Subgroups — C₆₁×#36975 #29540408

Order 15616.

1646 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2855	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#2854	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2774	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2772	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2767	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2763	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2761	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2754	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2723	C₂	1	2	yes	maximal, complemented
10	C₆₁×#2698	C₂	1	2	yes	maximal, complemented
11	C₆₁×#2659	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#2639	C₂	1	1	yes	maximal, characteristic
13	C₆₁×#2488	C₂	1	2	yes	maximal, complemented
14	C₆₁×#2481	C₂	1	2	yes	maximal, complemented
15	C₆₁×#2449	C₂	1	2	yes	maximal, complemented
16	C₆₁×#2419	C₂	1	2	yes	maximal, complemented
17	C₆₁×#2329	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#2325	C₂	1	1	yes	maximal, characteristic
19	C₂×C₆₁×#382	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#126×C₆₁	C₂²	1	2	yes	—
21	C₂×#123×C₆₁	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
25	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
27	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
30	C₆₁×#400	C₂²	1	2	yes	—
31	C₆₁×#400	C₂²	1	2	yes	—
32	C₆₁×#400	C₂²	1	2	yes	—
33	C₆₁×#400	C₂²	1	2	yes	—
34	C₆₁×#400	C₂²	1	2	yes	—
35	C₆₁×#400	C₂²	1	2	yes	—
36	C₆₁×#399	C₂²	1	2	yes	—
37	C₆₁×#398	C₂²	1	2	yes	—
38	C₆₁×#398	C₂²	1	2	yes	—
39	C₆₁×#398	C₂²	1	2	yes	—
40	C₆₁×#398	C₂²	1	2	yes	—
41	C₆₁×#397	C₂²	1	2	yes	—
42	C₆₁×#397	C₂²	1	2	yes	—
43	C₆₁×#397	C₂²	1	2	yes	—
44	C₆₁×#397	C₂²	1	2	yes	—
45	C₆₁×#397	C₂²	1	2	yes	—
46	C₆₁×#396	C₂²	1	2	yes	—
47	C₆₁×#396	C₂²	1	2	yes	—
48	C₆₁×#395	C₂²	1	2	yes	—
49	C₆₁×#395	C₂²	1	2	yes	—
50	C₆₁×#395	C₂²	1	2	yes	—
51	C₆₁×#394	C₂²	1	2	yes	—
52	C₆₁×#393	C₂²	1	2	yes	—
53	C₆₁×#393	C₂²	1	2	yes	—
54	C₆₁×#391	C₂²	1	2	yes	—
55	C₆₁×#391	C₂²	1	1	yes	characteristic
56	C₆₁×#391	C₂²	1	1	yes	characteristic
57	C₆₁×#391	C₂²	1	2	yes	—
58	C₆₁×#390	C₂²	1	1	yes	characteristic
59	C₆₁×#390	C₂²	1	1	yes	characteristic
60	C₆₁×#389	C₂²	1	2	yes	—
61	C₆₁×#389	C₂²	1	1	yes	characteristic
62	C₆₁×#389	C₂²	1	1	yes	characteristic
63	C₆₁×#389	C₂²	1	1	yes	characteristic
64	C₆₁×#389	C₂²	1	1	yes	characteristic
65	C₆₁×#389	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×#387	C₂²	1	2	yes	—
80	C₆₁×#387	C₂²	1	2	yes	—
81	C₆₁×#387	C₂²	1	2	yes	—
82	C₆₁×#386	C₂²	1	2	yes	—
83	C₆₁×#386	C₂²	1	2	yes	—
84	C₆₁×#386	C₂²	1	2	yes	—
85	C₆₁×#386	C₂²	1	2	yes	—
86	C₆₁×#386	C₂²	1	2	yes	—
87	C₆₁×#385	C₂²	1	2	yes	—
88	C₆₁×#385	C₂²	1	2	yes	—
89	C₆₁×#385	C₂²	1	2	yes	—
90	C₆₁×#385	C₂²	1	2	yes	—
91	C₆₁×#385	C₂²	1	2	yes	—
92	C₆₁×#382	C₂²	1	2	yes	—
93	C₆₁×#382	C₂²	1	2	yes	—
94	C₆₁×#382	C₂²	1	2	yes	—
95	C₆₁×#382	C₂²	1	2	yes	—
96	C₆₁×#382	C₂²	1	2	yes	—
97	C₆₁×#381	C₂²	1	2	yes	—
98	C₆₁×#381	C₂²	1	2	yes	—
99	C₆₁×#380	C₂²	1	1	yes	characteristic
100	C₆₁×#380	C₂²	1	1	yes	characteristic
101	C₆₁×#380	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
103	C₂×#95×C₆₁	C₂²	1	1	yes	characteristic
104	C₂×#95×C₆₁	C₂²	1	1	yes	characteristic
105	C₂×#95×C₆₁	C₂²	1	1	yes	characteristic
106	C₂×#95×C₆₁	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
109	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
110	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
118	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
119	#126×C₆₁	—	4	4	no	—
120	#123×C₆₁	—	4	4	no	—
121	C₂²⋊Q₈×C₆₁	—	2	4	no	—
122	C₂²⋊Q₈×C₆₁	—	4	4	no	—
123	C₂²⋊Q₈×C₆₁	—	4	4	no	—
124	#121×C₆₁	—	2	4	no	—
125	C₄×D₄×C₆₁	—	4	4	no	—
126	C₂×C₄⋊C₄×C₆₁	—	4	2	no	—
127	C₂×C₄⋊C₄×C₆₁	—	4	2	no	—
128	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
166	C₂×C₄²×C₆₁	—	2	4	no	—
167	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
172	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
173	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
174	#95×C₆₁	C₂³	1	2	yes	—
175	#95×C₆₁	C₂³	1	2	yes	—
176	#95×C₆₁	C₂³	1	2	yes	—
177	#95×C₆₁	C₂³	1	2	yes	—
178	#95×C₆₁	C₂³	1	2	yes	—
179	#95×C₆₁	C₂³	1	2	yes	—
180	#95×C₆₁	C₂³	1	2	yes	—
181	#95×C₆₁	C₂³	1	2	yes	—
182	#95×C₆₁	C₂³	1	2	yes	—
183	#95×C₆₁	C₂³	1	2	yes	—
184	#95×C₆₁	C₂³	1	2	yes	—
185	#95×C₆₁	C₂³	1	2	yes	—
186	#95×C₆₁	C₂³	1	2	yes	—
187	#95×C₆₁	C₂³	1	2	yes	—
188	#95×C₆₁	C₂³	1	2	yes	—
189	#95×C₆₁	C₂³	1	2	yes	—
190	#95×C₆₁	C₂³	1	2	yes	—
191	#95×C₆₁	C₂³	1	2	yes	—
192	#95×C₆₁	C₂³	1	2	yes	—
193	#95×C₆₁	C₂³	1	2	yes	—
194	#95×C₆₁	C₂³	1	2	yes	—
195	#95×C₆₁	C₂³	1	2	yes	—
196	#95×C₆₁	C₂³	1	2	yes	—
197	#95×C₆₁	C₂³	1	2	yes	—
198	#95×C₆₁	C₂³	1	2	yes	—
199	#95×C₆₁	C₂³	1	2	yes	—
200	#95×C₆₁	C₂³	1	2	yes	—
201	#95×C₆₁	C₂³	1	2	yes	—
202	#95×C₆₁	C₂³	1	2	yes	—
203	#95×C₆₁	C₂³	1	2	yes	—
204	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
205	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
206	C₂×Q₈×C₆₁	—	2	2	no	—
207	C₂×Q₈×C₆₁	—	4	2	no	—
208	C₂×Q₈×C₆₁	—	4	2	no	—
209	C₂×Q₈×C₆₁	—	4	1	no	—
210	C₂×Q₈×C₆₁	—	4	1	no	—
211	C₂×Q₈×C₆₁	—	4	2	no	—
212	C₂×D₄×C₆₁	—	2	4	no	—
213	C₂×D₄×C₆₁	—	2	4	no	—
214	C₂×D₄×C₆₁	—	2	4	no	—
215	C₂×D₄×C₆₁	—	2	2	no	—
216	C₂×D₄×C₆₁	—	4	1	no	—
217	C₂×D₄×C₆₁	—	4	1	no	—
218	C₂²×C₄×C₆₁	—	2	2	no	—
219	C₂²×C₄×C₆₁	—	2	2	no	—
220	C₂²×C₄×C₆₁	—	2	2	no	—
221	C₂²×C₄×C₆₁	—	2	2	no	—
222	C₂²×C₄×C₆₁	—	2	2	no	—
223	C₂²×C₄×C₆₁	—	2	2	no	—
224	C₂²×C₄×C₆₁	—	2	2	no	—
225	C₂²×C₄×C₆₁	—	2	2	no	—
226	C₂²×C₄×C₆₁	—	2	2	no	—
227	C₂²×C₄×C₆₁	—	2	2	no	—
228	C₂²×C₄×C₆₁	—	4	1	no	—
229	C₂²×C₄×C₆₁	—	4	1	no	—
230	C₂²×C₄×C₆₁	—	4	1	no	—
231	C₂²×C₄×C₆₁	—	4	1	no	—
232	C₂²×C₄×C₆₁	—	4	1	no	—
233	C₂²×C₄×C₆₁	—	4	1	no	—
234	C₂²×C₄×C₆₁	—	4	2	no	—
235	C₂²×C₄×C₆₁	—	4	2	no	—
236	C₂²×C₄×C₆₁	—	4	1	no	—
237	C₂²×C₄×C₆₁	—	4	1	no	—
238	C₂²×C₄×C₆₁	—	4	1	no	—
239	C₂²×C₄×C₆₁	—	4	1	no	—
240	C₂²×C₄×C₆₁	—	4	2	no	—
241	C₂²×C₄×C₆₁	#41	1	4	yes	—
242	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
259	C₄⋊C₄×C₆₁	—	2	2	no	—
260	C₄⋊C₄×C₆₁	—	2	2	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	4	no	—
265	C₄⋊C₄×C₆₁	—	2	4	no	—
266	C₄⋊C₄×C₆₁	—	4	2	no	—
267	C₄⋊C₄×C₆₁	—	4	2	no	—
268	C₄⋊C₄×C₆₁	—	4	1	no	—
269	C₄⋊C₄×C₆₁	—	4	1	no	—
270	C₄⋊C₄×C₆₁	—	4	1	no	—
271	C₄⋊C₄×C₆₁	—	4	1	no	—
272	C₄⋊C₄×C₆₁	—	4	2	no	—
273	C₄⋊C₄×C₆₁	—	4	2	no	—
274	C₄⋊C₄×C₆₁	—	4	2	no	—
275	C₄⋊C₄×C₆₁	—	4	2	no	—
276	C₄⋊C₄×C₆₁	—	4	2	no	—
277	C₄⋊C₄×C₆₁	—	4	2	no	—
278	C₄⋊C₄×C₆₁	—	4	2	no	—
279	C₄⋊C₄×C₆₁	—	4	2	no	—
280	C₄⋊C₄×C₆₁	—	4	2	no	—
281	C₄⋊C₄×C₆₁	—	4	2	no	—
282	C₂²⋊C₄×C₆₁	—	2	4	no	—
283	C₂²⋊C₄×C₆₁	—	2	4	no	—
284	C₂²⋊C₄×C₆₁	—	2	4	no	—
285	C₂²⋊C₄×C₆₁	—	2	4	no	—
286	C₂²⋊C₄×C₆₁	—	2	4	no	—
287	C₂²⋊C₄×C₆₁	—	2	4	no	—
288	C₂²⋊C₄×C₆₁	—	4	2	no	—
289	C₂²⋊C₄×C₆₁	—	4	2	no	—
290	C₂²⋊C₄×C₆₁	—	4	2	no	—
291	C₂²⋊C₄×C₆₁	—	4	2	no	—
292	C₂²⋊C₄×C₆₁	—	4	2	no	—
293	C₂²⋊C₄×C₆₁	—	4	2	no	—
294	C₂²⋊C₄×C₆₁	—	4	2	no	—
295	C₂²⋊C₄×C₆₁	—	4	2	no	—
296	C₂²⋊C₄×C₆₁	—	4	2	no	—
297	C₄²×C₆₁	—	2	2	no	—
298	C₄²×C₆₁	—	2	2	no	—
299	C₄²×C₆₁	—	2	2	no	—
300	C₄²×C₆₁	—	2	2	no	—
301	C₄²×C₆₁	—	4	2	no	—
302	C₄²×C₆₁	—	4	2	no	—
303	C₄²×C₆₁	—	4	2	no	—
304	C₂³×C₆₁	—	2	1	no	—
305	C₂³×C₆₁	—	2	1	no	—
306	C₂³×C₆₁	—	2	1	no	—
307	C₂³×C₆₁	—	2	1	no	—
308	C₂³×C₆₁	—	2	2	no	—
309	C₂³×C₆₁	—	2	2	no	—
310	C₂³×C₆₁	—	2	2	no	—
311	C₂³×C₆₁	—	2	2	no	—
312	C₂³×C₆₁	—	2	2	no	—
313	C₂³×C₆₁	—	2	2	no	—
314	C₂³×C₆₁	—	2	2	no	—
315	C₂³×C₆₁	C₂×#41	1	2	yes	—
316	C₂³×C₆₁	H(5,𝔽₂)	1	2	yes	—
317	C₂³×C₆₁	2₋¹⁺⁴	1	2	yes	—
318	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
319	Q₈×C₆₁	—	8	2	no	—
320	Q₈×C₆₁	—	8	4	no	—
321	D₄×C₆₁	—	4	8	no	—
322	D₄×C₆₁	—	8	2	no	—
323	C₂×C₄×C₆₁	—	2	8	no	—
324	C₂×C₄×C₆₁	—	2	1	no	—
325	C₂×C₄×C₆₁	—	2	1	no	—
326	C₂×C₄×C₆₁	—	2	1	no	—
327	C₂×C₄×C₆₁	—	2	1	no	—
328	C₂×C₄×C₆₁	—	2	1	no	—
329	C₂×C₄×C₆₁	—	2	1	no	—
330	C₂×C₄×C₆₁	—	2	1	no	—
331	C₂×C₄×C₆₁	—	2	1	no	—
332	C₂×C₄×C₆₁	—	2	1	no	—
333	C₂×C₄×C₆₁	—	2	1	no	—
334	C₂×C₄×C₆₁	—	2	2	no	—
335	C₂×C₄×C₆₁	—	2	2	no	—
336	C₂×C₄×C₆₁	—	2	2	no	—
337	C₂×C₄×C₆₁	—	2	2	no	—
338	C₂×C₄×C₆₁	—	2	2	no	—
339	C₂×C₄×C₆₁	—	2	2	no	—
340	C₂×C₄×C₆₁	—	2	2	no	—
341	C₂×C₄×C₆₁	—	2	2	no	—
342	C₂×C₄×C₆₁	—	2	2	no	—
343	C₂×C₄×C₆₁	—	2	2	no	—
344	C₂×C₄×C₆₁	—	2	2	no	—
345	C₂×C₄×C₆₁	—	2	2	no	—
346	C₂×C₄×C₆₁	—	2	1	no	—
347	C₂×C₄×C₆₁	—	2	1	no	—
348	C₂×C₄×C₆₁	—	2	2	no	—
349	C₂×C₄×C₆₁	—	2	2	no	—
350	C₂×C₄×C₆₁	—	2	2	no	—
351	C₂×C₄×C₆₁	—	2	2	no	—
352	C₂×C₄×C₆₁	—	2	2	no	—
353	C₂×C₄×C₆₁	—	2	2	no	—
354	C₂×C₄×C₆₁	—	2	2	no	—
355	C₂×C₄×C₆₁	—	2	2	no	—
356	C₂×C₄×C₆₁	—	2	1	no	—
357	C₂×C₄×C₆₁	—	2	1	no	—
358	C₂×C₄×C₆₁	—	2	2	no	—
359	C₂×C₄×C₆₁	—	2	2	no	—
360	C₂×C₄×C₆₁	—	2	2	no	—
361	C₂×C₄×C₆₁	—	2	2	no	—
362	C₂×C₄×C₆₁	—	2	2	no	—
363	C₂×C₄×C₆₁	—	2	2	no	—
364	C₂×C₄×C₆₁	—	2	2	no	—
365	C₂×C₄×C₆₁	—	2	2	no	—
366	C₂×C₄×C₆₁	—	2	2	no	—
367	C₂×C₄×C₆₁	—	2	2	no	—
368	C₂×C₄×C₆₁	—	2	2	no	—
369	C₂×C₄×C₆₁	—	2	2	no	—
370	C₂×C₄×C₆₁	—	2	2	no	—
371	C₂×C₄×C₆₁	—	4	4	no	—
372	C₂×C₄×C₆₁	—	4	4	no	—
373	C₂×C₄×C₆₁	—	8	2	no	—
374	C₂×C₄×C₆₁	—	8	2	no	—
375	C₂×C₄×C₆₁	—	8	2	no	—
376	C₂×C₄×C₆₁	—	8	2	no	—
377	C₂×C₄×C₆₁	—	8	4	no	—
378	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
379	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
380	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
381	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
382	#36975	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	2	no	—
389	C₂²×C₆₁	—	4	2	no	—
390	C₂²×C₆₁	—	4	2	no	—
391	C₂²×C₆₁	—	4	2	no	—
392	C₂²×C₆₁	—	4	2	no	—
393	C₂²×C₆₁	—	4	2	no	—
394	C₂²×C₆₁	—	4	2	no	—
395	C₂²×C₆₁	—	4	2	no	—
396	C₂²×C₆₁	#542	1	4	yes	—
397	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
398	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
399	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
400	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
401	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
402	C₂²×C₆₁	#585	1	1	yes	characteristic
403	C₂²×C₆₁	#585	1	1	yes	characteristic
404	C₄×C₆₁	—	2	2	no	—
405	C₄×C₆₁	—	2	2	no	—
406	C₄×C₆₁	—	2	2	no	—
407	C₄×C₆₁	—	2	2	no	—
408	C₄×C₆₁	—	4	1	no	—
409	C₄×C₆₁	—	4	1	no	—
410	C₄×C₆₁	—	4	2	no	—
411	C₄×C₆₁	—	4	2	no	—
412	C₄×C₆₁	—	4	2	no	—
413	C₄×C₆₁	—	4	2	no	—
414	C₄×C₆₁	—	4	2	no	—
415	C₄×C₆₁	—	4	2	no	—
416	C₄×C₆₁	—	4	2	no	—
417	C₄×C₆₁	—	4	2	no	—
418	C₄×C₆₁	—	4	2	no	—
419	C₄×C₆₁	—	4	2	no	—
420	C₄×C₆₁	—	4	2	no	—
421	#2855	C₂×C₆₁	1	1	yes	characteristic, complemented
422	#2854	C₂×C₆₁	1	1	yes	characteristic
423	#2774	C₂×C₆₁	1	2	yes	complemented
424	#2772	C₂×C₆₁	1	2	yes	complemented
425	#2767	C₂×C₆₁	1	2	yes	complemented
426	#2763	C₂×C₆₁	1	2	yes	complemented
427	#2761	C₂×C₆₁	1	2	yes	complemented
428	#2754	C₂×C₆₁	1	2	yes	complemented
429	#2723	C₂×C₆₁	1	2	yes	complemented
430	#2698	C₂×C₆₁	1	2	yes	complemented
431	#2659	C₂×C₆₁	1	1	yes	characteristic, complemented
432	#2639	C₂×C₆₁	1	1	yes	characteristic
433	#2488	C₂×C₆₁	1	2	yes	complemented
434	#2481	C₂×C₆₁	1	2	yes	complemented
435	#2449	C₂×C₆₁	1	2	yes	complemented
436	#2419	C₂×C₆₁	1	2	yes	complemented
437	#2329	C₂×C₆₁	1	1	yes	characteristic, complemented
438	#2325	C₂×C₆₁	1	1	yes	characteristic
439	C₂×#382	C₂×C₆₁	1	1	yes	characteristic, complemented
440	C₂×C₆₁	—	2	4	no	—
441	C₂×C₆₁	—	8	2	no	—
442	C₂×C₆₁	C₂×#542	1	1	yes	characteristic
443	C₂×C₆₁	#3491	1	1	yes	characteristic
444	C₂×C₆₁	#3492	1	1	yes	characteristic
445	C₂×C₆₁	#3558	1	1	yes	characteristic
446	C₂×C₆₁	#3559	1	1	yes	characteristic
447	C₂×C₆₁	#3561	1	1	yes	characteristic
448	C₂×C₆₁	#3563	1	1	yes	characteristic
449	C₂×#126	C₂²×C₆₁	1	2	yes	—
450	C₂×#123	C₂²×C₆₁	1	2	yes	—
451	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
452	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
453	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
454	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
455	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
456	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
457	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
458	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
459	#400	C₂²×C₆₁	1	2	yes	—
460	#400	C₂²×C₆₁	1	2	yes	—
461	#400	C₂²×C₆₁	1	2	yes	—
462	#400	C₂²×C₆₁	1	2	yes	—
463	#400	C₂²×C₆₁	1	2	yes	—
464	#400	C₂²×C₆₁	1	2	yes	—
465	#399	C₂²×C₆₁	1	2	yes	—
466	#398	C₂²×C₆₁	1	2	yes	—
467	#398	C₂²×C₆₁	1	2	yes	—
468	#398	C₂²×C₆₁	1	2	yes	—
469	#398	C₂²×C₆₁	1	2	yes	—
470	#397	C₂²×C₆₁	1	2	yes	—
471	#397	C₂²×C₆₁	1	2	yes	—
472	#397	C₂²×C₆₁	1	2	yes	—
473	#397	C₂²×C₆₁	1	2	yes	—
474	#397	C₂²×C₆₁	1	2	yes	—
475	#396	C₂²×C₆₁	1	2	yes	—
476	#396	C₂²×C₆₁	1	2	yes	—
477	#395	C₂²×C₆₁	1	2	yes	—
478	#395	C₂²×C₆₁	1	2	yes	—
479	#395	C₂²×C₆₁	1	2	yes	—
480	#394	C₂²×C₆₁	1	2	yes	—
481	#393	C₂²×C₆₁	1	2	yes	—
482	#393	C₂²×C₆₁	1	2	yes	—
483	#391	C₂²×C₆₁	1	2	yes	—
484	#391	C₂²×C₆₁	1	1	yes	characteristic
485	#391	C₂²×C₆₁	1	1	yes	characteristic
486	#391	C₂²×C₆₁	1	2	yes	—
487	#390	C₂²×C₆₁	1	1	yes	characteristic
488	#390	C₂²×C₆₁	1	1	yes	characteristic
489	#389	C₂²×C₆₁	1	2	yes	—
490	#389	C₂²×C₆₁	1	1	yes	characteristic
491	#389	C₂²×C₆₁	1	1	yes	characteristic
492	#389	C₂²×C₆₁	1	1	yes	characteristic
493	#389	C₂²×C₆₁	1	1	yes	characteristic
494	#389	C₂²×C₆₁	1	2	yes	—
495	#388	C₂²×C₆₁	1	2	yes	—
496	#388	C₂²×C₆₁	1	2	yes	—
497	#388	C₂²×C₆₁	1	2	yes	—
498	#388	C₂²×C₆₁	1	2	yes	—
499	#388	C₂²×C₆₁	1	2	yes	—
500	#388	C₂²×C₆₁	1	2	yes	—
501	#387	C₂²×C₆₁	1	2	yes	—
502	#387	C₂²×C₆₁	1	2	yes	—
503	#387	C₂²×C₆₁	1	2	yes	—
504	#387	C₂²×C₆₁	1	2	yes	—
505	#387	C₂²×C₆₁	1	2	yes	—
506	#387	C₂²×C₆₁	1	2	yes	—
507	#387	C₂²×C₆₁	1	2	yes	—
508	#387	C₂²×C₆₁	1	2	yes	—
509	#387	C₂²×C₆₁	1	2	yes	—
510	#387	C₂²×C₆₁	1	2	yes	—
511	#386	C₂²×C₆₁	1	2	yes	—
512	#386	C₂²×C₆₁	1	2	yes	—
513	#386	C₂²×C₆₁	1	2	yes	—
514	#386	C₂²×C₆₁	1	2	yes	—
515	#386	C₂²×C₆₁	1	2	yes	—
516	#385	C₂²×C₆₁	1	2	yes	—
517	#385	C₂²×C₆₁	1	2	yes	—
518	#385	C₂²×C₆₁	1	2	yes	—
519	#385	C₂²×C₆₁	1	2	yes	—
520	#385	C₂²×C₆₁	1	2	yes	—
521	#382	C₂²×C₆₁	1	2	yes	—
522	#382	C₂²×C₆₁	1	2	yes	—
523	#382	C₂²×C₆₁	1	2	yes	—
524	#382	C₂²×C₆₁	1	2	yes	—
525	#382	C₂²×C₆₁	1	2	yes	—
526	#381	C₂²×C₆₁	1	2	yes	—
527	#381	C₂²×C₆₁	1	2	yes	—
528	#380	C₂²×C₆₁	1	1	yes	characteristic
529	#380	C₂²×C₆₁	1	1	yes	characteristic
530	#380	C₂²×C₆₁	1	2	yes	—
531	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
532	C₂×#95	C₂²×C₆₁	1	1	yes	characteristic
533	C₂×#95	C₂²×C₆₁	1	1	yes	characteristic
534	C₂×#95	C₂²×C₆₁	1	1	yes	characteristic
535	C₂×#95	C₂²×C₆₁	1	1	yes	characteristic
536	C₆₁	#36975	1	1	yes	characteristic, direct product factor, Sylow
537	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
538	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
539	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
540	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
542	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
543	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
544	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
545	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
546	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
547	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
548	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
549	#126	—	4	4	no	—
550	#123	—	4	4	no	—
551	C₂²⋊Q₈	—	2	4	no	—
552	C₂²⋊Q₈	—	4	4	no	—
553	C₂²⋊Q₈	—	4	4	no	—
554	#121	—	2	4	no	—
555	C₄×D₄	—	4	4	no	—
556	C₂×C₄⋊C₄	—	4	2	no	—
557	C₂×C₄⋊C₄	—	4	2	no	—
558	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
596	C₂×C₄²	—	2	4	no	—
597	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
602	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
603	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
604	#95	C₂³×C₆₁	1	2	yes	—
605	#95	C₂³×C₆₁	1	2	yes	—
606	#95	C₂³×C₆₁	1	2	yes	—
607	#95	C₂³×C₆₁	1	2	yes	—
608	#95	C₂³×C₆₁	1	2	yes	—
609	#95	C₂³×C₆₁	1	2	yes	—
610	#95	C₂³×C₆₁	1	2	yes	—
611	#95	C₂³×C₆₁	1	2	yes	—
612	#95	C₂³×C₆₁	1	2	yes	—
613	#95	C₂³×C₆₁	1	2	yes	—
614	#95	C₂³×C₆₁	1	2	yes	—
615	#95	C₂³×C₆₁	1	2	yes	—
616	#95	C₂³×C₆₁	1	2	yes	—
617	#95	C₂³×C₆₁	1	2	yes	—
618	#95	C₂³×C₆₁	1	2	yes	—
619	#95	C₂³×C₆₁	1	2	yes	—
620	#95	C₂³×C₆₁	1	2	yes	—
621	#95	C₂³×C₆₁	1	2	yes	—
622	#95	C₂³×C₆₁	1	2	yes	—
623	#95	C₂³×C₆₁	1	2	yes	—
624	#95	C₂³×C₆₁	1	2	yes	—
625	#95	C₂³×C₆₁	1	2	yes	—
626	#95	C₂³×C₆₁	1	2	yes	—
627	#95	C₂³×C₆₁	1	2	yes	—
628	#95	C₂³×C₆₁	1	2	yes	—
629	#95	C₂³×C₆₁	1	2	yes	—
630	#95	C₂³×C₆₁	1	2	yes	—
631	#95	C₂³×C₆₁	1	2	yes	—
632	#95	C₂³×C₆₁	1	2	yes	—
633	#95	C₂³×C₆₁	1	2	yes	—
634	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
635	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
636	C₂×Q₈	—	2	2	no	—
637	C₂×Q₈	—	4	2	no	—
638	C₂×Q₈	—	4	2	no	—
639	C₂×Q₈	—	4	1	no	—
640	C₂×Q₈	—	4	1	no	—
641	C₂×Q₈	—	4	2	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	2	no	—
646	C₂×D₄	—	4	1	no	—
647	C₂×D₄	—	4	1	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	4	1	no	—
659	C₂²×C₄	—	4	1	no	—
660	C₂²×C₄	—	4	1	no	—
661	C₂²×C₄	—	4	1	no	—
662	C₂²×C₄	—	4	1	no	—
663	C₂²×C₄	—	4	1	no	—
664	C₂²×C₄	—	4	2	no	—
665	C₂²×C₄	—	4	2	no	—
666	C₂²×C₄	—	4	1	no	—
667	C₂²×C₄	—	4	1	no	—
668	C₂²×C₄	—	4	1	no	—
669	C₂²×C₄	—	4	1	no	—
670	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	#41×C₆₁	1	4	yes	—
672	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	4	2	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₄⋊C₄	—	4	2	no	—
701	C₄⋊C₄	—	4	2	no	—
702	C₄⋊C₄	—	4	2	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	—	4	2	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	—	4	1	no	—
707	C₄⋊C₄	—	4	1	no	—
708	C₄⋊C₄	—	4	1	no	—
709	C₄⋊C₄	—	4	1	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	4	2	no	—
721	C₂²⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₂²⋊C₄	—	4	2	no	—
725	C₂²⋊C₄	—	4	2	no	—
726	C₂²⋊C₄	—	4	2	no	—
727	C₄²	—	2	2	no	—
728	C₄²	—	2	2	no	—
729	C₄²	—	2	2	no	—
730	C₄²	—	2	2	no	—
731	C₄²	—	4	2	no	—
732	C₄²	—	4	2	no	—
733	C₄²	—	4	2	no	—
734	C₂³	—	2	1	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	C₂×#41×C₆₁	1	2	yes	—
746	C₂³	H(5,𝔽₂)×C₆₁	1	2	yes	—
747	C₂³	2₋¹⁺⁴×C₆₁	1	2	yes	—
748	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
749	Q₈	—	8	2	no	—
750	Q₈	—	8	4	no	—
751	D₄	—	4	8	no	—
752	D₄	—	8	2	no	—
753	C₂×C₄	—	2	8	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	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	1	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	4	4	no	—
802	C₂×C₄	—	4	4	no	—
803	C₂×C₄	—	8	2	no	—
804	C₂×C₄	—	8	2	no	—
805	C₂×C₄	—	8	2	no	—
806	C₂×C₄	—	8	2	no	—
807	C₂×C₄	—	8	4	no	—
808	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
809	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
810	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
811	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	2	no	—
825	C₂²	C₆₁×#542	1	4	yes	—
826	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
827	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
828	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
829	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
830	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
831	C₂²	C₆₁×#585	1	1	yes	characteristic
832	C₂²	C₆₁×#585	1	1	yes	characteristic
833	C₄	—	2	2	no	—
834	C₄	—	2	2	no	—
835	C₄	—	2	2	no	—
836	C₄	—	2	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	2	no	—
845	C₄	—	4	1	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	2	no	—
850	C₂	—	2	4	no	—
851	C₂	—	8	2	no	—
852	C₂	C₂×C₆₁×#542	1	1	yes	characteristic
853	C₂	C₆₁×#3491	1	1	yes	characteristic
854	C₂	C₆₁×#3492	1	1	yes	characteristic
855	C₂	C₆₁×#3558	1	1	yes	characteristic
856	C₂	C₆₁×#3559	1	1	yes	characteristic
857	C₂	C₆₁×#3561	1	1	yes	characteristic
858	C₂	C₆₁×#3563	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
prime radical	C₂×#121×C₆₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#2855	C₂	semidirect
3. C₆₁×#2774	C₂	semidirect
4. C₆₁×#2772	C₂	semidirect
5. C₆₁×#2767	C₂	semidirect
6. C₆₁×#2763	C₂	semidirect
7. C₆₁×#2761	C₂	semidirect
8. C₆₁×#2754	C₂	semidirect
9. C₆₁×#2723	C₂	semidirect
10. C₆₁×#2698	C₂	semidirect
11. C₆₁×#2659	C₂	semidirect
13. C₆₁×#2488	C₂	semidirect
14. C₆₁×#2481	C₂	semidirect
15. C₆₁×#2449	C₂	semidirect
16. C₆₁×#2419	C₂	semidirect
17. C₆₁×#2329	C₂	semidirect
19. C₂×C₆₁×#382	C₂	semidirect
382. #36975	C₆₁	direct (N × H)
421. #2855	C₂×C₆₁	semidirect
423. #2774	C₂×C₆₁	semidirect
424. #2772	C₂×C₆₁	semidirect
425. #2767	C₂×C₆₁	semidirect
426. #2763	C₂×C₆₁	semidirect
427. #2761	C₂×C₆₁	semidirect
428. #2754	C₂×C₆₁	semidirect
429. #2723	C₂×C₆₁	semidirect
430. #2698	C₂×C₆₁	semidirect
431. #2659	C₂×C₆₁	semidirect
433. #2488	C₂×C₆₁	semidirect
434. #2481	C₂×C₆₁	semidirect
435. #2449	C₂×C₆₁	semidirect
436. #2419	C₂×C₆₁	semidirect
437. #2329	C₂×C₆₁	semidirect
439. C₂×#382	C₂×C₆₁	semidirect
536. C₆₁	#36975	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₁×#2855	2
C₆₁×#2854	2
C₆₁×#2774	2
C₆₁×#2772	2
C₆₁×#2767	2
C₆₁×#2763	2
C₆₁×#2761	2
C₆₁×#2754	2
C₆₁×#2723	2
C₆₁×#2698	2
C₆₁×#2659	2
C₆₁×#2639	2
C₆₁×#2488	2
C₆₁×#2481	2
C₆₁×#2449	2
C₆₁×#2419	2
C₆₁×#2329	2
C₆₁×#2325	2
C₂×C₆₁×#382	2
#36975	61

Subgroups — C61×#36975 #29540408

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#36975 #29540408