Subgroups — C₂₉×#61185 #20356085

Order 7424.

2082 conjugacy classes of subgroups.

The subgroup lattice has 1230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3329	C₂	1	2	yes	maximal, complemented
4	C₂₉×#3326	C₂	1	2	yes	maximal, complemented
5	C₂₉×#3321	C₂	1	2	yes	maximal, complemented
6	C₂₉×#3320	C₂	1	2	yes	maximal, complemented
7	C₂₉×#3320	C₂	1	2	yes	maximal, complemented
8	C₂₉×#3308	C₂	1	2	yes	maximal, complemented
9	C₂₉×#3301	C₂	1	2	yes	maximal, complemented
10	C₂₉×#3298	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×#3057	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#3055	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₉×#3042	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₉×#3010	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₂₉×#448	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₉×#2949	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×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×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×#555	C₂²	1	2	yes	—
32	C₂₉×#553	C₂²	1	2	yes	—
33	C₂₉×#553	C₂²	1	2	yes	—
34	C₂₉×#551	—	2	2	no	—
35	D₄×Q₈×C₂₉	—	2	1	no	—
36	D₄×Q₈×C₂₉	—	2	1	no	—
37	D₄×Q₈×C₂₉	C₂²	1	2	yes	complemented
38	D₄×Q₈×C₂₉	C₂²	1	2	yes	complemented
39	C₂₉×#548	—	2	1	no	—
40	C₂₉×#548	—	2	1	no	—
41	C₂₉×#548	C₂²	1	2	yes	complemented
42	C₂₉×#548	C₂²	1	2	yes	complemented
43	C₂₉×#547	C₂²	1	2	yes	—
44	C₂₉×#546	—	2	2	no	—
45	C₂₉×#544	C₂²	1	1	yes	characteristic
46	C₂₉×#542	—	2	1	no	—
47	C₂₉×#540	—	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×#535	C₂²	1	1	yes	characteristic
52	C₂₉×#532	—	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×#121	C₂²	1	1	yes	characteristic
58	C₂₉×#520	C₂²	1	1	yes	characteristic
59	C₂₉×#519	C₂²	1	1	yes	characteristic
60	C₂₉×#518	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	2	yes	complemented
67	C₂₉×#485	C₂²	1	1	yes	characteristic, complemented
68	C₂₉×#485	C₂²	1	2	yes	complemented
69	C₂₉×#485	C₂²	1	1	yes	characteristic, complemented
70	C₂₉×#484	C₂²	1	2	yes	complemented
71	C₂₉×#484	C₂²	1	1	yes	characteristic, complemented
72	C₂₉×#483	C₂²	1	1	yes	characteristic, complemented
73	C₂₉×#483	C₂²	1	2	yes	complemented
74	C₂₉×#482	C₂²	1	1	yes	characteristic, complemented
75	C₂₉×#482	C₂²	1	1	yes	characteristic, complemented
76	C₂₉×#481	C₂²	1	1	yes	characteristic, complemented
77	C₂₉×#480	C₂²	1	1	yes	characteristic, complemented
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×#469	C₂²	1	2	yes	—
83	C₂₉×#468	C₂²	1	2	yes	—
84	C₂₉×#468	C₂²	1	2	yes	complemented
85	C₂₉×#468	C₂²	1	2	yes	complemented
86	C₂₉×#466	C₂²	1	2	yes	—
87	C₂₉×#465	C₂²	1	2	yes	—
88	C₂₉×#465	C₂²	1	2	yes	complemented
89	C₂₉×#465	C₂²	1	2	yes	complemented
90	C₂₉×#463	C₂²	1	2	yes	complemented
91	C₂₉×#463	C₂²	1	2	yes	complemented
92	C₂₉×#461	C₂²	1	2	yes	complemented
93	C₂₉×#461	C₂²	1	2	yes	complemented
94	C₂₉×#449	C₂²	1	2	yes	complemented
95	C₂₉×#449	C₂²	1	2	yes	complemented
96	C₂₉×#448	C₂²	1	2	yes	—
97	C₂₉×#448	C₂²	1	2	yes	—
98	C₂₉×#448	C₂²	1	2	yes	—
99	C₂₉×#448	C₂²	1	2	yes	—
100	C₂₉×#448	C₂²	1	2	yes	complemented
101	C₂₉×#448	C₂²	1	2	yes	complemented
102	C₂₉×#440	C₂²	1	2	yes	complemented
103	C₂₉×#440	C₂²	1	2	yes	complemented
104	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	complemented
106	C₂₉×#436	C₂²	1	2	yes	complemented
107	C₂₉×#435	C₂²	1	2	yes	complemented
108	C₂₉×#435	C₂²	1	2	yes	complemented
109	C₈×D₄×C₂₉	C₂²	1	2	yes	complemented
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	complemented
119	C₂₉×#419	C₂²	1	2	yes	complemented
120	C₂₉×#419	C₂²	1	2	yes	complemented
121	C₂₉×#418	C₂²	1	1	yes	characteristic
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	complemented
130	C₂×C₂₉×#103	C₂²	1	2	yes	complemented
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	—	2	2	no	—
140	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
141	C₂×#41×C₂₉	C₂³	1	2	yes	—
142	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
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	1	no	—
147	C₂²×Q₈×C₂₉	—	2	4	no	—
148	C₂²×Q₈×C₂₉	—	4	2	no	—
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	C₂²×D₄×C₂₉	—	2	1	no	—
155	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
156	C₂³×C₄×C₂₉	—	2	1	no	—
157	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
158	C₂₉×AGL(1,ℤ/8)	—	4	2	no	—
159	C₂×SD₁₆×C₂₉	—	2	4	no	—
160	C₂×SD₁₆×C₂₉	—	4	2	no	—
161	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
166	C₂×D₈×C₂₉	C₂³	1	2	yes	—
167	C₂₉×#131	—	4	2	no	—
168	C₂×M₁₆×C₂₉	—	4	2	no	—
169	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
170	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
171	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
172	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
173	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
174	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
176	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
177	C₂₉×C₄⋊Q₈	—	2	1	no	—
178	C₂₉×C₄⋊Q₈	—	2	1	no	—
179	C₂₉×C₄⋊Q₈	—	2	2	no	—
180	C₂₉×C₄⋊Q₈	—	2	2	no	—
181	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
182	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
183	C₂₉×#127	—	2	1	no	—
184	C₂₉×#126	—	2	2	no	—
185	C₂₉×#126	—	2	2	no	—
186	C₂₉×#125	—	2	1	no	—
187	C₂₉×#125	C₂³	1	2	yes	—
188	C₂₉×#124	—	2	1	no	—
189	C₂₉×#124	—	2	1	no	—
190	C₂₉×#124	—	2	2	no	—
191	C₂₉×#124	—	2	2	no	—
192	C₂₉×#124	—	2	2	no	—
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	D₄	1	2	yes	—
203	C₂₉×C₂²⋊Q₈	—	2	2	no	—
204	C₂₉×C₂²⋊Q₈	—	2	2	no	—
205	C₂₉×C₂²⋊Q₈	—	2	1	no	—
206	C₂₉×C₂²⋊Q₈	—	2	1	no	—
207	C₂₉×C₂²⋊Q₈	—	2	2	no	—
208	C₂₉×C₂²⋊Q₈	—	2	2	no	—
209	C₂₉×C₂²⋊Q₈	—	2	2	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	D₄	1	1	yes	characteristic
214	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
215	C₂₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
216	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₂₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
225	C₂₉×#121	—	2	1	no	—
226	C₂₉×#121	D₄	1	1	yes	characteristic
227	C₂₉×#121	D₄	1	1	yes	characteristic
228	C₂₉×#121	C₂³	1	2	yes	—
229	C₂₉×#121	C₂³	1	2	yes	—
230	C₂₉×#121	C₂³	1	2	yes	—
231	C₂₉×#121	C₂³	1	2	yes	—
232	C₂₉×#121	C₂³	1	1	yes	characteristic
233	C₂₉×#121	C₂³	1	1	yes	characteristic
234	C₂₉×#120	—	2	1	no	—
235	C₂₉×#120	—	2	2	no	—
236	C₂₉×#120	D₄	1	2	yes	—
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	C₂³	1	2	yes	—
241	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
242	C₄×D₄×C₂₉	—	2	1	no	—
243	C₄×D₄×C₂₉	—	2	2	no	—
244	C₄×D₄×C₂₉	—	2	2	no	—
245	C₄×D₄×C₂₉	—	2	2	no	—
246	C₄×D₄×C₂₉	—	2	1	no	—
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	2	no	—
251	C₄×D₄×C₂₉	—	2	2	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	C₄×D₄×C₂₉	C₂³	1	2	yes	—
257	C₄×D₄×C₂₉	C₂³	1	2	yes	—
258	C₂₉×#117	—	2	1	no	—
259	C₂₉×#117	—	2	1	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	C₂³	1	1	yes	characteristic
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	2	yes	—
273	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
274	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
275	C₂×C₂²⋊C₄×C₂₉	—	2	2	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	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	1	yes	characteristic
300	C₂₉×#103	C₂³	1	1	yes	characteristic
301	C₂₉×#103	C₂³	1	2	yes	—
302	C₂₉×#103	C₂³	1	2	yes	—
303	C₂₉×#103	C₂³	1	2	yes	—
304	C₂₉×#103	C₂³	1	2	yes	—
305	C₂₉×#103	C₂³	1	2	yes	—
306	C₂₉×#102	C₂³	1	2	yes	—
307	C₂₉×#102	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	—	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	4	no	—
326	#41×C₂₉	—	2	2	no	—
327	#41×C₂₉	—	2	2	no	—
328	#41×C₂₉	—	4	2	no	—
329	#41×C₂₉	—	4	8	no	—
330	#41×C₂₉	—	4	4	no	—
331	#41×C₂₉	—	8	4	no	—
332	C₂×Q₈×C₂₉	—	2	1	no	—
333	C₂×Q₈×C₂₉	—	2	2	no	—
334	C₂×Q₈×C₂₉	—	2	2	no	—
335	C₂×Q₈×C₂₉	—	2	1	no	—
336	C₂×Q₈×C₂₉	—	2	2	no	—
337	C₂×Q₈×C₂₉	—	2	2	no	—
338	C₂×Q₈×C₂₉	—	2	2	no	—
339	C₂×Q₈×C₂₉	—	2	4	no	—
340	C₂×Q₈×C₂₉	—	2	4	no	—
341	C₂×Q₈×C₂₉	—	2	4	no	—
342	C₂×Q₈×C₂₉	—	2	2	no	—
343	C₂×Q₈×C₂₉	—	2	2	no	—
344	C₂×Q₈×C₂₉	—	4	4	no	—
345	C₂×Q₈×C₂₉	—	4	2	no	—
346	C₂×Q₈×C₂₉	—	4	2	no	—
347	C₂×Q₈×C₂₉	—	4	2	no	—
348	C₂×Q₈×C₂₉	—	4	4	no	—
349	C₂×Q₈×C₂₉	—	4	4	no	—
350	C₂×Q₈×C₂₉	—	4	4	no	—
351	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
352	C₂×Q₈×C₂₉	#41	1	4	yes	complemented
353	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
354	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
355	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
356	C₂×D₄×C₂₉	—	2	1	no	—
357	C₂×D₄×C₂₉	—	2	1	no	—
358	C₂×D₄×C₂₉	—	2	2	no	—
359	C₂×D₄×C₂₉	—	2	1	no	—
360	C₂×D₄×C₂₉	—	2	2	no	—
361	C₂×D₄×C₂₉	—	2	2	no	—
362	C₂×D₄×C₂₉	—	2	2	no	—
363	C₂×D₄×C₂₉	—	2	2	no	—
364	C₂×D₄×C₂₉	—	2	1	no	—
365	C₂×D₄×C₂₉	—	2	2	no	—
366	C₂×D₄×C₂₉	—	2	2	no	—
367	C₂×D₄×C₂₉	—	8	2	no	—
368	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
369	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
370	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
371	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
372	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
373	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₂₉	—	2	1	no	—
375	C₂²×C₄×C₂₉	—	2	2	no	—
376	C₂²×C₄×C₂₉	—	2	2	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	2	no	—
381	C₂²×C₄×C₂₉	—	2	1	no	—
382	C₂²×C₄×C₂₉	—	2	1	no	—
383	C₂²×C₄×C₂₉	—	2	1	no	—
384	C₂²×C₄×C₂₉	—	2	2	no	—
385	C₂²×C₄×C₂₉	—	2	2	no	—
386	C₂²×C₄×C₂₉	—	2	1	no	—
387	C₂²×C₄×C₂₉	—	2	2	no	—
388	C₂²×C₄×C₂₉	—	2	2	no	—
389	C₂²×C₄×C₂₉	—	4	4	no	—
390	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
395	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
397	SD₁₆×C₂₉	—	2	4	no	—
398	SD₁₆×C₂₉	—	2	4	no	—
399	SD₁₆×C₂₉	—	4	2	no	—
400	SD₁₆×C₂₉	—	4	2	no	—
401	SD₁₆×C₂₉	—	4	2	no	—
402	D₈×C₂₉	—	4	2	no	—
403	M₁₆×C₂₉	—	2	2	no	—
404	M₁₆×C₂₉	—	2	2	no	—
405	M₁₆×C₂₉	—	4	2	no	—
406	M₁₆×C₂₉	—	4	2	no	—
407	C₂×C₈×C₂₉	—	2	2	no	—
408	C₂×C₈×C₂₉	—	2	2	no	—
409	C₂×C₈×C₂₉	—	4	2	no	—
410	C₂×C₈×C₂₉	—	4	2	no	—
411	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
412	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
413	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
414	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
415	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
416	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₂₉	—	2	1	no	—
418	C₄⋊C₄×C₂₉	—	2	1	no	—
419	C₄⋊C₄×C₂₉	—	2	1	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	2	no	—
427	C₄⋊C₄×C₂₉	—	2	2	no	—
428	C₄⋊C₄×C₂₉	—	2	2	no	—
429	C₄⋊C₄×C₂₉	—	2	2	no	—
430	C₄⋊C₄×C₂₉	—	2	1	no	—
431	C₄⋊C₄×C₂₉	—	2	1	no	—
432	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
433	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
434	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
435	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
436	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
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	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
442	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
443	C₂²⋊C₄×C₂₉	—	2	1	no	—
444	C₂²⋊C₄×C₂₉	—	2	1	no	—
445	C₂²⋊C₄×C₂₉	—	2	1	no	—
446	C₂²⋊C₄×C₂₉	—	2	1	no	—
447	C₂²⋊C₄×C₂₉	—	2	1	no	—
448	C₂²⋊C₄×C₂₉	—	2	2	no	—
449	C₂²⋊C₄×C₂₉	—	2	1	no	—
450	C₂²⋊C₄×C₂₉	—	2	1	no	—
451	C₂²⋊C₄×C₂₉	—	2	2	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	2	no	—
458	C₂²⋊C₄×C₂₉	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
464	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
465	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
466	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
467	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
468	C₄²×C₂₉	—	2	1	no	—
469	C₄²×C₂₉	—	2	1	no	—
470	C₄²×C₂₉	—	2	1	no	—
471	C₄²×C₂₉	—	2	1	no	—
472	C₄²×C₂₉	—	2	2	no	—
473	C₄²×C₂₉	—	2	2	no	—
474	C₄²×C₂₉	—	2	2	no	—
475	C₄²×C₂₉	—	2	1	no	—
476	C₄²×C₂₉	C₂⁴	1	2	yes	—
477	#61185	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
478	C₂³×C₂₉	—	2	2	no	—
479	C₂³×C₂₉	—	2	2	no	—
480	C₂³×C₂₉	—	2	1	no	—
481	C₂³×C₂₉	—	2	2	no	—
482	C₂³×C₂₉	—	4	1	no	—
483	C₂³×C₂₉	—	4	2	no	—
484	C₂³×C₂₉	—	8	1	no	—
485	C₂³×C₂₉	—	8	1	no	—
486	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
487	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
488	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
489	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
490	Q₈×C₂₉	—	2	4	no	—
491	Q₈×C₂₉	—	2	2	no	—
492	Q₈×C₂₉	—	2	2	no	—
493	Q₈×C₂₉	—	2	2	no	—
494	Q₈×C₂₉	—	2	1	no	—
495	Q₈×C₂₉	—	2	2	no	—
496	Q₈×C₂₉	—	2	1	no	—
497	Q₈×C₂₉	—	4	4	no	—
498	Q₈×C₂₉	—	4	4	no	—
499	Q₈×C₂₉	—	4	4	no	—
500	Q₈×C₂₉	—	4	2	no	—
501	Q₈×C₂₉	—	8	2	no	—
502	Q₈×C₂₉	C₂×#41	1	4	yes	—
503	D₄×C₂₉	—	2	4	no	—
504	D₄×C₂₉	—	2	4	no	—
505	D₄×C₂₉	—	2	2	no	—
506	D₄×C₂₉	—	2	2	no	—
507	D₄×C₂₉	—	2	1	no	—
508	D₄×C₂₉	—	2	1	no	—
509	D₄×C₂₉	—	2	2	no	—
510	D₄×C₂₉	—	4	2	no	—
511	D₄×C₂₉	—	4	4	no	—
512	D₄×C₂₉	—	4	2	no	—
513	D₄×C₂₉	—	4	2	no	—
514	D₄×C₂₉	—	4	2	no	—
515	D₄×C₂₉	—	4	4	no	—
516	D₄×C₂₉	—	4	2	no	—
517	D₄×C₂₉	—	8	2	no	—
518	D₄×C₂₉	—	8	2	no	—
519	D₄×C₂₉	—	8	2	no	—
520	C₂×C₄×C₂₉	—	2	2	no	—
521	C₂×C₄×C₂₉	—	2	4	no	—
522	C₂×C₄×C₂₉	—	2	2	no	—
523	C₂×C₄×C₂₉	—	2	2	no	—
524	C₂×C₄×C₂₉	—	2	2	no	—
525	C₂×C₄×C₂₉	—	2	1	no	—
526	C₂×C₄×C₂₉	—	2	1	no	—
527	C₂×C₄×C₂₉	—	2	2	no	—
528	C₂×C₄×C₂₉	—	2	1	no	—
529	C₂×C₄×C₂₉	—	2	2	no	—
530	C₂×C₄×C₂₉	—	2	1	no	—
531	C₂×C₄×C₂₉	—	2	1	no	—
532	C₂×C₄×C₂₉	—	2	1	no	—
533	C₂×C₄×C₂₉	—	2	1	no	—
534	C₂×C₄×C₂₉	—	2	1	no	—
535	C₂×C₄×C₂₉	—	2	1	no	—
536	C₂×C₄×C₂₉	—	2	1	no	—
537	C₂×C₄×C₂₉	—	2	2	no	—
538	C₂×C₄×C₂₉	—	2	2	no	—
539	C₂×C₄×C₂₉	—	2	1	no	—
540	C₂×C₄×C₂₉	—	4	4	no	—
541	C₂×C₄×C₂₉	—	4	4	no	—
542	C₂×C₄×C₂₉	—	4	4	no	—
543	C₂×C₄×C₂₉	—	4	4	no	—
544	C₂×C₄×C₂₉	—	4	2	no	—
545	C₂×C₄×C₂₉	—	4	2	no	—
546	C₂×C₄×C₂₉	—	4	2	no	—
547	C₂×C₄×C₂₉	—	8	2	no	—
548	C₂×C₄×C₂₉	—	8	2	no	—
549	C₂×C₄×C₂₉	—	8	1	no	—
550	C₂×C₄×C₂₉	—	8	1	no	—
551	C₂×C₄×C₂₉	—	8	2	no	—
552	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
554	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
555	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
556	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
559	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
560	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
561	C₈×C₂₉	—	2	1	no	—
562	C₈×C₂₉	—	2	1	no	—
563	C₈×C₂₉	—	2	1	no	—
564	C₈×C₂₉	—	2	1	no	—
565	C₈×C₂₉	—	2	2	no	—
566	C₈×C₂₉	—	2	2	no	—
567	#3494	C₂×C₂₉	1	1	yes	characteristic, complemented
568	#3486	C₂×C₂₉	1	1	yes	characteristic, complemented
569	#3329	C₂×C₂₉	1	2	yes	complemented
570	#3326	C₂×C₂₉	1	2	yes	complemented
571	#3321	C₂×C₂₉	1	2	yes	complemented
572	#3320	C₂×C₂₉	1	2	yes	complemented
573	#3320	C₂×C₂₉	1	2	yes	complemented
574	#3308	C₂×C₂₉	1	2	yes	complemented
575	#3301	C₂×C₂₉	1	2	yes	complemented
576	#3298	C₂×C₂₉	1	2	yes	complemented
577	#3137	C₂×C₂₉	1	1	yes	characteristic, complemented
578	#3097	C₂×C₂₉	1	1	yes	characteristic, complemented
579	#3091	C₂×C₂₉	1	1	yes	characteristic, complemented
580	#3082	C₂×C₂₉	1	1	yes	characteristic, complemented
581	#3057	C₂×C₂₉	1	1	yes	characteristic, complemented
582	#3055	C₂×C₂₉	1	1	yes	characteristic, complemented
583	#3042	C₂×C₂₉	1	1	yes	characteristic, complemented
584	#3010	C₂×C₂₉	1	1	yes	characteristic, complemented
585	C₂×#448	C₂×C₂₉	1	1	yes	characteristic, complemented
586	#2949	C₂×C₂₉	1	1	yes	characteristic, complemented
587	#2933	C₂×C₂₉	1	1	yes	characteristic, complemented
588	#2898	C₂×C₂₉	1	1	yes	characteristic, complemented
589	C₂×#419	C₂×C₂₉	1	1	yes	characteristic, complemented
590	C₂²×C₂₉	—	2	1	no	—
591	C₂²×C₂₉	—	2	1	no	—
592	C₂²×C₂₉	—	2	1	no	—
593	C₂²×C₂₉	—	2	1	no	—
594	C₂²×C₂₉	—	2	1	no	—
595	C₂²×C₂₉	—	2	2	no	—
596	C₂²×C₂₉	—	2	1	no	—
597	C₂²×C₂₉	—	2	2	no	—
598	C₂²×C₂₉	—	2	2	no	—
599	C₂²×C₂₉	—	2	1	no	—
600	C₂²×C₂₉	—	4	4	no	—
601	C₂²×C₂₉	—	4	2	no	—
602	C₂²×C₂₉	—	4	1	no	—
603	C₂²×C₂₉	—	4	1	no	—
604	C₂²×C₂₉	—	4	2	no	—
605	C₂²×C₂₉	—	4	2	no	—
606	C₂²×C₂₉	—	4	1	no	—
607	C₂²×C₂₉	—	16	2	no	—
608	C₂²×C₂₉	#546	1	2	yes	—
609	C₂²×C₂₉	#577	1	2	yes	—
610	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
611	C₄×C₂₉	—	2	2	no	—
612	C₄×C₂₉	—	2	1	no	—
613	C₄×C₂₉	—	2	1	no	—
614	C₄×C₂₉	—	2	4	no	—
615	C₄×C₂₉	—	2	2	no	—
616	C₄×C₂₉	—	2	2	no	—
617	C₄×C₂₉	—	4	1	no	—
618	C₄×C₂₉	—	4	1	no	—
619	C₄×C₂₉	—	4	1	no	—
620	C₄×C₂₉	—	4	1	no	—
621	C₄×C₂₉	—	4	2	no	—
622	C₄×C₂₉	—	4	1	no	—
623	C₄×C₂₉	—	4	1	no	—
624	C₄×C₂₉	—	4	2	no	—
625	C₄×C₂₉	—	4	1	no	—
626	C₄×C₂₉	#546	1	2	yes	—
627	C₄×C₂₉	C₂²×#41	1	1	yes	characteristic
628	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
629	C₂×2₋¹⁺⁴	C₂²×C₂₉	1	1	yes	characteristic
630	C₂³×Q₈	C₂²×C₂₉	1	1	yes	characteristic
631	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	1	yes	characteristic
632	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
633	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
634	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
635	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
636	#555	C₂²×C₂₉	1	2	yes	—
637	#553	C₂²×C₂₉	1	2	yes	—
638	#553	C₂²×C₂₉	1	2	yes	—
639	#551	—	2	2	no	—
640	D₄×Q₈	—	2	1	no	—
641	D₄×Q₈	—	2	1	no	—
642	D₄×Q₈	C₂²×C₂₉	1	2	yes	complemented
643	D₄×Q₈	C₂²×C₂₉	1	2	yes	complemented
644	#548	—	2	1	no	—
645	#548	—	2	1	no	—
646	#548	C₂²×C₂₉	1	2	yes	complemented
647	#548	C₂²×C₂₉	1	2	yes	complemented
648	#547	C₂²×C₂₉	1	2	yes	—
649	#546	—	2	2	no	—
650	#544	C₂²×C₂₉	1	1	yes	characteristic
651	#542	—	2	1	no	—
652	#540	—	2	1	no	—
653	#536	—	2	2	no	—
654	#536	C₂²×C₂₉	1	1	yes	characteristic
655	#536	C₂²×C₂₉	1	1	yes	characteristic
656	#535	C₂²×C₂₉	1	1	yes	characteristic
657	#532	—	2	1	no	—
658	#529	—	2	1	no	—
659	#525	—	2	2	no	—
660	#525	C₂²×C₂₉	1	1	yes	characteristic
661	#525	C₂²×C₂₉	1	1	yes	characteristic
662	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic
663	#520	C₂²×C₂₉	1	1	yes	characteristic
664	#519	C₂²×C₂₉	1	1	yes	characteristic
665	#518	C₂²×C₂₉	1	1	yes	characteristic
666	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
667	#491	C₂²×C₂₉	1	2	yes	complemented
668	#489	C₂²×C₂₉	1	2	yes	complemented
669	#488	C₂²×C₂₉	1	2	yes	complemented
670	#487	C₂²×C₂₉	1	2	yes	complemented
671	#485	C₂²×C₂₉	1	1	yes	characteristic, complemented
672	#485	C₂²×C₂₉	1	2	yes	complemented
673	#485	C₂²×C₂₉	1	1	yes	characteristic, complemented
674	#485	C₂²×C₂₉	1	2	yes	complemented
675	#484	C₂²×C₂₉	1	1	yes	characteristic, complemented
676	#484	C₂²×C₂₉	1	2	yes	complemented
677	#483	C₂²×C₂₉	1	1	yes	characteristic, complemented
678	#483	C₂²×C₂₉	1	2	yes	complemented
679	#482	C₂²×C₂₉	1	1	yes	characteristic, complemented
680	#482	C₂²×C₂₉	1	1	yes	characteristic, complemented
681	#481	C₂²×C₂₉	1	1	yes	characteristic, complemented
682	#480	C₂²×C₂₉	1	1	yes	characteristic, complemented
683	#479	C₂²×C₂₉	1	2	yes	complemented
684	#479	C₂²×C₂₉	1	2	yes	complemented
685	#477	C₂²×C₂₉	1	2	yes	complemented
686	#475	C₂²×C₂₉	1	2	yes	complemented
687	#469	C₂²×C₂₉	1	2	yes	—
688	#468	C₂²×C₂₉	1	2	yes	—
689	#468	C₂²×C₂₉	1	2	yes	complemented
690	#468	C₂²×C₂₉	1	2	yes	complemented
691	#466	C₂²×C₂₉	1	2	yes	—
692	#465	C₂²×C₂₉	1	2	yes	—
693	#465	C₂²×C₂₉	1	2	yes	complemented
694	#465	C₂²×C₂₉	1	2	yes	complemented
695	#463	C₂²×C₂₉	1	2	yes	complemented
696	#463	C₂²×C₂₉	1	2	yes	complemented
697	#461	C₂²×C₂₉	1	2	yes	complemented
698	#461	C₂²×C₂₉	1	2	yes	complemented
699	#449	C₂²×C₂₉	1	2	yes	complemented
700	#449	C₂²×C₂₉	1	2	yes	complemented
701	#448	C₂²×C₂₉	1	2	yes	—
702	#448	C₂²×C₂₉	1	2	yes	—
703	#448	C₂²×C₂₉	1	2	yes	—
704	#448	C₂²×C₂₉	1	2	yes	—
705	#448	C₂²×C₂₉	1	2	yes	complemented
706	#448	C₂²×C₂₉	1	2	yes	complemented
707	#440	C₂²×C₂₉	1	2	yes	complemented
708	#440	C₂²×C₂₉	1	2	yes	complemented
709	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
710	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
711	#436	C₂²×C₂₉	1	2	yes	complemented
712	#435	C₂²×C₂₉	1	2	yes	complemented
713	#435	C₂²×C₂₉	1	2	yes	complemented
714	C₈×D₄	C₂²×C₂₉	1	2	yes	complemented
715	#428	C₂²×C₂₉	1	1	yes	characteristic
716	#427	C₂²×C₂₉	1	1	yes	characteristic
717	#427	C₂²×C₂₉	1	1	yes	characteristic
718	#424	C₂²×C₂₉	1	1	yes	characteristic
719	#419	C₂²×C₂₉	1	1	yes	characteristic
720	#419	C₂²×C₂₉	1	1	yes	characteristic
721	#419	C₂²×C₂₉	1	1	yes	characteristic
722	#419	C₂²×C₂₉	1	1	yes	characteristic
723	#419	C₂²×C₂₉	1	2	yes	complemented
724	#419	C₂²×C₂₉	1	2	yes	complemented
725	#419	C₂²×C₂₉	1	2	yes	complemented
726	#418	C₂²×C₂₉	1	1	yes	characteristic
727	#417	C₂²×C₂₉	1	1	yes	characteristic
728	#417	C₂²×C₂₉	1	2	yes	complemented
729	#416	C₂²×C₂₉	1	1	yes	characteristic
730	#416	C₂²×C₂₉	1	1	yes	characteristic
731	#416	C₂²×C₂₉	1	2	yes	complemented
732	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
733	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
734	C₂×#103	C₂²×C₂₉	1	2	yes	complemented
735	C₂×#103	C₂²×C₂₉	1	2	yes	complemented
736	C₂×#103	C₂²×C₂₉	1	2	yes	complemented
737	#408	C₂²×C₂₉	1	1	yes	characteristic
738	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
739	#405	C₂²×C₂₉	1	1	yes	characteristic
740	C₂×C₂₉	—	2	2	no	—
741	C₂×C₂₉	—	2	2	no	—
742	C₂×C₂₉	—	4	2	no	—
743	C₂×C₂₉	—	4	1	no	—
744	C₂×C₂₉	—	8	1	no	—
745	C₂×C₂₉	—	8	2	no	—
746	C₂×C₂₉	C₂×#546	1	1	yes	characteristic
747	C₂×C₂₉	C₂×#577	1	1	yes	characteristic
748	C₂×C₂₉	#3586	1	1	yes	characteristic
749	2₋¹⁺⁴	—	2	4	no	—
750	2₋¹⁺⁴	—	4	2	no	—
751	C₂×#41	—	2	2	no	—
752	C₂×#41	—	2	1	no	—
753	C₂×#41	—	2	2	no	—
754	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
755	C₂×#41	C₂³×C₂₉	1	2	yes	—
756	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
757	C₂²×Q₈	—	2	1	no	—
758	C₂²×Q₈	—	2	1	no	—
759	C₂²×Q₈	—	2	1	no	—
760	C₂²×Q₈	—	2	1	no	—
761	C₂²×Q₈	—	2	4	no	—
762	C₂²×Q₈	—	4	2	no	—
763	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
764	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
765	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
766	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
767	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
768	C₂²×D₄	—	2	1	no	—
769	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
770	C₂³×C₄	—	2	1	no	—
771	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
772	AGL(1,ℤ/8)	—	4	2	no	—
773	C₂×SD₁₆	—	2	4	no	—
774	C₂×SD₁₆	—	4	2	no	—
775	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
776	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
777	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
778	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
779	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
780	C₂×D₈	C₂³×C₂₉	1	2	yes	—
781	#131	—	4	2	no	—
782	C₂×M₁₆	—	4	2	no	—
783	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
784	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
785	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
786	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
787	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
788	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
789	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
790	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
791	C₄⋊Q₈	—	2	1	no	—
792	C₄⋊Q₈	—	2	1	no	—
793	C₄⋊Q₈	—	2	2	no	—
794	C₄⋊Q₈	—	2	2	no	—
795	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
796	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
797	#127	—	2	1	no	—
798	#126	—	2	2	no	—
799	#126	—	2	2	no	—
800	#125	—	2	1	no	—
801	#125	C₂³×C₂₉	1	2	yes	—
802	#124	—	2	1	no	—
803	#124	—	2	1	no	—
804	#124	—	2	2	no	—
805	#124	—	2	2	no	—
806	#124	—	2	2	no	—
807	#124	—	2	2	no	—
808	#124	C₂³×C₂₉	1	2	yes	—
809	#123	—	2	2	no	—
810	#123	—	2	1	no	—
811	#123	—	2	2	no	—
812	#123	—	2	2	no	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	#123	D₄×C₂₉	1	2	yes	—
817	C₂²⋊Q₈	—	2	2	no	—
818	C₂²⋊Q₈	—	2	2	no	—
819	C₂²⋊Q₈	—	2	1	no	—
820	C₂²⋊Q₈	—	2	1	no	—
821	C₂²⋊Q₈	—	2	2	no	—
822	C₂²⋊Q₈	—	2	2	no	—
823	C₂²⋊Q₈	—	2	2	no	—
824	C₂²⋊Q₈	—	2	2	no	—
825	C₂²⋊Q₈	—	2	2	no	—
826	C₂²⋊Q₈	—	2	2	no	—
827	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
828	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
829	C₂²⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
830	C₂²⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
831	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
832	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
833	#121	—	2	2	no	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	—	2	2	no	—
837	#121	—	2	2	no	—
838	#121	—	2	1	no	—
839	#121	—	2	1	no	—
840	#121	D₄×C₂₉	1	1	yes	characteristic
841	#121	D₄×C₂₉	1	1	yes	characteristic
842	#121	C₂³×C₂₉	1	2	yes	—
843	#121	C₂³×C₂₉	1	2	yes	—
844	#121	C₂³×C₂₉	1	1	yes	characteristic
845	#121	C₂³×C₂₉	1	1	yes	characteristic
846	#121	C₂³×C₂₉	1	2	yes	—
847	#121	C₂³×C₂₉	1	2	yes	—
848	#120	—	2	1	no	—
849	#120	—	2	2	no	—
850	#120	D₄×C₂₉	1	2	yes	—
851	C₄×Q₈	—	2	1	no	—
852	C₄×Q₈	—	2	1	no	—
853	C₄×Q₈	—	2	1	no	—
854	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
855	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
856	C₄×D₄	—	2	1	no	—
857	C₄×D₄	—	2	2	no	—
858	C₄×D₄	—	2	2	no	—
859	C₄×D₄	—	2	2	no	—
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	—	2	1	no	—
862	C₄×D₄	—	2	1	no	—
863	C₄×D₄	—	2	1	no	—
864	C₄×D₄	—	2	2	no	—
865	C₄×D₄	—	2	2	no	—
866	C₄×D₄	—	2	2	no	—
867	C₄×D₄	—	2	2	no	—
868	C₄×D₄	C₂³×C₂₉	1	2	yes	—
869	C₄×D₄	C₂³×C₂₉	1	2	yes	—
870	C₄×D₄	C₂³×C₂₉	1	2	yes	—
871	C₄×D₄	C₂³×C₂₉	1	2	yes	—
872	#117	—	2	1	no	—
873	#117	—	2	1	no	—
874	#117	—	2	2	no	—
875	#117	—	2	2	no	—
876	#117	C₂³×C₂₉	1	1	yes	characteristic
877	#117	C₂³×C₂₉	1	1	yes	characteristic
878	#117	C₂³×C₂₉	1	1	yes	characteristic
879	#117	C₂³×C₂₉	1	1	yes	characteristic
880	#117	C₂³×C₂₉	1	1	yes	characteristic
881	#117	C₂³×C₂₉	1	2	yes	—
882	#117	C₂³×C₂₉	1	1	yes	characteristic
883	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
884	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
885	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
886	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
887	C₂×C₂²⋊C₄	—	2	1	no	—
888	C₂×C₂²⋊C₄	—	2	1	no	—
889	C₂×C₂²⋊C₄	—	2	2	no	—
890	C₂×C₄²	—	2	1	no	—
891	#107	C₂³×C₂₉	1	1	yes	characteristic
892	#107	C₂³×C₂₉	1	1	yes	characteristic
893	#107	C₂³×C₂₉	1	1	yes	characteristic
894	#107	C₂³×C₂₉	1	1	yes	characteristic
895	#107	C₂³×C₂₉	1	2	yes	—
896	#106	C₂³×C₂₉	1	1	yes	characteristic
897	#106	C₂³×C₂₉	1	1	yes	characteristic
898	#106	C₂³×C₂₉	1	1	yes	characteristic
899	#106	C₂³×C₂₉	1	1	yes	characteristic
900	#106	C₂³×C₂₉	1	2	yes	—
901	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
902	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
903	#103	C₂³×C₂₉	1	2	yes	—
904	#103	C₂³×C₂₉	1	2	yes	—
905	#103	C₂³×C₂₉	1	2	yes	—
906	#103	C₂³×C₂₉	1	2	yes	—
907	#103	C₂³×C₂₉	1	1	yes	characteristic
908	#103	C₂³×C₂₉	1	2	yes	—
909	#103	C₂³×C₂₉	1	2	yes	—
910	#103	C₂³×C₂₉	1	2	yes	—
911	#103	C₂³×C₂₉	1	2	yes	—
912	#103	C₂³×C₂₉	1	2	yes	—
913	#103	C₂³×C₂₉	1	2	yes	—
914	#103	C₂³×C₂₉	1	2	yes	—
915	#103	C₂³×C₂₉	1	2	yes	—
916	#103	C₂³×C₂₉	1	2	yes	—
917	#103	C₂³×C₂₉	1	1	yes	characteristic
918	#103	C₂³×C₂₉	1	1	yes	characteristic
919	#103	C₂³×C₂₉	1	1	yes	characteristic
920	#102	C₂³×C₂₉	1	1	yes	characteristic
921	#102	C₂³×C₂₉	1	1	yes	characteristic
922	#102	C₂³×C₂₉	1	1	yes	characteristic
923	#102	C₂³×C₂₉	1	1	yes	characteristic
924	#102	C₂³×C₂₉	1	2	yes	—
925	#102	C₂³×C₂₉	1	2	yes	—
926	#102	C₂³×C₂₉	1	2	yes	—
927	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
928	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
929	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
930	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
931	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
932	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
933	#97	C₂³×C₂₉	1	2	yes	—
934	C₄×C₈	C₂³×C₂₉	1	2	yes	—
935	C₂₉	#61185	1	1	yes	characteristic, direct product factor, Sylow
936	C₂⁴	—	2	1	no	—
937	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
938	#41	—	2	2	no	—
939	#41	—	2	2	no	—
940	#41	—	2	4	no	—
941	#41	—	2	2	no	—
942	#41	—	2	2	no	—
943	#41	—	4	2	no	—
944	#41	—	4	8	no	—
945	#41	—	4	4	no	—
946	#41	—	8	4	no	—
947	C₂×Q₈	—	2	1	no	—
948	C₂×Q₈	—	2	2	no	—
949	C₂×Q₈	—	2	2	no	—
950	C₂×Q₈	—	2	1	no	—
951	C₂×Q₈	—	2	2	no	—
952	C₂×Q₈	—	2	2	no	—
953	C₂×Q₈	—	2	2	no	—
954	C₂×Q₈	—	2	4	no	—
955	C₂×Q₈	—	2	4	no	—
956	C₂×Q₈	—	2	4	no	—
957	C₂×Q₈	—	2	2	no	—
958	C₂×Q₈	—	2	2	no	—
959	C₂×Q₈	—	4	4	no	—
960	C₂×Q₈	—	4	2	no	—
961	C₂×Q₈	—	4	2	no	—
962	C₂×Q₈	—	4	2	no	—
963	C₂×Q₈	—	4	4	no	—
964	C₂×Q₈	—	4	4	no	—
965	C₂×Q₈	—	4	4	no	—
966	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
967	C₂×Q₈	#41×C₂₉	1	4	yes	complemented
968	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
969	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
970	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
971	C₂×D₄	—	2	1	no	—
972	C₂×D₄	—	2	1	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	1	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	—	2	2	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	2	no	—
981	C₂×D₄	—	2	2	no	—
982	C₂×D₄	—	8	2	no	—
983	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
984	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
985	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
986	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
987	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
988	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
989	C₂²×C₄	—	2	1	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	2	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	1	no	—
999	C₂²×C₄	—	2	2	no	—
1000	C₂²×C₄	—	2	2	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	2	no	—
1004	C₂²×C₄	—	4	4	no	—
1005	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1006	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1007	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1008	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1009	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
1010	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1011	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1012	SD₁₆	—	2	4	no	—
1013	SD₁₆	—	2	4	no	—
1014	SD₁₆	—	4	2	no	—
1015	SD₁₆	—	4	2	no	—
1016	SD₁₆	—	4	2	no	—
1017	D₈	—	4	2	no	—
1018	M₁₆	—	2	2	no	—
1019	M₁₆	—	2	2	no	—
1020	M₁₆	—	4	2	no	—
1021	M₁₆	—	4	2	no	—
1022	C₂×C₈	—	2	2	no	—
1023	C₂×C₈	—	2	2	no	—
1024	C₂×C₈	—	4	2	no	—
1025	C₂×C₈	—	4	2	no	—
1026	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1027	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
1028	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1029	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1030	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
1031	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	2	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	2	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	2	no	—
1044	C₄⋊C₄	—	2	2	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1048	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1049	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1050	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1051	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1052	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1053	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1054	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
1055	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1056	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1057	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	1	no	—
1060	C₂²⋊C₄	—	2	1	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	2	no	—
1075	C₂²⋊C₄	—	2	2	no	—
1076	C₂²⋊C₄	—	2	1	no	—
1077	C₂²⋊C₄	—	2	1	no	—
1078	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1079	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1080	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1081	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1082	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1083	C₄²	—	2	1	no	—
1084	C₄²	—	2	1	no	—
1085	C₄²	—	2	1	no	—
1086	C₄²	—	2	1	no	—
1087	C₄²	—	2	2	no	—
1088	C₄²	—	2	2	no	—
1089	C₄²	—	2	2	no	—
1090	C₄²	—	2	1	no	—
1091	C₄²	C₂⁴×C₂₉	1	2	yes	—
1092	C₂³	—	2	2	no	—
1093	C₂³	—	2	2	no	—
1094	C₂³	—	2	1	no	—
1095	C₂³	—	2	2	no	—
1096	C₂³	—	4	1	no	—
1097	C₂³	—	4	2	no	—
1098	C₂³	—	8	1	no	—
1099	C₂³	—	8	1	no	—
1100	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1101	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
1102	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1103	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1104	Q₈	—	2	4	no	—
1105	Q₈	—	2	2	no	—
1106	Q₈	—	2	2	no	—
1107	Q₈	—	2	2	no	—
1108	Q₈	—	2	1	no	—
1109	Q₈	—	2	2	no	—
1110	Q₈	—	2	1	no	—
1111	Q₈	—	4	4	no	—
1112	Q₈	—	4	4	no	—
1113	Q₈	—	4	4	no	—
1114	Q₈	—	4	2	no	—
1115	Q₈	—	8	2	no	—
1116	Q₈	C₂×#41×C₂₉	1	4	yes	—
1117	D₄	—	2	4	no	—
1118	D₄	—	2	4	no	—
1119	D₄	—	2	2	no	—
1120	D₄	—	2	2	no	—
1121	D₄	—	2	1	no	—
1122	D₄	—	2	1	no	—
1123	D₄	—	2	2	no	—
1124	D₄	—	4	2	no	—
1125	D₄	—	4	4	no	—
1126	D₄	—	4	2	no	—
1127	D₄	—	4	2	no	—
1128	D₄	—	4	4	no	—
1129	D₄	—	4	2	no	—
1130	D₄	—	4	2	no	—
1131	D₄	—	8	2	no	—
1132	D₄	—	8	2	no	—
1133	D₄	—	8	2	no	—
1134	C₂×C₄	—	2	2	no	—
1135	C₂×C₄	—	2	4	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	2	no	—
1152	C₂×C₄	—	2	2	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	4	4	no	—
1155	C₂×C₄	—	4	4	no	—
1156	C₂×C₄	—	4	4	no	—
1157	C₂×C₄	—	4	4	no	—
1158	C₂×C₄	—	4	2	no	—
1159	C₂×C₄	—	4	2	no	—
1160	C₂×C₄	—	4	2	no	—
1161	C₂×C₄	—	8	2	no	—
1162	C₂×C₄	—	8	2	no	—
1163	C₂×C₄	—	8	1	no	—
1164	C₂×C₄	—	8	2	no	—
1165	C₂×C₄	—	8	1	no	—
1166	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1167	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1168	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1169	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1170	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1171	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1172	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
1173	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
1174	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1175	C₈	—	2	1	no	—
1176	C₈	—	2	1	no	—
1177	C₈	—	2	1	no	—
1178	C₈	—	2	1	no	—
1179	C₈	—	2	2	no	—
1180	C₈	—	2	2	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	2	1	no	—
1184	C₂²	—	2	1	no	—
1185	C₂²	—	2	1	no	—
1186	C₂²	—	2	2	no	—
1187	C₂²	—	2	2	no	—
1188	C₂²	—	2	1	no	—
1189	C₂²	—	2	1	no	—
1190	C₂²	—	2	2	no	—
1191	C₂²	—	4	4	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	2	no	—
1194	C₂²	—	4	2	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	4	2	no	—
1197	C₂²	—	4	1	no	—
1198	C₂²	—	16	2	no	—
1199	C₂²	C₂₉×#546	1	2	yes	—
1200	C₂²	C₂₉×#577	1	2	yes	—
1201	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
1202	C₄	—	2	1	no	—
1203	C₄	—	2	1	no	—
1204	C₄	—	2	4	no	—
1205	C₄	—	2	2	no	—
1206	C₄	—	2	2	no	—
1207	C₄	—	2	2	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	2	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	2	no	—
1213	C₄	—	4	1	no	—
1214	C₄	—	4	1	no	—
1215	C₄	—	4	1	no	—
1216	C₄	—	4	1	no	—
1217	C₄	C₂₉×#546	1	2	yes	—
1218	C₄	C₂²×#41×C₂₉	1	1	yes	characteristic
1219	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
1220	C₂	—	2	2	no	—
1221	C₂	—	2	2	no	—
1222	C₂	—	4	1	no	—
1223	C₂	—	4	2	no	—
1224	C₂	—	8	2	no	—
1225	C₂	—	8	1	no	—
1226	C₂	C₂×C₂₉×#546	1	1	yes	characteristic
1227	C₂	C₂×C₂₉×#577	1	1	yes	characteristic
1228	C₂	C₂₉×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3494	C₂	semidirect
2. C₂₉×#3486	C₂	semidirect
3. C₂₉×#3329	C₂	semidirect
4. C₂₉×#3326	C₂	semidirect
5. C₂₉×#3321	C₂	semidirect
6. C₂₉×#3320	C₂	semidirect
7. C₂₉×#3320	C₂	semidirect
8. C₂₉×#3308	C₂	semidirect
9. C₂₉×#3301	C₂	semidirect
10. C₂₉×#3298	C₂	semidirect
11. C₂₉×#3137	C₂	semidirect
12. C₂₉×#3097	C₂	semidirect
13. C₂₉×#3091	C₂	semidirect
14. C₂₉×#3082	C₂	semidirect
15. C₂₉×#3057	C₂	semidirect
16. C₂₉×#3055	C₂	semidirect
17. C₂₉×#3042	C₂	semidirect
18. C₂₉×#3010	C₂	semidirect
19. C₂×C₂₉×#448	C₂	semidirect
20. C₂₉×#2949	C₂	semidirect
21. C₂₉×#2933	C₂	semidirect
22. C₂₉×#2898	C₂	semidirect
23. C₂×C₂₉×#419	C₂	semidirect
37. D₄×Q₈×C₂₉	C₂²	semidirect
38. D₄×Q₈×C₂₉	C₂²	semidirect
41. C₂₉×#548	C₂²	semidirect
42. C₂₉×#548	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
67. C₂₉×#485	C₂²	semidirect
68. C₂₉×#485	C₂²	semidirect
69. C₂₉×#485	C₂²	semidirect
70. C₂₉×#484	C₂²	semidirect
71. C₂₉×#484	C₂²	semidirect
72. C₂₉×#483	C₂²	semidirect
73. C₂₉×#483	C₂²	semidirect
74. C₂₉×#482	C₂²	semidirect
75. C₂₉×#482	C₂²	semidirect
76. C₂₉×#481	C₂²	semidirect
77. C₂₉×#480	C₂²	semidirect
78. C₂₉×#479	C₂²	semidirect
79. C₂₉×#479	C₂²	semidirect
80. C₂₉×#477	C₂²	semidirect
81. C₂₉×#475	C₂²	semidirect
84. C₂₉×#468	C₂²	semidirect
85. C₂₉×#468	C₂²	semidirect
88. C₂₉×#465	C₂²	semidirect
89. C₂₉×#465	C₂²	semidirect
90. C₂₉×#463	C₂²	semidirect
91. C₂₉×#463	C₂²	semidirect
92. C₂₉×#461	C₂²	semidirect
93. C₂₉×#461	C₂²	semidirect
94. C₂₉×#449	C₂²	semidirect
95. C₂₉×#449	C₂²	semidirect
100. C₂₉×#448	C₂²	semidirect
101. C₂₉×#448	C₂²	semidirect
102. C₂₉×#440	C₂²	semidirect
103. C₂₉×#440	C₂²	semidirect
104. C₄×SD₁₆×C₂₉	C₂²	semidirect
105. C₄×SD₁₆×C₂₉	C₂²	semidirect
106. C₂₉×#436	C₂²	semidirect
107. C₂₉×#435	C₂²	semidirect
108. C₂₉×#435	C₂²	semidirect
109. C₈×D₄×C₂₉	C₂²	semidirect
118. C₂₉×#419	C₂²	semidirect
119. C₂₉×#419	C₂²	semidirect
120. C₂₉×#419	C₂²	semidirect
123. C₂₉×#417	C₂²	semidirect
126. C₂₉×#416	C₂²	semidirect
129. C₂×C₂₉×#103	C₂²	semidirect
130. C₂×C₂₉×#103	C₂²	semidirect
131. C₂×C₂₉×#103	C₂²	semidirect
352. C₂×Q₈×C₂₉	#41	semidirect
477. #61185	C₂₉	direct (N × H)
567. #3494	C₂×C₂₉	semidirect
568. #3486	C₂×C₂₉	semidirect
569. #3329	C₂×C₂₉	semidirect
570. #3326	C₂×C₂₉	semidirect
571. #3321	C₂×C₂₉	semidirect
572. #3320	C₂×C₂₉	semidirect
573. #3320	C₂×C₂₉	semidirect
574. #3308	C₂×C₂₉	semidirect
575. #3301	C₂×C₂₉	semidirect
576. #3298	C₂×C₂₉	semidirect
577. #3137	C₂×C₂₉	semidirect
578. #3097	C₂×C₂₉	semidirect
579. #3091	C₂×C₂₉	semidirect
580. #3082	C₂×C₂₉	semidirect
581. #3057	C₂×C₂₉	semidirect
582. #3055	C₂×C₂₉	semidirect
583. #3042	C₂×C₂₉	semidirect
584. #3010	C₂×C₂₉	semidirect
585. C₂×#448	C₂×C₂₉	semidirect
586. #2949	C₂×C₂₉	semidirect
587. #2933	C₂×C₂₉	semidirect
588. #2898	C₂×C₂₉	semidirect
589. C₂×#419	C₂×C₂₉	semidirect
642. D₄×Q₈	C₂²×C₂₉	semidirect
643. D₄×Q₈	C₂²×C₂₉	semidirect
646. #548	C₂²×C₂₉	semidirect
647. #548	C₂²×C₂₉	semidirect
667. #491	C₂²×C₂₉	semidirect
668. #489	C₂²×C₂₉	semidirect
669. #488	C₂²×C₂₉	semidirect
670. #487	C₂²×C₂₉	semidirect
671. #485	C₂²×C₂₉	semidirect
672. #485	C₂²×C₂₉	semidirect
673. #485	C₂²×C₂₉	semidirect
674. #485	C₂²×C₂₉	semidirect
675. #484	C₂²×C₂₉	semidirect
676. #484	C₂²×C₂₉	semidirect
677. #483	C₂²×C₂₉	semidirect
678. #483	C₂²×C₂₉	semidirect
679. #482	C₂²×C₂₉	semidirect
680. #482	C₂²×C₂₉	semidirect
681. #481	C₂²×C₂₉	semidirect
682. #480	C₂²×C₂₉	semidirect
683. #479	C₂²×C₂₉	semidirect
684. #479	C₂²×C₂₉	semidirect
685. #477	C₂²×C₂₉	semidirect
686. #475	C₂²×C₂₉	semidirect
689. #468	C₂²×C₂₉	semidirect
690. #468	C₂²×C₂₉	semidirect
693. #465	C₂²×C₂₉	semidirect
694. #465	C₂²×C₂₉	semidirect
695. #463	C₂²×C₂₉	semidirect
696. #463	C₂²×C₂₉	semidirect
697. #461	C₂²×C₂₉	semidirect
698. #461	C₂²×C₂₉	semidirect
699. #449	C₂²×C₂₉	semidirect
700. #449	C₂²×C₂₉	semidirect
705. #448	C₂²×C₂₉	semidirect
706. #448	C₂²×C₂₉	semidirect
707. #440	C₂²×C₂₉	semidirect
708. #440	C₂²×C₂₉	semidirect
709. C₄×SD₁₆	C₂²×C₂₉	semidirect
710. C₄×SD₁₆	C₂²×C₂₉	semidirect
711. #436	C₂²×C₂₉	semidirect
712. #435	C₂²×C₂₉	semidirect
713. #435	C₂²×C₂₉	semidirect
714. C₈×D₄	C₂²×C₂₉	semidirect
723. #419	C₂²×C₂₉	semidirect
724. #419	C₂²×C₂₉	semidirect
725. #419	C₂²×C₂₉	semidirect
728. #417	C₂²×C₂₉	semidirect
731. #416	C₂²×C₂₉	semidirect
734. C₂×#103	C₂²×C₂₉	semidirect
735. C₂×#103	C₂²×C₂₉	semidirect
736. C₂×#103	C₂²×C₂₉	semidirect
935. C₂₉	#61185	direct (N × H)
967. C₂×Q₈	#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×#3494	2
C₂₉×#3486	2
C₂₉×#3329	2
C₂₉×#3326	2
C₂₉×#3321	2
C₂₉×#3320	2
C₂₉×#3308	2
C₂₉×#3301	2
C₂₉×#3298	2
C₂₉×#3137	2
C₂₉×#3097	2
C₂₉×#3091	2
C₂₉×#3082	2
C₂₉×#3057	2
C₂₉×#3055	2
C₂₉×#3042	2
C₂₉×#3010	2
C₂×C₂₉×#448	2
C₂₉×#2949	2
C₂₉×#2933	2
C₂₉×#2898	2
C₂×C₂₉×#419	2
#61185	29

Subgroups — C29×#61185 #20356085

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#61185 #20356085