Subgroups — C₆₁×#60885 #29564318

Order 15616.

1682 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3510	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3244	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3243	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3240	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3240	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3239	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3238	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3162	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3140	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₆₁×#489	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3097	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3096	C₂	1	2	yes	maximal
15	C₆₁×#3082	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3081	C₂	1	2	yes	maximal, complemented
17	C₆₁×#2923	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#559	—	2	1	no	—
19	C₆₁×#559	—	2	1	no	—
20	Q₈²×C₆₁	—	2	1	no	—
21	C₆₁×#557	—	2	1	no	—
22	C₆₁×#556	—	2	1	no	—
23	C₆₁×#556	—	2	1	no	—
24	C₆₁×#554	—	2	2	no	—
25	C₆₁×#554	—	2	1	no	—
26	C₆₁×#551	—	2	2	no	—
27	C₆₁×#551	—	2	2	no	—
28	D₄×Q₈×C₆₁	—	2	2	no	—
29	D₄×Q₈×C₆₁	—	2	1	no	—
30	C₆₁×#544	C₂²	1	2	yes	—
31	C₆₁×#544	C₂²	1	4	yes	complemented
32	C₆₁×#542	C₂²	1	2	yes	—
33	C₆₁×#542	C₂²	1	2	yes	—
34	C₆₁×#536	C₂²	1	1	yes	characteristic
35	C₆₁×#535	C₂²	1	1	yes	characteristic
36	C₆₁×#533	C₂²	1	1	yes	characteristic
37	C₆₁×#533	C₂²	1	1	yes	characteristic
38	C₆₁×#533	C₂²	1	2	yes	complemented
39	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	complemented
41	C₆₁×#529	C₂²	1	2	yes	—
42	C₆₁×#529	C₂²	1	2	yes	—
43	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
44	C₆₁×#520	C₂²	1	2	yes	—
45	C₆₁×#519	C₂²	1	1	yes	characteristic
46	C₆₁×#518	C₂²	1	1	yes	characteristic
47	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
48	C₆₁×#501	C₂²	1	1	yes	characteristic, complemented
49	C₆₁×#501	C₂²	1	1	yes	characteristic, complemented
50	C₆₁×#501	C₂²	1	1	yes	characteristic, complemented
51	C₆₁×#501	C₂²	1	1	yes	characteristic, complemented
52	C₆₁×#501	C₂²	1	2	yes	complemented
53	C₆₁×#501	C₂²	1	2	yes	complemented
54	C₆₁×#501	C₂²	1	2	yes	complemented
55	C₆₁×#501	C₂²	1	2	yes	complemented
56	C₆₁×#500	C₂²	1	2	yes	complemented
57	C₆₁×#498	C₂²	1	2	yes	complemented
58	C₆₁×#489	C₂²	1	2	yes	—
59	C₆₁×#489	C₂²	1	2	yes	—
60	C₆₁×#489	C₂²	1	4	yes	—
61	C₆₁×#489	C₂²	1	2	yes	—
62	C₆₁×#489	C₂²	1	2	yes	—
63	C₆₁×#488	C₂²	1	4	yes	—
64	C₆₁×#485	C₂²	1	4	yes	complemented
65	C₆₁×#485	C₂²	1	4	yes	complemented
66	C₆₁×#484	C₂²	1	4	yes	complemented
67	C₆₁×#483	C₂²	1	4	yes	complemented
68	C₆₁×#482	C₂²	1	4	yes	—
69	C₆₁×#482	C₂²	1	4	yes	—
70	C₆₁×#481	C₂²	1	4	yes	—
71	C₆₁×#480	C₂²	1	4	yes	—
72	C₆₁×#479	C₂²	1	4	yes	complemented
73	C₆₁×#479	C₂²	1	4	yes	complemented
74	C₆₁×#478	C₂²	1	4	yes	—
75	C₆₁×#478	C₂²	1	4	yes	—
76	C₆₁×#477	C₂²	1	4	yes	complemented
77	C₆₁×#476	C₂²	1	4	yes	—
78	C₆₁×#475	C₂²	1	4	yes	complemented
79	C₆₁×#474	C₂²	1	4	yes	—
80	C₆₁×#433	C₂²	1	4	yes	complemented
81	C₆₁×#432	C₂²	1	2	yes	complemented
82	C₆₁×#432	C₂²	1	2	yes	complemented
83	C₆₁×#428	C₂²	1	2	yes	—
84	C₆₁×#428	C₂²	1	2	yes	—
85	C₆₁×#427	C₂²	1	2	yes	—
86	C₆₁×#427	C₂²	1	2	yes	—
87	C₆₁×#424	C₂²	1	2	yes	—
88	C₆₁×#419	C₂²	1	2	yes	—
89	C₆₁×#418	C₂²	1	2	yes	—
90	C₂×#103×C₆₁	C₂²	1	2	yes	—
91	C₂×#102×C₆₁	C₂²	1	2	yes	—
92	C₆₁×#408	C₂²	1	2	yes	—
93	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
94	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
95	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₆₁	—	2	1	no	—
97	C₂²×Q₈×C₆₁	—	2	2	no	—
98	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
101	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
102	C₄⋊Q₈×C₆₁	—	2	1	no	—
103	C₄⋊Q₈×C₆₁	—	2	2	no	—
104	C₄⋊Q₈×C₆₁	—	2	4	no	—
105	C₄⋊Q₈×C₆₁	—	2	1	no	—
106	C₄⋊Q₈×C₆₁	—	2	1	no	—
107	C₄⋊Q₈×C₆₁	—	2	2	no	—
108	C₄⋊Q₈×C₆₁	—	2	2	no	—
109	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
110	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
111	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
113	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
116	#127×C₆₁	—	2	1	no	—
117	#126×C₆₁	—	2	2	no	—
118	#126×C₆₁	—	2	2	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	C₂³	1	2	yes	—
124	#125×C₆₁	C₂³	1	1	yes	characteristic
125	#125×C₆₁	C₂³	1	1	yes	characteristic
126	#125×C₆₁	C₂³	1	4	yes	—
127	#124×C₆₁	—	2	1	no	—
128	#124×C₆₁	—	2	1	no	—
129	#124×C₆₁	—	2	2	no	—
130	#124×C₆₁	—	2	2	no	—
131	#124×C₆₁	—	2	1	no	—
132	#124×C₆₁	—	2	1	no	—
133	#124×C₆₁	C₂³	1	2	yes	—
134	#124×C₆₁	C₂³	1	2	yes	—
135	#123×C₆₁	—	2	2	no	—
136	#123×C₆₁	—	2	2	no	—
137	#123×C₆₁	—	2	2	no	—
138	#123×C₆₁	—	2	2	no	—
139	#123×C₆₁	—	2	2	no	—
140	C₂²⋊Q₈×C₆₁	—	2	1	no	—
141	C₂²⋊Q₈×C₆₁	—	2	1	no	—
142	C₂²⋊Q₈×C₆₁	—	2	1	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	—	2	2	no	—
147	C₂²⋊Q₈×C₆₁	—	2	2	no	—
148	C₂²⋊Q₈×C₆₁	—	2	4	no	—
149	C₂²⋊Q₈×C₆₁	—	2	4	no	—
150	C₂²⋊Q₈×C₆₁	—	2	4	no	—
151	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
152	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
153	#121×C₆₁	C₂³	1	2	yes	—
154	#121×C₆₁	C₂³	1	2	yes	—
155	#120×C₆₁	—	2	2	no	—
156	C₄×Q₈×C₆₁	—	2	2	no	—
157	C₄×Q₈×C₆₁	—	2	1	no	—
158	C₄×Q₈×C₆₁	—	2	1	no	—
159	C₄×Q₈×C₆₁	—	2	1	no	—
160	C₄×Q₈×C₆₁	—	2	1	no	—
161	C₄×Q₈×C₆₁	—	2	1	no	—
162	C₄×Q₈×C₆₁	—	2	1	no	—
163	C₄×Q₈×C₆₁	—	2	2	no	—
164	C₄×Q₈×C₆₁	—	2	2	no	—
165	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
166	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
167	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
168	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
169	C₄×D₄×C₆₁	—	2	4	no	—
170	C₄×D₄×C₆₁	—	2	2	no	—
171	C₄×D₄×C₆₁	—	2	2	no	—
172	C₄×D₄×C₆₁	—	2	2	no	—
173	C₄×D₄×C₆₁	—	2	1	no	—
174	C₄×D₄×C₆₁	—	2	1	no	—
175	C₄×D₄×C₆₁	D₄	1	2	yes	—
176	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
177	C₄×D₄×C₆₁	D₄	1	2	yes	—
178	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
179	C₄×D₄×C₆₁	C₂³	1	2	yes	—
180	C₄×D₄×C₆₁	C₂³	1	2	yes	—
181	#117×C₆₁	—	2	2	no	—
182	#117×C₆₁	—	2	2	no	—
183	#117×C₆₁	—	2	2	no	—
184	#117×C₆₁	C₂³	1	1	yes	characteristic
185	#117×C₆₁	C₂³	1	1	yes	characteristic
186	#117×C₆₁	C₂³	1	2	yes	—
187	#117×C₆₁	C₂³	1	4	yes	—
188	#117×C₆₁	C₂³	1	2	yes	—
189	#117×C₆₁	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
191	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
192	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
194	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
195	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
196	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
197	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
199	#107×C₆₁	C₂³	1	2	yes	—
200	#107×C₆₁	C₂³	1	2	yes	—
201	#107×C₆₁	C₂³	1	2	yes	—
202	#107×C₆₁	C₂³	1	2	yes	—
203	#107×C₆₁	C₂³	1	4	yes	—
204	#107×C₆₁	C₂³	1	4	yes	—
205	#106×C₆₁	C₂³	1	2	yes	—
206	#106×C₆₁	C₂³	1	2	yes	—
207	#106×C₆₁	C₂³	1	2	yes	—
208	#106×C₆₁	C₂³	1	2	yes	—
209	#106×C₆₁	C₂³	1	4	yes	—
210	#106×C₆₁	C₂³	1	4	yes	—
211	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
212	C₄⋊C₈×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	#103×C₆₁	C₂³	1	4	yes	—
217	#102×C₆₁	C₂³	1	4	yes	—
218	#102×C₆₁	C₂³	1	4	yes	—
219	#102×C₆₁	C₂³	1	4	yes	—
220	#102×C₆₁	C₂³	1	4	yes	—
221	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
222	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
223	#97×C₆₁	C₂³	1	1	yes	characteristic
224	#97×C₆₁	C₂³	1	1	yes	characteristic
225	#97×C₆₁	C₂³	1	2	yes	—
226	#97×C₆₁	C₂³	1	2	yes	—
227	C₄×C₈×C₆₁	C₂³	1	2	yes	—
228	C₂⁴×C₆₁	—	2	1	no	—
229	#41×C₆₁	—	2	4	no	—
230	C₂×Q₈×C₆₁	—	2	1	no	—
231	C₂×Q₈×C₆₁	—	2	1	no	—
232	C₂×Q₈×C₆₁	—	2	1	no	—
233	C₂×Q₈×C₆₁	—	2	2	no	—
234	C₂×Q₈×C₆₁	—	2	1	no	—
235	C₂×Q₈×C₆₁	—	2	1	no	—
236	C₂×Q₈×C₆₁	—	2	4	no	—
237	C₂×Q₈×C₆₁	—	2	2	no	—
238	C₂×Q₈×C₆₁	—	2	4	no	—
239	C₂×Q₈×C₆₁	—	8	2	no	—
240	C₂×Q₈×C₆₁	—	8	4	no	—
241	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
242	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
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	4	no	—
247	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
248	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
249	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₆₁	—	2	1	no	—
251	C₂²×C₄×C₆₁	—	2	4	no	—
252	C₂²×C₄×C₆₁	—	2	2	no	—
253	C₂²×C₄×C₆₁	—	2	2	no	—
254	C₂²×C₄×C₆₁	—	2	2	no	—
255	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
258	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
259	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
261	M₁₆×C₆₁	—	2	4	no	—
262	C₂×C₈×C₆₁	—	2	4	no	—
263	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
264	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
265	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₆₁	—	2	2	no	—
267	C₄⋊C₄×C₆₁	—	2	1	no	—
268	C₄⋊C₄×C₆₁	—	2	4	no	—
269	C₄⋊C₄×C₆₁	—	2	2	no	—
270	C₄⋊C₄×C₆₁	—	2	4	no	—
271	C₄⋊C₄×C₆₁	—	2	2	no	—
272	C₄⋊C₄×C₆₁	—	2	1	no	—
273	C₄⋊C₄×C₆₁	—	2	1	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	2	no	—
278	C₄⋊C₄×C₆₁	—	2	1	no	—
279	C₄⋊C₄×C₆₁	—	2	1	no	—
280	C₄⋊C₄×C₆₁	—	2	1	no	—
281	C₄⋊C₄×C₆₁	—	2	4	no	—
282	C₄⋊C₄×C₆₁	—	2	2	no	—
283	C₄⋊C₄×C₆₁	—	2	4	no	—
284	C₄⋊C₄×C₆₁	—	2	2	no	—
285	C₄⋊C₄×C₆₁	—	2	1	no	—
286	C₄⋊C₄×C₆₁	—	2	1	no	—
287	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
288	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
289	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
290	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
291	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
292	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
293	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
294	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
295	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
296	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
297	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
298	C₂²⋊C₄×C₆₁	—	2	1	no	—
299	C₂²⋊C₄×C₆₁	—	2	1	no	—
300	C₂²⋊C₄×C₆₁	—	2	4	no	—
301	C₂²⋊C₄×C₆₁	—	2	2	no	—
302	C₂²⋊C₄×C₆₁	—	2	2	no	—
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	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	—	2	2	no	—
311	C₂²⋊C₄×C₆₁	—	2	2	no	—
312	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
313	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
314	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
315	C₄²×C₆₁	—	2	2	no	—
316	C₄²×C₆₁	—	2	2	no	—
317	C₄²×C₆₁	—	2	1	no	—
318	C₄²×C₆₁	—	2	4	no	—
319	C₄²×C₆₁	—	2	2	no	—
320	C₄²×C₆₁	—	2	1	no	—
321	C₄²×C₆₁	C₂×D₄	1	2	yes	—
322	C₄²×C₆₁	C₂×D₄	1	2	yes	—
323	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
326	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
327	C₄²×C₆₁	C₂⁴	1	2	yes	—
328	C₂³×C₆₁	—	2	2	no	—
329	C₂³×C₆₁	—	4	2	no	—
330	C₂³×C₆₁	—	8	1	no	—
331	C₂³×C₆₁	—	8	1	no	—
332	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
333	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
334	Q₈×C₆₁	—	2	2	no	—
335	Q₈×C₆₁	—	2	4	no	—
336	Q₈×C₆₁	—	4	2	no	—
337	Q₈×C₆₁	—	4	2	no	—
338	Q₈×C₆₁	—	4	4	no	—
339	Q₈×C₆₁	—	4	2	no	—
340	Q₈×C₆₁	—	8	1	no	—
341	Q₈×C₆₁	—	8	1	no	—
342	Q₈×C₆₁	—	8	4	no	—
343	Q₈×C₆₁	—	8	2	no	—
344	D₄×C₆₁	—	2	4	no	—
345	D₄×C₆₁	—	2	2	no	—
346	D₄×C₆₁	—	2	4	no	—
347	D₄×C₆₁	—	4	2	no	—
348	D₄×C₆₁	—	8	2	no	—
349	D₄×C₆₁	—	8	2	no	—
350	C₂×C₄×C₆₁	—	2	4	no	—
351	C₂×C₄×C₆₁	—	2	2	no	—
352	C₂×C₄×C₆₁	—	2	1	no	—
353	C₂×C₄×C₆₁	—	2	1	no	—
354	C₂×C₄×C₆₁	—	2	2	no	—
355	C₂×C₄×C₆₁	—	2	1	no	—
356	C₂×C₄×C₆₁	—	2	1	no	—
357	C₂×C₄×C₆₁	—	2	4	no	—
358	C₂×C₄×C₆₁	—	2	2	no	—
359	C₂×C₄×C₆₁	—	4	2	no	—
360	C₂×C₄×C₆₁	—	4	1	no	—
361	C₂×C₄×C₆₁	—	4	2	no	—
362	C₂×C₄×C₆₁	—	4	1	no	—
363	C₂×C₄×C₆₁	—	4	2	no	—
364	C₂×C₄×C₆₁	—	8	2	no	—
365	C₂×C₄×C₆₁	—	8	2	no	—
366	C₂×C₄×C₆₁	—	8	2	no	—
367	C₂×C₄×C₆₁	—	8	4	no	—
368	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
369	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
370	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₆₁	2₋¹⁺⁴	1	4	yes	—
377	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
378	C₈×C₆₁	—	2	2	no	—
379	C₈×C₆₁	—	2	2	no	—
380	C₈×C₆₁	—	2	4	no	—
381	#60885	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
382	C₂²×C₆₁	—	2	1	no	—
383	C₂²×C₆₁	—	2	1	no	—
384	C₂²×C₆₁	—	2	2	no	—
385	C₂²×C₆₁	—	2	2	no	—
386	C₂²×C₆₁	—	2	2	no	—
387	C₂²×C₆₁	—	4	2	no	—
388	C₂²×C₆₁	—	4	2	no	—
389	C₂²×C₆₁	—	4	2	no	—
390	C₂²×C₆₁	—	16	2	no	—
391	C₂²×C₆₁	#536	1	2	yes	—
392	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
393	C₄×C₆₁	—	2	1	no	—
394	C₄×C₆₁	—	2	2	no	—
395	C₄×C₆₁	—	2	1	no	—
396	C₄×C₆₁	—	2	1	no	—
397	C₄×C₆₁	—	2	2	no	—
398	C₄×C₆₁	—	2	1	no	—
399	C₄×C₆₁	—	2	2	no	—
400	C₄×C₆₁	—	4	4	no	—
401	C₄×C₆₁	—	4	2	no	—
402	C₄×C₆₁	—	4	1	no	—
403	C₄×C₆₁	—	4	1	no	—
404	C₄×C₆₁	—	4	1	no	—
405	C₄×C₆₁	—	4	1	no	—
406	C₄×C₆₁	—	4	2	no	—
407	C₄×C₆₁	—	4	2	no	—
408	C₄×C₆₁	#536	1	2	yes	—
409	C₄×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
410	#3510	C₂×C₆₁	1	1	yes	characteristic
411	#3503	C₂×C₆₁	1	1	yes	characteristic, complemented
412	#3244	C₂×C₆₁	1	4	yes	complemented
413	#3243	C₂×C₆₁	1	4	yes	complemented
414	#3240	C₂×C₆₁	1	2	yes	complemented
415	#3240	C₂×C₆₁	1	2	yes	complemented
416	#3239	C₂×C₆₁	1	2	yes	complemented
417	#3238	C₂×C₆₁	1	2	yes	complemented
418	#3165	C₂×C₆₁	1	1	yes	characteristic, complemented
419	#3162	C₂×C₆₁	1	1	yes	characteristic, complemented
420	#3140	C₂×C₆₁	1	1	yes	characteristic, complemented
421	C₂×#489	C₂×C₆₁	1	1	yes	characteristic, complemented
422	#3097	C₂×C₆₁	1	2	yes	complemented
423	#3096	C₂×C₆₁	1	2	yes	—
424	#3082	C₂×C₆₁	1	2	yes	complemented
425	#3081	C₂×C₆₁	1	2	yes	complemented
426	#2923	C₂×C₆₁	1	1	yes	characteristic, complemented
427	C₂×C₆₁	—	2	2	no	—
428	C₂×C₆₁	—	4	2	no	—
429	C₂×C₆₁	—	8	2	no	—
430	C₂×C₆₁	C₂×#536	1	1	yes	characteristic
431	C₂×C₆₁	#3585	1	1	yes	characteristic
432	C₂×C₆₁	#3586	1	1	yes	characteristic
433	#559	—	2	1	no	—
434	#559	—	2	1	no	—
435	Q₈²	—	2	1	no	—
436	#557	—	2	1	no	—
437	#556	—	2	1	no	—
438	#556	—	2	1	no	—
439	#554	—	2	2	no	—
440	#554	—	2	1	no	—
441	#551	—	2	2	no	—
442	#551	—	2	2	no	—
443	D₄×Q₈	—	2	2	no	—
444	D₄×Q₈	—	2	1	no	—
445	#544	C₂²×C₆₁	1	2	yes	—
446	#544	C₂²×C₆₁	1	4	yes	complemented
447	#542	C₂²×C₆₁	1	2	yes	—
448	#542	C₂²×C₆₁	1	2	yes	—
449	#536	C₂²×C₆₁	1	1	yes	characteristic
450	#535	C₂²×C₆₁	1	1	yes	characteristic
451	#533	C₂²×C₆₁	1	1	yes	characteristic
452	#533	C₂²×C₆₁	1	1	yes	characteristic
453	#533	C₂²×C₆₁	1	2	yes	complemented
454	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
455	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	complemented
456	#529	C₂²×C₆₁	1	2	yes	—
457	#529	C₂²×C₆₁	1	2	yes	—
458	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
459	#520	C₂²×C₆₁	1	2	yes	—
460	#519	C₂²×C₆₁	1	1	yes	characteristic
461	#518	C₂²×C₆₁	1	1	yes	characteristic
462	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
463	#501	C₂²×C₆₁	1	1	yes	characteristic, complemented
464	#501	C₂²×C₆₁	1	1	yes	characteristic, complemented
465	#501	C₂²×C₆₁	1	1	yes	characteristic, complemented
466	#501	C₂²×C₆₁	1	1	yes	characteristic, complemented
467	#501	C₂²×C₆₁	1	2	yes	complemented
468	#501	C₂²×C₆₁	1	2	yes	complemented
469	#501	C₂²×C₆₁	1	2	yes	complemented
470	#501	C₂²×C₆₁	1	2	yes	complemented
471	#500	C₂²×C₆₁	1	2	yes	complemented
472	#498	C₂²×C₆₁	1	2	yes	complemented
473	#489	C₂²×C₆₁	1	2	yes	—
474	#489	C₂²×C₆₁	1	2	yes	—
475	#489	C₂²×C₆₁	1	4	yes	—
476	#489	C₂²×C₆₁	1	2	yes	—
477	#489	C₂²×C₆₁	1	2	yes	—
478	#488	C₂²×C₆₁	1	4	yes	—
479	#485	C₂²×C₆₁	1	4	yes	complemented
480	#485	C₂²×C₆₁	1	4	yes	complemented
481	#484	C₂²×C₆₁	1	4	yes	complemented
482	#483	C₂²×C₆₁	1	4	yes	complemented
483	#482	C₂²×C₆₁	1	4	yes	—
484	#482	C₂²×C₆₁	1	4	yes	—
485	#481	C₂²×C₆₁	1	4	yes	—
486	#480	C₂²×C₆₁	1	4	yes	—
487	#479	C₂²×C₆₁	1	4	yes	complemented
488	#479	C₂²×C₆₁	1	4	yes	complemented
489	#478	C₂²×C₆₁	1	4	yes	—
490	#478	C₂²×C₆₁	1	4	yes	—
491	#477	C₂²×C₆₁	1	4	yes	complemented
492	#476	C₂²×C₆₁	1	4	yes	—
493	#475	C₂²×C₆₁	1	4	yes	complemented
494	#474	C₂²×C₆₁	1	4	yes	—
495	#433	C₂²×C₆₁	1	4	yes	complemented
496	#432	C₂²×C₆₁	1	2	yes	complemented
497	#432	C₂²×C₆₁	1	2	yes	complemented
498	#428	C₂²×C₆₁	1	2	yes	—
499	#428	C₂²×C₆₁	1	2	yes	—
500	#427	C₂²×C₆₁	1	2	yes	—
501	#427	C₂²×C₆₁	1	2	yes	—
502	#424	C₂²×C₆₁	1	2	yes	—
503	#419	C₂²×C₆₁	1	2	yes	—
504	#418	C₂²×C₆₁	1	2	yes	—
505	C₂×#103	C₂²×C₆₁	1	2	yes	—
506	C₂×#102	C₂²×C₆₁	1	2	yes	—
507	#408	C₂²×C₆₁	1	2	yes	—
508	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
509	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
510	C₆₁	#60885	1	1	yes	characteristic, direct product factor, Sylow
511	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
512	C₂²×Q₈	—	2	1	no	—
513	C₂²×Q₈	—	2	2	no	—
514	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
515	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
516	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
517	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
518	C₄⋊Q₈	—	2	1	no	—
519	C₄⋊Q₈	—	2	2	no	—
520	C₄⋊Q₈	—	2	4	no	—
521	C₄⋊Q₈	—	2	1	no	—
522	C₄⋊Q₈	—	2	1	no	—
523	C₄⋊Q₈	—	2	2	no	—
524	C₄⋊Q₈	—	2	2	no	—
525	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
526	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
527	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
528	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
529	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
530	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
531	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
532	#127	—	2	1	no	—
533	#126	—	2	2	no	—
534	#126	—	2	2	no	—
535	#126	—	2	2	no	—
536	#126	—	2	2	no	—
537	#125	—	2	2	no	—
538	#125	—	2	4	no	—
539	#125	C₂³×C₆₁	1	1	yes	characteristic
540	#125	C₂³×C₆₁	1	1	yes	characteristic
541	#125	C₂³×C₆₁	1	2	yes	—
542	#125	C₂³×C₆₁	1	4	yes	—
543	#124	—	2	1	no	—
544	#124	—	2	1	no	—
545	#124	—	2	2	no	—
546	#124	—	2	2	no	—
547	#124	—	2	1	no	—
548	#124	—	2	1	no	—
549	#124	C₂³×C₆₁	1	2	yes	—
550	#124	C₂³×C₆₁	1	2	yes	—
551	#123	—	2	2	no	—
552	#123	—	2	2	no	—
553	#123	—	2	2	no	—
554	#123	—	2	2	no	—
555	#123	—	2	2	no	—
556	C₂²⋊Q₈	—	2	1	no	—
557	C₂²⋊Q₈	—	2	1	no	—
558	C₂²⋊Q₈	—	2	1	no	—
559	C₂²⋊Q₈	—	2	1	no	—
560	C₂²⋊Q₈	—	2	2	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	—	2	4	no	—
565	C₂²⋊Q₈	—	2	4	no	—
566	C₂²⋊Q₈	—	2	4	no	—
567	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
568	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
569	#121	C₂³×C₆₁	1	2	yes	—
570	#121	C₂³×C₆₁	1	2	yes	—
571	#120	—	2	2	no	—
572	C₄×Q₈	—	2	2	no	—
573	C₄×Q₈	—	2	1	no	—
574	C₄×Q₈	—	2	1	no	—
575	C₄×Q₈	—	2	1	no	—
576	C₄×Q₈	—	2	1	no	—
577	C₄×Q₈	—	2	1	no	—
578	C₄×Q₈	—	2	1	no	—
579	C₄×Q₈	—	2	2	no	—
580	C₄×Q₈	—	2	2	no	—
581	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
582	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
583	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
584	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
585	C₄×D₄	—	2	4	no	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	2	no	—
588	C₄×D₄	—	2	2	no	—
589	C₄×D₄	—	2	1	no	—
590	C₄×D₄	—	2	1	no	—
591	C₄×D₄	D₄×C₆₁	1	2	yes	—
592	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
593	C₄×D₄	D₄×C₆₁	1	2	yes	—
594	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
595	C₄×D₄	C₂³×C₆₁	1	2	yes	—
596	C₄×D₄	C₂³×C₆₁	1	2	yes	—
597	#117	—	2	2	no	—
598	#117	—	2	2	no	—
599	#117	—	2	2	no	—
600	#117	C₂³×C₆₁	1	1	yes	characteristic
601	#117	C₂³×C₆₁	1	1	yes	characteristic
602	#117	C₂³×C₆₁	1	2	yes	—
603	#117	C₂³×C₆₁	1	4	yes	—
604	#117	C₂³×C₆₁	1	1	yes	characteristic
605	#117	C₂³×C₆₁	1	2	yes	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	2	no	—
608	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
610	C₂×C₂²⋊C₄	—	2	1	no	—
611	C₂×C₂²⋊C₄	—	2	1	no	—
612	C₂×C₂²⋊C₄	—	2	2	no	—
613	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
615	#107	C₂³×C₆₁	1	2	yes	—
616	#107	C₂³×C₆₁	1	2	yes	—
617	#107	C₂³×C₆₁	1	2	yes	—
618	#107	C₂³×C₆₁	1	2	yes	—
619	#107	C₂³×C₆₁	1	4	yes	—
620	#107	C₂³×C₆₁	1	4	yes	—
621	#106	C₂³×C₆₁	1	2	yes	—
622	#106	C₂³×C₆₁	1	2	yes	—
623	#106	C₂³×C₆₁	1	2	yes	—
624	#106	C₂³×C₆₁	1	2	yes	—
625	#106	C₂³×C₆₁	1	4	yes	—
626	#106	C₂³×C₆₁	1	4	yes	—
627	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
628	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
629	#103	C₂³×C₆₁	1	4	yes	—
630	#103	C₂³×C₆₁	1	4	yes	—
631	#103	C₂³×C₆₁	1	4	yes	—
632	#103	C₂³×C₆₁	1	4	yes	—
633	#102	C₂³×C₆₁	1	4	yes	—
634	#102	C₂³×C₆₁	1	4	yes	—
635	#102	C₂³×C₆₁	1	4	yes	—
636	#102	C₂³×C₆₁	1	4	yes	—
637	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
638	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
639	#97	C₂³×C₆₁	1	1	yes	characteristic
640	#97	C₂³×C₆₁	1	1	yes	characteristic
641	#97	C₂³×C₆₁	1	2	yes	—
642	#97	C₂³×C₆₁	1	2	yes	—
643	C₄×C₈	C₂³×C₆₁	1	2	yes	—
644	C₂⁴	—	2	1	no	—
645	#41	—	2	4	no	—
646	C₂×Q₈	—	2	1	no	—
647	C₂×Q₈	—	2	1	no	—
648	C₂×Q₈	—	2	1	no	—
649	C₂×Q₈	—	2	2	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	4	no	—
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	—	2	4	no	—
655	C₂×Q₈	—	8	2	no	—
656	C₂×Q₈	—	8	4	no	—
657	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
658	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	2	4	no	—
663	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
664	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
665	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
672	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
673	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
674	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
677	M₁₆	—	2	4	no	—
678	C₂×C₈	—	2	4	no	—
679	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
680	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
681	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	4	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
704	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
705	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
706	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
707	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
708	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
709	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
710	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
711	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
712	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
713	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
714	C₂²⋊C₄	—	2	1	no	—
715	C₂²⋊C₄	—	2	1	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	2	no	—
718	C₂²⋊C₄	—	2	2	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
729	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
730	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
731	C₄²	—	2	2	no	—
732	C₄²	—	2	2	no	—
733	C₄²	—	2	1	no	—
734	C₄²	—	2	4	no	—
735	C₄²	—	2	2	no	—
736	C₄²	—	2	1	no	—
737	C₄²	C₂×D₄×C₆₁	1	2	yes	—
738	C₄²	C₂×D₄×C₆₁	1	2	yes	—
739	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
740	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
741	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
742	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
743	C₄²	C₂⁴×C₆₁	1	2	yes	—
744	C₂³	—	2	2	no	—
745	C₂³	—	4	2	no	—
746	C₂³	—	8	1	no	—
747	C₂³	—	8	1	no	—
748	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
749	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
750	Q₈	—	2	2	no	—
751	Q₈	—	2	4	no	—
752	Q₈	—	4	2	no	—
753	Q₈	—	4	2	no	—
754	Q₈	—	4	4	no	—
755	Q₈	—	4	2	no	—
756	Q₈	—	8	1	no	—
757	Q₈	—	8	1	no	—
758	Q₈	—	8	4	no	—
759	Q₈	—	8	2	no	—
760	D₄	—	2	4	no	—
761	D₄	—	2	2	no	—
762	D₄	—	2	4	no	—
763	D₄	—	4	2	no	—
764	D₄	—	8	2	no	—
765	D₄	—	8	2	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	4	2	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	2	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	2	no	—
780	C₂×C₄	—	8	2	no	—
781	C₂×C₄	—	8	2	no	—
782	C₂×C₄	—	8	2	no	—
783	C₂×C₄	—	8	4	no	—
784	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
785	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
786	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
787	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
788	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
789	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
790	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
791	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
792	C₂×C₄	2₋¹⁺⁴×C₆₁	1	4	yes	—
793	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
794	C₈	—	2	2	no	—
795	C₈	—	2	2	no	—
796	C₈	—	2	4	no	—
797	C₂²	—	2	1	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	2	2	no	—
800	C₂²	—	2	2	no	—
801	C₂²	—	2	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	16	2	no	—
806	C₂²	C₆₁×#536	1	2	yes	—
807	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
808	C₄	—	2	1	no	—
809	C₄	—	2	2	no	—
810	C₄	—	2	1	no	—
811	C₄	—	2	1	no	—
812	C₄	—	2	2	no	—
813	C₄	—	2	1	no	—
814	C₄	—	2	2	no	—
815	C₄	—	4	4	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	1	no	—
818	C₄	—	4	1	no	—
819	C₄	—	4	1	no	—
820	C₄	—	4	1	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	2	no	—
823	C₄	C₆₁×#536	1	2	yes	—
824	C₄	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
825	C₂	—	2	2	no	—
826	C₂	—	4	2	no	—
827	C₂	—	8	2	no	—
828	C₂	C₂×C₆₁×#536	1	1	yes	characteristic
829	C₂	C₆₁×#3585	1	1	yes	characteristic
830	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×#535	C₂²
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
2. C₆₁×#3503	C₂	semidirect
3. C₆₁×#3244	C₂	semidirect
4. C₆₁×#3243	C₂	semidirect
5. C₆₁×#3240	C₂	semidirect
6. C₆₁×#3240	C₂	semidirect
7. C₆₁×#3239	C₂	semidirect
8. C₆₁×#3238	C₂	semidirect
9. C₆₁×#3165	C₂	semidirect
10. C₆₁×#3162	C₂	semidirect
11. C₆₁×#3140	C₂	semidirect
12. C₂×C₆₁×#489	C₂	semidirect
13. C₆₁×#3097	C₂	semidirect
15. C₆₁×#3082	C₂	semidirect
16. C₆₁×#3081	C₂	semidirect
17. C₆₁×#2923	C₂	semidirect
31. C₆₁×#544	C₂²	semidirect
38. C₆₁×#533	C₂²	semidirect
40. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
48. C₆₁×#501	C₂²	semidirect
49. C₆₁×#501	C₂²	semidirect
50. C₆₁×#501	C₂²	semidirect
51. C₆₁×#501	C₂²	semidirect
52. C₆₁×#501	C₂²	semidirect
53. C₆₁×#501	C₂²	semidirect
54. C₆₁×#501	C₂²	semidirect
55. C₆₁×#501	C₂²	semidirect
56. C₆₁×#500	C₂²	semidirect
57. C₆₁×#498	C₂²	semidirect
64. C₆₁×#485	C₂²	semidirect
65. C₆₁×#485	C₂²	semidirect
66. C₆₁×#484	C₂²	semidirect
67. C₆₁×#483	C₂²	semidirect
72. C₆₁×#479	C₂²	semidirect
73. C₆₁×#479	C₂²	semidirect
76. C₆₁×#477	C₂²	semidirect
78. C₆₁×#475	C₂²	semidirect
80. C₆₁×#433	C₂²	semidirect
81. C₆₁×#432	C₂²	semidirect
82. C₆₁×#432	C₂²	semidirect
381. #60885	C₆₁	direct (N × H)
411. #3503	C₂×C₆₁	semidirect
412. #3244	C₂×C₆₁	semidirect
413. #3243	C₂×C₆₁	semidirect
414. #3240	C₂×C₆₁	semidirect
415. #3240	C₂×C₆₁	semidirect
416. #3239	C₂×C₆₁	semidirect
417. #3238	C₂×C₆₁	semidirect
418. #3165	C₂×C₆₁	semidirect
419. #3162	C₂×C₆₁	semidirect
420. #3140	C₂×C₆₁	semidirect
421. C₂×#489	C₂×C₆₁	semidirect
422. #3097	C₂×C₆₁	semidirect
424. #3082	C₂×C₆₁	semidirect
425. #3081	C₂×C₆₁	semidirect
426. #2923	C₂×C₆₁	semidirect
446. #544	C₂²×C₆₁	semidirect
453. #533	C₂²×C₆₁	semidirect
455. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
463. #501	C₂²×C₆₁	semidirect
464. #501	C₂²×C₆₁	semidirect
465. #501	C₂²×C₆₁	semidirect
466. #501	C₂²×C₆₁	semidirect
467. #501	C₂²×C₆₁	semidirect
468. #501	C₂²×C₆₁	semidirect
469. #501	C₂²×C₆₁	semidirect
470. #501	C₂²×C₆₁	semidirect
471. #500	C₂²×C₆₁	semidirect
472. #498	C₂²×C₆₁	semidirect
479. #485	C₂²×C₆₁	semidirect
480. #485	C₂²×C₆₁	semidirect
481. #484	C₂²×C₆₁	semidirect
482. #483	C₂²×C₆₁	semidirect
487. #479	C₂²×C₆₁	semidirect
488. #479	C₂²×C₆₁	semidirect
491. #477	C₂²×C₆₁	semidirect
493. #475	C₂²×C₆₁	semidirect
495. #433	C₂²×C₆₁	semidirect
496. #432	C₂²×C₆₁	semidirect
497. #432	C₂²×C₆₁	semidirect
510. C₆₁	#60885	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×#3510	2
C₆₁×#3503	2
C₆₁×#3244	2
C₆₁×#3243	2
C₆₁×#3240	2
C₆₁×#3239	2
C₆₁×#3238	2
C₆₁×#3165	2
C₆₁×#3162	2
C₆₁×#3140	2
C₂×C₆₁×#489	2
C₆₁×#3097	2
C₆₁×#3096	2
C₆₁×#3082	2
C₆₁×#3081	2
C₆₁×#2923	2
#60885	61

Subgroups — C61×#60885 #29564318

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60885 #29564318