Subgroups — C₆₁×#35036 #29538469

Order 15616.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2863	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#2861	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2854	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2649	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2630	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2587	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2578	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2518	C₂	1	2	yes	maximal, complemented
10	C₆₁×#2512	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2489	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#2467	C₂	1	2	yes	maximal, complemented
13	C₆₁×#2446	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#2441	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#2432	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#2426	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#2415	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#2407	C₂	1	1	yes	maximal, characteristic
19	C₆₁×#2335	C₂	1	2	yes	maximal, complemented
20	C₆₁×#2334	C₂	1	2	yes	maximal, complemented
21	C₄×C₂²⋊Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₁×#2297	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#126×C₆₁	C₂²	1	2	yes	—
27	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#123×C₆₁	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
41	C₆₁×#400	C₂²	1	2	yes	—
42	C₆₁×#400	C₂²	1	2	yes	—
43	C₆₁×#399	C₂²	1	2	yes	—
44	C₆₁×#398	C₂²	1	2	yes	—
45	C₆₁×#397	C₂²	1	2	yes	—
46	C₆₁×#397	C₂²	1	2	yes	—
47	C₆₁×#397	C₂²	1	2	yes	—
48	C₆₁×#396	C₂²	1	2	yes	—
49	C₆₁×#396	C₂²	1	2	yes	—
50	C₆₁×#396	C₂²	1	2	yes	—
51	C₆₁×#394	C₂²	1	2	yes	—
52	C₆₁×#394	C₂²	1	2	yes	—
53	C₆₁×#394	C₂²	1	2	yes	—
54	C₆₁×#394	C₂²	1	2	yes	—
55	C₆₁×#394	C₂²	1	2	yes	—
56	C₆₁×#392	C₂²	1	2	yes	—
57	C₆₁×#391	C₂²	1	1	yes	characteristic
58	C₆₁×#391	C₂²	1	1	yes	characteristic
59	C₆₁×#391	C₂²	1	1	yes	characteristic
60	C₆₁×#391	C₂²	1	1	yes	characteristic
61	C₆₁×#391	C₂²	1	1	yes	characteristic
62	C₆₁×#391	C₂²	1	1	yes	characteristic
63	C₆₁×#390	C₂²	1	1	yes	characteristic
64	C₆₁×#390	C₂²	1	1	yes	characteristic
65	C₆₁×#390	C₂²	1	2	yes	—
66	C₆₁×#390	C₂²	1	1	yes	characteristic
67	C₆₁×#390	C₂²	1	1	yes	characteristic
68	C₆₁×#389	C₂²	1	1	yes	characteristic
69	C₆₁×#389	C₂²	1	2	yes	—
70	C₆₁×#389	C₂²	1	2	yes	—
71	C₆₁×#389	C₂²	1	2	yes	—
72	C₆₁×#389	C₂²	1	2	yes	—
73	C₆₁×#389	C₂²	1	1	yes	characteristic
74	C₆₁×#389	C₂²	1	1	yes	characteristic
75	C₆₁×#389	C₂²	1	1	yes	characteristic
76	C₆₁×#388	C₂²	1	2	yes	—
77	C₆₁×#388	C₂²	1	2	yes	—
78	C₆₁×#388	C₂²	1	2	yes	—
79	C₆₁×#388	C₂²	1	2	yes	—
80	C₆₁×#388	C₂²	1	2	yes	—
81	C₆₁×#388	C₂²	1	2	yes	—
82	C₆₁×#388	C₂²	1	2	yes	—
83	C₆₁×#388	C₂²	1	2	yes	—
84	C₆₁×#388	C₂²	1	2	yes	—
85	C₆₁×#388	C₂²	1	2	yes	—
86	C₆₁×#387	C₂²	1	2	yes	—
87	C₆₁×#387	C₂²	1	2	yes	—
88	C₆₁×#387	C₂²	1	2	yes	—
89	C₆₁×#387	C₂²	1	2	yes	—
90	C₆₁×#387	C₂²	1	2	yes	—
91	C₆₁×#387	C₂²	1	2	yes	—
92	C₆₁×#387	C₂²	1	2	yes	—
93	C₆₁×#386	C₂²	1	2	yes	—
94	C₆₁×#386	C₂²	1	2	yes	—
95	C₆₁×#386	C₂²	1	2	yes	—
96	C₆₁×#386	C₂²	1	2	yes	—
97	C₆₁×#385	C₂²	1	2	yes	—
98	C₆₁×#385	C₂²	1	2	yes	—
99	C₆₁×#385	C₂²	1	2	yes	—
100	C₆₁×#385	C₂²	1	2	yes	—
101	C₆₁×#384	C₂²	1	1	yes	characteristic
102	C₆₁×#383	C₂²	1	2	yes	—
103	C₆₁×#382	C₂²	1	2	yes	—
104	C₆₁×#380	C₂²	1	1	yes	characteristic
105	C₆₁×#380	C₂²	1	2	yes	—
106	C₆₁×#380	C₂²	1	2	yes	—
107	C₆₁×#380	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
113	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
114	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
122	C₄³×C₆₁	C₂²	1	1	yes	characteristic
123	C₂×#41×C₆₁	—	2	4	no	—
124	C₂×#41×C₆₁	—	4	2	no	—
125	C₂×#41×C₆₁	—	4	2	no	—
126	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
131	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
132	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
137	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
139	C₄⋊Q₈×C₆₁	—	4	2	no	—
140	#126×C₆₁	—	2	8	no	—
141	#125×C₆₁	—	4	2	no	—
142	#124×C₆₁	—	4	2	no	—
143	#123×C₆₁	—	2	8	no	—
144	C₂²⋊Q₈×C₆₁	—	2	4	no	—
145	C₂²⋊Q₈×C₆₁	—	4	2	no	—
146	C₂²⋊Q₈×C₆₁	—	4	2	no	—
147	#121×C₆₁	—	4	2	no	—
148	C₄×Q₈×C₆₁	—	4	2	no	—
149	C₄×D₄×C₆₁	—	2	4	no	—
150	C₄×D₄×C₆₁	—	2	4	no	—
151	C₄×D₄×C₆₁	—	2	4	no	—
152	#117×C₆₁	—	4	2	no	—
153	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
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	2	yes	—
158	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
166	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
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	2	yes	—
172	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
196	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
198	C₂×C₄²×C₆₁	—	4	2	no	—
199	C₂×C₄²×C₆₁	—	4	2	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	1	yes	characteristic
203	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
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	2	yes	—
208	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
213	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
214	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
216	#95×C₆₁	C₂³	1	1	yes	characteristic
217	#95×C₆₁	C₂³	1	1	yes	characteristic
218	#95×C₆₁	C₂³	1	1	yes	characteristic
219	#95×C₆₁	C₂³	1	1	yes	characteristic
220	#95×C₆₁	C₂³	1	1	yes	characteristic
221	#95×C₆₁	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
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	2	yes	—
238	#95×C₆₁	C₂³	1	2	yes	—
239	#95×C₆₁	C₂³	1	2	yes	—
240	#95×C₆₁	C₂³	1	2	yes	—
241	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
242	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
243	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
244	#41×C₆₁	—	4	16	no	—
245	C₂×Q₈×C₆₁	—	2	2	no	—
246	C₂×Q₈×C₆₁	—	2	2	no	—
247	C₂×Q₈×C₆₁	—	2	2	no	—
248	C₂×Q₈×C₆₁	—	2	2	no	—
249	C₂×Q₈×C₆₁	—	2	2	no	—
250	C₂×Q₈×C₆₁	—	2	2	no	—
251	C₂×D₄×C₆₁	—	2	2	no	—
252	C₂×D₄×C₆₁	—	2	2	no	—
253	C₂×D₄×C₆₁	—	2	4	no	—
254	C₂×D₄×C₆₁	—	2	4	no	—
255	C₂×D₄×C₆₁	—	2	2	no	—
256	C₂×D₄×C₆₁	—	2	2	no	—
257	C₂×D₄×C₆₁	—	2	2	no	—
258	C₂×D₄×C₆₁	—	2	2	no	—
259	C₂×D₄×C₆₁	—	4	2	no	—
260	C₂×D₄×C₆₁	—	4	2	no	—
261	C₂×D₄×C₆₁	—	4	2	no	—
262	C₂×D₄×C₆₁	—	4	2	no	—
263	C₂²×C₄×C₆₁	—	2	2	no	—
264	C₂²×C₄×C₆₁	—	2	2	no	—
265	C₂²×C₄×C₆₁	—	2	2	no	—
266	C₂²×C₄×C₆₁	—	2	2	no	—
267	C₂²×C₄×C₆₁	—	2	2	no	—
268	C₂²×C₄×C₆₁	—	2	2	no	—
269	C₂²×C₄×C₆₁	—	2	4	no	—
270	C₂²×C₄×C₆₁	—	2	2	no	—
271	C₂²×C₄×C₆₁	—	2	2	no	—
272	C₂²×C₄×C₆₁	—	2	2	no	—
273	C₂²×C₄×C₆₁	—	2	2	no	—
274	C₂²×C₄×C₆₁	—	4	1	no	—
275	C₂²×C₄×C₆₁	—	4	1	no	—
276	C₂²×C₄×C₆₁	—	4	1	no	—
277	C₂²×C₄×C₆₁	—	4	1	no	—
278	C₂²×C₄×C₆₁	—	4	1	no	—
279	C₂²×C₄×C₆₁	—	4	1	no	—
280	C₂²×C₄×C₆₁	—	4	2	no	—
281	C₂²×C₄×C₆₁	—	4	2	no	—
282	C₂²×C₄×C₆₁	#41	1	4	yes	—
283	C₂²×C₄×C₆₁	#41	1	4	yes	complemented
284	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
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	2	yes	—
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	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
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	—	2	4	no	—
309	C₄⋊C₄×C₆₁	—	2	4	no	—
310	C₄⋊C₄×C₆₁	—	2	4	no	—
311	C₄⋊C₄×C₆₁	—	2	4	no	—
312	C₄⋊C₄×C₆₁	—	2	2	no	—
313	C₄⋊C₄×C₆₁	—	2	2	no	—
314	C₄⋊C₄×C₆₁	—	2	2	no	—
315	C₄⋊C₄×C₆₁	—	2	2	no	—
316	C₄⋊C₄×C₆₁	—	4	2	no	—
317	C₄⋊C₄×C₆₁	—	4	2	no	—
318	C₄⋊C₄×C₆₁	—	4	2	no	—
319	C₄⋊C₄×C₆₁	—	4	2	no	—
320	C₄⋊C₄×C₆₁	—	4	2	no	—
321	C₄⋊C₄×C₆₁	—	4	2	no	—
322	C₄⋊C₄×C₆₁	—	4	2	no	—
323	C₄⋊C₄×C₆₁	—	4	2	no	—
324	C₄⋊C₄×C₆₁	—	4	2	no	—
325	C₄⋊C₄×C₆₁	#41	1	4	yes	complemented
326	C₂²⋊C₄×C₆₁	—	2	2	no	—
327	C₂²⋊C₄×C₆₁	—	2	2	no	—
328	C₂²⋊C₄×C₆₁	—	2	4	no	—
329	C₂²⋊C₄×C₆₁	—	2	4	no	—
330	C₂²⋊C₄×C₆₁	—	2	2	no	—
331	C₂²⋊C₄×C₆₁	—	2	2	no	—
332	C₂²⋊C₄×C₆₁	—	2	2	no	—
333	C₂²⋊C₄×C₆₁	—	2	2	no	—
334	C₂²⋊C₄×C₆₁	—	2	4	no	—
335	C₂²⋊C₄×C₆₁	—	2	4	no	—
336	C₂²⋊C₄×C₆₁	—	2	4	no	—
337	C₂²⋊C₄×C₆₁	—	2	4	no	—
338	C₂²⋊C₄×C₆₁	—	2	4	no	—
339	C₂²⋊C₄×C₆₁	—	2	4	no	—
340	C₂²⋊C₄×C₆₁	—	4	2	no	—
341	C₂²⋊C₄×C₆₁	—	4	2	no	—
342	C₂²⋊C₄×C₆₁	—	4	2	no	—
343	C₂²⋊C₄×C₆₁	—	4	2	no	—
344	C₂²⋊C₄×C₆₁	—	4	2	no	—
345	C₂²⋊C₄×C₆₁	—	4	2	no	—
346	C₂²⋊C₄×C₆₁	—	4	2	no	—
347	C₂²⋊C₄×C₆₁	—	4	2	no	—
348	C₂²⋊C₄×C₆₁	—	4	2	no	—
349	C₄²×C₆₁	—	2	2	no	—
350	C₄²×C₆₁	—	2	2	no	—
351	C₄²×C₆₁	—	2	2	no	—
352	C₄²×C₆₁	—	2	4	no	—
353	C₄²×C₆₁	—	2	2	no	—
354	C₄²×C₆₁	—	2	2	no	—
355	C₄²×C₆₁	—	2	2	no	—
356	C₄²×C₆₁	—	2	2	no	—
357	C₄²×C₆₁	—	2	2	no	—
358	C₄²×C₆₁	—	4	1	no	—
359	C₄²×C₆₁	—	4	1	no	—
360	C₄²×C₆₁	—	4	1	no	—
361	C₄²×C₆₁	—	4	1	no	—
362	C₄²×C₆₁	—	4	1	no	—
363	C₄²×C₆₁	—	4	2	no	—
364	C₄²×C₆₁	—	4	2	no	—
365	C₂³×C₆₁	—	2	1	no	—
366	C₂³×C₆₁	—	2	1	no	—
367	C₂³×C₆₁	—	2	1	no	—
368	C₂³×C₆₁	—	2	1	no	—
369	C₂³×C₆₁	—	2	1	no	—
370	C₂³×C₆₁	—	2	1	no	—
371	C₂³×C₆₁	—	2	1	no	—
372	C₂³×C₆₁	—	2	1	no	—
373	C₂³×C₆₁	—	2	1	no	—
374	C₂³×C₆₁	—	2	1	no	—
375	C₂³×C₆₁	—	2	1	no	—
376	C₂³×C₆₁	—	2	1	no	—
377	C₂³×C₆₁	—	2	2	no	—
378	C₂³×C₆₁	—	2	2	no	—
379	C₂³×C₆₁	—	2	2	no	—
380	C₂³×C₆₁	—	2	2	no	—
381	C₂³×C₆₁	—	2	2	no	—
382	C₂³×C₆₁	—	2	2	no	—
383	C₂³×C₆₁	—	2	2	no	—
384	C₂³×C₆₁	C₂×#41	1	2	yes	—
385	C₂³×C₆₁	C₂×#41	1	2	yes	—
386	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
387	Q₈×C₆₁	—	4	4	no	—
388	Q₈×C₆₁	—	4	4	no	—
389	D₄×C₆₁	—	2	8	no	—
390	D₄×C₆₁	—	4	8	no	—
391	D₄×C₆₁	—	4	4	no	—
392	D₄×C₆₁	—	8	4	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	1	no	—
397	C₂×C₄×C₆₁	—	2	1	no	—
398	C₂×C₄×C₆₁	—	2	1	no	—
399	C₂×C₄×C₆₁	—	2	1	no	—
400	C₂×C₄×C₆₁	—	2	1	no	—
401	C₂×C₄×C₆₁	—	2	1	no	—
402	C₂×C₄×C₆₁	—	2	1	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	1	no	—
407	C₂×C₄×C₆₁	—	2	8	no	—
408	C₂×C₄×C₆₁	—	2	1	no	—
409	C₂×C₄×C₆₁	—	2	1	no	—
410	C₂×C₄×C₆₁	—	2	1	no	—
411	C₂×C₄×C₆₁	—	2	2	no	—
412	C₂×C₄×C₆₁	—	2	2	no	—
413	C₂×C₄×C₆₁	—	2	2	no	—
414	C₂×C₄×C₆₁	—	2	2	no	—
415	C₂×C₄×C₆₁	—	2	2	no	—
416	C₂×C₄×C₆₁	—	2	2	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	1	no	—
423	C₂×C₄×C₆₁	—	2	1	no	—
424	C₂×C₄×C₆₁	—	2	1	no	—
425	C₂×C₄×C₆₁	—	2	1	no	—
426	C₂×C₄×C₆₁	—	2	2	no	—
427	C₂×C₄×C₆₁	—	2	2	no	—
428	C₂×C₄×C₆₁	—	2	2	no	—
429	C₂×C₄×C₆₁	—	2	2	no	—
430	C₂×C₄×C₆₁	—	2	2	no	—
431	C₂×C₄×C₆₁	—	2	2	no	—
432	C₂×C₄×C₆₁	—	2	2	no	—
433	C₂×C₄×C₆₁	—	2	1	no	—
434	C₂×C₄×C₆₁	—	2	2	no	—
435	C₂×C₄×C₆₁	—	2	1	no	—
436	C₂×C₄×C₆₁	—	2	1	no	—
437	C₂×C₄×C₆₁	—	2	2	no	—
438	C₂×C₄×C₆₁	—	2	1	no	—
439	C₂×C₄×C₆₁	—	2	1	no	—
440	C₂×C₄×C₆₁	—	2	2	no	—
441	C₂×C₄×C₆₁	—	2	1	no	—
442	C₂×C₄×C₆₁	—	2	2	no	—
443	C₂×C₄×C₆₁	—	2	2	no	—
444	C₂×C₄×C₆₁	—	4	4	no	—
445	C₂×C₄×C₆₁	—	4	4	no	—
446	C₂×C₄×C₆₁	—	4	4	no	—
447	C₂×C₄×C₆₁	—	4	4	no	—
448	C₂×C₄×C₆₁	—	4	8	no	—
449	C₂×C₄×C₆₁	—	4	4	no	—
450	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
451	C₂×C₄×C₆₁	C₂×#41	1	2	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	C₂×#41	1	2	yes	—
457	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
458	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
459	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
460	#35036	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
461	C₂²×C₆₁	—	2	2	no	—
462	C₂²×C₆₁	—	2	2	no	—
463	C₂²×C₆₁	—	2	2	no	—
464	C₂²×C₆₁	—	2	2	no	—
465	C₂²×C₆₁	—	2	2	no	—
466	C₂²×C₆₁	—	2	2	no	—
467	C₂²×C₆₁	—	4	1	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	1	no	—
473	C₂²×C₆₁	—	4	1	no	—
474	C₂²×C₆₁	—	4	1	no	—
475	C₂²×C₆₁	—	4	2	no	—
476	C₂²×C₆₁	—	4	2	no	—
477	C₂²×C₆₁	—	4	2	no	—
478	C₂²×C₆₁	—	4	2	no	—
479	C₂²×C₆₁	—	4	2	no	—
480	C₂²×C₆₁	—	4	2	no	—
481	C₂²×C₆₁	—	4	2	no	—
482	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
483	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
484	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
485	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
486	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
487	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
488	C₂²×C₆₁	#585	1	1	yes	characteristic
489	C₄×C₆₁	—	2	2	no	—
490	C₄×C₆₁	—	2	2	no	—
491	C₄×C₆₁	—	2	2	no	—
492	C₄×C₆₁	—	2	2	no	—
493	C₄×C₆₁	—	2	2	no	—
494	C₄×C₆₁	—	2	2	no	—
495	C₄×C₆₁	—	2	2	no	—
496	C₄×C₆₁	—	4	2	no	—
497	C₄×C₆₁	—	4	1	no	—
498	C₄×C₆₁	—	4	2	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	—	4	1	no	—
506	C₄×C₆₁	—	4	2	no	—
507	C₄×C₆₁	—	4	2	no	—
508	C₄×C₆₁	#538	1	4	yes	—
509	#2863	C₂×C₆₁	1	1	yes	characteristic, complemented
510	#2861	C₂×C₆₁	1	1	yes	characteristic, complemented
511	#2857	C₂×C₆₁	1	1	yes	characteristic, complemented
512	#2854	C₂×C₆₁	1	1	yes	characteristic, complemented
513	#2649	C₂×C₆₁	1	2	yes	complemented
514	#2630	C₂×C₆₁	1	2	yes	complemented
515	#2587	C₂×C₆₁	1	2	yes	complemented
516	#2578	C₂×C₆₁	1	2	yes	complemented
517	#2518	C₂×C₆₁	1	2	yes	complemented
518	#2512	C₂×C₆₁	1	1	yes	characteristic, complemented
519	#2489	C₂×C₆₁	1	1	yes	characteristic, complemented
520	#2467	C₂×C₆₁	1	2	yes	complemented
521	#2446	C₂×C₆₁	1	1	yes	characteristic, complemented
522	#2441	C₂×C₆₁	1	1	yes	characteristic, complemented
523	#2432	C₂×C₆₁	1	1	yes	characteristic, complemented
524	#2426	C₂×C₆₁	1	1	yes	characteristic, complemented
525	#2415	C₂×C₆₁	1	1	yes	characteristic, complemented
526	#2407	C₂×C₆₁	1	1	yes	characteristic
527	#2335	C₂×C₆₁	1	2	yes	complemented
528	#2334	C₂×C₆₁	1	2	yes	complemented
529	C₄×C₂²⋊Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
530	#2297	C₂×C₆₁	1	1	yes	characteristic, complemented
531	C₄²×D₄	C₂×C₆₁	1	1	yes	characteristic, complemented
532	C₂×C₆₁	—	4	2	no	—
533	C₂×C₆₁	—	4	2	no	—
534	C₂×C₆₁	—	8	2	no	—
535	C₂×C₆₁	#3444	1	1	yes	characteristic
536	C₂×C₆₁	C₂×#538	1	1	yes	characteristic
537	C₂×C₆₁	#3461	1	1	yes	characteristic
538	C₂×C₆₁	#3505	1	1	yes	characteristic
539	C₂×C₆₁	#3511	1	1	yes	characteristic
540	C₂×C₆₁	#3517	1	1	yes	characteristic
541	C₂×C₆₁	#3520	1	1	yes	characteristic
542	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
543	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
544	C₂×#126	C₂²×C₆₁	1	2	yes	—
545	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
546	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
547	C₂×#123	C₂²×C₆₁	1	2	yes	—
548	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
549	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
550	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
551	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
552	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
553	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
554	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
555	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
556	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
557	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
558	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
559	#400	C₂²×C₆₁	1	2	yes	—
560	#400	C₂²×C₆₁	1	2	yes	—
561	#399	C₂²×C₆₁	1	2	yes	—
562	#398	C₂²×C₆₁	1	2	yes	—
563	#397	C₂²×C₆₁	1	2	yes	—
564	#397	C₂²×C₆₁	1	2	yes	—
565	#397	C₂²×C₆₁	1	2	yes	—
566	#396	C₂²×C₆₁	1	2	yes	—
567	#396	C₂²×C₆₁	1	2	yes	—
568	#396	C₂²×C₆₁	1	2	yes	—
569	#394	C₂²×C₆₁	1	2	yes	—
570	#394	C₂²×C₆₁	1	2	yes	—
571	#394	C₂²×C₆₁	1	2	yes	—
572	#394	C₂²×C₆₁	1	2	yes	—
573	#394	C₂²×C₆₁	1	2	yes	—
574	#392	C₂²×C₆₁	1	2	yes	—
575	#391	C₂²×C₆₁	1	1	yes	characteristic
576	#391	C₂²×C₆₁	1	1	yes	characteristic
577	#391	C₂²×C₆₁	1	1	yes	characteristic
578	#391	C₂²×C₆₁	1	1	yes	characteristic
579	#391	C₂²×C₆₁	1	1	yes	characteristic
580	#391	C₂²×C₆₁	1	1	yes	characteristic
581	#390	C₂²×C₆₁	1	2	yes	—
582	#390	C₂²×C₆₁	1	1	yes	characteristic
583	#390	C₂²×C₆₁	1	1	yes	characteristic
584	#390	C₂²×C₆₁	1	1	yes	characteristic
585	#390	C₂²×C₆₁	1	1	yes	characteristic
586	#389	C₂²×C₆₁	1	2	yes	—
587	#389	C₂²×C₆₁	1	2	yes	—
588	#389	C₂²×C₆₁	1	2	yes	—
589	#389	C₂²×C₆₁	1	2	yes	—
590	#389	C₂²×C₆₁	1	1	yes	characteristic
591	#389	C₂²×C₆₁	1	1	yes	characteristic
592	#389	C₂²×C₆₁	1	1	yes	characteristic
593	#389	C₂²×C₆₁	1	1	yes	characteristic
594	#388	C₂²×C₆₁	1	2	yes	—
595	#388	C₂²×C₆₁	1	2	yes	—
596	#388	C₂²×C₆₁	1	2	yes	—
597	#388	C₂²×C₆₁	1	2	yes	—
598	#388	C₂²×C₆₁	1	2	yes	—
599	#388	C₂²×C₆₁	1	2	yes	—
600	#388	C₂²×C₆₁	1	2	yes	—
601	#388	C₂²×C₆₁	1	2	yes	—
602	#388	C₂²×C₆₁	1	2	yes	—
603	#388	C₂²×C₆₁	1	2	yes	—
604	#387	C₂²×C₆₁	1	2	yes	—
605	#387	C₂²×C₆₁	1	2	yes	—
606	#387	C₂²×C₆₁	1	2	yes	—
607	#387	C₂²×C₆₁	1	2	yes	—
608	#387	C₂²×C₆₁	1	2	yes	—
609	#387	C₂²×C₆₁	1	2	yes	—
610	#387	C₂²×C₆₁	1	2	yes	—
611	#386	C₂²×C₆₁	1	2	yes	—
612	#386	C₂²×C₆₁	1	2	yes	—
613	#386	C₂²×C₆₁	1	2	yes	—
614	#386	C₂²×C₆₁	1	2	yes	—
615	#385	C₂²×C₆₁	1	2	yes	—
616	#385	C₂²×C₆₁	1	2	yes	—
617	#385	C₂²×C₆₁	1	2	yes	—
618	#385	C₂²×C₆₁	1	2	yes	—
619	#384	C₂²×C₆₁	1	1	yes	characteristic
620	#383	C₂²×C₆₁	1	2	yes	—
621	#382	C₂²×C₆₁	1	2	yes	—
622	#380	C₂²×C₆₁	1	2	yes	—
623	#380	C₂²×C₆₁	1	2	yes	—
624	#380	C₂²×C₆₁	1	1	yes	characteristic
625	#380	C₂²×C₆₁	1	1	yes	characteristic
626	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
627	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
628	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
629	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
630	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
631	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
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	1	yes	characteristic
635	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
636	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
637	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
638	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
639	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
640	C₄³	C₂²×C₆₁	1	1	yes	characteristic
641	C₆₁	#35036	1	1	yes	characteristic, direct product factor, Sylow
642	C₂×#41	—	2	4	no	—
643	C₂×#41	—	4	2	no	—
644	C₂×#41	—	4	2	no	—
645	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
646	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
647	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
648	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
649	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
650	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
651	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
652	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
653	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
654	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
655	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
656	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
657	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
658	C₄⋊Q₈	—	4	2	no	—
659	#126	—	2	8	no	—
660	#125	—	4	2	no	—
661	#124	—	4	2	no	—
662	#123	—	2	8	no	—
663	C₂²⋊Q₈	—	2	4	no	—
664	C₂²⋊Q₈	—	4	2	no	—
665	C₂²⋊Q₈	—	4	2	no	—
666	#121	—	4	2	no	—
667	C₄×Q₈	—	4	2	no	—
668	C₄×D₄	—	2	4	no	—
669	C₄×D₄	—	2	4	no	—
670	C₄×D₄	—	2	4	no	—
671	#117	—	4	2	no	—
672	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
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	2	yes	—
683	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
684	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
685	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
688	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
689	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
693	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
694	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
695	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
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	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
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	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
717	C₂×C₄²	—	4	2	no	—
718	C₂×C₄²	—	4	2	no	—
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	1	yes	characteristic
723	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
724	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
725	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
726	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
727	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
728	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
729	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
730	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
731	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
732	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
733	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
734	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
735	#95	C₂³×C₆₁	1	1	yes	characteristic
736	#95	C₂³×C₆₁	1	1	yes	characteristic
737	#95	C₂³×C₆₁	1	1	yes	characteristic
738	#95	C₂³×C₆₁	1	1	yes	characteristic
739	#95	C₂³×C₆₁	1	1	yes	characteristic
740	#95	C₂³×C₆₁	1	1	yes	characteristic
741	#95	C₂³×C₆₁	1	2	yes	—
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	2	yes	—
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	2	yes	—
754	#95	C₂³×C₆₁	1	2	yes	—
755	#95	C₂³×C₆₁	1	2	yes	—
756	#95	C₂³×C₆₁	1	2	yes	—
757	#95	C₂³×C₆₁	1	2	yes	—
758	#95	C₂³×C₆₁	1	2	yes	—
759	#95	C₂³×C₆₁	1	2	yes	—
760	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
761	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
762	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
763	#41	—	4	16	no	—
764	C₂×Q₈	—	2	2	no	—
765	C₂×Q₈	—	2	2	no	—
766	C₂×Q₈	—	2	2	no	—
767	C₂×Q₈	—	2	2	no	—
768	C₂×Q₈	—	2	2	no	—
769	C₂×Q₈	—	2	2	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	4	no	—
773	C₂×D₄	—	2	4	no	—
774	C₂×D₄	—	2	2	no	—
775	C₂×D₄	—	2	2	no	—
776	C₂×D₄	—	2	2	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	4	2	no	—
779	C₂×D₄	—	4	2	no	—
780	C₂×D₄	—	4	2	no	—
781	C₂×D₄	—	4	2	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	4	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	4	1	no	—
794	C₂²×C₄	—	4	1	no	—
795	C₂²×C₄	—	4	1	no	—
796	C₂²×C₄	—	4	1	no	—
797	C₂²×C₄	—	4	2	no	—
798	C₂²×C₄	—	4	2	no	—
799	C₂²×C₄	—	4	1	no	—
800	C₂²×C₄	—	4	1	no	—
801	C₂²×C₄	#41×C₆₁	1	4	yes	—
802	C₂²×C₄	#41×C₆₁	1	4	yes	complemented
803	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
804	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
805	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
806	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
807	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
808	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
809	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
810	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
812	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
813	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
814	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
815	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
816	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
817	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
819	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
822	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	4	no	—
827	C₄⋊C₄	—	2	4	no	—
828	C₄⋊C₄	—	2	4	no	—
829	C₄⋊C₄	—	2	4	no	—
830	C₄⋊C₄	—	2	4	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	4	2	no	—
836	C₄⋊C₄	—	4	2	no	—
837	C₄⋊C₄	—	4	2	no	—
838	C₄⋊C₄	—	4	2	no	—
839	C₄⋊C₄	—	4	2	no	—
840	C₄⋊C₄	—	4	2	no	—
841	C₄⋊C₄	—	4	2	no	—
842	C₄⋊C₄	—	4	2	no	—
843	C₄⋊C₄	—	4	2	no	—
844	C₄⋊C₄	#41×C₆₁	1	4	yes	complemented
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	4	no	—
848	C₂²⋊C₄	—	2	4	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	4	no	—
854	C₂²⋊C₄	—	2	4	no	—
855	C₂²⋊C₄	—	2	4	no	—
856	C₂²⋊C₄	—	2	4	no	—
857	C₂²⋊C₄	—	2	4	no	—
858	C₂²⋊C₄	—	2	4	no	—
859	C₂²⋊C₄	—	4	2	no	—
860	C₂²⋊C₄	—	4	2	no	—
861	C₂²⋊C₄	—	4	2	no	—
862	C₂²⋊C₄	—	4	2	no	—
863	C₂²⋊C₄	—	4	2	no	—
864	C₂²⋊C₄	—	4	2	no	—
865	C₂²⋊C₄	—	4	2	no	—
866	C₂²⋊C₄	—	4	2	no	—
867	C₂²⋊C₄	—	4	2	no	—
868	C₄²	—	2	2	no	—
869	C₄²	—	2	2	no	—
870	C₄²	—	2	2	no	—
871	C₄²	—	2	4	no	—
872	C₄²	—	2	2	no	—
873	C₄²	—	2	2	no	—
874	C₄²	—	2	2	no	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	4	1	no	—
878	C₄²	—	4	1	no	—
879	C₄²	—	4	1	no	—
880	C₄²	—	4	1	no	—
881	C₄²	—	4	2	no	—
882	C₄²	—	4	2	no	—
883	C₄²	—	4	1	no	—
884	C₂³	—	2	1	no	—
885	C₂³	—	2	1	no	—
886	C₂³	—	2	1	no	—
887	C₂³	—	2	1	no	—
888	C₂³	—	2	1	no	—
889	C₂³	—	2	1	no	—
890	C₂³	—	2	1	no	—
891	C₂³	—	2	1	no	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	1	no	—
894	C₂³	—	2	1	no	—
895	C₂³	—	2	1	no	—
896	C₂³	—	2	2	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	2	2	no	—
899	C₂³	—	2	2	no	—
900	C₂³	—	2	2	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	2	no	—
903	C₂³	C₂×#41×C₆₁	1	2	yes	—
904	C₂³	C₂×#41×C₆₁	1	2	yes	—
905	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
906	Q₈	—	4	4	no	—
907	Q₈	—	4	4	no	—
908	D₄	—	2	8	no	—
909	D₄	—	4	8	no	—
910	D₄	—	4	4	no	—
911	D₄	—	8	4	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	1	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	8	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	4	4	no	—
964	C₂×C₄	—	4	4	no	—
965	C₂×C₄	—	4	4	no	—
966	C₂×C₄	—	4	4	no	—
967	C₂×C₄	—	4	8	no	—
968	C₂×C₄	—	4	4	no	—
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	C₂×#41×C₆₁	1	2	yes	—
973	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
974	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
975	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
976	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
977	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
978	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
979	C₂²	—	2	2	no	—
980	C₂²	—	2	2	no	—
981	C₂²	—	2	2	no	—
982	C₂²	—	2	2	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	2	2	no	—
985	C₂²	—	4	1	no	—
986	C₂²	—	4	1	no	—
987	C₂²	—	4	1	no	—
988	C₂²	—	4	1	no	—
989	C₂²	—	4	1	no	—
990	C₂²	—	4	1	no	—
991	C₂²	—	4	1	no	—
992	C₂²	—	4	1	no	—
993	C₂²	—	4	2	no	—
994	C₂²	—	4	2	no	—
995	C₂²	—	4	2	no	—
996	C₂²	—	4	2	no	—
997	C₂²	—	4	2	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
1001	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
1002	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
1003	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1004	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1005	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1006	C₂²	C₆₁×#585	1	1	yes	characteristic
1007	C₄	—	2	2	no	—
1008	C₄	—	2	2	no	—
1009	C₄	—	2	2	no	—
1010	C₄	—	2	2	no	—
1011	C₄	—	2	2	no	—
1012	C₄	—	2	2	no	—
1013	C₄	—	2	2	no	—
1014	C₄	—	4	2	no	—
1015	C₄	—	4	1	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	2	no	—
1018	C₄	—	4	1	no	—
1019	C₄	—	4	1	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	1	no	—
1022	C₄	—	4	2	no	—
1023	C₄	—	4	1	no	—
1024	C₄	—	4	2	no	—
1025	C₄	—	4	2	no	—
1026	C₄	C₆₁×#538	1	4	yes	—
1027	C₂	—	4	2	no	—
1028	C₂	—	4	2	no	—
1029	C₂	—	8	2	no	—
1030	C₂	C₆₁×#3444	1	1	yes	characteristic
1031	C₂	C₂×C₆₁×#538	1	1	yes	characteristic
1032	C₂	C₆₁×#3461	1	1	yes	characteristic
1033	C₂	C₆₁×#3505	1	1	yes	characteristic
1034	C₂	C₆₁×#3511	1	1	yes	characteristic
1035	C₂	C₆₁×#3517	1	1	yes	characteristic
1036	C₂	C₆₁×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
prime radical	C₆₁×#2407	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×#2863	C₂	semidirect
2. C₆₁×#2861	C₂	semidirect
3. C₆₁×#2857	C₂	semidirect
4. C₆₁×#2854	C₂	semidirect
5. C₆₁×#2649	C₂	semidirect
6. C₆₁×#2630	C₂	semidirect
7. C₆₁×#2587	C₂	semidirect
8. C₆₁×#2578	C₂	semidirect
9. C₆₁×#2518	C₂	semidirect
10. C₆₁×#2512	C₂	semidirect
11. C₆₁×#2489	C₂	semidirect
12. C₆₁×#2467	C₂	semidirect
13. C₆₁×#2446	C₂	semidirect
14. C₆₁×#2441	C₂	semidirect
15. C₆₁×#2432	C₂	semidirect
16. C₆₁×#2426	C₂	semidirect
17. C₆₁×#2415	C₂	semidirect
19. C₆₁×#2335	C₂	semidirect
20. C₆₁×#2334	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₆₁	C₂	semidirect
22. C₆₁×#2297	C₂	semidirect
23. C₄²×D₄×C₆₁	C₂	semidirect
283. C₂²×C₄×C₆₁	#41	semidirect
325. C₄⋊C₄×C₆₁	#41	semidirect
460. #35036	C₆₁	direct (N × H)
509. #2863	C₂×C₆₁	semidirect
510. #2861	C₂×C₆₁	semidirect
511. #2857	C₂×C₆₁	semidirect
512. #2854	C₂×C₆₁	semidirect
513. #2649	C₂×C₆₁	semidirect
514. #2630	C₂×C₆₁	semidirect
515. #2587	C₂×C₆₁	semidirect
516. #2578	C₂×C₆₁	semidirect
517. #2518	C₂×C₆₁	semidirect
518. #2512	C₂×C₆₁	semidirect
519. #2489	C₂×C₆₁	semidirect
520. #2467	C₂×C₆₁	semidirect
521. #2446	C₂×C₆₁	semidirect
522. #2441	C₂×C₆₁	semidirect
523. #2432	C₂×C₆₁	semidirect
524. #2426	C₂×C₆₁	semidirect
525. #2415	C₂×C₆₁	semidirect
527. #2335	C₂×C₆₁	semidirect
528. #2334	C₂×C₆₁	semidirect
529. C₄×C₂²⋊Q₈	C₂×C₆₁	semidirect
530. #2297	C₂×C₆₁	semidirect
531. C₄²×D₄	C₂×C₆₁	semidirect
641. C₆₁	#35036	direct (N × H)
802. C₂²×C₄	#41×C₆₁	semidirect
844. C₄⋊C₄	#41×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#2863	2
C₆₁×#2861	2
C₆₁×#2857	2
C₆₁×#2854	2
C₆₁×#2649	2
C₆₁×#2630	2
C₆₁×#2587	2
C₆₁×#2578	2
C₆₁×#2518	2
C₆₁×#2512	2
C₆₁×#2489	2
C₆₁×#2467	2
C₆₁×#2446	2
C₆₁×#2441	2
C₆₁×#2432	2
C₆₁×#2426	2
C₆₁×#2415	2
C₆₁×#2407	2
C₆₁×#2335	2
C₆₁×#2334	2
C₄×C₂²⋊Q₈×C₆₁	2
C₆₁×#2297	2
C₄²×D₄×C₆₁	2
#35036	61

Subgroups — C61×#35036 #29538469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#35036 #29538469