Subgroups — C₆₁×#60957 #29564390

Order 15616.

1676 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3461	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3262	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3261	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3258	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3243	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3242	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3225	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3223	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3203	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#3202	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3201	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3172	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3170	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3168	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3108	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3107	C₂	1	2	yes	maximal, complemented
17	C₆₁×#3104	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3102	C₂	1	2	yes	maximal, complemented
19	C₆₁×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#544	C₂²	1	2	yes	—
21	C₆₁×#542	—	2	2	no	—
22	C₆₁×#542	C₂²	1	2	yes	—
23	C₆₁×#542	C₂²	1	2	yes	—
24	C₆₁×#541	—	2	2	no	—
25	C₆₁×#541	C₂²	1	2	yes	—
26	C₆₁×#541	C₂²	1	2	yes	—
27	C₆₁×#539	—	2	2	no	—
28	C₆₁×#539	—	2	2	no	—
29	C₆₁×#537	C₂²	1	2	yes	—
30	C₆₁×#536	C₂²	1	2	yes	—
31	C₆₁×#536	C₂²	1	2	yes	—
32	C₆₁×#533	—	2	2	no	—
33	C₆₁×#533	C₂²	1	2	yes	—
34	C₆₁×#533	C₂²	1	2	yes	—
35	C₆₁×#529	—	2	2	no	—
36	C₆₁×#529	—	2	2	no	—
37	C₆₁×#529	—	2	2	no	—
38	C₆₁×#529	C₂²	1	2	yes	—
39	C₆₁×#529	C₂²	1	2	yes	—
40	C₄×#41×C₆₁	C₂²	1	2	yes	—
41	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
43	C₆₁×#501	C₂²	1	2	yes	—
44	C₆₁×#500	C₂²	1	1	yes	characteristic
45	C₆₁×#499	C₂²	1	1	yes	characteristic
46	C₆₁×#497	C₂²	1	2	yes	—
47	C₆₁×#495	C₂²	1	1	yes	characteristic
48	C₆₁×#494	C₂²	1	1	yes	characteristic
49	C₆₁×#491	C₂²	1	2	yes	—
50	C₆₁×#489	C₂²	1	2	yes	—
51	C₆₁×#488	C₂²	1	2	yes	—
52	C₆₁×#487	C₂²	1	2	yes	—
53	C₆₁×#485	C₂²	1	2	yes	—
54	C₆₁×#485	C₂²	1	2	yes	—
55	C₆₁×#485	C₂²	1	2	yes	—
56	C₆₁×#484	C₂²	1	2	yes	—
57	C₆₁×#484	C₂²	1	2	yes	—
58	C₆₁×#483	C₂²	1	2	yes	—
59	C₆₁×#482	C₂²	1	2	yes	—
60	C₆₁×#480	C₂²	1	2	yes	—
61	C₆₁×#479	C₂²	1	2	yes	—
62	C₆₁×#479	C₂²	1	2	yes	—
63	C₆₁×#479	C₂²	1	2	yes	—
64	C₆₁×#478	C₂²	1	2	yes	—
65	C₆₁×#477	C₂²	1	2	yes	—
66	C₆₁×#477	C₂²	1	2	yes	—
67	C₆₁×#475	C₂²	1	2	yes	—
68	C₆₁×#474	C₂²	1	2	yes	—
69	C₆₁×#470	C₂²	1	2	yes	—
70	C₆₁×#470	C₂²	1	2	yes	—
71	C₆₁×#468	C₂²	1	2	yes	—
72	C₆₁×#468	C₂²	1	2	yes	—
73	C₆₁×#467	C₂²	1	1	yes	characteristic
74	C₆₁×#467	C₂²	1	2	yes	—
75	C₆₁×#467	C₂²	1	1	yes	characteristic
76	C₆₁×#467	C₂²	1	1	yes	characteristic
77	C₆₁×#466	C₂²	1	1	yes	characteristic
78	C₆₁×#465	C₂²	1	2	yes	—
79	C₆₁×#464	C₂²	1	2	yes	—
80	C₆₁×#464	C₂²	1	2	yes	—
81	C₆₁×#464	C₂²	1	2	yes	—
82	C₆₁×#463	C₂²	1	2	yes	—
83	C₆₁×#462	C₂²	1	2	yes	—
84	C₆₁×#462	C₂²	1	2	yes	—
85	C₆₁×#462	C₂²	1	2	yes	—
86	C₆₁×#461	C₂²	1	2	yes	—
87	C₆₁×#452	C₂²	1	2	yes	—
88	C₆₁×#452	C₂²	1	2	yes	—
89	C₆₁×#452	C₂²	1	2	yes	—
90	C₆₁×#451	C₂²	1	2	yes	—
91	C₆₁×#451	C₂²	1	2	yes	—
92	C₆₁×#451	C₂²	1	2	yes	—
93	C₆₁×#449	C₂²	1	2	yes	—
94	C₆₁×#448	C₂²	1	2	yes	—
95	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
96	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
97	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
98	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
99	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
100	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
101	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
102	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
103	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
104	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
105	C₆₁×#433	C₂²	1	2	yes	—
106	C₆₁×#433	C₂²	1	2	yes	—
107	C₆₁×#431	C₂²	1	2	yes	—
108	C₆₁×#431	C₂²	1	2	yes	—
109	C₆₁×#424	C₂²	1	1	yes	characteristic
110	C₆₁×#424	C₂²	1	1	yes	characteristic
111	C₆₁×#408	C₂²	1	1	yes	characteristic
112	C₆₁×#408	C₂²	1	1	yes	characteristic
113	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
114	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
115	C₂×#41×C₆₁	C₂³	1	2	yes	—
116	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
117	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
118	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
119	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
120	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
121	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
122	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
123	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
124	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
127	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
128	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
129	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
130	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
132	C₄⋊Q₈×C₆₁	—	2	2	no	—
133	C₄⋊Q₈×C₆₁	—	2	2	no	—
134	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
136	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
138	#126×C₆₁	—	2	2	no	—
139	#126×C₆₁	—	2	2	no	—
140	#126×C₆₁	—	2	2	no	—
141	#126×C₆₁	—	2	2	no	—
142	#126×C₆₁	—	2	2	no	—
143	#126×C₆₁	—	2	2	no	—
144	#126×C₆₁	—	2	2	no	—
145	#126×C₆₁	—	2	2	no	—
146	#125×C₆₁	—	2	2	no	—
147	#125×C₆₁	—	2	2	no	—
148	#125×C₆₁	—	2	2	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	C₂³	1	2	yes	—
154	#125×C₆₁	C₂³	1	2	yes	—
155	#124×C₆₁	—	2	2	no	—
156	#124×C₆₁	—	2	2	no	—
157	#124×C₆₁	—	2	2	no	—
158	#124×C₆₁	C₂³	1	2	yes	—
159	#124×C₆₁	C₂³	1	2	yes	—
160	#123×C₆₁	—	2	2	no	—
161	#123×C₆₁	—	2	2	no	—
162	#123×C₆₁	—	2	2	no	—
163	#123×C₆₁	—	2	2	no	—
164	#123×C₆₁	—	2	2	no	—
165	#123×C₆₁	—	2	2	no	—
166	#123×C₆₁	—	2	2	no	—
167	#123×C₆₁	—	2	2	no	—
168	C₂²⋊Q₈×C₆₁	—	2	2	no	—
169	C₂²⋊Q₈×C₆₁	—	2	2	no	—
170	C₂²⋊Q₈×C₆₁	—	2	2	no	—
171	C₂²⋊Q₈×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	2	no	—
176	C₂²⋊Q₈×C₆₁	—	2	2	no	—
177	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
178	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
179	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
180	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
181	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
182	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
183	#121×C₆₁	—	2	2	no	—
184	#121×C₆₁	—	2	2	no	—
185	#121×C₆₁	—	2	2	no	—
186	#121×C₆₁	C₂³	1	2	yes	—
187	#121×C₆₁	C₂³	1	2	yes	—
188	C₄×Q₈×C₆₁	—	2	2	no	—
189	C₄×Q₈×C₆₁	—	2	2	no	—
190	C₄×Q₈×C₆₁	—	2	2	no	—
191	C₄×Q₈×C₆₁	—	2	2	no	—
192	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
193	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
194	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
195	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
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×D₄×C₆₁	—	2	2	no	—
201	C₄×D₄×C₆₁	—	2	2	no	—
202	C₄×D₄×C₆₁	—	2	2	no	—
203	C₄×D₄×C₆₁	—	2	2	no	—
204	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
205	C₄×D₄×C₆₁	D₄	1	2	yes	—
206	C₄×D₄×C₆₁	D₄	1	2	yes	—
207	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
208	C₄×D₄×C₆₁	C₂³	1	2	yes	—
209	C₄×D₄×C₆₁	C₂³	1	2	yes	—
210	#117×C₆₁	—	2	2	no	—
211	#117×C₆₁	—	2	2	no	—
212	#117×C₆₁	—	2	2	no	—
213	#117×C₆₁	—	2	2	no	—
214	#117×C₆₁	—	2	2	no	—
215	#117×C₆₁	C₂³	1	2	yes	—
216	#117×C₆₁	C₂³	1	2	yes	—
217	#117×C₆₁	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
219	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
220	C₂×C₄²×C₆₁	—	2	2	no	—
221	C₂×C₄²×C₆₁	—	2	2	no	—
222	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
224	#107×C₆₁	C₂³	1	1	yes	characteristic
225	#107×C₆₁	C₂³	1	1	yes	characteristic
226	#107×C₆₁	C₂³	1	1	yes	characteristic
227	#107×C₆₁	C₂³	1	2	yes	—
228	#107×C₆₁	C₂³	1	1	yes	characteristic
229	#107×C₆₁	C₂³	1	2	yes	—
230	#107×C₆₁	C₂³	1	2	yes	—
231	#106×C₆₁	C₂³	1	2	yes	—
232	#106×C₆₁	C₂³	1	2	yes	—
233	#106×C₆₁	C₂³	1	2	yes	—
234	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
235	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
236	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
237	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
238	#103×C₆₁	C₂³	1	2	yes	—
239	#103×C₆₁	C₂³	1	2	yes	—
240	#103×C₆₁	C₂³	1	2	yes	—
241	#103×C₆₁	C₂³	1	2	yes	—
242	#103×C₆₁	C₂³	1	2	yes	—
243	#103×C₆₁	C₂³	1	2	yes	—
244	#103×C₆₁	C₂³	1	2	yes	—
245	#103×C₆₁	C₂³	1	2	yes	—
246	#103×C₆₁	C₂³	1	2	yes	—
247	#103×C₆₁	C₂³	1	2	yes	—
248	#103×C₆₁	C₂³	1	2	yes	—
249	#103×C₆₁	C₂³	1	2	yes	—
250	#102×C₆₁	C₂³	1	2	yes	—
251	#102×C₆₁	C₂³	1	2	yes	—
252	#102×C₆₁	C₂³	1	2	yes	—
253	#102×C₆₁	C₂³	1	2	yes	—
254	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
255	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
256	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
257	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
258	#97×C₆₁	C₂³	1	2	yes	—
259	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
260	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₆₁	C₂³	1	2	yes	—
264	#41×C₆₁	—	4	1	no	—
265	#41×C₆₁	—	4	1	no	—
266	#41×C₆₁	—	4	2	no	—
267	#41×C₆₁	—	4	2	no	—
268	C₂×Q₈×C₆₁	—	2	2	no	—
269	C₂×Q₈×C₆₁	—	2	2	no	—
270	C₂×Q₈×C₆₁	—	2	2	no	—
271	C₂×Q₈×C₆₁	—	4	2	no	—
272	C₂×Q₈×C₆₁	—	4	2	no	—
273	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
274	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
275	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
276	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
277	C₂×D₄×C₆₁	—	2	2	no	—
278	C₂×D₄×C₆₁	—	2	2	no	—
279	C₂×D₄×C₆₁	—	2	2	no	—
280	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
281	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
282	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₆₁	—	2	2	no	—
284	C₂²×C₄×C₆₁	—	2	2	no	—
285	C₂²×C₄×C₆₁	—	2	2	no	—
286	C₂²×C₄×C₆₁	—	2	2	no	—
287	C₂²×C₄×C₆₁	—	2	2	no	—
288	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
289	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
291	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
294	Q₁₆×C₆₁	—	4	1	no	—
295	Q₁₆×C₆₁	—	4	1	no	—
296	Q₁₆×C₆₁	—	4	2	no	—
297	Q₁₆×C₆₁	—	4	1	no	—
298	Q₁₆×C₆₁	—	4	2	no	—
299	Q₁₆×C₆₁	—	4	2	no	—
300	SD₁₆×C₆₁	—	4	2	no	—
301	SD₁₆×C₆₁	—	4	2	no	—
302	SD₁₆×C₆₁	—	4	2	no	—
303	D₈×C₆₁	—	4	1	no	—
304	M₁₆×C₆₁	—	4	1	no	—
305	M₁₆×C₆₁	—	4	1	no	—
306	C₂×C₈×C₆₁	—	4	1	no	—
307	C₂×C₈×C₆₁	—	4	1	no	—
308	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
309	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
310	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
311	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
312	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
313	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
314	C₄⋊C₄×C₆₁	—	2	2	no	—
315	C₄⋊C₄×C₆₁	—	2	2	no	—
316	C₄⋊C₄×C₆₁	—	2	2	no	—
317	C₄⋊C₄×C₆₁	—	2	2	no	—
318	C₄⋊C₄×C₆₁	—	2	2	no	—
319	C₄⋊C₄×C₆₁	—	2	2	no	—
320	C₄⋊C₄×C₆₁	—	2	2	no	—
321	C₄⋊C₄×C₆₁	—	2	2	no	—
322	C₄⋊C₄×C₆₁	—	2	2	no	—
323	C₄⋊C₄×C₆₁	—	2	2	no	—
324	C₄⋊C₄×C₆₁	—	2	2	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	2	no	—
334	C₄⋊C₄×C₆₁	—	2	2	no	—
335	C₄⋊C₄×C₆₁	—	2	2	no	—
336	C₄⋊C₄×C₆₁	—	2	2	no	—
337	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
338	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
339	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
340	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
341	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
342	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
343	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
345	C₂²⋊C₄×C₆₁	—	2	2	no	—
346	C₂²⋊C₄×C₆₁	—	2	2	no	—
347	C₂²⋊C₄×C₆₁	—	2	2	no	—
348	C₂²⋊C₄×C₆₁	—	2	2	no	—
349	C₂²⋊C₄×C₆₁	—	2	2	no	—
350	C₂²⋊C₄×C₆₁	—	2	2	no	—
351	C₂²⋊C₄×C₆₁	—	2	2	no	—
352	C₂²⋊C₄×C₆₁	—	2	2	no	—
353	C₂²⋊C₄×C₆₁	—	2	2	no	—
354	C₂²⋊C₄×C₆₁	—	2	2	no	—
355	C₂²⋊C₄×C₆₁	—	2	2	no	—
356	C₂²⋊C₄×C₆₁	—	2	2	no	—
357	C₂²⋊C₄×C₆₁	—	2	2	no	—
358	C₂²⋊C₄×C₆₁	—	2	2	no	—
359	C₂²⋊C₄×C₆₁	—	2	2	no	—
360	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
361	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
362	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
363	C₄²×C₆₁	—	2	2	no	—
364	C₄²×C₆₁	—	2	2	no	—
365	C₄²×C₆₁	—	2	2	no	—
366	C₄²×C₆₁	—	2	2	no	—
367	C₄²×C₆₁	—	2	2	no	—
368	C₄²×C₆₁	—	2	2	no	—
369	C₄²×C₆₁	—	2	2	no	—
370	C₄²×C₆₁	C₂×D₄	1	2	yes	—
371	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
372	C₄²×C₆₁	C₂×D₄	1	2	yes	—
373	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
374	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
375	C₄²×C₆₁	C₂⁴	1	2	yes	—
376	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
377	C₂³×C₆₁	—	2	2	no	—
378	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
379	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
380	Q₈×C₆₁	—	2	2	no	—
381	Q₈×C₆₁	—	2	2	no	—
382	Q₈×C₆₁	—	2	2	no	—
383	Q₈×C₆₁	—	2	2	no	—
384	Q₈×C₆₁	—	2	2	no	—
385	Q₈×C₆₁	—	2	2	no	—
386	Q₈×C₆₁	—	4	1	no	—
387	Q₈×C₆₁	—	4	4	no	—
388	Q₈×C₆₁	—	8	2	no	—
389	Q₈×C₆₁	—	8	2	no	—
390	D₄×C₆₁	—	2	2	no	—
391	D₄×C₆₁	—	2	2	no	—
392	D₄×C₆₁	—	4	2	no	—
393	D₄×C₆₁	—	4	1	no	—
394	D₄×C₆₁	—	4	4	no	—
395	D₄×C₆₁	—	8	2	no	—
396	D₄×C₆₁	—	8	2	no	—
397	C₂×C₄×C₆₁	—	2	4	no	—
398	C₂×C₄×C₆₁	—	2	2	no	—
399	C₂×C₄×C₆₁	—	2	1	no	—
400	C₂×C₄×C₆₁	—	2	1	no	—
401	C₂×C₄×C₆₁	—	2	2	no	—
402	C₂×C₄×C₆₁	—	2	2	no	—
403	C₂×C₄×C₆₁	—	2	2	no	—
404	C₂×C₄×C₆₁	—	2	2	no	—
405	C₂×C₄×C₆₁	—	2	2	no	—
406	C₂×C₄×C₆₁	—	2	2	no	—
407	C₂×C₄×C₆₁	—	2	2	no	—
408	C₂×C₄×C₆₁	—	2	2	no	—
409	C₂×C₄×C₆₁	—	2	2	no	—
410	C₂×C₄×C₆₁	—	4	2	no	—
411	C₂×C₄×C₆₁	—	4	1	no	—
412	C₂×C₄×C₆₁	—	4	4	no	—
413	C₂×C₄×C₆₁	—	4	4	no	—
414	C₂×C₄×C₆₁	—	4	4	no	—
415	C₂×C₄×C₆₁	—	8	2	no	—
416	C₂×C₄×C₆₁	—	8	2	no	—
417	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
426	C₈×C₆₁	—	2	1	no	—
427	C₈×C₆₁	—	2	1	no	—
428	C₈×C₆₁	—	2	1	no	—
429	C₈×C₆₁	—	2	1	no	—
430	C₈×C₆₁	—	2	2	no	—
431	C₈×C₆₁	—	2	2	no	—
432	#60957	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
433	C₂²×C₆₁	—	2	2	no	—
434	C₂²×C₆₁	—	2	1	no	—
435	C₂²×C₆₁	—	2	2	no	—
436	C₂²×C₆₁	—	2	1	no	—
437	C₂²×C₆₁	—	2	1	no	—
438	C₂²×C₆₁	—	2	2	no	—
439	C₂²×C₆₁	—	4	2	no	—
440	C₂²×C₆₁	—	4	2	no	—
441	C₂²×C₆₁	—	4	2	no	—
442	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
443	C₄×C₆₁	—	2	1	no	—
444	C₄×C₆₁	—	2	2	no	—
445	C₄×C₆₁	—	2	1	no	—
446	C₄×C₆₁	—	2	2	no	—
447	C₄×C₆₁	—	2	1	no	—
448	C₄×C₆₁	—	2	2	no	—
449	C₄×C₆₁	—	2	1	no	—
450	C₄×C₆₁	—	4	2	no	—
451	C₄×C₆₁	—	4	2	no	—
452	C₄×C₆₁	—	4	2	no	—
453	C₄×C₆₁	—	4	2	no	—
454	C₄×C₆₁	—	4	2	no	—
455	C₄×C₆₁	—	4	2	no	—
456	C₄×C₆₁	—	4	2	no	—
457	C₄×C₆₁	#578	1	2	yes	—
458	C₄×C₆₁	#585	1	1	yes	characteristic
459	C₄×C₆₁	#585	1	1	yes	characteristic
460	#3461	C₂×C₆₁	1	2	yes	complemented
461	#3262	C₂×C₆₁	1	1	yes	characteristic, complemented
462	#3261	C₂×C₆₁	1	1	yes	characteristic, complemented
463	#3258	C₂×C₆₁	1	2	yes	complemented
464	#3243	C₂×C₆₁	1	2	yes	complemented
465	#3242	C₂×C₆₁	1	2	yes	complemented
466	#3225	C₂×C₆₁	1	2	yes	complemented
467	#3223	C₂×C₆₁	1	2	yes	complemented
468	#3203	C₂×C₆₁	1	1	yes	characteristic
469	#3202	C₂×C₆₁	1	1	yes	characteristic, complemented
470	#3201	C₂×C₆₁	1	2	yes	complemented
471	#3172	C₂×C₆₁	1	2	yes	complemented
472	#3170	C₂×C₆₁	1	1	yes	characteristic, complemented
473	#3168	C₂×C₆₁	1	1	yes	characteristic, complemented
474	#3108	C₂×C₆₁	1	2	yes	complemented
475	#3107	C₂×C₆₁	1	2	yes	complemented
476	#3104	C₂×C₆₁	1	2	yes	complemented
477	#3102	C₂×C₆₁	1	2	yes	complemented
478	#2922	C₂×C₆₁	1	1	yes	characteristic, complemented
479	C₂×C₆₁	—	4	2	no	—
480	C₂×C₆₁	—	4	1	no	—
481	C₂×C₆₁	—	8	2	no	—
482	C₂×C₆₁	#3449	1	1	yes	characteristic
483	C₂×C₆₁	C₂×#578	1	1	yes	characteristic
484	C₂×C₆₁	#3584	1	1	yes	characteristic
485	#544	C₂²×C₆₁	1	2	yes	—
486	#542	—	2	2	no	—
487	#542	C₂²×C₆₁	1	2	yes	—
488	#542	C₂²×C₆₁	1	2	yes	—
489	#541	—	2	2	no	—
490	#541	C₂²×C₆₁	1	2	yes	—
491	#541	C₂²×C₆₁	1	2	yes	—
492	#539	—	2	2	no	—
493	#539	—	2	2	no	—
494	#537	C₂²×C₆₁	1	2	yes	—
495	#536	C₂²×C₆₁	1	2	yes	—
496	#536	C₂²×C₆₁	1	2	yes	—
497	#533	—	2	2	no	—
498	#533	C₂²×C₆₁	1	2	yes	—
499	#533	C₂²×C₆₁	1	2	yes	—
500	#529	—	2	2	no	—
501	#529	—	2	2	no	—
502	#529	—	2	2	no	—
503	#529	C₂²×C₆₁	1	2	yes	—
504	#529	C₂²×C₆₁	1	2	yes	—
505	C₄×#41	C₂²×C₆₁	1	2	yes	—
506	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
507	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
508	#501	C₂²×C₆₁	1	2	yes	—
509	#500	C₂²×C₆₁	1	1	yes	characteristic
510	#499	C₂²×C₆₁	1	1	yes	characteristic
511	#497	C₂²×C₆₁	1	2	yes	—
512	#495	C₂²×C₆₁	1	1	yes	characteristic
513	#494	C₂²×C₆₁	1	1	yes	characteristic
514	#491	C₂²×C₆₁	1	2	yes	—
515	#489	C₂²×C₆₁	1	2	yes	—
516	#488	C₂²×C₆₁	1	2	yes	—
517	#487	C₂²×C₆₁	1	2	yes	—
518	#485	C₂²×C₆₁	1	2	yes	—
519	#485	C₂²×C₆₁	1	2	yes	—
520	#485	C₂²×C₆₁	1	2	yes	—
521	#484	C₂²×C₆₁	1	2	yes	—
522	#484	C₂²×C₆₁	1	2	yes	—
523	#483	C₂²×C₆₁	1	2	yes	—
524	#482	C₂²×C₆₁	1	2	yes	—
525	#480	C₂²×C₆₁	1	2	yes	—
526	#479	C₂²×C₆₁	1	2	yes	—
527	#479	C₂²×C₆₁	1	2	yes	—
528	#479	C₂²×C₆₁	1	2	yes	—
529	#478	C₂²×C₆₁	1	2	yes	—
530	#477	C₂²×C₆₁	1	2	yes	—
531	#477	C₂²×C₆₁	1	2	yes	—
532	#475	C₂²×C₆₁	1	2	yes	—
533	#474	C₂²×C₆₁	1	2	yes	—
534	#470	C₂²×C₆₁	1	2	yes	—
535	#470	C₂²×C₆₁	1	2	yes	—
536	#468	C₂²×C₆₁	1	2	yes	—
537	#468	C₂²×C₆₁	1	2	yes	—
538	#467	C₂²×C₆₁	1	1	yes	characteristic
539	#467	C₂²×C₆₁	1	2	yes	—
540	#467	C₂²×C₆₁	1	1	yes	characteristic
541	#467	C₂²×C₆₁	1	1	yes	characteristic
542	#466	C₂²×C₆₁	1	1	yes	characteristic
543	#465	C₂²×C₆₁	1	2	yes	—
544	#464	C₂²×C₆₁	1	2	yes	—
545	#464	C₂²×C₆₁	1	2	yes	—
546	#464	C₂²×C₆₁	1	2	yes	—
547	#463	C₂²×C₆₁	1	2	yes	—
548	#462	C₂²×C₆₁	1	2	yes	—
549	#462	C₂²×C₆₁	1	2	yes	—
550	#462	C₂²×C₆₁	1	2	yes	—
551	#461	C₂²×C₆₁	1	2	yes	—
552	#452	C₂²×C₆₁	1	2	yes	—
553	#452	C₂²×C₆₁	1	2	yes	—
554	#452	C₂²×C₆₁	1	2	yes	—
555	#451	C₂²×C₆₁	1	2	yes	—
556	#451	C₂²×C₆₁	1	2	yes	—
557	#451	C₂²×C₆₁	1	2	yes	—
558	#449	C₂²×C₆₁	1	2	yes	—
559	#448	C₂²×C₆₁	1	2	yes	—
560	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
561	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
562	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
563	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
564	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
565	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
566	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
567	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
568	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
569	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
570	#433	C₂²×C₆₁	1	2	yes	—
571	#433	C₂²×C₆₁	1	2	yes	—
572	#431	C₂²×C₆₁	1	2	yes	—
573	#431	C₂²×C₆₁	1	2	yes	—
574	#424	C₂²×C₆₁	1	1	yes	characteristic
575	#424	C₂²×C₆₁	1	1	yes	characteristic
576	#408	C₂²×C₆₁	1	1	yes	characteristic
577	#408	C₂²×C₆₁	1	1	yes	characteristic
578	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
579	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
580	C₆₁	#60957	1	1	yes	characteristic, direct product factor, Sylow
581	C₂×#41	C₂³×C₆₁	1	2	yes	—
582	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
583	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
584	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
585	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
586	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
587	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
588	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
589	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
590	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
591	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
592	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
593	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
594	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
595	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
596	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
597	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
598	C₄⋊Q₈	—	2	2	no	—
599	C₄⋊Q₈	—	2	2	no	—
600	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
601	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
602	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
603	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
604	#126	—	2	2	no	—
605	#126	—	2	2	no	—
606	#126	—	2	2	no	—
607	#126	—	2	2	no	—
608	#126	—	2	2	no	—
609	#126	—	2	2	no	—
610	#126	—	2	2	no	—
611	#126	—	2	2	no	—
612	#125	—	2	2	no	—
613	#125	—	2	2	no	—
614	#125	—	2	2	no	—
615	#125	—	2	2	no	—
616	#125	—	2	2	no	—
617	#125	—	2	2	no	—
618	#125	—	2	2	no	—
619	#125	C₂³×C₆₁	1	2	yes	—
620	#125	C₂³×C₆₁	1	2	yes	—
621	#124	—	2	2	no	—
622	#124	—	2	2	no	—
623	#124	—	2	2	no	—
624	#124	C₂³×C₆₁	1	2	yes	—
625	#124	C₂³×C₆₁	1	2	yes	—
626	#123	—	2	2	no	—
627	#123	—	2	2	no	—
628	#123	—	2	2	no	—
629	#123	—	2	2	no	—
630	#123	—	2	2	no	—
631	#123	—	2	2	no	—
632	#123	—	2	2	no	—
633	#123	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	2	no	—
637	C₂²⋊Q₈	—	2	2	no	—
638	C₂²⋊Q₈	—	2	2	no	—
639	C₂²⋊Q₈	—	2	2	no	—
640	C₂²⋊Q₈	—	2	2	no	—
641	C₂²⋊Q₈	—	2	2	no	—
642	C₂²⋊Q₈	—	2	2	no	—
643	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
644	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
645	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
646	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
647	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
648	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
649	#121	—	2	2	no	—
650	#121	—	2	2	no	—
651	#121	—	2	2	no	—
652	#121	C₂³×C₆₁	1	2	yes	—
653	#121	C₂³×C₆₁	1	2	yes	—
654	C₄×Q₈	—	2	2	no	—
655	C₄×Q₈	—	2	2	no	—
656	C₄×Q₈	—	2	2	no	—
657	C₄×Q₈	—	2	2	no	—
658	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
659	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
660	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
661	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
662	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
663	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
664	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
665	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
666	C₄×D₄	—	2	2	no	—
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	D₄×C₆₁	1	2	yes	—
671	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
672	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
673	C₄×D₄	D₄×C₆₁	1	2	yes	—
674	C₄×D₄	C₂³×C₆₁	1	2	yes	—
675	C₄×D₄	C₂³×C₆₁	1	2	yes	—
676	#117	—	2	2	no	—
677	#117	—	2	2	no	—
678	#117	—	2	2	no	—
679	#117	—	2	2	no	—
680	#117	—	2	2	no	—
681	#117	C₂³×C₆₁	1	2	yes	—
682	#117	C₂³×C₆₁	1	2	yes	—
683	#117	C₂³×C₆₁	1	1	yes	characteristic
684	C₂×C₄⋊C₄	—	2	2	no	—
685	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
686	C₂×C₄²	—	2	2	no	—
687	C₂×C₄²	—	2	2	no	—
688	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
689	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
690	#107	C₂³×C₆₁	1	1	yes	characteristic
691	#107	C₂³×C₆₁	1	1	yes	characteristic
692	#107	C₂³×C₆₁	1	1	yes	characteristic
693	#107	C₂³×C₆₁	1	2	yes	—
694	#107	C₂³×C₆₁	1	1	yes	characteristic
695	#107	C₂³×C₆₁	1	2	yes	—
696	#107	C₂³×C₆₁	1	2	yes	—
697	#106	C₂³×C₆₁	1	2	yes	—
698	#106	C₂³×C₆₁	1	2	yes	—
699	#106	C₂³×C₆₁	1	2	yes	—
700	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
701	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
702	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
703	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
704	#103	C₂³×C₆₁	1	2	yes	—
705	#103	C₂³×C₆₁	1	2	yes	—
706	#103	C₂³×C₆₁	1	2	yes	—
707	#103	C₂³×C₆₁	1	2	yes	—
708	#103	C₂³×C₆₁	1	2	yes	—
709	#103	C₂³×C₆₁	1	2	yes	—
710	#103	C₂³×C₆₁	1	2	yes	—
711	#103	C₂³×C₆₁	1	2	yes	—
712	#103	C₂³×C₆₁	1	2	yes	—
713	#103	C₂³×C₆₁	1	2	yes	—
714	#103	C₂³×C₆₁	1	2	yes	—
715	#103	C₂³×C₆₁	1	2	yes	—
716	#102	C₂³×C₆₁	1	2	yes	—
717	#102	C₂³×C₆₁	1	2	yes	—
718	#102	C₂³×C₆₁	1	2	yes	—
719	#102	C₂³×C₆₁	1	2	yes	—
720	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
721	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
722	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
723	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
724	#97	C₂³×C₆₁	1	2	yes	—
725	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
726	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
727	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
728	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
729	C₄×C₈	C₂³×C₆₁	1	2	yes	—
730	#41	—	4	1	no	—
731	#41	—	4	1	no	—
732	#41	—	4	2	no	—
733	#41	—	4	2	no	—
734	C₂×Q₈	—	2	2	no	—
735	C₂×Q₈	—	2	2	no	—
736	C₂×Q₈	—	2	2	no	—
737	C₂×Q₈	—	4	2	no	—
738	C₂×Q₈	—	4	2	no	—
739	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
740	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
741	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
742	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
743	C₂×D₄	—	2	2	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
747	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
748	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
755	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
756	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
757	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
760	Q₁₆	—	4	1	no	—
761	Q₁₆	—	4	1	no	—
762	Q₁₆	—	4	2	no	—
763	Q₁₆	—	4	1	no	—
764	Q₁₆	—	4	2	no	—
765	Q₁₆	—	4	2	no	—
766	SD₁₆	—	4	2	no	—
767	SD₁₆	—	4	2	no	—
768	SD₁₆	—	4	2	no	—
769	D₈	—	4	1	no	—
770	M₁₆	—	4	1	no	—
771	M₁₆	—	4	1	no	—
772	C₂×C₈	—	4	1	no	—
773	C₂×C₈	—	4	1	no	—
774	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
775	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
776	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
777	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
778	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
779	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
804	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
805	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
806	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
807	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
808	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
809	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
810	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
827	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
828	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
829	C₄²	—	2	2	no	—
830	C₄²	—	2	2	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	2	no	—
836	C₄²	C₂×D₄×C₆₁	1	2	yes	—
837	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
838	C₄²	C₂×D₄×C₆₁	1	2	yes	—
839	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
840	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
841	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
842	C₄²	C₂⁴×C₆₁	1	2	yes	—
843	C₂³	—	2	2	no	—
844	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
845	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
846	Q₈	—	2	2	no	—
847	Q₈	—	2	2	no	—
848	Q₈	—	2	2	no	—
849	Q₈	—	2	2	no	—
850	Q₈	—	2	2	no	—
851	Q₈	—	2	2	no	—
852	Q₈	—	4	1	no	—
853	Q₈	—	4	4	no	—
854	Q₈	—	8	2	no	—
855	Q₈	—	8	2	no	—
856	D₄	—	2	2	no	—
857	D₄	—	2	2	no	—
858	D₄	—	4	2	no	—
859	D₄	—	4	1	no	—
860	D₄	—	4	4	no	—
861	D₄	—	8	2	no	—
862	D₄	—	8	2	no	—
863	C₂×C₄	—	2	4	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	4	2	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	4	no	—
879	C₂×C₄	—	4	4	no	—
880	C₂×C₄	—	4	4	no	—
881	C₂×C₄	—	8	2	no	—
882	C₂×C₄	—	8	2	no	—
883	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
884	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
885	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
886	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
887	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
888	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
889	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
890	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
891	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
892	C₈	—	2	1	no	—
893	C₈	—	2	1	no	—
894	C₈	—	2	1	no	—
895	C₈	—	2	1	no	—
896	C₈	—	2	2	no	—
897	C₈	—	2	2	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	2	no	—
900	C₂²	—	2	2	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	2	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	2	no	—
907	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
908	C₄	—	2	2	no	—
909	C₄	—	2	1	no	—
910	C₄	—	2	1	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	1	no	—
913	C₄	—	2	2	no	—
914	C₄	—	2	1	no	—
915	C₄	—	4	2	no	—
916	C₄	—	4	2	no	—
917	C₄	—	4	2	no	—
918	C₄	—	4	2	no	—
919	C₄	—	4	2	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	2	no	—
922	C₄	C₆₁×#578	1	2	yes	—
923	C₄	C₆₁×#585	1	1	yes	characteristic
924	C₄	C₆₁×#585	1	1	yes	characteristic
925	C₂	—	4	2	no	—
926	C₂	—	4	1	no	—
927	C₂	—	8	2	no	—
928	C₂	C₆₁×#3449	1	1	yes	characteristic
929	C₂	C₂×C₆₁×#578	1	1	yes	characteristic
930	C₂	C₆₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
socle	C₂²×C₆₁	C₂³×D₄
prime radical	C₆₁×#3203	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₁ ◁ C₄×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3461	C₂	semidirect
2. C₆₁×#3262	C₂	semidirect
3. C₆₁×#3261	C₂	semidirect
4. C₆₁×#3258	C₂	semidirect
5. C₆₁×#3243	C₂	semidirect
6. C₆₁×#3242	C₂	semidirect
7. C₆₁×#3225	C₂	semidirect
8. C₆₁×#3223	C₂	semidirect
10. C₆₁×#3202	C₂	semidirect
11. C₆₁×#3201	C₂	semidirect
12. C₆₁×#3172	C₂	semidirect
13. C₆₁×#3170	C₂	semidirect
14. C₆₁×#3168	C₂	semidirect
15. C₆₁×#3108	C₂	semidirect
16. C₆₁×#3107	C₂	semidirect
17. C₆₁×#3104	C₂	semidirect
18. C₆₁×#3102	C₂	semidirect
19. C₆₁×#2922	C₂	semidirect
432. #60957	C₆₁	direct (N × H)
460. #3461	C₂×C₆₁	semidirect
461. #3262	C₂×C₆₁	semidirect
462. #3261	C₂×C₆₁	semidirect
463. #3258	C₂×C₆₁	semidirect
464. #3243	C₂×C₆₁	semidirect
465. #3242	C₂×C₆₁	semidirect
466. #3225	C₂×C₆₁	semidirect
467. #3223	C₂×C₆₁	semidirect
469. #3202	C₂×C₆₁	semidirect
470. #3201	C₂×C₆₁	semidirect
471. #3172	C₂×C₆₁	semidirect
472. #3170	C₂×C₆₁	semidirect
473. #3168	C₂×C₆₁	semidirect
474. #3108	C₂×C₆₁	semidirect
475. #3107	C₂×C₆₁	semidirect
476. #3104	C₂×C₆₁	semidirect
477. #3102	C₂×C₆₁	semidirect
478. #2922	C₂×C₆₁	semidirect
580. C₆₁	#60957	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×#3461	2
C₆₁×#3262	2
C₆₁×#3261	2
C₆₁×#3258	2
C₆₁×#3243	2
C₆₁×#3242	2
C₆₁×#3225	2
C₆₁×#3223	2
C₆₁×#3203	2
C₆₁×#3202	2
C₆₁×#3201	2
C₆₁×#3172	2
C₆₁×#3170	2
C₆₁×#3168	2
C₆₁×#3108	2
C₆₁×#3107	2
C₆₁×#3104	2
C₆₁×#3102	2
C₆₁×#2922	2
#60957	61

Subgroups — C61×#60957 #29564390

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60957 #29564390