Subgroups — C₆₁×#61899 #29565332

Order 15616.

1780 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3401	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3397	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3394	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3376	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3369	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3360	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3213	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3211	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3206	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3117	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3103	C₂	1	2	yes	maximal, complemented
17	C₆₁×#2984	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#559	C₂²	1	1	yes	characteristic, complemented
19	C₆₁×#559	C₂²	1	2	yes	complemented
20	Q₈²×C₆₁	C₂²	1	1	yes	characteristic, complemented
21	C₆₁×#556	—	2	1	no	—
22	C₆₁×#556	—	2	2	no	—
23	C₆₁×#556	—	2	1	no	—
24	C₆₁×#556	C₂²	1	2	yes	—
25	C₆₁×#556	C₂²	1	2	yes	—
26	C₆₁×#556	C₂²	1	4	yes	—
27	C₆₁×#554	C₂²	1	1	yes	characteristic, complemented
28	C₆₁×#554	C₂²	1	2	yes	complemented
29	C₆₁×#550	C₂²	1	1	yes	characteristic, complemented
30	C₆₁×#548	—	2	1	no	—
31	C₆₁×#547	—	2	1	no	—
32	C₆₁×#547	—	2	2	no	—
33	C₆₁×#542	—	2	1	no	—
34	C₆₁×#542	—	2	2	no	—
35	C₆₁×#532	C₂²	1	2	yes	—
36	C₆₁×#532	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
38	C₆₁×#529	C₂²	1	1	yes	characteristic
39	C₆₁×#529	C₂²	1	2	yes	—
40	C₂×#126×C₆₁	—	2	2	no	—
41	C₂×#124×C₆₁	C₂²	1	2	yes	—
42	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
43	C₆₁×#520	—	2	1	no	—
44	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
45	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
47	C₂×#117×C₆₁	—	2	1	no	—
48	C₆₁×#497	C₂²	1	2	yes	complemented
49	C₆₁×#496	C₂²	1	4	yes	—
50	C₆₁×#495	C₂²	1	4	yes	—
51	C₆₁×#492	C₂²	1	2	yes	complemented
52	C₆₁×#491	C₂²	1	2	yes	complemented
53	C₆₁×#489	C₂²	1	4	yes	—
54	C₆₁×#488	C₂²	1	4	yes	—
55	C₆₁×#487	C₂²	1	2	yes	complemented
56	C₆₁×#484	C₂²	1	1	yes	characteristic
57	C₆₁×#481	C₂²	1	1	yes	characteristic
58	C₆₁×#481	C₂²	1	2	yes	—
59	C₆₁×#479	C₂²	1	4	yes	complemented
60	C₆₁×#478	C₂²	1	2	yes	—
61	C₆₁×#476	C₂²	1	2	yes	—
62	C₆₁×#475	C₂²	1	4	yes	complemented
63	C₆₁×#464	C₂²	1	4	yes	—
64	C₆₁×#464	C₂²	1	4	yes	complemented
65	C₆₁×#463	C₂²	1	4	yes	—
66	C₆₁×#463	C₂²	1	2	yes	—
67	C₆₁×#463	C₂²	1	4	yes	—
68	C₆₁×#463	C₂²	1	4	yes	—
69	C₆₁×#462	C₂²	1	2	yes	complemented
70	C₆₁×#461	C₂²	1	2	yes	complemented
71	C₆₁×#461	C₂²	1	4	yes	complemented
72	C₆₁×#460	C₂²	1	4	yes	complemented
73	C₆₁×#459	C₂²	1	2	yes	—
74	C₆₁×#451	C₂²	1	2	yes	—
75	C₆₁×#450	C₂²	1	1	yes	characteristic
76	C₆₁×#448	C₂²	1	2	yes	—
77	C₆₁×#448	C₂²	1	2	yes	—
78	C₆₁×#448	C₂²	1	2	yes	—
79	C₆₁×#447	C₂²	1	1	yes	characteristic
80	C₆₁×#447	C₂²	1	2	yes	—
81	C₆₁×#446	C₂²	1	2	yes	complemented
82	C₆₁×#446	C₂²	1	4	yes	complemented
83	C₈×Q₈×C₆₁	C₂²	1	2	yes	complemented
84	C₆₁×#442	C₂²	1	4	yes	—
85	C₆₁×#441	C₂²	1	4	yes	complemented
86	C₆₁×#440	C₂²	1	4	yes	complemented
87	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
88	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	complemented
89	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	complemented
90	C₄×D₈×C₆₁	C₂²	1	2	yes	—
91	C₆₁×#432	C₂²	1	1	yes	characteristic
92	C₆₁×#432	C₂²	1	2	yes	—
93	C₆₁×#431	C₂²	1	2	yes	—
94	C₆₁×#431	C₂²	1	1	yes	characteristic
95	C₂×#41×C₆₁	—	2	1	no	—
96	C₂×#41×C₆₁	—	2	2	no	—
97	C₂×#41×C₆₁	—	2	1	no	—
98	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
99	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
100	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₆₁	—	2	1	no	—
102	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
106	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
107	C₂×D₈×C₆₁	C₂³	1	2	yes	—
108	C₂×D₈×C₆₁	C₂³	1	4	yes	—
109	C₄⋊Q₈×C₆₁	—	2	1	no	—
110	C₄⋊Q₈×C₆₁	—	2	2	no	—
111	C₄⋊Q₈×C₆₁	—	2	1	no	—
112	C₄⋊Q₈×C₆₁	—	2	1	no	—
113	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
115	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
116	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
117	#127×C₆₁	C₂³	1	1	yes	characteristic
118	#127×C₆₁	C₂³	1	2	yes	—
119	#126×C₆₁	—	2	4	no	—
120	#126×C₆₁	—	2	4	no	—
121	#126×C₆₁	—	2	4	no	—
122	#126×C₆₁	—	2	4	no	—
123	#126×C₆₁	—	2	1	no	—
124	#126×C₆₁	—	2	2	no	—
125	#125×C₆₁	C₂³	1	1	yes	characteristic
126	#125×C₆₁	C₂³	1	2	yes	—
127	#124×C₆₁	—	2	1	no	—
128	#124×C₆₁	—	2	2	no	—
129	#124×C₆₁	—	2	1	no	—
130	#124×C₆₁	—	2	2	no	—
131	#124×C₆₁	—	2	2	no	—
132	#124×C₆₁	—	2	2	no	—
133	#124×C₆₁	C₂³	1	4	yes	—
134	#124×C₆₁	C₂³	1	4	yes	—
135	#124×C₆₁	C₂³	1	1	yes	characteristic
136	#124×C₆₁	C₂³	1	2	yes	—
137	#123×C₆₁	—	2	2	no	—
138	#123×C₆₁	—	2	1	no	—
139	#123×C₆₁	—	2	2	no	—
140	#123×C₆₁	—	2	2	no	—
141	#123×C₆₁	—	2	2	no	—
142	C₂²⋊Q₈×C₆₁	—	2	1	no	—
143	C₂²⋊Q₈×C₆₁	—	2	2	no	—
144	C₂²⋊Q₈×C₆₁	—	2	2	no	—
145	C₂²⋊Q₈×C₆₁	—	2	2	no	—
146	C₂²⋊Q₈×C₆₁	—	2	4	no	—
147	C₂²⋊Q₈×C₆₁	—	2	2	no	—
148	C₂²⋊Q₈×C₆₁	—	2	2	no	—
149	C₂²⋊Q₈×C₆₁	—	2	2	no	—
150	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
151	#121×C₆₁	—	2	1	no	—
152	#121×C₆₁	—	2	2	no	—
153	#121×C₆₁	—	2	1	no	—
154	#121×C₆₁	—	2	2	no	—
155	#121×C₆₁	C₂³	1	1	yes	characteristic
156	#121×C₆₁	C₂³	1	2	yes	—
157	C₄×Q₈×C₆₁	—	2	1	no	—
158	C₄×Q₈×C₆₁	—	2	2	no	—
159	C₄×Q₈×C₆₁	—	2	2	no	—
160	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
161	C₄×Q₈×C₆₁	D₄	1	2	yes	—
162	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
163	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
164	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
165	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
167	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
170	C₄×D₄×C₆₁	—	2	1	no	—
171	C₄×D₄×C₆₁	—	2	2	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	—	2	1	no	—
177	C₄×D₄×C₆₁	—	2	1	no	—
178	C₄×D₄×C₆₁	C₂³	1	2	yes	—
179	C₄×D₄×C₆₁	C₂³	1	2	yes	—
180	C₄×D₄×C₆₁	C₂³	1	2	yes	—
181	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₆₁	C₂³	1	2	yes	—
183	C₄×D₄×C₆₁	C₂³	1	2	yes	—
184	C₄×D₄×C₆₁	C₂³	1	2	yes	—
185	#117×C₆₁	—	2	2	no	—
186	#117×C₆₁	—	2	2	no	—
187	#117×C₆₁	—	2	4	no	—
188	#117×C₆₁	—	2	1	no	—
189	#117×C₆₁	—	2	2	no	—
190	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
191	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
192	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
193	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
194	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
195	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
197	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
200	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
201	C₂×C₄²×C₆₁	—	2	2	no	—
202	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
204	#107×C₆₁	C₂³	1	2	yes	—
205	#106×C₆₁	C₂³	1	2	yes	—
206	#106×C₆₁	C₂³	1	4	yes	—
207	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
208	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
209	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
210	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
211	#103×C₆₁	C₂³	1	2	yes	—
212	#103×C₆₁	C₂³	1	4	yes	—
213	#103×C₆₁	C₂³	1	4	yes	—
214	#103×C₆₁	C₂³	1	4	yes	—
215	#103×C₆₁	C₂³	1	4	yes	—
216	#102×C₆₁	C₂³	1	2	yes	—
217	#102×C₆₁	C₂³	1	2	yes	—
218	#102×C₆₁	C₂³	1	2	yes	—
219	#102×C₆₁	C₂³	1	4	yes	—
220	#102×C₆₁	C₂³	1	4	yes	—
221	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
222	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
223	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
224	#97×C₆₁	C₂³	1	4	yes	—
225	#97×C₆₁	C₂³	1	2	yes	—
226	C₄×C₈×C₆₁	C₂³	1	2	yes	—
227	C₄×C₈×C₆₁	C₂³	1	4	yes	—
228	C₂⁴×C₆₁	—	2	1	no	—
229	#41×C₆₁	—	4	4	no	—
230	#41×C₆₁	—	8	4	no	—
231	#41×C₆₁	—	8	2	no	—
232	C₂×Q₈×C₆₁	—	2	2	no	—
233	C₂×Q₈×C₆₁	—	2	2	no	—
234	C₂×Q₈×C₆₁	—	2	1	no	—
235	C₂×Q₈×C₆₁	—	4	2	no	—
236	C₂×Q₈×C₆₁	—	4	4	no	—
237	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
238	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
239	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
240	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
241	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
242	C₂×D₄×C₆₁	—	2	1	no	—
243	C₂×D₄×C₆₁	—	2	2	no	—
244	C₂×D₄×C₆₁	—	2	2	no	—
245	C₂×D₄×C₆₁	—	2	1	no	—
246	C₂×D₄×C₆₁	—	2	1	no	—
247	C₂×D₄×C₆₁	—	2	2	no	—
248	C₂×D₄×C₆₁	—	2	1	no	—
249	C₂×D₄×C₆₁	—	4	2	no	—
250	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
251	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
252	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₆₁	—	2	1	no	—
254	C₂²×C₄×C₆₁	—	2	2	no	—
255	C₂²×C₄×C₆₁	—	2	2	no	—
256	C₂²×C₄×C₆₁	—	2	1	no	—
257	C₂²×C₄×C₆₁	—	2	2	no	—
258	C₂²×C₄×C₆₁	—	2	2	no	—
259	C₂²×C₄×C₆₁	—	2	2	no	—
260	C₂²×C₄×C₆₁	—	2	2	no	—
261	C₂²×C₄×C₆₁	—	2	2	no	—
262	C₂²×C₄×C₆₁	—	4	4	no	—
263	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
268	Q₁₆×C₆₁	—	4	4	no	—
269	SD₁₆×C₆₁	—	4	4	no	—
270	SD₁₆×C₆₁	—	4	4	no	—
271	SD₁₆×C₆₁	—	4	4	no	—
272	SD₁₆×C₆₁	—	4	2	no	—
273	D₈×C₆₁	—	4	2	no	—
274	D₈×C₆₁	—	4	4	no	—
275	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
276	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
277	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
278	C₄⋊C₄×C₆₁	—	2	2	no	—
279	C₄⋊C₄×C₆₁	—	2	1	no	—
280	C₄⋊C₄×C₆₁	—	2	2	no	—
281	C₄⋊C₄×C₆₁	—	2	2	no	—
282	C₄⋊C₄×C₆₁	—	2	2	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	2	no	—
287	C₄⋊C₄×C₆₁	—	2	2	no	—
288	C₄⋊C₄×C₆₁	—	2	1	no	—
289	C₄⋊C₄×C₆₁	—	2	1	no	—
290	C₄⋊C₄×C₆₁	—	2	2	no	—
291	C₄⋊C₄×C₆₁	—	2	1	no	—
292	C₄⋊C₄×C₆₁	—	2	2	no	—
293	C₄⋊C₄×C₆₁	—	2	1	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	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
304	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
305	C₂²⋊C₄×C₆₁	—	2	1	no	—
306	C₂²⋊C₄×C₆₁	—	2	4	no	—
307	C₂²⋊C₄×C₆₁	—	2	4	no	—
308	C₂²⋊C₄×C₆₁	—	2	2	no	—
309	C₂²⋊C₄×C₆₁	—	2	2	no	—
310	C₂²⋊C₄×C₆₁	—	2	4	no	—
311	C₂²⋊C₄×C₆₁	—	2	4	no	—
312	C₂²⋊C₄×C₆₁	—	2	1	no	—
313	C₂²⋊C₄×C₆₁	—	2	2	no	—
314	C₂²⋊C₄×C₆₁	—	2	2	no	—
315	C₂²⋊C₄×C₆₁	—	2	1	no	—
316	C₂²⋊C₄×C₆₁	—	2	2	no	—
317	C₂²⋊C₄×C₆₁	—	2	1	no	—
318	C₂²⋊C₄×C₆₁	—	2	2	no	—
319	C₂²⋊C₄×C₆₁	—	2	1	no	—
320	C₂²⋊C₄×C₆₁	—	2	2	no	—
321	C₂²⋊C₄×C₆₁	—	2	2	no	—
322	C₂²⋊C₄×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	—	2	1	no	—
327	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₆₁	C₂×D₄	1	2	yes	—
329	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₆₁	C₂×D₄	1	2	yes	—
331	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
332	C₄²×C₆₁	C₂⁴	1	2	yes	—
333	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
334	C₄²×C₆₁	C₂⁴	1	2	yes	—
335	C₂³×C₆₁	—	2	2	no	—
336	C₂³×C₆₁	—	2	2	no	—
337	C₂³×C₆₁	—	2	1	no	—
338	C₂³×C₆₁	—	4	2	no	—
339	C₂³×C₆₁	—	4	2	no	—
340	C₂³×C₆₁	—	4	2	no	—
341	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
342	Q₈×C₆₁	—	2	2	no	—
343	Q₈×C₆₁	—	2	2	no	—
344	Q₈×C₆₁	—	2	4	no	—
345	Q₈×C₆₁	—	2	2	no	—
346	Q₈×C₆₁	—	2	4	no	—
347	Q₈×C₆₁	—	4	2	no	—
348	Q₈×C₆₁	—	4	4	no	—
349	Q₈×C₆₁	—	8	2	no	—
350	Q₈×C₆₁	—	8	1	no	—
351	D₄×C₆₁	—	2	2	no	—
352	D₄×C₆₁	—	2	2	no	—
353	D₄×C₆₁	—	2	4	no	—
354	D₄×C₆₁	—	2	2	no	—
355	D₄×C₆₁	—	4	2	no	—
356	D₄×C₆₁	—	4	4	no	—
357	D₄×C₆₁	—	4	2	no	—
358	D₄×C₆₁	—	4	4	no	—
359	D₄×C₆₁	—	4	2	no	—
360	D₄×C₆₁	—	8	2	no	—
361	D₄×C₆₁	—	8	1	no	—
362	C₂×C₄×C₆₁	—	2	4	no	—
363	C₂×C₄×C₆₁	—	2	2	no	—
364	C₂×C₄×C₆₁	—	2	2	no	—
365	C₂×C₄×C₆₁	—	2	2	no	—
366	C₂×C₄×C₆₁	—	2	2	no	—
367	C₂×C₄×C₆₁	—	2	1	no	—
368	C₂×C₄×C₆₁	—	2	4	no	—
369	C₂×C₄×C₆₁	—	2	2	no	—
370	C₂×C₄×C₆₁	—	2	1	no	—
371	C₂×C₄×C₆₁	—	2	1	no	—
372	C₂×C₄×C₆₁	—	4	2	no	—
373	C₂×C₄×C₆₁	—	4	4	no	—
374	C₂×C₄×C₆₁	—	4	4	no	—
375	C₂×C₄×C₆₁	—	4	2	no	—
376	C₂×C₄×C₆₁	—	4	4	no	—
377	C₂×C₄×C₆₁	—	4	4	no	—
378	C₂×C₄×C₆₁	—	4	2	no	—
379	C₂×C₄×C₆₁	—	8	2	no	—
380	C₂×C₄×C₆₁	—	8	2	no	—
381	C₂×C₄×C₆₁	—	8	2	no	—
382	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
383	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
387	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
392	C₈×C₆₁	—	2	2	no	—
393	C₈×C₆₁	—	2	4	no	—
394	C₈×C₆₁	—	2	2	no	—
395	#61899	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
396	C₂²×C₆₁	—	2	1	no	—
397	C₂²×C₆₁	—	2	1	no	—
398	C₂²×C₆₁	—	4	2	no	—
399	C₂²×C₆₁	—	4	2	no	—
400	C₂²×C₆₁	—	4	1	no	—
401	C₂²×C₆₁	—	4	2	no	—
402	C₂²×C₆₁	—	4	2	no	—
403	C₂²×C₆₁	—	4	1	no	—
404	C₂²×C₆₁	—	4	2	no	—
405	C₂²×C₆₁	—	4	1	no	—
406	C₂²×C₆₁	—	4	2	no	—
407	C₂²×C₆₁	—	8	4	no	—
408	C₂²×C₆₁	#577	1	2	yes	—
409	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
410	C₄×C₆₁	—	2	1	no	—
411	C₄×C₆₁	—	2	1	no	—
412	C₄×C₆₁	—	2	2	no	—
413	C₄×C₆₁	—	2	2	no	—
414	C₄×C₆₁	—	2	2	no	—
415	C₄×C₆₁	—	2	1	no	—
416	C₄×C₆₁	—	2	2	no	—
417	C₄×C₆₁	—	2	1	no	—
418	C₄×C₆₁	—	4	4	no	—
419	C₄×C₆₁	—	4	1	no	—
420	C₄×C₆₁	—	4	2	no	—
421	C₄×C₆₁	—	4	1	no	—
422	C₄×C₆₁	—	4	2	no	—
423	C₄×C₆₁	—	4	1	no	—
424	C₄×C₆₁	#575	1	2	yes	—
425	C₄×C₆₁	#585	1	2	yes	—
426	#3522	C₂×C₆₁	1	1	yes	characteristic, complemented
427	C₂×#556	C₂×C₆₁	1	1	yes	characteristic, complemented
428	#3401	C₂×C₆₁	1	4	yes	complemented
429	#3397	C₂×C₆₁	1	2	yes	complemented
430	#3394	C₂×C₆₁	1	2	yes	complemented
431	#3376	C₂×C₆₁	1	4	yes	complemented
432	#3369	C₂×C₆₁	1	2	yes	complemented
433	#3360	C₂×C₆₁	1	2	yes	complemented
434	#3218	C₂×C₆₁	1	1	yes	characteristic, complemented
435	#3213	C₂×C₆₁	1	2	yes	complemented
436	#3211	C₂×C₆₁	1	2	yes	complemented
437	#3206	C₂×C₆₁	1	1	yes	characteristic, complemented
438	#3117	C₂×C₆₁	1	2	yes	complemented
439	#3109	C₂×C₆₁	1	1	yes	characteristic, complemented
440	#3105	C₂×C₆₁	1	1	yes	characteristic, complemented
441	#3103	C₂×C₆₁	1	2	yes	complemented
442	#2984	C₂×C₆₁	1	1	yes	characteristic, complemented
443	C₂×C₆₁	—	2	2	no	—
444	C₂×C₆₁	—	8	2	no	—
445	C₂×C₆₁	—	8	1	no	—
446	C₂×C₆₁	—	8	2	no	—
447	C₂×C₆₁	#3487	1	1	yes	characteristic
448	C₂×C₆₁	C₂×#575	1	1	yes	characteristic
449	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
450	#559	C₂²×C₆₁	1	1	yes	characteristic, complemented
451	#559	C₂²×C₆₁	1	2	yes	complemented
452	Q₈²	C₂²×C₆₁	1	1	yes	characteristic, complemented
453	#556	—	2	1	no	—
454	#556	—	2	1	no	—
455	#556	—	2	2	no	—
456	#556	C₂²×C₆₁	1	2	yes	—
457	#556	C₂²×C₆₁	1	2	yes	—
458	#556	C₂²×C₆₁	1	4	yes	—
459	#554	C₂²×C₆₁	1	1	yes	characteristic, complemented
460	#554	C₂²×C₆₁	1	2	yes	complemented
461	#550	C₂²×C₆₁	1	1	yes	characteristic, complemented
462	#548	—	2	1	no	—
463	#547	—	2	1	no	—
464	#547	—	2	2	no	—
465	#542	—	2	1	no	—
466	#542	—	2	2	no	—
467	#532	C₂²×C₆₁	1	2	yes	—
468	#532	C₂²×C₆₁	1	1	yes	characteristic
469	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
470	#529	C₂²×C₆₁	1	1	yes	characteristic
471	#529	C₂²×C₆₁	1	2	yes	—
472	C₂×#126	—	2	2	no	—
473	C₂×#124	C₂²×C₆₁	1	2	yes	—
474	C₂×C₂²⋊Q₈	—	2	1	no	—
475	#520	—	2	1	no	—
476	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
477	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
478	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
479	C₂×#117	—	2	1	no	—
480	#497	C₂²×C₆₁	1	2	yes	complemented
481	#496	C₂²×C₆₁	1	4	yes	—
482	#495	C₂²×C₆₁	1	4	yes	—
483	#492	C₂²×C₆₁	1	2	yes	complemented
484	#491	C₂²×C₆₁	1	2	yes	complemented
485	#489	C₂²×C₆₁	1	4	yes	—
486	#488	C₂²×C₆₁	1	4	yes	—
487	#487	C₂²×C₆₁	1	2	yes	complemented
488	#484	C₂²×C₆₁	1	1	yes	characteristic
489	#481	C₂²×C₆₁	1	1	yes	characteristic
490	#481	C₂²×C₆₁	1	2	yes	—
491	#479	C₂²×C₆₁	1	4	yes	complemented
492	#478	C₂²×C₆₁	1	2	yes	—
493	#476	C₂²×C₆₁	1	2	yes	—
494	#475	C₂²×C₆₁	1	4	yes	complemented
495	#464	C₂²×C₆₁	1	4	yes	—
496	#464	C₂²×C₆₁	1	4	yes	complemented
497	#463	C₂²×C₆₁	1	4	yes	—
498	#463	C₂²×C₆₁	1	2	yes	—
499	#463	C₂²×C₆₁	1	4	yes	—
500	#463	C₂²×C₆₁	1	4	yes	—
501	#462	C₂²×C₆₁	1	2	yes	complemented
502	#461	C₂²×C₆₁	1	2	yes	complemented
503	#461	C₂²×C₆₁	1	4	yes	complemented
504	#460	C₂²×C₆₁	1	4	yes	complemented
505	#459	C₂²×C₆₁	1	2	yes	—
506	#451	C₂²×C₆₁	1	2	yes	—
507	#450	C₂²×C₆₁	1	1	yes	characteristic
508	#448	C₂²×C₆₁	1	2	yes	—
509	#448	C₂²×C₆₁	1	2	yes	—
510	#448	C₂²×C₆₁	1	2	yes	—
511	#447	C₂²×C₆₁	1	1	yes	characteristic
512	#447	C₂²×C₆₁	1	2	yes	—
513	#446	C₂²×C₆₁	1	2	yes	complemented
514	#446	C₂²×C₆₁	1	4	yes	complemented
515	C₈×Q₈	C₂²×C₆₁	1	2	yes	complemented
516	#442	C₂²×C₆₁	1	4	yes	—
517	#441	C₂²×C₆₁	1	4	yes	complemented
518	#440	C₂²×C₆₁	1	4	yes	complemented
519	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
520	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	complemented
521	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	complemented
522	C₄×D₈	C₂²×C₆₁	1	2	yes	—
523	#432	C₂²×C₆₁	1	1	yes	characteristic
524	#432	C₂²×C₆₁	1	2	yes	—
525	#431	C₂²×C₆₁	1	2	yes	—
526	#431	C₂²×C₆₁	1	1	yes	characteristic
527	C₆₁	#61899	1	1	yes	characteristic, direct product factor, Sylow
528	C₂×#41	—	2	1	no	—
529	C₂×#41	—	2	2	no	—
530	C₂×#41	—	2	1	no	—
531	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
532	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
533	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
534	C₂³×C₄	—	2	1	no	—
535	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
536	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
537	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
538	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
539	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
540	C₂×D₈	C₂³×C₆₁	1	2	yes	—
541	C₂×D₈	C₂³×C₆₁	1	4	yes	—
542	C₄⋊Q₈	—	2	1	no	—
543	C₄⋊Q₈	—	2	2	no	—
544	C₄⋊Q₈	—	2	1	no	—
545	C₄⋊Q₈	—	2	1	no	—
546	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
547	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
548	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
549	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
550	#127	C₂³×C₆₁	1	1	yes	characteristic
551	#127	C₂³×C₆₁	1	2	yes	—
552	#126	—	2	4	no	—
553	#126	—	2	4	no	—
554	#126	—	2	4	no	—
555	#126	—	2	4	no	—
556	#126	—	2	1	no	—
557	#126	—	2	2	no	—
558	#125	C₂³×C₆₁	1	1	yes	characteristic
559	#125	C₂³×C₆₁	1	2	yes	—
560	#124	—	2	1	no	—
561	#124	—	2	2	no	—
562	#124	—	2	2	no	—
563	#124	—	2	2	no	—
564	#124	—	2	1	no	—
565	#124	—	2	2	no	—
566	#124	C₂³×C₆₁	1	4	yes	—
567	#124	C₂³×C₆₁	1	4	yes	—
568	#124	C₂³×C₆₁	1	1	yes	characteristic
569	#124	C₂³×C₆₁	1	2	yes	—
570	#123	—	2	2	no	—
571	#123	—	2	1	no	—
572	#123	—	2	2	no	—
573	#123	—	2	2	no	—
574	#123	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	2	no	—
577	C₂²⋊Q₈	—	2	4	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	—	2	2	no	—
583	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
584	#121	—	2	1	no	—
585	#121	—	2	2	no	—
586	#121	—	2	1	no	—
587	#121	—	2	2	no	—
588	#121	C₂³×C₆₁	1	1	yes	characteristic
589	#121	C₂³×C₆₁	1	2	yes	—
590	C₄×Q₈	—	2	1	no	—
591	C₄×Q₈	—	2	2	no	—
592	C₄×Q₈	—	2	2	no	—
593	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
594	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
595	C₄×Q₈	D₄×C₆₁	1	2	yes	—
596	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
597	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
598	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
600	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
602	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	2	no	—
611	C₄×D₄	C₂³×C₆₁	1	2	yes	—
612	C₄×D₄	C₂³×C₆₁	1	2	yes	—
613	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
614	C₄×D₄	C₂³×C₆₁	1	2	yes	—
615	C₄×D₄	C₂³×C₆₁	1	2	yes	—
616	C₄×D₄	C₂³×C₆₁	1	2	yes	—
617	C₄×D₄	C₂³×C₆₁	1	2	yes	—
618	#117	—	2	2	no	—
619	#117	—	2	2	no	—
620	#117	—	2	4	no	—
621	#117	—	2	1	no	—
622	#117	—	2	2	no	—
623	C₂×C₄⋊C₄	—	2	1	no	—
624	C₂×C₄⋊C₄	—	2	2	no	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	—	2	2	no	—
628	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
629	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	—	2	2	no	—
632	C₂×C₂²⋊C₄	—	2	1	no	—
633	C₂×C₂²⋊C₄	—	2	2	no	—
634	C₂×C₄²	—	2	2	no	—
635	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
637	#107	C₂³×C₆₁	1	2	yes	—
638	#106	C₂³×C₆₁	1	2	yes	—
639	#106	C₂³×C₆₁	1	4	yes	—
640	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
641	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
642	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
643	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
644	#103	C₂³×C₆₁	1	2	yes	—
645	#103	C₂³×C₆₁	1	4	yes	—
646	#103	C₂³×C₆₁	1	4	yes	—
647	#103	C₂³×C₆₁	1	4	yes	—
648	#103	C₂³×C₆₁	1	4	yes	—
649	#102	C₂³×C₆₁	1	2	yes	—
650	#102	C₂³×C₆₁	1	2	yes	—
651	#102	C₂³×C₆₁	1	2	yes	—
652	#102	C₂³×C₆₁	1	4	yes	—
653	#102	C₂³×C₆₁	1	4	yes	—
654	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
655	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
656	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
657	#97	C₂³×C₆₁	1	4	yes	—
658	#97	C₂³×C₆₁	1	2	yes	—
659	C₄×C₈	C₂³×C₆₁	1	2	yes	—
660	C₄×C₈	C₂³×C₆₁	1	4	yes	—
661	C₂⁴	—	2	1	no	—
662	#41	—	4	4	no	—
663	#41	—	8	4	no	—
664	#41	—	8	2	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	4	2	no	—
669	C₂×Q₈	—	4	4	no	—
670	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
671	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
672	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
673	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
674	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	4	2	no	—
683	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
684	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
685	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	4	4	no	—
696	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
697	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
699	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
701	Q₁₆	—	4	4	no	—
702	SD₁₆	—	4	4	no	—
703	SD₁₆	—	4	4	no	—
704	SD₁₆	—	4	4	no	—
705	SD₁₆	—	4	2	no	—
706	D₈	—	4	2	no	—
707	D₈	—	4	4	no	—
708	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
709	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
710	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
728	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
729	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
730	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
731	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
732	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
733	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
734	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
735	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
736	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
738	C₂²⋊C₄	—	2	1	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₄²	—	2	4	no	—
757	C₄²	—	2	4	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	1	no	—
760	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
761	C₄²	C₂×D₄×C₆₁	1	2	yes	—
762	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
763	C₄²	C₂×D₄×C₆₁	1	2	yes	—
764	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
765	C₄²	C₂⁴×C₆₁	1	2	yes	—
766	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
767	C₄²	C₂⁴×C₆₁	1	2	yes	—
768	C₂³	—	2	2	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	4	2	no	—
772	C₂³	—	4	2	no	—
773	C₂³	—	4	2	no	—
774	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
775	Q₈	—	2	2	no	—
776	Q₈	—	2	2	no	—
777	Q₈	—	2	4	no	—
778	Q₈	—	2	2	no	—
779	Q₈	—	2	4	no	—
780	Q₈	—	4	2	no	—
781	Q₈	—	4	4	no	—
782	Q₈	—	8	2	no	—
783	Q₈	—	8	1	no	—
784	D₄	—	2	2	no	—
785	D₄	—	2	2	no	—
786	D₄	—	2	4	no	—
787	D₄	—	2	2	no	—
788	D₄	—	4	2	no	—
789	D₄	—	4	4	no	—
790	D₄	—	4	2	no	—
791	D₄	—	4	4	no	—
792	D₄	—	4	2	no	—
793	D₄	—	8	2	no	—
794	D₄	—	8	1	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	4	2	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	8	2	no	—
813	C₂×C₄	—	8	2	no	—
814	C₂×C₄	—	8	2	no	—
815	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
816	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
818	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
819	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
820	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
821	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
822	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
823	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
824	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
825	C₈	—	2	2	no	—
826	C₈	—	2	4	no	—
827	C₈	—	2	2	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	8	4	no	—
840	C₂²	C₆₁×#577	1	2	yes	—
841	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
842	C₄	—	2	1	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	1	no	—
847	C₄	—	2	2	no	—
848	C₄	—	2	1	no	—
849	C₄	—	2	1	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	4	no	—
855	C₄	—	4	1	no	—
856	C₄	C₆₁×#575	1	2	yes	—
857	C₄	C₆₁×#585	1	2	yes	—
858	C₂	—	2	2	no	—
859	C₂	—	8	2	no	—
860	C₂	—	8	2	no	—
861	C₂	—	8	1	no	—
862	C₂	C₆₁×#3487	1	1	yes	characteristic
863	C₂	C₂×C₆₁×#575	1	1	yes	characteristic
864	C₂	C₂×C₆₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄×Q₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3522	C₂	semidirect
2. C₂×C₆₁×#556	C₂	semidirect
3. C₆₁×#3401	C₂	semidirect
4. C₆₁×#3397	C₂	semidirect
5. C₆₁×#3394	C₂	semidirect
6. C₆₁×#3376	C₂	semidirect
7. C₆₁×#3369	C₂	semidirect
8. C₆₁×#3360	C₂	semidirect
9. C₆₁×#3218	C₂	semidirect
10. C₆₁×#3213	C₂	semidirect
11. C₆₁×#3211	C₂	semidirect
12. C₆₁×#3206	C₂	semidirect
13. C₆₁×#3117	C₂	semidirect
14. C₆₁×#3109	C₂	semidirect
15. C₆₁×#3105	C₂	semidirect
16. C₆₁×#3103	C₂	semidirect
17. C₆₁×#2984	C₂	semidirect
18. C₆₁×#559	C₂²	semidirect
19. C₆₁×#559	C₂²	semidirect
20. Q₈²×C₆₁	C₂²	semidirect
27. C₆₁×#554	C₂²	semidirect
28. C₆₁×#554	C₂²	semidirect
29. C₆₁×#550	C₂²	semidirect
48. C₆₁×#497	C₂²	semidirect
51. C₆₁×#492	C₂²	semidirect
52. C₆₁×#491	C₂²	semidirect
55. C₆₁×#487	C₂²	semidirect
59. C₆₁×#479	C₂²	semidirect
62. C₆₁×#475	C₂²	semidirect
64. C₆₁×#464	C₂²	semidirect
69. C₆₁×#462	C₂²	semidirect
70. C₆₁×#461	C₂²	semidirect
71. C₆₁×#461	C₂²	semidirect
72. C₆₁×#460	C₂²	semidirect
81. C₆₁×#446	C₂²	semidirect
82. C₆₁×#446	C₂²	semidirect
83. C₈×Q₈×C₆₁	C₂²	semidirect
85. C₆₁×#441	C₂²	semidirect
86. C₆₁×#440	C₂²	semidirect
88. C₄×SD₁₆×C₆₁	C₂²	semidirect
89. C₄×SD₁₆×C₆₁	C₂²	semidirect
395. #61899	C₆₁	direct (N × H)
426. #3522	C₂×C₆₁	semidirect
427. C₂×#556	C₂×C₆₁	semidirect
428. #3401	C₂×C₆₁	semidirect
429. #3397	C₂×C₆₁	semidirect
430. #3394	C₂×C₆₁	semidirect
431. #3376	C₂×C₆₁	semidirect
432. #3369	C₂×C₆₁	semidirect
433. #3360	C₂×C₆₁	semidirect
434. #3218	C₂×C₆₁	semidirect
435. #3213	C₂×C₆₁	semidirect
436. #3211	C₂×C₆₁	semidirect
437. #3206	C₂×C₆₁	semidirect
438. #3117	C₂×C₆₁	semidirect
439. #3109	C₂×C₆₁	semidirect
440. #3105	C₂×C₆₁	semidirect
441. #3103	C₂×C₆₁	semidirect
442. #2984	C₂×C₆₁	semidirect
450. #559	C₂²×C₆₁	semidirect
451. #559	C₂²×C₆₁	semidirect
452. Q₈²	C₂²×C₆₁	semidirect
459. #554	C₂²×C₆₁	semidirect
460. #554	C₂²×C₆₁	semidirect
461. #550	C₂²×C₆₁	semidirect
480. #497	C₂²×C₆₁	semidirect
483. #492	C₂²×C₆₁	semidirect
484. #491	C₂²×C₆₁	semidirect
487. #487	C₂²×C₆₁	semidirect
491. #479	C₂²×C₆₁	semidirect
494. #475	C₂²×C₆₁	semidirect
496. #464	C₂²×C₆₁	semidirect
501. #462	C₂²×C₆₁	semidirect
502. #461	C₂²×C₆₁	semidirect
503. #461	C₂²×C₆₁	semidirect
504. #460	C₂²×C₆₁	semidirect
513. #446	C₂²×C₆₁	semidirect
514. #446	C₂²×C₆₁	semidirect
515. C₈×Q₈	C₂²×C₆₁	semidirect
517. #441	C₂²×C₆₁	semidirect
518. #440	C₂²×C₆₁	semidirect
520. C₄×SD₁₆	C₂²×C₆₁	semidirect
521. C₄×SD₁₆	C₂²×C₆₁	semidirect
527. C₆₁	#61899	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×#3522	2
C₂×C₆₁×#556	2
C₆₁×#3401	2
C₆₁×#3397	2
C₆₁×#3394	2
C₆₁×#3376	2
C₆₁×#3369	2
C₆₁×#3360	2
C₆₁×#3218	2
C₆₁×#3213	2
C₆₁×#3211	2
C₆₁×#3206	2
C₆₁×#3117	2
C₆₁×#3109	2
C₆₁×#3105	2
C₆₁×#3103	2
C₆₁×#2984	2
#61899	61

Subgroups — C61×#61899 #29565332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61899 #29565332