—	2	1	no	—
510	C₂×C₄×C₂₉	—	2	2	no	—
511	C₂×C₄×C₂₉	—	2	2	no	—
512	C₂×C₄×C₂₉	—	2	1	no	—
513	C₂×C₄×C₂₉	—	2	1	no	—
514	C₂×C₄×C₂₉	—	2	2	no	—
515	C₂×C₄×C₂₉	—	2	1	no	—
516	C₂×C₄×C₂₉	—	2	2	no	—
517	C₂×C₄×C₂₉	—	2	2	no	—
518	C₂×C₄×C₂₉	—	2	1	no	—
519	C₂×C₄×C₂₉	—	2	1	no	—
520	C₂×C₄×C₂₉	—	2	1	no	—
521	C₂×C₄×C₂₉	—	2	1	no	—
522	C₂×C₄×C₂₉	—	4	1	no	—
523	C₂×C₄×C₂₉	—	4	2	no	—
524	C₂×C₄×C₂₉	—	4	4	no	—
525	C₂×C₄×C₂₉	—	4	2	no	—
526	C₂×C₄×C₂₉	—	4	2	no	—
527	C₂×C₄×C₂₉	—	8	1	no	—
528	C₂×C₄×C₂₉	—	8	2	no	—
529	C₂×C₄×C₂₉	—	8	2	no	—
530	C₂×C₄×C₂₉	—	8	2	no	—
531	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
535	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
536	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
537	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
540	C₈×C₂₉	—	2	1	no	—
541	C₈×C₂₉	—	2	2	no	—
542	C₈×C₂₉	—	2	2	no	—
543	C₈×C₂₉	—	2	1	no	—
544	C₈×C₂₉	—	2	1	no	—
545	C₈×C₂₉	—	2	1	no	—
546	#3543	C₂×C₂₉	1	1	yes	characteristic, complemented
547	#3518	C₂×C₂₉	1	1	yes	characteristic, complemented
548	#3397	C₂×C₂₉	1	1	yes	characteristic, complemented
549	#3394	C₂×C₂₉	1	1	yes	characteristic, complemented
550	#3375	C₂×C₂₉	1	1	yes	characteristic, complemented
551	#3362	C₂×C₂₉	1	1	yes	characteristic, complemented
552	#3325	C₂×C₂₉	1	1	yes	characteristic, complemented
553	#3324	C₂×C₂₉	1	2	yes	complemented
554	#3311	C₂×C₂₉	1	2	yes	complemented
555	#3305	C₂×C₂₉	1	1	yes	characteristic, complemented
556	D₄×SD₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
557	#3278	C₂×C₂₉	1	1	yes	characteristic, complemented
558	#3275	C₂×C₂₉	1	2	yes	complemented
559	#3265	C₂×C₂₉	1	2	yes	complemented
560	#3257	C₂×C₂₉	1	2	yes	complemented
561	#3252	C₂×C₂₉	1	1	yes	characteristic, complemented
562	#3224	C₂×C₂₉	1	2	yes	complemented
563	#3208	C₂×C₂₉	1	1	yes	characteristic, complemented
564	#3126	C₂×C₂₉	1	2	yes	complemented
565	#3102	C₂×C₂₉	1	1	yes	characteristic, complemented
566	#3043	C₂×C₂₉	1	2	yes	complemented
567	#3038	C₂×C₂₉	1	1	yes	characteristic, complemented
568	#2993	C₂×C₂₉	1	1	yes	characteristic, complemented
569	C₂²×C₂₉	—	2	1	no	—
570	C₂²×C₂₉	—	2	2	no	—
571	C₂²×C₂₉	—	2	2	no	—
572	C₂²×C₂₉	—	2	1	no	—
573	C₂²×C₂₉	—	2	1	no	—
574	C₂²×C₂₉	—	2	2	no	—
575	C₂²×C₂₉	—	4	1	no	—
576	C₂²×C₂₉	—	4	2	no	—
577	C₂²×C₂₉	—	4	1	no	—
578	C₂²×C₂₉	—	4	2	no	—
579	C₂²×C₂₉	—	4	1	no	—
580	C₂²×C₂₉	—	4	2	no	—
581	C₂²×C₂₉	—	4	2	no	—
582	C₂²×C₂₉	—	4	1	no	—
583	C₂²×C₂₉	—	4	1	no	—
584	C₂²×C₂₉	—	4	1	no	—
585	C₂²×C₂₉	—	4	2	no	—
586	C₂²×C₂₉	—	4	2	no	—
587	C₂²×C₂₉	—	16	4	no	—
588	C₂²×C₂₉	—	16	4	no	—
589	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
590	C₄×C₂₉	—	2	1	no	—
591	C₄×C₂₉	—	2	1	no	—
592	C₄×C₂₉	—	2	2	no	—
593	C₄×C₂₉	—	2	1	no	—
594	C₄×C₂₉	—	2	2	no	—
595	C₄×C₂₉	—	2	2	no	—
596	C₄×C₂₉	—	2	1	no	—
597	C₄×C₂₉	—	2	2	no	—
598	C₄×C₂₉	—	4	1	no	—
599	C₄×C₂₉	—	4	1	no	—
600	C₄×C₂₉	—	4	2	no	—
601	C₄×C₂₉	—	4	2	no	—
602	C₄×C₂₉	—	4	1	no	—
603	C₄×C₂₉	—	4	1	no	—
604	C₄×C₂₉	—	4	1	no	—
605	C₄×C₂₉	#577	1	2	yes	—
606	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
607	C₄×C₂₉	#585	1	1	yes	characteristic
608	C₂×#137	C₂²×C₂₉	1	2	yes	complemented
609	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	2	yes	complemented
610	C₂²×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
611	#560	—	2	2	no	—
612	#559	C₂²×C₂₉	1	1	yes	characteristic
613	Q₈²	C₂²×C₂₉	1	1	yes	characteristic, complemented
614	#556	—	2	2	no	—
615	#556	—	2	1	no	—
616	#556	C₂²×C₂₉	1	1	yes	characteristic, complemented
617	#556	C₂²×C₂₉	1	2	yes	complemented
618	#555	—	2	1	no	—
619	#555	C₂²×C₂₉	1	1	yes	characteristic, complemented
620	#550	C₂²×C₂₉	1	1	yes	characteristic
621	#550	C₂²×C₂₉	1	1	yes	characteristic
622	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
623	#548	C₂²×C₂₉	1	2	yes	complemented
624	#546	—	2	1	no	—
625	#546	C₂²×C₂₉	1	2	yes	—
626	D₄²	—	2	1	no	—
627	D₄²	C₂²×C₂₉	1	2	yes	—
628	D₄²	C₂²×C₂₉	1	1	yes	characteristic
629	#542	—	2	2	no	—
630	#542	C₂²×C₂₉	1	2	yes	complemented
631	#540	—	2	1	no	—
632	#540	C₂²×C₂₉	1	2	yes	—
633	#535	—	2	1	no	—
634	#535	C₂²×C₂₉	1	2	yes	—
635	#534	—	2	2	no	—
636	#533	—	2	1	no	—
637	#533	C₂²×C₂₉	1	1	yes	characteristic, complemented
638	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
639	#529	—	2	1	no	—
640	#529	C₂²×C₂₉	1	1	yes	characteristic
641	#529	C₂²×C₂₉	1	1	yes	characteristic
642	#519	C₂²×C₂₉	1	2	yes	complemented
643	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic, complemented
644	#496	C₂²×C₂₉	1	2	yes	complemented
645	#495	C₂²×C₂₉	1	2	yes	complemented
646	#492	C₂²×C₂₉	1	1	yes	characteristic
647	#492	C₂²×C₂₉	1	1	yes	characteristic, complemented
648	#489	C₂²×C₂₉	1	2	yes	complemented
649	#486	C₂²×C₂₉	1	1	yes	characteristic
650	#486	C₂²×C₂₉	1	1	yes	characteristic, complemented
651	#486	C₂²×C₂₉	1	2	yes	complemented
652	#485	C₂²×C₂₉	1	1	yes	characteristic, complemented
653	#482	C₂²×C₂₉	1	1	yes	characteristic
654	#482	C₂²×C₂₉	1	2	yes	complemented
655	#482	C₂²×C₂₉	1	2	yes	complemented
656	#479	C₂²×C₂₉	1	1	yes	characteristic, complemented
657	#479	C₂²×C₂₉	1	2	yes	complemented
658	#478	C₂²×C₂₉	1	1	yes	characteristic, complemented
659	#477	C₂²×C₂₉	1	1	yes	characteristic, complemented
660	#476	C₂²×C₂₉	1	1	yes	characteristic, complemented
661	#476	C₂²×C₂₉	1	2	yes	complemented
662	#474	C₂²×C₂₉	1	2	yes	complemented
663	#470	C₂²×C₂₉	1	2	yes	complemented
664	#469	C₂²×C₂₉	1	2	yes	complemented
665	#468	C₂²×C₂₉	1	2	yes	—
666	#468	C₂²×C₂₉	1	2	yes	complemented
667	#466	C₂²×C₂₉	1	2	yes	complemented
668	#465	C₂²×C₂₉	1	2	yes	complemented
669	#464	C₂²×C₂₉	1	1	yes	characteristic, complemented
670	#464	C₂²×C₂₉	1	2	yes	complemented
671	#464	C₂²×C₂₉	1	2	yes	complemented
672	#464	C₂²×C₂₉	1	2	yes	complemented
673	#463	C₂²×C₂₉	1	1	yes	characteristic, complemented
674	#463	C₂²×C₂₉	1	2	yes	complemented
675	#463	C₂²×C₂₉	1	2	yes	complemented
676	#462	C₂²×C₂₉	1	1	yes	characteristic, complemented
677	#461	C₂²×C₂₉	1	1	yes	characteristic, complemented
678	#460	C₂²×C₂₉	1	1	yes	characteristic
679	#460	C₂²×C₂₉	1	2	yes	complemented
680	#460	C₂²×C₂₉	1	1	yes	characteristic, complemented
681	#460	C₂²×C₂₉	1	2	yes	complemented
682	#460	C₂²×C₂₉	1	2	yes	complemented
683	#460	C₂²×C₂₉	1	2	yes	complemented
684	#460	C₂²×C₂₉	1	2	yes	complemented
685	#459	C₂²×C₂₉	1	1	yes	characteristic
686	#459	C₂²×C₂₉	1	1	yes	characteristic, complemented
687	#459	C₂²×C₂₉	1	2	yes	complemented
688	#452	C₂²×C₂₉	1	1	yes	characteristic, complemented
689	#452	C₂²×C₂₉	1	2	yes	complemented
690	#450	C₂²×C₂₉	1	2	yes	complemented
691	#450	C₂²×C₂₉	1	2	yes	complemented
692	#450	C₂²×C₂₉	1	2	yes	complemented
693	#449	C₂²×C₂₉	1	1	yes	characteristic
694	#449	C₂²×C₂₉	1	2	yes	complemented
695	#448	C₂²×C₂₉	1	2	yes	complemented
696	#448	C₂²×C₂₉	1	2	yes	complemented
697	#447	C₂²×C₂₉	1	2	yes	complemented
698	#446	C₂²×C₂₉	1	1	yes	characteristic, complemented
699	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
700	#440	C₂²×C₂₉	1	2	yes	complemented
701	#440	C₂²×C₂₉	1	2	yes	complemented
702	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
703	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
704	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
705	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
706	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
707	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
708	#436	C₂²×C₂₉	1	2	yes	complemented
709	#436	C₂²×C₂₉	1	1	yes	characteristic, complemented
710	#435	C₂²×C₂₉	1	2	yes	complemented
711	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
712	#433	C₂²×C₂₉	1	2	yes	complemented
713	#431	C₂²×C₂₉	1	1	yes	characteristic, complemented
714	#424	C₂²×C₂₉	1	2	yes	complemented
715	#423	C₂²×C₂₉	1	1	yes	characteristic, complemented
716	#418	C₂²×C₂₉	1	2	yes	complemented
717	#418	C₂²×C₂₉	1	2	yes	complemented
718	#416	C₂²×C₂₉	1	2	yes	complemented
719	C₂×C₂₉	—	4	2	no	—
720	C₂×C₂₉	—	4	1	no	—
721	C₂×C₂₉	—	8	1	no	—
722	C₂×C₂₉	—	8	2	no	—
723	C₂×C₂₉	—	8	2	no	—
724	C₂×C₂₉	—	8	1	no	—
725	C₂×C₂₉	#3488	1	1	yes	characteristic
726	C₂×C₂₉	C₂×#577	1	1	yes	characteristic
727	C₂×C₂₉	#3585	1	1	yes	characteristic
728	C₂×#41	—	2	1	no	—
729	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
730	C₂×#41	C₂³×C₂₉	1	2	yes	—
731	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
732	C₂²×D₄	—	2	2	no	—
733	C₂²×D₄	—	2	1	no	—
734	C₂²×D₄	—	2	1	no	—
735	C₂²×D₄	—	2	1	no	—
736	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
737	C₂²×D₄	C₂³×C₂₉	1	2	yes	—
738	#137	—	4	4	no	—
739	AGL(1,ℤ/8)	—	4	4	no	—
740	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
741	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
742	C₂×SD₁₆	—	4	4	no	—
743	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
744	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
745	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
746	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
747	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
748	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
749	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
750	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
751	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
752	C₂×D₈	C₂³×C₂₉	1	2	yes	—
753	C₂×D₈	C₂³×C₂₉	1	2	yes	—
754	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
755	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
756	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
757	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
758	C₄⋊Q₈	—	2	1	no	—
759	C₄⋊Q₈	—	2	1	no	—
760	C₄⋊Q₈	—	2	2	no	—
761	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
762	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
763	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
764	#127	—	2	1	no	—
765	#127	—	2	1	no	—
766	#127	—	2	1	no	—
767	#127	C₂³×C₂₉	1	2	yes	—
768	#127	C₂³×C₂₉	1	1	yes	characteristic
769	#127	C₂³×C₂₉	1	1	yes	characteristic
770	#127	C₂³×C₂₉	1	2	yes	—
771	#126	—	2	2	no	—
772	#126	—	2	2	no	—
773	#126	—	2	2	no	—
774	#126	—	2	2	no	—
775	#126	—	2	1	no	—
776	#126	D₄×C₂₉	1	2	yes	—
777	#125	—	2	1	no	—
778	#125	D₄×C₂₉	1	1	yes	characteristic
779	#125	C₂³×C₂₉	1	1	yes	characteristic
780	#124	—	2	1	no	—
781	#124	—	2	2	no	—
782	#124	—	2	2	no	—
783	#124	—	2	2	no	—
784	#124	—	2	2	no	—
785	#124	D₄×C₂₉	1	1	yes	characteristic
786	#124	C₂³×C₂₉	1	1	yes	characteristic
787	#124	C₂³×C₂₉	1	2	yes	—
788	#124	C₂³×C₂₉	1	2	yes	—
789	#123	—	2	1	no	—
790	#123	—	2	2	no	—
791	#123	—	2	2	no	—
792	#123	—	2	2	no	—
793	#123	—	2	2	no	—
794	#123	—	2	2	no	—
795	#123	D₄×C₂₉	1	2	yes	—
796	C₂²⋊Q₈	—	2	1	no	—
797	C₂²⋊Q₈	—	2	1	no	—
798	C₂²⋊Q₈	—	2	2	no	—
799	C₂²⋊Q₈	—	2	2	no	—
800	C₂²⋊Q₈	—	2	2	no	—
801	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
802	C₂²⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
803	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
804	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
805	#121	—	2	1	no	—
806	#121	—	2	2	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	1	no	—
811	#121	—	2	1	no	—
812	#121	—	2	2	no	—
813	#121	—	2	2	no	—
814	#121	—	2	2	no	—
815	#121	—	2	2	no	—
816	#121	—	2	2	no	—
817	#121	D₄×C₂₉	1	1	yes	characteristic
818	#121	C₂³×C₂₉	1	1	yes	characteristic
819	#121	C₂³×C₂₉	1	2	yes	—
820	#121	C₂³×C₂₉	1	2	yes	—
821	#121	C₂³×C₂₉	1	2	yes	—
822	#120	—	2	2	no	—
823	#120	—	2	2	no	—
824	#120	—	2	2	no	—
825	#120	—	2	2	no	—
826	#120	—	2	2	no	—
827	#120	—	2	2	no	—
828	C₄×Q₈	—	2	1	no	—
829	C₄×Q₈	—	2	2	no	—
830	C₄×Q₈	—	2	2	no	—
831	C₄×Q₈	—	2	2	no	—
832	C₄×Q₈	—	2	1	no	—
833	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
834	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
835	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
836	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
837	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
838	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
839	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
840	C₄×D₄	—	2	1	no	—
841	C₄×D₄	—	2	1	no	—
842	C₄×D₄	—	2	1	no	—
843	C₄×D₄	—	2	1	no	—
844	C₄×D₄	—	2	1	no	—
845	C₄×D₄	—	2	1	no	—
846	C₄×D₄	—	2	2	no	—
847	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
848	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
849	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
850	C₄×D₄	C₂³×C₂₉	1	2	yes	—
851	C₄×D₄	C₂³×C₂₉	1	2	yes	—
852	C₄×D₄	C₂³×C₂₉	1	2	yes	—
853	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
854	#117	—	2	1	no	—
855	#117	—	2	1	no	—
856	#117	—	2	1	no	—
857	#117	—	2	2	no	—
858	#117	—	2	2	no	—
859	#117	—	2	1	no	—
860	#117	—	2	1	no	—
861	#117	C₂³×C₂₉	1	1	yes	characteristic
862	#117	C₂³×C₂₉	1	2	yes	—
863	#117	C₂³×C₂₉	1	2	yes	—
864	C₂×C₂²⋊C₄	—	2	2	no	—
865	C₂×C₄²	—	2	1	no	—
866	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
867	#107	C₂³×C₂₉	1	1	yes	characteristic
868	#107	C₂³×C₂₉	1	1	yes	characteristic
869	#107	C₂³×C₂₉	1	2	yes	—
870	#106	C₂³×C₂₉	1	1	yes	characteristic
871	#106	C₂³×C₂₉	1	1	yes	characteristic
872	#106	C₂³×C₂₉	1	2	yes	—
873	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
874	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
875	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
876	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
877	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
878	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
879	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
880	#103	C₂³×C₂₉	1	1	yes	characteristic
881	#103	C₂³×C₂₉	1	2	yes	—
882	#103	C₂³×C₂₉	1	1	yes	characteristic
883	#103	C₂³×C₂₉	1	2	yes	—
884	#103	C₂³×C₂₉	1	1	yes	characteristic
885	#103	C₂³×C₂₉	1	1	yes	characteristic
886	#103	C₂³×C₂₉	1	2	yes	—
887	#102	C₂³×C₂₉	1	2	yes	—
888	#102	C₂³×C₂₉	1	2	yes	—
889	#102	C₂³×C₂₉	1	1	yes	characteristic
890	#102	C₂³×C₂₉	1	2	yes	—
891	#102	C₂³×C₂₉	1	2	yes	—
892	#102	C₂³×C₂₉	1	2	yes	—
893	#102	C₂³×C₂₉	1	2	yes	—
894	#102	C₂³×C₂₉	1	2	yes	—
895	#102	C₂³×C₂₉	1	1	yes	characteristic
896	#102	C₂³×C₂₉	1	1	yes	characteristic
897	#102	C₂³×C₂₉	1	2	yes	—
898	#102	C₂³×C₂₉	1	1	yes	characteristic
899	#102	C₂³×C₂₉	1	2	yes	—
900	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
901	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
902	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
903	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
904	#97	C₂³×C₂₉	1	2	yes	—
905	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
906	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
907	C₄×C₈	C₂³×C₂₉	1	2	yes	—
908	C₂₉	#62035	1	1	yes	characteristic, direct product factor, Sylow
909	C₂⁴	—	2	2	no	—
910	C₂⁴	—	2	2	no	—
911	#41	—	2	2	no	—
912	#41	—	4	1	no	—
913	#41	—	4	2	no	—
914	#41	—	4	2	no	—
915	#41	—	8	2	no	—
916	C₂×Q₈	—	2	2	no	—
917	C₂×Q₈	—	2	1	no	—
918	C₂×Q₈	—	2	2	no	—
919	C₂×Q₈	—	2	4	no	—
920	C₂×Q₈	—	4	2	no	—
921	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
922	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
923	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
924	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	1	no	—
941	C₂×D₄	—	4	2	no	—
942	C₂×D₄	—	4	2	no	—
943	C₂×D₄	—	4	2	no	—
944	C₂×D₄	—	4	2	no	—
945	C₂×D₄	—	8	2	no	—
946	C₂×D₄	—	8	2	no	—
947	C₂×D₄	—	8	2	no	—
948	C₂×D₄	—	8	4	no	—
949	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
950	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
951	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
952	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
953	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
954	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	1	no	—
958	C₂²×C₄	—	2	1	no	—
959	C₂²×C₄	—	2	1	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	—	2	2	no	—
963	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
964	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
965	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
966	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
967	Q₁₆	—	2	2	no	—
968	Q₁₆	—	4	2	no	—
969	SD₁₆	—	2	2	no	—
970	SD₁₆	—	2	4	no	—
971	SD₁₆	—	2	4	no	—
972	SD₁₆	—	4	2	no	—
973	SD₁₆	—	4	2	no	—
974	SD₁₆	—	4	2	no	—
975	SD₁₆	—	4	2	no	—
976	SD₁₆	—	4	1	no	—
977	SD₁₆	—	4	2	no	—
978	D₈	—	4	2	no	—
979	D₈	—	4	2	no	—
980	D₈	—	4	1	no	—
981	M₁₆	—	4	2	no	—
982	M₁₆	—	4	2	no	—
983	C₂×C₈	—	4	2	no	—
984	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
985	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
986	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
987	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
988	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
989	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	1	no	—
1005	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1006	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1007	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1008	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1009	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1010	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1011	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1012	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1013	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
1014	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1015	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
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	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	1	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1037	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1038	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1039	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1040	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	1	no	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	2	2	no	—
1045	C₄²	—	2	2	no	—
1046	C₄²	—	2	2	no	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	2	2	no	—
1049	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1050	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1051	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1052	C₄²	C₂⁴×C₂₉	1	2	yes	—
1053	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1054	C₂³	—	2	1	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	2	2	no	—
1058	C₂³	—	4	4	no	—
1059	C₂³	—	8	2	no	—
1060	C₂³	—	8	2	no	—
1061	C₂³	—	8	2	no	—
1062	C₂³	—	8	2	no	—
1063	C₂³	—	8	2	no	—
1064	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1065	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
1066	Q₈	—	2	2	no	—
1067	Q₈	—	2	1	no	—
1068	Q₈	—	2	2	no	—
1069	Q₈	—	2	1	no	—
1070	Q₈	—	2	2	no	—
1071	Q₈	—	2	1	no	—
1072	Q₈	—	4	4	no	—
1073	Q₈	—	8	1	no	—
1074	Q₈	—	8	2	no	—
1075	Q₈	C₂₉×H(5,𝔽₂)	1	2	yes	—
1076	D₄	—	2	2	no	—
1077	D₄	—	2	1	no	—
1078	D₄	—	2	2	no	—
1079	D₄	—	2	2	no	—
1080	D₄	—	2	1	no	—
1081	D₄	—	2	1	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	2	no	—
1084	D₄	—	2	2	no	—
1085	D₄	—	4	2	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	4	2	no	—
1088	D₄	—	4	2	no	—
1089	D₄	—	4	2	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	2	no	—
1093	D₄	—	8	2	no	—
1094	D₄	—	8	1	no	—
1095	D₄	—	8	1	no	—
1096	D₄	—	8	2	no	—
1097	D₄	—	8	2	no	—
1098	D₄	—	8	2	no	—
1099	D₄	—	8	2	no	—
1100	D₄	—	8	2	no	—
1101	D₄	—	8	2	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	4	1	no	—
1116	C₂×C₄	—	4	2	no	—
1117	C₂×C₄	—	4	4	no	—
1118	C₂×C₄	—	4	2	no	—
1119	C₂×C₄	—	4	2	no	—
1120	C₂×C₄	—	8	2	no	—
1121	C₂×C₄	—	8	2	no	—
1122	C₂×C₄	—	8	2	no	—
1123	C₂×C₄	—	8	1	no	—
1124	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1125	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1126	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1127	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1128	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1129	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1130	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1131	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1132	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1133	C₈	—	2	1	no	—
1134	C₈	—	2	2	no	—
1135	C₈	—	2	2	no	—
1136	C₈	—	2	1	no	—
1137	C₈	—	2	1	no	—
1138	C₈	—	2	1	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	1	no	—
1141	C₂²	—	2	1	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	1	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	2	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	1	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	1	no	—
1151	C₂²	—	4	2	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	2	no	—
1154	C₂²	—	4	1	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	2	no	—
1157	C₂²	—	16	4	no	—
1158	C₂²	—	16	4	no	—
1159	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
1160	C₄	—	2	1	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	1	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	2	1	no	—
1166	C₄	—	2	1	no	—
1167	C₄	—	2	2	no	—
1168	C₄	—	4	2	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	1	no	—
1172	C₄	—	4	1	no	—
1173	C₄	—	4	1	no	—
1174	C₄	—	4	2	no	—
1175	C₄	C₂₉×#577	1	2	yes	—
1176	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
1177	C₄	C₂₉×#585	1	1	yes	characteristic
1178	C₂	—	4	1	no	—
1179	C₂	—	4	2	no	—
1180	C₂	—	8	1	no	—
1181	C₂	—	8	2	no	—
1182	C₂	—	8	2	no	—
1183	C₂	—	8	1	no	—
1184	C₂	C₂₉×#3488	1	1	yes	characteristic
1185	C₂	C₂×C₂₉×#577	1	1	yes	characteristic
1186	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×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3543	C₂	semidirect
2. C₂₉×#3518	C₂	semidirect
3. C₂₉×#3397	C₂	semidirect
4. C₂₉×#3394	C₂	semidirect
5. C₂₉×#3375	C₂	semidirect
6. C₂₉×#3362	C₂	semidirect
7. C₂₉×#3325	C₂	semidirect
8. C₂₉×#3324	C₂	semidirect
9. C₂₉×#3311	C₂	semidirect
10. C₂₉×#3305	C₂	semidirect
11. D₄×SD₁₆×C₂₉	C₂	semidirect
12. C₂₉×#3278	C₂	semidirect
13. C₂₉×#3275	C₂	semidirect
14. C₂₉×#3265	C₂	semidirect
15. C₂₉×#3257	C₂	semidirect
16. C₂₉×#3252	C₂	semidirect
17. C₂₉×#3224	C₂	semidirect
18. C₂₉×#3208	C₂	semidirect
19. C₂₉×#3126	C₂	semidirect
20. C₂₉×#3102	C₂	semidirect
21. C₂₉×#3043	C₂	semidirect
22. C₂₉×#3038	C₂	semidirect
23. C₂₉×#2993	C₂	semidirect
24. C₂×C₂₉×#137	C₂²	semidirect
25. C₂×C₂₉×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂²×SD₁₆×C₂₉	C₂²	semidirect
29. Q₈²×C₂₉	C₂²	semidirect
32. C₂₉×#556	C₂²	semidirect
33. C₂₉×#556	C₂²	semidirect
35. C₂₉×#555	C₂²	semidirect
38. D₄×Q₈×C₂₉	C₂²	semidirect
39. C₂₉×#548	C₂²	semidirect
46. C₂₉×#542	C₂²	semidirect
53. C₂₉×#533	C₂²	semidirect
58. C₂₉×#519	C₂²	semidirect
59. C₄×#41×C₂₉	C₂²	semidirect
60. C₂₉×#496	C₂²	semidirect
61. C₂₉×#495	C₂²	semidirect
63. C₂₉×#492	C₂²	semidirect
64. C₂₉×#489	C₂²	semidirect
66. C₂₉×#486	C₂²	semidirect
67. C₂₉×#486	C₂²	semidirect
68. C₂₉×#485	C₂²	semidirect
70. C₂₉×#482	C₂²	semidirect
71. C₂₉×#482	C₂²	semidirect
72. C₂₉×#479	C₂²	semidirect
73. C₂₉×#479	C₂²	semidirect
74. C₂₉×#478	C₂²	semidirect
75. C₂₉×#477	C₂²	semidirect
76. C₂₉×#476	C₂²	semidirect
77. C₂₉×#476	C₂²	semidirect
78. C₂₉×#474	C₂²	semidirect
79. C₂₉×#470	C₂²	semidirect
80. C₂₉×#469	C₂²	semidirect
82. C₂₉×#468	C₂²	semidirect
83. C₂₉×#466	C₂²	semidirect
84. C₂₉×#465	C₂²	semidirect
85. C₂₉×#464	C₂²	semidirect
86. C₂₉×#464	C₂²	semidirect
87. C₂₉×#464	C₂²	semidirect
88. C₂₉×#464	C₂²	semidirect
89. C₂₉×#463	C₂²	semidirect
90. C₂₉×#463	C₂²	semidirect
91. C₂₉×#463	C₂²	semidirect
92. C₂₉×#462	C₂²	semidirect
93. C₂₉×#461	C₂²	semidirect
95. C₂₉×#460	C₂²	semidirect
96. C₂₉×#460	C₂²	semidirect
97. C₂₉×#460	C₂²	semidirect
98. C₂₉×#460	C₂²	semidirect
99. C₂₉×#460	C₂²	semidirect
100. C₂₉×#460	C₂²	semidirect
102. C₂₉×#459	C₂²	semidirect
103. C₂₉×#459	C₂²	semidirect
104. C₂₉×#452	C₂²	semidirect
105. C₂₉×#452	C₂²	semidirect
106. C₂₉×#450	C₂²	semidirect
107. C₂₉×#450	C₂²	semidirect
108. C₂₉×#450	C₂²	semidirect
110. C₂₉×#449	C₂²	semidirect
111. C₂₉×#448	C₂²	semidirect
112. C₂₉×#448	C₂²	semidirect
113. C₂₉×#447	C₂²	semidirect
114. C₂₉×#446	C₂²	semidirect
115. C₈×Q₈×C₂₉	C₂²	semidirect
116. C₂₉×#440	C₂²	semidirect
117. C₂₉×#440	C₂²	semidirect
118. C₄×Q₁₆×C₂₉	C₂²	semidirect
119. C₄×SD₁₆×C₂₉	C₂²	semidirect
120. C₄×SD₁₆×C₂₉	C₂²	semidirect
121. C₄×SD₁₆×C₂₉	C₂²	semidirect
122. C₄×SD₁₆×C₂₉	C₂²	semidirect
123. C₄×D₈×C₂₉	C₂²	semidirect
124. C₂₉×#436	C₂²	semidirect
125. C₂₉×#436	C₂²	semidirect
126. C₂₉×#435	C₂²	semidirect
127. C₈×D₄×C₂₉	C₂²	semidirect
128. C₂₉×#433	C₂²	semidirect
129. C₂₉×#431	C₂²	semidirect
130. C₂₉×#424	C₂²	semidirect
131. C₂₉×#423	C₂²	semidirect
132. C₂₉×#418	C₂²	semidirect
133. C₂₉×#418	C₂²	semidirect
134. C₂₉×#416	C₂²	semidirect
460. #62035	C₂₉	direct (N × H)
546. #3543	C₂×C₂₉	semidirect
547. #3518	C₂×C₂₉	semidirect
548. #3397	C₂×C₂₉	semidirect
549. #3394	C₂×C₂₉	semidirect
550. #3375	C₂×C₂₉	semidirect
551. #3362	C₂×C₂₉	semidirect
552. #3325	C₂×C₂₉	semidirect
553. #3324	C₂×C₂₉	semidirect
554. #3311	C₂×C₂₉	semidirect
555. #3305	C₂×C₂₉	semidirect
556. D₄×SD₁₆	C₂×C₂₉	semidirect
557. #3278	C₂×C₂₉	semidirect
558. #3275	C₂×C₂₉	semidirect
559. #3265	C₂×C₂₉	semidirect
560. #3257	C₂×C₂₉	semidirect
561. #3252	C₂×C₂₉	semidirect
562. #3224	C₂×C₂₉	semidirect
563. #3208	C₂×C₂₉	semidirect
564. #3126	C₂×C₂₉	semidirect
565. #3102	C₂×C₂₉	semidirect
566. #3043	C₂×C₂₉	semidirect
567. #3038	C₂×C₂₉	semidirect
568. #2993	C₂×C₂₉	semidirect
608. C₂×#137	C₂²×C₂₉	semidirect
609. C₂×AGL(1,ℤ/8)	C₂²×C₂₉	semidirect
610. C₂²×SD₁₆	C₂²×C₂₉	semidirect
613. Q₈²	C₂²×C₂₉	semidirect
616. #556	C₂²×C₂₉	semidirect
617. #556	C₂²×C₂₉	semidirect
619. #555	C₂²×C₂₉	semidirect
622. D₄×Q₈	C₂²×C₂₉	semidirect
623. #548	C₂²×C₂₉	semidirect
630. #542	C₂²×C₂₉	semidirect
637. #533	C₂²×C₂₉	semidirect
642. #519	C₂²×C₂₉	semidirect
643. C₄×#41	C₂²×C₂₉	semidirect
644. #496	C₂²×C₂₉	semidirect
645. #495	C₂²×C₂₉	semidirect
647. #492	C₂²×C₂₉	semidirect
648. #489	C₂²×C₂₉	semidirect
650. #486	C₂²×C₂₉	semidirect
651. #486	C₂²×C₂₉	semidirect
652. #485	C₂²×C₂₉	semidirect
654. #482	C₂²×C₂₉	semidirect
655. #482	C₂²×C₂₉	semidirect
656. #479	C₂²×C₂₉	semidirect
657. #479	C₂²×C₂₉	semidirect
658. #478	C₂²×C₂₉	semidirect
659. #477	C₂²×C₂₉	semidirect
660. #476	C₂²×C₂₉	semidirect
661. #476	C₂²×C₂₉	semidirect
662. #474	C₂²×C₂₉	semidirect
663. #470	C₂²×C₂₉	semidirect
664. #469	C₂²×C₂₉	semidirect
666. #468	C₂²×C₂₉	semidirect
667. #466	C₂²×C₂₉	semidirect
668. #465	C₂²×C₂₉	semidirect
669. #464	C₂²×C₂₉	semidirect
670. #464	C₂²×C₂₉	semidirect
671. #464	C₂²×C₂₉	semidirect
672. #464	C₂²×C₂₉	semidirect
673. #463	C₂²×C₂₉	semidirect
674. #463	C₂²×C₂₉	semidirect
675. #463	C₂²×C₂₉	semidirect
676. #462	C₂²×C₂₉	semidirect
677. #461	C₂²×C₂₉	semidirect
679. #460	C₂²×C₂₉	semidirect
680. #460	C₂²×C₂₉	semidirect
681. #460	C₂²×C₂₉	semidirect
682. #460	C₂²×C₂₉	semidirect
683. #460	C₂²×C₂₉	semidirect
684. #460	C₂²×C₂₉	semidirect
686. #459	C₂²×C₂₉	semidirect
687. #459	C₂²×C₂₉	semidirect
688. #452	C₂²×C₂₉	semidirect
689. #452	C₂²×C₂₉	semidirect
690. #450	C₂²×C₂₉	semidirect
691. #450	C₂²×C₂₉	semidirect
692. #450	C₂²×C₂₉	semidirect
694. #449	C₂²×C₂₉	semidirect
695. #448	C₂²×C₂₉	semidirect
696. #448	C₂²×C₂₉	semidirect
697. #447	C₂²×C₂₉	semidirect
698. #446	C₂²×C₂₉	semidirect
699. C₈×Q₈	C₂²×C₂₉	semidirect
700. #440	C₂²×C₂₉	semidirect
701. #440	C₂²×C₂₉	semidirect
702. C₄×Q₁₆	C₂²×C₂₉	semidirect
703. C₄×SD₁₆	C₂²×C₂₉	semidirect
704. C₄×SD₁₆	C₂²×C₂₉	semidirect
705. C₄×SD₁₆	C₂²×C₂₉	semidirect
706. C₄×SD₁₆	C₂²×C₂₉	semidirect
707. C₄×D₈	C₂²×C₂₉	semidirect
708. #436	C₂²×C₂₉	semidirect
709. #436	C₂²×C₂₉	semidirect
710. #435	C₂²×C₂₉	semidirect
711. C₈×D₄	C₂²×C₂₉	semidirect
712. #433	C₂²×C₂₉	semidirect
713. #431	C₂²×C₂₉	semidirect
714. #424	C₂²×C₂₉	semidirect
715. #423	C₂²×C₂₉	semidirect
716. #418	C₂²×C₂₉	semidirect
717. #418	C₂²×C₂₉	semidirect
718. #416	C₂²×C₂₉	semidirect
908. C₂₉	#62035	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×#3543	2
C₂₉×#3518	2
C₂₉×#3397	2
C₂₉×#3394	2
C₂₉×#3375	2
C₂₉×#3362	2
C₂₉×#3325	2
C₂₉×#3324	2
C₂₉×#3311	2
C₂₉×#3305	2
D₄×SD₁₆×C₂₉	2
C₂₉×#3278	2
C₂₉×#3275	2
C₂₉×#3265	2
C₂₉×#3257	2
C₂₉×#3252	2
C₂₉×#3224	2
C₂₉×#3208	2
C₂₉×#3126	2
C₂₉×#3102	2
C₂₉×#3043	2
C₂₉×#3038	2
C₂₉×#2993	2
#62035	29

Subgroups — C29×#62035 #20356935

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#62035 #20356935