Subgroups — C₆₁×#24437 #29527870

Order 15616.

1438 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#467	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#451	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#451	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#103×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2417	C₂	1	1	yes	maximal, characteristic
7	C₆₁×#2043	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2036	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2016	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#2001	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1872	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#1869	C₂	1	1	yes	maximal, characteristic
14	C₆₁×#1863	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1787	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
20	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
22	D₄×Q₈×C₆₁	—	2	4	no	—
23	D₄×Q₈×C₆₁	—	2	4	no	—
24	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
25	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
27	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
28	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₆₁	—	2	1	no	—
34	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
36	C₆₁×#467	—	2	4	no	—
37	C₆₁×#451	—	2	4	no	—
38	C₆₁×#451	—	2	4	no	—
39	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
40	C₂×#103×C₆₁	—	2	4	no	—
41	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
43	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
44	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
45	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
46	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
47	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
48	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
49	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
50	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
54	C₆₁×#398	—	2	1	no	—
55	C₆₁×#396	—	2	1	no	—
56	C₆₁×#391	C₂²	1	1	yes	characteristic
57	C₆₁×#389	C₂²	1	1	yes	characteristic
58	C₆₁×#386	—	2	1	no	—
59	C₆₁×#380	—	2	1	no	—
60	C₆₁×#380	C₂²	1	1	yes	characteristic
61	C₆₁×#340	C₂²	1	1	yes	characteristic
62	C₆₁×#340	C₂²	1	1	yes	characteristic
63	C₆₁×#336	C₂²	1	1	yes	characteristic
64	C₆₁×#336	C₂²	1	1	yes	characteristic
65	C₂²×Q₈×C₆₁	—	2	2	no	—
66	C₂²×Q₈×C₆₁	—	2	2	no	—
67	C₂²×Q₈×C₆₁	—	2	1	no	—
68	C₂²×Q₈×C₆₁	—	2	1	no	—
69	C₂²×Q₈×C₆₁	—	2	2	no	—
70	C₂²×Q₈×C₆₁	—	2	2	no	—
71	C₂²×Q₈×C₆₁	—	2	2	no	—
72	C₂²×Q₈×C₆₁	—	2	2	no	—
73	C₂²×Q₈×C₆₁	—	2	2	no	—
74	C₂²×Q₈×C₆₁	—	4	1	no	—
75	C₂²×Q₈×C₆₁	—	4	1	no	—
76	C₂²×Q₈×C₆₁	—	4	1	no	—
77	C₂²×Q₈×C₆₁	—	4	1	no	—
78	C₂²×Q₈×C₆₁	D₄	1	4	yes	—
79	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
81	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
82	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
84	C₂³×C₄×C₆₁	—	2	1	no	—
85	C₂³×C₄×C₆₁	—	2	1	no	—
86	C₂³×C₄×C₆₁	—	2	1	no	—
87	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
89	C₂×Q₁₆×C₆₁	—	2	2	no	—
90	C₂×Q₁₆×C₆₁	—	2	2	no	—
91	C₂×Q₁₆×C₆₁	—	2	2	no	—
92	C₂×Q₁₆×C₆₁	—	2	2	no	—
93	C₂×Q₁₆×C₆₁	—	2	2	no	—
94	C₂×Q₁₆×C₆₁	—	2	2	no	—
95	C₂×Q₁₆×C₆₁	—	4	1	no	—
96	C₂×Q₁₆×C₆₁	—	4	1	no	—
97	C₂×Q₁₆×C₆₁	—	4	1	no	—
98	C₂²×C₈×C₆₁	—	2	2	no	—
99	C₂²×C₈×C₆₁	—	2	2	no	—
100	C₂²×C₈×C₆₁	—	4	1	no	—
101	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
105	C₄⋊Q₈×C₆₁	—	2	8	no	—
106	C₄⋊Q₈×C₆₁	—	2	2	no	—
107	C₄⋊Q₈×C₆₁	—	2	2	no	—
108	C₂²⋊Q₈×C₆₁	—	2	8	no	—
109	C₂²⋊Q₈×C₆₁	—	2	8	no	—
110	C₂²⋊Q₈×C₆₁	—	2	2	no	—
111	C₂²⋊Q₈×C₆₁	—	2	2	no	—
112	C₂²⋊Q₈×C₆₁	—	2	2	no	—
113	C₂²⋊Q₈×C₆₁	—	2	2	no	—
114	C₂²⋊Q₈×C₆₁	—	2	2	no	—
115	C₂²⋊Q₈×C₆₁	—	2	2	no	—
116	C₂²⋊Q₈×C₆₁	—	4	1	no	—
117	C₂²⋊Q₈×C₆₁	D₄	1	4	yes	—
118	C₄×Q₈×C₆₁	—	2	2	no	—
119	C₄×Q₈×C₆₁	—	2	2	no	—
120	C₄×D₄×C₆₁	—	2	8	no	—
121	C₄×D₄×C₆₁	—	2	2	no	—
122	C₄×D₄×C₆₁	—	2	2	no	—
123	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
124	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
125	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
126	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
127	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
128	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
129	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
130	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
131	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
132	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
133	C₂×C₄⋊C₄×C₆₁	—	4	1	no	—
134	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
140	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
141	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
143	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
144	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
145	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
146	C₂×C₄²×C₆₁	—	2	1	no	—
147	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
148	#107×C₆₁	—	2	2	no	—
149	#103×C₆₁	—	2	2	no	—
150	#103×C₆₁	—	2	2	no	—
151	#103×C₆₁	—	2	2	no	—
152	#103×C₆₁	—	2	2	no	—
153	#103×C₆₁	—	2	2	no	—
154	#103×C₆₁	—	2	2	no	—
155	#103×C₆₁	—	2	2	no	—
156	#103×C₆₁	—	2	2	no	—
157	#103×C₆₁	—	4	1	no	—
158	#103×C₆₁	D₄	1	4	yes	complemented
159	C₂²⋊C₈×C₆₁	—	2	2	no	—
160	C₂²⋊C₈×C₆₁	—	2	2	no	—
161	C₂²⋊C₈×C₆₁	—	4	1	no	—
162	#95×C₆₁	—	2	1	no	—
163	#95×C₆₁	—	2	1	no	—
164	#95×C₆₁	—	2	1	no	—
165	#95×C₆₁	—	2	1	no	—
166	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
167	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
168	C₂×Q₈×C₆₁	—	2	4	no	—
169	C₂×Q₈×C₆₁	—	2	4	no	—
170	C₂×Q₈×C₆₁	—	2	1	no	—
171	C₂×Q₈×C₆₁	—	2	1	no	—
172	C₂×Q₈×C₆₁	—	2	1	no	—
173	C₂×Q₈×C₆₁	—	2	1	no	—
174	C₂×Q₈×C₆₁	—	2	1	no	—
175	C₂×Q₈×C₆₁	—	2	8	no	—
176	C₂×Q₈×C₆₁	—	2	1	no	—
177	C₂×Q₈×C₆₁	—	2	1	no	—
178	C₂×Q₈×C₆₁	—	2	1	no	—
179	C₂×Q₈×C₆₁	—	2	1	no	—
180	C₂×Q₈×C₆₁	—	2	1	no	—
181	C₂×Q₈×C₆₁	—	2	1	no	—
182	C₂×Q₈×C₆₁	—	2	1	no	—
183	C₂×Q₈×C₆₁	—	2	1	no	—
184	C₂×Q₈×C₆₁	—	2	1	no	—
185	C₂×Q₈×C₆₁	—	2	1	no	—
186	C₂×Q₈×C₆₁	—	2	1	no	—
187	C₂×Q₈×C₆₁	—	2	1	no	—
188	C₂×Q₈×C₆₁	—	2	1	no	—
189	C₂×Q₈×C₆₁	—	2	1	no	—
190	C₂×Q₈×C₆₁	—	4	2	no	—
191	C₂×Q₈×C₆₁	—	4	2	no	—
192	C₂×Q₈×C₆₁	—	4	2	no	—
193	C₂×Q₈×C₆₁	—	4	2	no	—
194	C₂×Q₈×C₆₁	—	4	4	no	—
195	C₂×Q₈×C₆₁	—	4	4	no	—
196	C₂×Q₈×C₆₁	—	4	4	no	—
197	C₂×Q₈×C₆₁	—	4	4	no	—
198	C₂×Q₈×C₆₁	—	4	4	no	—
199	C₂×Q₈×C₆₁	—	4	4	no	—
200	C₂×Q₈×C₆₁	—	4	4	no	—
201	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
202	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
203	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
204	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
205	C₂×Q₈×C₆₁	#41	1	2	yes	—
206	C₂×D₄×C₆₁	—	2	2	no	—
207	C₂×D₄×C₆₁	—	2	2	no	—
208	C₂×D₄×C₆₁	Q₁₆	1	4	yes	complemented
209	C₂²×C₄×C₆₁	—	2	1	no	—
210	C₂²×C₄×C₆₁	—	2	1	no	—
211	C₂²×C₄×C₆₁	—	2	1	no	—
212	C₂²×C₄×C₆₁	—	2	1	no	—
213	C₂²×C₄×C₆₁	—	2	1	no	—
214	C₂²×C₄×C₆₁	—	2	4	no	—
215	C₂²×C₄×C₆₁	—	2	4	no	—
216	C₂²×C₄×C₆₁	—	2	1	no	—
217	C₂²×C₄×C₆₁	—	2	1	no	—
218	C₂²×C₄×C₆₁	—	2	1	no	—
219	C₂²×C₄×C₆₁	—	2	1	no	—
220	C₂²×C₄×C₆₁	—	2	1	no	—
221	C₂²×C₄×C₆₁	—	2	1	no	—
222	C₂²×C₄×C₆₁	—	2	1	no	—
223	C₂²×C₄×C₆₁	—	2	1	no	—
224	C₂²×C₄×C₆₁	—	2	1	no	—
225	C₂²×C₄×C₆₁	—	2	1	no	—
226	C₂²×C₄×C₆₁	—	2	1	no	—
227	C₂²×C₄×C₆₁	—	2	1	no	—
228	C₂²×C₄×C₆₁	—	2	1	no	—
229	C₂²×C₄×C₆₁	—	4	2	no	—
230	C₂²×C₄×C₆₁	—	4	2	no	—
231	C₂²×C₄×C₆₁	—	4	2	no	—
232	C₂²×C₄×C₆₁	—	4	2	no	—
233	C₂²×C₄×C₆₁	—	4	2	no	—
234	C₂²×C₄×C₆₁	—	4	2	no	—
235	C₂²×C₄×C₆₁	—	8	1	no	—
236	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
240	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
241	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
243	Q₁₆×C₆₁	—	4	4	no	—
244	Q₁₆×C₆₁	—	4	4	no	—
245	Q₁₆×C₆₁	—	4	4	no	—
246	C₂×C₈×C₆₁	—	2	1	no	—
247	C₂×C₈×C₆₁	—	2	1	no	—
248	C₂×C₈×C₆₁	—	2	1	no	—
249	C₂×C₈×C₆₁	—	2	1	no	—
250	C₂×C₈×C₆₁	—	2	1	no	—
251	C₂×C₈×C₆₁	—	2	1	no	—
252	C₂×C₈×C₆₁	—	2	1	no	—
253	C₂×C₈×C₆₁	—	2	1	no	—
254	C₂×C₈×C₆₁	—	2	1	no	—
255	C₂×C₈×C₆₁	—	2	1	no	—
256	C₂×C₈×C₆₁	—	2	1	no	—
257	C₂×C₈×C₆₁	—	4	4	no	—
258	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
259	C₄⋊C₄×C₆₁	—	2	4	no	—
260	C₄⋊C₄×C₆₁	—	2	4	no	—
261	C₄⋊C₄×C₆₁	—	2	4	no	—
262	C₄⋊C₄×C₆₁	—	2	4	no	—
263	C₄⋊C₄×C₆₁	—	2	4	no	—
264	C₄⋊C₄×C₆₁	—	2	2	no	—
265	C₄⋊C₄×C₆₁	—	2	1	no	—
266	C₄⋊C₄×C₆₁	—	2	1	no	—
267	C₄⋊C₄×C₆₁	—	2	1	no	—
268	C₄⋊C₄×C₆₁	—	2	1	no	—
269	C₄⋊C₄×C₆₁	—	2	1	no	—
270	C₄⋊C₄×C₆₁	—	2	1	no	—
271	C₄⋊C₄×C₆₁	—	4	2	no	—
272	C₄⋊C₄×C₆₁	—	4	2	no	—
273	C₄⋊C₄×C₆₁	—	4	2	no	—
274	C₄⋊C₄×C₆₁	—	8	1	no	—
275	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
277	C₂²⋊C₄×C₆₁	—	2	4	no	—
278	C₂²⋊C₄×C₆₁	—	2	4	no	—
279	C₂²⋊C₄×C₆₁	—	2	2	no	—
280	C₂²⋊C₄×C₆₁	—	2	2	no	—
281	C₂²⋊C₄×C₆₁	—	4	2	no	—
282	C₂²⋊C₄×C₆₁	—	4	2	no	—
283	C₂²⋊C₄×C₆₁	—	8	1	no	—
284	C₄²×C₆₁	—	2	4	no	—
285	C₄²×C₆₁	—	2	1	no	—
286	C₄²×C₆₁	—	2	1	no	—
287	C₂³×C₆₁	—	2	1	no	—
288	C₂³×C₆₁	—	2	1	no	—
289	C₂³×C₆₁	—	2	1	no	—
290	C₂³×C₆₁	—	2	1	no	—
291	C₂³×C₆₁	—	2	1	no	—
292	C₂³×C₆₁	—	2	1	no	—
293	C₂³×C₆₁	—	2	1	no	—
294	C₂³×C₆₁	—	2	1	no	—
295	C₂³×C₆₁	—	2	1	no	—
296	C₂³×C₆₁	—	2	1	no	—
297	C₂³×C₆₁	#120	1	2	yes	—
298	C₂³×C₆₁	C₂×Q₁₆	1	2	yes	—
299	C₂³×C₆₁	C₂×Q₁₆	1	2	yes	—
300	C₂³×C₆₁	#137	1	2	yes	—
301	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
302	Q₈×C₆₁	—	2	2	no	—
303	Q₈×C₆₁	—	2	2	no	—
304	Q₈×C₆₁	—	2	2	no	—
305	Q₈×C₆₁	—	2	2	no	—
306	Q₈×C₆₁	—	2	2	no	—
307	Q₈×C₆₁	—	2	2	no	—
308	Q₈×C₆₁	—	2	2	no	—
309	Q₈×C₆₁	—	4	8	no	—
310	Q₈×C₆₁	—	4	8	no	—
311	Q₈×C₆₁	—	4	1	no	—
312	Q₈×C₆₁	—	4	1	no	—
313	Q₈×C₆₁	—	4	1	no	—
314	Q₈×C₆₁	—	4	1	no	—
315	Q₈×C₆₁	—	4	1	no	—
316	Q₈×C₆₁	—	4	1	no	—
317	Q₈×C₆₁	—	4	1	no	—
318	Q₈×C₆₁	—	4	1	no	—
319	Q₈×C₆₁	#121	1	4	yes	—
320	D₄×C₆₁	—	2	8	no	—
321	C₂×C₄×C₆₁	—	2	1	no	—
322	C₂×C₄×C₆₁	—	2	2	no	—
323	C₂×C₄×C₆₁	—	2	1	no	—
324	C₂×C₄×C₆₁	—	2	2	no	—
325	C₂×C₄×C₆₁	—	2	1	no	—
326	C₂×C₄×C₆₁	—	2	2	no	—
327	C₂×C₄×C₆₁	—	2	1	no	—
328	C₂×C₄×C₆₁	—	2	2	no	—
329	C₂×C₄×C₆₁	—	2	2	no	—
330	C₂×C₄×C₆₁	—	2	2	no	—
331	C₂×C₄×C₆₁	—	2	2	no	—
332	C₂×C₄×C₆₁	—	2	1	no	—
333	C₂×C₄×C₆₁	—	2	2	no	—
334	C₂×C₄×C₆₁	—	2	2	no	—
335	C₂×C₄×C₆₁	—	2	2	no	—
336	C₂×C₄×C₆₁	—	2	1	no	—
337	C₂×C₄×C₆₁	—	2	2	no	—
338	C₂×C₄×C₆₁	—	2	1	no	—
339	C₂×C₄×C₆₁	—	2	1	no	—
340	C₂×C₄×C₆₁	—	2	1	no	—
341	C₂×C₄×C₆₁	—	2	1	no	—
342	C₂×C₄×C₆₁	—	4	8	no	—
343	C₂×C₄×C₆₁	—	4	8	no	—
344	C₂×C₄×C₆₁	—	4	1	no	—
345	C₂×C₄×C₆₁	—	4	1	no	—
346	C₂×C₄×C₆₁	—	4	1	no	—
347	C₂×C₄×C₆₁	—	4	1	no	—
348	C₂×C₄×C₆₁	—	4	1	no	—
349	C₂×C₄×C₆₁	—	4	1	no	—
350	C₂×C₄×C₆₁	—	4	1	no	—
351	C₂×C₄×C₆₁	—	4	1	no	—
352	C₂×C₄×C₆₁	—	4	1	no	—
353	C₂×C₄×C₆₁	—	4	1	no	—
354	C₂×C₄×C₆₁	—	4	1	no	—
355	C₂×C₄×C₆₁	—	4	1	no	—
356	C₂×C₄×C₆₁	—	4	1	no	—
357	C₂×C₄×C₆₁	—	4	1	no	—
358	C₂×C₄×C₆₁	—	4	1	no	—
359	C₂×C₄×C₆₁	—	4	1	no	—
360	C₂×C₄×C₆₁	—	4	1	no	—
361	C₂×C₄×C₆₁	—	4	1	no	—
362	C₂×C₄×C₆₁	—	4	1	no	—
363	C₂×C₄×C₆₁	—	4	1	no	—
364	C₂×C₄×C₆₁	—	4	1	no	—
365	C₂×C₄×C₆₁	—	8	4	no	—
366	C₂×C₄×C₆₁	#120	1	2	yes	—
367	C₂×C₄×C₆₁	C₂×Q₁₆	1	2	yes	—
368	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
372	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
373	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
374	C₈×C₆₁	—	2	2	no	—
375	C₈×C₆₁	—	4	1	no	—
376	C₈×C₆₁	—	4	1	no	—
377	C₈×C₆₁	—	4	1	no	—
378	#24437	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
379	C₂²×C₆₁	—	2	2	no	—
380	C₂²×C₆₁	—	2	2	no	—
381	C₂²×C₆₁	—	2	2	no	—
382	C₂²×C₆₁	—	2	2	no	—
383	C₂²×C₆₁	—	2	2	no	—
384	C₂²×C₆₁	—	2	2	no	—
385	C₂²×C₆₁	—	2	2	no	—
386	C₂²×C₆₁	—	2	2	no	—
387	C₂²×C₆₁	—	2	2	no	—
388	C₂²×C₆₁	—	4	1	no	—
389	C₂²×C₆₁	—	4	1	no	—
390	C₂²×C₆₁	—	4	1	no	—
391	C₂²×C₆₁	—	4	1	no	—
392	C₂²×C₆₁	#451	1	4	yes	complemented
393	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
394	C₂²×C₆₁	D₄²	1	1	yes	characteristic
395	C₂²×C₆₁	#546	1	1	yes	characteristic
396	C₂²×C₆₁	C₂²×Q₁₆	1	1	yes	characteristic
397	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
398	C₂²×C₆₁	#577	1	1	yes	characteristic
399	C₂²×C₆₁	#578	1	1	yes	characteristic
400	C₄×C₆₁	—	2	2	no	—
401	C₄×C₆₁	—	2	4	no	—
402	C₄×C₆₁	—	2	2	no	—
403	C₄×C₆₁	—	4	1	no	—
404	C₄×C₆₁	—	4	2	no	—
405	C₄×C₆₁	—	4	2	no	—
406	C₄×C₆₁	—	4	2	no	—
407	C₄×C₆₁	—	4	1	no	—
408	C₄×C₆₁	—	4	2	no	—
409	C₄×C₆₁	—	8	1	no	—
410	C₄×C₆₁	—	8	1	no	—
411	C₄×C₆₁	—	8	1	no	—
412	C₄×C₆₁	C₂×#121	1	1	yes	characteristic
413	C₄×C₆₁	#534	1	1	yes	characteristic
414	C₄×C₆₁	D₄²	1	1	yes	characteristic
415	C₄×C₆₁	#546	1	1	yes	characteristic
416	C₂×D₄×Q₈	C₂×C₆₁	1	1	yes	characteristic
417	C₂×#467	C₂×C₆₁	1	1	yes	characteristic, complemented
418	C₂×#451	C₂×C₆₁	1	1	yes	characteristic, complemented
419	C₂×#451	C₂×C₆₁	1	1	yes	characteristic, complemented
420	C₂²×#103	C₂×C₆₁	1	1	yes	characteristic, complemented
421	#2417	C₂×C₆₁	1	1	yes	characteristic
422	#2043	C₂×C₆₁	1	1	yes	characteristic, complemented
423	#2036	C₂×C₆₁	1	1	yes	characteristic, complemented
424	#2016	C₂×C₆₁	1	1	yes	characteristic, complemented
425	#2001	C₂×C₆₁	1	1	yes	characteristic, complemented
426	#1878	C₂×C₆₁	1	1	yes	characteristic, complemented
427	#1872	C₂×C₆₁	1	1	yes	characteristic, complemented
428	#1869	C₂×C₆₁	1	1	yes	characteristic
429	#1863	C₂×C₆₁	1	1	yes	characteristic, complemented
430	#1787	C₂×C₆₁	1	1	yes	characteristic, complemented
431	C₂×C₆₁	—	2	4	no	—
432	C₂×C₆₁	—	4	2	no	—
433	C₂×C₆₁	#2410	1	1	yes	characteristic
434	C₂×C₆₁	C₂×#451	1	1	yes	characteristic
435	C₂×C₆₁	#3013	1	1	yes	characteristic
436	C₂×C₆₁	#3266	1	1	yes	characteristic
437	C₂×C₆₁	D₄×Q₁₆	1	1	yes	characteristic
438	C₂×C₆₁	#3299	1	1	yes	characteristic
439	C₂×C₆₁	#3312	1	1	yes	characteristic
440	C₂³×Q₈	C₂²×C₆₁	1	1	yes	characteristic
441	C₂³×Q₈	C₂²×C₆₁	1	1	yes	characteristic
442	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
443	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
444	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
445	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
446	D₄×Q₈	—	2	4	no	—
447	D₄×Q₈	—	2	4	no	—
448	C₂×C₄⋊Q₈	—	2	1	no	—
449	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
450	C₂×C₂²⋊Q₈	—	2	1	no	—
451	C₂×C₂²⋊Q₈	—	2	1	no	—
452	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
453	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
454	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
455	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
456	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
457	C₂×C₄×D₄	—	2	1	no	—
458	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
459	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
460	#467	—	2	4	no	—
461	#451	—	2	4	no	—
462	#451	—	2	4	no	—
463	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
464	C₂×#103	—	2	4	no	—
465	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
466	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
467	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
468	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
469	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
470	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
471	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
472	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
473	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
474	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
475	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
476	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
477	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
478	#398	—	2	1	no	—
479	#396	—	2	1	no	—
480	#391	C₂²×C₆₁	1	1	yes	characteristic
481	#389	C₂²×C₆₁	1	1	yes	characteristic
482	#386	—	2	1	no	—
483	#380	—	2	1	no	—
484	#380	C₂²×C₆₁	1	1	yes	characteristic
485	#340	C₂²×C₆₁	1	1	yes	characteristic
486	#340	C₂²×C₆₁	1	1	yes	characteristic
487	#336	C₂²×C₆₁	1	1	yes	characteristic
488	#336	C₂²×C₆₁	1	1	yes	characteristic
489	C₆₁	#24437	1	1	yes	characteristic, direct product factor, Sylow
490	C₂²×Q₈	—	2	2	no	—
491	C₂²×Q₈	—	2	2	no	—
492	C₂²×Q₈	—	2	1	no	—
493	C₂²×Q₈	—	2	1	no	—
494	C₂²×Q₈	—	2	2	no	—
495	C₂²×Q₈	—	2	2	no	—
496	C₂²×Q₈	—	2	2	no	—
497	C₂²×Q₈	—	2	2	no	—
498	C₂²×Q₈	—	2	2	no	—
499	C₂²×Q₈	—	4	1	no	—
500	C₂²×Q₈	—	4	1	no	—
501	C₂²×Q₈	—	4	1	no	—
502	C₂²×Q₈	—	4	1	no	—
503	C₂²×Q₈	D₄×C₆₁	1	4	yes	—
504	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
505	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
506	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
507	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
508	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
509	C₂³×C₄	—	2	1	no	—
510	C₂³×C₄	—	2	1	no	—
511	C₂³×C₄	—	2	1	no	—
512	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
514	C₂×Q₁₆	—	2	2	no	—
515	C₂×Q₁₆	—	2	2	no	—
516	C₂×Q₁₆	—	2	2	no	—
517	C₂×Q₁₆	—	2	2	no	—
518	C₂×Q₁₆	—	2	2	no	—
519	C₂×Q₁₆	—	2	2	no	—
520	C₂×Q₁₆	—	4	1	no	—
521	C₂×Q₁₆	—	4	1	no	—
522	C₂×Q₁₆	—	4	1	no	—
523	C₂²×C₈	—	2	2	no	—
524	C₂²×C₈	—	2	2	no	—
525	C₂²×C₈	—	4	1	no	—
526	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
527	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
528	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
529	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
530	C₄⋊Q₈	—	2	8	no	—
531	C₄⋊Q₈	—	2	2	no	—
532	C₄⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	8	no	—
534	C₂²⋊Q₈	—	2	8	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	2	no	—
538	C₂²⋊Q₈	—	2	2	no	—
539	C₂²⋊Q₈	—	2	2	no	—
540	C₂²⋊Q₈	—	2	2	no	—
541	C₂²⋊Q₈	—	4	1	no	—
542	C₂²⋊Q₈	D₄×C₆₁	1	4	yes	—
543	C₄×Q₈	—	2	2	no	—
544	C₄×Q₈	—	2	2	no	—
545	C₄×D₄	—	2	8	no	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	2	2	no	—
548	C₂×C₄⋊C₄	—	2	1	no	—
549	C₂×C₄⋊C₄	—	2	1	no	—
550	C₂×C₄⋊C₄	—	2	1	no	—
551	C₂×C₄⋊C₄	—	2	1	no	—
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	—	2	2	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	—	4	1	no	—
559	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
563	C₂×C₄⋊C₄	C₂³×C₆₁	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	D₄×C₆₁	1	1	yes	characteristic
570	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
571	C₂×C₄²	—	2	1	no	—
572	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
573	#107	—	2	2	no	—
574	#103	—	2	2	no	—
575	#103	—	2	2	no	—
576	#103	—	2	2	no	—
577	#103	—	2	2	no	—
578	#103	—	2	2	no	—
579	#103	—	2	2	no	—
580	#103	—	2	2	no	—
581	#103	—	2	2	no	—
582	#103	—	4	1	no	—
583	#103	D₄×C₆₁	1	4	yes	complemented
584	C₂²⋊C₈	—	2	2	no	—
585	C₂²⋊C₈	—	2	2	no	—
586	C₂²⋊C₈	—	4	1	no	—
587	#95	—	2	1	no	—
588	#95	—	2	1	no	—
589	#95	—	2	1	no	—
590	#95	—	2	1	no	—
591	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
592	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
593	C₂×Q₈	—	2	4	no	—
594	C₂×Q₈	—	2	4	no	—
595	C₂×Q₈	—	2	1	no	—
596	C₂×Q₈	—	2	1	no	—
597	C₂×Q₈	—	2	1	no	—
598	C₂×Q₈	—	2	1	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	2	8	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	2	1	no	—
604	C₂×Q₈	—	2	1	no	—
605	C₂×Q₈	—	2	1	no	—
606	C₂×Q₈	—	2	1	no	—
607	C₂×Q₈	—	2	1	no	—
608	C₂×Q₈	—	2	1	no	—
609	C₂×Q₈	—	2	1	no	—
610	C₂×Q₈	—	2	1	no	—
611	C₂×Q₈	—	2	1	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	4	2	no	—
616	C₂×Q₈	—	4	2	no	—
617	C₂×Q₈	—	4	2	no	—
618	C₂×Q₈	—	4	2	no	—
619	C₂×Q₈	—	4	4	no	—
620	C₂×Q₈	—	4	4	no	—
621	C₂×Q₈	—	4	4	no	—
622	C₂×Q₈	—	4	4	no	—
623	C₂×Q₈	—	4	4	no	—
624	C₂×Q₈	—	4	4	no	—
625	C₂×Q₈	—	4	4	no	—
626	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
627	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
628	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
629	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
630	C₂×Q₈	#41×C₆₁	1	2	yes	—
631	C₂×D₄	—	2	2	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	Q₁₆×C₆₁	1	4	yes	complemented
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	—	4	2	no	—
658	C₂²×C₄	—	4	2	no	—
659	C₂²×C₄	—	4	2	no	—
660	C₂²×C₄	—	8	1	no	—
661	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
662	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
663	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
664	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
665	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
666	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
667	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
668	Q₁₆	—	4	4	no	—
669	Q₁₆	—	4	4	no	—
670	Q₁₆	—	4	4	no	—
671	C₂×C₈	—	2	1	no	—
672	C₂×C₈	—	2	1	no	—
673	C₂×C₈	—	2	1	no	—
674	C₂×C₈	—	2	1	no	—
675	C₂×C₈	—	2	1	no	—
676	C₂×C₈	—	2	1	no	—
677	C₂×C₈	—	2	1	no	—
678	C₂×C₈	—	2	1	no	—
679	C₂×C₈	—	2	1	no	—
680	C₂×C₈	—	2	1	no	—
681	C₂×C₈	—	2	1	no	—
682	C₂×C₈	—	4	4	no	—
683	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	4	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	4	2	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	—	8	1	no	—
700	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
701	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	4	2	no	—
707	C₂²⋊C₄	—	4	2	no	—
708	C₂²⋊C₄	—	8	1	no	—
709	C₄²	—	2	4	no	—
710	C₄²	—	2	1	no	—
711	C₄²	—	2	1	no	—
712	C₂³	—	2	1	no	—
713	C₂³	—	2	1	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	#120×C₆₁	1	2	yes	—
723	C₂³	C₂×Q₁₆×C₆₁	1	2	yes	—
724	C₂³	C₂×Q₁₆×C₆₁	1	2	yes	—
725	C₂³	#137×C₆₁	1	2	yes	—
726	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
727	Q₈	—	2	2	no	—
728	Q₈	—	2	2	no	—
729	Q₈	—	2	2	no	—
730	Q₈	—	2	2	no	—
731	Q₈	—	2	2	no	—
732	Q₈	—	2	2	no	—
733	Q₈	—	2	2	no	—
734	Q₈	—	4	8	no	—
735	Q₈	—	4	8	no	—
736	Q₈	—	4	1	no	—
737	Q₈	—	4	1	no	—
738	Q₈	—	4	1	no	—
739	Q₈	—	4	1	no	—
740	Q₈	—	4	1	no	—
741	Q₈	—	4	1	no	—
742	Q₈	—	4	1	no	—
743	Q₈	—	4	1	no	—
744	Q₈	#121×C₆₁	1	4	yes	—
745	D₄	—	2	8	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	4	8	no	—
768	C₂×C₄	—	4	8	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	—	4	1	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	8	4	no	—
791	C₂×C₄	#120×C₆₁	1	2	yes	—
792	C₂×C₄	C₂×Q₁₆×C₆₁	1	2	yes	—
793	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
794	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
795	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
796	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
797	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
798	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
799	C₈	—	2	2	no	—
800	C₈	—	4	1	no	—
801	C₈	—	4	1	no	—
802	C₈	—	4	1	no	—
803	C₂²	—	2	2	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	2	no	—
806	C₂²	—	2	2	no	—
807	C₂²	—	2	2	no	—
808	C₂²	—	2	2	no	—
809	C₂²	—	2	2	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	2	2	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	4	1	no	—
814	C₂²	—	4	1	no	—
815	C₂²	—	4	1	no	—
816	C₂²	C₆₁×#451	1	4	yes	complemented
817	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
818	C₂²	D₄²×C₆₁	1	1	yes	characteristic
819	C₂²	C₆₁×#546	1	1	yes	characteristic
820	C₂²	C₂²×Q₁₆×C₆₁	1	1	yes	characteristic
821	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
822	C₂²	C₆₁×#577	1	1	yes	characteristic
823	C₂²	C₆₁×#578	1	1	yes	characteristic
824	C₄	—	2	2	no	—
825	C₄	—	2	4	no	—
826	C₄	—	2	2	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	2	no	—
833	C₄	—	8	1	no	—
834	C₄	—	8	1	no	—
835	C₄	—	8	1	no	—
836	C₄	C₂×#121×C₆₁	1	1	yes	characteristic
837	C₄	C₆₁×#534	1	1	yes	characteristic
838	C₄	D₄²×C₆₁	1	1	yes	characteristic
839	C₄	C₆₁×#546	1	1	yes	characteristic
840	C₂	—	2	4	no	—
841	C₂	—	4	2	no	—
842	C₂	C₆₁×#2410	1	1	yes	characteristic
843	C₂	C₂×C₆₁×#451	1	1	yes	characteristic
844	C₂	C₆₁×#3013	1	1	yes	characteristic
845	C₂	C₆₁×#3266	1	1	yes	characteristic
846	C₂	D₄×Q₁₆×C₆₁	1	1	yes	characteristic
847	C₂	C₆₁×#3299	1	1	yes	characteristic
848	C₂	C₆₁×#3312	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂²×D₄×C₆₁	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄×D₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#467	C₂	semidirect
3. C₂×C₆₁×#451	C₂	semidirect
4. C₂×C₆₁×#451	C₂	semidirect
5. C₂²×#103×C₆₁	C₂	semidirect
7. C₆₁×#2043	C₂	semidirect
8. C₆₁×#2036	C₂	semidirect
9. C₆₁×#2016	C₂	semidirect
10. C₆₁×#2001	C₂	semidirect
11. C₆₁×#1878	C₂	semidirect
12. C₆₁×#1872	C₂	semidirect
14. C₆₁×#1863	C₂	semidirect
15. C₆₁×#1787	C₂	semidirect
158. #103×C₆₁	D₄	semidirect
208. C₂×D₄×C₆₁	Q₁₆	semidirect
378. #24437	C₆₁	direct (N × H)
392. C₂²×C₆₁	#451	semidirect
417. C₂×#467	C₂×C₆₁	semidirect
418. C₂×#451	C₂×C₆₁	semidirect
419. C₂×#451	C₂×C₆₁	semidirect
420. C₂²×#103	C₂×C₆₁	semidirect
422. #2043	C₂×C₆₁	semidirect
423. #2036	C₂×C₆₁	semidirect
424. #2016	C₂×C₆₁	semidirect
425. #2001	C₂×C₆₁	semidirect
426. #1878	C₂×C₆₁	semidirect
427. #1872	C₂×C₆₁	semidirect
429. #1863	C₂×C₆₁	semidirect
430. #1787	C₂×C₆₁	semidirect
489. C₆₁	#24437	direct (N × H)
583. #103	D₄×C₆₁	semidirect
633. C₂×D₄	Q₁₆×C₆₁	semidirect
816. C₂²	C₆₁×#451	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₆₁	2
C₂×C₆₁×#467	2
C₂×C₆₁×#451	2
C₂²×#103×C₆₁	2
C₆₁×#2417	2
C₆₁×#2043	2
C₆₁×#2036	2
C₆₁×#2016	2
C₆₁×#2001	2
C₆₁×#1878	2
C₆₁×#1872	2
C₆₁×#1869	2
C₆₁×#1863	2
C₆₁×#1787	2
#24437	61

Subgroups — C61×#24437 #29527870

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24437 #29527870