Subgroups — C₆₁×#61878 #29565311

Order 15616.

1656 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3387	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3386	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3385	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3384	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3377	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3376	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3371	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3370	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3244	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3243	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3236	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3234	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3125	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3124	C₂	1	2	yes	maximal, complemented
17	C₆₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#3115	C₂	1	1	yes	maximal, characteristic
19	C₆₁×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#563	—	2	1	no	—
21	C₆₁×#563	—	2	1	no	—
22	C₆₁×#559	C₂²	1	2	yes	—
23	Q₈²×C₆₁	C₂²	1	2	yes	—
24	C₆₁×#557	C₂²	1	2	yes	—
25	C₆₁×#557	C₂²	1	2	yes	—
26	C₆₁×#556	—	2	1	no	—
27	C₆₁×#556	C₂²	1	2	yes	—
28	C₆₁×#554	—	2	2	no	—
29	C₆₁×#554	—	2	2	no	—
30	C₆₁×#554	C₂²	1	2	yes	—
31	C₆₁×#554	C₂²	1	2	yes	—
32	D₄×Q₈×C₆₁	—	2	1	no	—
33	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
34	C₆₁×#544	—	2	1	no	—
35	C₆₁×#544	—	2	1	no	—
36	C₆₁×#544	C₂²	1	1	yes	characteristic
37	C₆₁×#544	C₂²	1	1	yes	characteristic
38	C₆₁×#542	—	2	2	no	—
39	C₆₁×#542	C₂²	1	2	yes	—
40	C₆₁×#542	C₂²	1	2	yes	—
41	C₆₁×#536	—	2	2	no	—
42	C₆₁×#533	—	2	1	no	—
43	C₆₁×#533	C₂²	1	1	yes	characteristic
44	C₆₁×#533	C₂²	1	1	yes	characteristic
45	C₆₁×#532	C₂²	1	1	yes	characteristic
46	C₂×#125×C₆₁	—	2	1	no	—
47	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
48	C₆₁×#520	C₂²	1	1	yes	characteristic
49	C₆₁×#520	C₂²	1	1	yes	characteristic
50	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
51	C₆₁×#501	C₂²	1	2	yes	—
52	C₆₁×#501	C₂²	1	2	yes	—
53	C₆₁×#501	C₂²	1	2	yes	—
54	C₆₁×#501	C₂²	1	2	yes	—
55	C₆₁×#500	C₂²	1	2	yes	—
56	C₆₁×#498	C₂²	1	2	yes	—
57	C₆₁×#491	C₂²	1	2	yes	—
58	C₆₁×#490	C₂²	1	2	yes	—
59	C₆₁×#489	C₂²	1	2	yes	—
60	C₆₁×#489	C₂²	1	2	yes	—
61	C₆₁×#488	C₂²	1	2	yes	—
62	C₆₁×#488	C₂²	1	2	yes	—
63	C₆₁×#485	C₂²	1	2	yes	—
64	C₆₁×#484	C₂²	1	2	yes	—
65	C₆₁×#483	C₂²	1	2	yes	—
66	C₆₁×#482	C₂²	1	2	yes	—
67	C₆₁×#481	C₂²	1	2	yes	—
68	C₆₁×#480	C₂²	1	2	yes	—
69	C₆₁×#479	C₂²	1	2	yes	—
70	C₆₁×#479	C₂²	1	2	yes	—
71	C₆₁×#479	C₂²	1	2	yes	—
72	C₆₁×#479	C₂²	1	2	yes	—
73	C₆₁×#478	C₂²	1	2	yes	—
74	C₆₁×#478	C₂²	1	2	yes	—
75	C₆₁×#478	C₂²	1	2	yes	—
76	C₆₁×#478	C₂²	1	2	yes	—
77	C₆₁×#477	C₂²	1	1	yes	characteristic
78	C₆₁×#477	C₂²	1	2	yes	—
79	C₆₁×#477	C₂²	1	2	yes	—
80	C₆₁×#476	C₂²	1	2	yes	—
81	C₆₁×#476	C₂²	1	1	yes	characteristic
82	C₆₁×#476	C₂²	1	2	yes	—
83	C₆₁×#475	C₂²	1	1	yes	characteristic
84	C₆₁×#475	C₂²	1	2	yes	—
85	C₆₁×#475	C₂²	1	2	yes	—
86	C₆₁×#474	C₂²	1	2	yes	—
87	C₆₁×#474	C₂²	1	1	yes	characteristic
88	C₆₁×#474	C₂²	1	2	yes	—
89	C₆₁×#464	C₂²	1	2	yes	—
90	C₆₁×#464	C₂²	1	2	yes	—
91	C₆₁×#463	C₂²	1	2	yes	—
92	C₆₁×#463	C₂²	1	2	yes	—
93	C₆₁×#462	C₂²	1	1	yes	characteristic
94	C₆₁×#461	C₂²	1	1	yes	characteristic
95	C₆₁×#460	C₂²	1	1	yes	characteristic
96	C₆₁×#459	C₂²	1	1	yes	characteristic
97	C₆₁×#452	C₂²	1	2	yes	—
98	C₆₁×#449	C₂²	1	2	yes	—
99	C₆₁×#446	C₂²	1	2	yes	—
100	C₆₁×#446	C₂²	1	2	yes	—
101	C₆₁×#446	C₂²	1	2	yes	—
102	C₆₁×#446	C₂²	1	2	yes	—
103	C₆₁×#442	C₂²	1	2	yes	—
104	C₆₁×#442	C₂²	1	2	yes	—
105	C₆₁×#441	C₂²	1	2	yes	—
106	C₆₁×#441	C₂²	1	2	yes	—
107	C₆₁×#440	C₂²	1	2	yes	—
108	C₆₁×#440	C₂²	1	2	yes	—
109	C₆₁×#440	C₂²	1	2	yes	—
110	C₆₁×#440	C₂²	1	2	yes	—
111	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
112	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
114	C₄×D₈×C₆₁	C₂²	1	2	yes	—
115	C₆₁×#433	C₂²	1	2	yes	—
116	C₆₁×#433	C₂²	1	2	yes	—
117	C₆₁×#432	C₂²	1	1	yes	characteristic
118	C₆₁×#432	C₂²	1	1	yes	characteristic
119	C₂×#41×C₆₁	—	2	1	no	—
120	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
121	C₂²×Q₈×C₆₁	—	2	2	no	—
122	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
125	C₂×D₈×C₆₁	C₂³	1	2	yes	—
126	C₄⋊Q₈×C₆₁	—	2	2	no	—
127	C₄⋊Q₈×C₆₁	—	2	2	no	—
128	C₄⋊Q₈×C₆₁	—	2	1	no	—
129	C₄⋊Q₈×C₆₁	—	2	1	no	—
130	C₄⋊Q₈×C₆₁	—	2	2	no	—
131	C₄⋊Q₈×C₆₁	—	2	2	no	—
132	C₄⋊Q₈×C₆₁	—	2	2	no	—
133	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
134	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
135	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
136	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
137	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
138	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
139	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
140	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
141	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
142	#127×C₆₁	C₂³	1	1	yes	characteristic
143	#126×C₆₁	—	2	2	no	—
144	#126×C₆₁	—	2	2	no	—
145	#126×C₆₁	—	2	2	no	—
146	#126×C₆₁	—	2	2	no	—
147	#125×C₆₁	—	2	1	no	—
148	#125×C₆₁	—	2	1	no	—
149	#125×C₆₁	—	2	2	no	—
150	#125×C₆₁	—	2	2	no	—
151	#125×C₆₁	—	2	2	no	—
152	#125×C₆₁	—	2	2	no	—
153	#125×C₆₁	—	2	1	no	—
154	#125×C₆₁	—	2	1	no	—
155	#125×C₆₁	—	2	1	no	—
156	#125×C₆₁	D₄	1	1	yes	characteristic
157	#125×C₆₁	D₄	1	1	yes	characteristic
158	#125×C₆₁	C₂³	1	2	yes	—
159	#125×C₆₁	C₂³	1	2	yes	—
160	#125×C₆₁	C₂³	1	2	yes	—
161	#125×C₆₁	C₂³	1	2	yes	—
162	#124×C₆₁	—	2	2	no	—
163	#124×C₆₁	—	2	2	no	—
164	#124×C₆₁	—	2	2	no	—
165	#124×C₆₁	—	2	1	no	—
166	#124×C₆₁	C₂³	1	2	yes	—
167	#124×C₆₁	C₂³	1	2	yes	—
168	#123×C₆₁	—	2	2	no	—
169	#123×C₆₁	—	2	2	no	—
170	#123×C₆₁	—	2	2	no	—
171	#123×C₆₁	—	2	2	no	—
172	C₂²⋊Q₈×C₆₁	—	2	2	no	—
173	C₂²⋊Q₈×C₆₁	—	2	2	no	—
174	C₂²⋊Q₈×C₆₁	—	2	2	no	—
175	C₂²⋊Q₈×C₆₁	—	2	1	no	—
176	C₂²⋊Q₈×C₆₁	—	2	2	no	—
177	C₂²⋊Q₈×C₆₁	—	2	2	no	—
178	C₂²⋊Q₈×C₆₁	—	2	2	no	—
179	C₂²⋊Q₈×C₆₁	—	2	2	no	—
180	C₂²⋊Q₈×C₆₁	—	2	2	no	—
181	C₂²⋊Q₈×C₆₁	—	2	2	no	—
182	C₂²⋊Q₈×C₆₁	—	2	2	no	—
183	C₂²⋊Q₈×C₆₁	—	2	2	no	—
184	C₂²⋊Q₈×C₆₁	—	2	2	no	—
185	C₂²⋊Q₈×C₆₁	—	2	2	no	—
186	C₂²⋊Q₈×C₆₁	—	2	2	no	—
187	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
188	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
189	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
190	#121×C₆₁	—	2	1	no	—
191	#121×C₆₁	C₂³	1	2	yes	—
192	C₄×Q₈×C₆₁	—	2	2	no	—
193	C₄×Q₈×C₆₁	—	2	2	no	—
194	C₄×Q₈×C₆₁	—	2	2	no	—
195	C₄×Q₈×C₆₁	—	2	1	no	—
196	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
197	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
198	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
199	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
200	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
201	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
202	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
203	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
204	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
205	C₄×D₄×C₆₁	—	2	1	no	—
206	C₄×D₄×C₆₁	—	2	1	no	—
207	C₄×D₄×C₆₁	—	2	2	no	—
208	C₄×D₄×C₆₁	—	2	2	no	—
209	C₄×D₄×C₆₁	—	2	2	no	—
210	C₄×D₄×C₆₁	—	2	1	no	—
211	C₄×D₄×C₆₁	C₂³	1	2	yes	—
212	C₄×D₄×C₆₁	C₂³	1	2	yes	—
213	C₄×D₄×C₆₁	C₂³	1	2	yes	—
214	C₄×D₄×C₆₁	C₂³	1	2	yes	—
215	C₄×D₄×C₆₁	C₂³	1	2	yes	—
216	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
218	#117×C₆₁	—	2	1	no	—
219	#117×C₆₁	—	2	1	no	—
220	#117×C₆₁	—	2	1	no	—
221	#117×C₆₁	—	2	2	no	—
222	#117×C₆₁	—	2	1	no	—
223	#117×C₆₁	C₂³	1	1	yes	characteristic
224	#117×C₆₁	C₂³	1	1	yes	characteristic
225	#117×C₆₁	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
227	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
228	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
229	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
230	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
231	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
232	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₆₁	—	2	1	no	—
235	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
236	#107×C₆₁	C₂³	1	2	yes	—
237	#107×C₆₁	C₂³	1	2	yes	—
238	#107×C₆₁	C₂³	1	2	yes	—
239	#107×C₆₁	C₂³	1	2	yes	—
240	#107×C₆₁	C₂³	1	2	yes	—
241	#107×C₆₁	C₂³	1	2	yes	—
242	#106×C₆₁	C₂³	1	2	yes	—
243	#106×C₆₁	C₂³	1	2	yes	—
244	#106×C₆₁	C₂³	1	2	yes	—
245	#106×C₆₁	C₂³	1	2	yes	—
246	#106×C₆₁	C₂³	1	2	yes	—
247	#106×C₆₁	C₂³	1	2	yes	—
248	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
249	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
250	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
251	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
252	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
253	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
254	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
255	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
256	#103×C₆₁	C₂³	1	2	yes	—
257	#103×C₆₁	C₂³	1	2	yes	—
258	#103×C₆₁	C₂³	1	2	yes	—
259	#103×C₆₁	C₂³	1	2	yes	—
260	#103×C₆₁	C₂³	1	2	yes	—
261	#103×C₆₁	C₂³	1	2	yes	—
262	#103×C₆₁	C₂³	1	2	yes	—
263	#103×C₆₁	C₂³	1	2	yes	—
264	#102×C₆₁	C₂³	1	2	yes	—
265	#102×C₆₁	C₂³	1	2	yes	—
266	#102×C₆₁	C₂³	1	2	yes	—
267	#102×C₆₁	C₂³	1	2	yes	—
268	#102×C₆₁	C₂³	1	2	yes	—
269	#102×C₆₁	C₂³	1	2	yes	—
270	#102×C₆₁	C₂³	1	2	yes	—
271	#102×C₆₁	C₂³	1	2	yes	—
272	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
273	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
274	#97×C₆₁	C₂³	1	2	yes	—
275	#97×C₆₁	C₂³	1	2	yes	—
276	#97×C₆₁	C₂³	1	2	yes	—
277	#97×C₆₁	C₂³	1	2	yes	—
278	C₄×C₈×C₆₁	C₂³	1	2	yes	—
279	C₄×C₈×C₆₁	C₂³	1	2	yes	—
280	#41×C₆₁	—	2	2	no	—
281	#41×C₆₁	—	2	2	no	—
282	#41×C₆₁	—	8	2	no	—
283	C₂×Q₈×C₆₁	—	2	1	no	—
284	C₂×Q₈×C₆₁	—	2	2	no	—
285	C₂×Q₈×C₆₁	—	2	2	no	—
286	C₂×Q₈×C₆₁	—	2	2	no	—
287	C₂×Q₈×C₆₁	—	2	2	no	—
288	C₂×Q₈×C₆₁	—	2	1	no	—
289	C₂×Q₈×C₆₁	—	8	4	no	—
290	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
291	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
292	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
293	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
294	C₂×D₄×C₆₁	—	2	1	no	—
295	C₂×D₄×C₆₁	—	2	2	no	—
296	C₂×D₄×C₆₁	—	2	1	no	—
297	C₂×D₄×C₆₁	—	2	1	no	—
298	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
299	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₆₁	—	2	1	no	—
301	C₂²×C₄×C₆₁	—	2	1	no	—
302	C₂²×C₄×C₆₁	—	2	1	no	—
303	C₂²×C₄×C₆₁	—	2	2	no	—
304	C₂²×C₄×C₆₁	—	2	1	no	—
305	C₂²×C₄×C₆₁	—	2	1	no	—
306	C₂²×C₄×C₆₁	—	2	2	no	—
307	C₂²×C₄×C₆₁	—	2	2	no	—
308	C₂²×C₄×C₆₁	—	2	2	no	—
309	C₂²×C₄×C₆₁	—	2	2	no	—
310	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
313	Q₁₆×C₆₁	—	2	4	no	—
314	SD₁₆×C₆₁	—	2	4	no	—
315	SD₁₆×C₆₁	—	2	4	no	—
316	D₈×C₆₁	—	2	4	no	—
317	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
318	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
319	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
320	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
321	C₄⋊C₄×C₆₁	—	2	2	no	—
322	C₄⋊C₄×C₆₁	—	2	2	no	—
323	C₄⋊C₄×C₆₁	—	2	1	no	—
324	C₄⋊C₄×C₆₁	—	2	1	no	—
325	C₄⋊C₄×C₆₁	—	2	2	no	—
326	C₄⋊C₄×C₆₁	—	2	2	no	—
327	C₄⋊C₄×C₆₁	—	2	2	no	—
328	C₄⋊C₄×C₆₁	—	2	2	no	—
329	C₄⋊C₄×C₆₁	—	2	2	no	—
330	C₄⋊C₄×C₆₁	—	2	2	no	—
331	C₄⋊C₄×C₆₁	—	2	2	no	—
332	C₄⋊C₄×C₆₁	—	2	2	no	—
333	C₄⋊C₄×C₆₁	—	2	1	no	—
334	C₄⋊C₄×C₆₁	—	2	1	no	—
335	C₄⋊C₄×C₆₁	—	2	1	no	—
336	C₄⋊C₄×C₆₁	—	2	1	no	—
337	C₄⋊C₄×C₆₁	—	2	1	no	—
338	C₄⋊C₄×C₆₁	—	2	1	no	—
339	C₄⋊C₄×C₆₁	—	2	2	no	—
340	C₄⋊C₄×C₆₁	—	2	2	no	—
341	C₄⋊C₄×C₆₁	—	2	2	no	—
342	C₄⋊C₄×C₆₁	—	2	2	no	—
343	C₄⋊C₄×C₆₁	—	2	2	no	—
344	C₄⋊C₄×C₆₁	—	2	2	no	—
345	C₄⋊C₄×C₆₁	—	2	2	no	—
346	C₄⋊C₄×C₆₁	—	2	2	no	—
347	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
348	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
349	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
350	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
351	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
352	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
353	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
354	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
355	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
357	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
358	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
359	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
360	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
361	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
362	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
363	C₂²⋊C₄×C₆₁	—	2	2	no	—
364	C₂²⋊C₄×C₆₁	—	2	1	no	—
365	C₂²⋊C₄×C₆₁	—	2	1	no	—
366	C₂²⋊C₄×C₆₁	—	2	1	no	—
367	C₂²⋊C₄×C₆₁	—	2	2	no	—
368	C₂²⋊C₄×C₆₁	—	2	2	no	—
369	C₂²⋊C₄×C₆₁	—	2	2	no	—
370	C₂²⋊C₄×C₆₁	—	2	2	no	—
371	C₂²⋊C₄×C₆₁	—	2	2	no	—
372	C₂²⋊C₄×C₆₁	—	2	2	no	—
373	C₂²⋊C₄×C₆₁	—	2	2	no	—
374	C₂²⋊C₄×C₆₁	—	2	2	no	—
375	C₂²⋊C₄×C₆₁	—	2	2	no	—
376	C₂²⋊C₄×C₆₁	—	2	2	no	—
377	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
378	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
379	C₄²×C₆₁	—	2	1	no	—
380	C₄²×C₆₁	—	2	1	no	—
381	C₄²×C₆₁	—	2	1	no	—
382	C₄²×C₆₁	—	2	2	no	—
383	C₄²×C₆₁	—	2	2	no	—
384	C₄²×C₆₁	—	2	2	no	—
385	C₄²×C₆₁	—	2	2	no	—
386	C₄²×C₆₁	—	2	2	no	—
387	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
388	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
389	C₄²×C₆₁	C₂⁴	1	2	yes	—
390	C₄²×C₆₁	C₂⁴	1	2	yes	—
391	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
392	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
393	C₂³×C₆₁	—	2	1	no	—
394	C₂³×C₆₁	—	2	2	no	—
395	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
396	Q₈×C₆₁	—	2	1	no	—
397	Q₈×C₆₁	—	2	2	no	—
398	Q₈×C₆₁	—	2	2	no	—
399	Q₈×C₆₁	—	4	2	no	—
400	Q₈×C₆₁	—	4	2	no	—
401	Q₈×C₆₁	—	4	2	no	—
402	Q₈×C₆₁	—	8	2	no	—
403	Q₈×C₆₁	—	8	2	no	—
404	Q₈×C₆₁	—	8	2	no	—
405	Q₈×C₆₁	—	8	2	no	—
406	Q₈×C₆₁	—	8	1	no	—
407	Q₈×C₆₁	2₋¹⁺⁴	1	2	yes	—
408	D₄×C₆₁	—	2	4	no	—
409	D₄×C₆₁	—	2	1	no	—
410	D₄×C₆₁	—	2	2	no	—
411	D₄×C₆₁	—	2	2	no	—
412	D₄×C₆₁	—	4	2	no	—
413	D₄×C₆₁	—	8	1	no	—
414	D₄×C₆₁	—	8	2	no	—
415	D₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
416	C₂×C₄×C₆₁	—	2	4	no	—
417	C₂×C₄×C₆₁	—	2	1	no	—
418	C₂×C₄×C₆₁	—	2	1	no	—
419	C₂×C₄×C₆₁	—	2	1	no	—
420	C₂×C₄×C₆₁	—	2	2	no	—
421	C₂×C₄×C₆₁	—	2	1	no	—
422	C₂×C₄×C₆₁	—	2	1	no	—
423	C₂×C₄×C₆₁	—	2	2	no	—
424	C₂×C₄×C₆₁	—	2	2	no	—
425	C₂×C₄×C₆₁	—	2	2	no	—
426	C₂×C₄×C₆₁	—	2	2	no	—
427	C₂×C₄×C₆₁	—	4	1	no	—
428	C₂×C₄×C₆₁	—	4	1	no	—
429	C₂×C₄×C₆₁	—	4	4	no	—
430	C₂×C₄×C₆₁	—	8	1	no	—
431	C₂×C₄×C₆₁	—	8	2	no	—
432	C₂×C₄×C₆₁	—	8	1	no	—
433	C₂×C₄×C₆₁	—	8	2	no	—
434	C₂×C₄×C₆₁	—	8	2	no	—
435	C₂×C₄×C₆₁	—	8	2	no	—
436	C₂×C₄×C₆₁	—	8	1	no	—
437	C₂×C₄×C₆₁	—	8	1	no	—
438	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
440	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
444	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
447	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
448	C₈×C₆₁	—	2	2	no	—
449	C₈×C₆₁	—	2	2	no	—
450	C₈×C₆₁	—	2	2	no	—
451	C₈×C₆₁	—	2	2	no	—
452	#61878	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
453	C₂²×C₆₁	—	2	1	no	—
454	C₂²×C₆₁	—	2	1	no	—
455	C₂²×C₆₁	—	2	1	no	—
456	C₂²×C₆₁	—	2	2	no	—
457	C₂²×C₆₁	—	4	1	no	—
458	C₂²×C₆₁	—	4	1	no	—
459	C₂²×C₆₁	—	4	2	no	—
460	C₂²×C₆₁	—	4	2	no	—
461	C₂²×C₆₁	—	4	2	no	—
462	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
463	C₄×C₆₁	—	2	1	no	—
464	C₄×C₆₁	—	2	1	no	—
465	C₄×C₆₁	—	2	2	no	—
466	C₄×C₆₁	—	2	2	no	—
467	C₄×C₆₁	—	2	1	no	—
468	C₄×C₆₁	—	2	1	no	—
469	C₄×C₆₁	—	2	2	no	—
470	C₄×C₆₁	—	2	2	no	—
471	C₄×C₆₁	—	2	1	no	—
472	C₄×C₆₁	—	2	2	no	—
473	C₄×C₆₁	—	4	2	no	—
474	C₄×C₆₁	—	4	2	no	—
475	C₄×C₆₁	—	4	2	no	—
476	C₄×C₆₁	—	4	1	no	—
477	C₄×C₆₁	—	4	2	no	—
478	C₄×C₆₁	—	4	1	no	—
479	C₄×C₆₁	—	4	2	no	—
480	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
481	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
482	#3550	C₂×C₆₁	1	1	yes	characteristic, complemented
483	#3504	C₂×C₆₁	1	1	yes	characteristic, complemented
484	#3387	C₂×C₆₁	1	2	yes	complemented
485	#3386	C₂×C₆₁	1	2	yes	complemented
486	#3385	C₂×C₆₁	1	2	yes	complemented
487	#3384	C₂×C₆₁	1	2	yes	complemented
488	#3377	C₂×C₆₁	1	2	yes	complemented
489	#3376	C₂×C₆₁	1	2	yes	complemented
490	#3371	C₂×C₆₁	1	2	yes	complemented
491	#3370	C₂×C₆₁	1	2	yes	complemented
492	#3244	C₂×C₆₁	1	2	yes	complemented
493	#3243	C₂×C₆₁	1	2	yes	complemented
494	#3236	C₂×C₆₁	1	1	yes	characteristic, complemented
495	#3234	C₂×C₆₁	1	1	yes	characteristic, complemented
496	#3125	C₂×C₆₁	1	2	yes	complemented
497	#3124	C₂×C₆₁	1	2	yes	complemented
498	#3116	C₂×C₆₁	1	1	yes	characteristic, complemented
499	#3115	C₂×C₆₁	1	1	yes	characteristic
500	#2987	C₂×C₆₁	1	1	yes	characteristic, complemented
501	C₂×C₆₁	—	4	1	no	—
502	C₂×C₆₁	—	4	2	no	—
503	C₂×C₆₁	—	8	2	no	—
504	C₂×C₆₁	#3486	1	1	yes	characteristic
505	C₂×C₆₁	#3585	1	1	yes	characteristic
506	C₂×C₆₁	#3586	1	1	yes	characteristic
507	#563	—	2	1	no	—
508	#563	—	2	1	no	—
509	#559	C₂²×C₆₁	1	2	yes	—
510	Q₈²	C₂²×C₆₁	1	2	yes	—
511	#557	C₂²×C₆₁	1	2	yes	—
512	#557	C₂²×C₆₁	1	2	yes	—
513	#556	—	2	1	no	—
514	#556	C₂²×C₆₁	1	2	yes	—
515	#554	—	2	2	no	—
516	#554	—	2	2	no	—
517	#554	C₂²×C₆₁	1	2	yes	—
518	#554	C₂²×C₆₁	1	2	yes	—
519	D₄×Q₈	—	2	1	no	—
520	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
521	#544	—	2	1	no	—
522	#544	—	2	1	no	—
523	#544	C₂²×C₆₁	1	1	yes	characteristic
524	#544	C₂²×C₆₁	1	1	yes	characteristic
525	#542	—	2	2	no	—
526	#542	C₂²×C₆₁	1	2	yes	—
527	#542	C₂²×C₆₁	1	2	yes	—
528	#536	—	2	2	no	—
529	#533	—	2	1	no	—
530	#533	C₂²×C₆₁	1	1	yes	characteristic
531	#533	C₂²×C₆₁	1	1	yes	characteristic
532	#532	C₂²×C₆₁	1	1	yes	characteristic
533	C₂×#125	—	2	1	no	—
534	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
535	#520	C₂²×C₆₁	1	1	yes	characteristic
536	#520	C₂²×C₆₁	1	1	yes	characteristic
537	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
538	#501	C₂²×C₆₁	1	2	yes	—
539	#501	C₂²×C₆₁	1	2	yes	—
540	#501	C₂²×C₆₁	1	2	yes	—
541	#501	C₂²×C₆₁	1	2	yes	—
542	#500	C₂²×C₆₁	1	2	yes	—
543	#498	C₂²×C₆₁	1	2	yes	—
544	#491	C₂²×C₆₁	1	2	yes	—
545	#490	C₂²×C₆₁	1	2	yes	—
546	#489	C₂²×C₆₁	1	2	yes	—
547	#489	C₂²×C₆₁	1	2	yes	—
548	#488	C₂²×C₆₁	1	2	yes	—
549	#488	C₂²×C₆₁	1	2	yes	—
550	#485	C₂²×C₆₁	1	2	yes	—
551	#484	C₂²×C₆₁	1	2	yes	—
552	#483	C₂²×C₆₁	1	2	yes	—
553	#482	C₂²×C₆₁	1	2	yes	—
554	#481	C₂²×C₆₁	1	2	yes	—
555	#480	C₂²×C₆₁	1	2	yes	—
556	#479	C₂²×C₆₁	1	2	yes	—
557	#479	C₂²×C₆₁	1	2	yes	—
558	#479	C₂²×C₆₁	1	2	yes	—
559	#479	C₂²×C₆₁	1	2	yes	—
560	#478	C₂²×C₆₁	1	2	yes	—
561	#478	C₂²×C₆₁	1	2	yes	—
562	#478	C₂²×C₆₁	1	2	yes	—
563	#478	C₂²×C₆₁	1	2	yes	—
564	#477	C₂²×C₆₁	1	1	yes	characteristic
565	#477	C₂²×C₆₁	1	2	yes	—
566	#477	C₂²×C₆₁	1	2	yes	—
567	#476	C₂²×C₆₁	1	2	yes	—
568	#476	C₂²×C₆₁	1	1	yes	characteristic
569	#476	C₂²×C₆₁	1	2	yes	—
570	#475	C₂²×C₆₁	1	1	yes	characteristic
571	#475	C₂²×C₆₁	1	2	yes	—
572	#475	C₂²×C₆₁	1	2	yes	—
573	#474	C₂²×C₆₁	1	2	yes	—
574	#474	C₂²×C₆₁	1	1	yes	characteristic
575	#474	C₂²×C₆₁	1	2	yes	—
576	#464	C₂²×C₆₁	1	2	yes	—
577	#464	C₂²×C₆₁	1	2	yes	—
578	#463	C₂²×C₆₁	1	2	yes	—
579	#463	C₂²×C₆₁	1	2	yes	—
580	#462	C₂²×C₆₁	1	1	yes	characteristic
581	#461	C₂²×C₆₁	1	1	yes	characteristic
582	#460	C₂²×C₆₁	1	1	yes	characteristic
583	#459	C₂²×C₆₁	1	1	yes	characteristic
584	#452	C₂²×C₆₁	1	2	yes	—
585	#449	C₂²×C₆₁	1	2	yes	—
586	#446	C₂²×C₆₁	1	2	yes	—
587	#446	C₂²×C₆₁	1	2	yes	—
588	#446	C₂²×C₆₁	1	2	yes	—
589	#446	C₂²×C₆₁	1	2	yes	—
590	#442	C₂²×C₆₁	1	2	yes	—
591	#442	C₂²×C₆₁	1	2	yes	—
592	#441	C₂²×C₆₁	1	2	yes	—
593	#441	C₂²×C₆₁	1	2	yes	—
594	#440	C₂²×C₆₁	1	2	yes	—
595	#440	C₂²×C₆₁	1	2	yes	—
596	#440	C₂²×C₆₁	1	2	yes	—
597	#440	C₂²×C₆₁	1	2	yes	—
598	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
599	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
600	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
601	C₄×D₈	C₂²×C₆₁	1	2	yes	—
602	#433	C₂²×C₆₁	1	2	yes	—
603	#433	C₂²×C₆₁	1	2	yes	—
604	#432	C₂²×C₆₁	1	1	yes	characteristic
605	#432	C₂²×C₆₁	1	1	yes	characteristic
606	C₆₁	#61878	1	1	yes	characteristic, direct product factor, Sylow
607	C₂×#41	—	2	1	no	—
608	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
609	C₂²×Q₈	—	2	2	no	—
610	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
611	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
612	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
613	C₂×D₈	C₂³×C₆₁	1	2	yes	—
614	C₄⋊Q₈	—	2	2	no	—
615	C₄⋊Q₈	—	2	2	no	—
616	C₄⋊Q₈	—	2	1	no	—
617	C₄⋊Q₈	—	2	1	no	—
618	C₄⋊Q₈	—	2	2	no	—
619	C₄⋊Q₈	—	2	2	no	—
620	C₄⋊Q₈	—	2	2	no	—
621	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
622	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
623	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
624	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
625	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
626	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
627	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
628	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
629	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
630	#127	C₂³×C₆₁	1	1	yes	characteristic
631	#126	—	2	2	no	—
632	#126	—	2	2	no	—
633	#126	—	2	2	no	—
634	#126	—	2	2	no	—
635	#125	—	2	1	no	—
636	#125	—	2	1	no	—
637	#125	—	2	2	no	—
638	#125	—	2	2	no	—
639	#125	—	2	2	no	—
640	#125	—	2	2	no	—
641	#125	—	2	1	no	—
642	#125	—	2	1	no	—
643	#125	—	2	1	no	—
644	#125	D₄×C₆₁	1	1	yes	characteristic
645	#125	D₄×C₆₁	1	1	yes	characteristic
646	#125	C₂³×C₆₁	1	2	yes	—
647	#125	C₂³×C₆₁	1	2	yes	—
648	#125	C₂³×C₆₁	1	2	yes	—
649	#125	C₂³×C₆₁	1	2	yes	—
650	#124	—	2	2	no	—
651	#124	—	2	2	no	—
652	#124	—	2	2	no	—
653	#124	—	2	1	no	—
654	#124	C₂³×C₆₁	1	2	yes	—
655	#124	C₂³×C₆₁	1	2	yes	—
656	#123	—	2	2	no	—
657	#123	—	2	2	no	—
658	#123	—	2	2	no	—
659	#123	—	2	2	no	—
660	C₂²⋊Q₈	—	2	2	no	—
661	C₂²⋊Q₈	—	2	2	no	—
662	C₂²⋊Q₈	—	2	2	no	—
663	C₂²⋊Q₈	—	2	1	no	—
664	C₂²⋊Q₈	—	2	2	no	—
665	C₂²⋊Q₈	—	2	2	no	—
666	C₂²⋊Q₈	—	2	2	no	—
667	C₂²⋊Q₈	—	2	2	no	—
668	C₂²⋊Q₈	—	2	2	no	—
669	C₂²⋊Q₈	—	2	2	no	—
670	C₂²⋊Q₈	—	2	2	no	—
671	C₂²⋊Q₈	—	2	2	no	—
672	C₂²⋊Q₈	—	2	2	no	—
673	C₂²⋊Q₈	—	2	2	no	—
674	C₂²⋊Q₈	—	2	2	no	—
675	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
676	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
677	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
678	#121	—	2	1	no	—
679	#121	C₂³×C₆₁	1	2	yes	—
680	C₄×Q₈	—	2	2	no	—
681	C₄×Q₈	—	2	2	no	—
682	C₄×Q₈	—	2	2	no	—
683	C₄×Q₈	—	2	1	no	—
684	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
685	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
686	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
687	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
688	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
689	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
690	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
691	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
692	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
693	C₄×D₄	—	2	1	no	—
694	C₄×D₄	—	2	1	no	—
695	C₄×D₄	—	2	2	no	—
696	C₄×D₄	—	2	2	no	—
697	C₄×D₄	—	2	2	no	—
698	C₄×D₄	—	2	1	no	—
699	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
700	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
701	C₄×D₄	C₂³×C₆₁	1	2	yes	—
702	C₄×D₄	C₂³×C₆₁	1	2	yes	—
703	C₄×D₄	C₂³×C₆₁	1	2	yes	—
704	C₄×D₄	C₂³×C₆₁	1	2	yes	—
705	C₄×D₄	C₂³×C₆₁	1	2	yes	—
706	#117	—	2	1	no	—
707	#117	—	2	1	no	—
708	#117	—	2	1	no	—
709	#117	—	2	2	no	—
710	#117	—	2	1	no	—
711	#117	C₂³×C₆₁	1	1	yes	characteristic
712	#117	C₂³×C₆₁	1	1	yes	characteristic
713	#117	C₂³×C₆₁	1	1	yes	characteristic
714	C₂×C₄⋊C₄	—	2	1	no	—
715	C₂×C₄⋊C₄	—	2	1	no	—
716	C₂×C₄⋊C₄	—	2	1	no	—
717	C₂×C₄⋊C₄	—	2	1	no	—
718	C₂×C₄⋊C₄	—	2	2	no	—
719	C₂×C₄⋊C₄	—	2	2	no	—
720	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
721	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
722	C₂×C₄²	—	2	1	no	—
723	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
724	#107	C₂³×C₆₁	1	2	yes	—
725	#107	C₂³×C₆₁	1	2	yes	—
726	#107	C₂³×C₆₁	1	2	yes	—
727	#107	C₂³×C₆₁	1	2	yes	—
728	#107	C₂³×C₆₁	1	2	yes	—
729	#107	C₂³×C₆₁	1	2	yes	—
730	#106	C₂³×C₆₁	1	2	yes	—
731	#106	C₂³×C₆₁	1	2	yes	—
732	#106	C₂³×C₆₁	1	2	yes	—
733	#106	C₂³×C₆₁	1	2	yes	—
734	#106	C₂³×C₆₁	1	2	yes	—
735	#106	C₂³×C₆₁	1	2	yes	—
736	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
737	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
738	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
739	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
740	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
741	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
742	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
743	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
744	#103	C₂³×C₆₁	1	2	yes	—
745	#103	C₂³×C₆₁	1	2	yes	—
746	#103	C₂³×C₆₁	1	2	yes	—
747	#103	C₂³×C₆₁	1	2	yes	—
748	#103	C₂³×C₆₁	1	2	yes	—
749	#103	C₂³×C₆₁	1	2	yes	—
750	#103	C₂³×C₆₁	1	2	yes	—
751	#103	C₂³×C₆₁	1	2	yes	—
752	#102	C₂³×C₆₁	1	2	yes	—
753	#102	C₂³×C₆₁	1	2	yes	—
754	#102	C₂³×C₆₁	1	2	yes	—
755	#102	C₂³×C₆₁	1	2	yes	—
756	#102	C₂³×C₆₁	1	2	yes	—
757	#102	C₂³×C₆₁	1	2	yes	—
758	#102	C₂³×C₆₁	1	2	yes	—
759	#102	C₂³×C₆₁	1	2	yes	—
760	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
761	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
762	#97	C₂³×C₆₁	1	2	yes	—
763	#97	C₂³×C₆₁	1	2	yes	—
764	#97	C₂³×C₆₁	1	2	yes	—
765	#97	C₂³×C₆₁	1	2	yes	—
766	C₄×C₈	C₂³×C₆₁	1	2	yes	—
767	C₄×C₈	C₂³×C₆₁	1	2	yes	—
768	#41	—	2	2	no	—
769	#41	—	2	2	no	—
770	#41	—	8	2	no	—
771	C₂×Q₈	—	2	1	no	—
772	C₂×Q₈	—	2	2	no	—
773	C₂×Q₈	—	2	2	no	—
774	C₂×Q₈	—	2	2	no	—
775	C₂×Q₈	—	2	2	no	—
776	C₂×Q₈	—	2	1	no	—
777	C₂×Q₈	—	8	4	no	—
778	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
779	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
780	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
781	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
782	C₂×D₄	—	2	1	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	1	no	—
786	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
787	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
788	C₂²×C₄	—	2	1	no	—
789	C₂²×C₄	—	2	1	no	—
790	C₂²×C₄	—	2	1	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	2	1	no	—
793	C₂²×C₄	—	2	1	no	—
794	C₂²×C₄	—	2	2	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	2	no	—
798	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
799	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
801	Q₁₆	—	2	4	no	—
802	SD₁₆	—	2	4	no	—
803	SD₁₆	—	2	4	no	—
804	D₈	—	2	4	no	—
805	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
806	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
807	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
808	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	1	no	—
812	C₄⋊C₄	—	2	1	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	1	no	—
822	C₄⋊C₄	—	2	1	no	—
823	C₄⋊C₄	—	2	1	no	—
824	C₄⋊C₄	—	2	1	no	—
825	C₄⋊C₄	—	2	1	no	—
826	C₄⋊C₄	—	2	1	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
836	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
837	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
838	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
839	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
840	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
841	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
842	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
843	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
844	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
845	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
846	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
847	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
848	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
849	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
850	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	1	no	—
853	C₂²⋊C₄	—	2	1	no	—
854	C₂²⋊C₄	—	2	1	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
866	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
867	C₄²	—	2	1	no	—
868	C₄²	—	2	1	no	—
869	C₄²	—	2	1	no	—
870	C₄²	—	2	2	no	—
871	C₄²	—	2	2	no	—
872	C₄²	—	2	2	no	—
873	C₄²	—	2	2	no	—
874	C₄²	—	2	2	no	—
875	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
876	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
877	C₄²	C₂⁴×C₆₁	1	2	yes	—
878	C₄²	C₂⁴×C₆₁	1	2	yes	—
879	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
880	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
881	C₂³	—	2	1	no	—
882	C₂³	—	2	2	no	—
883	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
884	Q₈	—	2	1	no	—
885	Q₈	—	2	2	no	—
886	Q₈	—	2	2	no	—
887	Q₈	—	4	2	no	—
888	Q₈	—	4	2	no	—
889	Q₈	—	4	2	no	—
890	Q₈	—	8	2	no	—
891	Q₈	—	8	2	no	—
892	Q₈	—	8	2	no	—
893	Q₈	—	8	2	no	—
894	Q₈	—	8	1	no	—
895	Q₈	2₋¹⁺⁴×C₆₁	1	2	yes	—
896	D₄	—	2	4	no	—
897	D₄	—	2	1	no	—
898	D₄	—	2	2	no	—
899	D₄	—	2	2	no	—
900	D₄	—	4	2	no	—
901	D₄	—	8	1	no	—
902	D₄	—	8	2	no	—
903	D₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
904	C₂×C₄	—	2	4	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	4	1	no	—
916	C₂×C₄	—	4	1	no	—
917	C₂×C₄	—	4	4	no	—
918	C₂×C₄	—	8	1	no	—
919	C₂×C₄	—	8	2	no	—
920	C₂×C₄	—	8	1	no	—
921	C₂×C₄	—	8	2	no	—
922	C₂×C₄	—	8	2	no	—
923	C₂×C₄	—	8	2	no	—
924	C₂×C₄	—	8	1	no	—
925	C₂×C₄	—	8	1	no	—
926	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
927	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
928	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
929	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
930	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
931	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
932	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
933	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
934	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
935	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
936	C₈	—	2	2	no	—
937	C₈	—	2	2	no	—
938	C₈	—	2	2	no	—
939	C₈	—	2	2	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	1	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	4	1	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	2	no	—
953	C₄	—	2	2	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	2	no	—
957	C₄	—	2	2	no	—
958	C₄	—	2	1	no	—
959	C₄	—	2	2	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	1	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	1	no	—
966	C₄	—	4	2	no	—
967	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
968	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
969	C₂	—	4	1	no	—
970	C₂	—	4	2	no	—
971	C₂	—	8	2	no	—
972	C₂	C₆₁×#3486	1	1	yes	characteristic
973	C₂	C₆₁×#3585	1	1	yes	characteristic
974	C₂	C₆₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3115	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3550	C₂	semidirect
2. C₆₁×#3504	C₂	semidirect
3. C₆₁×#3387	C₂	semidirect
4. C₆₁×#3386	C₂	semidirect
5. C₆₁×#3385	C₂	semidirect
6. C₆₁×#3384	C₂	semidirect
7. C₆₁×#3377	C₂	semidirect
8. C₆₁×#3376	C₂	semidirect
9. C₆₁×#3371	C₂	semidirect
10. C₆₁×#3370	C₂	semidirect
11. C₆₁×#3244	C₂	semidirect
12. C₆₁×#3243	C₂	semidirect
13. C₆₁×#3236	C₂	semidirect
14. C₆₁×#3234	C₂	semidirect
15. C₆₁×#3125	C₂	semidirect
16. C₆₁×#3124	C₂	semidirect
17. C₆₁×#3116	C₂	semidirect
19. C₆₁×#2987	C₂	semidirect
452. #61878	C₆₁	direct (N × H)
482. #3550	C₂×C₆₁	semidirect
483. #3504	C₂×C₆₁	semidirect
484. #3387	C₂×C₆₁	semidirect
485. #3386	C₂×C₆₁	semidirect
486. #3385	C₂×C₆₁	semidirect
487. #3384	C₂×C₆₁	semidirect
488. #3377	C₂×C₆₁	semidirect
489. #3376	C₂×C₆₁	semidirect
490. #3371	C₂×C₆₁	semidirect
491. #3370	C₂×C₆₁	semidirect
492. #3244	C₂×C₆₁	semidirect
493. #3243	C₂×C₆₁	semidirect
494. #3236	C₂×C₆₁	semidirect
495. #3234	C₂×C₆₁	semidirect
496. #3125	C₂×C₆₁	semidirect
497. #3124	C₂×C₆₁	semidirect
498. #3116	C₂×C₆₁	semidirect
500. #2987	C₂×C₆₁	semidirect
606. C₆₁	#61878	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×#3550	2
C₆₁×#3504	2
C₆₁×#3387	2
C₆₁×#3386	2
C₆₁×#3385	2
C₆₁×#3384	2
C₆₁×#3377	2
C₆₁×#3376	2
C₆₁×#3371	2
C₆₁×#3370	2
C₆₁×#3244	2
C₆₁×#3243	2
C₆₁×#3236	2
C₆₁×#3234	2
C₆₁×#3125	2
C₆₁×#3124	2
C₆₁×#3116	2
C₆₁×#3115	2
C₆₁×#2987	2
#61878	61

Subgroups — C61×#61878 #29565311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61878 #29565311