Subgroups — C₆₁×#61220 #29564653

Order 15616.

2082 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3321	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3320	C₂	1	4	yes	maximal, complemented
5	C₆₁×#3309	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3308	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3135	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3098	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3078	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3062	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3036	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3010	C₂	1	2	yes	maximal, complemented
13	C₂×C₆₁×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#2932	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#2898	C₂	1	2	yes	maximal, complemented
16	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	2	yes	—
17	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
18	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×#131×C₆₁	C₂²	1	2	yes	—
20	C₆₁×#559	—	2	2	no	—
21	C₆₁×#556	—	2	1	no	—
22	C₆₁×#555	C₂²	1	2	yes	—
23	C₆₁×#553	C₂²	1	4	yes	—
24	C₆₁×#550	—	2	1	no	—
25	C₆₁×#550	—	2	1	no	—
26	C₆₁×#550	C₂²	1	2	yes	complemented
27	D₄×Q₈×C₆₁	—	2	1	no	—
28	D₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
29	C₆₁×#548	—	2	2	no	—
30	C₆₁×#548	C₂²	1	4	yes	complemented
31	C₆₁×#547	C₂²	1	2	yes	—
32	C₆₁×#538	—	2	2	no	—
33	C₆₁×#537	—	2	2	no	—
34	C₆₁×#537	C₂²	1	2	yes	—
35	C₆₁×#535	C₂²	1	2	yes	—
36	C₆₁×#533	C₂²	1	1	yes	characteristic
37	C₆₁×#532	—	2	2	no	—
38	C₆₁×#532	C₂²	1	1	yes	characteristic
39	C₆₁×#532	C₂²	1	1	yes	characteristic
40	C₆₁×#525	—	2	2	no	—
41	C₆₁×#520	C₂²	1	2	yes	—
42	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
44	C₆₁×#491	C₂²	1	2	yes	complemented
45	C₆₁×#490	C₂²	1	2	yes	complemented
46	C₆₁×#489	C₂²	1	2	yes	complemented
47	C₆₁×#489	C₂²	1	2	yes	complemented
48	C₆₁×#485	C₂²	1	4	yes	complemented
49	C₆₁×#484	C₂²	1	4	yes	complemented
50	C₆₁×#482	C₂²	1	4	yes	complemented
51	C₆₁×#480	C₂²	1	4	yes	complemented
52	C₆₁×#479	C₂²	1	4	yes	complemented
53	C₆₁×#477	C₂²	1	2	yes	complemented
54	C₆₁×#475	C₂²	1	2	yes	complemented
55	C₆₁×#469	C₂²	1	4	yes	—
56	C₆₁×#468	C₂²	1	4	yes	—
57	C₆₁×#466	C₂²	1	4	yes	—
58	C₆₁×#465	C₂²	1	4	yes	—
59	C₆₁×#463	C₂²	1	4	yes	—
60	C₆₁×#461	C₂²	1	2	yes	—
61	C₆₁×#459	C₂²	1	2	yes	—
62	C₆₁×#449	C₂²	1	4	yes	—
63	C₆₁×#449	C₂²	1	4	yes	—
64	C₆₁×#448	C₂²	1	4	yes	—
65	C₆₁×#448	C₂²	1	4	yes	—
66	C₆₁×#440	C₂²	1	4	yes	—
67	C₆₁×#440	C₂²	1	4	yes	—
68	C₆₁×#435	C₂²	1	4	yes	complemented
69	C₆₁×#435	C₂²	1	4	yes	complemented
70	C₆₁×#428	C₂²	1	2	yes	—
71	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
72	C₆₁×#423	C₂²	1	1	yes	characteristic
73	C₆₁×#419	C₂²	1	2	yes	—
74	C₆₁×#419	C₂²	1	4	yes	complemented
75	C₆₁×#417	C₂²	1	2	yes	—
76	C₆₁×#417	C₂²	1	4	yes	complemented
77	C₆₁×#416	C₂²	1	2	yes	—
78	C₆₁×#416	C₂²	1	2	yes	—
79	C₆₁×#416	C₂²	1	4	yes	complemented
80	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
81	C₂×#103×C₆₁	C₂²	1	4	yes	complemented
82	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
83	C₆₁×#408	C₂²	1	2	yes	—
84	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
85	2₋¹⁺⁴×C₆₁	—	2	8	no	—
86	2₋¹⁺⁴×C₆₁	—	4	4	no	—
87	C₂×#41×C₆₁	—	2	4	no	—
88	C₂×#41×C₆₁	—	2	2	no	—
89	C₂×#41×C₆₁	—	2	2	no	—
90	C₂×#41×C₆₁	C₂³	1	2	yes	—
91	C₂×#41×C₆₁	C₂³	1	4	yes	—
92	C₂×#41×C₆₁	C₂³	1	2	yes	—
93	C₂²×Q₈×C₆₁	—	2	2	no	—
94	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
95	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₆₁	—	2	1	no	—
98	AGL(1,ℤ/8)×C₆₁	—	4	4	no	—
99	C₂×SD₁₆×C₆₁	—	2	4	no	—
100	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
102	C₂×D₈×C₆₁	C₂³	1	4	yes	—
103	#131×C₆₁	—	4	4	no	—
104	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
105	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
106	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
109	C₄⋊Q₈×C₆₁	—	2	2	no	—
110	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
111	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
114	#127×C₆₁	—	2	2	no	—
115	#127×C₆₁	—	2	2	no	—
116	#127×C₆₁	D₄	1	1	yes	characteristic
117	#127×C₆₁	C₂³	1	1	yes	characteristic
118	#126×C₆₁	—	2	4	no	—
119	#125×C₆₁	C₂³	1	2	yes	—
120	#124×C₆₁	—	2	2	no	—
121	#124×C₆₁	—	2	4	no	—
122	#124×C₆₁	—	2	4	no	—
123	#124×C₆₁	D₄	1	2	yes	—
124	#124×C₆₁	C₂³	1	2	yes	—
125	#123×C₆₁	—	2	4	no	—
126	#123×C₆₁	—	2	4	no	—
127	C₂²⋊Q₈×C₆₁	—	2	2	no	—
128	C₂²⋊Q₈×C₆₁	—	2	1	no	—
129	C₂²⋊Q₈×C₆₁	—	2	1	no	—
130	C₂²⋊Q₈×C₆₁	—	2	4	no	—
131	C₂²⋊Q₈×C₆₁	—	2	2	no	—
132	C₂²⋊Q₈×C₆₁	—	2	4	no	—
133	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
134	#121×C₆₁	—	2	4	no	—
135	#121×C₆₁	—	2	4	no	—
136	#121×C₆₁	—	2	2	no	—
137	#121×C₆₁	—	2	4	no	—
138	#121×C₆₁	—	2	2	no	—
139	#121×C₆₁	—	2	1	no	—
140	#121×C₆₁	—	2	1	no	—
141	#121×C₆₁	—	2	4	no	—
142	#121×C₆₁	D₄	1	2	yes	—
143	#121×C₆₁	D₄	1	2	yes	—
144	#121×C₆₁	C₂³	1	4	yes	—
145	#121×C₆₁	C₂³	1	4	yes	—
146	#121×C₆₁	C₂³	1	4	yes	—
147	#120×C₆₁	—	2	4	no	—
148	C₄×Q₈×C₆₁	—	2	2	no	—
149	C₄×Q₈×C₆₁	—	2	1	no	—
150	C₄×Q₈×C₆₁	—	2	1	no	—
151	C₄×Q₈×C₆₁	—	2	1	no	—
152	C₄×Q₈×C₆₁	—	2	1	no	—
153	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
154	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
155	C₄×D₄×C₆₁	—	2	2	no	—
156	C₄×D₄×C₆₁	—	2	4	no	—
157	C₄×D₄×C₆₁	—	2	2	no	—
158	C₄×D₄×C₆₁	—	2	2	no	—
159	C₄×D₄×C₆₁	—	2	4	no	—
160	C₄×D₄×C₆₁	—	2	4	no	—
161	C₄×D₄×C₆₁	—	2	1	no	—
162	C₄×D₄×C₆₁	—	2	1	no	—
163	C₄×D₄×C₆₁	—	2	1	no	—
164	C₄×D₄×C₆₁	—	2	1	no	—
165	C₄×D₄×C₆₁	C₂³	1	2	yes	—
166	C₄×D₄×C₆₁	C₂³	1	2	yes	—
167	C₄×D₄×C₆₁	C₂³	1	2	yes	—
168	C₄×D₄×C₆₁	C₂³	1	2	yes	—
169	#117×C₆₁	—	2	2	no	—
170	#117×C₆₁	C₂³	1	2	yes	—
171	#117×C₆₁	C₂³	1	4	yes	—
172	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
173	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
175	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
177	C₂×C₄²×C₆₁	—	2	1	no	—
178	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
179	#107×C₆₁	C₂³	1	4	yes	—
180	#107×C₆₁	C₂³	1	4	yes	—
181	#106×C₆₁	C₂³	1	4	yes	—
182	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
183	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
184	#103×C₆₁	C₂³	1	4	yes	—
185	#103×C₆₁	C₂³	1	2	yes	—
186	#103×C₆₁	C₂³	1	4	yes	—
187	#103×C₆₁	C₂³	1	4	yes	—
188	#103×C₆₁	C₂³	1	2	yes	—
189	#103×C₆₁	C₂³	1	2	yes	—
190	#103×C₆₁	C₂³	1	2	yes	—
191	#103×C₆₁	C₂³	1	4	yes	—
192	#102×C₆₁	C₂³	1	4	yes	—
193	#102×C₆₁	C₂³	1	2	yes	—
194	#102×C₆₁	C₂³	1	2	yes	—
195	#102×C₆₁	C₂³	1	2	yes	—
196	#102×C₆₁	C₂³	1	2	yes	—
197	#102×C₆₁	C₂³	1	4	yes	—
198	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
199	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
200	#97×C₆₁	C₂³	1	2	yes	—
201	#97×C₆₁	C₂³	1	2	yes	—
202	C₂⁴×C₆₁	—	2	1	no	—
203	#41×C₆₁	—	2	4	no	—
204	#41×C₆₁	—	2	4	no	—
205	#41×C₆₁	—	2	8	no	—
206	#41×C₆₁	—	2	4	no	—
207	#41×C₆₁	—	2	4	no	—
208	#41×C₆₁	—	4	4	no	—
209	#41×C₆₁	—	4	16	no	—
210	#41×C₆₁	—	4	8	no	—
211	#41×C₆₁	—	8	4	no	—
212	C₂×Q₈×C₆₁	—	2	1	no	—
213	C₂×Q₈×C₆₁	—	2	1	no	—
214	C₂×Q₈×C₆₁	—	2	4	no	—
215	C₂×Q₈×C₆₁	—	2	1	no	—
216	C₂×Q₈×C₆₁	—	2	2	no	—
217	C₂×Q₈×C₆₁	—	2	8	no	—
218	C₂×Q₈×C₆₁	—	4	4	no	—
219	C₂×Q₈×C₆₁	—	4	8	no	—
220	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
221	C₂×Q₈×C₆₁	#41	1	4	yes	complemented
222	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
223	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
224	C₂×D₄×C₆₁	—	2	2	no	—
225	C₂×D₄×C₆₁	—	2	4	no	—
226	C₂×D₄×C₆₁	—	2	4	no	—
227	C₂×D₄×C₆₁	—	2	4	no	—
228	C₂×D₄×C₆₁	—	2	4	no	—
229	C₂×D₄×C₆₁	—	2	1	no	—
230	C₂×D₄×C₆₁	—	2	1	no	—
231	C₂×D₄×C₆₁	—	2	1	no	—
232	C₂×D₄×C₆₁	—	2	2	no	—
233	C₂×D₄×C₆₁	—	2	2	no	—
234	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
235	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
237	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
238	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
239	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₆₁	—	2	1	no	—
241	C₂²×C₄×C₆₁	—	2	4	no	—
242	C₂²×C₄×C₆₁	—	2	1	no	—
243	C₂²×C₄×C₆₁	—	2	1	no	—
244	C₂²×C₄×C₆₁	—	2	4	no	—
245	C₂²×C₄×C₆₁	—	2	2	no	—
246	C₂²×C₄×C₆₁	—	2	4	no	—
247	C₂²×C₄×C₆₁	—	2	2	no	—
248	C₂²×C₄×C₆₁	—	2	2	no	—
249	C₂²×C₄×C₆₁	—	8	2	no	—
250	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
253	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
254	SD₁₆×C₆₁	—	2	8	no	—
255	SD₁₆×C₆₁	—	4	4	no	—
256	D₈×C₆₁	—	4	4	no	—
257	M₁₆×C₆₁	—	2	4	no	—
258	M₁₆×C₆₁	—	4	4	no	—
259	C₂×C₈×C₆₁	—	2	2	no	—
260	C₂×C₈×C₆₁	—	2	2	no	—
261	C₂×C₈×C₆₁	—	4	4	no	—
262	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
263	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
264	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
265	C₄⋊C₄×C₆₁	—	2	2	no	—
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	1	no	—
270	C₄⋊C₄×C₆₁	—	2	1	no	—
271	C₄⋊C₄×C₆₁	—	2	1	no	—
272	C₄⋊C₄×C₆₁	—	2	2	no	—
273	C₄⋊C₄×C₆₁	—	2	1	no	—
274	C₄⋊C₄×C₆₁	—	2	4	no	—
275	C₄⋊C₄×C₆₁	—	2	2	no	—
276	C₄⋊C₄×C₆₁	—	2	1	no	—
277	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₆₁	C₂⁴	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	4	no	—
286	C₂²⋊C₄×C₆₁	—	2	2	no	—
287	C₂²⋊C₄×C₆₁	—	2	2	no	—
288	C₂²⋊C₄×C₆₁	—	2	4	no	—
289	C₂²⋊C₄×C₆₁	—	2	2	no	—
290	C₂²⋊C₄×C₆₁	—	2	4	no	—
291	C₂²⋊C₄×C₆₁	—	2	2	no	—
292	C₂²⋊C₄×C₆₁	—	2	4	no	—
293	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
294	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
295	C₄²×C₆₁	—	2	2	no	—
296	C₄²×C₆₁	—	2	2	no	—
297	C₄²×C₆₁	—	2	4	no	—
298	C₄²×C₆₁	—	2	2	no	—
299	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
302	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
303	C₂³×C₆₁	—	2	2	no	—
304	C₂³×C₆₁	—	2	2	no	—
305	C₂³×C₆₁	—	4	2	no	—
306	C₂³×C₆₁	—	8	1	no	—
307	C₂³×C₆₁	—	8	1	no	—
308	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
309	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
310	Q₈×C₆₁	—	2	4	no	—
311	Q₈×C₆₁	—	2	4	no	—
312	Q₈×C₆₁	—	2	2	no	—
313	Q₈×C₆₁	—	2	2	no	—
314	Q₈×C₆₁	—	2	2	no	—
315	Q₈×C₆₁	—	4	8	no	—
316	Q₈×C₆₁	—	4	2	no	—
317	Q₈×C₆₁	—	8	1	no	—
318	Q₈×C₆₁	C₂×#41	1	4	yes	—
319	D₄×C₆₁	—	2	8	no	—
320	D₄×C₆₁	—	2	4	no	—
321	D₄×C₆₁	—	2	2	no	—
322	D₄×C₆₁	—	2	2	no	—
323	D₄×C₆₁	—	2	2	no	—
324	D₄×C₆₁	—	2	2	no	—
325	D₄×C₆₁	—	4	2	no	—
326	D₄×C₆₁	—	4	2	no	—
327	D₄×C₆₁	—	4	8	no	—
328	D₄×C₆₁	—	4	2	no	—
329	D₄×C₆₁	—	4	4	no	—
330	D₄×C₆₁	—	4	2	no	—
331	D₄×C₆₁	—	8	1	no	—
332	D₄×C₆₁	—	8	4	no	—
333	D₄×C₆₁	—	8	4	no	—
334	D₄×C₆₁	—	8	4	no	—
335	C₂×C₄×C₆₁	—	2	4	no	—
336	C₂×C₄×C₆₁	—	2	2	no	—
337	C₂×C₄×C₆₁	—	2	4	no	—
338	C₂×C₄×C₆₁	—	2	4	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	—	4	1	no	—
345	C₂×C₄×C₆₁	—	4	1	no	—
346	C₂×C₄×C₆₁	—	4	8	no	—
347	C₂×C₄×C₆₁	—	4	8	no	—
348	C₂×C₄×C₆₁	—	4	4	no	—
349	C₂×C₄×C₆₁	—	4	4	no	—
350	C₂×C₄×C₆₁	—	8	2	no	—
351	C₂×C₄×C₆₁	—	8	1	no	—
352	C₂×C₄×C₆₁	—	8	1	no	—
353	C₂×C₄×C₆₁	—	8	4	no	—
354	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
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	1	yes	characteristic
360	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
361	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
362	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
363	C₈×C₆₁	—	2	2	no	—
364	C₈×C₆₁	—	2	2	no	—
365	C₈×C₆₁	—	2	4	no	—
366	#61220	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
367	C₂²×C₆₁	—	2	1	no	—
368	C₂²×C₆₁	—	2	1	no	—
369	C₂²×C₆₁	—	2	4	no	—
370	C₂²×C₆₁	—	2	4	no	—
371	C₂²×C₆₁	—	2	4	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	—	4	2	no	—
377	C₂²×C₆₁	—	4	2	no	—
378	C₂²×C₆₁	—	8	4	no	—
379	C₂²×C₆₁	#546	1	2	yes	—
380	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
381	C₄×C₆₁	—	2	1	no	—
382	C₄×C₆₁	—	2	1	no	—
383	C₄×C₆₁	—	2	1	no	—
384	C₄×C₆₁	—	2	1	no	—
385	C₄×C₆₁	—	2	4	no	—
386	C₄×C₆₁	—	2	4	no	—
387	C₄×C₆₁	—	4	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	#546	1	2	yes	—
393	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
394	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
395	#3506	C₂×C₆₁	1	1	yes	characteristic, complemented
396	#3497	C₂×C₆₁	1	1	yes	characteristic, complemented
397	#3321	C₂×C₆₁	1	4	yes	complemented
398	#3320	C₂×C₆₁	1	4	yes	complemented
399	#3309	C₂×C₆₁	1	4	yes	complemented
400	#3308	C₂×C₆₁	1	4	yes	complemented
401	#3135	C₂×C₆₁	1	1	yes	characteristic, complemented
402	#3098	C₂×C₆₁	1	2	yes	complemented
403	#3078	C₂×C₆₁	1	1	yes	characteristic, complemented
404	#3062	C₂×C₆₁	1	2	yes	complemented
405	#3036	C₂×C₆₁	1	1	yes	characteristic, complemented
406	#3010	C₂×C₆₁	1	2	yes	complemented
407	C₂×#440	C₂×C₆₁	1	1	yes	characteristic, complemented
408	#2932	C₂×C₆₁	1	1	yes	characteristic, complemented
409	#2898	C₂×C₆₁	1	2	yes	complemented
410	C₂×C₆₁	—	2	2	no	—
411	C₂×C₆₁	—	4	4	no	—
412	C₂×C₆₁	—	8	2	no	—
413	C₂×C₆₁	—	8	2	no	—
414	C₂×C₆₁	C₂×#546	1	1	yes	characteristic
415	C₂×C₆₁	#3585	1	1	yes	characteristic
416	C₂×C₆₁	#3586	1	1	yes	characteristic
417	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	2	yes	—
418	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
419	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
420	C₂×#131	C₂²×C₆₁	1	2	yes	—
421	#559	—	2	2	no	—
422	#556	—	2	1	no	—
423	#555	C₂²×C₆₁	1	2	yes	—
424	#553	C₂²×C₆₁	1	4	yes	—
425	#550	—	2	1	no	—
426	#550	—	2	1	no	—
427	#550	C₂²×C₆₁	1	2	yes	complemented
428	D₄×Q₈	—	2	1	no	—
429	D₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
430	#548	—	2	2	no	—
431	#548	C₂²×C₆₁	1	4	yes	complemented
432	#547	C₂²×C₆₁	1	2	yes	—
433	#538	—	2	2	no	—
434	#537	—	2	2	no	—
435	#537	C₂²×C₆₁	1	2	yes	—
436	#535	C₂²×C₆₁	1	2	yes	—
437	#533	C₂²×C₆₁	1	1	yes	characteristic
438	#532	—	2	2	no	—
439	#532	C₂²×C₆₁	1	1	yes	characteristic
440	#532	C₂²×C₆₁	1	1	yes	characteristic
441	#525	—	2	2	no	—
442	#520	C₂²×C₆₁	1	2	yes	—
443	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
444	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
445	#491	C₂²×C₆₁	1	2	yes	complemented
446	#490	C₂²×C₆₁	1	2	yes	complemented
447	#489	C₂²×C₆₁	1	2	yes	complemented
448	#489	C₂²×C₆₁	1	2	yes	complemented
449	#485	C₂²×C₆₁	1	4	yes	complemented
450	#484	C₂²×C₆₁	1	4	yes	complemented
451	#482	C₂²×C₆₁	1	4	yes	complemented
452	#480	C₂²×C₆₁	1	4	yes	complemented
453	#479	C₂²×C₆₁	1	4	yes	complemented
454	#477	C₂²×C₆₁	1	2	yes	complemented
455	#475	C₂²×C₆₁	1	2	yes	complemented
456	#469	C₂²×C₆₁	1	4	yes	—
457	#468	C₂²×C₆₁	1	4	yes	—
458	#466	C₂²×C₆₁	1	4	yes	—
459	#465	C₂²×C₆₁	1	4	yes	—
460	#463	C₂²×C₆₁	1	4	yes	—
461	#461	C₂²×C₆₁	1	2	yes	—
462	#459	C₂²×C₆₁	1	2	yes	—
463	#449	C₂²×C₆₁	1	4	yes	—
464	#449	C₂²×C₆₁	1	4	yes	—
465	#448	C₂²×C₆₁	1	4	yes	—
466	#448	C₂²×C₆₁	1	4	yes	—
467	#440	C₂²×C₆₁	1	4	yes	—
468	#440	C₂²×C₆₁	1	4	yes	—
469	#435	C₂²×C₆₁	1	4	yes	complemented
470	#435	C₂²×C₆₁	1	4	yes	complemented
471	#428	C₂²×C₆₁	1	2	yes	—
472	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
473	#423	C₂²×C₆₁	1	1	yes	characteristic
474	#419	C₂²×C₆₁	1	2	yes	—
475	#419	C₂²×C₆₁	1	4	yes	complemented
476	#417	C₂²×C₆₁	1	2	yes	—
477	#417	C₂²×C₆₁	1	4	yes	complemented
478	#416	C₂²×C₆₁	1	2	yes	—
479	#416	C₂²×C₆₁	1	2	yes	—
480	#416	C₂²×C₆₁	1	4	yes	complemented
481	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
482	C₂×#103	C₂²×C₆₁	1	4	yes	complemented
483	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
484	#408	C₂²×C₆₁	1	2	yes	—
485	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
486	C₆₁	#61220	1	1	yes	characteristic, direct product factor, Sylow
487	2₋¹⁺⁴	—	2	8	no	—
488	2₋¹⁺⁴	—	4	4	no	—
489	C₂×#41	—	2	4	no	—
490	C₂×#41	—	2	2	no	—
491	C₂×#41	—	2	2	no	—
492	C₂×#41	C₂³×C₆₁	1	2	yes	—
493	C₂×#41	C₂³×C₆₁	1	4	yes	—
494	C₂×#41	C₂³×C₆₁	1	2	yes	—
495	C₂²×Q₈	—	2	2	no	—
496	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
497	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
498	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
499	C₂³×C₄	—	2	1	no	—
500	AGL(1,ℤ/8)	—	4	4	no	—
501	C₂×SD₁₆	—	2	4	no	—
502	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
503	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
504	C₂×D₈	C₂³×C₆₁	1	4	yes	—
505	#131	—	4	4	no	—
506	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
507	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
508	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
509	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
510	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
511	C₄⋊Q₈	—	2	2	no	—
512	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
513	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
514	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
515	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
516	#127	—	2	2	no	—
517	#127	—	2	2	no	—
518	#127	D₄×C₆₁	1	1	yes	characteristic
519	#127	C₂³×C₆₁	1	1	yes	characteristic
520	#126	—	2	4	no	—
521	#125	C₂³×C₆₁	1	2	yes	—
522	#124	—	2	2	no	—
523	#124	—	2	4	no	—
524	#124	—	2	4	no	—
525	#124	D₄×C₆₁	1	2	yes	—
526	#124	C₂³×C₆₁	1	2	yes	—
527	#123	—	2	4	no	—
528	#123	—	2	4	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	1	no	—
531	C₂²⋊Q₈	—	2	1	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	4	no	—
534	C₂²⋊Q₈	—	2	4	no	—
535	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
536	#121	—	2	2	no	—
537	#121	—	2	4	no	—
538	#121	—	2	4	no	—
539	#121	—	2	2	no	—
540	#121	—	2	4	no	—
541	#121	—	2	1	no	—
542	#121	—	2	1	no	—
543	#121	—	2	4	no	—
544	#121	D₄×C₆₁	1	2	yes	—
545	#121	D₄×C₆₁	1	2	yes	—
546	#121	C₂³×C₆₁	1	4	yes	—
547	#121	C₂³×C₆₁	1	4	yes	—
548	#121	C₂³×C₆₁	1	4	yes	—
549	#120	—	2	4	no	—
550	C₄×Q₈	—	2	2	no	—
551	C₄×Q₈	—	2	1	no	—
552	C₄×Q₈	—	2	1	no	—
553	C₄×Q₈	—	2	1	no	—
554	C₄×Q₈	—	2	1	no	—
555	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
556	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
557	C₄×D₄	—	2	4	no	—
558	C₄×D₄	—	2	2	no	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	4	no	—
562	C₄×D₄	—	2	4	no	—
563	C₄×D₄	—	2	1	no	—
564	C₄×D₄	—	2	1	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	C₂³×C₆₁	1	2	yes	—
568	C₄×D₄	C₂³×C₆₁	1	2	yes	—
569	C₄×D₄	C₂³×C₆₁	1	2	yes	—
570	C₄×D₄	C₂³×C₆₁	1	2	yes	—
571	#117	—	2	2	no	—
572	#117	C₂³×C₆₁	1	2	yes	—
573	#117	C₂³×C₆₁	1	4	yes	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
578	C₂×C₂²⋊C₄	—	2	1	no	—
579	C₂×C₄²	—	2	1	no	—
580	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
581	#107	C₂³×C₆₁	1	4	yes	—
582	#107	C₂³×C₆₁	1	4	yes	—
583	#106	C₂³×C₆₁	1	4	yes	—
584	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
585	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
586	#103	C₂³×C₆₁	1	4	yes	—
587	#103	C₂³×C₆₁	1	2	yes	—
588	#103	C₂³×C₆₁	1	4	yes	—
589	#103	C₂³×C₆₁	1	4	yes	—
590	#103	C₂³×C₆₁	1	2	yes	—
591	#103	C₂³×C₆₁	1	2	yes	—
592	#103	C₂³×C₆₁	1	2	yes	—
593	#103	C₂³×C₆₁	1	4	yes	—
594	#102	C₂³×C₆₁	1	4	yes	—
595	#102	C₂³×C₆₁	1	2	yes	—
596	#102	C₂³×C₆₁	1	2	yes	—
597	#102	C₂³×C₆₁	1	2	yes	—
598	#102	C₂³×C₆₁	1	2	yes	—
599	#102	C₂³×C₆₁	1	4	yes	—
600	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
601	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
602	#97	C₂³×C₆₁	1	2	yes	—
603	#97	C₂³×C₆₁	1	2	yes	—
604	C₂⁴	—	2	1	no	—
605	#41	—	2	4	no	—
606	#41	—	2	4	no	—
607	#41	—	2	8	no	—
608	#41	—	2	4	no	—
609	#41	—	2	4	no	—
610	#41	—	4	4	no	—
611	#41	—	4	16	no	—
612	#41	—	4	8	no	—
613	#41	—	8	4	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	—	2	4	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	2	no	—
619	C₂×Q₈	—	2	8	no	—
620	C₂×Q₈	—	4	4	no	—
621	C₂×Q₈	—	4	8	no	—
622	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
623	C₂×Q₈	#41×C₆₁	1	4	yes	complemented
624	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
625	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
637	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
638	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
639	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
640	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
641	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	8	2	no	—
652	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
653	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
654	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
655	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
656	SD₁₆	—	2	8	no	—
657	SD₁₆	—	4	4	no	—
658	D₈	—	4	4	no	—
659	M₁₆	—	2	4	no	—
660	M₁₆	—	4	4	no	—
661	C₂×C₈	—	2	2	no	—
662	C₂×C₈	—	2	2	no	—
663	C₂×C₈	—	4	4	no	—
664	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
665	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
666	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	1	no	—
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	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
696	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
697	C₄²	—	2	2	no	—
698	C₄²	—	2	2	no	—
699	C₄²	—	2	4	no	—
700	C₄²	—	2	2	no	—
701	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
702	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
703	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
704	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	4	2	no	—
708	C₂³	—	8	1	no	—
709	C₂³	—	8	1	no	—
710	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
711	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
712	Q₈	—	2	4	no	—
713	Q₈	—	2	4	no	—
714	Q₈	—	2	2	no	—
715	Q₈	—	2	2	no	—
716	Q₈	—	2	2	no	—
717	Q₈	—	4	8	no	—
718	Q₈	—	4	2	no	—
719	Q₈	—	8	1	no	—
720	Q₈	C₂×#41×C₆₁	1	4	yes	—
721	D₄	—	2	8	no	—
722	D₄	—	2	4	no	—
723	D₄	—	2	2	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	2	2	no	—
727	D₄	—	4	2	no	—
728	D₄	—	4	2	no	—
729	D₄	—	4	8	no	—
730	D₄	—	4	2	no	—
731	D₄	—	4	4	no	—
732	D₄	—	4	2	no	—
733	D₄	—	8	1	no	—
734	D₄	—	8	4	no	—
735	D₄	—	8	4	no	—
736	D₄	—	8	4	no	—
737	C₂×C₄	—	2	4	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	4	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	8	no	—
749	C₂×C₄	—	4	8	no	—
750	C₂×C₄	—	4	4	no	—
751	C₂×C₄	—	4	4	no	—
752	C₂×C₄	—	8	2	no	—
753	C₂×C₄	—	8	1	no	—
754	C₂×C₄	—	8	1	no	—
755	C₂×C₄	—	8	4	no	—
756	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
757	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
758	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
759	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
760	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
761	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
762	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
763	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
764	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
765	C₈	—	2	2	no	—
766	C₈	—	2	2	no	—
767	C₈	—	2	4	no	—
768	C₂²	—	2	1	no	—
769	C₂²	—	2	1	no	—
770	C₂²	—	2	4	no	—
771	C₂²	—	2	4	no	—
772	C₂²	—	2	4	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	8	4	no	—
780	C₂²	C₆₁×#546	1	2	yes	—
781	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
782	C₄	—	2	1	no	—
783	C₄	—	2	1	no	—
784	C₄	—	2	1	no	—
785	C₄	—	2	1	no	—
786	C₄	—	2	4	no	—
787	C₄	—	2	4	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	C₆₁×#546	1	2	yes	—
794	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
795	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
796	C₂	—	2	2	no	—
797	C₂	—	4	4	no	—
798	C₂	—	8	2	no	—
799	C₂	—	8	2	no	—
800	C₂	C₂×C₆₁×#546	1	1	yes	characteristic
801	C₂	C₆₁×#3585	1	1	yes	characteristic
802	C₂	C₆₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3506	C₂	semidirect
2. C₆₁×#3497	C₂	semidirect
3. C₆₁×#3321	C₂	semidirect
4. C₆₁×#3320	C₂	semidirect
5. C₆₁×#3309	C₂	semidirect
6. C₆₁×#3308	C₂	semidirect
7. C₆₁×#3135	C₂	semidirect
8. C₆₁×#3098	C₂	semidirect
9. C₆₁×#3078	C₂	semidirect
10. C₆₁×#3062	C₂	semidirect
11. C₆₁×#3036	C₂	semidirect
12. C₆₁×#3010	C₂	semidirect
13. C₂×C₆₁×#440	C₂	semidirect
14. C₆₁×#2932	C₂	semidirect
15. C₆₁×#2898	C₂	semidirect
26. C₆₁×#550	C₂²	semidirect
28. D₄×Q₈×C₆₁	C₂²	semidirect
30. C₆₁×#548	C₂²	semidirect
44. C₆₁×#491	C₂²	semidirect
45. C₆₁×#490	C₂²	semidirect
46. C₆₁×#489	C₂²	semidirect
47. C₆₁×#489	C₂²	semidirect
48. C₆₁×#485	C₂²	semidirect
49. C₆₁×#484	C₂²	semidirect
50. C₆₁×#482	C₂²	semidirect
51. C₆₁×#480	C₂²	semidirect
52. C₆₁×#479	C₂²	semidirect
53. C₆₁×#477	C₂²	semidirect
54. C₆₁×#475	C₂²	semidirect
68. C₆₁×#435	C₂²	semidirect
69. C₆₁×#435	C₂²	semidirect
74. C₆₁×#419	C₂²	semidirect
76. C₆₁×#417	C₂²	semidirect
79. C₆₁×#416	C₂²	semidirect
81. C₂×#103×C₆₁	C₂²	semidirect
221. C₂×Q₈×C₆₁	#41	semidirect
366. #61220	C₆₁	direct (N × H)
395. #3506	C₂×C₆₁	semidirect
396. #3497	C₂×C₆₁	semidirect
397. #3321	C₂×C₆₁	semidirect
398. #3320	C₂×C₆₁	semidirect
399. #3309	C₂×C₆₁	semidirect
400. #3308	C₂×C₆₁	semidirect
401. #3135	C₂×C₆₁	semidirect
402. #3098	C₂×C₆₁	semidirect
403. #3078	C₂×C₆₁	semidirect
404. #3062	C₂×C₆₁	semidirect
405. #3036	C₂×C₆₁	semidirect
406. #3010	C₂×C₆₁	semidirect
407. C₂×#440	C₂×C₆₁	semidirect
408. #2932	C₂×C₆₁	semidirect
409. #2898	C₂×C₆₁	semidirect
427. #550	C₂²×C₆₁	semidirect
429. D₄×Q₈	C₂²×C₆₁	semidirect
431. #548	C₂²×C₆₁	semidirect
445. #491	C₂²×C₆₁	semidirect
446. #490	C₂²×C₆₁	semidirect
447. #489	C₂²×C₆₁	semidirect
448. #489	C₂²×C₆₁	semidirect
449. #485	C₂²×C₆₁	semidirect
450. #484	C₂²×C₆₁	semidirect
451. #482	C₂²×C₆₁	semidirect
452. #480	C₂²×C₆₁	semidirect
453. #479	C₂²×C₆₁	semidirect
454. #477	C₂²×C₆₁	semidirect
455. #475	C₂²×C₆₁	semidirect
469. #435	C₂²×C₆₁	semidirect
470. #435	C₂²×C₆₁	semidirect
475. #419	C₂²×C₆₁	semidirect
477. #417	C₂²×C₆₁	semidirect
480. #416	C₂²×C₆₁	semidirect
482. C₂×#103	C₂²×C₆₁	semidirect
486. C₆₁	#61220	direct (N × H)
623. C₂×Q₈	#41×C₆₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₆₁×#3506	2
C₆₁×#3497	2
C₆₁×#3321	2
C₆₁×#3320	2
C₆₁×#3309	2
C₆₁×#3308	2
C₆₁×#3135	2
C₆₁×#3098	2
C₆₁×#3078	2
C₆₁×#3062	2
C₆₁×#3036	2
C₆₁×#3010	2
C₂×C₆₁×#440	2
C₆₁×#2932	2
C₆₁×#2898	2
#61220	61

Subgroups — C61×#61220 #29564653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61220 #29564653