Subgroups — C₆₁×#34881 #29538314

Order 15616.

1826 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2593	C₂	1	2	yes	maximal, complemented
2	C₆₁×#2585	C₂	1	2	yes	maximal, complemented
3	C₆₁×#2573	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2554	C₂	1	2	yes	maximal
5	C₆₁×#2525	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2516	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2469	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2458	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2402	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#2398	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2396	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#2392	C₂	1	1	yes	maximal, characteristic
13	C₄×#126×C₆₁	C₂	1	2	yes	maximal, complemented
14	C₄×#123×C₆₁	C₂	1	2	yes	maximal, complemented
15	C₆₁×#2298	C₂	1	2	yes	maximal, complemented
16	C₆₁×#2293	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#2293	C₂	1	2	yes	maximal, complemented
18	C₄²×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#117×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#126×C₆₁	C₂²	1	2	yes	—
21	C₂×#123×C₆₁	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#117×C₆₁	C₂²	1	2	yes	—
29	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
30	C₆₁×#400	C₂²	1	1	yes	characteristic
31	C₆₁×#400	C₂²	1	2	yes	—
32	C₆₁×#400	C₂²	1	2	yes	—
33	C₆₁×#400	C₂²	1	2	yes	—
34	C₆₁×#399	C₂²	1	1	yes	characteristic
35	C₆₁×#398	C₂²	1	2	yes	—
36	C₆₁×#398	C₂²	1	2	yes	—
37	C₆₁×#398	C₂²	1	1	yes	characteristic
38	C₆₁×#398	C₂²	1	2	yes	—
39	C₆₁×#397	C₂²	1	2	yes	—
40	C₆₁×#397	C₂²	1	1	yes	characteristic
41	C₆₁×#396	C₂²	1	2	yes	—
42	C₆₁×#396	C₂²	1	2	yes	—
43	C₆₁×#395	C₂²	1	1	yes	characteristic
44	C₆₁×#394	C₂²	1	2	yes	—
45	C₆₁×#394	C₂²	1	1	yes	characteristic
46	C₆₁×#394	C₂²	1	2	yes	—
47	C₆₁×#393	C₂²	1	1	yes	characteristic
48	C₆₁×#393	C₂²	1	2	yes	—
49	C₆₁×#392	C₂²	1	1	yes	characteristic
50	C₆₁×#390	C₂²	1	2	yes	—
51	C₆₁×#390	C₂²	1	2	yes	—
52	C₆₁×#390	C₂²	1	2	yes	—
53	C₆₁×#389	C₂²	1	2	yes	—
54	C₆₁×#389	C₂²	1	2	yes	—
55	C₆₁×#389	C₂²	1	2	yes	—
56	C₆₁×#388	C₂²	1	2	yes	—
57	C₆₁×#388	C₂²	1	2	yes	—
58	C₆₁×#388	C₂²	1	2	yes	—
59	C₆₁×#388	C₂²	1	2	yes	—
60	C₆₁×#388	C₂²	1	2	yes	—
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	—
66	C₆₁×#388	C₂²	1	2	yes	—
67	C₆₁×#388	C₂²	1	2	yes	—
68	C₆₁×#388	C₂²	1	2	yes	—
69	C₆₁×#388	C₂²	1	2	yes	—
70	C₆₁×#388	C₂²	1	2	yes	—
71	C₆₁×#387	C₂²	1	2	yes	—
72	C₆₁×#387	C₂²	1	2	yes	—
73	C₆₁×#387	C₂²	1	2	yes	—
74	C₆₁×#387	C₂²	1	2	yes	—
75	C₆₁×#387	C₂²	1	2	yes	—
76	C₆₁×#387	C₂²	1	2	yes	—
77	C₆₁×#387	C₂²	1	2	yes	—
78	C₆₁×#387	C₂²	1	2	yes	—
79	C₆₁×#387	C₂²	1	2	yes	—
80	C₆₁×#386	C₂²	1	2	yes	—
81	C₆₁×#385	C₂²	1	2	yes	—
82	C₆₁×#383	C₂²	1	2	yes	—
83	C₆₁×#381	C₂²	1	2	yes	—
84	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
85	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
86	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
87	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
88	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
89	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
91	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
93	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
95	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
102	C₆₁×#376	C₂²	1	1	yes	characteristic
103	C₆₁×#376	C₂²	1	1	yes	characteristic
104	C₄³×C₆₁	C₂²	1	1	yes	characteristic
105	C₄³×C₆₁	C₂²	1	1	yes	characteristic
106	C₄³×C₆₁	C₂²	1	2	yes	—
107	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
109	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
111	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
112	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
113	#126×C₆₁	—	2	8	no	—
114	#123×C₆₁	—	2	8	no	—
115	C₄×Q₈×C₆₁	—	2	8	no	—
116	C₄×Q₈×C₆₁	—	2	4	no	—
117	C₄×D₄×C₆₁	—	2	8	no	—
118	C₄×D₄×C₆₁	—	2	4	no	—
119	#117×C₆₁	—	2	4	no	—
120	#117×C₆₁	—	2	8	no	—
121	#117×C₆₁	—	2	4	no	—
122	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₆₁	C₂³	1	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×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
159	C₂×C₄²×C₆₁	—	2	4	no	—
160	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
161	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
162	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
163	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
164	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
165	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
169	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
170	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
172	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
173	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
174	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
175	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
176	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
178	#95×C₆₁	C₂³	1	2	yes	—
179	#95×C₆₁	C₂³	1	2	yes	—
180	#95×C₆₁	C₂³	1	2	yes	—
181	#95×C₆₁	C₂³	1	2	yes	—
182	#95×C₆₁	C₂³	1	2	yes	—
183	#95×C₆₁	C₂³	1	2	yes	—
184	#95×C₆₁	C₂³	1	2	yes	—
185	#95×C₆₁	C₂³	1	2	yes	—
186	#95×C₆₁	C₂³	1	2	yes	—
187	#95×C₆₁	C₂³	1	2	yes	—
188	#95×C₆₁	C₂³	1	2	yes	—
189	#95×C₆₁	C₂³	1	2	yes	—
190	#95×C₆₁	C₂³	1	2	yes	—
191	#95×C₆₁	C₂³	1	2	yes	—
192	#95×C₆₁	C₂³	1	2	yes	—
193	#95×C₆₁	C₂³	1	2	yes	—
194	#95×C₆₁	C₂³	1	1	yes	characteristic
195	#95×C₆₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
203	#95×C₆₁	C₂³	1	1	yes	characteristic
204	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
205	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
206	C₂×Q₈×C₆₁	—	2	4	no	—
207	C₂×Q₈×C₆₁	—	2	2	no	—
208	C₂×D₄×C₆₁	—	2	4	no	—
209	C₂×D₄×C₆₁	—	2	2	no	—
210	C₂×D₄×C₆₁	—	2	4	no	—
211	C₂×D₄×C₆₁	—	4	2	no	—
212	C₂×D₄×C₆₁	—	4	2	no	—
213	C₂²×C₄×C₆₁	—	2	2	no	—
214	C₂²×C₄×C₆₁	—	2	2	no	—
215	C₂²×C₄×C₆₁	—	2	4	no	—
216	C₂²×C₄×C₆₁	—	2	4	no	—
217	C₂²×C₄×C₆₁	—	2	4	no	—
218	C₂²×C₄×C₆₁	—	2	4	no	—
219	C₂²×C₄×C₆₁	—	2	4	no	—
220	C₂²×C₄×C₆₁	—	4	2	no	—
221	C₂²×C₄×C₆₁	#41	1	4	yes	—
222	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
239	C₄⋊C₄×C₆₁	—	2	4	no	—
240	C₄⋊C₄×C₆₁	—	2	2	no	—
241	C₄⋊C₄×C₆₁	—	2	2	no	—
242	C₄⋊C₄×C₆₁	—	2	4	no	—
243	C₄⋊C₄×C₆₁	—	2	4	no	—
244	C₄⋊C₄×C₆₁	—	2	4	no	—
245	C₄⋊C₄×C₆₁	—	2	2	no	—
246	C₄⋊C₄×C₆₁	—	2	4	no	—
247	C₄⋊C₄×C₆₁	—	2	4	no	—
248	C₄⋊C₄×C₆₁	—	2	4	no	—
249	C₄⋊C₄×C₆₁	—	2	2	no	—
250	C₄⋊C₄×C₆₁	—	2	4	no	—
251	C₄⋊C₄×C₆₁	—	2	4	no	—
252	C₄⋊C₄×C₆₁	—	2	4	no	—
253	C₄⋊C₄×C₆₁	—	4	2	no	—
254	C₄⋊C₄×C₆₁	—	4	2	no	—
255	C₄⋊C₄×C₆₁	—	4	2	no	—
256	C₄⋊C₄×C₆₁	—	4	2	no	—
257	C₄⋊C₄×C₆₁	#41	1	8	yes	—
258	C₂²⋊C₄×C₆₁	—	2	4	no	—
259	C₂²⋊C₄×C₆₁	—	2	4	no	—
260	C₂²⋊C₄×C₆₁	—	2	4	no	—
261	C₂²⋊C₄×C₆₁	—	2	4	no	—
262	C₂²⋊C₄×C₆₁	—	2	2	no	—
263	C₂²⋊C₄×C₆₁	—	2	2	no	—
264	C₂²⋊C₄×C₆₁	—	2	4	no	—
265	C₂²⋊C₄×C₆₁	—	2	4	no	—
266	C₂²⋊C₄×C₆₁	—	2	4	no	—
267	C₂²⋊C₄×C₆₁	—	2	4	no	—
268	C₂²⋊C₄×C₆₁	—	2	4	no	—
269	C₂²⋊C₄×C₆₁	—	2	4	no	—
270	C₂²⋊C₄×C₆₁	—	2	4	no	—
271	C₂²⋊C₄×C₆₁	—	2	4	no	—
272	C₂²⋊C₄×C₆₁	—	4	2	no	—
273	C₂²⋊C₄×C₆₁	—	4	2	no	—
274	C₂²⋊C₄×C₆₁	—	4	2	no	—
275	C₂²⋊C₄×C₆₁	—	4	2	no	—
276	C₄²×C₆₁	—	2	2	no	—
277	C₄²×C₆₁	—	2	4	no	—
278	C₄²×C₆₁	—	2	2	no	—
279	C₄²×C₆₁	—	2	2	no	—
280	C₄²×C₆₁	—	2	2	no	—
281	C₄²×C₆₁	—	2	4	no	—
282	C₄²×C₆₁	—	2	4	no	—
283	C₄²×C₆₁	—	2	4	no	—
284	C₄²×C₆₁	—	2	4	no	—
285	C₄²×C₆₁	—	2	4	no	—
286	C₄²×C₆₁	—	2	4	no	—
287	C₄²×C₆₁	—	2	4	no	—
288	C₄²×C₆₁	—	4	2	no	—
289	C₄²×C₆₁	—	4	2	no	—
290	C₄²×C₆₁	—	4	2	no	—
291	C₄²×C₆₁	—	4	2	no	—
292	C₄²×C₆₁	#41	1	4	yes	—
293	C₄²×C₆₁	#41	1	4	yes	—
294	C₂³×C₆₁	—	2	1	no	—
295	C₂³×C₆₁	—	2	1	no	—
296	C₂³×C₆₁	—	2	2	no	—
297	C₂³×C₆₁	—	2	2	no	—
298	C₂³×C₆₁	—	2	2	no	—
299	C₂³×C₆₁	—	2	2	no	—
300	C₂³×C₆₁	—	2	2	no	—
301	C₂³×C₆₁	—	2	2	no	—
302	C₂³×C₆₁	—	2	2	no	—
303	C₂³×C₆₁	—	2	2	no	—
304	C₂³×C₆₁	—	2	2	no	—
305	C₂³×C₆₁	C₂×#41	1	2	yes	—
306	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
307	Q₈×C₆₁	—	2	8	no	—
308	D₄×C₆₁	—	4	8	no	—
309	D₄×C₆₁	—	4	4	no	—
310	C₂×C₄×C₆₁	—	2	2	no	—
311	C₂×C₄×C₆₁	—	2	2	no	—
312	C₂×C₄×C₆₁	—	2	2	no	—
313	C₂×C₄×C₆₁	—	2	2	no	—
314	C₂×C₄×C₆₁	—	2	2	no	—
315	C₂×C₄×C₆₁	—	2	2	no	—
316	C₂×C₄×C₆₁	—	2	1	no	—
317	C₂×C₄×C₆₁	—	2	1	no	—
318	C₂×C₄×C₆₁	—	2	2	no	—
319	C₂×C₄×C₆₁	—	2	2	no	—
320	C₂×C₄×C₆₁	—	2	2	no	—
321	C₂×C₄×C₆₁	—	2	2	no	—
322	C₂×C₄×C₆₁	—	2	8	no	—
323	C₂×C₄×C₆₁	—	2	2	no	—
324	C₂×C₄×C₆₁	—	2	2	no	—
325	C₂×C₄×C₆₁	—	2	1	no	—
326	C₂×C₄×C₆₁	—	2	2	no	—
327	C₂×C₄×C₆₁	—	2	1	no	—
328	C₂×C₄×C₆₁	—	2	2	no	—
329	C₂×C₄×C₆₁	—	2	2	no	—
330	C₂×C₄×C₆₁	—	2	2	no	—
331	C₂×C₄×C₆₁	—	2	2	no	—
332	C₂×C₄×C₆₁	—	2	2	no	—
333	C₂×C₄×C₆₁	—	2	2	no	—
334	C₂×C₄×C₆₁	—	2	2	no	—
335	C₂×C₄×C₆₁	—	2	2	no	—
336	C₂×C₄×C₆₁	—	2	2	no	—
337	C₂×C₄×C₆₁	—	2	2	no	—
338	C₂×C₄×C₆₁	—	2	2	no	—
339	C₂×C₄×C₆₁	—	2	2	no	—
340	C₂×C₄×C₆₁	—	2	2	no	—
341	C₂×C₄×C₆₁	—	2	2	no	—
342	C₂×C₄×C₆₁	—	2	2	no	—
343	C₂×C₄×C₆₁	—	2	2	no	—
344	C₂×C₄×C₆₁	—	2	2	no	—
345	C₂×C₄×C₆₁	—	2	2	no	—
346	C₂×C₄×C₆₁	—	2	2	no	—
347	C₂×C₄×C₆₁	—	2	2	no	—
348	C₂×C₄×C₆₁	—	4	8	no	—
349	C₂×C₄×C₆₁	—	4	8	no	—
350	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
351	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
352	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
353	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
354	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
355	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
356	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
357	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
358	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
359	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
360	#34881	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
361	C₂²×C₆₁	—	2	2	no	—
362	C₂²×C₆₁	—	2	4	no	—
363	C₂²×C₆₁	—	4	1	no	—
364	C₂²×C₆₁	—	4	1	no	—
365	C₂²×C₆₁	—	4	2	no	—
366	C₂²×C₆₁	—	4	2	no	—
367	C₂²×C₆₁	—	4	2	no	—
368	C₂²×C₆₁	—	4	2	no	—
369	C₂²×C₆₁	—	4	2	no	—
370	C₂²×C₆₁	—	4	2	no	—
371	C₂²×C₆₁	—	4	2	no	—
372	C₂²×C₆₁	—	4	2	no	—
373	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
374	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
375	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
376	C₂²×C₆₁	C₂²×#41	1	2	yes	—
377	C₂²×C₆₁	#585	1	2	yes	—
378	C₄×C₆₁	—	2	2	no	—
379	C₄×C₆₁	—	2	4	no	—
380	C₄×C₆₁	—	2	2	no	—
381	C₄×C₆₁	—	2	2	no	—
382	C₄×C₆₁	—	2	4	no	—
383	C₄×C₆₁	—	2	4	no	—
384	C₄×C₆₁	—	2	4	no	—
385	C₄×C₆₁	—	4	2	no	—
386	C₄×C₆₁	—	4	1	no	—
387	C₄×C₆₁	—	4	1	no	—
388	C₄×C₆₁	—	4	2	no	—
389	C₄×C₆₁	—	4	2	no	—
390	C₄×C₆₁	—	4	2	no	—
391	C₄×C₆₁	—	4	2	no	—
392	C₄×C₆₁	—	4	2	no	—
393	C₄×C₆₁	—	4	2	no	—
394	C₄×C₆₁	#529	1	4	yes	—
395	#2593	C₂×C₆₁	1	2	yes	complemented
396	#2585	C₂×C₆₁	1	2	yes	complemented
397	#2573	C₂×C₆₁	1	2	yes	complemented
398	#2554	C₂×C₆₁	1	2	yes	—
399	#2525	C₂×C₆₁	1	2	yes	complemented
400	#2516	C₂×C₆₁	1	2	yes	complemented
401	#2469	C₂×C₆₁	1	2	yes	complemented
402	#2458	C₂×C₆₁	1	2	yes	complemented
403	#2402	C₂×C₆₁	1	1	yes	characteristic, complemented
404	#2398	C₂×C₆₁	1	1	yes	characteristic, complemented
405	#2396	C₂×C₆₁	1	1	yes	characteristic, complemented
406	#2392	C₂×C₆₁	1	1	yes	characteristic
407	C₄×#126	C₂×C₆₁	1	2	yes	complemented
408	C₄×#123	C₂×C₆₁	1	2	yes	complemented
409	#2298	C₂×C₆₁	1	2	yes	complemented
410	#2293	C₂×C₆₁	1	2	yes	complemented
411	#2293	C₂×C₆₁	1	1	yes	characteristic, complemented
412	C₄²×Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
413	C₄×#117	C₂×C₆₁	1	1	yes	characteristic, complemented
414	C₂×C₆₁	—	4	2	no	—
415	C₂×C₆₁	—	8	2	no	—
416	C₂×C₆₁	C₂×#529	1	1	yes	characteristic
417	C₂×C₆₁	#3444	1	1	yes	characteristic
418	C₂×C₆₁	#3455	1	1	yes	characteristic
419	C₂×C₆₁	#3475	1	2	yes	—
420	C₂×C₆₁	#3480	1	2	yes	—
421	C₂×#126	C₂²×C₆₁	1	2	yes	—
422	C₂×#123	C₂²×C₆₁	1	2	yes	—
423	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
424	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
425	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
426	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
427	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
428	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
429	C₂×#117	C₂²×C₆₁	1	2	yes	—
430	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
431	#400	C₂²×C₆₁	1	2	yes	—
432	#400	C₂²×C₆₁	1	2	yes	—
433	#400	C₂²×C₆₁	1	1	yes	characteristic
434	#400	C₂²×C₆₁	1	2	yes	—
435	#399	C₂²×C₆₁	1	1	yes	characteristic
436	#398	C₂²×C₆₁	1	1	yes	characteristic
437	#398	C₂²×C₆₁	1	2	yes	—
438	#398	C₂²×C₆₁	1	2	yes	—
439	#398	C₂²×C₆₁	1	2	yes	—
440	#397	C₂²×C₆₁	1	1	yes	characteristic
441	#397	C₂²×C₆₁	1	2	yes	—
442	#396	C₂²×C₆₁	1	2	yes	—
443	#396	C₂²×C₆₁	1	2	yes	—
444	#395	C₂²×C₆₁	1	1	yes	characteristic
445	#394	C₂²×C₆₁	1	1	yes	characteristic
446	#394	C₂²×C₆₁	1	2	yes	—
447	#394	C₂²×C₆₁	1	2	yes	—
448	#393	C₂²×C₆₁	1	1	yes	characteristic
449	#393	C₂²×C₆₁	1	2	yes	—
450	#392	C₂²×C₆₁	1	1	yes	characteristic
451	#390	C₂²×C₆₁	1	2	yes	—
452	#390	C₂²×C₆₁	1	2	yes	—
453	#390	C₂²×C₆₁	1	2	yes	—
454	#389	C₂²×C₆₁	1	2	yes	—
455	#389	C₂²×C₆₁	1	2	yes	—
456	#389	C₂²×C₆₁	1	2	yes	—
457	#388	C₂²×C₆₁	1	2	yes	—
458	#388	C₂²×C₆₁	1	2	yes	—
459	#388	C₂²×C₆₁	1	2	yes	—
460	#388	C₂²×C₆₁	1	2	yes	—
461	#388	C₂²×C₆₁	1	2	yes	—
462	#388	C₂²×C₆₁	1	2	yes	—
463	#388	C₂²×C₆₁	1	2	yes	—
464	#388	C₂²×C₆₁	1	2	yes	—
465	#388	C₂²×C₆₁	1	2	yes	—
466	#388	C₂²×C₆₁	1	2	yes	—
467	#388	C₂²×C₆₁	1	2	yes	—
468	#388	C₂²×C₆₁	1	2	yes	—
469	#388	C₂²×C₆₁	1	2	yes	—
470	#388	C₂²×C₆₁	1	2	yes	—
471	#388	C₂²×C₆₁	1	2	yes	—
472	#387	C₂²×C₆₁	1	2	yes	—
473	#387	C₂²×C₆₁	1	2	yes	—
474	#387	C₂²×C₆₁	1	2	yes	—
475	#387	C₂²×C₆₁	1	2	yes	—
476	#387	C₂²×C₆₁	1	2	yes	—
477	#387	C₂²×C₆₁	1	2	yes	—
478	#387	C₂²×C₆₁	1	2	yes	—
479	#387	C₂²×C₆₁	1	2	yes	—
480	#387	C₂²×C₆₁	1	2	yes	—
481	#386	C₂²×C₆₁	1	2	yes	—
482	#385	C₂²×C₆₁	1	2	yes	—
483	#383	C₂²×C₆₁	1	2	yes	—
484	#381	C₂²×C₆₁	1	2	yes	—
485	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
486	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
487	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
488	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
489	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
490	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
491	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
492	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
493	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
494	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
495	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
496	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
497	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
498	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
499	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
500	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
501	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
502	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
503	#376	C₂²×C₆₁	1	1	yes	characteristic
504	#376	C₂²×C₆₁	1	1	yes	characteristic
505	C₄³	C₂²×C₆₁	1	1	yes	characteristic
506	C₄³	C₂²×C₆₁	1	1	yes	characteristic
507	C₄³	C₂²×C₆₁	1	2	yes	—
508	C₆₁	#34881	1	1	yes	characteristic, direct product factor, Sylow
509	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
510	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
511	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
513	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
514	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
515	#126	—	2	8	no	—
516	#123	—	2	8	no	—
517	C₄×Q₈	—	2	8	no	—
518	C₄×Q₈	—	2	4	no	—
519	C₄×D₄	—	2	8	no	—
520	C₄×D₄	—	2	4	no	—
521	#117	—	2	4	no	—
522	#117	—	2	8	no	—
523	#117	—	2	4	no	—
524	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
535	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
545	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
561	C₂×C₄²	—	2	4	no	—
562	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
564	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
565	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
566	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
567	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
568	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
569	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
570	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
571	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
572	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
573	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
574	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
575	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
576	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
577	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
578	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
579	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
580	#95	C₂³×C₆₁	1	2	yes	—
581	#95	C₂³×C₆₁	1	2	yes	—
582	#95	C₂³×C₆₁	1	2	yes	—
583	#95	C₂³×C₆₁	1	2	yes	—
584	#95	C₂³×C₆₁	1	2	yes	—
585	#95	C₂³×C₆₁	1	2	yes	—
586	#95	C₂³×C₆₁	1	2	yes	—
587	#95	C₂³×C₆₁	1	2	yes	—
588	#95	C₂³×C₆₁	1	2	yes	—
589	#95	C₂³×C₆₁	1	2	yes	—
590	#95	C₂³×C₆₁	1	2	yes	—
591	#95	C₂³×C₆₁	1	2	yes	—
592	#95	C₂³×C₆₁	1	2	yes	—
593	#95	C₂³×C₆₁	1	2	yes	—
594	#95	C₂³×C₆₁	1	2	yes	—
595	#95	C₂³×C₆₁	1	2	yes	—
596	#95	C₂³×C₆₁	1	1	yes	characteristic
597	#95	C₂³×C₆₁	1	1	yes	characteristic
598	#95	C₂³×C₆₁	1	2	yes	—
599	#95	C₂³×C₆₁	1	2	yes	—
600	#95	C₂³×C₆₁	1	2	yes	—
601	#95	C₂³×C₆₁	1	2	yes	—
602	#95	C₂³×C₆₁	1	2	yes	—
603	#95	C₂³×C₆₁	1	2	yes	—
604	#95	C₂³×C₆₁	1	1	yes	characteristic
605	#95	C₂³×C₆₁	1	1	yes	characteristic
606	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
607	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
608	C₂×Q₈	—	2	4	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	2	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	4	2	no	—
614	C₂×D₄	—	4	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	4	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	4	2	no	—
623	C₂²×C₄	#41×C₆₁	1	4	yes	—
624	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
628	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
630	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
636	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	4	2	no	—
656	C₄⋊C₄	—	4	2	no	—
657	C₄⋊C₄	—	4	2	no	—
658	C₄⋊C₄	—	4	2	no	—
659	C₄⋊C₄	#41×C₆₁	1	8	yes	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	2	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	4	2	no	—
675	C₂²⋊C₄	—	4	2	no	—
676	C₂²⋊C₄	—	4	2	no	—
677	C₂²⋊C₄	—	4	2	no	—
678	C₄²	—	2	2	no	—
679	C₄²	—	2	4	no	—
680	C₄²	—	2	2	no	—
681	C₄²	—	2	2	no	—
682	C₄²	—	2	2	no	—
683	C₄²	—	2	4	no	—
684	C₄²	—	2	4	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	4	no	—
687	C₄²	—	2	4	no	—
688	C₄²	—	2	4	no	—
689	C₄²	—	2	4	no	—
690	C₄²	—	4	2	no	—
691	C₄²	—	4	2	no	—
692	C₄²	—	4	2	no	—
693	C₄²	—	4	2	no	—
694	C₄²	#41×C₆₁	1	4	yes	—
695	C₄²	#41×C₆₁	1	4	yes	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	C₂×#41×C₆₁	1	2	yes	—
708	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
709	Q₈	—	2	8	no	—
710	D₄	—	4	8	no	—
711	D₄	—	4	4	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	8	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	4	8	no	—
751	C₂×C₄	—	4	8	no	—
752	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
753	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
754	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
755	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
756	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
757	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
758	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
759	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
760	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
761	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	4	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
775	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
776	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
777	C₂²	C₂²×#41×C₆₁	1	2	yes	—
778	C₂²	C₆₁×#585	1	2	yes	—
779	C₄	—	2	2	no	—
780	C₄	—	2	4	no	—
781	C₄	—	2	2	no	—
782	C₄	—	2	2	no	—
783	C₄	—	2	4	no	—
784	C₄	—	2	4	no	—
785	C₄	—	2	4	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	1	no	—
788	C₄	—	4	1	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	C₆₁×#529	1	4	yes	—
796	C₂	—	4	2	no	—
797	C₂	—	8	2	no	—
798	C₂	C₂×C₆₁×#529	1	1	yes	characteristic
799	C₂	C₆₁×#3444	1	1	yes	characteristic
800	C₂	C₆₁×#3455	1	1	yes	characteristic
801	C₂	C₆₁×#3475	1	2	yes	—
802	C₂	C₆₁×#3480	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
socle	C₂³×C₆₁	C₂⁵
prime radical	C₆₁×#392	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#2593	C₂	semidirect
2. C₆₁×#2585	C₂	semidirect
3. C₆₁×#2573	C₂	semidirect
5. C₆₁×#2525	C₂	semidirect
6. C₆₁×#2516	C₂	semidirect
7. C₆₁×#2469	C₂	semidirect
8. C₆₁×#2458	C₂	semidirect
9. C₆₁×#2402	C₂	semidirect
10. C₆₁×#2398	C₂	semidirect
11. C₆₁×#2396	C₂	semidirect
13. C₄×#126×C₆₁	C₂	semidirect
14. C₄×#123×C₆₁	C₂	semidirect
15. C₆₁×#2298	C₂	semidirect
16. C₆₁×#2293	C₂	semidirect
17. C₆₁×#2293	C₂	semidirect
18. C₄²×Q₈×C₆₁	C₂	semidirect
19. C₄×#117×C₆₁	C₂	semidirect
360. #34881	C₆₁	direct (N × H)
395. #2593	C₂×C₆₁	semidirect
396. #2585	C₂×C₆₁	semidirect
397. #2573	C₂×C₆₁	semidirect
399. #2525	C₂×C₆₁	semidirect
400. #2516	C₂×C₆₁	semidirect
401. #2469	C₂×C₆₁	semidirect
402. #2458	C₂×C₆₁	semidirect
403. #2402	C₂×C₆₁	semidirect
404. #2398	C₂×C₆₁	semidirect
405. #2396	C₂×C₆₁	semidirect
407. C₄×#126	C₂×C₆₁	semidirect
408. C₄×#123	C₂×C₆₁	semidirect
409. #2298	C₂×C₆₁	semidirect
410. #2293	C₂×C₆₁	semidirect
411. #2293	C₂×C₆₁	semidirect
412. C₄²×Q₈	C₂×C₆₁	semidirect
413. C₄×#117	C₂×C₆₁	semidirect
508. C₆₁	#34881	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×#2593	2
C₆₁×#2585	2
C₆₁×#2573	2
C₆₁×#2554	2
C₆₁×#2525	2
C₆₁×#2516	2
C₆₁×#2469	2
C₆₁×#2458	2
C₆₁×#2402	2
C₆₁×#2398	2
C₆₁×#2396	2
C₆₁×#2392	2
C₄×#126×C₆₁	2
C₄×#123×C₆₁	2
C₆₁×#2298	2
C₆₁×#2293	2
C₄²×Q₈×C₆₁	2
C₄×#117×C₆₁	2
#34881	61

Subgroups — C61×#34881 #29538314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#34881 #29538314