Subgroups — C₆₁×#36974 #29540407

Order 15616.

1866 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2849	C₂	1	2	yes	maximal, complemented
2	C₆₁×#2771	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2765	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2764	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2761	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2760	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2752	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2751	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2750	C₂	1	2	yes	maximal, complemented
10	C₆₁×#2749	C₂	1	2	yes	maximal, complemented
11	C₆₁×#2743	C₂	1	2	yes	maximal, complemented
12	C₆₁×#2626	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#2617	C₂	1	1	yes	maximal, characteristic
14	C₆₁×#2493	C₂	1	2	yes	maximal, complemented
15	C₆₁×#2488	C₂	1	2	yes	maximal, complemented
16	C₆₁×#2425	C₂	1	2	yes	maximal, complemented
17	C₆₁×#2419	C₂	1	2	yes	maximal, complemented
18	C₆₁×#2321	C₂	1	2	yes	maximal, complemented
19	C₂×C₆₁×#381	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#123×C₆₁	C₂²	1	2	yes	—
22	C₂×#123×C₆₁	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#120×C₆₁	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
29	C₆₁×#401	C₂²	1	2	yes	complemented
30	C₆₁×#400	C₂²	1	2	yes	complemented
31	C₆₁×#400	C₂²	1	2	yes	complemented
32	C₆₁×#400	C₂²	1	2	yes	complemented
33	C₆₁×#400	C₂²	1	2	yes	complemented
34	C₆₁×#400	C₂²	1	2	yes	complemented
35	C₆₁×#400	C₂²	1	2	yes	complemented
36	C₆₁×#399	C₂²	1	1	yes	characteristic
37	C₆₁×#399	C₂²	1	1	yes	characteristic
38	C₆₁×#398	C₂²	1	2	yes	complemented
39	C₆₁×#398	C₂²	1	2	yes	complemented
40	C₆₁×#397	C₂²	1	1	yes	characteristic
41	C₆₁×#397	C₂²	1	1	yes	characteristic
42	C₆₁×#397	C₂²	1	2	yes	complemented
43	C₆₁×#397	C₂²	1	2	yes	complemented
44	C₆₁×#397	C₂²	1	2	yes	complemented
45	C₆₁×#397	C₂²	1	2	yes	complemented
46	C₆₁×#396	C₂²	1	2	yes	—
47	C₆₁×#396	C₂²	1	2	yes	—
48	C₆₁×#396	C₂²	1	2	yes	complemented
49	C₆₁×#394	C₂²	1	2	yes	—
50	C₆₁×#394	C₂²	1	2	yes	—
51	C₆₁×#394	C₂²	1	2	yes	complemented
52	C₆₁×#393	C₂²	1	1	yes	characteristic
53	C₆₁×#393	C₂²	1	1	yes	characteristic
54	C₆₁×#393	C₂²	1	2	yes	complemented
55	C₆₁×#392	C₂²	1	1	yes	characteristic
56	C₆₁×#392	C₂²	1	1	yes	characteristic
57	C₆₁×#391	C₂²	1	2	yes	complemented
58	C₆₁×#390	C₂²	1	2	yes	—
59	C₆₁×#390	C₂²	1	2	yes	—
60	C₆₁×#389	C₂²	1	2	yes	complemented
61	C₆₁×#388	C₂²	1	2	yes	—
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	complemented
66	C₆₁×#388	C₂²	1	2	yes	complemented
67	C₆₁×#388	C₂²	1	2	yes	complemented
68	C₆₁×#387	C₂²	1	2	yes	complemented
69	C₆₁×#387	C₂²	1	2	yes	complemented
70	C₆₁×#387	C₂²	1	2	yes	complemented
71	C₆₁×#387	C₂²	1	2	yes	complemented
72	C₆₁×#387	C₂²	1	2	yes	complemented
73	C₆₁×#386	C₂²	1	2	yes	—
74	C₆₁×#386	C₂²	1	2	yes	—
75	C₆₁×#386	C₂²	1	2	yes	—
76	C₆₁×#386	C₂²	1	2	yes	—
77	C₆₁×#386	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	complemented
82	C₆₁×#385	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×#385	C₂²	1	2	yes	complemented
89	C₆₁×#383	C₂²	1	2	yes	complemented
90	C₆₁×#382	C₂²	1	2	yes	complemented
91	C₆₁×#381	C₂²	1	2	yes	—
92	C₆₁×#381	C₂²	1	2	yes	—
93	C₆₁×#381	C₂²	1	1	yes	characteristic
94	C₆₁×#381	C₂²	1	1	yes	characteristic
95	C₆₁×#381	C₂²	1	1	yes	characteristic
96	C₆₁×#381	C₂²	1	1	yes	characteristic
97	C₆₁×#381	C₂²	1	2	yes	—
98	C₆₁×#381	C₂²	1	2	yes	—
99	C₆₁×#381	C₂²	1	2	yes	complemented
100	C₆₁×#380	C₂²	1	1	yes	characteristic
101	C₆₁×#380	C₂²	1	1	yes	characteristic
102	C₆₁×#380	C₂²	1	2	yes	complemented
103	C₆₁×#379	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
105	C₂×#95×C₆₁	C₂²	1	2	yes	—
106	C₂×#95×C₆₁	C₂²	1	2	yes	—
107	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
110	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
111	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
112	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₆₁	—	2	4	no	—
114	C₂³×C₄×C₆₁	—	4	2	no	—
115	C₂³×C₄×C₆₁	—	4	2	no	—
116	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
117	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
118	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
121	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
124	#123×C₆₁	—	4	4	no	—
125	#123×C₆₁	—	4	4	no	—
126	C₂²⋊Q₈×C₆₁	—	4	2	no	—
127	#121×C₆₁	—	4	2	no	—
128	#120×C₆₁	—	2	8	no	—
129	C₄×D₄×C₆₁	—	4	4	no	—
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	2	yes	—
134	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
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	1	yes	characteristic
143	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊C₄×C₆₁	—	4	2	no	—
145	C₂×C₂²⋊C₄×C₆₁	—	4	2	no	—
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	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
160	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
161	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
162	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
164	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
172	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
173	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
174	C₂×C₄²×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	1	yes	characteristic
186	#95×C₆₁	C₂³	1	1	yes	characteristic
187	#95×C₆₁	C₂³	1	1	yes	characteristic
188	#95×C₆₁	C₂³	1	1	yes	characteristic
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	#95×C₆₁	C₂³	1	2	yes	—
205	C₂⁴×C₆₁	—	2	2	no	—
206	C₂⁴×C₆₁	—	2	2	no	—
207	C₂⁴×C₆₁	—	4	2	no	—
208	C₂⁴×C₆₁	—	4	2	no	—
209	C₂⁴×C₆₁	#41	1	4	yes	—
210	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
211	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
212	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
213	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
214	C₂×Q₈×C₆₁	—	4	1	no	—
215	C₂×Q₈×C₆₁	—	4	2	no	—
216	C₂×D₄×C₆₁	—	2	4	no	—
217	C₂×D₄×C₆₁	—	2	4	no	—
218	C₂×D₄×C₆₁	—	2	4	no	—
219	C₂×D₄×C₆₁	—	2	4	no	—
220	C₂×D₄×C₆₁	—	2	4	no	—
221	C₂×D₄×C₆₁	—	4	1	no	—
222	C₂×D₄×C₆₁	—	4	2	no	—
223	C₂×D₄×C₆₁	—	4	2	no	—
224	C₂×D₄×C₆₁	—	4	2	no	—
225	C₂×D₄×C₆₁	—	4	2	no	—
226	C₂×D₄×C₆₁	—	4	2	no	—
227	C₂²×C₄×C₆₁	—	2	4	no	—
228	C₂²×C₄×C₆₁	—	2	2	no	—
229	C₂²×C₄×C₆₁	—	2	2	no	—
230	C₂²×C₄×C₆₁	—	2	4	no	—
231	C₂²×C₄×C₆₁	—	2	4	no	—
232	C₂²×C₄×C₆₁	—	2	4	no	—
233	C₂²×C₄×C₆₁	—	2	4	no	—
234	C₂²×C₄×C₆₁	—	2	2	no	—
235	C₂²×C₄×C₆₁	—	2	2	no	—
236	C₂²×C₄×C₆₁	—	4	2	no	—
237	C₂²×C₄×C₆₁	—	4	2	no	—
238	C₂²×C₄×C₆₁	—	4	1	no	—
239	C₂²×C₄×C₆₁	—	4	1	no	—
240	C₂²×C₄×C₆₁	—	4	1	no	—
241	C₂²×C₄×C₆₁	—	4	1	no	—
242	C₂²×C₄×C₆₁	—	4	2	no	—
243	C₂²×C₄×C₆₁	—	4	2	no	—
244	C₂²×C₄×C₆₁	—	4	2	no	—
245	C₂²×C₄×C₆₁	—	4	2	no	—
246	C₂²×C₄×C₆₁	—	4	2	no	—
247	C₂²×C₄×C₆₁	—	4	2	no	—
248	C₂²×C₄×C₆₁	—	4	2	no	—
249	C₂²×C₄×C₆₁	—	4	16	no	—
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	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
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	1	no	—
273	C₄⋊C₄×C₆₁	—	4	1	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	C₂²⋊C₄×C₆₁	—	2	4	no	—
280	C₂²⋊C₄×C₆₁	—	2	4	no	—
281	C₂²⋊C₄×C₆₁	—	2	4	no	—
282	C₂²⋊C₄×C₆₁	—	2	4	no	—
283	C₂²⋊C₄×C₆₁	—	2	4	no	—
284	C₂²⋊C₄×C₆₁	—	4	1	no	—
285	C₂²⋊C₄×C₆₁	—	4	2	no	—
286	C₂²⋊C₄×C₆₁	—	4	1	no	—
287	C₂²⋊C₄×C₆₁	—	4	1	no	—
288	C₂²⋊C₄×C₆₁	—	4	1	no	—
289	C₂²⋊C₄×C₆₁	—	4	1	no	—
290	C₂²⋊C₄×C₆₁	—	4	1	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	C₂²⋊C₄×C₆₁	—	4	2	no	—
298	C₂²⋊C₄×C₆₁	—	4	2	no	—
299	C₂²⋊C₄×C₆₁	—	4	2	no	—
300	C₂²⋊C₄×C₆₁	—	4	2	no	—
301	C₂²⋊C₄×C₆₁	—	4	2	no	—
302	C₂²⋊C₄×C₆₁	—	4	2	no	—
303	C₂²⋊C₄×C₆₁	—	4	2	no	—
304	C₂²⋊C₄×C₆₁	—	4	2	no	—
305	C₄²×C₆₁	—	4	2	no	—
306	C₄²×C₆₁	—	4	2	no	—
307	C₄²×C₆₁	—	4	2	no	—
308	C₂³×C₆₁	—	2	2	no	—
309	C₂³×C₆₁	—	2	2	no	—
310	C₂³×C₆₁	—	2	8	no	—
311	C₂³×C₆₁	—	2	1	no	—
312	C₂³×C₆₁	—	2	1	no	—
313	C₂³×C₆₁	—	2	1	no	—
314	C₂³×C₆₁	—	2	1	no	—
315	C₂³×C₆₁	—	2	2	no	—
316	C₂³×C₆₁	—	2	2	no	—
317	C₂³×C₆₁	—	2	2	no	—
318	C₂³×C₆₁	—	2	2	no	—
319	C₂³×C₆₁	—	2	2	no	—
320	C₂³×C₆₁	—	2	2	no	—
321	C₂³×C₆₁	—	2	2	no	—
322	C₂³×C₆₁	—	2	2	no	—
323	C₂³×C₆₁	—	2	2	no	—
324	C₂³×C₆₁	—	2	2	no	—
325	C₂³×C₆₁	—	2	2	no	—
326	C₂³×C₆₁	—	4	8	no	—
327	C₂³×C₆₁	—	4	4	no	—
328	C₂³×C₆₁	—	4	8	no	—
329	C₂³×C₆₁	—	4	4	no	—
330	C₂³×C₆₁	C₂×#41	1	2	yes	—
331	C₂³×C₆₁	C₂×#41	1	2	yes	—
332	C₂³×C₆₁	C₂×#41	1	2	yes	—
333	C₂³×C₆₁	H(5,𝔽₂)	1	2	yes	—
334	C₂³×C₆₁	H(5,𝔽₂)	1	2	yes	—
335	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
336	Q₈×C₆₁	—	8	2	no	—
337	D₄×C₆₁	—	4	8	no	—
338	D₄×C₆₁	—	8	4	no	—
339	D₄×C₆₁	—	8	4	no	—
340	D₄×C₆₁	—	8	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	2	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	1	no	—
353	C₂×C₄×C₆₁	—	2	2	no	—
354	C₂×C₄×C₆₁	—	2	1	no	—
355	C₂×C₄×C₆₁	—	2	1	no	—
356	C₂×C₄×C₆₁	—	2	1	no	—
357	C₂×C₄×C₆₁	—	2	2	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	—	2	2	no	—
372	C₂×C₄×C₆₁	—	2	2	no	—
373	C₂×C₄×C₆₁	—	2	2	no	—
374	C₂×C₄×C₆₁	—	2	2	no	—
375	C₂×C₄×C₆₁	—	2	2	no	—
376	C₂×C₄×C₆₁	—	2	2	no	—
377	C₂×C₄×C₆₁	—	2	2	no	—
378	C₂×C₄×C₆₁	—	2	2	no	—
379	C₂×C₄×C₆₁	—	2	2	no	—
380	C₂×C₄×C₆₁	—	2	2	no	—
381	C₂×C₄×C₆₁	—	2	2	no	—
382	C₂×C₄×C₆₁	—	4	8	no	—
383	C₂×C₄×C₆₁	—	4	4	no	—
384	C₂×C₄×C₆₁	—	4	4	no	—
385	C₂×C₄×C₆₁	—	4	8	no	—
386	C₂×C₄×C₆₁	—	8	4	no	—
387	C₂×C₄×C₆₁	—	8	2	no	—
388	C₂×C₄×C₆₁	—	8	2	no	—
389	C₂×C₄×C₆₁	—	8	4	no	—
390	#36974	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
391	C₂²×C₆₁	—	2	4	no	—
392	C₂²×C₆₁	—	2	2	no	—
393	C₂²×C₆₁	—	2	4	no	—
394	C₂²×C₆₁	—	2	2	no	—
395	C₂²×C₆₁	—	2	2	no	—
396	C₂²×C₆₁	—	2	2	no	—
397	C₂²×C₆₁	—	2	4	no	—
398	C₂²×C₆₁	—	2	4	no	—
399	C₂²×C₆₁	—	4	16	no	—
400	C₂²×C₆₁	—	4	1	no	—
401	C₂²×C₆₁	—	4	1	no	—
402	C₂²×C₆₁	—	4	2	no	—
403	C₂²×C₆₁	—	4	2	no	—
404	C₂²×C₆₁	—	4	1	no	—
405	C₂²×C₆₁	—	4	1	no	—
406	C₂²×C₆₁	—	4	2	no	—
407	C₂²×C₆₁	—	4	2	no	—
408	C₂²×C₆₁	—	4	2	no	—
409	C₂²×C₆₁	—	4	2	no	—
410	C₂²×C₆₁	—	4	2	no	—
411	C₂²×C₆₁	—	4	2	no	—
412	C₂²×C₆₁	—	4	2	no	—
413	C₂²×C₆₁	#538	1	4	yes	—
414	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
415	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
416	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
417	C₂²×C₆₁	#585	1	2	yes	—
418	C₂²×C₆₁	#585	1	2	yes	—
419	C₄×C₆₁	—	4	2	no	—
420	C₄×C₆₁	—	4	2	no	—
421	C₄×C₆₁	—	4	2	no	—
422	C₄×C₆₁	—	4	2	no	—
423	C₄×C₆₁	—	4	2	no	—
424	C₄×C₆₁	—	4	2	no	—
425	C₄×C₆₁	—	4	2	no	—
426	C₄×C₆₁	—	4	2	no	—
427	C₄×C₆₁	—	4	1	no	—
428	C₄×C₆₁	—	4	2	no	—
429	C₄×C₆₁	—	4	1	no	—
430	C₄×C₆₁	—	4	2	no	—
431	C₄×C₆₁	—	4	1	no	—
432	C₄×C₆₁	—	4	1	no	—
433	C₄×C₆₁	—	4	2	no	—
434	#2849	C₂×C₆₁	1	2	yes	complemented
435	#2771	C₂×C₆₁	1	1	yes	characteristic, complemented
436	#2765	C₂×C₆₁	1	2	yes	complemented
437	#2764	C₂×C₆₁	1	1	yes	characteristic, complemented
438	#2761	C₂×C₆₁	1	2	yes	complemented
439	#2760	C₂×C₆₁	1	1	yes	characteristic, complemented
440	#2752	C₂×C₆₁	1	1	yes	characteristic, complemented
441	#2751	C₂×C₆₁	1	2	yes	complemented
442	#2750	C₂×C₆₁	1	2	yes	complemented
443	#2749	C₂×C₆₁	1	2	yes	complemented
444	#2743	C₂×C₆₁	1	2	yes	complemented
445	#2626	C₂×C₆₁	1	1	yes	characteristic, complemented
446	#2617	C₂×C₆₁	1	1	yes	characteristic
447	#2493	C₂×C₆₁	1	2	yes	complemented
448	#2488	C₂×C₆₁	1	2	yes	complemented
449	#2425	C₂×C₆₁	1	2	yes	complemented
450	#2419	C₂×C₆₁	1	2	yes	complemented
451	#2321	C₂×C₆₁	1	2	yes	complemented
452	C₂×#381	C₂×C₆₁	1	1	yes	characteristic, complemented
453	C₂×C₆₁	—	2	4	no	—
454	C₂×C₆₁	—	4	2	no	—
455	C₂×C₆₁	—	4	2	no	—
456	C₂×C₆₁	—	8	2	no	—
457	C₂×C₆₁	C₂×#538	1	1	yes	characteristic
458	C₂×C₆₁	#3491	1	2	yes	—
459	C₂×C₆₁	#3533	1	1	yes	characteristic
460	C₂×C₆₁	#3533	1	2	yes	—
461	C₂×C₆₁	#3533	1	1	yes	characteristic
462	C₂⁴×C₄	C₂²×C₆₁	1	1	yes	characteristic
463	C₂×#123	C₂²×C₆₁	1	2	yes	—
464	C₂×#123	C₂²×C₆₁	1	2	yes	—
465	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
466	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
467	C₂×#120	C₂²×C₆₁	1	2	yes	—
468	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
469	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
470	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
471	#401	C₂²×C₆₁	1	2	yes	complemented
472	#400	C₂²×C₆₁	1	2	yes	complemented
473	#400	C₂²×C₆₁	1	2	yes	complemented
474	#400	C₂²×C₆₁	1	2	yes	complemented
475	#400	C₂²×C₆₁	1	2	yes	complemented
476	#400	C₂²×C₆₁	1	2	yes	complemented
477	#400	C₂²×C₆₁	1	2	yes	complemented
478	#399	C₂²×C₆₁	1	1	yes	characteristic
479	#399	C₂²×C₆₁	1	1	yes	characteristic
480	#398	C₂²×C₆₁	1	2	yes	complemented
481	#398	C₂²×C₆₁	1	2	yes	complemented
482	#397	C₂²×C₆₁	1	1	yes	characteristic
483	#397	C₂²×C₆₁	1	1	yes	characteristic
484	#397	C₂²×C₆₁	1	2	yes	complemented
485	#397	C₂²×C₆₁	1	2	yes	complemented
486	#397	C₂²×C₆₁	1	2	yes	complemented
487	#397	C₂²×C₆₁	1	2	yes	complemented
488	#396	C₂²×C₆₁	1	2	yes	—
489	#396	C₂²×C₆₁	1	2	yes	—
490	#396	C₂²×C₆₁	1	2	yes	complemented
491	#394	C₂²×C₆₁	1	2	yes	—
492	#394	C₂²×C₆₁	1	2	yes	—
493	#394	C₂²×C₆₁	1	2	yes	complemented
494	#393	C₂²×C₆₁	1	1	yes	characteristic
495	#393	C₂²×C₆₁	1	1	yes	characteristic
496	#393	C₂²×C₆₁	1	2	yes	complemented
497	#392	C₂²×C₆₁	1	1	yes	characteristic
498	#392	C₂²×C₆₁	1	1	yes	characteristic
499	#391	C₂²×C₆₁	1	2	yes	complemented
500	#390	C₂²×C₆₁	1	2	yes	—
501	#390	C₂²×C₆₁	1	2	yes	—
502	#389	C₂²×C₆₁	1	2	yes	complemented
503	#388	C₂²×C₆₁	1	2	yes	—
504	#388	C₂²×C₆₁	1	2	yes	—
505	#388	C₂²×C₆₁	1	2	yes	—
506	#388	C₂²×C₆₁	1	2	yes	—
507	#388	C₂²×C₆₁	1	2	yes	complemented
508	#388	C₂²×C₆₁	1	2	yes	complemented
509	#388	C₂²×C₆₁	1	2	yes	complemented
510	#387	C₂²×C₆₁	1	2	yes	complemented
511	#387	C₂²×C₆₁	1	2	yes	complemented
512	#387	C₂²×C₆₁	1	2	yes	complemented
513	#387	C₂²×C₆₁	1	2	yes	complemented
514	#387	C₂²×C₆₁	1	2	yes	complemented
515	#386	C₂²×C₆₁	1	2	yes	—
516	#386	C₂²×C₆₁	1	2	yes	—
517	#386	C₂²×C₆₁	1	2	yes	—
518	#386	C₂²×C₆₁	1	2	yes	—
519	#386	C₂²×C₆₁	1	2	yes	—
520	#386	C₂²×C₆₁	1	2	yes	—
521	#386	C₂²×C₆₁	1	2	yes	—
522	#386	C₂²×C₆₁	1	2	yes	—
523	#386	C₂²×C₆₁	1	2	yes	complemented
524	#385	C₂²×C₆₁	1	2	yes	—
525	#385	C₂²×C₆₁	1	2	yes	—
526	#385	C₂²×C₆₁	1	2	yes	—
527	#385	C₂²×C₆₁	1	2	yes	—
528	#385	C₂²×C₆₁	1	2	yes	—
529	#385	C₂²×C₆₁	1	2	yes	—
530	#385	C₂²×C₆₁	1	2	yes	complemented
531	#383	C₂²×C₆₁	1	2	yes	complemented
532	#382	C₂²×C₆₁	1	2	yes	complemented
533	#381	C₂²×C₆₁	1	2	yes	—
534	#381	C₂²×C₆₁	1	2	yes	—
535	#381	C₂²×C₆₁	1	2	yes	—
536	#381	C₂²×C₆₁	1	2	yes	—
537	#381	C₂²×C₆₁	1	1	yes	characteristic
538	#381	C₂²×C₆₁	1	1	yes	characteristic
539	#381	C₂²×C₆₁	1	1	yes	characteristic
540	#381	C₂²×C₆₁	1	1	yes	characteristic
541	#381	C₂²×C₆₁	1	2	yes	complemented
542	#380	C₂²×C₆₁	1	1	yes	characteristic
543	#380	C₂²×C₆₁	1	1	yes	characteristic
544	#380	C₂²×C₆₁	1	2	yes	complemented
545	#379	C₂²×C₆₁	1	2	yes	—
546	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
547	C₂×#95	C₂²×C₆₁	1	2	yes	—
548	C₂×#95	C₂²×C₆₁	1	2	yes	—
549	C₆₁	#36974	1	1	yes	characteristic, direct product factor, Sylow
550	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
551	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
552	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
553	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
554	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
555	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
556	C₂³×C₄	—	2	4	no	—
557	C₂³×C₄	—	4	2	no	—
558	C₂³×C₄	—	4	2	no	—
559	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
560	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
561	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
562	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
563	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
564	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
565	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
566	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
567	#123	—	4	4	no	—
568	#123	—	4	4	no	—
569	C₂²⋊Q₈	—	4	2	no	—
570	#121	—	4	2	no	—
571	#120	—	2	8	no	—
572	C₄×D₄	—	4	4	no	—
573	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
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	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
587	C₂×C₂²⋊C₄	—	4	2	no	—
588	C₂×C₂²⋊C₄	—	4	2	no	—
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	1	yes	characteristic
595	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
598	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
599	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
600	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
601	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
615	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
616	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
617	C₂×C₄²	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	1	yes	characteristic
629	#95	C₂³×C₆₁	1	1	yes	characteristic
630	#95	C₂³×C₆₁	1	1	yes	characteristic
631	#95	C₂³×C₆₁	1	1	yes	characteristic
632	#95	C₂³×C₆₁	1	2	yes	—
633	#95	C₂³×C₆₁	1	2	yes	—
634	#95	C₂³×C₆₁	1	2	yes	—
635	#95	C₂³×C₆₁	1	2	yes	—
636	#95	C₂³×C₆₁	1	2	yes	—
637	#95	C₂³×C₆₁	1	2	yes	—
638	#95	C₂³×C₆₁	1	2	yes	—
639	#95	C₂³×C₆₁	1	2	yes	—
640	#95	C₂³×C₆₁	1	2	yes	—
641	#95	C₂³×C₆₁	1	2	yes	—
642	#95	C₂³×C₆₁	1	2	yes	—
643	#95	C₂³×C₆₁	1	2	yes	—
644	#95	C₂³×C₆₁	1	2	yes	—
645	#95	C₂³×C₆₁	1	2	yes	—
646	#95	C₂³×C₆₁	1	2	yes	—
647	#95	C₂³×C₆₁	1	2	yes	—
648	C₂⁴	—	2	2	no	—
649	C₂⁴	—	2	2	no	—
650	C₂⁴	—	4	2	no	—
651	C₂⁴	—	4	2	no	—
652	C₂⁴	#41×C₆₁	1	4	yes	—
653	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
654	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
655	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
656	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
657	C₂×Q₈	—	4	1	no	—
658	C₂×Q₈	—	4	2	no	—
659	C₂×D₄	—	2	4	no	—
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	4	no	—
663	C₂×D₄	—	2	4	no	—
664	C₂×D₄	—	4	1	no	—
665	C₂×D₄	—	4	2	no	—
666	C₂×D₄	—	4	2	no	—
667	C₂×D₄	—	4	2	no	—
668	C₂×D₄	—	4	2	no	—
669	C₂×D₄	—	4	2	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	2	4	no	—
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	2	4	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	2	no	—
681	C₂²×C₄	—	4	1	no	—
682	C₂²×C₄	—	4	1	no	—
683	C₂²×C₄	—	4	1	no	—
684	C₂²×C₄	—	4	1	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	—	4	2	no	—
687	C₂²×C₄	—	4	2	no	—
688	C₂²×C₄	—	4	2	no	—
689	C₂²×C₄	—	4	2	no	—
690	C₂²×C₄	—	4	2	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	—	4	16	no	—
693	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	4	1	no	—
710	C₄⋊C₄	—	4	1	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₄⋊C₄	—	4	2	no	—
713	C₄⋊C₄	—	4	2	no	—
714	C₄⋊C₄	—	4	2	no	—
715	C₄⋊C₄	—	4	2	no	—
716	C₄⋊C₄	—	4	2	no	—
717	C₄⋊C₄	—	4	2	no	—
718	C₄⋊C₄	—	4	2	no	—
719	C₄⋊C₄	—	4	2	no	—
720	C₄⋊C₄	—	4	2	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	4	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	4	1	no	—
728	C₂²⋊C₄	—	4	2	no	—
729	C₂²⋊C₄	—	4	1	no	—
730	C₂²⋊C₄	—	4	1	no	—
731	C₂²⋊C₄	—	4	1	no	—
732	C₂²⋊C₄	—	4	1	no	—
733	C₂²⋊C₄	—	4	1	no	—
734	C₂²⋊C₄	—	4	2	no	—
735	C₂²⋊C₄	—	4	2	no	—
736	C₂²⋊C₄	—	4	2	no	—
737	C₂²⋊C₄	—	4	2	no	—
738	C₂²⋊C₄	—	4	2	no	—
739	C₂²⋊C₄	—	4	2	no	—
740	C₂²⋊C₄	—	4	2	no	—
741	C₂²⋊C₄	—	4	2	no	—
742	C₂²⋊C₄	—	4	2	no	—
743	C₂²⋊C₄	—	4	2	no	—
744	C₂²⋊C₄	—	4	2	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₄²	—	4	2	no	—
749	C₄²	—	4	2	no	—
750	C₄²	—	4	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	8	no	—
754	C₂³	—	2	1	no	—
755	C₂³	—	2	1	no	—
756	C₂³	—	2	1	no	—
757	C₂³	—	2	1	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	2	no	—
769	C₂³	—	4	8	no	—
770	C₂³	—	4	4	no	—
771	C₂³	—	4	8	no	—
772	C₂³	—	4	4	no	—
773	C₂³	C₂×#41×C₆₁	1	2	yes	—
774	C₂³	C₂×#41×C₆₁	1	2	yes	—
775	C₂³	C₂×#41×C₆₁	1	2	yes	—
776	C₂³	H(5,𝔽₂)×C₆₁	1	2	yes	—
777	C₂³	H(5,𝔽₂)×C₆₁	1	2	yes	—
778	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
779	Q₈	—	8	2	no	—
780	D₄	—	4	8	no	—
781	D₄	—	8	4	no	—
782	D₄	—	8	4	no	—
783	D₄	—	8	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	2	no	—
789	C₂×C₄	—	2	2	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	1	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	4	8	no	—
826	C₂×C₄	—	4	4	no	—
827	C₂×C₄	—	4	4	no	—
828	C₂×C₄	—	4	8	no	—
829	C₂×C₄	—	8	4	no	—
830	C₂×C₄	—	8	2	no	—
831	C₂×C₄	—	8	2	no	—
832	C₂×C₄	—	8	4	no	—
833	C₂²	—	2	4	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	2	4	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	4	no	—
840	C₂²	—	2	4	no	—
841	C₂²	—	4	16	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	2	no	—
855	C₂²	C₆₁×#538	1	4	yes	—
856	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
857	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
858	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
859	C₂²	C₆₁×#585	1	2	yes	—
860	C₂²	C₆₁×#585	1	2	yes	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	2	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	1	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	1	no	—
874	C₄	—	4	1	no	—
875	C₄	—	4	2	no	—
876	C₂	—	2	4	no	—
877	C₂	—	4	2	no	—
878	C₂	—	4	2	no	—
879	C₂	—	8	2	no	—
880	C₂	C₂×C₆₁×#538	1	1	yes	characteristic
881	C₂	C₆₁×#3491	1	2	yes	—
882	C₂	C₆₁×#3533	1	1	yes	characteristic
883	C₂	C₆₁×#3533	1	2	yes	—
884	C₂	C₆₁×#3533	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
prime radical	C₆₁×#2617	C₂
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×#2849	C₂	semidirect
2. C₆₁×#2771	C₂	semidirect
3. C₆₁×#2765	C₂	semidirect
4. C₆₁×#2764	C₂	semidirect
5. C₆₁×#2761	C₂	semidirect
6. C₆₁×#2760	C₂	semidirect
7. C₆₁×#2752	C₂	semidirect
8. C₆₁×#2751	C₂	semidirect
9. C₆₁×#2750	C₂	semidirect
10. C₆₁×#2749	C₂	semidirect
11. C₆₁×#2743	C₂	semidirect
12. C₆₁×#2626	C₂	semidirect
14. C₆₁×#2493	C₂	semidirect
15. C₆₁×#2488	C₂	semidirect
16. C₆₁×#2425	C₂	semidirect
17. C₆₁×#2419	C₂	semidirect
18. C₆₁×#2321	C₂	semidirect
19. C₂×C₆₁×#381	C₂	semidirect
29. C₆₁×#401	C₂²	semidirect
30. C₆₁×#400	C₂²	semidirect
31. C₆₁×#400	C₂²	semidirect
32. C₆₁×#400	C₂²	semidirect
33. C₆₁×#400	C₂²	semidirect
34. C₆₁×#400	C₂²	semidirect
35. C₆₁×#400	C₂²	semidirect
38. C₆₁×#398	C₂²	semidirect
39. C₆₁×#398	C₂²	semidirect
42. C₆₁×#397	C₂²	semidirect
43. C₆₁×#397	C₂²	semidirect
44. C₆₁×#397	C₂²	semidirect
45. C₆₁×#397	C₂²	semidirect
48. C₆₁×#396	C₂²	semidirect
51. C₆₁×#394	C₂²	semidirect
54. C₆₁×#393	C₂²	semidirect
57. C₆₁×#391	C₂²	semidirect
60. C₆₁×#389	C₂²	semidirect
65. C₆₁×#388	C₂²	semidirect
66. C₆₁×#388	C₂²	semidirect
67. C₆₁×#388	C₂²	semidirect
68. C₆₁×#387	C₂²	semidirect
69. C₆₁×#387	C₂²	semidirect
70. C₆₁×#387	C₂²	semidirect
71. C₆₁×#387	C₂²	semidirect
72. C₆₁×#387	C₂²	semidirect
81. C₆₁×#386	C₂²	semidirect
88. C₆₁×#385	C₂²	semidirect
89. C₆₁×#383	C₂²	semidirect
90. C₆₁×#382	C₂²	semidirect
99. C₆₁×#381	C₂²	semidirect
102. C₆₁×#380	C₂²	semidirect
390. #36974	C₆₁	direct (N × H)
434. #2849	C₂×C₆₁	semidirect
435. #2771	C₂×C₆₁	semidirect
436. #2765	C₂×C₆₁	semidirect
437. #2764	C₂×C₆₁	semidirect
438. #2761	C₂×C₆₁	semidirect
439. #2760	C₂×C₆₁	semidirect
440. #2752	C₂×C₆₁	semidirect
441. #2751	C₂×C₆₁	semidirect
442. #2750	C₂×C₆₁	semidirect
443. #2749	C₂×C₆₁	semidirect
444. #2743	C₂×C₆₁	semidirect
445. #2626	C₂×C₆₁	semidirect
447. #2493	C₂×C₆₁	semidirect
448. #2488	C₂×C₆₁	semidirect
449. #2425	C₂×C₆₁	semidirect
450. #2419	C₂×C₆₁	semidirect
451. #2321	C₂×C₆₁	semidirect
452. C₂×#381	C₂×C₆₁	semidirect
471. #401	C₂²×C₆₁	semidirect
472. #400	C₂²×C₆₁	semidirect
473. #400	C₂²×C₆₁	semidirect
474. #400	C₂²×C₆₁	semidirect
475. #400	C₂²×C₆₁	semidirect
476. #400	C₂²×C₆₁	semidirect
477. #400	C₂²×C₆₁	semidirect
480. #398	C₂²×C₆₁	semidirect
481. #398	C₂²×C₆₁	semidirect
484. #397	C₂²×C₆₁	semidirect
485. #397	C₂²×C₆₁	semidirect
486. #397	C₂²×C₆₁	semidirect
487. #397	C₂²×C₆₁	semidirect
490. #396	C₂²×C₆₁	semidirect
493. #394	C₂²×C₆₁	semidirect
496. #393	C₂²×C₆₁	semidirect
499. #391	C₂²×C₆₁	semidirect
502. #389	C₂²×C₆₁	semidirect
507. #388	C₂²×C₆₁	semidirect
508. #388	C₂²×C₆₁	semidirect
509. #388	C₂²×C₆₁	semidirect
510. #387	C₂²×C₆₁	semidirect
511. #387	C₂²×C₆₁	semidirect
512. #387	C₂²×C₆₁	semidirect
513. #387	C₂²×C₆₁	semidirect
514. #387	C₂²×C₆₁	semidirect
523. #386	C₂²×C₆₁	semidirect
530. #385	C₂²×C₆₁	semidirect
531. #383	C₂²×C₆₁	semidirect
532. #382	C₂²×C₆₁	semidirect
541. #381	C₂²×C₆₁	semidirect
544. #380	C₂²×C₆₁	semidirect
549. C₆₁	#36974	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×#2849	2
C₆₁×#2771	2
C₆₁×#2765	2
C₆₁×#2764	2
C₆₁×#2761	2
C₆₁×#2760	2
C₆₁×#2752	2
C₆₁×#2751	2
C₆₁×#2750	2
C₆₁×#2749	2
C₆₁×#2743	2
C₆₁×#2626	2
C₆₁×#2617	2
C₆₁×#2493	2
C₆₁×#2488	2
C₆₁×#2425	2
C₆₁×#2419	2
C₆₁×#2321	2
C₂×C₆₁×#381	2
#36974	61

Subgroups — C61×#36974 #29540407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#36974 #29540407