Subgroups — C₆₁×#62146 #29565579

Order 15616.

1700 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3482	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#3383	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3364	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3353	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3352	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3328	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3327	C₂	1	4	yes	maximal, complemented
9	C₆₁×#3255	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3252	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3233	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3230	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3104	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3079	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3078	C₂	1	2	yes	maximal, complemented
17	C₆₁×#2991	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#557	—	2	1	no	—
19	C₆₁×#557	C₂²	1	2	yes	—
20	C₆₁×#557	C₂²	1	1	yes	characteristic
21	C₆₁×#556	—	2	1	no	—
22	C₆₁×#556	—	2	1	no	—
23	C₆₁×#556	C₂²	1	1	yes	characteristic
24	C₆₁×#556	C₂²	1	2	yes	—
25	C₆₁×#552	—	2	2	no	—
26	C₆₁×#552	—	2	2	no	—
27	C₆₁×#552	C₂²	1	4	yes	—
28	C₆₁×#552	C₂²	1	2	yes	—
29	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₆₁×#548	C₂²	1	2	yes	—
31	C₆₁×#547	—	2	1	no	—
32	C₆₁×#547	C₂²	1	1	yes	characteristic
33	C₆₁×#541	—	2	2	no	—
34	C₆₁×#536	—	2	1	no	—
35	C₆₁×#533	—	2	1	no	—
36	C₆₁×#533	C₂²	1	2	yes	—
37	C₆₁×#533	C₂²	1	1	yes	characteristic
38	C₆₁×#533	C₂²	1	1	yes	characteristic
39	C₆₁×#533	C₂²	1	2	yes	—
40	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
41	C₆₁×#529	—	2	2	no	—
42	C₆₁×#529	C₂²	1	2	yes	—
43	C₆₁×#519	—	2	1	no	—
44	C₄×#41×C₆₁	—	2	1	no	—
45	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
46	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
48	C₆₁×#500	C₂²	1	2	yes	—
49	C₆₁×#499	C₂²	1	4	yes	—
50	C₆₁×#488	C₂²	1	4	yes	—
51	C₆₁×#487	C₂²	1	2	yes	—
52	C₆₁×#485	C₂²	1	4	yes	—
53	C₆₁×#485	C₂²	1	2	yes	—
54	C₆₁×#484	C₂²	1	4	yes	—
55	C₆₁×#484	C₂²	1	4	yes	—
56	C₆₁×#482	C₂²	1	4	yes	—
57	C₆₁×#479	C₂²	1	4	yes	—
58	C₆₁×#479	C₂²	1	4	yes	—
59	C₆₁×#479	C₂²	1	4	yes	—
60	C₆₁×#477	C₂²	1	2	yes	—
61	C₆₁×#477	C₂²	1	2	yes	—
62	C₆₁×#477	C₂²	1	2	yes	—
63	C₆₁×#476	C₂²	1	2	yes	—
64	C₆₁×#475	C₂²	1	2	yes	—
65	C₆₁×#475	C₂²	1	1	yes	characteristic
66	C₆₁×#475	C₂²	1	2	yes	—
67	C₆₁×#475	C₂²	1	2	yes	—
68	C₆₁×#474	C₂²	1	2	yes	—
69	C₆₁×#474	C₂²	1	1	yes	characteristic
70	C₆₁×#470	C₂²	1	4	yes	—
71	C₆₁×#470	C₂²	1	4	yes	—
72	C₆₁×#468	C₂²	1	4	yes	—
73	C₆₁×#464	C₂²	1	4	yes	—
74	C₆₁×#462	C₂²	1	2	yes	—
75	C₆₁×#462	C₂²	1	1	yes	characteristic
76	C₆₁×#462	C₂²	1	2	yes	—
77	C₆₁×#461	C₂²	1	1	yes	characteristic
78	C₆₁×#452	C₂²	1	2	yes	—
79	C₆₁×#451	C₂²	1	4	yes	—
80	C₈×Q₈×C₆₁	C₂²	1	2	yes	—
81	C₄×Q₁₆×C₆₁	C₂²	1	4	yes	—
82	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
83	C₄×Q₁₆×C₆₁	C₂²	1	4	yes	—
84	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
85	C₆₁×#436	C₂²	1	4	yes	—
86	C₆₁×#436	C₂²	1	2	yes	—
87	C₆₁×#431	C₂²	1	2	yes	—
88	C₆₁×#431	C₂²	1	1	yes	characteristic
89	C₆₁×#428	C₂²	1	4	yes	—
90	C₆₁×#428	C₂²	1	2	yes	—
91	C₆₁×#423	C₂²	1	2	yes	—
92	C₆₁×#423	C₂²	1	1	yes	characteristic
93	C₆₁×#419	C₂²	1	4	yes	—
94	C₆₁×#417	C₂²	1	2	yes	—
95	C₂×#41×C₆₁	—	2	1	no	—
96	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
97	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₆₁	—	2	1	no	—
99	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
100	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
101	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
103	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
104	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
105	C₄⋊Q₈×C₆₁	—	2	1	no	—
106	C₄⋊Q₈×C₆₁	—	2	2	no	—
107	C₄⋊Q₈×C₆₁	—	2	1	no	—
108	C₄⋊Q₈×C₆₁	—	2	1	no	—
109	C₄⋊Q₈×C₆₁	—	2	1	no	—
110	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
111	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
116	#126×C₆₁	—	2	2	no	—
117	#126×C₆₁	—	2	4	no	—
118	#126×C₆₁	—	2	4	no	—
119	#126×C₆₁	—	2	2	no	—
120	#126×C₆₁	—	2	2	no	—
121	#125×C₆₁	—	2	2	no	—
122	#125×C₆₁	—	2	4	no	—
123	#125×C₆₁	—	2	4	no	—
124	#125×C₆₁	—	2	2	no	—
125	#125×C₆₁	—	2	1	no	—
126	#125×C₆₁	—	2	1	no	—
127	#125×C₆₁	—	2	2	no	—
128	#125×C₆₁	C₂³	1	4	yes	—
129	#125×C₆₁	C₂³	1	2	yes	—
130	#124×C₆₁	—	2	2	no	—
131	#124×C₆₁	—	2	2	no	—
132	#124×C₆₁	C₂³	1	2	yes	—
133	#123×C₆₁	—	2	4	no	—
134	#123×C₆₁	—	2	2	no	—
135	#123×C₆₁	—	2	2	no	—
136	#123×C₆₁	—	2	2	no	—
137	C₂²⋊Q₈×C₆₁	—	2	1	no	—
138	C₂²⋊Q₈×C₆₁	—	2	2	no	—
139	C₂²⋊Q₈×C₆₁	—	2	2	no	—
140	C₂²⋊Q₈×C₆₁	—	2	1	no	—
141	C₂²⋊Q₈×C₆₁	—	2	1	no	—
142	C₂²⋊Q₈×C₆₁	—	2	2	no	—
143	C₂²⋊Q₈×C₆₁	—	2	1	no	—
144	C₂²⋊Q₈×C₆₁	—	2	2	no	—
145	C₂²⋊Q₈×C₆₁	—	2	2	no	—
146	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
147	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
148	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
149	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
150	#121×C₆₁	—	2	2	no	—
151	#121×C₆₁	C₂³	1	2	yes	—
152	C₄×Q₈×C₆₁	—	2	1	no	—
153	C₄×Q₈×C₆₁	—	2	2	no	—
154	C₄×Q₈×C₆₁	—	2	2	no	—
155	C₄×Q₈×C₆₁	—	2	1	no	—
156	C₄×Q₈×C₆₁	—	2	2	no	—
157	C₄×Q₈×C₆₁	—	2	2	no	—
158	C₄×Q₈×C₆₁	—	2	2	no	—
159	C₄×Q₈×C₆₁	—	2	2	no	—
160	C₄×Q₈×C₆₁	—	2	1	no	—
161	C₄×Q₈×C₆₁	—	2	2	no	—
162	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
163	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
164	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
165	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
166	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
167	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
169	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
171	C₄×D₄×C₆₁	—	2	1	no	—
172	C₄×D₄×C₆₁	—	2	1	no	—
173	C₄×D₄×C₆₁	—	2	2	no	—
174	C₄×D₄×C₆₁	—	2	1	no	—
175	C₄×D₄×C₆₁	—	2	2	no	—
176	C₄×D₄×C₆₁	D₄	1	2	yes	—
177	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
178	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₆₁	C₂³	1	2	yes	—
182	#117×C₆₁	—	2	1	no	—
183	#117×C₆₁	—	2	2	no	—
184	#117×C₆₁	—	2	1	no	—
185	#117×C₆₁	—	2	1	no	—
186	#117×C₆₁	—	2	2	no	—
187	#117×C₆₁	—	2	4	no	—
188	#117×C₆₁	—	2	2	no	—
189	#117×C₆₁	—	2	1	no	—
190	#117×C₆₁	D₄	1	2	yes	—
191	#117×C₆₁	D₄	1	1	yes	characteristic
192	#117×C₆₁	C₂³	1	4	yes	—
193	#117×C₆₁	C₂³	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
195	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
196	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
198	C₂×C₄²×C₆₁	—	2	2	no	—
199	C₂×C₄²×C₆₁	—	2	1	no	—
200	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
202	#107×C₆₁	C₂³	1	4	yes	—
203	#107×C₆₁	C₂³	1	4	yes	—
204	#107×C₆₁	C₂³	1	2	yes	—
205	#107×C₆₁	C₂³	1	4	yes	—
206	#106×C₆₁	C₂³	1	2	yes	—
207	#106×C₆₁	C₂³	1	4	yes	—
208	#106×C₆₁	C₂³	1	4	yes	—
209	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
210	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
211	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
212	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
213	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
214	#103×C₆₁	C₂³	1	4	yes	—
215	#103×C₆₁	C₂³	1	2	yes	—
216	#103×C₆₁	C₂³	1	4	yes	—
217	#103×C₆₁	C₂³	1	4	yes	—
218	#103×C₆₁	C₂³	1	2	yes	—
219	#103×C₆₁	C₂³	1	4	yes	—
220	#103×C₆₁	C₂³	1	2	yes	—
221	#103×C₆₁	C₂³	1	4	yes	—
222	#102×C₆₁	C₂³	1	4	yes	—
223	#102×C₆₁	C₂³	1	2	yes	—
224	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
225	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
226	C₄×C₈×C₆₁	C₂³	1	2	yes	—
227	C₄×C₈×C₆₁	C₂³	1	4	yes	—
228	#41×C₆₁	—	2	2	no	—
229	#41×C₆₁	—	4	2	no	—
230	#41×C₆₁	—	4	1	no	—
231	#41×C₆₁	—	4	4	no	—
232	C₂×Q₈×C₆₁	—	2	1	no	—
233	C₂×Q₈×C₆₁	—	2	2	no	—
234	C₂×Q₈×C₆₁	—	2	2	no	—
235	C₂×Q₈×C₆₁	—	2	1	no	—
236	C₂×Q₈×C₆₁	—	2	2	no	—
237	C₂×Q₈×C₆₁	—	2	4	no	—
238	C₂×Q₈×C₆₁	—	4	2	no	—
239	C₂×Q₈×C₆₁	—	4	4	no	—
240	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
241	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
242	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
243	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
244	C₂×D₄×C₆₁	—	2	1	no	—
245	C₂×D₄×C₆₁	—	2	2	no	—
246	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
247	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
248	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₆₁	—	2	2	no	—
250	C₂²×C₄×C₆₁	—	2	2	no	—
251	C₂²×C₄×C₆₁	—	2	2	no	—
252	C₂²×C₄×C₆₁	—	2	1	no	—
253	C₂²×C₄×C₆₁	—	2	1	no	—
254	C₂²×C₄×C₆₁	—	2	1	no	—
255	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
256	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
259	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
261	Q₁₆×C₆₁	—	2	4	no	—
262	Q₁₆×C₆₁	—	4	4	no	—
263	SD₁₆×C₆₁	—	4	2	no	—
264	M₁₆×C₆₁	—	4	4	no	—
265	M₁₆×C₆₁	—	4	2	no	—
266	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
267	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
268	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
269	C₄⋊C₄×C₆₁	—	2	1	no	—
270	C₄⋊C₄×C₆₁	—	2	2	no	—
271	C₄⋊C₄×C₆₁	—	2	2	no	—
272	C₄⋊C₄×C₆₁	—	2	2	no	—
273	C₄⋊C₄×C₆₁	—	2	2	no	—
274	C₄⋊C₄×C₆₁	—	2	2	no	—
275	C₄⋊C₄×C₆₁	—	2	2	no	—
276	C₄⋊C₄×C₆₁	—	2	2	no	—
277	C₄⋊C₄×C₆₁	—	2	1	no	—
278	C₄⋊C₄×C₆₁	—	2	1	no	—
279	C₄⋊C₄×C₆₁	—	2	2	no	—
280	C₄⋊C₄×C₆₁	—	2	2	no	—
281	C₄⋊C₄×C₆₁	—	2	1	no	—
282	C₄⋊C₄×C₆₁	—	2	1	no	—
283	C₄⋊C₄×C₆₁	—	2	1	no	—
284	C₄⋊C₄×C₆₁	—	2	4	no	—
285	C₄⋊C₄×C₆₁	—	2	4	no	—
286	C₄⋊C₄×C₆₁	—	2	1	no	—
287	C₄⋊C₄×C₆₁	—	2	2	no	—
288	C₄⋊C₄×C₆₁	—	2	1	no	—
289	C₄⋊C₄×C₆₁	—	2	2	no	—
290	C₄⋊C₄×C₆₁	—	2	4	no	—
291	C₄⋊C₄×C₆₁	—	2	2	no	—
292	C₄⋊C₄×C₆₁	—	2	4	no	—
293	C₄⋊C₄×C₆₁	—	2	2	no	—
294	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
295	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
300	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
303	C₂²⋊C₄×C₆₁	—	2	2	no	—
304	C₂²⋊C₄×C₆₁	—	2	2	no	—
305	C₂²⋊C₄×C₆₁	—	2	2	no	—
306	C₂²⋊C₄×C₆₁	—	2	4	no	—
307	C₂²⋊C₄×C₆₁	—	2	1	no	—
308	C₂²⋊C₄×C₆₁	—	2	4	no	—
309	C₂²⋊C₄×C₆₁	—	2	2	no	—
310	C₂²⋊C₄×C₆₁	—	2	1	no	—
311	C₂²⋊C₄×C₆₁	—	2	1	no	—
312	C₂²⋊C₄×C₆₁	—	2	2	no	—
313	C₂²⋊C₄×C₆₁	—	2	2	no	—
314	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
315	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
316	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
317	C₄²×C₆₁	—	2	1	no	—
318	C₄²×C₆₁	—	2	1	no	—
319	C₄²×C₆₁	—	2	2	no	—
320	C₄²×C₆₁	—	2	2	no	—
321	C₄²×C₆₁	—	2	1	no	—
322	C₄²×C₆₁	—	2	2	no	—
323	C₄²×C₆₁	—	2	4	no	—
324	C₄²×C₆₁	—	2	4	no	—
325	C₄²×C₆₁	—	2	2	no	—
326	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₆₁	C₂×D₄	1	2	yes	—
329	C₄²×C₆₁	C₂×D₄	1	2	yes	—
330	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
331	C₄²×C₆₁	C₂⁴	1	2	yes	—
332	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
333	C₂³×C₆₁	—	2	1	no	—
334	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
335	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
336	Q₈×C₆₁	—	2	2	no	—
337	Q₈×C₆₁	—	2	1	no	—
338	Q₈×C₆₁	—	2	2	no	—
339	Q₈×C₆₁	—	2	2	no	—
340	Q₈×C₆₁	—	2	2	no	—
341	Q₈×C₆₁	—	2	2	no	—
342	Q₈×C₆₁	—	4	4	no	—
343	Q₈×C₆₁	—	4	4	no	—
344	Q₈×C₆₁	—	4	4	no	—
345	Q₈×C₆₁	—	4	2	no	—
346	Q₈×C₆₁	—	4	2	no	—
347	Q₈×C₆₁	2₋¹⁺⁴	1	2	yes	—
348	D₄×C₆₁	—	2	2	no	—
349	D₄×C₆₁	—	2	1	no	—
350	D₄×C₆₁	—	2	1	no	—
351	D₄×C₆₁	—	4	2	no	—
352	D₄×C₆₁	—	4	2	no	—
353	D₄×C₆₁	—	4	4	no	—
354	C₂×C₄×C₆₁	—	2	1	no	—
355	C₂×C₄×C₆₁	—	2	2	no	—
356	C₂×C₄×C₆₁	—	2	4	no	—
357	C₂×C₄×C₆₁	—	2	2	no	—
358	C₂×C₄×C₆₁	—	2	2	no	—
359	C₂×C₄×C₆₁	—	2	1	no	—
360	C₂×C₄×C₆₁	—	2	2	no	—
361	C₂×C₄×C₆₁	—	2	1	no	—
362	C₂×C₄×C₆₁	—	2	1	no	—
363	C₂×C₄×C₆₁	—	2	2	no	—
364	C₂×C₄×C₆₁	—	2	2	no	—
365	C₂×C₄×C₆₁	—	2	1	no	—
366	C₂×C₄×C₆₁	—	2	2	no	—
367	C₂×C₄×C₆₁	—	2	2	no	—
368	C₂×C₄×C₆₁	—	2	4	no	—
369	C₂×C₄×C₆₁	—	4	2	no	—
370	C₂×C₄×C₆₁	—	4	2	no	—
371	C₂×C₄×C₆₁	—	4	4	no	—
372	C₂×C₄×C₆₁	—	4	4	no	—
373	C₂×C₄×C₆₁	—	4	4	no	—
374	C₂×C₄×C₆₁	—	4	2	no	—
375	C₂×C₄×C₆₁	—	4	2	no	—
376	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
378	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
385	C₈×C₆₁	—	2	2	no	—
386	C₈×C₆₁	—	2	2	no	—
387	C₈×C₆₁	—	2	4	no	—
388	#62146	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
389	C₂²×C₆₁	—	2	2	no	—
390	C₂²×C₆₁	—	2	1	no	—
391	C₂²×C₆₁	—	2	1	no	—
392	C₂²×C₆₁	—	2	2	no	—
393	C₂²×C₆₁	—	2	2	no	—
394	C₂²×C₆₁	—	2	1	no	—
395	C₂²×C₆₁	—	4	1	no	—
396	C₂²×C₆₁	—	4	1	no	—
397	C₂²×C₆₁	—	4	1	no	—
398	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
399	C₄×C₆₁	—	2	1	no	—
400	C₄×C₆₁	—	2	2	no	—
401	C₄×C₆₁	—	2	2	no	—
402	C₄×C₆₁	—	2	1	no	—
403	C₄×C₆₁	—	2	2	no	—
404	C₄×C₆₁	—	2	2	no	—
405	C₄×C₆₁	—	2	1	no	—
406	C₄×C₆₁	—	4	2	no	—
407	C₄×C₆₁	—	4	2	no	—
408	C₄×C₆₁	—	4	1	no	—
409	C₄×C₆₁	—	4	2	no	—
410	C₄×C₆₁	—	4	4	no	—
411	C₄×C₆₁	—	4	1	no	—
412	C₄×C₆₁	—	4	2	no	—
413	C₄×C₆₁	#575	1	2	yes	—
414	C₄×C₆₁	#578	1	2	yes	—
415	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
416	C₄×C₆₁	#585	1	1	yes	characteristic
417	#3509	C₂×C₆₁	1	1	yes	characteristic, complemented
418	#3482	C₂×C₆₁	1	1	yes	characteristic
419	#3383	C₂×C₆₁	1	2	yes	complemented
420	#3364	C₂×C₆₁	1	2	yes	complemented
421	#3353	C₂×C₆₁	1	2	yes	complemented
422	#3352	C₂×C₆₁	1	4	yes	complemented
423	#3328	C₂×C₆₁	1	2	yes	complemented
424	#3327	C₂×C₆₁	1	4	yes	complemented
425	#3255	C₂×C₆₁	1	1	yes	characteristic, complemented
426	#3252	C₂×C₆₁	1	2	yes	complemented
427	#3233	C₂×C₆₁	1	2	yes	complemented
428	#3230	C₂×C₆₁	1	1	yes	characteristic, complemented
429	#3107	C₂×C₆₁	1	1	yes	characteristic, complemented
430	#3104	C₂×C₆₁	1	2	yes	complemented
431	#3079	C₂×C₆₁	1	1	yes	characteristic, complemented
432	#3078	C₂×C₆₁	1	2	yes	complemented
433	#2991	C₂×C₆₁	1	1	yes	characteristic, complemented
434	C₂×C₆₁	—	4	2	no	—
435	C₂×C₆₁	—	4	1	no	—
436	C₂×C₆₁	—	8	1	no	—
437	C₂×C₆₁	#3489	1	1	yes	characteristic
438	C₂×C₆₁	C₂×#575	1	1	yes	characteristic
439	C₂×C₆₁	C₂×#578	1	1	yes	characteristic
440	#557	—	2	1	no	—
441	#557	C₂²×C₆₁	1	2	yes	—
442	#557	C₂²×C₆₁	1	1	yes	characteristic
443	#556	—	2	1	no	—
444	#556	—	2	1	no	—
445	#556	C₂²×C₆₁	1	1	yes	characteristic
446	#556	C₂²×C₆₁	1	2	yes	—
447	#552	—	2	2	no	—
448	#552	—	2	2	no	—
449	#552	C₂²×C₆₁	1	2	yes	—
450	#552	C₂²×C₆₁	1	4	yes	—
451	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
452	#548	C₂²×C₆₁	1	2	yes	—
453	#547	—	2	1	no	—
454	#547	C₂²×C₆₁	1	1	yes	characteristic
455	#541	—	2	2	no	—
456	#536	—	2	1	no	—
457	#533	—	2	1	no	—
458	#533	C₂²×C₆₁	1	2	yes	—
459	#533	C₂²×C₆₁	1	1	yes	characteristic
460	#533	C₂²×C₆₁	1	1	yes	characteristic
461	#533	C₂²×C₆₁	1	2	yes	—
462	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
463	#529	—	2	2	no	—
464	#529	C₂²×C₆₁	1	2	yes	—
465	#519	—	2	1	no	—
466	C₄×#41	—	2	1	no	—
467	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
468	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
469	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
470	#500	C₂²×C₆₁	1	2	yes	—
471	#499	C₂²×C₆₁	1	4	yes	—
472	#488	C₂²×C₆₁	1	4	yes	—
473	#487	C₂²×C₆₁	1	2	yes	—
474	#485	C₂²×C₆₁	1	4	yes	—
475	#485	C₂²×C₆₁	1	2	yes	—
476	#484	C₂²×C₆₁	1	4	yes	—
477	#484	C₂²×C₆₁	1	4	yes	—
478	#482	C₂²×C₆₁	1	4	yes	—
479	#479	C₂²×C₆₁	1	4	yes	—
480	#479	C₂²×C₆₁	1	4	yes	—
481	#479	C₂²×C₆₁	1	4	yes	—
482	#477	C₂²×C₆₁	1	2	yes	—
483	#477	C₂²×C₆₁	1	2	yes	—
484	#477	C₂²×C₆₁	1	2	yes	—
485	#476	C₂²×C₆₁	1	2	yes	—
486	#475	C₂²×C₆₁	1	2	yes	—
487	#475	C₂²×C₆₁	1	1	yes	characteristic
488	#475	C₂²×C₆₁	1	2	yes	—
489	#475	C₂²×C₆₁	1	2	yes	—
490	#474	C₂²×C₆₁	1	2	yes	—
491	#474	C₂²×C₆₁	1	1	yes	characteristic
492	#470	C₂²×C₆₁	1	4	yes	—
493	#470	C₂²×C₆₁	1	4	yes	—
494	#468	C₂²×C₆₁	1	4	yes	—
495	#464	C₂²×C₆₁	1	4	yes	—
496	#462	C₂²×C₆₁	1	2	yes	—
497	#462	C₂²×C₆₁	1	1	yes	characteristic
498	#462	C₂²×C₆₁	1	2	yes	—
499	#461	C₂²×C₆₁	1	1	yes	characteristic
500	#452	C₂²×C₆₁	1	2	yes	—
501	#451	C₂²×C₆₁	1	4	yes	—
502	C₈×Q₈	C₂²×C₆₁	1	2	yes	—
503	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
504	C₄×Q₁₆	C₂²×C₆₁	1	4	yes	—
505	C₄×Q₁₆	C₂²×C₆₁	1	4	yes	—
506	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
507	#436	C₂²×C₆₁	1	2	yes	—
508	#436	C₂²×C₆₁	1	4	yes	—
509	#431	C₂²×C₆₁	1	2	yes	—
510	#431	C₂²×C₆₁	1	1	yes	characteristic
511	#428	C₂²×C₆₁	1	4	yes	—
512	#428	C₂²×C₆₁	1	2	yes	—
513	#423	C₂²×C₆₁	1	2	yes	—
514	#423	C₂²×C₆₁	1	1	yes	characteristic
515	#419	C₂²×C₆₁	1	4	yes	—
516	#417	C₂²×C₆₁	1	2	yes	—
517	C₆₁	#62146	1	1	yes	characteristic, direct product factor, Sylow
518	C₂×#41	—	2	1	no	—
519	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
520	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
521	C₂²×Q₈	—	2	1	no	—
522	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
523	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
524	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
525	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
526	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
527	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
528	C₄⋊Q₈	—	2	1	no	—
529	C₄⋊Q₈	—	2	2	no	—
530	C₄⋊Q₈	—	2	1	no	—
531	C₄⋊Q₈	—	2	1	no	—
532	C₄⋊Q₈	—	2	1	no	—
533	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
534	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
535	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
536	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
537	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
538	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
539	#126	—	2	2	no	—
540	#126	—	2	2	no	—
541	#126	—	2	4	no	—
542	#126	—	2	4	no	—
543	#126	—	2	2	no	—
544	#125	—	2	2	no	—
545	#125	—	2	2	no	—
546	#125	—	2	4	no	—
547	#125	—	2	4	no	—
548	#125	—	2	1	no	—
549	#125	—	2	1	no	—
550	#125	—	2	2	no	—
551	#125	C₂³×C₆₁	1	2	yes	—
552	#125	C₂³×C₆₁	1	4	yes	—
553	#124	—	2	2	no	—
554	#124	—	2	2	no	—
555	#124	C₂³×C₆₁	1	2	yes	—
556	#123	—	2	2	no	—
557	#123	—	2	4	no	—
558	#123	—	2	2	no	—
559	#123	—	2	2	no	—
560	C₂²⋊Q₈	—	2	1	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	1	no	—
564	C₂²⋊Q₈	—	2	1	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	1	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
570	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
571	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
572	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
573	#121	—	2	2	no	—
574	#121	C₂³×C₆₁	1	2	yes	—
575	C₄×Q₈	—	2	1	no	—
576	C₄×Q₈	—	2	2	no	—
577	C₄×Q₈	—	2	2	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	—	2	2	no	—
580	C₄×Q₈	—	2	1	no	—
581	C₄×Q₈	—	2	2	no	—
582	C₄×Q₈	—	2	2	no	—
583	C₄×Q₈	—	2	2	no	—
584	C₄×Q₈	—	2	1	no	—
585	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
586	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
587	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
588	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
589	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
590	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
591	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
592	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
593	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
600	C₄×D₄	D₄×C₆₁	1	2	yes	—
601	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
602	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
603	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
604	C₄×D₄	C₂³×C₆₁	1	2	yes	—
605	#117	—	2	1	no	—
606	#117	—	2	1	no	—
607	#117	—	2	2	no	—
608	#117	—	2	1	no	—
609	#117	—	2	2	no	—
610	#117	—	2	4	no	—
611	#117	—	2	1	no	—
612	#117	—	2	2	no	—
613	#117	D₄×C₆₁	1	1	yes	characteristic
614	#117	D₄×C₆₁	1	2	yes	—
615	#117	C₂³×C₆₁	1	1	yes	characteristic
616	#117	C₂³×C₆₁	1	4	yes	—
617	C₂×C₄⋊C₄	—	2	2	no	—
618	C₂×C₄⋊C₄	—	2	1	no	—
619	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
621	C₂×C₄²	—	2	2	no	—
622	C₂×C₄²	—	2	1	no	—
623	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
624	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
625	#107	C₂³×C₆₁	1	4	yes	—
626	#107	C₂³×C₆₁	1	4	yes	—
627	#107	C₂³×C₆₁	1	2	yes	—
628	#107	C₂³×C₆₁	1	4	yes	—
629	#106	C₂³×C₆₁	1	2	yes	—
630	#106	C₂³×C₆₁	1	4	yes	—
631	#106	C₂³×C₆₁	1	4	yes	—
632	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
633	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
634	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
635	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
636	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
637	#103	C₂³×C₆₁	1	4	yes	—
638	#103	C₂³×C₆₁	1	2	yes	—
639	#103	C₂³×C₆₁	1	4	yes	—
640	#103	C₂³×C₆₁	1	4	yes	—
641	#103	C₂³×C₆₁	1	2	yes	—
642	#103	C₂³×C₆₁	1	4	yes	—
643	#103	C₂³×C₆₁	1	2	yes	—
644	#103	C₂³×C₆₁	1	4	yes	—
645	#102	C₂³×C₆₁	1	4	yes	—
646	#102	C₂³×C₆₁	1	2	yes	—
647	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
648	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
649	C₄×C₈	C₂³×C₆₁	1	2	yes	—
650	C₄×C₈	C₂³×C₆₁	1	4	yes	—
651	#41	—	2	2	no	—
652	#41	—	4	2	no	—
653	#41	—	4	1	no	—
654	#41	—	4	4	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	2	no	—
657	C₂×Q₈	—	2	2	no	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	2	no	—
660	C₂×Q₈	—	2	4	no	—
661	C₂×Q₈	—	4	2	no	—
662	C₂×Q₈	—	4	4	no	—
663	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
664	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
665	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
666	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
670	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
671	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
679	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
684	Q₁₆	—	2	4	no	—
685	Q₁₆	—	4	4	no	—
686	SD₁₆	—	4	2	no	—
687	M₁₆	—	4	4	no	—
688	M₁₆	—	4	2	no	—
689	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
690	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
691	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
718	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
719	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
720	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
721	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
722	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
723	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
724	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
725	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	1	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
738	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
739	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
740	C₄²	—	2	1	no	—
741	C₄²	—	2	1	no	—
742	C₄²	—	2	2	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	1	no	—
745	C₄²	—	2	2	no	—
746	C₄²	—	2	4	no	—
747	C₄²	—	2	4	no	—
748	C₄²	—	2	2	no	—
749	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
750	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
751	C₄²	C₂×D₄×C₆₁	1	2	yes	—
752	C₄²	C₂×D₄×C₆₁	1	2	yes	—
753	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
754	C₄²	C₂⁴×C₆₁	1	2	yes	—
755	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
756	C₂³	—	2	1	no	—
757	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
758	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
759	Q₈	—	2	2	no	—
760	Q₈	—	2	1	no	—
761	Q₈	—	2	2	no	—
762	Q₈	—	2	2	no	—
763	Q₈	—	2	2	no	—
764	Q₈	—	2	2	no	—
765	Q₈	—	4	4	no	—
766	Q₈	—	4	4	no	—
767	Q₈	—	4	4	no	—
768	Q₈	—	4	2	no	—
769	Q₈	—	4	2	no	—
770	Q₈	2₋¹⁺⁴×C₆₁	1	2	yes	—
771	D₄	—	2	2	no	—
772	D₄	—	2	1	no	—
773	D₄	—	2	1	no	—
774	D₄	—	4	2	no	—
775	D₄	—	4	2	no	—
776	D₄	—	4	4	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	4	no	—
792	C₂×C₄	—	4	2	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	4	4	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	—	4	4	no	—
797	C₂×C₄	—	4	2	no	—
798	C₂×C₄	—	4	2	no	—
799	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
800	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
801	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
803	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
805	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
806	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
807	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
808	C₈	—	2	2	no	—
809	C₈	—	2	2	no	—
810	C₈	—	2	4	no	—
811	C₂²	—	2	1	no	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	4	1	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	1	no	—
820	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
821	C₄	—	2	1	no	—
822	C₄	—	2	2	no	—
823	C₄	—	2	2	no	—
824	C₄	—	2	1	no	—
825	C₄	—	2	1	no	—
826	C₄	—	2	2	no	—
827	C₄	—	2	2	no	—
828	C₄	—	4	1	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	4	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	C₆₁×#575	1	2	yes	—
836	C₄	C₆₁×#578	1	2	yes	—
837	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
838	C₄	C₆₁×#585	1	1	yes	characteristic
839	C₂	—	4	1	no	—
840	C₂	—	4	2	no	—
841	C₂	—	8	1	no	—
842	C₂	C₆₁×#3489	1	1	yes	characteristic
843	C₂	C₂×C₆₁×#575	1	1	yes	characteristic
844	C₂	C₂×C₆₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3482	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₄×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3509	C₂	semidirect
3. C₆₁×#3383	C₂	semidirect
4. C₆₁×#3364	C₂	semidirect
5. C₆₁×#3353	C₂	semidirect
6. C₆₁×#3352	C₂	semidirect
7. C₆₁×#3328	C₂	semidirect
8. C₆₁×#3327	C₂	semidirect
9. C₆₁×#3255	C₂	semidirect
10. C₆₁×#3252	C₂	semidirect
11. C₆₁×#3233	C₂	semidirect
12. C₆₁×#3230	C₂	semidirect
13. C₆₁×#3107	C₂	semidirect
14. C₆₁×#3104	C₂	semidirect
15. C₆₁×#3079	C₂	semidirect
16. C₆₁×#3078	C₂	semidirect
17. C₆₁×#2991	C₂	semidirect
388. #62146	C₆₁	direct (N × H)
417. #3509	C₂×C₆₁	semidirect
419. #3383	C₂×C₆₁	semidirect
420. #3364	C₂×C₆₁	semidirect
421. #3353	C₂×C₆₁	semidirect
422. #3352	C₂×C₆₁	semidirect
423. #3328	C₂×C₆₁	semidirect
424. #3327	C₂×C₆₁	semidirect
425. #3255	C₂×C₆₁	semidirect
426. #3252	C₂×C₆₁	semidirect
427. #3233	C₂×C₆₁	semidirect
428. #3230	C₂×C₆₁	semidirect
429. #3107	C₂×C₆₁	semidirect
430. #3104	C₂×C₆₁	semidirect
431. #3079	C₂×C₆₁	semidirect
432. #3078	C₂×C₆₁	semidirect
433. #2991	C₂×C₆₁	semidirect
517. C₆₁	#62146	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×#3509	2
C₆₁×#3482	2
C₆₁×#3383	2
C₆₁×#3364	2
C₆₁×#3353	2
C₆₁×#3352	2
C₆₁×#3328	2
C₆₁×#3327	2
C₆₁×#3255	2
C₆₁×#3252	2
C₆₁×#3233	2
C₆₁×#3230	2
C₆₁×#3107	2
C₆₁×#3104	2
C₆₁×#3079	2
C₆₁×#3078	2
C₆₁×#2991	2
#62146	61

Subgroups — C61×#62146 #29565579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62146 #29565579