Subgroups — C₆₁×#61836 #29565269

Order 15616.

1724 conjugacy classes of subgroups.

The subgroup lattice has 838 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
2	C₂×C₆₁×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3388	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3387	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3381	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3371	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3368	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3365	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3239	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3234	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3232	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3117	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3108	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
19	C₆₁×#559	C₂²	1	2	yes	—
20	Q₈²×C₆₁	C₂²	1	1	yes	characteristic
21	C₆₁×#557	—	2	1	no	—
22	C₆₁×#557	—	2	2	no	—
23	C₆₁×#557	—	2	1	no	—
24	C₆₁×#557	C₂²	1	2	yes	—
25	C₆₁×#557	C₂²	1	2	yes	—
26	C₆₁×#557	C₂²	1	4	yes	—
27	C₆₁×#554	C₂²	1	1	yes	characteristic
28	C₆₁×#554	C₂²	1	2	yes	—
29	C₆₁×#550	C₂²	1	1	yes	characteristic
30	C₆₁×#548	—	2	1	no	—
31	C₆₁×#547	—	2	1	no	—
32	C₆₁×#547	—	2	2	no	—
33	C₆₁×#542	—	2	2	no	—
34	C₆₁×#542	—	2	1	no	—
35	C₆₁×#532	C₂²	1	2	yes	—
36	C₆₁×#532	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
38	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
39	C₆₁×#529	C₂²	1	1	yes	characteristic
40	C₆₁×#529	C₂²	1	2	yes	—
41	C₂×#125×C₆₁	—	2	2	no	—
42	C₂×#125×C₆₁	C₂²	1	2	yes	—
43	C₆₁×#520	—	2	1	no	—
44	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
45	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
48	C₆₁×#501	C₂²	1	4	yes	—
49	C₆₁×#501	C₂²	1	2	yes	—
50	C₆₁×#499	C₂²	1	4	yes	—
51	C₆₁×#498	C₂²	1	2	yes	—
52	C₆₁×#490	C₂²	1	4	yes	—
53	C₆₁×#489	C₂²	1	2	yes	—
54	C₆₁×#488	C₂²	1	4	yes	—
55	C₆₁×#486	C₂²	1	2	yes	—
56	C₆₁×#484	C₂²	1	2	yes	—
57	C₆₁×#483	C₂²	1	1	yes	characteristic
58	C₆₁×#481	C₂²	1	2	yes	—
59	C₆₁×#481	C₂²	1	2	yes	—
60	C₆₁×#481	C₂²	1	2	yes	—
61	C₆₁×#480	C₂²	1	1	yes	characteristic
62	C₆₁×#480	C₂²	1	2	yes	—
63	C₆₁×#479	C₂²	1	2	yes	—
64	C₆₁×#479	C₂²	1	4	yes	—
65	C₆₁×#479	C₂²	1	4	yes	—
66	C₆₁×#478	C₂²	1	4	yes	—
67	C₆₁×#478	C₂²	1	4	yes	—
68	C₆₁×#478	C₂²	1	4	yes	—
69	C₆₁×#477	C₂²	1	2	yes	—
70	C₆₁×#476	C₂²	1	4	yes	—
71	C₆₁×#475	C₂²	1	4	yes	—
72	C₆₁×#475	C₂²	1	2	yes	—
73	C₆₁×#474	C₂²	1	2	yes	—
74	C₆₁×#464	C₂²	1	2	yes	—
75	C₆₁×#464	C₂²	1	4	yes	—
76	C₆₁×#460	C₂²	1	4	yes	—
77	C₆₁×#460	C₂²	1	2	yes	—
78	C₆₁×#451	C₂²	1	1	yes	characteristic
79	C₆₁×#448	C₂²	1	1	yes	characteristic
80	C₆₁×#448	C₂²	1	2	yes	—
81	C₆₁×#446	C₂²	1	2	yes	—
82	C₆₁×#446	C₂²	1	4	yes	—
83	C₈×Q₈×C₆₁	C₂²	1	2	yes	—
84	C₆₁×#441	C₂²	1	4	yes	—
85	C₆₁×#440	C₂²	1	4	yes	—
86	C₆₁×#440	C₂²	1	4	yes	—
87	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
88	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	—
89	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	—
90	C₄×SD₁₆×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	—	2	1	no	—
99	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
100	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
101	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
104	C₄⋊Q₈×C₆₁	—	2	2	no	—
105	C₄⋊Q₈×C₆₁	—	2	2	no	—
106	C₄⋊Q₈×C₆₁	—	2	4	no	—
107	C₄⋊Q₈×C₆₁	—	2	1	no	—
108	C₄⋊Q₈×C₆₁	—	2	2	no	—
109	C₄⋊Q₈×C₆₁	—	2	1	no	—
110	C₄⋊Q₈×C₆₁	—	2	1	no	—
111	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
115	#127×C₆₁	C₂³	1	1	yes	characteristic
116	#127×C₆₁	C₂³	1	2	yes	—
117	#126×C₆₁	—	2	2	no	—
118	#126×C₆₁	—	2	1	no	—
119	#125×C₆₁	—	2	4	no	—
120	#125×C₆₁	—	2	4	no	—
121	#125×C₆₁	—	2	4	no	—
122	#125×C₆₁	—	2	4	no	—
123	#125×C₆₁	—	2	2	no	—
124	#125×C₆₁	—	2	2	no	—
125	#125×C₆₁	C₂³	1	2	yes	—
126	#125×C₆₁	C₂³	1	1	yes	characteristic
127	#125×C₆₁	C₂³	1	4	yes	—
128	#125×C₆₁	C₂³	1	4	yes	—
129	#124×C₆₁	—	2	1	no	—
130	#124×C₆₁	—	2	2	no	—
131	#124×C₆₁	—	2	2	no	—
132	#124×C₆₁	—	2	1	no	—
133	#124×C₆₁	C₂³	1	2	yes	—
134	#124×C₆₁	C₂³	1	1	yes	characteristic
135	#123×C₆₁	—	2	2	no	—
136	#123×C₆₁	—	2	1	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	2	no	—
142	C₂²⋊Q₈×C₆₁	—	2	2	no	—
143	C₂²⋊Q₈×C₆₁	—	2	2	no	—
144	C₂²⋊Q₈×C₆₁	—	2	2	no	—
145	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
146	#121×C₆₁	—	2	1	no	—
147	#121×C₆₁	—	2	2	no	—
148	#121×C₆₁	—	2	1	no	—
149	#121×C₆₁	—	2	2	no	—
150	#121×C₆₁	C₂³	1	1	yes	characteristic
151	#121×C₆₁	C₂³	1	2	yes	—
152	C₄×Q₈×C₆₁	—	2	1	no	—
153	C₄×Q₈×C₆₁	—	2	2	no	—
154	C₄×Q₈×C₆₁	—	2	2	no	—
155	C₄×Q₈×C₆₁	—	2	4	no	—
156	C₄×Q₈×C₆₁	—	2	2	no	—
157	C₄×Q₈×C₆₁	—	2	2	no	—
158	C₄×Q₈×C₆₁	—	2	1	no	—
159	C₄×Q₈×C₆₁	—	2	1	no	—
160	C₄×Q₈×C₆₁	D₄	1	2	yes	—
161	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
162	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
163	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
164	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
165	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
166	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
167	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
169	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
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	2	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	#117×C₆₁	—	2	2	no	—
184	#117×C₆₁	—	2	1	no	—
185	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
186	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
187	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
188	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
189	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
190	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
191	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
192	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
194	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₆₁	—	2	1	no	—
197	C₂×C₄²×C₆₁	—	2	2	no	—
198	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
200	#107×C₆₁	C₂³	1	2	yes	—
201	#107×C₆₁	C₂³	1	4	yes	—
202	#107×C₆₁	C₂³	1	4	yes	—
203	#106×C₆₁	C₂³	1	4	yes	—
204	#106×C₆₁	C₂³	1	4	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	2	yes	—
213	#103×C₆₁	C₂³	1	4	yes	—
214	#103×C₆₁	C₂³	1	2	yes	—
215	#103×C₆₁	C₂³	1	4	yes	—
216	#102×C₆₁	C₂³	1	4	yes	—
217	#102×C₆₁	C₂³	1	4	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	2	yes	—
223	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
224	#97×C₆₁	C₂³	1	2	yes	—
225	#97×C₆₁	C₂³	1	4	yes	—
226	C₄×C₈×C₆₁	C₂³	1	4	yes	—
227	C₄×C₈×C₆₁	C₂³	1	2	yes	—
228	#41×C₆₁	—	4	4	no	—
229	#41×C₆₁	—	8	4	no	—
230	#41×C₆₁	—	8	2	no	—
231	C₂×Q₈×C₆₁	—	2	4	no	—
232	C₂×Q₈×C₆₁	—	2	1	no	—
233	C₂×Q₈×C₆₁	—	2	2	no	—
234	C₂×Q₈×C₆₁	—	2	2	no	—
235	C₂×Q₈×C₆₁	—	2	2	no	—
236	C₂×Q₈×C₆₁	—	2	1	no	—
237	C₂×Q₈×C₆₁	—	4	2	no	—
238	C₂×Q₈×C₆₁	—	4	4	no	—
239	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
240	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
241	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
242	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
243	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
244	C₂×D₄×C₆₁	—	2	1	no	—
245	C₂×D₄×C₆₁	—	2	2	no	—
246	C₂×D₄×C₆₁	—	2	2	no	—
247	C₂×D₄×C₆₁	—	2	1	no	—
248	C₂×D₄×C₆₁	—	2	2	no	—
249	C₂×D₄×C₆₁	—	2	1	no	—
250	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
251	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₆₁	—	2	1	no	—
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	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
265	Q₁₆×C₆₁	—	2	4	no	—
266	SD₁₆×C₆₁	—	2	4	no	—
267	SD₁₆×C₆₁	—	2	8	no	—
268	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
269	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
270	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
271	C₄⋊C₄×C₆₁	—	2	2	no	—
272	C₄⋊C₄×C₆₁	—	2	1	no	—
273	C₄⋊C₄×C₆₁	—	2	2	no	—
274	C₄⋊C₄×C₆₁	—	2	1	no	—
275	C₄⋊C₄×C₆₁	—	2	4	no	—
276	C₄⋊C₄×C₆₁	—	2	4	no	—
277	C₄⋊C₄×C₆₁	—	2	2	no	—
278	C₄⋊C₄×C₆₁	—	2	2	no	—
279	C₄⋊C₄×C₆₁	—	2	4	no	—
280	C₄⋊C₄×C₆₁	—	2	4	no	—
281	C₄⋊C₄×C₆₁	—	2	2	no	—
282	C₄⋊C₄×C₆₁	—	2	2	no	—
283	C₄⋊C₄×C₆₁	—	2	4	no	—
284	C₄⋊C₄×C₆₁	—	2	4	no	—
285	C₄⋊C₄×C₆₁	—	2	1	no	—
286	C₄⋊C₄×C₆₁	—	2	2	no	—
287	C₄⋊C₄×C₆₁	—	2	1	no	—
288	C₄⋊C₄×C₆₁	—	2	1	no	—
289	C₄⋊C₄×C₆₁	—	2	2	no	—
290	C₄⋊C₄×C₆₁	—	2	2	no	—
291	C₄⋊C₄×C₆₁	—	2	1	no	—
292	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
293	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
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	2	yes	—
297	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
300	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
304	C₂²⋊C₄×C₆₁	—	2	1	no	—
305	C₂²⋊C₄×C₆₁	—	2	2	no	—
306	C₂²⋊C₄×C₆₁	—	2	1	no	—
307	C₂²⋊C₄×C₆₁	—	2	2	no	—
308	C₂²⋊C₄×C₆₁	—	2	1	no	—
309	C₂²⋊C₄×C₆₁	—	2	1	no	—
310	C₂²⋊C₄×C₆₁	—	2	2	no	—
311	C₂²⋊C₄×C₆₁	—	2	2	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	2	no	—
316	C₄²×C₆₁	—	2	4	no	—
317	C₄²×C₆₁	—	2	4	no	—
318	C₄²×C₆₁	—	2	2	no	—
319	C₄²×C₆₁	—	2	2	no	—
320	C₄²×C₆₁	—	2	2	no	—
321	C₄²×C₆₁	—	2	1	no	—
322	C₄²×C₆₁	C₂×D₄	1	2	yes	—
323	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₆₁	C₂×D₄	1	2	yes	—
325	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₆₁	C₂⁴	1	2	yes	—
327	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
328	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
329	C₄²×C₆₁	C₂⁴	1	2	yes	—
330	C₂³×C₆₁	—	2	2	no	—
331	C₂³×C₆₁	—	2	1	no	—
332	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
333	Q₈×C₆₁	—	2	4	no	—
334	Q₈×C₆₁	—	2	2	no	—
335	Q₈×C₆₁	—	2	2	no	—
336	Q₈×C₆₁	—	2	2	no	—
337	Q₈×C₆₁	—	2	2	no	—
338	Q₈×C₆₁	—	4	2	no	—
339	Q₈×C₆₁	—	4	4	no	—
340	Q₈×C₆₁	—	4	4	no	—
341	Q₈×C₆₁	—	8	2	no	—
342	Q₈×C₆₁	—	8	1	no	—
343	Q₈×C₆₁	2₋¹⁺⁴	1	4	yes	—
344	D₄×C₆₁	—	2	2	no	—
345	D₄×C₆₁	—	2	4	no	—
346	D₄×C₆₁	—	4	4	no	—
347	D₄×C₆₁	—	4	2	no	—
348	D₄×C₆₁	—	4	4	no	—
349	D₄×C₆₁	—	4	2	no	—
350	D₄×C₆₁	—	8	2	no	—
351	D₄×C₆₁	—	8	1	no	—
352	C₂×C₄×C₆₁	—	2	4	no	—
353	C₂×C₄×C₆₁	—	2	4	no	—
354	C₂×C₄×C₆₁	—	2	2	no	—
355	C₂×C₄×C₆₁	—	2	2	no	—
356	C₂×C₄×C₆₁	—	2	2	no	—
357	C₂×C₄×C₆₁	—	2	2	no	—
358	C₂×C₄×C₆₁	—	2	1	no	—
359	C₂×C₄×C₆₁	—	2	2	no	—
360	C₂×C₄×C₆₁	—	2	4	no	—
361	C₂×C₄×C₆₁	—	2	2	no	—
362	C₂×C₄×C₆₁	—	2	1	no	—
363	C₂×C₄×C₆₁	—	2	1	no	—
364	C₂×C₄×C₆₁	—	4	2	no	—
365	C₂×C₄×C₆₁	—	4	4	no	—
366	C₂×C₄×C₆₁	—	4	4	no	—
367	C₂×C₄×C₆₁	—	4	2	no	—
368	C₂×C₄×C₆₁	—	4	2	no	—
369	C₂×C₄×C₆₁	—	8	2	no	—
370	C₂×C₄×C₆₁	—	8	2	no	—
371	C₂×C₄×C₆₁	—	8	2	no	—
372	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
374	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
378	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
382	C₈×C₆₁	—	2	2	no	—
383	C₈×C₆₁	—	2	4	no	—
384	C₈×C₆₁	—	2	2	no	—
385	#61836	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
386	C₂²×C₆₁	—	2	1	no	—
387	C₂²×C₆₁	—	2	1	no	—
388	C₂²×C₆₁	—	4	2	no	—
389	C₂²×C₆₁	—	4	1	no	—
390	C₂²×C₆₁	—	4	2	no	—
391	C₂²×C₆₁	—	4	1	no	—
392	C₂²×C₆₁	—	4	2	no	—
393	C₂²×C₆₁	—	4	1	no	—
394	C₂²×C₆₁	#577	1	2	yes	—
395	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
396	C₄×C₆₁	—	2	4	no	—
397	C₄×C₆₁	—	2	1	no	—
398	C₄×C₆₁	—	2	1	no	—
399	C₄×C₆₁	—	2	2	no	—
400	C₄×C₆₁	—	2	2	no	—
401	C₄×C₆₁	—	2	2	no	—
402	C₄×C₆₁	—	2	1	no	—
403	C₄×C₆₁	—	2	2	no	—
404	C₄×C₆₁	—	2	1	no	—
405	C₄×C₆₁	—	4	1	no	—
406	C₄×C₆₁	—	4	1	no	—
407	C₄×C₆₁	—	4	4	no	—
408	C₄×C₆₁	—	4	2	no	—
409	C₄×C₆₁	—	4	2	no	—
410	C₄×C₆₁	—	4	1	no	—
411	C₄×C₆₁	#575	1	2	yes	—
412	C₄×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
413	#3522	C₂×C₆₁	1	1	yes	characteristic
414	C₂×#557	C₂×C₆₁	1	1	yes	characteristic, complemented
415	#3388	C₂×C₆₁	1	4	yes	complemented
416	#3387	C₂×C₆₁	1	2	yes	complemented
417	#3381	C₂×C₆₁	1	2	yes	complemented
418	#3371	C₂×C₆₁	1	4	yes	complemented
419	#3368	C₂×C₆₁	1	2	yes	complemented
420	#3365	C₂×C₆₁	1	2	yes	complemented
421	#3239	C₂×C₆₁	1	1	yes	characteristic, complemented
422	#3234	C₂×C₆₁	1	2	yes	complemented
423	#3232	C₂×C₆₁	1	2	yes	complemented
424	#3227	C₂×C₆₁	1	1	yes	characteristic, complemented
425	#3117	C₂×C₆₁	1	2	yes	complemented
426	#3112	C₂×C₆₁	1	1	yes	characteristic, complemented
427	#3108	C₂×C₆₁	1	1	yes	characteristic, complemented
428	#3103	C₂×C₆₁	1	2	yes	complemented
429	#2984	C₂×C₆₁	1	1	yes	characteristic, complemented
430	C₂×C₆₁	—	2	2	no	—
431	C₂×C₆₁	—	8	2	no	—
432	C₂×C₆₁	—	8	1	no	—
433	C₂×C₆₁	#3486	1	1	yes	characteristic
434	C₂×C₆₁	C₂×#575	1	1	yes	characteristic
435	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
436	#559	C₂²×C₆₁	1	1	yes	characteristic
437	#559	C₂²×C₆₁	1	2	yes	—
438	Q₈²	C₂²×C₆₁	1	1	yes	characteristic
439	#557	—	2	1	no	—
440	#557	—	2	1	no	—
441	#557	—	2	2	no	—
442	#557	C₂²×C₆₁	1	2	yes	—
443	#557	C₂²×C₆₁	1	2	yes	—
444	#557	C₂²×C₆₁	1	4	yes	—
445	#554	C₂²×C₆₁	1	1	yes	characteristic
446	#554	C₂²×C₆₁	1	2	yes	—
447	#550	C₂²×C₆₁	1	1	yes	characteristic
448	#548	—	2	1	no	—
449	#547	—	2	1	no	—
450	#547	—	2	2	no	—
451	#542	—	2	2	no	—
452	#542	—	2	1	no	—
453	#532	C₂²×C₆₁	1	2	yes	—
454	#532	C₂²×C₆₁	1	1	yes	characteristic
455	C₂×C₄⋊Q₈	—	2	1	no	—
456	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
457	#529	C₂²×C₆₁	1	1	yes	characteristic
458	#529	C₂²×C₆₁	1	2	yes	—
459	C₂×#125	—	2	2	no	—
460	C₂×#125	C₂²×C₆₁	1	2	yes	—
461	#520	—	2	1	no	—
462	C₂×C₄×Q₈	—	2	1	no	—
463	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
464	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
465	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
466	#501	C₂²×C₆₁	1	4	yes	—
467	#501	C₂²×C₆₁	1	2	yes	—
468	#499	C₂²×C₆₁	1	4	yes	—
469	#498	C₂²×C₆₁	1	2	yes	—
470	#490	C₂²×C₆₁	1	4	yes	—
471	#489	C₂²×C₆₁	1	2	yes	—
472	#488	C₂²×C₆₁	1	4	yes	—
473	#486	C₂²×C₆₁	1	2	yes	—
474	#484	C₂²×C₆₁	1	2	yes	—
475	#483	C₂²×C₆₁	1	1	yes	characteristic
476	#481	C₂²×C₆₁	1	2	yes	—
477	#481	C₂²×C₆₁	1	2	yes	—
478	#481	C₂²×C₆₁	1	2	yes	—
479	#480	C₂²×C₆₁	1	1	yes	characteristic
480	#480	C₂²×C₆₁	1	2	yes	—
481	#479	C₂²×C₆₁	1	2	yes	—
482	#479	C₂²×C₆₁	1	4	yes	—
483	#479	C₂²×C₆₁	1	4	yes	—
484	#478	C₂²×C₆₁	1	4	yes	—
485	#478	C₂²×C₆₁	1	4	yes	—
486	#478	C₂²×C₆₁	1	4	yes	—
487	#477	C₂²×C₆₁	1	2	yes	—
488	#476	C₂²×C₆₁	1	4	yes	—
489	#475	C₂²×C₆₁	1	4	yes	—
490	#475	C₂²×C₆₁	1	2	yes	—
491	#474	C₂²×C₆₁	1	2	yes	—
492	#464	C₂²×C₆₁	1	2	yes	—
493	#464	C₂²×C₆₁	1	4	yes	—
494	#460	C₂²×C₆₁	1	4	yes	—
495	#460	C₂²×C₆₁	1	2	yes	—
496	#451	C₂²×C₆₁	1	1	yes	characteristic
497	#448	C₂²×C₆₁	1	1	yes	characteristic
498	#448	C₂²×C₆₁	1	2	yes	—
499	#446	C₂²×C₆₁	1	2	yes	—
500	#446	C₂²×C₆₁	1	4	yes	—
501	C₈×Q₈	C₂²×C₆₁	1	2	yes	—
502	#441	C₂²×C₆₁	1	4	yes	—
503	#440	C₂²×C₆₁	1	4	yes	—
504	#440	C₂²×C₆₁	1	4	yes	—
505	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
506	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	—
507	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	—
508	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
509	#432	C₂²×C₆₁	1	1	yes	characteristic
510	#432	C₂²×C₆₁	1	2	yes	—
511	#431	C₂²×C₆₁	1	2	yes	—
512	#431	C₂²×C₆₁	1	1	yes	characteristic
513	C₆₁	#61836	1	1	yes	characteristic, direct product factor, Sylow
514	C₂×#41	—	2	1	no	—
515	C₂×#41	—	2	2	no	—
516	C₂×#41	—	2	1	no	—
517	C₂²×Q₈	—	2	1	no	—
518	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
519	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
520	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
521	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
522	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
523	C₄⋊Q₈	—	2	2	no	—
524	C₄⋊Q₈	—	2	2	no	—
525	C₄⋊Q₈	—	2	4	no	—
526	C₄⋊Q₈	—	2	1	no	—
527	C₄⋊Q₈	—	2	2	no	—
528	C₄⋊Q₈	—	2	1	no	—
529	C₄⋊Q₈	—	2	1	no	—
530	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
531	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
532	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
533	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
534	#127	C₂³×C₆₁	1	1	yes	characteristic
535	#127	C₂³×C₆₁	1	2	yes	—
536	#126	—	2	2	no	—
537	#126	—	2	1	no	—
538	#125	—	2	4	no	—
539	#125	—	2	4	no	—
540	#125	—	2	4	no	—
541	#125	—	2	4	no	—
542	#125	—	2	2	no	—
543	#125	—	2	2	no	—
544	#125	C₂³×C₆₁	1	4	yes	—
545	#125	C₂³×C₆₁	1	4	yes	—
546	#125	C₂³×C₆₁	1	2	yes	—
547	#125	C₂³×C₆₁	1	1	yes	characteristic
548	#124	—	2	1	no	—
549	#124	—	2	2	no	—
550	#124	—	2	2	no	—
551	#124	—	2	1	no	—
552	#124	C₂³×C₆₁	1	2	yes	—
553	#124	C₂³×C₆₁	1	1	yes	characteristic
554	#123	—	2	2	no	—
555	#123	—	2	1	no	—
556	#123	—	2	2	no	—
557	#123	—	2	2	no	—
558	#123	—	2	2	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	C₂³×C₆₁	1	1	yes	characteristic
565	#121	—	2	1	no	—
566	#121	—	2	2	no	—
567	#121	—	2	1	no	—
568	#121	—	2	2	no	—
569	#121	C₂³×C₆₁	1	1	yes	characteristic
570	#121	C₂³×C₆₁	1	2	yes	—
571	C₄×Q₈	—	2	1	no	—
572	C₄×Q₈	—	2	2	no	—
573	C₄×Q₈	—	2	2	no	—
574	C₄×Q₈	—	2	4	no	—
575	C₄×Q₈	—	2	2	no	—
576	C₄×Q₈	—	2	2	no	—
577	C₄×Q₈	—	2	1	no	—
578	C₄×Q₈	—	2	1	no	—
579	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
580	C₄×Q₈	D₄×C₆₁	1	2	yes	—
581	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
582	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
583	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
584	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
585	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
586	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
587	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
588	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
589	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
590	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
598	C₄×D₄	C₂³×C₆₁	1	2	yes	—
599	C₄×D₄	C₂³×C₆₁	1	2	yes	—
600	C₄×D₄	C₂³×C₆₁	1	2	yes	—
601	C₄×D₄	C₂³×C₆₁	1	2	yes	—
602	#117	—	2	2	no	—
603	#117	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	2	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	2	no	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	—	2	2	no	—
609	C₂×C₄⋊C₄	—	2	1	no	—
610	C₂×C₄⋊C₄	—	2	2	no	—
611	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
612	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
615	C₂×C₄²	—	2	2	no	—
616	C₂×C₄²	—	2	1	no	—
617	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
618	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
619	#107	C₂³×C₆₁	1	2	yes	—
620	#107	C₂³×C₆₁	1	4	yes	—
621	#107	C₂³×C₆₁	1	4	yes	—
622	#106	C₂³×C₆₁	1	4	yes	—
623	#106	C₂³×C₆₁	1	4	yes	—
624	#106	C₂³×C₆₁	1	2	yes	—
625	#106	C₂³×C₆₁	1	4	yes	—
626	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
627	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
628	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
629	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
630	#103	C₂³×C₆₁	1	2	yes	—
631	#103	C₂³×C₆₁	1	2	yes	—
632	#103	C₂³×C₆₁	1	4	yes	—
633	#103	C₂³×C₆₁	1	2	yes	—
634	#103	C₂³×C₆₁	1	4	yes	—
635	#102	C₂³×C₆₁	1	4	yes	—
636	#102	C₂³×C₆₁	1	4	yes	—
637	#102	C₂³×C₆₁	1	2	yes	—
638	#102	C₂³×C₆₁	1	4	yes	—
639	#102	C₂³×C₆₁	1	4	yes	—
640	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
641	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
642	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
643	#97	C₂³×C₆₁	1	2	yes	—
644	#97	C₂³×C₆₁	1	4	yes	—
645	C₄×C₈	C₂³×C₆₁	1	4	yes	—
646	C₄×C₈	C₂³×C₆₁	1	2	yes	—
647	#41	—	4	4	no	—
648	#41	—	8	4	no	—
649	#41	—	8	2	no	—
650	C₂×Q₈	—	2	4	no	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	2	no	—
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	4	2	no	—
657	C₂×Q₈	—	4	4	no	—
658	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
659	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
660	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
661	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
662	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
663	C₂×D₄	—	2	1	no	—
664	C₂×D₄	—	2	2	no	—
665	C₂×D₄	—	2	2	no	—
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
670	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
680	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
682	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
684	Q₁₆	—	2	4	no	—
685	SD₁₆	—	2	4	no	—
686	SD₁₆	—	2	8	no	—
687	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
688	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
689	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
712	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
713	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
714	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
715	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
716	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
717	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
718	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
719	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
720	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
721	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
722	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
723	C₂²⋊C₄	—	2	1	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	1	no	—
726	C₂²⋊C₄	—	2	2	no	—
727	C₂²⋊C₄	—	2	1	no	—
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₄²	—	2	4	no	—
736	C₄²	—	2	4	no	—
737	C₄²	—	2	2	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	2	no	—
740	C₄²	—	2	1	no	—
741	C₄²	C₂×D₄×C₆₁	1	2	yes	—
742	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
743	C₄²	C₂×D₄×C₆₁	1	2	yes	—
744	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
745	C₄²	C₂⁴×C₆₁	1	2	yes	—
746	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
747	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
748	C₄²	C₂⁴×C₆₁	1	2	yes	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	1	no	—
751	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
752	Q₈	—	2	4	no	—
753	Q₈	—	2	2	no	—
754	Q₈	—	2	2	no	—
755	Q₈	—	2	2	no	—
756	Q₈	—	2	2	no	—
757	Q₈	—	4	2	no	—
758	Q₈	—	4	4	no	—
759	Q₈	—	4	4	no	—
760	Q₈	—	8	2	no	—
761	Q₈	—	8	1	no	—
762	Q₈	2₋¹⁺⁴×C₆₁	1	4	yes	—
763	D₄	—	2	2	no	—
764	D₄	—	2	4	no	—
765	D₄	—	4	4	no	—
766	D₄	—	4	2	no	—
767	D₄	—	4	4	no	—
768	D₄	—	4	2	no	—
769	D₄	—	8	2	no	—
770	D₄	—	8	1	no	—
771	C₂×C₄	—	2	4	no	—
772	C₂×C₄	—	2	4	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	4	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	4	2	no	—
784	C₂×C₄	—	4	4	no	—
785	C₂×C₄	—	4	4	no	—
786	C₂×C₄	—	4	2	no	—
787	C₂×C₄	—	4	2	no	—
788	C₂×C₄	—	8	2	no	—
789	C₂×C₄	—	8	2	no	—
790	C₂×C₄	—	8	2	no	—
791	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
792	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
793	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
795	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
796	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
797	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
799	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
800	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
801	C₈	—	2	2	no	—
802	C₈	—	2	4	no	—
803	C₈	—	2	2	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	1	no	—
812	C₂²	C₆₁×#577	1	2	yes	—
813	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
814	C₄	—	2	1	no	—
815	C₄	—	2	2	no	—
816	C₄	—	2	2	no	—
817	C₄	—	2	2	no	—
818	C₄	—	2	1	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	1	no	—
821	C₄	—	2	4	no	—
822	C₄	—	2	1	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	4	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	1	no	—
829	C₄	C₆₁×#575	1	2	yes	—
830	C₄	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
831	C₂	—	2	2	no	—
832	C₂	—	8	2	no	—
833	C₂	—	8	1	no	—
834	C₂	C₆₁×#3486	1	1	yes	characteristic
835	C₂	C₂×C₆₁×#575	1	1	yes	characteristic
836	C₂	C₂×C₆₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3522	C₂
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
2. C₂×C₆₁×#557	C₂	semidirect
3. C₆₁×#3388	C₂	semidirect
4. C₆₁×#3387	C₂	semidirect
5. C₆₁×#3381	C₂	semidirect
6. C₆₁×#3371	C₂	semidirect
7. C₆₁×#3368	C₂	semidirect
8. C₆₁×#3365	C₂	semidirect
9. C₆₁×#3239	C₂	semidirect
10. C₆₁×#3234	C₂	semidirect
11. C₆₁×#3232	C₂	semidirect
12. C₆₁×#3227	C₂	semidirect
13. C₆₁×#3117	C₂	semidirect
14. C₆₁×#3112	C₂	semidirect
15. C₆₁×#3108	C₂	semidirect
16. C₆₁×#3103	C₂	semidirect
17. C₆₁×#2984	C₂	semidirect
385. #61836	C₆₁	direct (N × H)
414. C₂×#557	C₂×C₆₁	semidirect
415. #3388	C₂×C₆₁	semidirect
416. #3387	C₂×C₆₁	semidirect
417. #3381	C₂×C₆₁	semidirect
418. #3371	C₂×C₆₁	semidirect
419. #3368	C₂×C₆₁	semidirect
420. #3365	C₂×C₆₁	semidirect
421. #3239	C₂×C₆₁	semidirect
422. #3234	C₂×C₆₁	semidirect
423. #3232	C₂×C₆₁	semidirect
424. #3227	C₂×C₆₁	semidirect
425. #3117	C₂×C₆₁	semidirect
426. #3112	C₂×C₆₁	semidirect
427. #3108	C₂×C₆₁	semidirect
428. #3103	C₂×C₆₁	semidirect
429. #2984	C₂×C₆₁	semidirect
513. C₆₁	#61836	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×#557	2
C₆₁×#3388	2
C₆₁×#3387	2
C₆₁×#3381	2
C₆₁×#3371	2
C₆₁×#3368	2
C₆₁×#3365	2
C₆₁×#3239	2
C₆₁×#3234	2
C₆₁×#3232	2
C₆₁×#3227	2
C₆₁×#3117	2
C₆₁×#3112	2
C₆₁×#3108	2
C₆₁×#3103	2
C₆₁×#2984	2
#61836	61

Subgroups — C61×#61836 #29565269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61836 #29565269