Subgroups — C₆₁×#61894 #29565327

Order 15616.

1730 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3402	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3401	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3377	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3376	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3218	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3215	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3213	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#3211	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3114	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3113	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3108	C₂	1	2	yes	maximal, complemented
15	C₆₁×#2983	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#559	C₂²	1	2	yes	complemented
17	C₆₁×#557	C₂²	1	2	yes	complemented
18	C₆₁×#556	—	2	2	no	—
19	C₆₁×#556	—	2	2	no	—
20	C₆₁×#556	—	2	2	no	—
21	C₆₁×#556	C₂²	1	4	yes	—
22	C₆₁×#556	C₂²	1	4	yes	—
23	C₆₁×#556	C₂²	1	2	yes	complemented
24	C₆₁×#554	C₂²	1	2	yes	complemented
25	C₆₁×#552	—	2	2	no	—
26	C₆₁×#539	—	2	1	no	—
27	C₆₁×#539	—	2	1	no	—
28	C₆₁×#536	—	2	1	no	—
29	C₆₁×#533	C₂²	1	1	yes	characteristic
30	C₆₁×#532	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
32	C₆₁×#529	C₂²	1	2	yes	—
33	C₆₁×#529	C₂²	1	2	yes	—
34	C₂×#126×C₆₁	—	2	1	no	—
35	C₂×#126×C₆₁	—	2	1	no	—
36	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
39	C₆₁×#520	—	2	1	no	—
40	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
44	C₂×#117×C₆₁	—	2	1	no	—
45	C₆₁×#497	C₂²	1	2	yes	—
46	C₆₁×#497	C₂²	1	4	yes	complemented
47	C₆₁×#496	C₂²	1	2	yes	—
48	C₆₁×#495	C₂²	1	4	yes	—
49	C₆₁×#491	C₂²	1	4	yes	complemented
50	C₆₁×#489	C₂²	1	2	yes	—
51	C₆₁×#489	C₂²	1	2	yes	—
52	C₆₁×#488	C₂²	1	4	yes	—
53	C₆₁×#483	C₂²	1	2	yes	—
54	C₆₁×#480	C₂²	1	2	yes	—
55	C₆₁×#479	C₂²	1	4	yes	complemented
56	C₆₁×#478	C₂²	1	4	yes	—
57	C₆₁×#477	C₂²	1	2	yes	complemented
58	C₆₁×#475	C₂²	1	2	yes	complemented
59	C₆₁×#464	C₂²	1	4	yes	—
60	C₆₁×#464	C₂²	1	4	yes	—
61	C₆₁×#464	C₂²	1	4	yes	complemented
62	C₆₁×#463	C₂²	1	4	yes	—
63	C₆₁×#463	C₂²	1	4	yes	—
64	C₆₁×#463	C₂²	1	4	yes	—
65	C₆₁×#462	C₂²	1	2	yes	complemented
66	C₆₁×#462	C₂²	1	4	yes	complemented
67	C₆₁×#461	C₂²	1	4	yes	complemented
68	C₆₁×#460	C₂²	1	2	yes	complemented
69	C₆₁×#451	C₂²	1	2	yes	—
70	C₆₁×#451	C₂²	1	2	yes	—
71	C₆₁×#450	C₂²	1	2	yes	—
72	C₆₁×#448	C₂²	1	2	yes	—
73	C₆₁×#448	C₂²	1	2	yes	—
74	C₆₁×#447	C₂²	1	2	yes	—
75	C₆₁×#446	C₂²	1	4	yes	complemented
76	C₆₁×#446	C₂²	1	4	yes	complemented
77	C₆₁×#442	C₂²	1	4	yes	—
78	C₆₁×#441	C₂²	1	4	yes	complemented
79	C₆₁×#440	C₂²	1	4	yes	—
80	C₆₁×#440	C₂²	1	4	yes	complemented
81	C₄×Q₁₆×C₆₁	C₂²	1	4	yes	complemented
82	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	complemented
83	C₆₁×#432	C₂²	1	1	yes	characteristic
84	C₆₁×#432	C₂²	1	1	yes	characteristic
85	C₆₁×#432	C₂²	1	2	yes	—
86	C₆₁×#431	C₂²	1	2	yes	—
87	C₂×#41×C₆₁	—	2	1	no	—
88	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
89	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
90	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₆₁	—	2	1	no	—
93	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
94	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
95	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
96	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
97	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
98	C₂×D₈×C₆₁	C₂³	1	4	yes	—
99	C₄⋊Q₈×C₆₁	—	2	2	no	—
100	C₄⋊Q₈×C₆₁	—	2	2	no	—
101	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
102	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
103	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
104	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
105	#127×C₆₁	C₂³	1	1	yes	characteristic
106	#126×C₆₁	—	2	2	no	—
107	#126×C₆₁	—	2	2	no	—
108	#126×C₆₁	—	2	4	no	—
109	#126×C₆₁	—	2	4	no	—
110	#126×C₆₁	—	2	4	no	—
111	#126×C₆₁	—	2	4	no	—
112	#126×C₆₁	—	2	2	no	—
113	#126×C₆₁	—	2	2	no	—
114	#125×C₆₁	—	2	2	no	—
115	#125×C₆₁	—	2	2	no	—
116	#125×C₆₁	—	2	1	no	—
117	#125×C₆₁	C₂³	1	2	yes	—
118	#125×C₆₁	C₂³	1	2	yes	—
119	#124×C₆₁	—	2	2	no	—
120	#124×C₆₁	—	2	1	no	—
121	#124×C₆₁	—	2	2	no	—
122	#124×C₆₁	—	2	1	no	—
123	#124×C₆₁	—	2	1	no	—
124	#124×C₆₁	C₂³	1	2	yes	—
125	#124×C₆₁	C₂³	1	4	yes	—
126	#124×C₆₁	C₂³	1	2	yes	—
127	#124×C₆₁	C₂³	1	2	yes	—
128	#124×C₆₁	C₂³	1	2	yes	—
129	#123×C₆₁	—	2	2	no	—
130	#123×C₆₁	—	2	2	no	—
131	#123×C₆₁	—	2	2	no	—
132	#123×C₆₁	—	2	2	no	—
133	C₂²⋊Q₈×C₆₁	—	2	2	no	—
134	C₂²⋊Q₈×C₆₁	—	2	2	no	—
135	C₂²⋊Q₈×C₆₁	—	2	4	no	—
136	C₂²⋊Q₈×C₆₁	—	2	4	no	—
137	C₂²⋊Q₈×C₆₁	—	2	1	no	—
138	C₂²⋊Q₈×C₆₁	—	2	2	no	—
139	C₂²⋊Q₈×C₆₁	—	2	2	no	—
140	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
141	#121×C₆₁	—	2	1	no	—
142	#121×C₆₁	C₂³	1	2	yes	—
143	C₄×Q₈×C₆₁	—	2	2	no	—
144	C₄×Q₈×C₆₁	—	2	1	no	—
145	C₄×Q₈×C₆₁	—	2	2	no	—
146	C₄×Q₈×C₆₁	—	2	1	no	—
147	C₄×Q₈×C₆₁	—	2	1	no	—
148	C₄×Q₈×C₆₁	D₄	1	2	yes	—
149	C₄×Q₈×C₆₁	D₄	1	2	yes	—
150	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
151	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
152	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
153	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
154	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
155	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
156	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
157	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
158	C₄×D₄×C₆₁	—	2	2	no	—
159	C₄×D₄×C₆₁	—	2	2	no	—
160	C₄×D₄×C₆₁	—	2	2	no	—
161	C₄×D₄×C₆₁	—	2	1	no	—
162	C₄×D₄×C₆₁	—	2	2	no	—
163	C₄×D₄×C₆₁	C₂³	1	2	yes	—
164	C₄×D₄×C₆₁	C₂³	1	2	yes	—
165	C₄×D₄×C₆₁	C₂³	1	2	yes	—
166	C₄×D₄×C₆₁	C₂³	1	4	yes	—
167	#117×C₆₁	—	2	1	no	—
168	#117×C₆₁	—	2	2	no	—
169	#117×C₆₁	—	2	4	no	—
170	#117×C₆₁	—	2	4	no	—
171	#117×C₆₁	—	2	2	no	—
172	#117×C₆₁	—	2	2	no	—
173	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
174	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
175	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
176	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
177	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
178	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
184	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
185	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
186	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
187	C₂×C₄²×C₆₁	—	2	1	no	—
188	C₂×C₄²×C₆₁	—	2	1	no	—
189	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
192	#107×C₆₁	C₂³	1	4	yes	—
193	#106×C₆₁	C₂³	1	4	yes	—
194	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
195	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
196	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
197	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
198	#103×C₆₁	C₂³	1	4	yes	—
199	#103×C₆₁	C₂³	1	4	yes	—
200	#103×C₆₁	C₂³	1	4	yes	—
201	#103×C₆₁	C₂³	1	4	yes	—
202	#103×C₆₁	C₂³	1	4	yes	—
203	#102×C₆₁	C₂³	1	4	yes	—
204	#102×C₆₁	C₂³	1	4	yes	—
205	#102×C₆₁	C₂³	1	4	yes	—
206	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
207	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
208	#97×C₆₁	C₂³	1	4	yes	—
209	#97×C₆₁	C₂³	1	2	yes	—
210	#97×C₆₁	C₂³	1	2	yes	—
211	C₄×C₈×C₆₁	C₂³	1	4	yes	—
212	C₂⁴×C₆₁	—	2	1	no	—
213	#41×C₆₁	—	4	4	no	—
214	C₂×Q₈×C₆₁	—	2	1	no	—
215	C₂×Q₈×C₆₁	—	2	1	no	—
216	C₂×Q₈×C₆₁	—	2	1	no	—
217	C₂×Q₈×C₆₁	—	2	1	no	—
218	C₂×Q₈×C₆₁	—	4	2	no	—
219	C₂×Q₈×C₆₁	—	4	2	no	—
220	C₂×Q₈×C₆₁	—	4	2	no	—
221	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
222	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
223	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
224	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
225	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
226	C₂×D₄×C₆₁	—	2	2	no	—
227	C₂×D₄×C₆₁	—	2	1	no	—
228	C₂×D₄×C₆₁	—	2	1	no	—
229	C₂×D₄×C₆₁	—	2	1	no	—
230	C₂×D₄×C₆₁	—	4	2	no	—
231	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
232	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₆₁	—	2	1	no	—
234	C₂²×C₄×C₆₁	—	2	1	no	—
235	C₂²×C₄×C₆₁	—	2	1	no	—
236	C₂²×C₄×C₆₁	—	2	2	no	—
237	C₂²×C₄×C₆₁	—	2	4	no	—
238	C₂²×C₄×C₆₁	—	2	2	no	—
239	C₂²×C₄×C₆₁	—	2	2	no	—
240	C₂²×C₄×C₆₁	—	4	4	no	—
241	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
248	Q₁₆×C₆₁	—	4	4	no	—
249	Q₁₆×C₆₁	—	4	4	no	—
250	SD₁₆×C₆₁	—	4	4	no	—
251	SD₁₆×C₆₁	—	4	4	no	—
252	SD₁₆×C₆₁	—	4	4	no	—
253	D₈×C₆₁	—	4	4	no	—
254	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
255	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
256	C₄⋊C₄×C₆₁	—	2	1	no	—
257	C₄⋊C₄×C₆₁	—	2	4	no	—
258	C₄⋊C₄×C₆₁	—	2	2	no	—
259	C₄⋊C₄×C₆₁	—	2	2	no	—
260	C₄⋊C₄×C₆₁	—	2	2	no	—
261	C₄⋊C₄×C₆₁	—	2	4	no	—
262	C₄⋊C₄×C₆₁	—	2	2	no	—
263	C₄⋊C₄×C₆₁	—	2	4	no	—
264	C₄⋊C₄×C₆₁	—	2	1	no	—
265	C₄⋊C₄×C₆₁	—	2	1	no	—
266	C₄⋊C₄×C₆₁	—	2	2	no	—
267	C₄⋊C₄×C₆₁	—	2	2	no	—
268	C₄⋊C₄×C₆₁	—	2	2	no	—
269	C₄⋊C₄×C₆₁	—	2	1	no	—
270	C₄⋊C₄×C₆₁	—	2	1	no	—
271	C₄⋊C₄×C₆₁	—	2	2	no	—
272	C₄⋊C₄×C₆₁	—	2	2	no	—
273	C₄⋊C₄×C₆₁	—	2	2	no	—
274	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
275	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
277	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
283	C₂²⋊C₄×C₆₁	—	2	2	no	—
284	C₂²⋊C₄×C₆₁	—	2	4	no	—
285	C₂²⋊C₄×C₆₁	—	2	2	no	—
286	C₂²⋊C₄×C₆₁	—	2	2	no	—
287	C₂²⋊C₄×C₆₁	—	2	4	no	—
288	C₂²⋊C₄×C₆₁	—	2	2	no	—
289	C₂²⋊C₄×C₆₁	—	2	4	no	—
290	C₂²⋊C₄×C₆₁	—	2	2	no	—
291	C₂²⋊C₄×C₆₁	—	2	2	no	—
292	C₂²⋊C₄×C₆₁	—	2	2	no	—
293	C₂²⋊C₄×C₆₁	—	2	2	no	—
294	C₂²⋊C₄×C₆₁	—	2	2	no	—
295	C₂²⋊C₄×C₆₁	—	2	2	no	—
296	C₂²⋊C₄×C₆₁	—	2	2	no	—
297	C₂²⋊C₄×C₆₁	—	2	2	no	—
298	C₂²⋊C₄×C₆₁	—	2	2	no	—
299	C₄²×C₆₁	—	2	4	no	—
300	C₄²×C₆₁	—	2	2	no	—
301	C₄²×C₆₁	—	2	2	no	—
302	C₄²×C₆₁	—	2	2	no	—
303	C₄²×C₆₁	—	2	2	no	—
304	C₄²×C₆₁	—	2	2	no	—
305	C₄²×C₆₁	C₂×D₄	1	2	yes	—
306	C₄²×C₆₁	C₂×D₄	1	2	yes	—
307	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₆₁	C₂⁴	1	2	yes	—
310	C₄²×C₆₁	C₂⁴	1	2	yes	—
311	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
312	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
313	C₂³×C₆₁	—	2	2	no	—
314	C₂³×C₆₁	—	2	2	no	—
315	C₂³×C₆₁	—	4	2	no	—
316	C₂³×C₆₁	—	4	2	no	—
317	C₂³×C₆₁	—	4	2	no	—
318	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
319	Q₈×C₆₁	—	2	2	no	—
320	Q₈×C₆₁	—	2	4	no	—
321	Q₈×C₆₁	—	2	4	no	—
322	Q₈×C₆₁	—	2	2	no	—
323	Q₈×C₆₁	—	4	2	no	—
324	Q₈×C₆₁	—	4	2	no	—
325	Q₈×C₆₁	—	4	2	no	—
326	Q₈×C₆₁	—	4	2	no	—
327	Q₈×C₆₁	—	4	2	no	—
328	Q₈×C₆₁	—	8	1	no	—
329	D₄×C₆₁	—	2	4	no	—
330	D₄×C₆₁	—	2	4	no	—
331	D₄×C₆₁	—	4	2	no	—
332	D₄×C₆₁	—	4	2	no	—
333	D₄×C₆₁	—	4	4	no	—
334	D₄×C₆₁	—	8	1	no	—
335	C₂×C₄×C₆₁	—	2	2	no	—
336	C₂×C₄×C₆₁	—	2	2	no	—
337	C₂×C₄×C₆₁	—	2	2	no	—
338	C₂×C₄×C₆₁	—	2	2	no	—
339	C₂×C₄×C₆₁	—	2	2	no	—
340	C₂×C₄×C₆₁	—	2	2	no	—
341	C₂×C₄×C₆₁	—	2	2	no	—
342	C₂×C₄×C₆₁	—	2	2	no	—
343	C₂×C₄×C₆₁	—	2	2	no	—
344	C₂×C₄×C₆₁	—	2	2	no	—
345	C₂×C₄×C₆₁	—	4	1	no	—
346	C₂×C₄×C₆₁	—	4	1	no	—
347	C₂×C₄×C₆₁	—	4	1	no	—
348	C₂×C₄×C₆₁	—	4	8	no	—
349	C₂×C₄×C₆₁	—	4	4	no	—
350	C₂×C₄×C₆₁	—	4	2	no	—
351	C₂×C₄×C₆₁	—	4	2	no	—
352	C₂×C₄×C₆₁	—	4	2	no	—
353	C₂×C₄×C₆₁	—	8	2	no	—
354	C₂×C₄×C₆₁	—	8	2	no	—
355	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
356	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
360	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
362	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
363	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
365	C₈×C₆₁	—	2	4	no	—
366	C₈×C₆₁	—	2	4	no	—
367	#61894	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
368	C₂²×C₆₁	—	2	1	no	—
369	C₂²×C₆₁	—	2	1	no	—
370	C₂²×C₆₁	—	4	2	no	—
371	C₂²×C₆₁	—	4	2	no	—
372	C₂²×C₆₁	—	4	2	no	—
373	C₂²×C₆₁	—	4	2	no	—
374	C₂²×C₆₁	—	4	2	no	—
375	C₂²×C₆₁	—	4	2	no	—
376	C₂²×C₆₁	—	8	4	no	—
377	C₂²×C₆₁	#575	1	2	yes	—
378	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
379	C₄×C₆₁	—	2	2	no	—
380	C₄×C₆₁	—	2	2	no	—
381	C₄×C₆₁	—	2	1	no	—
382	C₄×C₆₁	—	2	1	no	—
383	C₄×C₆₁	—	2	1	no	—
384	C₄×C₆₁	—	2	2	no	—
385	C₄×C₆₁	—	2	1	no	—
386	C₄×C₆₁	—	2	1	no	—
387	C₄×C₆₁	—	2	2	no	—
388	C₄×C₆₁	—	4	2	no	—
389	C₄×C₆₁	—	4	2	no	—
390	C₄×C₆₁	—	4	2	no	—
391	C₄×C₆₁	—	4	2	no	—
392	C₄×C₆₁	—	4	2	no	—
393	C₄×C₆₁	—	4	2	no	—
394	C₄×C₆₁	#585	1	2	yes	—
395	#3507	C₂×C₆₁	1	1	yes	characteristic, complemented
396	C₂×#556	C₂×C₆₁	1	1	yes	characteristic, complemented
397	#3402	C₂×C₆₁	1	4	yes	complemented
398	#3401	C₂×C₆₁	1	4	yes	complemented
399	#3377	C₂×C₆₁	1	4	yes	complemented
400	#3376	C₂×C₆₁	1	4	yes	complemented
401	#3218	C₂×C₆₁	1	2	yes	complemented
402	#3215	C₂×C₆₁	1	1	yes	characteristic, complemented
403	#3213	C₂×C₆₁	1	1	yes	characteristic
404	#3211	C₂×C₆₁	1	2	yes	complemented
405	#3114	C₂×C₆₁	1	2	yes	complemented
406	#3113	C₂×C₆₁	1	1	yes	characteristic, complemented
407	#3112	C₂×C₆₁	1	1	yes	characteristic, complemented
408	#3108	C₂×C₆₁	1	2	yes	complemented
409	#2983	C₂×C₆₁	1	1	yes	characteristic, complemented
410	C₂×C₆₁	—	2	2	no	—
411	C₂×C₆₁	—	8	2	no	—
412	C₂×C₆₁	—	8	2	no	—
413	C₂×C₆₁	#3487	1	1	yes	characteristic
414	C₂×C₆₁	C₂×#575	1	1	yes	characteristic
415	C₂×C₆₁	#3586	1	1	yes	characteristic
416	#559	C₂²×C₆₁	1	2	yes	complemented
417	#557	C₂²×C₆₁	1	2	yes	complemented
418	#556	—	2	2	no	—
419	#556	—	2	2	no	—
420	#556	—	2	2	no	—
421	#556	C₂²×C₆₁	1	4	yes	—
422	#556	C₂²×C₆₁	1	4	yes	—
423	#556	C₂²×C₆₁	1	2	yes	complemented
424	#554	C₂²×C₆₁	1	2	yes	complemented
425	#552	—	2	2	no	—
426	#539	—	2	1	no	—
427	#539	—	2	1	no	—
428	#536	—	2	1	no	—
429	#533	C₂²×C₆₁	1	1	yes	characteristic
430	#532	C₂²×C₆₁	1	1	yes	characteristic
431	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
432	#529	C₂²×C₆₁	1	2	yes	—
433	#529	C₂²×C₆₁	1	2	yes	—
434	C₂×#126	—	2	1	no	—
435	C₂×#126	—	2	1	no	—
436	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
437	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
438	C₂×C₂²⋊Q₈	—	2	1	no	—
439	#520	—	2	1	no	—
440	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
441	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
442	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
443	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
444	C₂×#117	—	2	1	no	—
445	#497	C₂²×C₆₁	1	2	yes	—
446	#497	C₂²×C₆₁	1	4	yes	complemented
447	#496	C₂²×C₆₁	1	2	yes	—
448	#495	C₂²×C₆₁	1	4	yes	—
449	#491	C₂²×C₆₁	1	4	yes	complemented
450	#489	C₂²×C₆₁	1	2	yes	—
451	#489	C₂²×C₆₁	1	2	yes	—
452	#488	C₂²×C₆₁	1	4	yes	—
453	#483	C₂²×C₆₁	1	2	yes	—
454	#480	C₂²×C₆₁	1	2	yes	—
455	#479	C₂²×C₆₁	1	4	yes	complemented
456	#478	C₂²×C₆₁	1	4	yes	—
457	#477	C₂²×C₆₁	1	2	yes	complemented
458	#475	C₂²×C₆₁	1	2	yes	complemented
459	#464	C₂²×C₆₁	1	4	yes	—
460	#464	C₂²×C₆₁	1	4	yes	—
461	#464	C₂²×C₆₁	1	4	yes	complemented
462	#463	C₂²×C₆₁	1	4	yes	—
463	#463	C₂²×C₆₁	1	4	yes	—
464	#463	C₂²×C₆₁	1	4	yes	—
465	#462	C₂²×C₆₁	1	2	yes	complemented
466	#462	C₂²×C₆₁	1	4	yes	complemented
467	#461	C₂²×C₆₁	1	4	yes	complemented
468	#460	C₂²×C₆₁	1	2	yes	complemented
469	#451	C₂²×C₆₁	1	2	yes	—
470	#451	C₂²×C₆₁	1	2	yes	—
471	#450	C₂²×C₆₁	1	2	yes	—
472	#448	C₂²×C₆₁	1	2	yes	—
473	#448	C₂²×C₆₁	1	2	yes	—
474	#447	C₂²×C₆₁	1	2	yes	—
475	#446	C₂²×C₆₁	1	4	yes	complemented
476	#446	C₂²×C₆₁	1	4	yes	complemented
477	#442	C₂²×C₆₁	1	4	yes	—
478	#441	C₂²×C₆₁	1	4	yes	complemented
479	#440	C₂²×C₆₁	1	4	yes	—
480	#440	C₂²×C₆₁	1	4	yes	complemented
481	C₄×Q₁₆	C₂²×C₆₁	1	4	yes	complemented
482	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	complemented
483	#432	C₂²×C₆₁	1	1	yes	characteristic
484	#432	C₂²×C₆₁	1	1	yes	characteristic
485	#432	C₂²×C₆₁	1	2	yes	—
486	#431	C₂²×C₆₁	1	2	yes	—
487	C₆₁	#61894	1	1	yes	characteristic, direct product factor, Sylow
488	C₂×#41	—	2	1	no	—
489	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
490	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
491	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
492	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
493	C₂³×C₄	—	2	1	no	—
494	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
495	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
496	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
497	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
498	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
499	C₂×D₈	C₂³×C₆₁	1	4	yes	—
500	C₄⋊Q₈	—	2	2	no	—
501	C₄⋊Q₈	—	2	2	no	—
502	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
503	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
504	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
505	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
506	#127	C₂³×C₆₁	1	1	yes	characteristic
507	#126	—	2	4	no	—
508	#126	—	2	4	no	—
509	#126	—	2	4	no	—
510	#126	—	2	4	no	—
511	#126	—	2	2	no	—
512	#126	—	2	2	no	—
513	#126	—	2	2	no	—
514	#126	—	2	2	no	—
515	#125	—	2	2	no	—
516	#125	—	2	2	no	—
517	#125	—	2	1	no	—
518	#125	C₂³×C₆₁	1	2	yes	—
519	#125	C₂³×C₆₁	1	2	yes	—
520	#124	—	2	2	no	—
521	#124	—	2	2	no	—
522	#124	—	2	1	no	—
523	#124	—	2	1	no	—
524	#124	—	2	1	no	—
525	#124	C₂³×C₆₁	1	2	yes	—
526	#124	C₂³×C₆₁	1	4	yes	—
527	#124	C₂³×C₆₁	1	2	yes	—
528	#124	C₂³×C₆₁	1	2	yes	—
529	#124	C₂³×C₆₁	1	2	yes	—
530	#123	—	2	2	no	—
531	#123	—	2	2	no	—
532	#123	—	2	2	no	—
533	#123	—	2	2	no	—
534	C₂²⋊Q₈	—	2	4	no	—
535	C₂²⋊Q₈	—	2	4	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	2	no	—
538	C₂²⋊Q₈	—	2	1	no	—
539	C₂²⋊Q₈	—	2	2	no	—
540	C₂²⋊Q₈	—	2	2	no	—
541	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
542	#121	—	2	1	no	—
543	#121	C₂³×C₆₁	1	2	yes	—
544	C₄×Q₈	—	2	2	no	—
545	C₄×Q₈	—	2	2	no	—
546	C₄×Q₈	—	2	1	no	—
547	C₄×Q₈	—	2	1	no	—
548	C₄×Q₈	—	2	1	no	—
549	C₄×Q₈	D₄×C₆₁	1	2	yes	—
550	C₄×Q₈	D₄×C₆₁	1	2	yes	—
551	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
552	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
553	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
554	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
555	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
556	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
557	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
558	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	2	2	no	—
563	C₄×D₄	—	2	1	no	—
564	C₄×D₄	C₂³×C₆₁	1	4	yes	—
565	C₄×D₄	C₂³×C₆₁	1	2	yes	—
566	C₄×D₄	C₂³×C₆₁	1	2	yes	—
567	C₄×D₄	C₂³×C₆₁	1	2	yes	—
568	#117	—	2	1	no	—
569	#117	—	2	4	no	—
570	#117	—	2	4	no	—
571	#117	—	2	2	no	—
572	#117	—	2	2	no	—
573	#117	—	2	2	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	2	no	—
579	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
580	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
581	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
583	C₂×C₂²⋊C₄	—	2	1	no	—
584	C₂×C₂²⋊C₄	—	2	1	no	—
585	C₂×C₂²⋊C₄	—	2	1	no	—
586	C₂×C₂²⋊C₄	—	2	1	no	—
587	C₂×C₂²⋊C₄	—	2	1	no	—
588	C₂×C₄²	—	2	1	no	—
589	C₂×C₄²	—	2	1	no	—
590	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
591	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
593	#107	C₂³×C₆₁	1	4	yes	—
594	#106	C₂³×C₆₁	1	4	yes	—
595	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
596	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
597	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
598	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
599	#103	C₂³×C₆₁	1	4	yes	—
600	#103	C₂³×C₆₁	1	4	yes	—
601	#103	C₂³×C₆₁	1	4	yes	—
602	#103	C₂³×C₆₁	1	4	yes	—
603	#103	C₂³×C₆₁	1	4	yes	—
604	#102	C₂³×C₆₁	1	4	yes	—
605	#102	C₂³×C₆₁	1	4	yes	—
606	#102	C₂³×C₆₁	1	4	yes	—
607	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
608	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
609	#97	C₂³×C₆₁	1	4	yes	—
610	#97	C₂³×C₆₁	1	2	yes	—
611	#97	C₂³×C₆₁	1	2	yes	—
612	C₄×C₈	C₂³×C₆₁	1	4	yes	—
613	C₂⁴	—	2	1	no	—
614	#41	—	4	4	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	4	2	no	—
620	C₂×Q₈	—	4	2	no	—
621	C₂×Q₈	—	4	2	no	—
622	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
623	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
624	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
625	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
626	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
627	C₂×D₄	—	2	2	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	4	2	no	—
632	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
633	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	4	4	no	—
642	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
644	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
645	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
646	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
649	Q₁₆	—	4	4	no	—
650	Q₁₆	—	4	4	no	—
651	SD₁₆	—	4	4	no	—
652	SD₁₆	—	4	4	no	—
653	SD₁₆	—	4	4	no	—
654	D₈	—	4	4	no	—
655	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
656	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
676	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
677	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
678	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
679	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
680	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
681	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
682	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
683	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	2	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	4	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	—	2	2	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₄²	—	2	4	no	—
701	C₄²	—	2	2	no	—
702	C₄²	—	2	2	no	—
703	C₄²	—	2	2	no	—
704	C₄²	—	2	2	no	—
705	C₄²	—	2	2	no	—
706	C₄²	C₂×D₄×C₆₁	1	2	yes	—
707	C₄²	C₂×D₄×C₆₁	1	2	yes	—
708	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
709	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
710	C₄²	C₂⁴×C₆₁	1	2	yes	—
711	C₄²	C₂⁴×C₆₁	1	2	yes	—
712	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
713	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	4	2	no	—
717	C₂³	—	4	2	no	—
718	C₂³	—	4	2	no	—
719	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
720	Q₈	—	2	2	no	—
721	Q₈	—	2	4	no	—
722	Q₈	—	2	4	no	—
723	Q₈	—	2	2	no	—
724	Q₈	—	4	2	no	—
725	Q₈	—	4	2	no	—
726	Q₈	—	4	2	no	—
727	Q₈	—	4	2	no	—
728	Q₈	—	4	2	no	—
729	Q₈	—	8	1	no	—
730	D₄	—	2	4	no	—
731	D₄	—	2	4	no	—
732	D₄	—	4	2	no	—
733	D₄	—	4	2	no	—
734	D₄	—	4	4	no	—
735	D₄	—	8	1	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	4	8	no	—
750	C₂×C₄	—	4	4	no	—
751	C₂×C₄	—	4	2	no	—
752	C₂×C₄	—	4	2	no	—
753	C₂×C₄	—	4	2	no	—
754	C₂×C₄	—	8	2	no	—
755	C₂×C₄	—	8	2	no	—
756	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
757	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
758	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
759	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
760	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
761	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
762	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
763	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
764	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
765	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
766	C₈	—	2	4	no	—
767	C₈	—	2	4	no	—
768	C₂²	—	2	1	no	—
769	C₂²	—	2	1	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	8	4	no	—
777	C₂²	C₆₁×#575	1	2	yes	—
778	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
779	C₄	—	2	2	no	—
780	C₄	—	2	1	no	—
781	C₄	—	2	1	no	—
782	C₄	—	2	2	no	—
783	C₄	—	2	2	no	—
784	C₄	—	2	2	no	—
785	C₄	—	2	1	no	—
786	C₄	—	2	1	no	—
787	C₄	—	2	1	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₄	C₆₁×#585	1	2	yes	—
795	C₂	—	2	2	no	—
796	C₂	—	8	2	no	—
797	C₂	—	8	2	no	—
798	C₂	C₆₁×#3487	1	1	yes	characteristic
799	C₂	C₂×C₆₁×#575	1	1	yes	characteristic
800	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×#3213	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
1. C₆₁×#3507	C₂	semidirect
2. C₂×C₆₁×#556	C₂	semidirect
3. C₆₁×#3402	C₂	semidirect
4. C₆₁×#3401	C₂	semidirect
5. C₆₁×#3377	C₂	semidirect
6. C₆₁×#3376	C₂	semidirect
7. C₆₁×#3218	C₂	semidirect
8. C₆₁×#3215	C₂	semidirect
10. C₆₁×#3211	C₂	semidirect
11. C₆₁×#3114	C₂	semidirect
12. C₆₁×#3113	C₂	semidirect
13. C₆₁×#3112	C₂	semidirect
14. C₆₁×#3108	C₂	semidirect
15. C₆₁×#2983	C₂	semidirect
16. C₆₁×#559	C₂²	semidirect
17. C₆₁×#557	C₂²	semidirect
23. C₆₁×#556	C₂²	semidirect
24. C₆₁×#554	C₂²	semidirect
46. C₆₁×#497	C₂²	semidirect
49. C₆₁×#491	C₂²	semidirect
55. C₆₁×#479	C₂²	semidirect
57. C₆₁×#477	C₂²	semidirect
58. C₆₁×#475	C₂²	semidirect
61. C₆₁×#464	C₂²	semidirect
65. C₆₁×#462	C₂²	semidirect
66. C₆₁×#462	C₂²	semidirect
67. C₆₁×#461	C₂²	semidirect
68. C₆₁×#460	C₂²	semidirect
75. C₆₁×#446	C₂²	semidirect
76. C₆₁×#446	C₂²	semidirect
78. C₆₁×#441	C₂²	semidirect
80. C₆₁×#440	C₂²	semidirect
81. C₄×Q₁₆×C₆₁	C₂²	semidirect
82. C₄×SD₁₆×C₆₁	C₂²	semidirect
367. #61894	C₆₁	direct (N × H)
395. #3507	C₂×C₆₁	semidirect
396. C₂×#556	C₂×C₆₁	semidirect
397. #3402	C₂×C₆₁	semidirect
398. #3401	C₂×C₆₁	semidirect
399. #3377	C₂×C₆₁	semidirect
400. #3376	C₂×C₆₁	semidirect
401. #3218	C₂×C₆₁	semidirect
402. #3215	C₂×C₆₁	semidirect
404. #3211	C₂×C₆₁	semidirect
405. #3114	C₂×C₆₁	semidirect
406. #3113	C₂×C₆₁	semidirect
407. #3112	C₂×C₆₁	semidirect
408. #3108	C₂×C₆₁	semidirect
409. #2983	C₂×C₆₁	semidirect
416. #559	C₂²×C₆₁	semidirect
417. #557	C₂²×C₆₁	semidirect
423. #556	C₂²×C₆₁	semidirect
424. #554	C₂²×C₆₁	semidirect
446. #497	C₂²×C₆₁	semidirect
449. #491	C₂²×C₆₁	semidirect
455. #479	C₂²×C₆₁	semidirect
457. #477	C₂²×C₆₁	semidirect
458. #475	C₂²×C₆₁	semidirect
461. #464	C₂²×C₆₁	semidirect
465. #462	C₂²×C₆₁	semidirect
466. #462	C₂²×C₆₁	semidirect
467. #461	C₂²×C₆₁	semidirect
468. #460	C₂²×C₆₁	semidirect
475. #446	C₂²×C₆₁	semidirect
476. #446	C₂²×C₆₁	semidirect
478. #441	C₂²×C₆₁	semidirect
480. #440	C₂²×C₆₁	semidirect
481. C₄×Q₁₆	C₂²×C₆₁	semidirect
482. C₄×SD₁₆	C₂²×C₆₁	semidirect
487. C₆₁	#61894	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×#3507	2
C₂×C₆₁×#556	2
C₆₁×#3402	2
C₆₁×#3401	2
C₆₁×#3377	2
C₆₁×#3376	2
C₆₁×#3218	2
C₆₁×#3215	2
C₆₁×#3213	2
C₆₁×#3211	2
C₆₁×#3114	2
C₆₁×#3113	2
C₆₁×#3112	2
C₆₁×#3108	2
C₆₁×#2983	2
#61894	61

Subgroups — C61×#61894 #29565327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61894 #29565327