Subgroups — C₆₁×#35080 #29538513

Order 15616.

2154 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#2850	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2848	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2847	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2653	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2649	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2510	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2495	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2494	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#2492	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2491	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#2472	C₂	1	2	yes	maximal, complemented
13	C₆₁×#2450	C₂	1	2	yes	maximal, complemented
14	C₆₁×#2427	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#2426	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#2423	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#2422	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#2418	C₂	1	2	yes	maximal, complemented
19	C₆₁×#2337	C₂	1	2	yes	maximal, complemented
20	C₆₁×#2335	C₂	1	2	yes	maximal, complemented
21	C₄×C₂²⋊Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×C₂²⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
26	C₂×#124×C₆₁	C₂²	1	2	yes	—
27	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic, complemented
28	C₂×#123×C₆₁	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
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	2	yes	—
33	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×#120×C₆₁	C₂²	1	2	yes	—
37	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
42	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
44	C₆₁×#401	C₂²	1	2	yes	complemented
45	C₆₁×#400	C₂²	1	2	yes	complemented
46	C₆₁×#400	C₂²	1	2	yes	complemented
47	C₆₁×#399	C₂²	1	2	yes	—
48	C₆₁×#398	C₂²	1	2	yes	complemented
49	C₆₁×#397	C₂²	1	2	yes	—
50	C₆₁×#397	C₂²	1	2	yes	—
51	C₆₁×#397	C₂²	1	2	yes	complemented
52	C₆₁×#397	C₂²	1	2	yes	complemented
53	C₆₁×#396	C₂²	1	2	yes	complemented
54	C₆₁×#394	C₂²	1	2	yes	—
55	C₆₁×#394	C₂²	1	2	yes	—
56	C₆₁×#394	C₂²	1	2	yes	—
57	C₆₁×#394	C₂²	1	2	yes	—
58	C₆₁×#393	C₂²	1	2	yes	—
59	C₆₁×#393	C₂²	1	2	yes	complemented
60	C₆₁×#391	C₂²	1	1	yes	characteristic, complemented
61	C₆₁×#391	C₂²	1	2	yes	complemented
62	C₆₁×#391	C₂²	1	2	yes	complemented
63	C₆₁×#391	C₂²	1	1	yes	characteristic, complemented
64	C₆₁×#390	C₂²	1	2	yes	—
65	C₆₁×#390	C₂²	1	1	yes	characteristic, complemented
66	C₆₁×#390	C₂²	1	1	yes	characteristic, complemented
67	C₆₁×#389	C₂²	1	1	yes	characteristic, complemented
68	C₆₁×#389	C₂²	1	1	yes	characteristic, complemented
69	C₆₁×#389	C₂²	1	2	yes	complemented
70	C₆₁×#389	C₂²	1	1	yes	characteristic, complemented
71	C₆₁×#389	C₂²	1	1	yes	characteristic, complemented
72	C₆₁×#388	C₂²	1	2	yes	—
73	C₆₁×#388	C₂²	1	2	yes	—
74	C₆₁×#388	C₂²	1	2	yes	—
75	C₆₁×#388	C₂²	1	2	yes	—
76	C₆₁×#388	C₂²	1	2	yes	complemented
77	C₆₁×#388	C₂²	1	2	yes	complemented
78	C₆₁×#388	C₂²	1	2	yes	complemented
79	C₆₁×#388	C₂²	1	2	yes	complemented
80	C₆₁×#388	C₂²	1	2	yes	complemented
81	C₆₁×#387	C₂²	1	2	yes	complemented
82	C₆₁×#387	C₂²	1	2	yes	complemented
83	C₆₁×#387	C₂²	1	2	yes	complemented
84	C₆₁×#386	C₂²	1	2	yes	—
85	C₆₁×#386	C₂²	1	2	yes	—
86	C₆₁×#386	C₂²	1	2	yes	—
87	C₆₁×#386	C₂²	1	2	yes	—
88	C₆₁×#386	C₂²	1	2	yes	—
89	C₆₁×#386	C₂²	1	2	yes	—
90	C₆₁×#386	C₂²	1	2	yes	—
91	C₆₁×#385	C₂²	1	2	yes	—
92	C₆₁×#385	C₂²	1	2	yes	—
93	C₆₁×#385	C₂²	1	2	yes	—
94	C₆₁×#385	C₂²	1	2	yes	—
95	C₆₁×#385	C₂²	1	2	yes	complemented
96	C₆₁×#384	C₂²	1	1	yes	characteristic, complemented
97	C₆₁×#383	C₂²	1	2	yes	complemented
98	C₆₁×#382	C₂²	1	1	yes	characteristic, complemented
99	C₆₁×#380	C₂²	1	1	yes	characteristic
100	C₆₁×#380	C₂²	1	1	yes	characteristic
101	C₆₁×#380	C₂²	1	1	yes	characteristic
102	C₆₁×#380	C₂²	1	1	yes	characteristic
103	C₆₁×#380	C₂²	1	1	yes	characteristic
104	C₆₁×#380	C₂²	1	1	yes	characteristic
105	C₆₁×#380	C₂²	1	2	yes	—
106	C₆₁×#380	C₂²	1	2	yes	complemented
107	C₆₁×#379	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
109	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	complemented
110	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
112	C₄×C₂²⋊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	complemented
121	C₂×#95×C₆₁	C₂²	1	1	yes	characteristic
122	C₂×#95×C₆₁	C₂²	1	1	yes	characteristic
123	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
126	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
127	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
129	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
130	C₂³×C₄×C₆₁	—	2	4	no	—
131	C₂³×C₄×C₆₁	—	4	2	no	—
132	C₂³×C₄×C₆₁	—	4	2	no	—
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	1	yes	characteristic
137	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
144	C₄⋊Q₈×C₆₁	—	4	2	no	—
145	#124×C₆₁	—	2	8	no	—
146	#124×C₆₁	—	4	2	no	—
147	#123×C₆₁	—	2	8	no	—
148	C₂²⋊Q₈×C₆₁	—	2	4	no	—
149	C₂²⋊Q₈×C₆₁	—	4	4	no	—
150	C₂²⋊Q₈×C₆₁	—	4	2	no	—
151	C₂²⋊Q₈×C₆₁	—	4	2	no	—
152	#121×C₆₁	—	2	4	no	—
153	#121×C₆₁	—	4	2	no	—
154	#121×C₆₁	—	4	2	no	—
155	#120×C₆₁	—	4	4	no	—
156	C₄×Q₈×C₆₁	—	4	2	no	—
157	C₄×D₄×C₆₁	—	4	2	no	—
158	C₄×D₄×C₆₁	—	4	4	no	—
159	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
166	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₆₁	C₂³	1	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	2	yes	—
175	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
177	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
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	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₆₁	C₂³	1	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×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₆₁	—	4	2	no	—
206	C₂×C₄²×C₆₁	—	4	2	no	—
207	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
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	2	yes	—
212	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
217	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
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	1	yes	characteristic
223	#95×C₆₁	C₂³	1	1	yes	characteristic
224	#95×C₆₁	C₂³	1	1	yes	characteristic
225	#95×C₆₁	C₂³	1	1	yes	characteristic
226	#95×C₆₁	C₂³	1	2	yes	—
227	#95×C₆₁	C₂³	1	2	yes	—
228	#95×C₆₁	C₂³	1	2	yes	—
229	#95×C₆₁	C₂³	1	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	#95×C₆₁	C₂³	1	2	yes	—
242	#95×C₆₁	C₂³	1	2	yes	—
243	#95×C₆₁	C₂³	1	2	yes	—
244	C₂⁴×C₆₁	—	2	2	no	—
245	C₂⁴×C₆₁	—	2	2	no	—
246	C₂⁴×C₆₁	—	2	2	no	—
247	C₂⁴×C₆₁	—	2	2	no	—
248	C₂⁴×C₆₁	—	2	2	no	—
249	C₂⁴×C₆₁	—	4	1	no	—
250	C₂⁴×C₆₁	—	4	1	no	—
251	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
252	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
253	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
254	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
255	C₂×Q₈×C₆₁	—	2	2	no	—
256	C₂×Q₈×C₆₁	—	2	4	no	—
257	C₂×Q₈×C₆₁	—	2	2	no	—
258	C₂×Q₈×C₆₁	—	2	2	no	—
259	C₂×Q₈×C₆₁	—	4	2	no	—
260	C₂×Q₈×C₆₁	—	4	2	no	—
261	C₂×D₄×C₆₁	—	2	4	no	—
262	C₂×D₄×C₆₁	—	2	4	no	—
263	C₂×D₄×C₆₁	—	2	4	no	—
264	C₂×D₄×C₆₁	—	2	4	no	—
265	C₂×D₄×C₆₁	—	2	4	no	—
266	C₂×D₄×C₆₁	—	2	2	no	—
267	C₂×D₄×C₆₁	—	2	2	no	—
268	C₂×D₄×C₆₁	—	2	2	no	—
269	C₂×D₄×C₆₁	—	4	2	no	—
270	C₂×D₄×C₆₁	—	4	2	no	—
271	C₂×D₄×C₆₁	—	4	2	no	—
272	C₂×D₄×C₆₁	—	4	2	no	—
273	C₂²×C₄×C₆₁	—	2	2	no	—
274	C₂²×C₄×C₆₁	—	2	2	no	—
275	C₂²×C₄×C₆₁	—	2	2	no	—
276	C₂²×C₄×C₆₁	—	2	2	no	—
277	C₂²×C₄×C₆₁	—	2	2	no	—
278	C₂²×C₄×C₆₁	—	2	2	no	—
279	C₂²×C₄×C₆₁	—	2	2	no	—
280	C₂²×C₄×C₆₁	—	2	2	no	—
281	C₂²×C₄×C₆₁	—	2	2	no	—
282	C₂²×C₄×C₆₁	—	2	2	no	—
283	C₂²×C₄×C₆₁	—	2	2	no	—
284	C₂²×C₄×C₆₁	—	2	2	no	—
285	C₂²×C₄×C₆₁	—	2	2	no	—
286	C₂²×C₄×C₆₁	—	2	2	no	—
287	C₂²×C₄×C₆₁	—	2	2	no	—
288	C₂²×C₄×C₆₁	—	2	2	no	—
289	C₂²×C₄×C₆₁	—	2	2	no	—
290	C₂²×C₄×C₆₁	—	2	2	no	—
291	C₂²×C₄×C₆₁	—	2	2	no	—
292	C₂²×C₄×C₆₁	—	2	4	no	—
293	C₂²×C₄×C₆₁	—	4	1	no	—
294	C₂²×C₄×C₆₁	—	4	1	no	—
295	C₂²×C₄×C₆₁	—	4	1	no	—
296	C₂²×C₄×C₆₁	—	4	1	no	—
297	C₂²×C₄×C₆₁	—	4	1	no	—
298	C₂²×C₄×C₆₁	—	4	1	no	—
299	C₂²×C₄×C₆₁	—	4	1	no	—
300	C₂²×C₄×C₆₁	—	4	1	no	—
301	C₂²×C₄×C₆₁	—	4	1	no	—
302	C₂²×C₄×C₆₁	—	4	1	no	—
303	C₂²×C₄×C₆₁	—	4	2	no	—
304	C₂²×C₄×C₆₁	—	4	2	no	—
305	C₂²×C₄×C₆₁	—	4	16	no	—
306	C₂²×C₄×C₆₁	#41	1	4	yes	—
307	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
326	C₄⋊C₄×C₆₁	—	2	2	no	—
327	C₄⋊C₄×C₆₁	—	2	2	no	—
328	C₄⋊C₄×C₆₁	—	2	4	no	—
329	C₄⋊C₄×C₆₁	—	2	4	no	—
330	C₄⋊C₄×C₆₁	—	2	4	no	—
331	C₄⋊C₄×C₆₁	—	2	2	no	—
332	C₄⋊C₄×C₆₁	—	2	2	no	—
333	C₄⋊C₄×C₆₁	—	2	2	no	—
334	C₄⋊C₄×C₆₁	—	2	2	no	—
335	C₄⋊C₄×C₆₁	—	4	2	no	—
336	C₄⋊C₄×C₆₁	—	4	2	no	—
337	C₄⋊C₄×C₆₁	—	4	2	no	—
338	C₄⋊C₄×C₆₁	—	4	2	no	—
339	C₄⋊C₄×C₆₁	—	4	2	no	—
340	C₄⋊C₄×C₆₁	—	4	2	no	—
341	C₄⋊C₄×C₆₁	—	4	2	no	—
342	C₄⋊C₄×C₆₁	—	4	2	no	—
343	C₂²⋊C₄×C₆₁	—	2	2	no	—
344	C₂²⋊C₄×C₆₁	—	2	2	no	—
345	C₂²⋊C₄×C₆₁	—	2	4	no	—
346	C₂²⋊C₄×C₆₁	—	2	4	no	—
347	C₂²⋊C₄×C₆₁	—	2	4	no	—
348	C₂²⋊C₄×C₆₁	—	2	4	no	—
349	C₂²⋊C₄×C₆₁	—	2	4	no	—
350	C₂²⋊C₄×C₆₁	—	2	2	no	—
351	C₂²⋊C₄×C₆₁	—	2	2	no	—
352	C₂²⋊C₄×C₆₁	—	2	2	no	—
353	C₂²⋊C₄×C₆₁	—	2	2	no	—
354	C₂²⋊C₄×C₆₁	—	2	4	no	—
355	C₂²⋊C₄×C₆₁	—	2	4	no	—
356	C₂²⋊C₄×C₆₁	—	2	4	no	—
357	C₂²⋊C₄×C₆₁	—	2	4	no	—
358	C₂²⋊C₄×C₆₁	—	4	2	no	—
359	C₂²⋊C₄×C₆₁	—	4	2	no	—
360	C₂²⋊C₄×C₆₁	—	4	2	no	—
361	C₂²⋊C₄×C₆₁	—	4	2	no	—
362	C₂²⋊C₄×C₆₁	—	4	2	no	—
363	C₂²⋊C₄×C₆₁	—	4	2	no	—
364	C₂²⋊C₄×C₆₁	—	4	2	no	—
365	C₂²⋊C₄×C₆₁	—	4	2	no	—
366	C₂²⋊C₄×C₆₁	—	4	2	no	—
367	C₂²⋊C₄×C₆₁	—	4	2	no	—
368	C₂²⋊C₄×C₆₁	#41	1	4	yes	—
369	C₂²⋊C₄×C₆₁	#41	1	4	yes	—
370	C₄²×C₆₁	—	2	4	no	—
371	C₄²×C₆₁	—	2	2	no	—
372	C₄²×C₆₁	—	2	2	no	—
373	C₄²×C₆₁	—	2	2	no	—
374	C₄²×C₆₁	—	2	2	no	—
375	C₄²×C₆₁	—	4	1	no	—
376	C₄²×C₆₁	—	4	1	no	—
377	C₄²×C₆₁	—	4	1	no	—
378	C₄²×C₆₁	—	4	1	no	—
379	C₄²×C₆₁	—	4	2	no	—
380	C₄²×C₆₁	—	4	2	no	—
381	C₂³×C₆₁	—	2	1	no	—
382	C₂³×C₆₁	—	2	1	no	—
383	C₂³×C₆₁	—	2	1	no	—
384	C₂³×C₆₁	—	2	1	no	—
385	C₂³×C₆₁	—	2	8	no	—
386	C₂³×C₆₁	—	2	1	no	—
387	C₂³×C₆₁	—	2	1	no	—
388	C₂³×C₆₁	—	2	1	no	—
389	C₂³×C₆₁	—	2	1	no	—
390	C₂³×C₆₁	—	2	1	no	—
391	C₂³×C₆₁	—	2	1	no	—
392	C₂³×C₆₁	—	2	1	no	—
393	C₂³×C₆₁	—	2	1	no	—
394	C₂³×C₆₁	—	2	1	no	—
395	C₂³×C₆₁	—	2	1	no	—
396	C₂³×C₆₁	—	2	1	no	—
397	C₂³×C₆₁	—	2	1	no	—
398	C₂³×C₆₁	—	2	2	no	—
399	C₂³×C₆₁	—	2	2	no	—
400	C₂³×C₆₁	—	2	2	no	—
401	C₂³×C₆₁	—	2	2	no	—
402	C₂³×C₆₁	—	2	2	no	—
403	C₂³×C₆₁	—	2	2	no	—
404	C₂³×C₆₁	—	2	2	no	—
405	C₂³×C₆₁	—	4	4	no	—
406	C₂³×C₆₁	—	4	4	no	—
407	C₂³×C₆₁	—	4	4	no	—
408	C₂³×C₆₁	—	4	4	no	—
409	C₂³×C₆₁	—	4	4	no	—
410	C₂³×C₆₁	—	4	4	no	—
411	C₂³×C₆₁	C₂×#41	1	2	yes	—
412	C₂³×C₆₁	C₂×#41	1	2	yes	—
413	C₂³×C₆₁	C₂×#41	1	2	yes	—
414	C₂³×C₆₁	H(5,𝔽₂)	1	2	yes	—
415	C₂³×C₆₁	2₋¹⁺⁴	1	2	yes	—
416	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
417	Q₈×C₆₁	—	4	4	no	—
418	Q₈×C₆₁	—	8	4	no	—
419	D₄×C₆₁	—	4	8	no	—
420	D₄×C₆₁	—	4	4	no	—
421	D₄×C₆₁	—	8	4	no	—
422	D₄×C₆₁	—	8	4	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	1	no	—
427	C₂×C₄×C₆₁	—	2	1	no	—
428	C₂×C₄×C₆₁	—	2	1	no	—
429	C₂×C₄×C₆₁	—	2	1	no	—
430	C₂×C₄×C₆₁	—	2	1	no	—
431	C₂×C₄×C₆₁	—	2	1	no	—
432	C₂×C₄×C₆₁	—	2	1	no	—
433	C₂×C₄×C₆₁	—	2	8	no	—
434	C₂×C₄×C₆₁	—	2	2	no	—
435	C₂×C₄×C₆₁	—	2	2	no	—
436	C₂×C₄×C₆₁	—	2	2	no	—
437	C₂×C₄×C₆₁	—	2	1	no	—
438	C₂×C₄×C₆₁	—	2	1	no	—
439	C₂×C₄×C₆₁	—	2	1	no	—
440	C₂×C₄×C₆₁	—	2	1	no	—
441	C₂×C₄×C₆₁	—	2	2	no	—
442	C₂×C₄×C₆₁	—	2	2	no	—
443	C₂×C₄×C₆₁	—	2	2	no	—
444	C₂×C₄×C₆₁	—	2	2	no	—
445	C₂×C₄×C₆₁	—	2	2	no	—
446	C₂×C₄×C₆₁	—	2	2	no	—
447	C₂×C₄×C₆₁	—	2	1	no	—
448	C₂×C₄×C₆₁	—	2	1	no	—
449	C₂×C₄×C₆₁	—	2	1	no	—
450	C₂×C₄×C₆₁	—	2	1	no	—
451	C₂×C₄×C₆₁	—	2	1	no	—
452	C₂×C₄×C₆₁	—	2	1	no	—
453	C₂×C₄×C₆₁	—	2	2	no	—
454	C₂×C₄×C₆₁	—	2	2	no	—
455	C₂×C₄×C₆₁	—	2	2	no	—
456	C₂×C₄×C₆₁	—	2	2	no	—
457	C₂×C₄×C₆₁	—	2	2	no	—
458	C₂×C₄×C₆₁	—	2	2	no	—
459	C₂×C₄×C₆₁	—	2	2	no	—
460	C₂×C₄×C₆₁	—	2	2	no	—
461	C₂×C₄×C₆₁	—	2	2	no	—
462	C₂×C₄×C₆₁	—	2	1	no	—
463	C₂×C₄×C₆₁	—	2	1	no	—
464	C₂×C₄×C₆₁	—	2	1	no	—
465	C₂×C₄×C₆₁	—	2	2	no	—
466	C₂×C₄×C₆₁	—	2	2	no	—
467	C₂×C₄×C₆₁	—	2	1	no	—
468	C₂×C₄×C₆₁	—	2	1	no	—
469	C₂×C₄×C₆₁	—	2	1	no	—
470	C₂×C₄×C₆₁	—	2	1	no	—
471	C₂×C₄×C₆₁	—	2	1	no	—
472	C₂×C₄×C₆₁	—	2	2	no	—
473	C₂×C₄×C₆₁	—	4	4	no	—
474	C₂×C₄×C₆₁	—	4	4	no	—
475	C₂×C₄×C₆₁	—	4	4	no	—
476	C₂×C₄×C₆₁	—	4	4	no	—
477	C₂×C₄×C₆₁	—	4	4	no	—
478	C₂×C₄×C₆₁	—	4	4	no	—
479	C₂×C₄×C₆₁	—	4	4	no	—
480	C₂×C₄×C₆₁	—	4	4	no	—
481	C₂×C₄×C₆₁	—	4	4	no	—
482	C₂×C₄×C₆₁	—	8	4	no	—
483	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
484	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
485	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
486	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
487	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
488	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
489	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
490	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
491	#35080	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
492	C₂²×C₆₁	—	2	2	no	—
493	C₂²×C₆₁	—	2	2	no	—
494	C₂²×C₆₁	—	2	2	no	—
495	C₂²×C₆₁	—	2	2	no	—
496	C₂²×C₆₁	—	2	2	no	—
497	C₂²×C₆₁	—	2	2	no	—
498	C₂²×C₆₁	—	2	2	no	—
499	C₂²×C₆₁	—	2	2	no	—
500	C₂²×C₆₁	—	2	2	no	—
501	C₂²×C₆₁	—	2	2	no	—
502	C₂²×C₆₁	—	2	2	no	—
503	C₂²×C₆₁	—	2	2	no	—
504	C₂²×C₆₁	—	4	16	no	—
505	C₂²×C₆₁	—	4	1	no	—
506	C₂²×C₆₁	—	4	1	no	—
507	C₂²×C₆₁	—	4	1	no	—
508	C₂²×C₆₁	—	4	1	no	—
509	C₂²×C₆₁	—	4	1	no	—
510	C₂²×C₆₁	—	4	1	no	—
511	C₂²×C₆₁	—	4	1	no	—
512	C₂²×C₆₁	—	4	1	no	—
513	C₂²×C₆₁	—	4	2	no	—
514	C₂²×C₆₁	—	4	2	no	—
515	C₂²×C₆₁	—	4	2	no	—
516	C₂²×C₆₁	—	4	2	no	—
517	C₂²×C₆₁	—	4	2	no	—
518	C₂²×C₆₁	—	4	2	no	—
519	C₂²×C₆₁	—	4	2	no	—
520	C₂²×C₆₁	#542	1	4	yes	—
521	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
522	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
523	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
524	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
525	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
526	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
527	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
528	C₄×C₆₁	—	2	2	no	—
529	C₄×C₆₁	—	2	2	no	—
530	C₄×C₆₁	—	2	2	no	—
531	C₄×C₆₁	—	2	2	no	—
532	C₄×C₆₁	—	2	2	no	—
533	C₄×C₆₁	—	4	2	no	—
534	C₄×C₆₁	—	4	1	no	—
535	C₄×C₆₁	—	4	1	no	—
536	C₄×C₆₁	—	4	2	no	—
537	C₄×C₆₁	—	4	2	no	—
538	C₄×C₆₁	—	4	1	no	—
539	C₄×C₆₁	—	4	1	no	—
540	C₄×C₆₁	—	4	2	no	—
541	C₄×C₆₁	—	4	2	no	—
542	C₄×C₆₁	—	4	2	no	—
543	C₄×C₆₁	—	4	2	no	—
544	C₄×C₆₁	—	4	1	no	—
545	C₄×C₆₁	—	4	1	no	—
546	C₄×C₆₁	#538	1	4	yes	—
547	#2857	C₂×C₆₁	1	1	yes	characteristic, complemented
548	#2850	C₂×C₆₁	1	1	yes	characteristic, complemented
549	#2848	C₂×C₆₁	1	1	yes	characteristic, complemented
550	#2847	C₂×C₆₁	1	1	yes	characteristic
551	#2653	C₂×C₆₁	1	2	yes	complemented
552	#2649	C₂×C₆₁	1	2	yes	complemented
553	#2510	C₂×C₆₁	1	2	yes	complemented
554	#2495	C₂×C₆₁	1	1	yes	characteristic, complemented
555	#2494	C₂×C₆₁	1	1	yes	characteristic, complemented
556	#2492	C₂×C₆₁	1	1	yes	characteristic, complemented
557	#2491	C₂×C₆₁	1	1	yes	characteristic, complemented
558	#2472	C₂×C₆₁	1	2	yes	complemented
559	#2450	C₂×C₆₁	1	2	yes	complemented
560	#2427	C₂×C₆₁	1	1	yes	characteristic, complemented
561	#2426	C₂×C₆₁	1	1	yes	characteristic, complemented
562	#2423	C₂×C₆₁	1	1	yes	characteristic, complemented
563	#2422	C₂×C₆₁	1	1	yes	characteristic, complemented
564	#2418	C₂×C₆₁	1	2	yes	complemented
565	#2337	C₂×C₆₁	1	2	yes	complemented
566	#2335	C₂×C₆₁	1	2	yes	complemented
567	C₄×C₂²⋊Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
568	C₄×#121	C₂×C₆₁	1	1	yes	characteristic, complemented
569	C₂×C₄×C₂²⋊C₄	C₂×C₆₁	1	1	yes	characteristic, complemented
570	C₂×C₆₁	—	2	4	no	—
571	C₂×C₆₁	—	4	2	no	—
572	C₂×C₆₁	—	4	2	no	—
573	C₂×C₆₁	—	8	2	no	—
574	C₂×C₆₁	#3444	1	1	yes	characteristic
575	C₂×C₆₁	C₂×#538	1	1	yes	characteristic
576	C₂×C₆₁	C₂×#542	1	1	yes	characteristic
577	C₂×C₆₁	#3519	1	1	yes	characteristic
578	C₂×C₆₁	#3519	1	1	yes	characteristic
579	C₂×C₆₁	#3520	1	1	yes	characteristic
580	C₂×C₆₁	#3520	1	1	yes	characteristic
581	C₂⁴×C₄	C₂²×C₆₁	1	1	yes	characteristic
582	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
583	C₂×#124	C₂²×C₆₁	1	2	yes	—
584	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic, complemented
585	C₂×#123	C₂²×C₆₁	1	2	yes	—
586	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
587	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
588	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
589	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
590	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
591	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
592	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
593	C₂×#120	C₂²×C₆₁	1	2	yes	—
594	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
595	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
596	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
597	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
598	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
599	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
600	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
601	#401	C₂²×C₆₁	1	2	yes	complemented
602	#400	C₂²×C₆₁	1	2	yes	complemented
603	#400	C₂²×C₆₁	1	2	yes	complemented
604	#399	C₂²×C₆₁	1	2	yes	—
605	#398	C₂²×C₆₁	1	2	yes	complemented
606	#397	C₂²×C₆₁	1	2	yes	—
607	#397	C₂²×C₆₁	1	2	yes	—
608	#397	C₂²×C₆₁	1	2	yes	complemented
609	#397	C₂²×C₆₁	1	2	yes	complemented
610	#396	C₂²×C₆₁	1	2	yes	complemented
611	#394	C₂²×C₆₁	1	2	yes	—
612	#394	C₂²×C₆₁	1	2	yes	—
613	#394	C₂²×C₆₁	1	2	yes	—
614	#394	C₂²×C₆₁	1	2	yes	—
615	#393	C₂²×C₆₁	1	2	yes	—
616	#393	C₂²×C₆₁	1	2	yes	complemented
617	#391	C₂²×C₆₁	1	2	yes	complemented
618	#391	C₂²×C₆₁	1	2	yes	complemented
619	#391	C₂²×C₆₁	1	1	yes	characteristic, complemented
620	#391	C₂²×C₆₁	1	1	yes	characteristic, complemented
621	#390	C₂²×C₆₁	1	2	yes	—
622	#390	C₂²×C₆₁	1	1	yes	characteristic, complemented
623	#390	C₂²×C₆₁	1	1	yes	characteristic, complemented
624	#389	C₂²×C₆₁	1	2	yes	complemented
625	#389	C₂²×C₆₁	1	1	yes	characteristic, complemented
626	#389	C₂²×C₆₁	1	1	yes	characteristic, complemented
627	#389	C₂²×C₆₁	1	1	yes	characteristic, complemented
628	#389	C₂²×C₆₁	1	1	yes	characteristic, complemented
629	#388	C₂²×C₆₁	1	2	yes	—
630	#388	C₂²×C₆₁	1	2	yes	—
631	#388	C₂²×C₆₁	1	2	yes	—
632	#388	C₂²×C₆₁	1	2	yes	—
633	#388	C₂²×C₆₁	1	2	yes	complemented
634	#388	C₂²×C₆₁	1	2	yes	complemented
635	#388	C₂²×C₆₁	1	2	yes	complemented
636	#388	C₂²×C₆₁	1	2	yes	complemented
637	#388	C₂²×C₆₁	1	2	yes	complemented
638	#387	C₂²×C₆₁	1	2	yes	complemented
639	#387	C₂²×C₆₁	1	2	yes	complemented
640	#387	C₂²×C₆₁	1	2	yes	complemented
641	#386	C₂²×C₆₁	1	2	yes	—
642	#386	C₂²×C₆₁	1	2	yes	—
643	#386	C₂²×C₆₁	1	2	yes	—
644	#386	C₂²×C₆₁	1	2	yes	—
645	#386	C₂²×C₆₁	1	2	yes	—
646	#386	C₂²×C₆₁	1	2	yes	—
647	#386	C₂²×C₆₁	1	2	yes	—
648	#385	C₂²×C₆₁	1	2	yes	—
649	#385	C₂²×C₆₁	1	2	yes	—
650	#385	C₂²×C₆₁	1	2	yes	—
651	#385	C₂²×C₆₁	1	2	yes	—
652	#385	C₂²×C₆₁	1	2	yes	complemented
653	#384	C₂²×C₆₁	1	1	yes	characteristic, complemented
654	#383	C₂²×C₆₁	1	2	yes	complemented
655	#382	C₂²×C₆₁	1	1	yes	characteristic, complemented
656	#380	C₂²×C₆₁	1	1	yes	characteristic
657	#380	C₂²×C₆₁	1	1	yes	characteristic
658	#380	C₂²×C₆₁	1	1	yes	characteristic
659	#380	C₂²×C₆₁	1	1	yes	characteristic
660	#380	C₂²×C₆₁	1	1	yes	characteristic
661	#380	C₂²×C₆₁	1	1	yes	characteristic
662	#380	C₂²×C₆₁	1	2	yes	—
663	#380	C₂²×C₆₁	1	2	yes	complemented
664	#379	C₂²×C₆₁	1	2	yes	—
665	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	complemented
666	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
667	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
668	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
669	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
670	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
671	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
672	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
673	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
674	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
675	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
676	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
677	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	complemented
678	C₂×#95	C₂²×C₆₁	1	1	yes	characteristic
679	C₂×#95	C₂²×C₆₁	1	1	yes	characteristic
680	C₆₁	#35080	1	1	yes	characteristic, direct product factor, Sylow
681	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
682	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
683	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
684	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
685	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
686	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
687	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
688	C₂³×C₄	—	2	4	no	—
689	C₂³×C₄	—	4	2	no	—
690	C₂³×C₄	—	4	2	no	—
691	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
692	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
693	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
694	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
695	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
696	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
697	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
698	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
699	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
700	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
701	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
702	C₄⋊Q₈	—	4	2	no	—
703	#124	—	2	8	no	—
704	#124	—	4	2	no	—
705	#123	—	2	8	no	—
706	C₂²⋊Q₈	—	2	4	no	—
707	C₂²⋊Q₈	—	4	4	no	—
708	C₂²⋊Q₈	—	4	2	no	—
709	C₂²⋊Q₈	—	4	2	no	—
710	#121	—	2	4	no	—
711	#121	—	4	2	no	—
712	#121	—	4	2	no	—
713	#120	—	4	4	no	—
714	C₄×Q₈	—	4	2	no	—
715	C₄×D₄	—	4	2	no	—
716	C₄×D₄	—	4	4	no	—
717	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
719	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
720	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
721	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
722	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
723	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
725	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
728	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
729	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
730	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
731	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
732	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
733	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
734	C₂×C₂²⋊C₄	—	2	4	no	—
735	C₂×C₂²⋊C₄	—	2	4	no	—
736	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
737	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
738	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
739	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
740	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
741	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
742	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
760	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
762	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
763	C₂×C₄²	—	4	2	no	—
764	C₂×C₄²	—	4	2	no	—
765	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
766	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
767	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
768	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
769	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
770	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
771	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
772	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
773	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
774	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
775	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
776	#95	C₂³×C₆₁	1	1	yes	characteristic
777	#95	C₂³×C₆₁	1	1	yes	characteristic
778	#95	C₂³×C₆₁	1	1	yes	characteristic
779	#95	C₂³×C₆₁	1	1	yes	characteristic
780	#95	C₂³×C₆₁	1	1	yes	characteristic
781	#95	C₂³×C₆₁	1	1	yes	characteristic
782	#95	C₂³×C₆₁	1	1	yes	characteristic
783	#95	C₂³×C₆₁	1	1	yes	characteristic
784	#95	C₂³×C₆₁	1	2	yes	—
785	#95	C₂³×C₆₁	1	2	yes	—
786	#95	C₂³×C₆₁	1	2	yes	—
787	#95	C₂³×C₆₁	1	2	yes	—
788	#95	C₂³×C₆₁	1	2	yes	—
789	#95	C₂³×C₆₁	1	2	yes	—
790	#95	C₂³×C₆₁	1	2	yes	—
791	#95	C₂³×C₆₁	1	2	yes	—
792	#95	C₂³×C₆₁	1	2	yes	—
793	#95	C₂³×C₆₁	1	2	yes	—
794	#95	C₂³×C₆₁	1	2	yes	—
795	#95	C₂³×C₆₁	1	2	yes	—
796	#95	C₂³×C₆₁	1	2	yes	—
797	#95	C₂³×C₆₁	1	2	yes	—
798	#95	C₂³×C₆₁	1	2	yes	—
799	#95	C₂³×C₆₁	1	2	yes	—
800	#95	C₂³×C₆₁	1	2	yes	—
801	#95	C₂³×C₆₁	1	2	yes	—
802	C₂⁴	—	2	2	no	—
803	C₂⁴	—	2	2	no	—
804	C₂⁴	—	2	2	no	—
805	C₂⁴	—	2	2	no	—
806	C₂⁴	—	2	2	no	—
807	C₂⁴	—	4	1	no	—
808	C₂⁴	—	4	1	no	—
809	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
810	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
811	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
812	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
813	C₂×Q₈	—	2	2	no	—
814	C₂×Q₈	—	2	4	no	—
815	C₂×Q₈	—	2	2	no	—
816	C₂×Q₈	—	2	2	no	—
817	C₂×Q₈	—	4	2	no	—
818	C₂×Q₈	—	4	2	no	—
819	C₂×D₄	—	2	4	no	—
820	C₂×D₄	—	2	4	no	—
821	C₂×D₄	—	2	4	no	—
822	C₂×D₄	—	2	4	no	—
823	C₂×D₄	—	2	4	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	4	2	no	—
828	C₂×D₄	—	4	2	no	—
829	C₂×D₄	—	4	2	no	—
830	C₂×D₄	—	4	2	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	2	no	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	2	no	—
846	C₂²×C₄	—	2	2	no	—
847	C₂²×C₄	—	2	2	no	—
848	C₂²×C₄	—	2	2	no	—
849	C₂²×C₄	—	2	2	no	—
850	C₂²×C₄	—	2	4	no	—
851	C₂²×C₄	—	4	1	no	—
852	C₂²×C₄	—	4	1	no	—
853	C₂²×C₄	—	4	1	no	—
854	C₂²×C₄	—	4	1	no	—
855	C₂²×C₄	—	4	1	no	—
856	C₂²×C₄	—	4	1	no	—
857	C₂²×C₄	—	4	1	no	—
858	C₂²×C₄	—	4	1	no	—
859	C₂²×C₄	—	4	1	no	—
860	C₂²×C₄	—	4	1	no	—
861	C₂²×C₄	—	4	2	no	—
862	C₂²×C₄	—	4	2	no	—
863	C₂²×C₄	—	4	16	no	—
864	C₂²×C₄	#41×C₆₁	1	4	yes	—
865	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
866	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
868	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
871	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
872	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
873	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
874	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
875	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
876	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
877	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
878	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
880	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
882	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	4	no	—
887	C₄⋊C₄	—	2	4	no	—
888	C₄⋊C₄	—	2	4	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	4	2	no	—
894	C₄⋊C₄	—	4	2	no	—
895	C₄⋊C₄	—	4	2	no	—
896	C₄⋊C₄	—	4	2	no	—
897	C₄⋊C₄	—	4	2	no	—
898	C₄⋊C₄	—	4	2	no	—
899	C₄⋊C₄	—	4	2	no	—
900	C₄⋊C₄	—	4	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	4	no	—
904	C₂²⋊C₄	—	2	4	no	—
905	C₂²⋊C₄	—	2	4	no	—
906	C₂²⋊C₄	—	2	4	no	—
907	C₂²⋊C₄	—	2	4	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	4	no	—
913	C₂²⋊C₄	—	2	4	no	—
914	C₂²⋊C₄	—	2	4	no	—
915	C₂²⋊C₄	—	2	4	no	—
916	C₂²⋊C₄	—	4	2	no	—
917	C₂²⋊C₄	—	4	2	no	—
918	C₂²⋊C₄	—	4	2	no	—
919	C₂²⋊C₄	—	4	2	no	—
920	C₂²⋊C₄	—	4	2	no	—
921	C₂²⋊C₄	—	4	2	no	—
922	C₂²⋊C₄	—	4	2	no	—
923	C₂²⋊C₄	—	4	2	no	—
924	C₂²⋊C₄	—	4	2	no	—
925	C₂²⋊C₄	—	4	2	no	—
926	C₂²⋊C₄	#41×C₆₁	1	4	yes	—
927	C₂²⋊C₄	#41×C₆₁	1	4	yes	—
928	C₄²	—	2	4	no	—
929	C₄²	—	2	2	no	—
930	C₄²	—	2	2	no	—
931	C₄²	—	2	2	no	—
932	C₄²	—	2	2	no	—
933	C₄²	—	4	1	no	—
934	C₄²	—	4	1	no	—
935	C₄²	—	4	1	no	—
936	C₄²	—	4	1	no	—
937	C₄²	—	4	2	no	—
938	C₄²	—	4	2	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	1	no	—
941	C₂³	—	2	1	no	—
942	C₂³	—	2	1	no	—
943	C₂³	—	2	8	no	—
944	C₂³	—	2	1	no	—
945	C₂³	—	2	1	no	—
946	C₂³	—	2	1	no	—
947	C₂³	—	2	1	no	—
948	C₂³	—	2	1	no	—
949	C₂³	—	2	1	no	—
950	C₂³	—	2	1	no	—
951	C₂³	—	2	1	no	—
952	C₂³	—	2	1	no	—
953	C₂³	—	2	1	no	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	1	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	2	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	2	2	no	—
962	C₂³	—	2	2	no	—
963	C₂³	—	4	4	no	—
964	C₂³	—	4	4	no	—
965	C₂³	—	4	4	no	—
966	C₂³	—	4	4	no	—
967	C₂³	—	4	4	no	—
968	C₂³	—	4	4	no	—
969	C₂³	C₂×#41×C₆₁	1	2	yes	—
970	C₂³	C₂×#41×C₆₁	1	2	yes	—
971	C₂³	C₂×#41×C₆₁	1	2	yes	—
972	C₂³	H(5,𝔽₂)×C₆₁	1	2	yes	—
973	C₂³	2₋¹⁺⁴×C₆₁	1	2	yes	—
974	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
975	Q₈	—	4	4	no	—
976	Q₈	—	8	4	no	—
977	D₄	—	4	8	no	—
978	D₄	—	4	4	no	—
979	D₄	—	8	4	no	—
980	D₄	—	8	4	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	8	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	4	4	no	—
1032	C₂×C₄	—	4	4	no	—
1033	C₂×C₄	—	4	4	no	—
1034	C₂×C₄	—	4	4	no	—
1035	C₂×C₄	—	4	4	no	—
1036	C₂×C₄	—	4	4	no	—
1037	C₂×C₄	—	4	4	no	—
1038	C₂×C₄	—	4	4	no	—
1039	C₂×C₄	—	4	4	no	—
1040	C₂×C₄	—	8	4	no	—
1041	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1042	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1043	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1044	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1045	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1046	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1047	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
1048	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
1049	C₂²	—	2	2	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	2	2	no	—
1054	C₂²	—	2	2	no	—
1055	C₂²	—	2	2	no	—
1056	C₂²	—	2	2	no	—
1057	C₂²	—	2	2	no	—
1058	C₂²	—	2	2	no	—
1059	C₂²	—	2	2	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	4	16	no	—
1062	C₂²	—	4	1	no	—
1063	C₂²	—	4	1	no	—
1064	C₂²	—	4	1	no	—
1065	C₂²	—	4	1	no	—
1066	C₂²	—	4	1	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	1	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	4	2	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	4	2	no	—
1077	C₂²	C₆₁×#542	1	4	yes	—
1078	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
1079	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
1080	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
1081	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1082	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1083	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1084	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1085	C₄	—	2	2	no	—
1086	C₄	—	2	2	no	—
1087	C₄	—	2	2	no	—
1088	C₄	—	2	2	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	4	2	no	—
1091	C₄	—	4	1	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	2	no	—
1094	C₄	—	4	2	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	2	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	2	no	—
1100	C₄	—	4	2	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	1	no	—
1103	C₄	C₆₁×#538	1	4	yes	—
1104	C₂	—	2	4	no	—
1105	C₂	—	4	2	no	—
1106	C₂	—	4	2	no	—
1107	C₂	—	8	2	no	—
1108	C₂	C₆₁×#3444	1	1	yes	characteristic
1109	C₂	C₂×C₆₁×#538	1	1	yes	characteristic
1110	C₂	C₂×C₆₁×#542	1	1	yes	characteristic
1111	C₂	C₆₁×#3519	1	1	yes	characteristic
1112	C₂	C₆₁×#3519	1	1	yes	characteristic
1113	C₂	C₆₁×#3520	1	1	yes	characteristic
1114	C₂	C₆₁×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
prime radical	C₆₁×#2847	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×#2857	C₂	semidirect
2. C₆₁×#2850	C₂	semidirect
3. C₆₁×#2848	C₂	semidirect
5. C₆₁×#2653	C₂	semidirect
6. C₆₁×#2649	C₂	semidirect
7. C₆₁×#2510	C₂	semidirect
8. C₆₁×#2495	C₂	semidirect
9. C₆₁×#2494	C₂	semidirect
10. C₆₁×#2492	C₂	semidirect
11. C₆₁×#2491	C₂	semidirect
12. C₆₁×#2472	C₂	semidirect
13. C₆₁×#2450	C₂	semidirect
14. C₆₁×#2427	C₂	semidirect
15. C₆₁×#2426	C₂	semidirect
16. C₆₁×#2423	C₂	semidirect
17. C₆₁×#2422	C₂	semidirect
18. C₆₁×#2418	C₂	semidirect
19. C₆₁×#2337	C₂	semidirect
20. C₆₁×#2335	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₆₁	C₂	semidirect
22. C₄×#121×C₆₁	C₂	semidirect
23. C₂×C₄×C₂²⋊C₄×C₆₁	C₂	semidirect
25. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
27. C₂×#124×C₆₁	C₂²	semidirect
37. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
39. C₂×C₄×D₄×C₆₁	C₂²	semidirect
44. C₆₁×#401	C₂²	semidirect
45. C₆₁×#400	C₂²	semidirect
46. C₆₁×#400	C₂²	semidirect
48. C₆₁×#398	C₂²	semidirect
51. C₆₁×#397	C₂²	semidirect
52. C₆₁×#397	C₂²	semidirect
53. C₆₁×#396	C₂²	semidirect
59. C₆₁×#393	C₂²	semidirect
60. C₆₁×#391	C₂²	semidirect
61. C₆₁×#391	C₂²	semidirect
62. C₆₁×#391	C₂²	semidirect
63. C₆₁×#391	C₂²	semidirect
65. C₆₁×#390	C₂²	semidirect
66. C₆₁×#390	C₂²	semidirect
67. C₆₁×#389	C₂²	semidirect
68. C₆₁×#389	C₂²	semidirect
69. C₆₁×#389	C₂²	semidirect
70. C₆₁×#389	C₂²	semidirect
71. C₆₁×#389	C₂²	semidirect
76. C₆₁×#388	C₂²	semidirect
77. C₆₁×#388	C₂²	semidirect
78. C₆₁×#388	C₂²	semidirect
79. C₆₁×#388	C₂²	semidirect
80. C₆₁×#388	C₂²	semidirect
81. C₆₁×#387	C₂²	semidirect
82. C₆₁×#387	C₂²	semidirect
83. C₆₁×#387	C₂²	semidirect
95. C₆₁×#385	C₂²	semidirect
96. C₆₁×#384	C₂²	semidirect
97. C₆₁×#383	C₂²	semidirect
98. C₆₁×#382	C₂²	semidirect
106. C₆₁×#380	C₂²	semidirect
108. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
109. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
110. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₆₁	C₂²	semidirect
491. #35080	C₆₁	direct (N × H)
547. #2857	C₂×C₆₁	semidirect
548. #2850	C₂×C₆₁	semidirect
549. #2848	C₂×C₆₁	semidirect
551. #2653	C₂×C₆₁	semidirect
552. #2649	C₂×C₆₁	semidirect
553. #2510	C₂×C₆₁	semidirect
554. #2495	C₂×C₆₁	semidirect
555. #2494	C₂×C₆₁	semidirect
556. #2492	C₂×C₆₁	semidirect
557. #2491	C₂×C₆₁	semidirect
558. #2472	C₂×C₆₁	semidirect
559. #2450	C₂×C₆₁	semidirect
560. #2427	C₂×C₆₁	semidirect
561. #2426	C₂×C₆₁	semidirect
562. #2423	C₂×C₆₁	semidirect
563. #2422	C₂×C₆₁	semidirect
564. #2418	C₂×C₆₁	semidirect
565. #2337	C₂×C₆₁	semidirect
566. #2335	C₂×C₆₁	semidirect
567. C₄×C₂²⋊Q₈	C₂×C₆₁	semidirect
568. C₄×#121	C₂×C₆₁	semidirect
569. C₂×C₄×C₂²⋊C₄	C₂×C₆₁	semidirect
582. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
584. C₂×#124	C₂²×C₆₁	semidirect
594. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
596. C₂×C₄×D₄	C₂²×C₆₁	semidirect
601. #401	C₂²×C₆₁	semidirect
602. #400	C₂²×C₆₁	semidirect
603. #400	C₂²×C₆₁	semidirect
605. #398	C₂²×C₆₁	semidirect
608. #397	C₂²×C₆₁	semidirect
609. #397	C₂²×C₆₁	semidirect
610. #396	C₂²×C₆₁	semidirect
616. #393	C₂²×C₆₁	semidirect
617. #391	C₂²×C₆₁	semidirect
618. #391	C₂²×C₆₁	semidirect
619. #391	C₂²×C₆₁	semidirect
620. #391	C₂²×C₆₁	semidirect
622. #390	C₂²×C₆₁	semidirect
623. #390	C₂²×C₆₁	semidirect
624. #389	C₂²×C₆₁	semidirect
625. #389	C₂²×C₆₁	semidirect
626. #389	C₂²×C₆₁	semidirect
627. #389	C₂²×C₆₁	semidirect
628. #389	C₂²×C₆₁	semidirect
633. #388	C₂²×C₆₁	semidirect
634. #388	C₂²×C₆₁	semidirect
635. #388	C₂²×C₆₁	semidirect
636. #388	C₂²×C₆₁	semidirect
637. #388	C₂²×C₆₁	semidirect
638. #387	C₂²×C₆₁	semidirect
639. #387	C₂²×C₆₁	semidirect
640. #387	C₂²×C₆₁	semidirect
652. #385	C₂²×C₆₁	semidirect
653. #384	C₂²×C₆₁	semidirect
654. #383	C₂²×C₆₁	semidirect
655. #382	C₂²×C₆₁	semidirect
663. #380	C₂²×C₆₁	semidirect
665. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
666. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
667. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
677. C₄×C₂²⋊C₄	C₂²×C₆₁	semidirect
680. C₆₁	#35080	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×#2857	2
C₆₁×#2850	2
C₆₁×#2848	2
C₆₁×#2847	2
C₆₁×#2653	2
C₆₁×#2649	2
C₆₁×#2510	2
C₆₁×#2495	2
C₆₁×#2494	2
C₆₁×#2492	2
C₆₁×#2491	2
C₆₁×#2472	2
C₆₁×#2450	2
C₆₁×#2427	2
C₆₁×#2426	2
C₆₁×#2423	2
C₆₁×#2422	2
C₆₁×#2418	2
C₆₁×#2337	2
C₆₁×#2335	2
C₄×C₂²⋊Q₈×C₆₁	2
C₄×#121×C₆₁	2
C₂×C₄×C₂²⋊C₄×C₆₁	2
#35080	61

Subgroups — C61×#35080 #29538513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#35080 #29538513