Subgroups — C₆₁×#34319 #29537752

Order 15616.

2344 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#553	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2374	C₂	1	2	yes	maximal, complemented
3	C₆₁×#2373	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2370	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2363	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2361	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2357	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2357	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#2352	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2346	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#2344	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#2334	C₂	1	2	yes	maximal, complemented
14	C₆₁×#2333	C₂	1	2	yes	maximal, complemented
15	C₆₁×#2324	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#2324	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×#125×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#123×C₆₁	C₂	1	2	yes	maximal, complemented
19	C₆₁×#2293	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#2290	C₂	1	2	yes	maximal, complemented
21	C₆₁×#2274	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₁×#2274	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₆₁×#553	C₄	1	16	yes	complemented
25	C₂×#126×C₆₁	C₂²	1	2	yes	—
26	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#123×C₆₁	C₂²	1	2	yes	—
28	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#121×C₆₁	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
40	C₂×#117×C₆₁	C₂²	1	2	yes	—
41	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
43	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₆₁	C₂²	1	2	yes	—
45	C₆₁×#390	C₂²	1	1	yes	characteristic
46	C₆₁×#390	C₂²	1	1	yes	characteristic
47	C₆₁×#390	C₂²	1	1	yes	characteristic
48	C₆₁×#390	C₂²	1	1	yes	characteristic
49	C₆₁×#390	C₂²	1	2	yes	—
50	C₆₁×#390	C₂²	1	2	yes	—
51	C₆₁×#390	C₂²	1	2	yes	—
52	C₆₁×#389	C₂²	1	1	yes	characteristic
53	C₆₁×#389	C₂²	1	1	yes	characteristic
54	C₆₁×#389	C₂²	1	1	yes	characteristic
55	C₆₁×#389	C₂²	1	1	yes	characteristic
56	C₆₁×#389	C₂²	1	1	yes	characteristic
57	C₆₁×#389	C₂²	1	1	yes	characteristic
58	C₆₁×#389	C₂²	1	2	yes	—
59	C₆₁×#388	C₂²	1	1	yes	characteristic
60	C₆₁×#388	C₂²	1	2	yes	—
61	C₆₁×#388	C₂²	1	1	yes	characteristic
62	C₆₁×#388	C₂²	1	1	yes	characteristic
63	C₆₁×#388	C₂²	1	1	yes	characteristic
64	C₆₁×#388	C₂²	1	2	yes	—
65	C₆₁×#388	C₂²	1	2	yes	—
66	C₆₁×#388	C₂²	1	2	yes	—
67	C₆₁×#388	C₂²	1	2	yes	—
68	C₆₁×#388	C₂²	1	2	yes	—
69	C₆₁×#388	C₂²	1	2	yes	—
70	C₆₁×#388	C₂²	1	2	yes	—
71	C₆₁×#388	C₂²	1	2	yes	—
72	C₆₁×#387	C₂²	1	2	yes	—
73	C₆₁×#387	C₂²	1	2	yes	—
74	C₆₁×#387	C₂²	1	2	yes	—
75	C₆₁×#387	C₂²	1	2	yes	—
76	C₆₁×#387	C₂²	1	2	yes	—
77	C₆₁×#387	C₂²	1	2	yes	—
78	C₆₁×#387	C₂²	1	2	yes	—
79	C₆₁×#386	C₂²	1	2	yes	—
80	C₆₁×#386	C₂²	1	2	yes	—
81	C₆₁×#386	C₂²	1	2	yes	—
82	C₆₁×#386	C₂²	1	2	yes	—
83	C₆₁×#386	C₂²	1	2	yes	—
84	C₆₁×#385	C₂²	1	2	yes	—
85	C₆₁×#385	C₂²	1	2	yes	—
86	C₆₁×#385	C₂²	1	2	yes	—
87	C₆₁×#382	C₂²	1	1	yes	characteristic
88	C₆₁×#382	C₂²	1	2	yes	—
89	C₆₁×#381	C₂²	1	2	yes	—
90	C₆₁×#381	C₂²	1	2	yes	—
91	C₆₁×#380	C₂²	1	1	yes	characteristic
92	C₆₁×#380	C₂²	1	1	yes	characteristic
93	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
95	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
96	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
99	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
100	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
103	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
110	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
111	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
112	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
114	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
122	C₆₁×#376	C₂²	1	2	yes	—
123	C₄³×C₆₁	C₂²	1	1	yes	characteristic
124	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
126	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
128	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
129	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
132	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
133	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
134	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
135	#126×C₆₁	C₂×C₄	1	16	yes	complemented
136	#125×C₆₁	C₂×C₄	1	8	yes	complemented
137	#123×C₆₁	C₂×C₄	1	16	yes	complemented
138	#121×C₆₁	C₂×C₄	1	8	yes	—
139	#121×C₆₁	C₂×C₄	1	16	yes	complemented
140	#121×C₆₁	C₂×C₄	1	8	yes	complemented
141	C₄×D₄×C₆₁	—	2	4	no	—
142	C₄×D₄×C₆₁	—	2	4	no	—
143	C₄×D₄×C₆₁	—	4	4	no	—
144	C₄×D₄×C₆₁	C₂×C₄	1	16	yes	complemented
145	C₄×D₄×C₆₁	C₂×C₄	1	8	yes	complemented
146	C₄×D₄×C₆₁	C₂×C₄	1	8	yes	complemented
147	#117×C₆₁	—	2	4	no	—
148	#117×C₆₁	—	2	4	no	—
149	#117×C₆₁	—	2	4	no	—
150	#117×C₆₁	—	4	4	no	—
151	#117×C₆₁	C₂×C₄	1	8	yes	complemented
152	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
153	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	8	yes	complemented
154	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₆₁	—	4	4	no	—
200	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
203	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
204	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
210	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
211	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
212	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
213	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
214	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
215	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
216	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
217	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
219	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
220	#95×C₆₁	C₂³	1	1	yes	characteristic
221	#95×C₆₁	C₂³	1	2	yes	—
222	#95×C₆₁	C₂³	1	2	yes	—
223	#95×C₆₁	C₂³	1	2	yes	—
224	#95×C₆₁	C₂³	1	2	yes	—
225	#95×C₆₁	C₂³	1	1	yes	characteristic
226	#95×C₆₁	C₂³	1	2	yes	—
227	#95×C₆₁	C₂³	1	2	yes	—
228	#95×C₆₁	C₂³	1	2	yes	—
229	#95×C₆₁	C₂³	1	1	yes	characteristic
230	#95×C₆₁	C₂³	1	2	yes	—
231	#95×C₆₁	C₂³	1	2	yes	—
232	#95×C₆₁	C₂³	1	2	yes	—
233	#95×C₆₁	C₂³	1	2	yes	—
234	#95×C₆₁	C₂³	1	2	yes	—
235	#95×C₆₁	C₂³	1	2	yes	—
236	#95×C₆₁	C₂³	1	2	yes	—
237	#95×C₆₁	C₂³	1	1	yes	characteristic
238	#95×C₆₁	C₂³	1	1	yes	characteristic
239	#95×C₆₁	C₂³	1	1	yes	characteristic
240	#95×C₆₁	C₂³	1	2	yes	—
241	#95×C₆₁	C₂³	1	2	yes	—
242	#95×C₆₁	C₂³	1	2	yes	—
243	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
244	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
245	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
246	C₂×D₄×C₆₁	—	2	2	no	—
247	C₂×D₄×C₆₁	—	2	2	no	—
248	C₂×D₄×C₆₁	—	4	2	no	—
249	C₂×D₄×C₆₁	—	4	2	no	—
250	C₂×D₄×C₆₁	—	4	1	no	—
251	C₂×D₄×C₆₁	—	4	1	no	—
252	C₂×D₄×C₆₁	—	4	2	no	—
253	C₂×D₄×C₆₁	—	4	2	no	—
254	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
255	C₂×D₄×C₆₁	C₂²×C₄	1	8	yes	—
256	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
257	C₂×D₄×C₆₁	C₂²×C₄	1	8	yes	—
258	C₂²×C₄×C₆₁	—	2	2	no	—
259	C₂²×C₄×C₆₁	—	2	2	no	—
260	C₂²×C₄×C₆₁	—	2	2	no	—
261	C₂²×C₄×C₆₁	—	2	2	no	—
262	C₂²×C₄×C₆₁	—	2	4	no	—
263	C₂²×C₄×C₆₁	—	2	4	no	—
264	C₂²×C₄×C₆₁	—	2	4	no	—
265	C₂²×C₄×C₆₁	—	2	4	no	—
266	C₂²×C₄×C₆₁	—	4	2	no	—
267	C₂²×C₄×C₆₁	—	4	2	no	—
268	C₂²×C₄×C₆₁	—	4	2	no	—
269	C₂²×C₄×C₆₁	—	4	2	no	—
270	C₂²×C₄×C₆₁	—	4	2	no	—
271	C₂²×C₄×C₆₁	—	4	2	no	—
272	C₂²×C₄×C₆₁	—	4	2	no	—
273	C₂²×C₄×C₆₁	—	4	2	no	—
274	C₂²×C₄×C₆₁	—	4	2	no	—
275	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
276	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
277	C₂²×C₄×C₆₁	C₂²×C₄	1	8	yes	—
278	C₂²×C₄×C₆₁	C₂²×C₄	1	8	yes	—
279	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
299	C₄⋊C₄×C₆₁	—	2	4	no	—
300	C₄⋊C₄×C₆₁	—	2	2	no	—
301	C₄⋊C₄×C₆₁	—	2	2	no	—
302	C₄⋊C₄×C₆₁	—	2	2	no	—
303	C₄⋊C₄×C₆₁	—	2	2	no	—
304	C₄⋊C₄×C₆₁	—	2	2	no	—
305	C₄⋊C₄×C₆₁	—	2	2	no	—
306	C₄⋊C₄×C₆₁	—	2	2	no	—
307	C₄⋊C₄×C₆₁	—	2	4	no	—
308	C₄⋊C₄×C₆₁	—	4	1	no	—
309	C₄⋊C₄×C₆₁	—	4	1	no	—
310	C₄⋊C₄×C₆₁	—	4	2	no	—
311	C₄⋊C₄×C₆₁	—	4	2	no	—
312	C₄⋊C₄×C₆₁	—	4	2	no	—
313	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
314	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
315	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
316	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
317	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
318	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
319	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
320	C₄⋊C₄×C₆₁	#41	1	4	yes	—
321	C₂²⋊C₄×C₆₁	—	2	4	no	—
322	C₂²⋊C₄×C₆₁	—	2	2	no	—
323	C₂²⋊C₄×C₆₁	—	2	2	no	—
324	C₂²⋊C₄×C₆₁	—	2	2	no	—
325	C₂²⋊C₄×C₆₁	—	2	2	no	—
326	C₂²⋊C₄×C₆₁	—	2	4	no	—
327	C₂²⋊C₄×C₆₁	—	2	4	no	—
328	C₂²⋊C₄×C₆₁	—	2	2	no	—
329	C₂²⋊C₄×C₆₁	—	2	2	no	—
330	C₂²⋊C₄×C₆₁	—	4	1	no	—
331	C₂²⋊C₄×C₆₁	—	4	2	no	—
332	C₂²⋊C₄×C₆₁	—	4	1	no	—
333	C₂²⋊C₄×C₆₁	—	4	2	no	—
334	C₂²⋊C₄×C₆₁	—	4	2	no	—
335	C₂²⋊C₄×C₆₁	—	4	2	no	—
336	C₂²⋊C₄×C₆₁	—	4	2	no	—
337	C₂²⋊C₄×C₆₁	—	4	2	no	—
338	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
339	C₂²⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
340	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
341	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
342	C₂²⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
343	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
344	C₄²×C₆₁	—	2	4	no	—
345	C₄²×C₆₁	—	2	2	no	—
346	C₄²×C₆₁	—	2	2	no	—
347	C₄²×C₆₁	—	2	2	no	—
348	C₄²×C₆₁	—	2	2	no	—
349	C₄²×C₆₁	—	2	4	no	—
350	C₄²×C₆₁	—	4	2	no	—
351	C₄²×C₆₁	—	4	2	no	—
352	C₄²×C₆₁	—	4	2	no	—
353	C₄²×C₆₁	—	4	1	no	—
354	C₄²×C₆₁	—	4	1	no	—
355	C₄²×C₆₁	—	4	2	no	—
356	C₄²×C₆₁	—	4	2	no	—
357	C₄²×C₆₁	—	4	1	no	—
358	C₄²×C₆₁	—	4	2	no	—
359	C₄²×C₆₁	—	4	2	no	—
360	C₄²×C₆₁	—	4	2	no	—
361	C₄²×C₆₁	C₂²×C₄	1	8	yes	—
362	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
363	C₄²×C₆₁	#41	1	4	yes	—
364	C₂³×C₆₁	—	2	1	no	—
365	C₂³×C₆₁	—	2	1	no	—
366	C₂³×C₆₁	—	2	1	no	—
367	C₂³×C₆₁	—	2	2	no	—
368	C₂³×C₆₁	—	2	2	no	—
369	C₂³×C₆₁	—	2	1	no	—
370	C₂³×C₆₁	—	2	1	no	—
371	C₂³×C₆₁	—	2	1	no	—
372	C₂³×C₆₁	—	2	2	no	—
373	C₂³×C₆₁	—	2	1	no	—
374	C₂³×C₆₁	—	2	1	no	—
375	C₂³×C₆₁	—	2	2	no	—
376	C₂³×C₆₁	—	2	2	no	—
377	C₂³×C₆₁	—	2	2	no	—
378	C₂³×C₆₁	—	2	1	no	—
379	C₂³×C₆₁	—	2	1	no	—
380	C₂³×C₆₁	—	2	1	no	—
381	C₂³×C₆₁	—	2	1	no	—
382	C₂³×C₆₁	C₂³×C₄	1	2	yes	—
383	C₂³×C₆₁	C₂³×C₄	1	4	yes	—
384	C₂³×C₆₁	C₂³×C₄	1	2	yes	—
385	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
386	D₄×C₆₁	—	2	8	no	—
387	D₄×C₆₁	—	4	8	no	—
388	D₄×C₆₁	—	4	4	no	—
389	D₄×C₆₁	—	4	8	no	—
390	C₂×C₄×C₆₁	—	2	1	no	—
391	C₂×C₄×C₆₁	—	2	1	no	—
392	C₂×C₄×C₆₁	—	2	1	no	—
393	C₂×C₄×C₆₁	—	2	1	no	—
394	C₂×C₄×C₆₁	—	2	1	no	—
395	C₂×C₄×C₆₁	—	2	1	no	—
396	C₂×C₄×C₆₁	—	2	2	no	—
397	C₂×C₄×C₆₁	—	2	1	no	—
398	C₂×C₄×C₆₁	—	2	2	no	—
399	C₂×C₄×C₆₁	—	2	2	no	—
400	C₂×C₄×C₆₁	—	2	1	no	—
401	C₂×C₄×C₆₁	—	2	1	no	—
402	C₂×C₄×C₆₁	—	2	2	no	—
403	C₂×C₄×C₆₁	—	2	1	no	—
404	C₂×C₄×C₆₁	—	2	1	no	—
405	C₂×C₄×C₆₁	—	2	1	no	—
406	C₂×C₄×C₆₁	—	2	2	no	—
407	C₂×C₄×C₆₁	—	2	1	no	—
408	C₂×C₄×C₆₁	—	2	1	no	—
409	C₂×C₄×C₆₁	—	2	2	no	—
410	C₂×C₄×C₆₁	—	2	2	no	—
411	C₂×C₄×C₆₁	—	2	2	no	—
412	C₂×C₄×C₆₁	—	2	8	no	—
413	C₂×C₄×C₆₁	—	2	8	no	—
414	C₂×C₄×C₆₁	—	2	1	no	—
415	C₂×C₄×C₆₁	—	2	1	no	—
416	C₂×C₄×C₆₁	—	2	1	no	—
417	C₂×C₄×C₆₁	—	2	1	no	—
418	C₂×C₄×C₆₁	—	2	1	no	—
419	C₂×C₄×C₆₁	—	2	2	no	—
420	C₂×C₄×C₆₁	—	2	2	no	—
421	C₂×C₄×C₆₁	—	2	2	no	—
422	C₂×C₄×C₆₁	—	2	2	no	—
423	C₂×C₄×C₆₁	—	2	1	no	—
424	C₂×C₄×C₆₁	—	2	1	no	—
425	C₂×C₄×C₆₁	—	2	2	no	—
426	C₂×C₄×C₆₁	—	2	1	no	—
427	C₂×C₄×C₆₁	—	2	2	no	—
428	C₂×C₄×C₆₁	—	2	1	no	—
429	C₂×C₄×C₆₁	—	2	1	no	—
430	C₂×C₄×C₆₁	—	2	2	no	—
431	C₂×C₄×C₆₁	—	2	1	no	—
432	C₂×C₄×C₆₁	—	2	1	no	—
433	C₂×C₄×C₆₁	—	2	1	no	—
434	C₂×C₄×C₆₁	—	2	1	no	—
435	C₂×C₄×C₆₁	—	2	2	no	—
436	C₂×C₄×C₆₁	—	2	2	no	—
437	C₂×C₄×C₆₁	—	2	1	no	—
438	C₂×C₄×C₆₁	—	4	8	no	—
439	C₂×C₄×C₆₁	—	4	8	no	—
440	C₂×C₄×C₆₁	—	4	8	no	—
441	C₂×C₄×C₆₁	—	4	8	no	—
442	C₂×C₄×C₆₁	—	8	4	no	—
443	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
444	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
445	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
446	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
447	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
448	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
449	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
450	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
451	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
452	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
453	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
454	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
455	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
456	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
457	#34319	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
458	C₂²×C₆₁	—	2	2	no	—
459	C₂²×C₆₁	—	2	2	no	—
460	C₂²×C₆₁	—	2	4	no	—
461	C₂²×C₆₁	—	2	2	no	—
462	C₂²×C₆₁	—	2	2	no	—
463	C₂²×C₆₁	—	2	4	no	—
464	C₂²×C₆₁	—	2	2	no	—
465	C₂²×C₆₁	—	2	4	no	—
466	C₂²×C₆₁	—	2	2	no	—
467	C₂²×C₆₁	—	4	2	no	—
468	C₂²×C₆₁	—	4	1	no	—
469	C₂²×C₆₁	—	4	1	no	—
470	C₂²×C₆₁	—	4	1	no	—
471	C₂²×C₆₁	—	4	1	no	—
472	C₂²×C₆₁	—	4	2	no	—
473	C₂²×C₆₁	—	4	2	no	—
474	C₂²×C₆₁	—	4	1	no	—
475	C₂²×C₆₁	—	4	1	no	—
476	C₂²×C₆₁	—	4	1	no	—
477	C₂²×C₆₁	—	4	2	no	—
478	C₂²×C₆₁	—	4	1	no	—
479	C₂²×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
480	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
481	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
482	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
483	C₂²×C₆₁	#585	1	1	yes	characteristic
484	C₂²×C₆₁	#585	1	1	yes	characteristic
485	C₂²×C₆₁	#585	1	1	yes	characteristic
486	C₄×C₆₁	—	2	2	no	—
487	C₄×C₆₁	—	2	2	no	—
488	C₄×C₆₁	—	2	4	no	—
489	C₄×C₆₁	—	2	2	no	—
490	C₄×C₆₁	—	2	2	no	—
491	C₄×C₆₁	—	2	4	no	—
492	C₄×C₆₁	—	2	4	no	—
493	C₄×C₆₁	—	2	2	no	—
494	C₄×C₆₁	—	2	2	no	—
495	C₄×C₆₁	—	2	2	no	—
496	C₄×C₆₁	—	2	4	no	—
497	C₄×C₆₁	—	4	1	no	—
498	C₄×C₆₁	—	4	1	no	—
499	C₄×C₆₁	—	4	2	no	—
500	C₄×C₆₁	—	4	1	no	—
501	C₄×C₆₁	—	4	1	no	—
502	C₄×C₆₁	—	4	2	no	—
503	C₄×C₆₁	—	4	1	no	—
504	C₄×C₆₁	—	4	2	no	—
505	C₄×C₆₁	C₄×#41	1	4	yes	—
506	C₂×#553	C₂×C₆₁	1	1	yes	characteristic
507	#2374	C₂×C₆₁	1	2	yes	complemented
508	#2373	C₂×C₆₁	1	2	yes	complemented
509	#2370	C₂×C₆₁	1	1	yes	characteristic, complemented
510	#2363	C₂×C₆₁	1	1	yes	characteristic, complemented
511	#2363	C₂×C₆₁	1	2	yes	complemented
512	#2361	C₂×C₆₁	1	1	yes	characteristic, complemented
513	#2357	C₂×C₆₁	1	1	yes	characteristic, complemented
514	#2357	C₂×C₆₁	1	2	yes	complemented
515	#2352	C₂×C₆₁	1	1	yes	characteristic, complemented
516	#2346	C₂×C₆₁	1	1	yes	characteristic, complemented
517	#2344	C₂×C₆₁	1	1	yes	characteristic, complemented
518	#2334	C₂×C₆₁	1	2	yes	complemented
519	#2333	C₂×C₆₁	1	2	yes	complemented
520	#2324	C₂×C₆₁	1	1	yes	characteristic, complemented
521	#2324	C₂×C₆₁	1	1	yes	characteristic, complemented
522	C₄×#125	C₂×C₆₁	1	1	yes	characteristic, complemented
523	C₄×#123	C₂×C₆₁	1	2	yes	complemented
524	#2293	C₂×C₆₁	1	1	yes	characteristic, complemented
525	#2290	C₂×C₆₁	1	2	yes	complemented
526	#2274	C₂×C₆₁	1	1	yes	characteristic, complemented
527	#2274	C₂×C₆₁	1	1	yes	characteristic, complemented
528	C₄²×D₄	C₂×C₆₁	1	1	yes	characteristic, complemented
529	C₂×C₆₁	—	4	2	no	—
530	C₂×C₆₁	—	4	2	no	—
531	C₂×C₆₁	—	4	4	no	—
532	C₂×C₆₁	C₂×C₄×#41	1	1	yes	characteristic
533	C₂×C₆₁	#3428	1	1	yes	characteristic
534	C₂×C₆₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
535	C₂×C₆₁	#3506	1	1	yes	characteristic
536	C₂×C₆₁	#3512	1	1	yes	characteristic
537	C₂×C₆₁	#3513	1	1	yes	characteristic
538	C₂×C₆₁	#3524	1	1	yes	characteristic
539	#553	C₄×C₆₁	1	16	yes	complemented
540	C₂×#126	C₂²×C₆₁	1	2	yes	—
541	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
542	C₂×#123	C₂²×C₆₁	1	2	yes	—
543	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
544	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
545	C₂×#121	C₂²×C₆₁	1	2	yes	—
546	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
547	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
548	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
549	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
550	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
551	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
552	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
553	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
554	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
555	C₂×#117	C₂²×C₆₁	1	2	yes	—
556	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
557	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
558	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
559	C₂²×C₄²	C₂²×C₆₁	1	2	yes	—
560	#390	C₂²×C₆₁	1	1	yes	characteristic
561	#390	C₂²×C₆₁	1	1	yes	characteristic
562	#390	C₂²×C₆₁	1	2	yes	—
563	#390	C₂²×C₆₁	1	2	yes	—
564	#390	C₂²×C₆₁	1	1	yes	characteristic
565	#390	C₂²×C₆₁	1	2	yes	—
566	#390	C₂²×C₆₁	1	1	yes	characteristic
567	#389	C₂²×C₆₁	1	1	yes	characteristic
568	#389	C₂²×C₆₁	1	1	yes	characteristic
569	#389	C₂²×C₆₁	1	1	yes	characteristic
570	#389	C₂²×C₆₁	1	1	yes	characteristic
571	#389	C₂²×C₆₁	1	1	yes	characteristic
572	#389	C₂²×C₆₁	1	2	yes	—
573	#389	C₂²×C₆₁	1	1	yes	characteristic
574	#388	C₂²×C₆₁	1	2	yes	—
575	#388	C₂²×C₆₁	1	2	yes	—
576	#388	C₂²×C₆₁	1	2	yes	—
577	#388	C₂²×C₆₁	1	2	yes	—
578	#388	C₂²×C₆₁	1	2	yes	—
579	#388	C₂²×C₆₁	1	2	yes	—
580	#388	C₂²×C₆₁	1	2	yes	—
581	#388	C₂²×C₆₁	1	2	yes	—
582	#388	C₂²×C₆₁	1	2	yes	—
583	#388	C₂²×C₆₁	1	1	yes	characteristic
584	#388	C₂²×C₆₁	1	1	yes	characteristic
585	#388	C₂²×C₆₁	1	1	yes	characteristic
586	#388	C₂²×C₆₁	1	1	yes	characteristic
587	#387	C₂²×C₆₁	1	2	yes	—
588	#387	C₂²×C₆₁	1	2	yes	—
589	#387	C₂²×C₆₁	1	2	yes	—
590	#387	C₂²×C₆₁	1	2	yes	—
591	#387	C₂²×C₆₁	1	2	yes	—
592	#387	C₂²×C₆₁	1	2	yes	—
593	#387	C₂²×C₆₁	1	2	yes	—
594	#386	C₂²×C₆₁	1	2	yes	—
595	#386	C₂²×C₆₁	1	2	yes	—
596	#386	C₂²×C₆₁	1	2	yes	—
597	#386	C₂²×C₆₁	1	2	yes	—
598	#386	C₂²×C₆₁	1	2	yes	—
599	#385	C₂²×C₆₁	1	2	yes	—
600	#385	C₂²×C₆₁	1	2	yes	—
601	#385	C₂²×C₆₁	1	2	yes	—
602	#382	C₂²×C₆₁	1	1	yes	characteristic
603	#382	C₂²×C₆₁	1	2	yes	—
604	#381	C₂²×C₆₁	1	2	yes	—
605	#381	C₂²×C₆₁	1	2	yes	—
606	#380	C₂²×C₆₁	1	1	yes	characteristic
607	#380	C₂²×C₆₁	1	1	yes	characteristic
608	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
609	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
610	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
611	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
612	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
613	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
614	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
615	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
616	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
617	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
618	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
619	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
620	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
621	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
622	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
623	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
624	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
625	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
626	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
627	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
628	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
629	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
630	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
631	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
632	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
633	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
634	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
635	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
636	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
637	#376	C₂²×C₆₁	1	2	yes	—
638	C₄³	C₂²×C₆₁	1	1	yes	characteristic
639	C₆₁	#34319	1	1	yes	characteristic, direct product factor, Sylow
640	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
641	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
642	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
643	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
644	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
645	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
646	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
647	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
648	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
649	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
650	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
651	#126	C₂×C₄×C₆₁	1	16	yes	complemented
652	#125	C₂×C₄×C₆₁	1	8	yes	complemented
653	#123	C₂×C₄×C₆₁	1	16	yes	complemented
654	#121	C₂×C₄×C₆₁	1	8	yes	—
655	#121	C₂×C₄×C₆₁	1	16	yes	complemented
656	#121	C₂×C₄×C₆₁	1	8	yes	complemented
657	C₄×D₄	—	2	4	no	—
658	C₄×D₄	—	2	4	no	—
659	C₄×D₄	—	4	4	no	—
660	C₄×D₄	C₂×C₄×C₆₁	1	16	yes	complemented
661	C₄×D₄	C₂×C₄×C₆₁	1	8	yes	complemented
662	C₄×D₄	C₂×C₄×C₆₁	1	8	yes	complemented
663	#117	—	2	4	no	—
664	#117	—	2	4	no	—
665	#117	—	2	4	no	—
666	#117	—	4	4	no	—
667	#117	C₂×C₄×C₆₁	1	8	yes	complemented
668	C₂×C₄⋊C₄	—	2	4	no	—
669	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	8	yes	complemented
670	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
677	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
678	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
679	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
680	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
681	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
682	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
683	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
684	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
685	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
686	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
689	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
692	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
693	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
694	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
695	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
697	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
698	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
699	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
705	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
709	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
711	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
714	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
715	C₂×C₄²	—	4	4	no	—
716	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
717	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
718	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
719	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
720	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
721	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
722	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
723	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
724	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
725	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
726	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
727	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
728	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
729	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
730	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
731	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
732	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
733	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
734	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
735	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
736	#95	C₂³×C₆₁	1	1	yes	characteristic
737	#95	C₂³×C₆₁	1	2	yes	—
738	#95	C₂³×C₆₁	1	2	yes	—
739	#95	C₂³×C₆₁	1	2	yes	—
740	#95	C₂³×C₆₁	1	2	yes	—
741	#95	C₂³×C₆₁	1	1	yes	characteristic
742	#95	C₂³×C₆₁	1	2	yes	—
743	#95	C₂³×C₆₁	1	2	yes	—
744	#95	C₂³×C₆₁	1	2	yes	—
745	#95	C₂³×C₆₁	1	1	yes	characteristic
746	#95	C₂³×C₆₁	1	2	yes	—
747	#95	C₂³×C₆₁	1	2	yes	—
748	#95	C₂³×C₆₁	1	2	yes	—
749	#95	C₂³×C₆₁	1	2	yes	—
750	#95	C₂³×C₆₁	1	2	yes	—
751	#95	C₂³×C₆₁	1	2	yes	—
752	#95	C₂³×C₆₁	1	2	yes	—
753	#95	C₂³×C₆₁	1	1	yes	characteristic
754	#95	C₂³×C₆₁	1	1	yes	characteristic
755	#95	C₂³×C₆₁	1	1	yes	characteristic
756	#95	C₂³×C₆₁	1	2	yes	—
757	#95	C₂³×C₆₁	1	2	yes	—
758	#95	C₂³×C₆₁	1	2	yes	—
759	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
760	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
761	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	4	2	no	—
765	C₂×D₄	—	4	2	no	—
766	C₂×D₄	—	4	1	no	—
767	C₂×D₄	—	4	1	no	—
768	C₂×D₄	—	4	2	no	—
769	C₂×D₄	—	4	2	no	—
770	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
771	C₂×D₄	C₂²×C₄×C₆₁	1	8	yes	—
772	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
773	C₂×D₄	C₂²×C₄×C₆₁	1	8	yes	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	4	no	—
779	C₂²×C₄	—	2	4	no	—
780	C₂²×C₄	—	2	4	no	—
781	C₂²×C₄	—	2	4	no	—
782	C₂²×C₄	—	4	2	no	—
783	C₂²×C₄	—	4	2	no	—
784	C₂²×C₄	—	4	2	no	—
785	C₂²×C₄	—	4	2	no	—
786	C₂²×C₄	—	4	2	no	—
787	C₂²×C₄	—	4	2	no	—
788	C₂²×C₄	—	4	2	no	—
789	C₂²×C₄	—	4	2	no	—
790	C₂²×C₄	—	4	2	no	—
791	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
792	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
793	C₂²×C₄	C₂²×C₄×C₆₁	1	8	yes	—
794	C₂²×C₄	C₂²×C₄×C₆₁	1	8	yes	—
795	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
796	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
798	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
800	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
801	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
802	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
804	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
805	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
806	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
809	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
810	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
812	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
813	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
814	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
815	C₄⋊C₄	—	2	4	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	4	no	—
824	C₄⋊C₄	—	4	2	no	—
825	C₄⋊C₄	—	4	1	no	—
826	C₄⋊C₄	—	4	1	no	—
827	C₄⋊C₄	—	4	2	no	—
828	C₄⋊C₄	—	4	2	no	—
829	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
830	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
831	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
832	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
833	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
834	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
835	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
836	C₄⋊C₄	#41×C₆₁	1	4	yes	—
837	C₂²⋊C₄	—	2	4	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	4	no	—
843	C₂²⋊C₄	—	2	4	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	4	2	no	—
847	C₂²⋊C₄	—	4	2	no	—
848	C₂²⋊C₄	—	4	1	no	—
849	C₂²⋊C₄	—	4	2	no	—
850	C₂²⋊C₄	—	4	1	no	—
851	C₂²⋊C₄	—	4	2	no	—
852	C₂²⋊C₄	—	4	2	no	—
853	C₂²⋊C₄	—	4	2	no	—
854	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
855	C₂²⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
856	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
857	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
858	C₂²⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
859	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
860	C₄²	—	2	4	no	—
861	C₄²	—	2	2	no	—
862	C₄²	—	2	2	no	—
863	C₄²	—	2	2	no	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	4	no	—
866	C₄²	—	4	2	no	—
867	C₄²	—	4	2	no	—
868	C₄²	—	4	2	no	—
869	C₄²	—	4	2	no	—
870	C₄²	—	4	2	no	—
871	C₄²	—	4	1	no	—
872	C₄²	—	4	1	no	—
873	C₄²	—	4	2	no	—
874	C₄²	—	4	2	no	—
875	C₄²	—	4	1	no	—
876	C₄²	—	4	2	no	—
877	C₄²	C₂²×C₄×C₆₁	1	8	yes	—
878	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
879	C₄²	#41×C₆₁	1	4	yes	—
880	C₂³	—	2	1	no	—
881	C₂³	—	2	1	no	—
882	C₂³	—	2	1	no	—
883	C₂³	—	2	2	no	—
884	C₂³	—	2	2	no	—
885	C₂³	—	2	1	no	—
886	C₂³	—	2	1	no	—
887	C₂³	—	2	1	no	—
888	C₂³	—	2	2	no	—
889	C₂³	—	2	1	no	—
890	C₂³	—	2	1	no	—
891	C₂³	—	2	2	no	—
892	C₂³	—	2	2	no	—
893	C₂³	—	2	2	no	—
894	C₂³	—	2	1	no	—
895	C₂³	—	2	1	no	—
896	C₂³	—	2	1	no	—
897	C₂³	—	2	1	no	—
898	C₂³	C₂³×C₄×C₆₁	1	2	yes	—
899	C₂³	C₂³×C₄×C₆₁	1	4	yes	—
900	C₂³	C₂³×C₄×C₆₁	1	2	yes	—
901	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
902	D₄	—	2	8	no	—
903	D₄	—	4	8	no	—
904	D₄	—	4	4	no	—
905	D₄	—	4	8	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	8	no	—
929	C₂×C₄	—	2	8	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	4	8	no	—
955	C₂×C₄	—	4	8	no	—
956	C₂×C₄	—	4	8	no	—
957	C₂×C₄	—	4	8	no	—
958	C₂×C₄	—	8	4	no	—
959	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
960	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
961	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
962	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
963	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
964	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
965	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
966	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
967	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
968	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
969	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
970	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
971	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
972	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
973	C₂²	—	2	2	no	—
974	C₂²	—	2	2	no	—
975	C₂²	—	2	4	no	—
976	C₂²	—	2	2	no	—
977	C₂²	—	2	2	no	—
978	C₂²	—	2	4	no	—
979	C₂²	—	2	2	no	—
980	C₂²	—	2	4	no	—
981	C₂²	—	2	2	no	—
982	C₂²	—	4	2	no	—
983	C₂²	—	4	1	no	—
984	C₂²	—	4	1	no	—
985	C₂²	—	4	1	no	—
986	C₂²	—	4	1	no	—
987	C₂²	—	4	2	no	—
988	C₂²	—	4	2	no	—
989	C₂²	—	4	1	no	—
990	C₂²	—	4	1	no	—
991	C₂²	—	4	1	no	—
992	C₂²	—	4	2	no	—
993	C₂²	—	4	1	no	—
994	C₂²	C₂⁴×C₄×C₆₁	1	1	yes	characteristic
995	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
996	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
997	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
998	C₂²	C₆₁×#585	1	1	yes	characteristic
999	C₂²	C₆₁×#585	1	1	yes	characteristic
1000	C₂²	C₆₁×#585	1	1	yes	characteristic
1001	C₄	—	2	2	no	—
1002	C₄	—	2	2	no	—
1003	C₄	—	2	4	no	—
1004	C₄	—	2	2	no	—
1005	C₄	—	2	2	no	—
1006	C₄	—	2	4	no	—
1007	C₄	—	2	4	no	—
1008	C₄	—	2	2	no	—
1009	C₄	—	2	2	no	—
1010	C₄	—	2	2	no	—
1011	C₄	—	2	4	no	—
1012	C₄	—	4	1	no	—
1013	C₄	—	4	1	no	—
1014	C₄	—	4	2	no	—
1015	C₄	—	4	1	no	—
1016	C₄	—	4	1	no	—
1017	C₄	—	4	2	no	—
1018	C₄	—	4	1	no	—
1019	C₄	—	4	2	no	—
1020	C₄	C₄×#41×C₆₁	1	4	yes	—
1021	C₂	—	4	2	no	—
1022	C₂	—	4	2	no	—
1023	C₂	—	4	4	no	—
1024	C₂	C₂×C₄×#41×C₆₁	1	1	yes	characteristic
1025	C₂	C₆₁×#3428	1	1	yes	characteristic
1026	C₂	C₄×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1027	C₂	C₆₁×#3506	1	1	yes	characteristic
1028	C₂	C₆₁×#3512	1	1	yes	characteristic
1029	C₂	C₆₁×#3513	1	1	yes	characteristic
1030	C₂	C₆₁×#3524	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₁
Frattini, cosocle	C₂³	C₂⁵×C₆₁
prime radical	C₂×C₆₁×#553	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#2374	C₂	semidirect
3. C₆₁×#2373	C₂	semidirect
4. C₆₁×#2370	C₂	semidirect
5. C₆₁×#2363	C₂	semidirect
6. C₆₁×#2363	C₂	semidirect
7. C₆₁×#2361	C₂	semidirect
8. C₆₁×#2357	C₂	semidirect
9. C₆₁×#2357	C₂	semidirect
10. C₆₁×#2352	C₂	semidirect
11. C₆₁×#2346	C₂	semidirect
12. C₆₁×#2344	C₂	semidirect
13. C₆₁×#2334	C₂	semidirect
14. C₆₁×#2333	C₂	semidirect
15. C₆₁×#2324	C₂	semidirect
16. C₆₁×#2324	C₂	semidirect
17. C₄×#125×C₆₁	C₂	semidirect
18. C₄×#123×C₆₁	C₂	semidirect
19. C₆₁×#2293	C₂	semidirect
20. C₆₁×#2290	C₂	semidirect
21. C₆₁×#2274	C₂	semidirect
22. C₆₁×#2274	C₂	semidirect
23. C₄²×D₄×C₆₁	C₂	semidirect
24. C₆₁×#553	C₄	semidirect
135. #126×C₆₁	C₂×C₄	semidirect
136. #125×C₆₁	C₂×C₄	semidirect
137. #123×C₆₁	C₂×C₄	semidirect
139. #121×C₆₁	C₂×C₄	semidirect
140. #121×C₆₁	C₂×C₄	semidirect
144. C₄×D₄×C₆₁	C₂×C₄	semidirect
145. C₄×D₄×C₆₁	C₂×C₄	semidirect
146. C₄×D₄×C₆₁	C₂×C₄	semidirect
151. #117×C₆₁	C₂×C₄	semidirect
153. C₂×C₄⋊C₄×C₆₁	C₂×C₄	semidirect
457. #34319	C₆₁	direct (N × H)
507. #2374	C₂×C₆₁	semidirect
508. #2373	C₂×C₆₁	semidirect
509. #2370	C₂×C₆₁	semidirect
510. #2363	C₂×C₆₁	semidirect
511. #2363	C₂×C₆₁	semidirect
512. #2361	C₂×C₆₁	semidirect
513. #2357	C₂×C₆₁	semidirect
514. #2357	C₂×C₆₁	semidirect
515. #2352	C₂×C₆₁	semidirect
516. #2346	C₂×C₆₁	semidirect
517. #2344	C₂×C₆₁	semidirect
518. #2334	C₂×C₆₁	semidirect
519. #2333	C₂×C₆₁	semidirect
520. #2324	C₂×C₆₁	semidirect
521. #2324	C₂×C₆₁	semidirect
522. C₄×#125	C₂×C₆₁	semidirect
523. C₄×#123	C₂×C₆₁	semidirect
524. #2293	C₂×C₆₁	semidirect
525. #2290	C₂×C₆₁	semidirect
526. #2274	C₂×C₆₁	semidirect
527. #2274	C₂×C₆₁	semidirect
528. C₄²×D₄	C₂×C₆₁	semidirect
539. #553	C₄×C₆₁	semidirect
639. C₆₁	#34319	direct (N × H)
651. #126	C₂×C₄×C₆₁	semidirect
652. #125	C₂×C₄×C₆₁	semidirect
653. #123	C₂×C₄×C₆₁	semidirect
655. #121	C₂×C₄×C₆₁	semidirect
656. #121	C₂×C₄×C₆₁	semidirect
660. C₄×D₄	C₂×C₄×C₆₁	semidirect
661. C₄×D₄	C₂×C₄×C₆₁	semidirect
662. C₄×D₄	C₂×C₄×C₆₁	semidirect
667. #117	C₂×C₄×C₆₁	semidirect
669. C₂×C₄⋊C₄	C₂×C₄×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#553	2
C₆₁×#2374	2
C₆₁×#2373	2
C₆₁×#2370	2
C₆₁×#2363	2
C₆₁×#2361	2
C₆₁×#2357	2
C₆₁×#2352	2
C₆₁×#2346	2
C₆₁×#2344	2
C₆₁×#2334	2
C₆₁×#2333	2
C₆₁×#2324	2
C₄×#125×C₆₁	2
C₄×#123×C₆₁	2
C₆₁×#2293	2
C₆₁×#2290	2
C₆₁×#2274	2
C₄²×D₄×C₆₁	2
#34319	61

Subgroups — C61×#34319 #29537752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#34319 #29537752