Subgroups — C₆₁×#36980 #29540413

Order 15616.

1562 conjugacy classes of subgroups.

The subgroup lattice has 844 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×#2775	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2770	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2766	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2764	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2759	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2758	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2757	C₂	1	2	yes	maximal, complemented
10	C₆₁×#2737	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×#2510	C₂	1	2	yes	maximal, complemented
14	C₆₁×#2488	C₂	1	2	yes	maximal, complemented
15	C₆₁×#2450	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×#383	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#123×C₆₁	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
23	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
25	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#401	C₂²	1	2	yes	—
27	C₆₁×#400	C₂²	1	2	yes	—
28	C₆₁×#400	C₂²	1	2	yes	—
29	C₆₁×#400	C₂²	1	2	yes	—
30	C₆₁×#400	C₂²	1	2	yes	—
31	C₆₁×#400	C₂²	1	2	yes	—
32	C₆₁×#400	C₂²	1	2	yes	—
33	C₆₁×#398	C₂²	1	2	yes	—
34	C₆₁×#398	C₂²	1	2	yes	—
35	C₆₁×#398	C₂²	1	2	yes	—
36	C₆₁×#398	C₂²	1	2	yes	—
37	C₆₁×#397	C₂²	1	2	yes	—
38	C₆₁×#397	C₂²	1	2	yes	—
39	C₆₁×#397	C₂²	1	2	yes	—
40	C₆₁×#397	C₂²	1	2	yes	—
41	C₆₁×#397	C₂²	1	2	yes	—
42	C₆₁×#397	C₂²	1	2	yes	—
43	C₆₁×#396	C₂²	1	2	yes	—
44	C₆₁×#395	C₂²	1	2	yes	—
45	C₆₁×#395	C₂²	1	2	yes	—
46	C₆₁×#394	C₂²	1	2	yes	—
47	C₆₁×#393	C₂²	1	2	yes	—
48	C₆₁×#393	C₂²	1	2	yes	—
49	C₆₁×#393	C₂²	1	2	yes	—
50	C₆₁×#391	C₂²	1	2	yes	—
51	C₆₁×#391	C₂²	1	2	yes	—
52	C₆₁×#391	C₂²	1	1	yes	characteristic
53	C₆₁×#391	C₂²	1	1	yes	characteristic
54	C₆₁×#391	C₂²	1	2	yes	—
55	C₆₁×#390	C₂²	1	1	yes	characteristic
56	C₆₁×#390	C₂²	1	1	yes	characteristic
57	C₆₁×#389	C₂²	1	1	yes	characteristic
58	C₆₁×#389	C₂²	1	2	yes	—
59	C₆₁×#389	C₂²	1	1	yes	characteristic
60	C₆₁×#389	C₂²	1	1	yes	characteristic
61	C₆₁×#389	C₂²	1	1	yes	characteristic
62	C₆₁×#388	C₂²	1	2	yes	—
63	C₆₁×#388	C₂²	1	2	yes	—
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×#387	C₂²	1	2	yes	—
70	C₆₁×#387	C₂²	1	2	yes	—
71	C₆₁×#387	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×#386	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×#385	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×#385	C₂²	1	2	yes	—
88	C₆₁×#383	C₂²	1	2	yes	—
89	C₆₁×#383	C₂²	1	2	yes	—
90	C₆₁×#383	C₂²	1	2	yes	—
91	C₆₁×#383	C₂²	1	2	yes	—
92	C₆₁×#383	C₂²	1	2	yes	—
93	C₆₁×#382	C₂²	1	2	yes	—
94	C₆₁×#381	C₂²	1	2	yes	—
95	C₆₁×#381	C₂²	1	2	yes	—
96	C₆₁×#380	C₂²	1	1	yes	characteristic
97	C₆₁×#380	C₂²	1	1	yes	characteristic
98	C₆₁×#380	C₂²	1	2	yes	—
99	C₆₁×#380	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
101	C₂×#95×C₆₁	C₂²	1	1	yes	characteristic
102	C₂×#95×C₆₁	C₂²	1	1	yes	characteristic
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	#123×C₆₁	—	4	4	no	—
120	C₂²⋊Q₈×C₆₁	—	2	4	no	—
121	C₂²⋊Q₈×C₆₁	—	4	4	no	—
122	#121×C₆₁	—	2	4	no	—
123	C₄×D₄×C₆₁	—	4	4	no	—
124	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
131	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊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×C₄²×C₆₁	—	2	4	no	—
159	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
164	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
165	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
166	#95×C₆₁	C₂³	1	2	yes	—
167	#95×C₆₁	C₂³	1	2	yes	—
168	#95×C₆₁	C₂³	1	2	yes	—
169	#95×C₆₁	C₂³	1	2	yes	—
170	#95×C₆₁	C₂³	1	2	yes	—
171	#95×C₆₁	C₂³	1	2	yes	—
172	#95×C₆₁	C₂³	1	2	yes	—
173	#95×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	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
201	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
202	C₂×Q₈×C₆₁	—	2	2	no	—
203	C₂×Q₈×C₆₁	—	4	2	no	—
204	C₂×Q₈×C₆₁	—	4	1	no	—
205	C₂×Q₈×C₆₁	—	4	1	no	—
206	C₂×Q₈×C₆₁	—	4	2	no	—
207	C₂×Q₈×C₆₁	—	4	2	no	—
208	C₂×D₄×C₆₁	—	2	4	no	—
209	C₂×D₄×C₆₁	—	2	4	no	—
210	C₂×D₄×C₆₁	—	2	4	no	—
211	C₂×D₄×C₆₁	—	2	2	no	—
212	C₂×D₄×C₆₁	—	4	1	no	—
213	C₂×D₄×C₆₁	—	4	1	no	—
214	C₂²×C₄×C₆₁	—	2	2	no	—
215	C₂²×C₄×C₆₁	—	2	2	no	—
216	C₂²×C₄×C₆₁	—	2	2	no	—
217	C₂²×C₄×C₆₁	—	2	2	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	—	4	1	no	—
223	C₂²×C₄×C₆₁	—	4	1	no	—
224	C₂²×C₄×C₆₁	—	4	1	no	—
225	C₂²×C₄×C₆₁	—	4	1	no	—
226	C₂²×C₄×C₆₁	—	4	2	no	—
227	C₂²×C₄×C₆₁	—	4	1	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	2	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	1	no	—
236	C₂²×C₄×C₆₁	—	4	1	no	—
237	C₂²×C₄×C₆₁	#41	1	4	yes	—
238	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
254	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
255	C₄⋊C₄×C₆₁	—	2	2	no	—
256	C₄⋊C₄×C₆₁	—	2	2	no	—
257	C₄⋊C₄×C₆₁	—	2	4	no	—
258	C₄⋊C₄×C₆₁	—	4	1	no	—
259	C₄⋊C₄×C₆₁	—	4	1	no	—
260	C₄⋊C₄×C₆₁	—	4	1	no	—
261	C₄⋊C₄×C₆₁	—	4	1	no	—
262	C₄⋊C₄×C₆₁	—	4	2	no	—
263	C₄⋊C₄×C₆₁	—	4	2	no	—
264	C₄⋊C₄×C₆₁	—	4	2	no	—
265	C₄⋊C₄×C₆₁	—	4	2	no	—
266	C₄⋊C₄×C₆₁	—	4	2	no	—
267	C₄⋊C₄×C₆₁	—	4	2	no	—
268	C₄⋊C₄×C₆₁	—	4	2	no	—
269	C₄⋊C₄×C₆₁	—	4	2	no	—
270	C₄⋊C₄×C₆₁	—	4	2	no	—
271	C₄⋊C₄×C₆₁	—	4	2	no	—
272	C₄⋊C₄×C₆₁	—	4	2	no	—
273	C₄⋊C₄×C₆₁	—	4	2	no	—
274	C₂²⋊C₄×C₆₁	—	2	4	no	—
275	C₂²⋊C₄×C₆₁	—	2	4	no	—
276	C₂²⋊C₄×C₆₁	—	2	4	no	—
277	C₂²⋊C₄×C₆₁	—	2	4	no	—
278	C₂²⋊C₄×C₆₁	—	4	2	no	—
279	C₂²⋊C₄×C₆₁	—	4	2	no	—
280	C₂²⋊C₄×C₆₁	—	4	2	no	—
281	C₂²⋊C₄×C₆₁	—	4	2	no	—
282	C₂²⋊C₄×C₆₁	—	4	2	no	—
283	C₂²⋊C₄×C₆₁	—	4	2	no	—
284	C₂²⋊C₄×C₆₁	—	4	2	no	—
285	C₂²⋊C₄×C₆₁	—	4	2	no	—
286	C₂²⋊C₄×C₆₁	—	4	2	no	—
287	C₂²⋊C₄×C₆₁	—	4	2	no	—
288	C₂²⋊C₄×C₆₁	—	4	2	no	—
289	C₄²×C₆₁	—	2	2	no	—
290	C₄²×C₆₁	—	2	2	no	—
291	C₄²×C₆₁	—	2	2	no	—
292	C₄²×C₆₁	—	2	2	no	—
293	C₄²×C₆₁	—	4	2	no	—
294	C₄²×C₆₁	—	4	2	no	—
295	C₄²×C₆₁	—	4	2	no	—
296	C₂³×C₆₁	—	2	1	no	—
297	C₂³×C₆₁	—	2	1	no	—
298	C₂³×C₆₁	—	2	1	no	—
299	C₂³×C₆₁	—	2	1	no	—
300	C₂³×C₆₁	—	2	2	no	—
301	C₂³×C₆₁	—	2	2	no	—
302	C₂³×C₆₁	—	2	2	no	—
303	C₂³×C₆₁	—	2	2	no	—
304	C₂³×C₆₁	—	2	2	no	—
305	C₂³×C₆₁	—	2	2	no	—
306	C₂³×C₆₁	—	2	2	no	—
307	C₂³×C₆₁	C₂×#41	1	2	yes	—
308	C₂³×C₆₁	H(5,𝔽₂)	1	2	yes	—
309	C₂³×C₆₁	2₋¹⁺⁴	1	2	yes	—
310	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
311	Q₈×C₆₁	—	8	2	no	—
312	Q₈×C₆₁	—	8	4	no	—
313	D₄×C₆₁	—	4	8	no	—
314	D₄×C₆₁	—	8	2	no	—
315	C₂×C₄×C₆₁	—	2	1	no	—
316	C₂×C₄×C₆₁	—	2	1	no	—
317	C₂×C₄×C₆₁	—	2	1	no	—
318	C₂×C₄×C₆₁	—	2	1	no	—
319	C₂×C₄×C₆₁	—	2	1	no	—
320	C₂×C₄×C₆₁	—	2	1	no	—
321	C₂×C₄×C₆₁	—	2	1	no	—
322	C₂×C₄×C₆₁	—	2	1	no	—
323	C₂×C₄×C₆₁	—	2	2	no	—
324	C₂×C₄×C₆₁	—	2	2	no	—
325	C₂×C₄×C₆₁	—	2	2	no	—
326	C₂×C₄×C₆₁	—	2	2	no	—
327	C₂×C₄×C₆₁	—	2	2	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	1	no	—
334	C₂×C₄×C₆₁	—	2	2	no	—
335	C₂×C₄×C₆₁	—	2	1	no	—
336	C₂×C₄×C₆₁	—	2	1	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	2	no	—
347	C₂×C₄×C₆₁	—	2	1	no	—
348	C₂×C₄×C₆₁	—	2	1	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	2	no	—
357	C₂×C₄×C₆₁	—	2	2	no	—
358	C₂×C₄×C₆₁	—	2	1	no	—
359	C₂×C₄×C₆₁	—	2	1	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	—	4	4	no	—
365	C₂×C₄×C₆₁	—	4	4	no	—
366	C₂×C₄×C₆₁	—	4	4	no	—
367	C₂×C₄×C₆₁	—	8	2	no	—
368	C₂×C₄×C₆₁	—	8	2	no	—
369	C₂×C₄×C₆₁	—	8	2	no	—
370	C₂×C₄×C₆₁	—	8	2	no	—
371	C₂×C₄×C₆₁	—	8	4	no	—
372	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
373	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
374	#36980	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
375	C₂²×C₆₁	—	2	2	no	—
376	C₂²×C₆₁	—	2	2	no	—
377	C₂²×C₆₁	—	2	2	no	—
378	C₂²×C₆₁	—	2	2	no	—
379	C₂²×C₆₁	—	2	2	no	—
380	C₂²×C₆₁	—	2	2	no	—
381	C₂²×C₆₁	—	4	2	no	—
382	C₂²×C₆₁	—	4	2	no	—
383	C₂²×C₆₁	—	4	2	no	—
384	C₂²×C₆₁	—	4	2	no	—
385	C₂²×C₆₁	—	4	2	no	—
386	C₂²×C₆₁	—	4	2	no	—
387	C₂²×C₆₁	—	4	2	no	—
388	C₂²×C₆₁	#542	1	4	yes	—
389	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
390	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
391	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
392	C₂²×C₆₁	#585	1	1	yes	characteristic
393	C₂²×C₆₁	#585	1	1	yes	characteristic
394	C₂²×C₆₁	#585	1	1	yes	characteristic
395	C₂²×C₆₁	#585	1	1	yes	characteristic
396	C₄×C₆₁	—	2	2	no	—
397	C₄×C₆₁	—	2	2	no	—
398	C₄×C₆₁	—	4	1	no	—
399	C₄×C₆₁	—	4	1	no	—
400	C₄×C₆₁	—	4	2	no	—
401	C₄×C₆₁	—	4	2	no	—
402	C₄×C₆₁	—	4	2	no	—
403	C₄×C₆₁	—	4	1	no	—
404	C₄×C₆₁	—	4	1	no	—
405	C₄×C₆₁	—	4	2	no	—
406	C₄×C₆₁	—	4	2	no	—
407	C₄×C₆₁	—	4	2	no	—
408	C₄×C₆₁	—	4	2	no	—
409	C₄×C₆₁	—	4	2	no	—
410	C₄×C₆₁	—	4	2	no	—
411	C₄×C₆₁	—	4	2	no	—
412	C₄×C₆₁	—	4	2	no	—
413	#2855	C₂×C₆₁	1	1	yes	characteristic, complemented
414	#2854	C₂×C₆₁	1	1	yes	characteristic
415	#2775	C₂×C₆₁	1	2	yes	complemented
416	#2770	C₂×C₆₁	1	2	yes	complemented
417	#2766	C₂×C₆₁	1	2	yes	complemented
418	#2764	C₂×C₆₁	1	2	yes	complemented
419	#2759	C₂×C₆₁	1	2	yes	complemented
420	#2758	C₂×C₆₁	1	2	yes	complemented
421	#2757	C₂×C₆₁	1	2	yes	complemented
422	#2737	C₂×C₆₁	1	2	yes	complemented
423	#2659	C₂×C₆₁	1	1	yes	characteristic, complemented
424	#2639	C₂×C₆₁	1	1	yes	characteristic
425	#2510	C₂×C₆₁	1	2	yes	complemented
426	#2488	C₂×C₆₁	1	2	yes	complemented
427	#2450	C₂×C₆₁	1	2	yes	complemented
428	#2419	C₂×C₆₁	1	2	yes	complemented
429	#2329	C₂×C₆₁	1	1	yes	characteristic, complemented
430	#2325	C₂×C₆₁	1	1	yes	characteristic
431	C₂×#383	C₂×C₆₁	1	1	yes	characteristic, complemented
432	C₂×C₆₁	—	2	4	no	—
433	C₂×C₆₁	—	8	2	no	—
434	C₂×C₆₁	C₂×#542	1	1	yes	characteristic
435	C₂×C₆₁	#3491	1	1	yes	characteristic
436	C₂×C₆₁	#3493	1	1	yes	characteristic
437	C₂×C₆₁	#3560	1	1	yes	characteristic
438	C₂×C₆₁	#3560	1	1	yes	characteristic
439	C₂×C₆₁	#3564	1	1	yes	characteristic
440	C₂×C₆₁	#3564	1	1	yes	characteristic
441	C₂×#123	C₂²×C₆₁	1	2	yes	—
442	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
443	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
444	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
445	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
446	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
447	#401	C₂²×C₆₁	1	2	yes	—
448	#400	C₂²×C₆₁	1	2	yes	—
449	#400	C₂²×C₆₁	1	2	yes	—
450	#400	C₂²×C₆₁	1	2	yes	—
451	#400	C₂²×C₆₁	1	2	yes	—
452	#400	C₂²×C₆₁	1	2	yes	—
453	#400	C₂²×C₆₁	1	2	yes	—
454	#398	C₂²×C₆₁	1	2	yes	—
455	#398	C₂²×C₆₁	1	2	yes	—
456	#398	C₂²×C₆₁	1	2	yes	—
457	#398	C₂²×C₆₁	1	2	yes	—
458	#397	C₂²×C₆₁	1	2	yes	—
459	#397	C₂²×C₆₁	1	2	yes	—
460	#397	C₂²×C₆₁	1	2	yes	—
461	#397	C₂²×C₆₁	1	2	yes	—
462	#397	C₂²×C₆₁	1	2	yes	—
463	#397	C₂²×C₆₁	1	2	yes	—
464	#396	C₂²×C₆₁	1	2	yes	—
465	#395	C₂²×C₆₁	1	2	yes	—
466	#395	C₂²×C₆₁	1	2	yes	—
467	#394	C₂²×C₆₁	1	2	yes	—
468	#393	C₂²×C₆₁	1	2	yes	—
469	#393	C₂²×C₆₁	1	2	yes	—
470	#393	C₂²×C₆₁	1	2	yes	—
471	#391	C₂²×C₆₁	1	2	yes	—
472	#391	C₂²×C₆₁	1	1	yes	characteristic
473	#391	C₂²×C₆₁	1	1	yes	characteristic
474	#391	C₂²×C₆₁	1	2	yes	—
475	#391	C₂²×C₆₁	1	2	yes	—
476	#390	C₂²×C₆₁	1	1	yes	characteristic
477	#390	C₂²×C₆₁	1	1	yes	characteristic
478	#389	C₂²×C₆₁	1	2	yes	—
479	#389	C₂²×C₆₁	1	1	yes	characteristic
480	#389	C₂²×C₆₁	1	1	yes	characteristic
481	#389	C₂²×C₆₁	1	1	yes	characteristic
482	#389	C₂²×C₆₁	1	1	yes	characteristic
483	#388	C₂²×C₆₁	1	2	yes	—
484	#388	C₂²×C₆₁	1	2	yes	—
485	#388	C₂²×C₆₁	1	2	yes	—
486	#388	C₂²×C₆₁	1	2	yes	—
487	#388	C₂²×C₆₁	1	2	yes	—
488	#388	C₂²×C₆₁	1	2	yes	—
489	#388	C₂²×C₆₁	1	2	yes	—
490	#387	C₂²×C₆₁	1	2	yes	—
491	#387	C₂²×C₆₁	1	2	yes	—
492	#387	C₂²×C₆₁	1	2	yes	—
493	#387	C₂²×C₆₁	1	2	yes	—
494	#387	C₂²×C₆₁	1	2	yes	—
495	#387	C₂²×C₆₁	1	2	yes	—
496	#387	C₂²×C₆₁	1	2	yes	—
497	#387	C₂²×C₆₁	1	2	yes	—
498	#387	C₂²×C₆₁	1	2	yes	—
499	#386	C₂²×C₆₁	1	2	yes	—
500	#386	C₂²×C₆₁	1	2	yes	—
501	#386	C₂²×C₆₁	1	2	yes	—
502	#386	C₂²×C₆₁	1	2	yes	—
503	#386	C₂²×C₆₁	1	2	yes	—
504	#385	C₂²×C₆₁	1	2	yes	—
505	#385	C₂²×C₆₁	1	2	yes	—
506	#385	C₂²×C₆₁	1	2	yes	—
507	#385	C₂²×C₆₁	1	2	yes	—
508	#385	C₂²×C₆₁	1	2	yes	—
509	#383	C₂²×C₆₁	1	2	yes	—
510	#383	C₂²×C₆₁	1	2	yes	—
511	#383	C₂²×C₆₁	1	2	yes	—
512	#383	C₂²×C₆₁	1	2	yes	—
513	#383	C₂²×C₆₁	1	2	yes	—
514	#382	C₂²×C₆₁	1	2	yes	—
515	#381	C₂²×C₆₁	1	2	yes	—
516	#381	C₂²×C₆₁	1	2	yes	—
517	#380	C₂²×C₆₁	1	1	yes	characteristic
518	#380	C₂²×C₆₁	1	1	yes	characteristic
519	#380	C₂²×C₆₁	1	2	yes	—
520	#380	C₂²×C₆₁	1	2	yes	—
521	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
522	C₂×#95	C₂²×C₆₁	1	1	yes	characteristic
523	C₂×#95	C₂²×C₆₁	1	1	yes	characteristic
524	C₂×#95	C₂²×C₆₁	1	1	yes	characteristic
525	C₂×#95	C₂²×C₆₁	1	1	yes	characteristic
526	C₂×#95	C₂²×C₆₁	1	1	yes	characteristic
527	C₂×#95	C₂²×C₆₁	1	1	yes	characteristic
528	C₆₁	#36980	1	1	yes	characteristic, direct product factor, Sylow
529	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
530	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
531	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
532	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
533	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
535	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
536	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
537	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
540	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
541	#123	—	4	4	no	—
542	C₂²⋊Q₈	—	2	4	no	—
543	C₂²⋊Q₈	—	4	4	no	—
544	#121	—	2	4	no	—
545	C₄×D₄	—	4	4	no	—
546	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
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	1	yes	characteristic
562	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
580	C₂×C₄²	—	2	4	no	—
581	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
582	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
583	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
585	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
586	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
587	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
588	#95	C₂³×C₆₁	1	2	yes	—
589	#95	C₂³×C₆₁	1	2	yes	—
590	#95	C₂³×C₆₁	1	2	yes	—
591	#95	C₂³×C₆₁	1	2	yes	—
592	#95	C₂³×C₆₁	1	2	yes	—
593	#95	C₂³×C₆₁	1	2	yes	—
594	#95	C₂³×C₆₁	1	2	yes	—
595	#95	C₂³×C₆₁	1	2	yes	—
596	#95	C₂³×C₆₁	1	2	yes	—
597	#95	C₂³×C₆₁	1	2	yes	—
598	#95	C₂³×C₆₁	1	2	yes	—
599	#95	C₂³×C₆₁	1	2	yes	—
600	#95	C₂³×C₆₁	1	2	yes	—
601	#95	C₂³×C₆₁	1	2	yes	—
602	#95	C₂³×C₆₁	1	2	yes	—
603	#95	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	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
623	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
624	C₂×Q₈	—	2	2	no	—
625	C₂×Q₈	—	4	2	no	—
626	C₂×Q₈	—	4	1	no	—
627	C₂×Q₈	—	4	1	no	—
628	C₂×Q₈	—	4	2	no	—
629	C₂×Q₈	—	4	2	no	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	4	1	no	—
635	C₂×D₄	—	4	1	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	4	1	no	—
645	C₂²×C₄	—	4	1	no	—
646	C₂²×C₄	—	4	1	no	—
647	C₂²×C₄	—	4	1	no	—
648	C₂²×C₄	—	4	2	no	—
649	C₂²×C₄	—	4	1	no	—
650	C₂²×C₄	—	4	1	no	—
651	C₂²×C₄	—	4	1	no	—
652	C₂²×C₄	—	4	1	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	1	no	—
655	C₂²×C₄	—	4	1	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	—	4	1	no	—
658	C₂²×C₄	—	4	1	no	—
659	C₂²×C₄	#41×C₆₁	1	4	yes	—
660	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
665	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
666	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
671	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	—	4	2	no	—
681	C₄⋊C₄	—	4	2	no	—
682	C₄⋊C₄	—	4	2	no	—
683	C₄⋊C₄	—	4	2	no	—
684	C₄⋊C₄	—	4	2	no	—
685	C₄⋊C₄	—	4	2	no	—
686	C₄⋊C₄	—	4	1	no	—
687	C₄⋊C₄	—	4	1	no	—
688	C₄⋊C₄	—	4	1	no	—
689	C₄⋊C₄	—	4	1	no	—
690	C₄⋊C₄	—	4	2	no	—
691	C₄⋊C₄	—	4	2	no	—
692	C₄⋊C₄	—	4	2	no	—
693	C₄⋊C₄	—	4	2	no	—
694	C₄⋊C₄	—	4	2	no	—
695	C₄⋊C₄	—	4	2	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	4	2	no	—
701	C₂²⋊C₄	—	4	2	no	—
702	C₂²⋊C₄	—	4	2	no	—
703	C₂²⋊C₄	—	4	2	no	—
704	C₂²⋊C₄	—	4	2	no	—
705	C₂²⋊C₄	—	4	2	no	—
706	C₂²⋊C₄	—	4	2	no	—
707	C₂²⋊C₄	—	4	2	no	—
708	C₂²⋊C₄	—	4	2	no	—
709	C₂²⋊C₄	—	4	2	no	—
710	C₂²⋊C₄	—	4	2	no	—
711	C₄²	—	2	2	no	—
712	C₄²	—	2	2	no	—
713	C₄²	—	2	2	no	—
714	C₄²	—	2	2	no	—
715	C₄²	—	4	2	no	—
716	C₄²	—	4	2	no	—
717	C₄²	—	4	2	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	C₂×#41×C₆₁	1	2	yes	—
730	C₂³	H(5,𝔽₂)×C₆₁	1	2	yes	—
731	C₂³	2₋¹⁺⁴×C₆₁	1	2	yes	—
732	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
733	Q₈	—	8	2	no	—
734	Q₈	—	8	4	no	—
735	D₄	—	4	8	no	—
736	D₄	—	8	2	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	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	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	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	1	no	—
770	C₂×C₄	—	2	1	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	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	4	4	no	—
787	C₂×C₄	—	4	4	no	—
788	C₂×C₄	—	4	4	no	—
789	C₂×C₄	—	8	2	no	—
790	C₂×C₄	—	8	2	no	—
791	C₂×C₄	—	8	2	no	—
792	C₂×C₄	—	8	2	no	—
793	C₂×C₄	—	8	4	no	—
794	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
795	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
796	C₂²	—	2	2	no	—
797	C₂²	—	2	2	no	—
798	C₂²	—	2	2	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	C₆₁×#542	1	4	yes	—
810	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
811	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
812	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
813	C₂²	C₆₁×#585	1	1	yes	characteristic
814	C₂²	C₆₁×#585	1	1	yes	characteristic
815	C₂²	C₆₁×#585	1	1	yes	characteristic
816	C₂²	C₆₁×#585	1	1	yes	characteristic
817	C₄	—	2	2	no	—
818	C₄	—	2	2	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	1	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	1	no	—
833	C₄	—	4	1	no	—
834	C₂	—	2	4	no	—
835	C₂	—	8	2	no	—
836	C₂	C₂×C₆₁×#542	1	1	yes	characteristic
837	C₂	C₆₁×#3491	1	1	yes	characteristic
838	C₂	C₆₁×#3493	1	1	yes	characteristic
839	C₂	C₆₁×#3560	1	1	yes	characteristic
840	C₂	C₆₁×#3560	1	1	yes	characteristic
841	C₂	C₆₁×#3564	1	1	yes	characteristic
842	C₂	C₆₁×#3564	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×#2775	C₂	semidirect
4. C₆₁×#2770	C₂	semidirect
5. C₆₁×#2766	C₂	semidirect
6. C₆₁×#2764	C₂	semidirect
7. C₆₁×#2759	C₂	semidirect
8. C₆₁×#2758	C₂	semidirect
9. C₆₁×#2757	C₂	semidirect
10. C₆₁×#2737	C₂	semidirect
11. C₆₁×#2659	C₂	semidirect
13. C₆₁×#2510	C₂	semidirect
14. C₆₁×#2488	C₂	semidirect
15. C₆₁×#2450	C₂	semidirect
16. C₆₁×#2419	C₂	semidirect
17. C₆₁×#2329	C₂	semidirect
19. C₂×C₆₁×#383	C₂	semidirect
374. #36980	C₆₁	direct (N × H)
413. #2855	C₂×C₆₁	semidirect
415. #2775	C₂×C₆₁	semidirect
416. #2770	C₂×C₆₁	semidirect
417. #2766	C₂×C₆₁	semidirect
418. #2764	C₂×C₆₁	semidirect
419. #2759	C₂×C₆₁	semidirect
420. #2758	C₂×C₆₁	semidirect
421. #2757	C₂×C₆₁	semidirect
422. #2737	C₂×C₆₁	semidirect
423. #2659	C₂×C₆₁	semidirect
425. #2510	C₂×C₆₁	semidirect
426. #2488	C₂×C₆₁	semidirect
427. #2450	C₂×C₆₁	semidirect
428. #2419	C₂×C₆₁	semidirect
429. #2329	C₂×C₆₁	semidirect
431. C₂×#383	C₂×C₆₁	semidirect
528. C₆₁	#36980	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×#2775	2
C₆₁×#2770	2
C₆₁×#2766	2
C₆₁×#2764	2
C₆₁×#2759	2
C₆₁×#2758	2
C₆₁×#2757	2
C₆₁×#2737	2
C₆₁×#2659	2
C₆₁×#2639	2
C₆₁×#2510	2
C₆₁×#2488	2
C₆₁×#2450	2
C₆₁×#2419	2
C₆₁×#2329	2
C₆₁×#2325	2
C₂×C₆₁×#383	2
#36980	61

Subgroups — C61×#36980 #29540413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#36980 #29540413