Subgroups — C₆₁×#36831 #29540264

Order 15616.

1526 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2852	C₂	1	2	yes	maximal, complemented
2	C₆₁×#2807	C₂	1	2	yes	maximal, complemented
3	C₆₁×#2797	C₂	1	2	yes	maximal
4	C₆₁×#2776	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2748	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2746	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2738	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2727	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2722	C₂	1	2	yes	maximal, complemented
10	C₆₁×#2654	C₂	1	2	yes	maximal, complemented
11	C₆₁×#2611	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#2606	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#2598	C₂	1	1	yes	maximal, characteristic
14	C₆₁×#2594	C₂	1	2	yes	maximal, complemented
15	C₆₁×#2562	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#2479	C₂	1	2	yes	maximal, complemented
17	C₆₁×#2336	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#2319	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#2296	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#126×C₆₁	C₂²	1	2	yes	—
21	C₂×#126×C₆₁	C₂²	1	2	yes	—
22	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
27	C₆₁×#401	C₂²	1	2	yes	—
28	C₆₁×#400	C₂²	1	1	yes	characteristic
29	C₆₁×#400	C₂²	1	2	yes	—
30	C₆₁×#400	C₂²	1	2	yes	—
31	C₆₁×#400	C₂²	1	2	yes	—
32	C₆₁×#400	C₂²	1	1	yes	characteristic
33	C₆₁×#399	C₂²	1	1	yes	characteristic
34	C₆₁×#399	C₂²	1	2	yes	—
35	C₆₁×#399	C₂²	1	1	yes	characteristic
36	C₆₁×#399	C₂²	1	2	yes	—
37	C₆₁×#399	C₂²	1	2	yes	—
38	C₆₁×#398	C₂²	1	2	yes	—
39	C₆₁×#398	C₂²	1	2	yes	—
40	C₆₁×#398	C₂²	1	2	yes	—
41	C₆₁×#398	C₂²	1	2	yes	—
42	C₆₁×#398	C₂²	1	2	yes	—
43	C₆₁×#398	C₂²	1	2	yes	—
44	C₆₁×#398	C₂²	1	1	yes	characteristic
45	C₆₁×#397	C₂²	1	2	yes	—
46	C₆₁×#397	C₂²	1	2	yes	—
47	C₆₁×#397	C₂²	1	2	yes	—
48	C₆₁×#397	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
54	C₆₁×#392	C₂²	1	1	yes	characteristic
55	C₆₁×#390	C₂²	1	2	yes	—
56	C₆₁×#390	C₂²	1	2	yes	—
57	C₆₁×#389	C₂²	1	2	yes	—
58	C₆₁×#389	C₂²	1	2	yes	—
59	C₆₁×#389	C₂²	1	2	yes	—
60	C₆₁×#389	C₂²	1	2	yes	—
61	C₆₁×#389	C₂²	1	2	yes	—
62	C₆₁×#389	C₂²	1	2	yes	—
63	C₆₁×#389	C₂²	1	2	yes	—
64	C₆₁×#389	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×#388	C₂²	1	2	yes	—
72	C₆₁×#388	C₂²	1	2	yes	—
73	C₆₁×#388	C₂²	1	2	yes	—
74	C₆₁×#388	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×#387	C₂²	1	2	yes	—
81	C₆₁×#387	C₂²	1	2	yes	—
82	C₆₁×#387	C₂²	1	2	yes	—
83	C₆₁×#387	C₂²	1	2	yes	—
84	C₆₁×#387	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×#385	C₂²	1	2	yes	—
90	C₆₁×#385	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×#383	C₂²	1	2	yes	—
96	C₆₁×#383	C₂²	1	1	yes	characteristic
97	C₆₁×#381	C₂²	1	2	yes	—
98	C₆₁×#380	C₂²	1	2	yes	—
99	C₆₁×#380	C₂²	1	2	yes	—
100	C₆₁×#380	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
106	C₆₁×#376	C₂²	1	1	yes	characteristic
107	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
108	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
111	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
112	#126×C₆₁	—	4	4	no	—
113	#126×C₆₁	—	4	4	no	—
114	#125×C₆₁	—	2	4	no	—
115	C₄×D₄×C₆₁	—	2	4	no	—
116	#117×C₆₁	—	2	4	no	—
117	#117×C₆₁	—	4	2	no	—
118	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
126	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
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	1	yes	characteristic
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×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
161	C₂×C₄²×C₆₁	—	4	2	no	—
162	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
164	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
165	C₂×C₄²×C₆₁	C₂³	1	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	1	yes	characteristic
169	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
170	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
171	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
172	#95×C₆₁	C₂³	1	1	yes	characteristic
173	#95×C₆₁	C₂³	1	1	yes	characteristic
174	#95×C₆₁	C₂³	1	2	yes	—
175	#95×C₆₁	C₂³	1	2	yes	—
176	#95×C₆₁	C₂³	1	2	yes	—
177	#95×C₆₁	C₂³	1	2	yes	—
178	#95×C₆₁	C₂³	1	2	yes	—
179	#95×C₆₁	C₂³	1	2	yes	—
180	#95×C₆₁	C₂³	1	2	yes	—
181	#95×C₆₁	C₂³	1	2	yes	—
182	#95×C₆₁	C₂³	1	2	yes	—
183	#95×C₆₁	C₂³	1	2	yes	—
184	#95×C₆₁	C₂³	1	2	yes	—
185	#95×C₆₁	C₂³	1	2	yes	—
186	#95×C₆₁	C₂³	1	2	yes	—
187	#95×C₆₁	C₂³	1	2	yes	—
188	#95×C₆₁	C₂³	1	2	yes	—
189	#95×C₆₁	C₂³	1	2	yes	—
190	#95×C₆₁	C₂³	1	2	yes	—
191	#95×C₆₁	C₂³	1	2	yes	—
192	#95×C₆₁	C₂³	1	1	yes	characteristic
193	#95×C₆₁	C₂³	1	1	yes	characteristic
194	#95×C₆₁	C₂³	1	2	yes	—
195	#95×C₆₁	C₂³	1	2	yes	—
196	#95×C₆₁	C₂³	1	2	yes	—
197	#95×C₆₁	C₂³	1	2	yes	—
198	#95×C₆₁	C₂³	1	2	yes	—
199	#95×C₆₁	C₂³	1	2	yes	—
200	#95×C₆₁	C₂³	1	2	yes	—
201	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
202	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
203	C₂×D₄×C₆₁	—	2	4	no	—
204	C₂×D₄×C₆₁	—	2	2	no	—
205	C₂×D₄×C₆₁	—	4	2	no	—
206	C₂×D₄×C₆₁	—	4	2	no	—
207	C₂×D₄×C₆₁	—	4	2	no	—
208	C₂²×C₄×C₆₁	—	2	2	no	—
209	C₂²×C₄×C₆₁	—	2	2	no	—
210	C₂²×C₄×C₆₁	—	2	2	no	—
211	C₂²×C₄×C₆₁	—	2	4	no	—
212	C₂²×C₄×C₆₁	—	4	2	no	—
213	C₂²×C₄×C₆₁	—	4	2	no	—
214	C₂²×C₄×C₆₁	—	4	2	no	—
215	C₂²×C₄×C₆₁	—	4	2	no	—
216	C₂²×C₄×C₆₁	—	4	2	no	—
217	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
234	C₄⋊C₄×C₆₁	—	2	2	no	—
235	C₄⋊C₄×C₆₁	—	2	2	no	—
236	C₄⋊C₄×C₆₁	—	2	2	no	—
237	C₄⋊C₄×C₆₁	—	2	4	no	—
238	C₄⋊C₄×C₆₁	—	2	4	no	—
239	C₄⋊C₄×C₆₁	—	2	2	no	—
240	C₄⋊C₄×C₆₁	—	2	2	no	—
241	C₄⋊C₄×C₆₁	—	2	4	no	—
242	C₄⋊C₄×C₆₁	—	2	4	no	—
243	C₄⋊C₄×C₆₁	—	4	2	no	—
244	C₄⋊C₄×C₆₁	—	4	2	no	—
245	C₄⋊C₄×C₆₁	—	4	2	no	—
246	C₄⋊C₄×C₆₁	—	4	2	no	—
247	C₄⋊C₄×C₆₁	—	4	2	no	—
248	C₄⋊C₄×C₆₁	—	4	2	no	—
249	C₄⋊C₄×C₆₁	—	4	2	no	—
250	C₄⋊C₄×C₆₁	—	4	2	no	—
251	C₄⋊C₄×C₆₁	—	4	2	no	—
252	C₄⋊C₄×C₆₁	—	4	2	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	—	4	2	no	—
258	C₄⋊C₄×C₆₁	—	4	2	no	—
259	C₂²⋊C₄×C₆₁	—	2	4	no	—
260	C₂²⋊C₄×C₆₁	—	2	2	no	—
261	C₂²⋊C₄×C₆₁	—	2	2	no	—
262	C₂²⋊C₄×C₆₁	—	2	4	no	—
263	C₂²⋊C₄×C₆₁	—	2	4	no	—
264	C₂²⋊C₄×C₆₁	—	4	2	no	—
265	C₂²⋊C₄×C₆₁	—	4	2	no	—
266	C₂²⋊C₄×C₆₁	—	4	2	no	—
267	C₂²⋊C₄×C₆₁	—	4	2	no	—
268	C₂²⋊C₄×C₆₁	—	4	2	no	—
269	C₂²⋊C₄×C₆₁	—	4	2	no	—
270	C₂²⋊C₄×C₆₁	—	4	2	no	—
271	C₂²⋊C₄×C₆₁	—	4	2	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	C₂²⋊C₄×C₆₁	—	4	2	no	—
277	C₄²×C₆₁	—	2	2	no	—
278	C₄²×C₆₁	—	2	4	no	—
279	C₄²×C₆₁	—	4	1	no	—
280	C₄²×C₆₁	—	4	1	no	—
281	C₄²×C₆₁	—	4	2	no	—
282	C₄²×C₆₁	—	4	2	no	—
283	C₄²×C₆₁	—	4	1	no	—
284	C₄²×C₆₁	—	4	1	no	—
285	C₄²×C₆₁	—	4	2	no	—
286	C₄²×C₆₁	#41	1	4	yes	—
287	C₂³×C₆₁	—	2	1	no	—
288	C₂³×C₆₁	—	2	1	no	—
289	C₂³×C₆₁	—	2	2	no	—
290	C₂³×C₆₁	—	2	2	no	—
291	C₂³×C₆₁	—	2	2	no	—
292	C₂³×C₆₁	—	2	2	no	—
293	C₂³×C₆₁	—	2	2	no	—
294	C₂³×C₆₁	—	2	2	no	—
295	C₂³×C₆₁	—	2	2	no	—
296	C₂³×C₆₁	—	2	2	no	—
297	C₂³×C₆₁	—	2	2	no	—
298	C₂³×C₆₁	2₋¹⁺⁴	1	2	yes	—
299	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
300	D₄×C₆₁	—	4	4	no	—
301	D₄×C₆₁	—	8	4	no	—
302	C₂×C₄×C₆₁	—	2	8	no	—
303	C₂×C₄×C₆₁	—	2	1	no	—
304	C₂×C₄×C₆₁	—	2	1	no	—
305	C₂×C₄×C₆₁	—	2	1	no	—
306	C₂×C₄×C₆₁	—	2	1	no	—
307	C₂×C₄×C₆₁	—	2	2	no	—
308	C₂×C₄×C₆₁	—	2	2	no	—
309	C₂×C₄×C₆₁	—	2	1	no	—
310	C₂×C₄×C₆₁	—	2	1	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	2	no	—
317	C₂×C₄×C₆₁	—	2	2	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	2	no	—
323	C₂×C₄×C₆₁	—	2	2	no	—
324	C₂×C₄×C₆₁	—	2	2	no	—
325	C₂×C₄×C₆₁	—	2	2	no	—
326	C₂×C₄×C₆₁	—	2	2	no	—
327	C₂×C₄×C₆₁	—	2	2	no	—
328	C₂×C₄×C₆₁	—	2	2	no	—
329	C₂×C₄×C₆₁	—	2	2	no	—
330	C₂×C₄×C₆₁	—	2	2	no	—
331	C₂×C₄×C₆₁	—	2	2	no	—
332	C₂×C₄×C₆₁	—	2	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	—	4	8	no	—
347	C₂×C₄×C₆₁	—	8	4	no	—
348	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
349	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
350	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
351	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
352	#36831	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
353	C₂²×C₆₁	—	2	2	no	—
354	C₂²×C₆₁	—	2	4	no	—
355	C₂²×C₆₁	—	4	1	no	—
356	C₂²×C₆₁	—	4	1	no	—
357	C₂²×C₆₁	—	4	2	no	—
358	C₂²×C₆₁	—	4	2	no	—
359	C₂²×C₆₁	—	4	2	no	—
360	C₂²×C₆₁	—	4	2	no	—
361	C₂²×C₆₁	—	4	2	no	—
362	C₂²×C₆₁	—	4	2	no	—
363	C₂²×C₆₁	—	4	2	no	—
364	C₂²×C₆₁	—	4	2	no	—
365	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
366	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
367	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
368	C₂²×C₆₁	#585	1	2	yes	—
369	C₂²×C₆₁	#585	1	2	yes	—
370	C₄×C₆₁	—	2	2	no	—
371	C₄×C₆₁	—	2	2	no	—
372	C₄×C₆₁	—	2	2	no	—
373	C₄×C₆₁	—	2	2	no	—
374	C₄×C₆₁	—	4	1	no	—
375	C₄×C₆₁	—	4	2	no	—
376	C₄×C₆₁	—	4	2	no	—
377	C₄×C₆₁	—	4	1	no	—
378	C₄×C₆₁	—	4	2	no	—
379	C₄×C₆₁	—	4	2	no	—
380	C₄×C₆₁	—	4	2	no	—
381	C₄×C₆₁	—	4	2	no	—
382	C₄×C₆₁	—	4	2	no	—
383	C₄×C₆₁	—	4	2	no	—
384	C₄×C₆₁	—	4	2	no	—
385	C₄×C₆₁	—	4	2	no	—
386	C₄×C₆₁	—	4	2	no	—
387	#2852	C₂×C₆₁	1	2	yes	complemented
388	#2807	C₂×C₆₁	1	2	yes	complemented
389	#2797	C₂×C₆₁	1	2	yes	—
390	#2776	C₂×C₆₁	1	2	yes	complemented
391	#2748	C₂×C₆₁	1	2	yes	complemented
392	#2746	C₂×C₆₁	1	2	yes	complemented
393	#2738	C₂×C₆₁	1	2	yes	complemented
394	#2727	C₂×C₆₁	1	2	yes	complemented
395	#2722	C₂×C₆₁	1	2	yes	complemented
396	#2654	C₂×C₆₁	1	2	yes	complemented
397	#2611	C₂×C₆₁	1	1	yes	characteristic, complemented
398	#2606	C₂×C₆₁	1	1	yes	characteristic, complemented
399	#2598	C₂×C₆₁	1	1	yes	characteristic
400	#2594	C₂×C₆₁	1	2	yes	complemented
401	#2562	C₂×C₆₁	1	1	yes	characteristic, complemented
402	#2479	C₂×C₆₁	1	2	yes	complemented
403	#2336	C₂×C₆₁	1	1	yes	characteristic, complemented
404	#2319	C₂×C₆₁	1	1	yes	characteristic, complemented
405	#2296	C₂×C₆₁	1	1	yes	characteristic, complemented
406	C₂×C₆₁	—	4	2	no	—
407	C₂×C₆₁	—	8	2	no	—
408	C₂×C₆₁	#3455	1	1	yes	characteristic
409	C₂×C₆₁	#3492	1	1	yes	characteristic
410	C₂×C₆₁	#3510	1	1	yes	characteristic
411	C₂×C₆₁	#3539	1	2	yes	—
412	C₂×C₆₁	#3564	1	2	yes	—
413	C₂×#126	C₂²×C₆₁	1	2	yes	—
414	C₂×#126	C₂²×C₆₁	1	2	yes	—
415	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
416	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
417	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
418	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
419	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
420	#401	C₂²×C₆₁	1	2	yes	—
421	#400	C₂²×C₆₁	1	2	yes	—
422	#400	C₂²×C₆₁	1	1	yes	characteristic
423	#400	C₂²×C₆₁	1	1	yes	characteristic
424	#400	C₂²×C₆₁	1	2	yes	—
425	#400	C₂²×C₆₁	1	2	yes	—
426	#399	C₂²×C₆₁	1	1	yes	characteristic
427	#399	C₂²×C₆₁	1	1	yes	characteristic
428	#399	C₂²×C₆₁	1	2	yes	—
429	#399	C₂²×C₆₁	1	2	yes	—
430	#399	C₂²×C₆₁	1	2	yes	—
431	#398	C₂²×C₆₁	1	2	yes	—
432	#398	C₂²×C₆₁	1	2	yes	—
433	#398	C₂²×C₆₁	1	2	yes	—
434	#398	C₂²×C₆₁	1	1	yes	characteristic
435	#398	C₂²×C₆₁	1	2	yes	—
436	#398	C₂²×C₆₁	1	2	yes	—
437	#398	C₂²×C₆₁	1	2	yes	—
438	#397	C₂²×C₆₁	1	2	yes	—
439	#397	C₂²×C₆₁	1	1	yes	characteristic
440	#397	C₂²×C₆₁	1	2	yes	—
441	#397	C₂²×C₆₁	1	2	yes	—
442	#396	C₂²×C₆₁	1	2	yes	—
443	#396	C₂²×C₆₁	1	2	yes	—
444	#394	C₂²×C₆₁	1	2	yes	—
445	#394	C₂²×C₆₁	1	1	yes	characteristic
446	#394	C₂²×C₆₁	1	2	yes	—
447	#392	C₂²×C₆₁	1	1	yes	characteristic
448	#390	C₂²×C₆₁	1	2	yes	—
449	#390	C₂²×C₆₁	1	2	yes	—
450	#389	C₂²×C₆₁	1	2	yes	—
451	#389	C₂²×C₆₁	1	2	yes	—
452	#389	C₂²×C₆₁	1	2	yes	—
453	#389	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	#389	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	#387	C₂²×C₆₁	1	2	yes	—
469	#387	C₂²×C₆₁	1	2	yes	—
470	#387	C₂²×C₆₁	1	2	yes	—
471	#387	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	#386	C₂²×C₆₁	1	2	yes	—
479	#386	C₂²×C₆₁	1	2	yes	—
480	#386	C₂²×C₆₁	1	2	yes	—
481	#386	C₂²×C₆₁	1	2	yes	—
482	#385	C₂²×C₆₁	1	2	yes	—
483	#385	C₂²×C₆₁	1	2	yes	—
484	#385	C₂²×C₆₁	1	2	yes	—
485	#385	C₂²×C₆₁	1	2	yes	—
486	#385	C₂²×C₆₁	1	2	yes	—
487	#385	C₂²×C₆₁	1	2	yes	—
488	#383	C₂²×C₆₁	1	1	yes	characteristic
489	#383	C₂²×C₆₁	1	2	yes	—
490	#381	C₂²×C₆₁	1	2	yes	—
491	#380	C₂²×C₆₁	1	2	yes	—
492	#380	C₂²×C₆₁	1	2	yes	—
493	#380	C₂²×C₆₁	1	2	yes	—
494	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
495	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
496	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
497	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
498	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
499	#376	C₂²×C₆₁	1	1	yes	characteristic
500	C₆₁	#36831	1	1	yes	characteristic, direct product factor, Sylow
501	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
502	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
503	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
504	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
505	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
506	#126	—	4	4	no	—
507	#126	—	4	4	no	—
508	#125	—	2	4	no	—
509	C₄×D₄	—	2	4	no	—
510	#117	—	2	4	no	—
511	#117	—	4	2	no	—
512	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
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	2	yes	—
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	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
538	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
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×C₄²	—	4	2	no	—
556	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
557	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
558	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
559	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
561	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
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	1	yes	characteristic
566	#95	C₂³×C₆₁	1	1	yes	characteristic
567	#95	C₂³×C₆₁	1	1	yes	characteristic
568	#95	C₂³×C₆₁	1	2	yes	—
569	#95	C₂³×C₆₁	1	2	yes	—
570	#95	C₂³×C₆₁	1	2	yes	—
571	#95	C₂³×C₆₁	1	2	yes	—
572	#95	C₂³×C₆₁	1	2	yes	—
573	#95	C₂³×C₆₁	1	2	yes	—
574	#95	C₂³×C₆₁	1	2	yes	—
575	#95	C₂³×C₆₁	1	2	yes	—
576	#95	C₂³×C₆₁	1	2	yes	—
577	#95	C₂³×C₆₁	1	2	yes	—
578	#95	C₂³×C₆₁	1	2	yes	—
579	#95	C₂³×C₆₁	1	2	yes	—
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	1	yes	characteristic
587	#95	C₂³×C₆₁	1	1	yes	characteristic
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	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
596	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	4	2	no	—
600	C₂×D₄	—	4	2	no	—
601	C₂×D₄	—	4	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	4	2	no	—
607	C₂²×C₄	—	4	2	no	—
608	C₂²×C₄	—	4	2	no	—
609	C₂²×C₄	—	4	2	no	—
610	C₂²×C₄	—	4	2	no	—
611	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
622	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
625	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	4	2	no	—
638	C₄⋊C₄	—	4	2	no	—
639	C₄⋊C₄	—	4	2	no	—
640	C₄⋊C₄	—	4	2	no	—
641	C₄⋊C₄	—	4	2	no	—
642	C₄⋊C₄	—	4	2	no	—
643	C₄⋊C₄	—	4	2	no	—
644	C₄⋊C₄	—	4	2	no	—
645	C₄⋊C₄	—	4	2	no	—
646	C₄⋊C₄	—	4	2	no	—
647	C₄⋊C₄	—	4	2	no	—
648	C₄⋊C₄	—	4	2	no	—
649	C₄⋊C₄	—	4	2	no	—
650	C₄⋊C₄	—	4	2	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	—	4	2	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	4	2	no	—
659	C₂²⋊C₄	—	4	2	no	—
660	C₂²⋊C₄	—	4	2	no	—
661	C₂²⋊C₄	—	4	2	no	—
662	C₂²⋊C₄	—	4	2	no	—
663	C₂²⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	—	4	2	no	—
665	C₂²⋊C₄	—	4	2	no	—
666	C₂²⋊C₄	—	4	2	no	—
667	C₂²⋊C₄	—	4	2	no	—
668	C₂²⋊C₄	—	4	2	no	—
669	C₂²⋊C₄	—	4	2	no	—
670	C₂²⋊C₄	—	4	2	no	—
671	C₄²	—	2	2	no	—
672	C₄²	—	2	4	no	—
673	C₄²	—	4	1	no	—
674	C₄²	—	4	1	no	—
675	C₄²	—	4	1	no	—
676	C₄²	—	4	1	no	—
677	C₄²	—	4	2	no	—
678	C₄²	—	4	2	no	—
679	C₄²	—	4	2	no	—
680	C₄²	#41×C₆₁	1	4	yes	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	2₋¹⁺⁴×C₆₁	1	2	yes	—
693	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
694	D₄	—	4	4	no	—
695	D₄	—	8	4	no	—
696	C₂×C₄	—	2	8	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	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	2	no	—
719	C₂×C₄	—	2	2	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	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	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	—	4	8	no	—
741	C₂×C₄	—	8	4	no	—
742	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
743	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
744	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
745	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
746	C₂²	—	2	4	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	4	1	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
759	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
760	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
761	C₂²	C₆₁×#585	1	2	yes	—
762	C₂²	C₆₁×#585	1	2	yes	—
763	C₄	—	2	2	no	—
764	C₄	—	2	2	no	—
765	C₄	—	2	2	no	—
766	C₄	—	2	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	1	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	1	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	2	no	—
780	C₂	—	4	2	no	—
781	C₂	—	8	2	no	—
782	C₂	C₆₁×#3455	1	1	yes	characteristic
783	C₂	C₆₁×#3492	1	1	yes	characteristic
784	C₂	C₆₁×#3510	1	1	yes	characteristic
785	C₂	C₆₁×#3539	1	2	yes	—
786	C₂	C₆₁×#3564	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₆₁×#2852	C₂	semidirect
2. C₆₁×#2807	C₂	semidirect
4. C₆₁×#2776	C₂	semidirect
5. C₆₁×#2748	C₂	semidirect
6. C₆₁×#2746	C₂	semidirect
7. C₆₁×#2738	C₂	semidirect
8. C₆₁×#2727	C₂	semidirect
9. C₆₁×#2722	C₂	semidirect
10. C₆₁×#2654	C₂	semidirect
11. C₆₁×#2611	C₂	semidirect
12. C₆₁×#2606	C₂	semidirect
14. C₆₁×#2594	C₂	semidirect
15. C₆₁×#2562	C₂	semidirect
16. C₆₁×#2479	C₂	semidirect
17. C₆₁×#2336	C₂	semidirect
18. C₆₁×#2319	C₂	semidirect
19. C₆₁×#2296	C₂	semidirect
352. #36831	C₆₁	direct (N × H)
387. #2852	C₂×C₆₁	semidirect
388. #2807	C₂×C₆₁	semidirect
390. #2776	C₂×C₆₁	semidirect
391. #2748	C₂×C₆₁	semidirect
392. #2746	C₂×C₆₁	semidirect
393. #2738	C₂×C₆₁	semidirect
394. #2727	C₂×C₆₁	semidirect
395. #2722	C₂×C₆₁	semidirect
396. #2654	C₂×C₆₁	semidirect
397. #2611	C₂×C₆₁	semidirect
398. #2606	C₂×C₆₁	semidirect
400. #2594	C₂×C₆₁	semidirect
401. #2562	C₂×C₆₁	semidirect
402. #2479	C₂×C₆₁	semidirect
403. #2336	C₂×C₆₁	semidirect
404. #2319	C₂×C₆₁	semidirect
405. #2296	C₂×C₆₁	semidirect
500. C₆₁	#36831	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×#2852	2
C₆₁×#2807	2
C₆₁×#2797	2
C₆₁×#2776	2
C₆₁×#2748	2
C₆₁×#2746	2
C₆₁×#2738	2
C₆₁×#2727	2
C₆₁×#2722	2
C₆₁×#2654	2
C₆₁×#2611	2
C₆₁×#2606	2
C₆₁×#2598	2
C₆₁×#2594	2
C₆₁×#2562	2
C₆₁×#2479	2
C₆₁×#2336	2
C₆₁×#2319	2
C₆₁×#2296	2
#36831	61

Subgroups — C61×#36831 #29540264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#36831 #29540264