Subgroups — C₂×C₂₉×#3225 #20355696

Order 7424.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3225	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₉×#497	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₉×#495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₉×#489	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₉×#487	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₉×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₉×#462	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₉×#463	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₉×#461	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₉×#452	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₉×#449	C₂	1	1	yes	maximal, characteristic
14	C₂×C₂₉×#451	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₉×#448	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×#433	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₂₉	C₂²	1	1	yes	characteristic
18	C₂³×Q₈×C₂₉	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
20	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
21	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
22	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
23	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
24	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
25	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
26	C₂²×D₈×C₂₉	C₂²	1	1	yes	characteristic
27	C₂₉×#542	—	2	4	no	—
28	C₂₉×#542	C₂²	1	8	yes	complemented
29	C₂₉×#536	—	2	4	no	—
30	C₂₉×#536	C₂²	1	8	yes	complemented
31	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₂₉×#126	—	2	1	no	—
35	C₂×C₂₉×#124	—	2	1	no	—
36	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
37	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
38	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
39	C₂×C₂₉×#123	—	2	1	no	—
40	C₂×C₂₉×#123	—	2	1	no	—
41	C₂×C₂₉×#123	—	2	1	no	—
42	C₂×C₂₉×C₂²⋊Q₈	—	2	1	no	—
43	C₂×C₂₉×C₂²⋊Q₈	—	2	1	no	—
44	C₂×C₂₉×C₂²⋊Q₈	—	2	1	no	—
45	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₂₉×#121	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
49	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
50	C₂₉×#497	C₂²	1	8	yes	complemented
51	C₂₉×#495	C₂²	1	8	yes	complemented
52	C₂₉×#489	C₂²	1	8	yes	complemented
53	C₂₉×#487	C₂²	1	8	yes	complemented
54	C₂₉×#464	C₂²	1	8	yes	complemented
55	C₂₉×#463	C₂²	1	8	yes	complemented
56	C₂₉×#462	C₂²	1	8	yes	complemented
57	C₂₉×#461	C₂²	1	8	yes	complemented
58	C₂₉×#452	C₂²	1	8	yes	complemented
59	C₂₉×#451	C₂²	1	8	yes	complemented
60	C₂₉×#449	C₂²	1	8	yes	—
61	C₂₉×#448	C₂²	1	8	yes	complemented
62	C₂₉×#433	C₂²	1	8	yes	complemented
63	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
66	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
67	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
68	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
69	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
70	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
71	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
72	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
73	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
74	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
77	C₂×#41×C₂₉	—	2	2	no	—
78	C₂×#41×C₂₉	—	4	2	no	—
79	C₂×#41×C₂₉	—	4	2	no	—
80	C₂×#41×C₂₉	C₂³	1	4	yes	—
81	C₂²×Q₈×C₂₉	—	2	1	no	—
82	C₂²×Q₈×C₂₉	—	2	2	no	—
83	C₂²×Q₈×C₂₉	—	2	1	no	—
84	C₂²×Q₈×C₂₉	—	4	2	no	—
85	C₂²×Q₈×C₂₉	—	4	2	no	—
86	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₂₉	C₂³	1	4	yes	—
91	C₂²×D₄×C₂₉	—	2	1	no	—
92	C₂²×D₄×C₂₉	—	2	1	no	—
93	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₂₉	—	2	1	no	—
96	C₂³×C₄×C₂₉	—	2	1	no	—
97	C₂³×C₄×C₂₉	—	2	1	no	—
98	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
99	C₂×Q₁₆×C₂₉	—	4	2	no	—
100	C₂×Q₁₆×C₂₉	—	4	2	no	—
101	C₂×Q₁₆×C₂₉	—	4	2	no	—
102	C₂×Q₁₆×C₂₉	C₂³	1	4	yes	—
103	C₂×Q₁₆×C₂₉	C₂³	1	4	yes	—
104	C₂×Q₁₆×C₂₉	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₂₉	—	4	2	no	—
106	C₂×SD₁₆×C₂₉	—	4	2	no	—
107	C₂×SD₁₆×C₂₉	—	4	2	no	—
108	C₂×SD₁₆×C₂₉	—	4	2	no	—
109	C₂×SD₁₆×C₂₉	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₂₉	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₂₉	C₂³	1	4	yes	—
112	C₂×SD₁₆×C₂₉	C₂³	1	4	yes	—
113	C₂×D₈×C₂₉	—	4	2	no	—
114	C₂×D₈×C₂₉	C₂³	1	4	yes	—
115	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
119	C₂₉×C₄⋊Q₈	—	2	2	no	—
120	C₂₉×C₄⋊Q₈	—	2	2	no	—
121	C₂₉×C₄⋊Q₈	—	2	2	no	—
122	C₂₉×C₄⋊Q₈	C₂³	1	4	yes	—
123	C₂₉×C₄⋊Q₈	C₂³	1	4	yes	—
124	C₂₉×C₄⋊Q₈	C₂³	1	4	yes	—
125	C₂₉×#126	—	2	8	no	—
126	C₂₉×#124	—	2	8	no	—
127	C₂₉×#124	—	2	2	no	—
128	C₂₉×#124	—	2	2	no	—
129	C₂₉×#124	—	2	2	no	—
130	C₂₉×#124	C₂³	1	4	yes	—
131	C₂₉×#124	C₂³	1	4	yes	—
132	C₂₉×#124	C₂³	1	4	yes	—
133	C₂₉×#123	—	2	8	no	—
134	C₂₉×#123	—	2	8	no	—
135	C₂₉×#123	—	2	8	no	—
136	C₂₉×C₂²⋊Q₈	—	2	2	no	—
137	C₂₉×C₂²⋊Q₈	—	2	8	no	—
138	C₂₉×C₂²⋊Q₈	—	2	8	no	—
139	C₂₉×C₂²⋊Q₈	—	2	8	no	—
140	C₂₉×C₂²⋊Q₈	C₂³	1	4	yes	—
141	C₂₉×#121	—	2	2	no	—
142	C₂₉×#121	C₂³	1	4	yes	—
143	C₄×Q₈×C₂₉	—	2	2	no	—
144	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
145	C₄×D₄×C₂₉	—	2	2	no	—
146	C₄×D₄×C₂₉	C₂³	1	4	yes	—
147	C₂₉×#117	D₄	1	4	yes	—
148	C₂₉×#117	C₂³	1	4	yes	—
149	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
150	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
151	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
152	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
153	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
154	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
155	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
156	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
160	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
162	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
163	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
164	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
165	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
166	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
167	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
168	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
169	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₂₉	D₄	1	1	yes	characteristic
171	C₂×C₄²×C₂₉	—	2	1	no	—
172	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
174	C₂₉×C₄⋊C₈	C₂³	1	4	yes	—
175	C₂₉×C₄⋊C₈	C₂³	1	4	yes	—
176	C₂₉×#103	C₂³	1	4	yes	—
177	C₂₉×#103	C₂³	1	4	yes	—
178	C₂₉×#103	C₂³	1	4	yes	—
179	C₂₉×#103	C₂³	1	4	yes	—
180	C₂₉×#103	C₂³	1	4	yes	—
181	C₂₉×#103	C₂³	1	4	yes	—
182	C₂₉×#102	C₂³	1	4	yes	—
183	C₂₉×#102	C₂³	1	4	yes	—
184	C₂₉×C₂²⋊C₈	C₂³	1	4	yes	—
185	C₂₉×C₂²⋊C₈	C₂³	1	4	yes	—
186	C₂₉×#97	C₂³	1	4	yes	—
187	C₄×C₈×C₂₉	C₂³	1	4	yes	—
188	C₂⁴×C₂₉	—	2	1	no	—
189	C₂⁴×C₂₉	—	2	1	no	—
190	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
191	#41×C₂₉	—	4	4	no	—
192	#41×C₂₉	—	4	4	no	—
193	#41×C₂₉	—	4	8	no	—
194	C₂×Q₈×C₂₉	—	2	1	no	—
195	C₂×Q₈×C₂₉	—	2	4	no	—
196	C₂×Q₈×C₂₉	—	2	1	no	—
197	C₂×Q₈×C₂₉	—	2	1	no	—
198	C₂×Q₈×C₂₉	—	2	1	no	—
199	C₂×Q₈×C₂₉	—	2	4	no	—
200	C₂×Q₈×C₂₉	—	2	2	no	—
201	C₂×Q₈×C₂₉	—	2	2	no	—
202	C₂×Q₈×C₂₉	—	2	2	no	—
203	C₂×Q₈×C₂₉	—	2	2	no	—
204	C₂×Q₈×C₂₉	—	2	2	no	—
205	C₂×Q₈×C₂₉	—	2	2	no	—
206	C₂×Q₈×C₂₉	—	2	2	no	—
207	C₂×Q₈×C₂₉	—	2	2	no	—
208	C₂×Q₈×C₂₉	—	4	4	no	—
209	C₂×Q₈×C₂₉	—	4	4	no	—
210	C₂×Q₈×C₂₉	—	4	4	no	—
211	C₂×Q₈×C₂₉	—	4	8	no	—
212	C₂×Q₈×C₂₉	—	8	2	no	—
213	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
214	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
215	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
216	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
217	C₂×D₄×C₂₉	—	2	4	no	—
218	C₂×D₄×C₂₉	—	2	4	no	—
219	C₂×D₄×C₂₉	—	2	1	no	—
220	C₂×D₄×C₂₉	—	2	1	no	—
221	C₂×D₄×C₂₉	—	2	2	no	—
222	C₂×D₄×C₂₉	—	2	2	no	—
223	C₂×D₄×C₂₉	—	2	2	no	—
224	C₂×D₄×C₂₉	—	2	2	no	—
225	C₂×D₄×C₂₉	—	4	4	no	—
226	C₂×D₄×C₂₉	—	8	2	no	—
227	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
228	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₂₉	—	2	2	no	—
230	C₂²×C₄×C₂₉	—	2	2	no	—
231	C₂²×C₄×C₂₉	—	2	4	no	—
232	C₂²×C₄×C₂₉	—	2	1	no	—
233	C₂²×C₄×C₂₉	—	2	1	no	—
234	C₂²×C₄×C₂₉	—	2	1	no	—
235	C₂²×C₄×C₂₉	—	2	1	no	—
236	C₂²×C₄×C₂₉	—	2	1	no	—
237	C₂²×C₄×C₂₉	—	2	1	no	—
238	C₂²×C₄×C₂₉	—	2	4	no	—
239	C₂²×C₄×C₂₉	—	2	4	no	—
240	C₂²×C₄×C₂₉	—	4	4	no	—
241	C₂²×C₄×C₂₉	—	4	4	no	—
242	C₂²×C₄×C₂₉	—	8	2	no	—
243	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
244	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
251	Q₁₆×C₂₉	—	4	4	no	—
252	Q₁₆×C₂₉	—	4	4	no	—
253	Q₁₆×C₂₉	—	4	4	no	—
254	SD₁₆×C₂₉	—	4	4	no	—
255	SD₁₆×C₂₉	—	4	4	no	—
256	SD₁₆×C₂₉	—	4	4	no	—
257	SD₁₆×C₂₉	—	4	4	no	—
258	D₈×C₂₉	—	4	4	no	—
259	C₂×C₈×C₂₉	—	2	2	no	—
260	C₂×C₈×C₂₉	—	2	2	no	—
261	C₂×C₈×C₂₉	—	2	2	no	—
262	C₂×C₈×C₂₉	—	2	2	no	—
263	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
264	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
265	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
266	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
267	C₄⋊C₄×C₂₉	—	2	4	no	—
268	C₄⋊C₄×C₂₉	—	2	4	no	—
269	C₄⋊C₄×C₂₉	—	2	4	no	—
270	C₄⋊C₄×C₂₉	—	2	4	no	—
271	C₄⋊C₄×C₂₉	—	2	4	no	—
272	C₄⋊C₄×C₂₉	—	2	4	no	—
273	C₄⋊C₄×C₂₉	—	2	4	no	—
274	C₄⋊C₄×C₂₉	—	2	1	no	—
275	C₄⋊C₄×C₂₉	—	2	1	no	—
276	C₄⋊C₄×C₂₉	C₂×D₄	1	4	yes	—
277	C₄⋊C₄×C₂₉	C₂×D₄	1	4	yes	—
278	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
279	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
280	C₂²⋊C₄×C₂₉	—	2	4	no	—
281	C₂²⋊C₄×C₂₉	—	2	4	no	—
282	C₂²⋊C₄×C₂₉	—	2	4	no	—
283	C₂²⋊C₄×C₂₉	—	2	4	no	—
284	C₂²⋊C₄×C₂₉	—	2	4	no	—
285	C₂²⋊C₄×C₂₉	—	2	4	no	—
286	C₂²⋊C₄×C₂₉	—	2	4	no	—
287	C₂²⋊C₄×C₂₉	—	2	4	no	—
288	C₂²⋊C₄×C₂₉	—	2	4	no	—
289	C₂²⋊C₄×C₂₉	C₂×D₄	1	4	yes	—
290	C₂²⋊C₄×C₂₉	C₂×D₄	1	4	yes	—
291	C₄²×C₂₉	—	2	4	no	—
292	C₄²×C₂₉	C₂×D₄	1	2	yes	—
293	C₄²×C₂₉	C₂×D₄	1	2	yes	—
294	C₄²×C₂₉	C₂⁴	1	2	yes	—
295	C₄²×C₂₉	C₂⁴	1	2	yes	—
296	C₂×#3225	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
297	C₂³×C₂₉	—	2	2	no	—
298	C₂³×C₂₉	—	2	2	no	—
299	C₂³×C₂₉	—	2	2	no	—
300	C₂³×C₂₉	—	2	2	no	—
301	C₂³×C₂₉	—	2	2	no	—
302	C₂³×C₂₉	—	4	2	no	—
303	C₂³×C₂₉	—	4	2	no	—
304	C₂³×C₂₉	—	4	2	no	—
305	C₂³×C₂₉	—	4	2	no	—
306	C₂³×C₂₉	—	4	2	no	—
307	C₂³×C₂₉	—	4	2	no	—
308	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
309	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
310	Q₈×C₂₉	—	2	2	no	—
311	Q₈×C₂₉	—	2	2	no	—
312	Q₈×C₂₉	—	2	2	no	—
313	Q₈×C₂₉	—	2	2	no	—
314	Q₈×C₂₉	—	2	2	no	—
315	Q₈×C₂₉	—	2	2	no	—
316	Q₈×C₂₉	—	2	2	no	—
317	Q₈×C₂₉	—	2	2	no	—
318	Q₈×C₂₉	—	4	8	no	—
319	Q₈×C₂₉	—	4	2	no	—
320	Q₈×C₂₉	—	4	2	no	—
321	Q₈×C₂₉	—	4	2	no	—
322	Q₈×C₂₉	—	4	2	no	—
323	Q₈×C₂₉	—	8	4	no	—
324	D₄×C₂₉	—	2	2	no	—
325	D₄×C₂₉	—	2	2	no	—
326	D₄×C₂₉	—	2	2	no	—
327	D₄×C₂₉	—	2	2	no	—
328	D₄×C₂₉	—	4	8	no	—
329	D₄×C₂₉	—	4	2	no	—
330	D₄×C₂₉	—	4	2	no	—
331	D₄×C₂₉	—	8	4	no	—
332	C₂×C₄×C₂₉	—	2	2	no	—
333	C₂×C₄×C₂₉	—	2	2	no	—
334	C₂×C₄×C₂₉	—	2	2	no	—
335	C₂×C₄×C₂₉	—	2	2	no	—
336	C₂×C₄×C₂₉	—	2	2	no	—
337	C₂×C₄×C₂₉	—	2	4	no	—
338	C₂×C₄×C₂₉	—	2	2	no	—
339	C₂×C₄×C₂₉	—	2	2	no	—
340	C₂×C₄×C₂₉	—	2	2	no	—
341	C₂×C₄×C₂₉	—	2	2	no	—
342	C₂×C₄×C₂₉	—	2	2	no	—
343	C₂×C₄×C₂₉	—	2	2	no	—
344	C₂×C₄×C₂₉	—	2	2	no	—
345	C₂×C₄×C₂₉	—	2	2	no	—
346	C₂×C₄×C₂₉	—	4	8	no	—
347	C₂×C₄×C₂₉	—	4	8	no	—
348	C₂×C₄×C₂₉	—	4	2	no	—
349	C₂×C₄×C₂₉	—	4	2	no	—
350	C₂×C₄×C₂₉	—	4	2	no	—
351	C₂×C₄×C₂₉	—	4	2	no	—
352	C₂×C₄×C₂₉	—	4	2	no	—
353	C₂×C₄×C₂₉	—	4	2	no	—
354	C₂×C₄×C₂₉	—	8	4	no	—
355	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
356	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
357	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
358	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
359	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
360	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
362	C₂×C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
363	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
364	C₈×C₂₉	—	2	2	no	—
365	C₈×C₂₉	—	2	2	no	—
366	C₈×C₂₉	—	2	2	no	—
367	C₈×C₂₉	—	2	2	no	—
368	C₂×#542	C₂×C₂₉	1	1	yes	characteristic, complemented
369	C₂×#536	C₂×C₂₉	1	1	yes	characteristic, complemented
370	#3225	C₂×C₂₉	1	16	yes	direct product factor
371	C₂×#497	C₂×C₂₉	1	1	yes	characteristic, complemented
372	C₂×#495	C₂×C₂₉	1	1	yes	characteristic, complemented
373	C₂×#489	C₂×C₂₉	1	1	yes	characteristic, complemented
374	C₂×#487	C₂×C₂₉	1	1	yes	characteristic, complemented
375	C₂×#464	C₂×C₂₉	1	1	yes	characteristic, complemented
376	C₂×#462	C₂×C₂₉	1	1	yes	characteristic, complemented
377	C₂×#463	C₂×C₂₉	1	1	yes	characteristic, complemented
378	C₂×#461	C₂×C₂₉	1	1	yes	characteristic, complemented
379	C₂×#452	C₂×C₂₉	1	1	yes	characteristic, complemented
380	C₂×#449	C₂×C₂₉	1	1	yes	characteristic
381	C₂×#451	C₂×C₂₉	1	1	yes	characteristic, complemented
382	C₂×#448	C₂×C₂₉	1	1	yes	characteristic, complemented
383	C₂×#433	C₂×C₂₉	1	1	yes	characteristic, complemented
384	C₂²×C₂₉	—	2	2	no	—
385	C₂²×C₂₉	—	2	2	no	—
386	C₂²×C₂₉	—	2	2	no	—
387	C₂²×C₂₉	—	4	4	no	—
388	C₂²×C₂₉	—	4	2	no	—
389	C₂²×C₂₉	—	4	2	no	—
390	C₂²×C₂₉	—	4	2	no	—
391	C₂²×C₂₉	—	4	2	no	—
392	C₂²×C₂₉	—	4	2	no	—
393	C₂²×C₂₉	—	4	2	no	—
394	C₂²×C₂₉	—	8	4	no	—
395	C₂²×C₂₉	—	8	4	no	—
396	C₂²×C₂₉	#535	1	2	yes	—
397	C₂²×C₂₉	#577	1	2	yes	—
398	C₂²×C₂₉	#578	1	2	yes	—
399	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
400	C₄×C₂₉	—	2	2	no	—
401	C₄×C₂₉	—	2	2	no	—
402	C₄×C₂₉	—	2	2	no	—
403	C₄×C₂₉	—	2	2	no	—
404	C₄×C₂₉	—	2	2	no	—
405	C₄×C₂₉	—	4	2	no	—
406	C₄×C₂₉	—	4	2	no	—
407	C₄×C₂₉	—	4	2	no	—
408	C₄×C₂₉	—	4	2	no	—
409	C₄×C₂₉	—	4	2	no	—
410	C₄×C₂₉	—	4	2	no	—
411	C₄×C₂₉	#535	1	2	yes	—
412	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
413	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂²×#41	C₂²×C₂₉	1	1	yes	characteristic
415	C₂³×Q₈	C₂²×C₂₉	1	1	yes	characteristic
416	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
417	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
418	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
419	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
420	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
421	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
422	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
423	C₂²×D₈	C₂²×C₂₉	1	1	yes	characteristic
424	#542	—	2	4	no	—
425	#542	C₂²×C₂₉	1	8	yes	complemented
426	#536	—	2	4	no	—
427	#536	C₂²×C₂₉	1	8	yes	complemented
428	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
429	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
430	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
431	C₂×#126	—	2	1	no	—
432	C₂×#124	—	2	1	no	—
433	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
434	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
435	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
436	C₂×#123	—	2	1	no	—
437	C₂×#123	—	2	1	no	—
438	C₂×#123	—	2	1	no	—
439	C₂×C₂²⋊Q₈	—	2	1	no	—
440	C₂×C₂²⋊Q₈	—	2	1	no	—
441	C₂×C₂²⋊Q₈	—	2	1	no	—
442	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
443	C₂×#121	C₂²×C₂₉	1	1	yes	characteristic
444	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
445	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
446	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
447	#497	C₂²×C₂₉	1	8	yes	complemented
448	#495	C₂²×C₂₉	1	8	yes	complemented
449	#489	C₂²×C₂₉	1	8	yes	complemented
450	#487	C₂²×C₂₉	1	8	yes	complemented
451	#464	C₂²×C₂₉	1	8	yes	complemented
452	#463	C₂²×C₂₉	1	8	yes	complemented
453	#462	C₂²×C₂₉	1	8	yes	complemented
454	#461	C₂²×C₂₉	1	8	yes	complemented
455	#452	C₂²×C₂₉	1	8	yes	complemented
456	#451	C₂²×C₂₉	1	8	yes	complemented
457	#449	C₂²×C₂₉	1	8	yes	—
458	#448	C₂²×C₂₉	1	8	yes	complemented
459	#433	C₂²×C₂₉	1	8	yes	complemented
460	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
461	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
462	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
463	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
464	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
465	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
466	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
467	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
468	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
469	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
470	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
471	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
472	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
473	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
474	C₂×C₂₉	—	4	2	no	—
475	C₂×C₂₉	—	8	2	no	—
476	C₂×C₂₉	—	8	2	no	—
477	C₂×C₂₉	#3225	1	4	yes	direct product factor
478	C₂×C₂₉	C₂×#535	1	1	yes	characteristic
479	C₂×C₂₉	C₂×#577	1	1	yes	characteristic
480	C₂×C₂₉	C₂×#578	1	1	yes	characteristic
481	C₂×#41	—	2	2	no	—
482	C₂×#41	—	4	2	no	—
483	C₂×#41	—	4	2	no	—
484	C₂×#41	C₂³×C₂₉	1	4	yes	—
485	C₂²×Q₈	—	2	1	no	—
486	C₂²×Q₈	—	2	2	no	—
487	C₂²×Q₈	—	2	1	no	—
488	C₂²×Q₈	—	4	2	no	—
489	C₂²×Q₈	—	4	2	no	—
490	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
491	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
492	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
493	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
494	C₂²×Q₈	C₂³×C₂₉	1	4	yes	—
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
498	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
499	C₂³×C₄	—	2	1	no	—
500	C₂³×C₄	—	2	1	no	—
501	C₂³×C₄	—	2	1	no	—
502	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
503	C₂×Q₁₆	—	4	2	no	—
504	C₂×Q₁₆	—	4	2	no	—
505	C₂×Q₁₆	—	4	2	no	—
506	C₂×Q₁₆	C₂³×C₂₉	1	4	yes	—
507	C₂×Q₁₆	C₂³×C₂₉	1	4	yes	—
508	C₂×Q₁₆	C₂³×C₂₉	1	4	yes	—
509	C₂×SD₁₆	—	4	2	no	—
510	C₂×SD₁₆	—	4	2	no	—
511	C₂×SD₁₆	—	4	2	no	—
512	C₂×SD₁₆	—	4	2	no	—
513	C₂×SD₁₆	C₂³×C₂₉	1	4	yes	—
514	C₂×SD₁₆	C₂³×C₂₉	1	4	yes	—
515	C₂×SD₁₆	C₂³×C₂₉	1	4	yes	—
516	C₂×SD₁₆	C₂³×C₂₉	1	4	yes	—
517	C₂×D₈	—	4	2	no	—
518	C₂×D₈	C₂³×C₂₉	1	4	yes	—
519	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
520	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
521	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
522	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
523	C₄⋊Q₈	—	2	2	no	—
524	C₄⋊Q₈	—	2	2	no	—
525	C₄⋊Q₈	—	2	2	no	—
526	C₄⋊Q₈	C₂³×C₂₉	1	4	yes	—
527	C₄⋊Q₈	C₂³×C₂₉	1	4	yes	—
528	C₄⋊Q₈	C₂³×C₂₉	1	4	yes	—
529	#126	—	2	8	no	—
530	#124	—	2	8	no	—
531	#124	—	2	2	no	—
532	#124	—	2	2	no	—
533	#124	—	2	2	no	—
534	#124	C₂³×C₂₉	1	4	yes	—
535	#124	C₂³×C₂₉	1	4	yes	—
536	#124	C₂³×C₂₉	1	4	yes	—
537	#123	—	2	8	no	—
538	#123	—	2	8	no	—
539	#123	—	2	8	no	—
540	C₂²⋊Q₈	—	2	2	no	—
541	C₂²⋊Q₈	—	2	8	no	—
542	C₂²⋊Q₈	—	2	8	no	—
543	C₂²⋊Q₈	—	2	8	no	—
544	C₂²⋊Q₈	C₂³×C₂₉	1	4	yes	—
545	#121	—	2	2	no	—
546	#121	C₂³×C₂₉	1	4	yes	—
547	C₄×Q₈	—	2	2	no	—
548	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	C₂³×C₂₉	1	4	yes	—
551	#117	D₄×C₂₉	1	4	yes	—
552	#117	C₂³×C₂₉	1	4	yes	—
553	C₂×C₄⋊C₄	—	2	1	no	—
554	C₂×C₄⋊C₄	—	2	1	no	—
555	C₂×C₄⋊C₄	—	2	1	no	—
556	C₂×C₄⋊C₄	—	2	1	no	—
557	C₂×C₄⋊C₄	—	2	1	no	—
558	C₂×C₄⋊C₄	—	2	1	no	—
559	C₂×C₄⋊C₄	—	2	1	no	—
560	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
561	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
564	C₂×C₂²⋊C₄	—	2	1	no	—
565	C₂×C₂²⋊C₄	—	2	1	no	—
566	C₂×C₂²⋊C₄	—	2	1	no	—
567	C₂×C₂²⋊C₄	—	2	1	no	—
568	C₂×C₂²⋊C₄	—	2	1	no	—
569	C₂×C₂²⋊C₄	—	2	1	no	—
570	C₂×C₂²⋊C₄	—	2	1	no	—
571	C₂×C₂²⋊C₄	—	2	1	no	—
572	C₂×C₂²⋊C₄	—	2	1	no	—
573	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
574	C₂×C₂²⋊C₄	D₄×C₂₉	1	1	yes	characteristic
575	C₂×C₄²	—	2	1	no	—
576	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
577	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
578	C₄⋊C₈	C₂³×C₂₉	1	4	yes	—
579	C₄⋊C₈	C₂³×C₂₉	1	4	yes	—
580	#103	C₂³×C₂₉	1	4	yes	—
581	#103	C₂³×C₂₉	1	4	yes	—
582	#103	C₂³×C₂₉	1	4	yes	—
583	#103	C₂³×C₂₉	1	4	yes	—
584	#103	C₂³×C₂₉	1	4	yes	—
585	#103	C₂³×C₂₉	1	4	yes	—
586	#102	C₂³×C₂₉	1	4	yes	—
587	#102	C₂³×C₂₉	1	4	yes	—
588	C₂²⋊C₈	C₂³×C₂₉	1	4	yes	—
589	C₂²⋊C₈	C₂³×C₂₉	1	4	yes	—
590	#97	C₂³×C₂₉	1	4	yes	—
591	C₄×C₈	C₂³×C₂₉	1	4	yes	—
592	C₂₉	C₂×#3225	1	1	yes	characteristic, direct product factor, Sylow
593	C₂⁴	—	2	1	no	—
594	C₂⁴	—	2	1	no	—
595	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
596	#41	—	4	4	no	—
597	#41	—	4	4	no	—
598	#41	—	4	8	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	2	4	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	2	1	no	—
604	C₂×Q₈	—	2	4	no	—
605	C₂×Q₈	—	2	2	no	—
606	C₂×Q₈	—	2	2	no	—
607	C₂×Q₈	—	2	2	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	—	2	2	no	—
611	C₂×Q₈	—	2	2	no	—
612	C₂×Q₈	—	2	2	no	—
613	C₂×Q₈	—	4	4	no	—
614	C₂×Q₈	—	4	4	no	—
615	C₂×Q₈	—	4	4	no	—
616	C₂×Q₈	—	4	8	no	—
617	C₂×Q₈	—	8	2	no	—
618	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
619	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
620	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
621	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	2	2	no	—
628	C₂×D₄	—	2	2	no	—
629	C₂×D₄	—	2	2	no	—
630	C₂×D₄	—	4	4	no	—
631	C₂×D₄	—	8	2	no	—
632	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
633	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	4	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	4	4	no	—
646	C₂²×C₄	—	4	4	no	—
647	C₂²×C₄	—	8	2	no	—
648	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
649	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
650	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
653	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
656	Q₁₆	—	4	4	no	—
657	Q₁₆	—	4	4	no	—
658	Q₁₆	—	4	4	no	—
659	SD₁₆	—	4	4	no	—
660	SD₁₆	—	4	4	no	—
661	SD₁₆	—	4	4	no	—
662	SD₁₆	—	4	4	no	—
663	D₈	—	4	4	no	—
664	C₂×C₈	—	2	2	no	—
665	C₂×C₈	—	2	2	no	—
666	C₂×C₈	—	2	2	no	—
667	C₂×C₈	—	2	2	no	—
668	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
669	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
670	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
671	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	C₂×D₄×C₂₉	1	4	yes	—
682	C₄⋊C₄	C₂×D₄×C₂₉	1	4	yes	—
683	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
684	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	C₂×D₄×C₂₉	1	4	yes	—
695	C₂²⋊C₄	C₂×D₄×C₂₉	1	4	yes	—
696	C₄²	—	2	4	no	—
697	C₄²	C₂×D₄×C₂₉	1	2	yes	—
698	C₄²	C₂×D₄×C₂₉	1	2	yes	—
699	C₄²	C₂⁴×C₂₉	1	2	yes	—
700	C₄²	C₂⁴×C₂₉	1	2	yes	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	4	2	no	—
707	C₂³	—	4	2	no	—
708	C₂³	—	4	2	no	—
709	C₂³	—	4	2	no	—
710	C₂³	—	4	2	no	—
711	C₂³	—	4	2	no	—
712	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
713	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
714	Q₈	—	2	2	no	—
715	Q₈	—	2	2	no	—
716	Q₈	—	2	2	no	—
717	Q₈	—	2	2	no	—
718	Q₈	—	2	2	no	—
719	Q₈	—	2	2	no	—
720	Q₈	—	2	2	no	—
721	Q₈	—	2	2	no	—
722	Q₈	—	4	8	no	—
723	Q₈	—	4	2	no	—
724	Q₈	—	4	2	no	—
725	Q₈	—	4	2	no	—
726	Q₈	—	4	2	no	—
727	Q₈	—	8	4	no	—
728	D₄	—	2	2	no	—
729	D₄	—	2	2	no	—
730	D₄	—	2	2	no	—
731	D₄	—	2	2	no	—
732	D₄	—	4	8	no	—
733	D₄	—	4	2	no	—
734	D₄	—	4	2	no	—
735	D₄	—	8	4	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	4	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	4	8	no	—
751	C₂×C₄	—	4	8	no	—
752	C₂×C₄	—	4	2	no	—
753	C₂×C₄	—	4	2	no	—
754	C₂×C₄	—	4	2	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	4	2	no	—
758	C₂×C₄	—	8	4	no	—
759	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
760	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
761	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
762	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
763	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
764	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
765	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
766	C₂×C₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
767	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
768	C₈	—	2	2	no	—
769	C₈	—	2	2	no	—
770	C₈	—	2	2	no	—
771	C₈	—	2	2	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	4	4	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	8	4	no	—
783	C₂²	—	8	4	no	—
784	C₂²	C₂₉×#535	1	2	yes	—
785	C₂²	C₂₉×#577	1	2	yes	—
786	C₂²	C₂₉×#578	1	2	yes	—
787	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
788	C₄	—	2	2	no	—
789	C₄	—	2	2	no	—
790	C₄	—	2	2	no	—
791	C₄	—	2	2	no	—
792	C₄	—	2	2	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₄	C₂₉×#535	1	2	yes	—
800	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
801	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
802	C₂	—	4	2	no	—
803	C₂	—	8	2	no	—
804	C₂	—	8	2	no	—
805	C₂	C₂₉×#3225	1	4	yes	direct product factor
806	C₂	C₂×C₂₉×#535	1	1	yes	characteristic
807	C₂	C₂×C₂₉×#577	1	1	yes	characteristic
808	C₂	C₂×C₂₉×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
prime radical	C₂×C₂₉×#449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₂₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#542	C₂	semidirect
2. C₂×C₂₉×#536	C₂	semidirect
3. C₂₉×#3225	C₂	direct (N × H)
4. C₂×C₂₉×#497	C₂	semidirect
5. C₂×C₂₉×#495	C₂	semidirect
6. C₂×C₂₉×#489	C₂	semidirect
7. C₂×C₂₉×#487	C₂	semidirect
8. C₂×C₂₉×#464	C₂	semidirect
9. C₂×C₂₉×#462	C₂	semidirect
10. C₂×C₂₉×#463	C₂	semidirect
11. C₂×C₂₉×#461	C₂	semidirect
12. C₂×C₂₉×#452	C₂	semidirect
14. C₂×C₂₉×#451	C₂	semidirect
15. C₂×C₂₉×#448	C₂	semidirect
16. C₂×C₂₉×#433	C₂	semidirect
28. C₂₉×#542	C₂²	semidirect
30. C₂₉×#536	C₂²	semidirect
50. C₂₉×#497	C₂²	semidirect
51. C₂₉×#495	C₂²	semidirect
52. C₂₉×#489	C₂²	semidirect
53. C₂₉×#487	C₂²	semidirect
54. C₂₉×#464	C₂²	semidirect
55. C₂₉×#463	C₂²	semidirect
56. C₂₉×#462	C₂²	semidirect
57. C₂₉×#461	C₂²	semidirect
58. C₂₉×#452	C₂²	semidirect
59. C₂₉×#451	C₂²	semidirect
61. C₂₉×#448	C₂²	semidirect
62. C₂₉×#433	C₂²	semidirect
296. C₂×#3225	C₂₉	direct (N × H)
368. C₂×#542	C₂×C₂₉	semidirect
369. C₂×#536	C₂×C₂₉	semidirect
370. #3225	C₂×C₂₉	direct (N × H)
371. C₂×#497	C₂×C₂₉	semidirect
372. C₂×#495	C₂×C₂₉	semidirect
373. C₂×#489	C₂×C₂₉	semidirect
374. C₂×#487	C₂×C₂₉	semidirect
375. C₂×#464	C₂×C₂₉	semidirect
376. C₂×#462	C₂×C₂₉	semidirect
377. C₂×#463	C₂×C₂₉	semidirect
378. C₂×#461	C₂×C₂₉	semidirect
379. C₂×#452	C₂×C₂₉	semidirect
381. C₂×#451	C₂×C₂₉	semidirect
382. C₂×#448	C₂×C₂₉	semidirect
383. C₂×#433	C₂×C₂₉	semidirect
425. #542	C₂²×C₂₉	semidirect
427. #536	C₂²×C₂₉	semidirect
447. #497	C₂²×C₂₉	semidirect
448. #495	C₂²×C₂₉	semidirect
449. #489	C₂²×C₂₉	semidirect
450. #487	C₂²×C₂₉	semidirect
451. #464	C₂²×C₂₉	semidirect
452. #463	C₂²×C₂₉	semidirect
453. #462	C₂²×C₂₉	semidirect
454. #461	C₂²×C₂₉	semidirect
455. #452	C₂²×C₂₉	semidirect
456. #451	C₂²×C₂₉	semidirect
458. #448	C₂²×C₂₉	semidirect
459. #433	C₂²×C₂₉	semidirect
477. C₂×C₂₉	#3225	direct (N × H)
592. C₂₉	C₂×#3225	direct (N × H)
805. C₂	C₂₉×#3225	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#542	2
C₂×C₂₉×#536	2
C₂₉×#3225	2
C₂×C₂₉×#497	2
C₂×C₂₉×#495	2
C₂×C₂₉×#489	2
C₂×C₂₉×#487	2
C₂×C₂₉×#464	2
C₂×C₂₉×#462	2
C₂×C₂₉×#463	2
C₂×C₂₉×#461	2
C₂×C₂₉×#452	2
C₂×C₂₉×#449	2
C₂×C₂₉×#451	2
C₂×C₂₉×#448	2
C₂×C₂₉×#433	2
C₂×#3225	29

Subgroups — C2×C29×#3225 #20355696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#3225 #20355696