Subgroups — C₆₁×#25791 #29529224

Order 15616.

1760 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#492	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#468	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₆₁×#449	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₆₁×#450	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2433	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2432	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2014	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#2013	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2012	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#2011	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#1973	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1970	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
19	C₂×AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
20	C₂×AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
21	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
22	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
23	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
24	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
25	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
26	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
28	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
30	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
32	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×#120×C₆₁	—	2	2	no	—
38	C₆₁×#496	—	2	4	no	—
39	C₆₁×#492	—	2	4	no	—
40	C₆₁×#468	—	2	4	no	—
41	C₆₁×#450	—	2	4	no	—
42	C₆₁×#449	—	2	4	no	—
43	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic, complemented
44	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic, complemented
45	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic, complemented
46	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
47	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
48	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic, complemented
49	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
51	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
53	C₆₁×#394	—	2	2	no	—
54	C₆₁×#392	—	2	2	no	—
55	C₆₁×#391	C₂²	1	1	yes	characteristic, complemented
56	C₆₁×#390	C₂²	1	1	yes	characteristic
57	C₆₁×#390	C₂²	1	1	yes	characteristic
58	C₆₁×#390	C₂²	1	1	yes	characteristic, complemented
59	C₆₁×#385	—	2	2	no	—
60	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
61	C₆₁×#336	C₂²	1	1	yes	characteristic, complemented
62	C₆₁×#336	C₂²	1	1	yes	characteristic, complemented
63	C₂⁵×C₆₁	—	2	1	no	—
64	C₂×#41×C₆₁	—	2	2	no	—
65	C₂×#41×C₆₁	—	2	2	no	—
66	C₂×#41×C₆₁	—	2	2	no	—
67	C₂×#41×C₆₁	—	2	2	no	—
68	C₂×#41×C₆₁	—	4	1	no	—
69	C₂×#41×C₆₁	—	4	1	no	—
70	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₆₁	—	2	2	no	—
73	C₂²×D₄×C₆₁	—	2	2	no	—
74	C₂²×D₄×C₆₁	—	2	1	no	—
75	C₂²×D₄×C₆₁	—	2	1	no	—
76	C₂²×D₄×C₆₁	—	2	2	no	—
77	C₂²×D₄×C₆₁	—	2	2	no	—
78	C₂²×D₄×C₆₁	—	2	1	no	—
79	C₂²×D₄×C₆₁	—	2	2	no	—
80	C₂²×D₄×C₆₁	—	2	2	no	—
81	C₂²×D₄×C₆₁	—	4	1	no	—
82	C₂²×D₄×C₆₁	—	4	1	no	—
83	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₆₁	—	2	1	no	—
88	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
89	AGL(1,ℤ/8)×C₆₁	—	2	32	no	—
90	C₂×SD₁₆×C₆₁	—	2	2	no	—
91	C₂×SD₁₆×C₆₁	—	2	2	no	—
92	C₂×SD₁₆×C₆₁	—	2	2	no	—
93	C₂×SD₁₆×C₆₁	—	2	2	no	—
94	C₂×SD₁₆×C₆₁	—	2	2	no	—
95	C₂×SD₁₆×C₆₁	—	2	2	no	—
96	C₂×SD₁₆×C₆₁	—	2	2	no	—
97	C₂×SD₁₆×C₆₁	—	2	2	no	—
98	C₂×SD₁₆×C₆₁	—	2	2	no	—
99	C₂×SD₁₆×C₆₁	—	2	2	no	—
100	C₂×SD₁₆×C₆₁	—	2	2	no	—
101	C₂×SD₁₆×C₆₁	—	2	2	no	—
102	C₂×SD₁₆×C₆₁	—	2	2	no	—
103	C₂×SD₁₆×C₆₁	—	2	2	no	—
104	C₂×SD₁₆×C₆₁	—	4	1	no	—
105	C₂×SD₁₆×C₆₁	—	4	1	no	—
106	C₂×SD₁₆×C₆₁	—	4	1	no	—
107	C₂×SD₁₆×C₆₁	D₄	1	4	yes	complemented
108	C₂×D₈×C₆₁	—	2	2	no	—
109	C₂×D₈×C₆₁	—	2	2	no	—
110	C₂×D₈×C₆₁	—	2	2	no	—
111	C₂×D₈×C₆₁	—	2	2	no	—
112	C₂×D₈×C₆₁	—	2	2	no	—
113	C₂×D₈×C₆₁	—	2	2	no	—
114	C₂×D₈×C₆₁	—	2	2	no	—
115	C₂×D₈×C₆₁	—	4	1	no	—
116	C₂×D₈×C₆₁	D₄	1	4	yes	complemented
117	C₂×M₁₆×C₆₁	—	2	2	no	—
118	C₂×M₁₆×C₆₁	—	2	2	no	—
119	C₂×M₁₆×C₆₁	D₄	1	4	yes	complemented
120	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
124	C₄⋊Q₈×C₆₁	—	2	2	no	—
125	C₄⋊Q₈×C₆₁	—	4	1	no	—
126	#127×C₆₁	—	2	2	no	—
127	#127×C₆₁	—	2	2	no	—
128	#127×C₆₁	—	4	1	no	—
129	#127×C₆₁	—	4	1	no	—
130	#124×C₆₁	—	2	2	no	—
131	#124×C₆₁	—	4	1	no	—
132	C₂²⋊Q₈×C₆₁	—	2	2	no	—
133	C₂²⋊Q₈×C₆₁	—	2	2	no	—
134	#121×C₆₁	—	2	2	no	—
135	#121×C₆₁	—	2	2	no	—
136	#120×C₆₁	—	4	8	no	—
137	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
138	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
139	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
143	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
144	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
145	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
146	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
147	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
148	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
150	#107×C₆₁	—	2	2	no	—
151	#103×C₆₁	—	2	2	no	—
152	#103×C₆₁	—	2	2	no	—
153	#102×C₆₁	—	2	2	no	—
154	#102×C₆₁	—	2	2	no	—
155	#102×C₆₁	—	2	2	no	—
156	#102×C₆₁	—	2	2	no	—
157	C₂²⋊C₈×C₆₁	D₄	1	4	yes	complemented
158	#97×C₆₁	—	2	2	no	—
159	C₄×C₈×C₆₁	—	2	2	no	—
160	#95×C₆₁	—	2	2	no	—
161	#95×C₆₁	D₄	1	2	yes	—
162	C₂⁴×C₆₁	—	2	1	no	—
163	C₂⁴×C₆₁	—	2	1	no	—
164	C₂⁴×C₆₁	—	2	1	no	—
165	C₂⁴×C₆₁	—	2	1	no	—
166	C₂⁴×C₆₁	—	4	2	no	—
167	C₂⁴×C₆₁	—	4	2	no	—
168	C₂⁴×C₆₁	—	4	4	no	—
169	C₂⁴×C₆₁	—	4	2	no	—
170	C₂⁴×C₆₁	—	8	2	no	—
171	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
172	#41×C₆₁	—	2	8	no	—
173	#41×C₆₁	—	4	4	no	—
174	#41×C₆₁	—	4	4	no	—
175	#41×C₆₁	—	4	4	no	—
176	C₂×Q₈×C₆₁	—	2	1	no	—
177	C₂×Q₈×C₆₁	—	2	1	no	—
178	C₂×Q₈×C₆₁	—	2	1	no	—
179	C₂×Q₈×C₆₁	—	2	1	no	—
180	C₂×Q₈×C₆₁	—	2	1	no	—
181	C₂×Q₈×C₆₁	—	2	1	no	—
182	C₂×Q₈×C₆₁	—	2	1	no	—
183	C₂×Q₈×C₆₁	—	2	1	no	—
184	C₂×Q₈×C₆₁	—	2	1	no	—
185	C₂×Q₈×C₆₁	—	2	1	no	—
186	C₂×Q₈×C₆₁	—	2	1	no	—
187	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
188	C₂×D₄×C₆₁	—	2	8	no	—
189	C₂×D₄×C₆₁	—	2	1	no	—
190	C₂×D₄×C₆₁	—	2	1	no	—
191	C₂×D₄×C₆₁	—	2	1	no	—
192	C₂×D₄×C₆₁	—	2	1	no	—
193	C₂×D₄×C₆₁	—	2	1	no	—
194	C₂×D₄×C₆₁	—	2	1	no	—
195	C₂×D₄×C₆₁	—	2	1	no	—
196	C₂×D₄×C₆₁	—	2	1	no	—
197	C₂×D₄×C₆₁	—	2	1	no	—
198	C₂×D₄×C₆₁	—	2	1	no	—
199	C₂×D₄×C₆₁	—	2	1	no	—
200	C₂×D₄×C₆₁	—	2	1	no	—
201	C₂×D₄×C₆₁	—	2	1	no	—
202	C₂×D₄×C₆₁	—	2	1	no	—
203	C₂×D₄×C₆₁	—	2	1	no	—
204	C₂×D₄×C₆₁	—	2	1	no	—
205	C₂×D₄×C₆₁	—	2	1	no	—
206	C₂×D₄×C₆₁	—	2	1	no	—
207	C₂×D₄×C₆₁	—	2	1	no	—
208	C₂×D₄×C₆₁	—	2	1	no	—
209	C₂×D₄×C₆₁	—	2	1	no	—
210	C₂×D₄×C₆₁	—	4	4	no	—
211	C₂×D₄×C₆₁	—	4	4	no	—
212	C₂×D₄×C₆₁	—	4	2	no	—
213	C₂×D₄×C₆₁	—	4	2	no	—
214	C₂×D₄×C₆₁	—	4	2	no	—
215	C₂×D₄×C₆₁	—	4	4	no	—
216	C₂×D₄×C₆₁	—	4	4	no	—
217	C₂×D₄×C₆₁	—	4	4	no	—
218	C₂×D₄×C₆₁	—	4	4	no	—
219	C₂×D₄×C₆₁	—	4	2	no	—
220	C₂×D₄×C₆₁	—	4	2	no	—
221	C₂×D₄×C₆₁	—	4	4	no	—
222	C₂×D₄×C₆₁	—	4	2	no	—
223	C₂×D₄×C₆₁	—	4	2	no	—
224	C₂×D₄×C₆₁	—	4	4	no	—
225	C₂×D₄×C₆₁	—	8	2	no	—
226	C₂×D₄×C₆₁	—	8	2	no	—
227	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
228	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
229	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
230	C₂²×C₄×C₆₁	—	2	1	no	—
231	C₂²×C₄×C₆₁	—	2	1	no	—
232	C₂²×C₄×C₆₁	—	2	1	no	—
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	1	no	—
237	C₂²×C₄×C₆₁	—	2	1	no	—
238	C₂²×C₄×C₆₁	—	4	2	no	—
239	C₂²×C₄×C₆₁	—	4	2	no	—
240	C₂²×C₄×C₆₁	—	4	2	no	—
241	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
242	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
244	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
245	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
246	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
247	SD₁₆×C₆₁	—	2	8	no	—
248	SD₁₆×C₆₁	—	2	8	no	—
249	SD₁₆×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	—	2	8	no	—
254	D₈×C₆₁	—	2	8	no	—
255	D₈×C₆₁	—	4	4	no	—
256	M₁₆×C₆₁	—	2	8	no	—
257	C₂×C₈×C₆₁	—	2	1	no	—
258	C₂×C₈×C₆₁	—	2	1	no	—
259	C₂×C₈×C₆₁	—	2	1	no	—
260	C₂×C₈×C₆₁	—	2	1	no	—
261	C₂×C₈×C₆₁	—	2	1	no	—
262	C₂×C₈×C₆₁	—	2	1	no	—
263	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
264	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
265	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
266	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
267	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
268	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
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	1	no	—
273	C₄⋊C₄×C₆₁	—	4	4	no	—
274	C₄⋊C₄×C₆₁	—	4	2	no	—
275	C₂²⋊C₄×C₆₁	—	2	4	no	—
276	C₂²⋊C₄×C₆₁	—	4	4	no	—
277	C₂²⋊C₄×C₆₁	—	4	4	no	—
278	C₂²⋊C₄×C₆₁	—	4	2	no	—
279	C₂²⋊C₄×C₆₁	—	4	2	no	—
280	C₂²⋊C₄×C₆₁	—	4	4	no	—
281	C₂²⋊C₄×C₆₁	—	4	4	no	—
282	C₄²×C₆₁	—	2	1	no	—
283	C₄²×C₆₁	—	2	1	no	—
284	C₄²×C₆₁	—	2	1	no	—
285	C₄²×C₆₁	—	2	1	no	—
286	C₂³×C₆₁	—	2	1	no	—
287	C₂³×C₆₁	—	2	1	no	—
288	C₂³×C₆₁	—	2	2	no	—
289	C₂³×C₆₁	—	2	2	no	—
290	C₂³×C₆₁	—	2	2	no	—
291	C₂³×C₆₁	—	2	2	no	—
292	C₂³×C₆₁	—	2	2	no	—
293	C₂³×C₆₁	—	4	8	no	—
294	C₂³×C₆₁	—	4	1	no	—
295	C₂³×C₆₁	—	4	1	no	—
296	C₂³×C₆₁	—	4	1	no	—
297	C₂³×C₆₁	—	4	1	no	—
298	C₂³×C₆₁	—	4	1	no	—
299	C₂³×C₆₁	—	4	1	no	—
300	C₂³×C₆₁	—	4	2	no	—
301	C₂³×C₆₁	—	4	2	no	—
302	C₂³×C₆₁	—	4	2	no	—
303	C₂³×C₆₁	—	4	2	no	—
304	C₂³×C₆₁	—	4	2	no	—
305	C₂³×C₆₁	—	4	2	no	—
306	C₂³×C₆₁	—	4	1	no	—
307	C₂³×C₆₁	—	4	1	no	—
308	C₂³×C₆₁	—	4	1	no	—
309	C₂³×C₆₁	—	4	2	no	—
310	C₂³×C₆₁	—	4	2	no	—
311	C₂³×C₆₁	—	8	4	no	—
312	C₂³×C₆₁	—	8	4	no	—
313	C₂³×C₆₁	—	8	8	no	—
314	C₂³×C₆₁	—	8	8	no	—
315	C₂³×C₆₁	#127	1	2	yes	—
316	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
317	Q₈×C₆₁	—	2	2	no	—
318	Q₈×C₆₁	—	2	2	no	—
319	Q₈×C₆₁	—	4	1	no	—
320	Q₈×C₆₁	—	4	1	no	—
321	Q₈×C₆₁	—	4	1	no	—
322	Q₈×C₆₁	—	4	1	no	—
323	Q₈×C₆₁	—	4	1	no	—
324	Q₈×C₆₁	—	4	1	no	—
325	D₄×C₆₁	—	2	2	no	—
326	D₄×C₆₁	—	2	2	no	—
327	D₄×C₆₁	—	2	2	no	—
328	D₄×C₆₁	—	2	2	no	—
329	D₄×C₆₁	—	2	2	no	—
330	D₄×C₆₁	—	2	2	no	—
331	D₄×C₆₁	—	4	8	no	—
332	D₄×C₆₁	—	4	8	no	—
333	D₄×C₆₁	—	4	1	no	—
334	D₄×C₆₁	—	4	1	no	—
335	D₄×C₆₁	—	4	1	no	—
336	D₄×C₆₁	—	4	1	no	—
337	D₄×C₆₁	—	4	1	no	—
338	D₄×C₆₁	—	4	1	no	—
339	D₄×C₆₁	—	4	1	no	—
340	D₄×C₆₁	—	4	1	no	—
341	D₄×C₆₁	—	4	1	no	—
342	D₄×C₆₁	—	4	1	no	—
343	D₄×C₆₁	—	8	8	no	—
344	D₄×C₆₁	—	8	8	no	—
345	D₄×C₆₁	—	8	4	no	—
346	C₂×C₄×C₆₁	—	2	2	no	—
347	C₂×C₄×C₆₁	—	2	1	no	—
348	C₂×C₄×C₆₁	—	2	1	no	—
349	C₂×C₄×C₆₁	—	2	2	no	—
350	C₂×C₄×C₆₁	—	2	2	no	—
351	C₂×C₄×C₆₁	—	2	2	no	—
352	C₂×C₄×C₆₁	—	2	2	no	—
353	C₂×C₄×C₆₁	—	2	2	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	—	4	8	no	—
359	C₂×C₄×C₆₁	—	4	1	no	—
360	C₂×C₄×C₆₁	—	4	1	no	—
361	C₂×C₄×C₆₁	—	4	1	no	—
362	C₂×C₄×C₆₁	—	4	1	no	—
363	C₂×C₄×C₆₁	—	4	1	no	—
364	C₂×C₄×C₆₁	—	4	1	no	—
365	C₂×C₄×C₆₁	—	4	1	no	—
366	C₂×C₄×C₆₁	—	4	2	no	—
367	C₂×C₄×C₆₁	—	4	2	no	—
368	C₂×C₄×C₆₁	#127	1	2	yes	—
369	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	4	yes	complemented
370	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
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	H(5,𝔽₂)	1	1	yes	characteristic
375	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
376	C₈×C₆₁	—	2	2	no	—
377	C₈×C₆₁	—	2	2	no	—
378	C₈×C₆₁	—	2	2	no	—
379	C₈×C₆₁	#120	1	4	yes	complemented
380	#25791	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
381	C₂²×C₆₁	—	2	2	no	—
382	C₂²×C₆₁	—	2	2	no	—
383	C₂²×C₆₁	—	2	2	no	—
384	C₂²×C₆₁	—	4	2	no	—
385	C₂²×C₆₁	—	4	2	no	—
386	C₂²×C₆₁	—	4	2	no	—
387	C₂²×C₆₁	—	4	2	no	—
388	C₂²×C₆₁	—	4	2	no	—
389	C₂²×C₆₁	—	4	4	no	—
390	C₂²×C₆₁	—	4	4	no	—
391	C₂²×C₆₁	—	4	4	no	—
392	C₂²×C₆₁	—	8	16	no	—
393	C₂²×C₆₁	—	8	1	no	—
394	C₂²×C₆₁	—	8	1	no	—
395	C₂²×C₆₁	—	8	1	no	—
396	C₂²×C₆₁	—	8	1	no	—
397	C₂²×C₆₁	—	8	1	no	—
398	C₂²×C₆₁	—	8	1	no	—
399	C₂²×C₆₁	—	8	2	no	—
400	C₂²×C₆₁	—	8	2	no	—
401	C₂²×C₆₁	—	8	2	no	—
402	C₂²×C₆₁	—	8	1	no	—
403	C₂²×C₆₁	—	8	1	no	—
404	C₂²×C₆₁	—	8	1	no	—
405	C₂²×C₆₁	—	8	2	no	—
406	C₂²×C₆₁	—	8	2	no	—
407	C₂²×C₆₁	C₂×#127	1	1	yes	characteristic
408	C₂²×C₆₁	D₄²	1	1	yes	characteristic
409	C₂²×C₆₁	D₄²	1	1	yes	characteristic
410	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
411	C₂²×C₆₁	#577	1	2	yes	—
412	C₄×C₆₁	—	2	2	no	—
413	C₄×C₆₁	—	2	4	no	—
414	C₄×C₆₁	—	4	2	no	—
415	C₄×C₆₁	—	4	2	no	—
416	C₄×C₆₁	—	8	1	no	—
417	C₄×C₆₁	—	8	1	no	—
418	C₄×C₆₁	—	8	1	no	—
419	C₄×C₆₁	C₂×#120	1	1	yes	characteristic
420	C₄×C₆₁	#535	1	1	yes	characteristic
421	C₄×C₆₁	D₄²	1	1	yes	characteristic
422	C₄×C₆₁	D₄²	1	1	yes	characteristic
423	C₂²×AGL(1,ℤ/8)	C₂×C₆₁	1	1	yes	characteristic, complemented
424	C₂×#496	C₂×C₆₁	1	1	yes	characteristic, complemented
425	C₂×#492	C₂×C₆₁	1	1	yes	characteristic, complemented
426	C₂×#468	C₂×C₆₁	1	1	yes	characteristic, complemented
427	C₂×#449	C₂×C₆₁	1	1	yes	characteristic, complemented
428	C₂×#450	C₂×C₆₁	1	1	yes	characteristic, complemented
429	#2433	C₂×C₆₁	1	1	yes	characteristic, complemented
430	#2432	C₂×C₆₁	1	1	yes	characteristic, complemented
431	#2014	C₂×C₆₁	1	1	yes	characteristic, complemented
432	#2013	C₂×C₆₁	1	1	yes	characteristic, complemented
433	#2012	C₂×C₆₁	1	1	yes	characteristic, complemented
434	#2011	C₂×C₆₁	1	1	yes	characteristic, complemented
435	#1973	C₂×C₆₁	1	1	yes	characteristic, complemented
436	#1970	C₂×C₆₁	1	1	yes	characteristic, complemented
437	#1753	C₂×C₆₁	1	1	yes	characteristic, complemented
438	C₂×C₆₁	—	4	2	no	—
439	C₂×C₆₁	—	8	2	no	—
440	C₂×C₆₁	—	8	2	no	—
441	C₂×C₆₁	—	8	2	no	—
442	C₂×C₆₁	—	16	1	no	—
443	C₂×C₆₁	#2433	1	1	yes	characteristic
444	C₂×C₆₁	#3151	1	1	yes	characteristic
445	C₂×C₆₁	#3154	1	1	yes	characteristic
446	C₂×C₆₁	#3265	1	2	yes	—
447	C₂×C₆₁	#3272	1	2	yes	—
448	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
449	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
450	C₂×AGL(1,ℤ/8)	—	2	4	no	—
451	C₂×AGL(1,ℤ/8)	—	2	4	no	—
452	C₂×AGL(1,ℤ/8)	—	2	4	no	—
453	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
454	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
455	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
456	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
457	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
458	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
459	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
460	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
461	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
462	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
463	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
464	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
465	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
466	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic, complemented
467	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
468	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
469	C₂×#120	—	2	2	no	—
470	#496	—	2	4	no	—
471	#492	—	2	4	no	—
472	#468	—	2	4	no	—
473	#450	—	2	4	no	—
474	#449	—	2	4	no	—
475	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic, complemented
476	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic, complemented
477	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic, complemented
478	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
479	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
480	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic, complemented
481	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic, complemented
482	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
483	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic, complemented
484	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
485	#394	—	2	2	no	—
486	#392	—	2	2	no	—
487	#391	C₂²×C₆₁	1	1	yes	characteristic, complemented
488	#390	C₂²×C₆₁	1	1	yes	characteristic
489	#390	C₂²×C₆₁	1	1	yes	characteristic
490	#390	C₂²×C₆₁	1	1	yes	characteristic, complemented
491	#385	—	2	2	no	—
492	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
493	#336	C₂²×C₆₁	1	1	yes	characteristic, complemented
494	#336	C₂²×C₆₁	1	1	yes	characteristic, complemented
495	C₆₁	#25791	1	1	yes	characteristic, direct product factor, Sylow
496	C₂⁵	—	2	1	no	—
497	C₂×#41	—	2	2	no	—
498	C₂×#41	—	2	2	no	—
499	C₂×#41	—	2	2	no	—
500	C₂×#41	—	2	2	no	—
501	C₂×#41	—	4	1	no	—
502	C₂×#41	—	4	1	no	—
503	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
504	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
505	C₂²×D₄	—	2	2	no	—
506	C₂²×D₄	—	2	2	no	—
507	C₂²×D₄	—	2	1	no	—
508	C₂²×D₄	—	2	1	no	—
509	C₂²×D₄	—	2	2	no	—
510	C₂²×D₄	—	2	2	no	—
511	C₂²×D₄	—	2	1	no	—
512	C₂²×D₄	—	2	2	no	—
513	C₂²×D₄	—	2	2	no	—
514	C₂²×D₄	—	4	1	no	—
515	C₂²×D₄	—	4	1	no	—
516	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
517	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
518	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
519	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
520	C₂³×C₄	—	2	1	no	—
521	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
522	AGL(1,ℤ/8)	—	2	32	no	—
523	C₂×SD₁₆	—	2	2	no	—
524	C₂×SD₁₆	—	2	2	no	—
525	C₂×SD₁₆	—	2	2	no	—
526	C₂×SD₁₆	—	2	2	no	—
527	C₂×SD₁₆	—	2	2	no	—
528	C₂×SD₁₆	—	2	2	no	—
529	C₂×SD₁₆	—	2	2	no	—
530	C₂×SD₁₆	—	2	2	no	—
531	C₂×SD₁₆	—	2	2	no	—
532	C₂×SD₁₆	—	2	2	no	—
533	C₂×SD₁₆	—	2	2	no	—
534	C₂×SD₁₆	—	2	2	no	—
535	C₂×SD₁₆	—	2	2	no	—
536	C₂×SD₁₆	—	2	2	no	—
537	C₂×SD₁₆	—	4	1	no	—
538	C₂×SD₁₆	—	4	1	no	—
539	C₂×SD₁₆	—	4	1	no	—
540	C₂×SD₁₆	D₄×C₆₁	1	4	yes	complemented
541	C₂×D₈	—	2	2	no	—
542	C₂×D₈	—	2	2	no	—
543	C₂×D₈	—	2	2	no	—
544	C₂×D₈	—	2	2	no	—
545	C₂×D₈	—	2	2	no	—
546	C₂×D₈	—	2	2	no	—
547	C₂×D₈	—	2	2	no	—
548	C₂×D₈	—	4	1	no	—
549	C₂×D₈	D₄×C₆₁	1	4	yes	complemented
550	C₂×M₁₆	—	2	2	no	—
551	C₂×M₁₆	—	2	2	no	—
552	C₂×M₁₆	D₄×C₆₁	1	4	yes	complemented
553	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
554	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
555	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
556	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
557	C₄⋊Q₈	—	2	2	no	—
558	C₄⋊Q₈	—	4	1	no	—
559	#127	—	2	2	no	—
560	#127	—	2	2	no	—
561	#127	—	4	1	no	—
562	#127	—	4	1	no	—
563	#124	—	2	2	no	—
564	#124	—	4	1	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	#121	—	2	2	no	—
568	#121	—	2	2	no	—
569	#120	—	4	8	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	2	no	—
572	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
574	C₂×C₂²⋊C₄	—	2	1	no	—
575	C₂×C₂²⋊C₄	—	2	2	no	—
576	C₂×C₂²⋊C₄	—	2	2	no	—
577	C₂×C₂²⋊C₄	—	2	1	no	—
578	C₂×C₂²⋊C₄	—	2	2	no	—
579	C₂×C₂²⋊C₄	—	2	2	no	—
580	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
581	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
582	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
583	#107	—	2	2	no	—
584	#103	—	2	2	no	—
585	#103	—	2	2	no	—
586	#102	—	2	2	no	—
587	#102	—	2	2	no	—
588	#102	—	2	2	no	—
589	#102	—	2	2	no	—
590	C₂²⋊C₈	D₄×C₆₁	1	4	yes	complemented
591	#97	—	2	2	no	—
592	C₄×C₈	—	2	2	no	—
593	#95	—	2	2	no	—
594	#95	D₄×C₆₁	1	2	yes	—
595	C₂⁴	—	2	1	no	—
596	C₂⁴	—	2	1	no	—
597	C₂⁴	—	2	1	no	—
598	C₂⁴	—	2	1	no	—
599	C₂⁴	—	4	2	no	—
600	C₂⁴	—	4	2	no	—
601	C₂⁴	—	4	4	no	—
602	C₂⁴	—	4	2	no	—
603	C₂⁴	—	8	2	no	—
604	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
605	#41	—	2	8	no	—
606	#41	—	4	4	no	—
607	#41	—	4	4	no	—
608	#41	—	4	4	no	—
609	C₂×Q₈	—	2	1	no	—
610	C₂×Q₈	—	2	1	no	—
611	C₂×Q₈	—	2	1	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	1	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	—	2	1	no	—
620	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
621	C₂×D₄	—	2	8	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	4	4	no	—
644	C₂×D₄	—	4	4	no	—
645	C₂×D₄	—	4	2	no	—
646	C₂×D₄	—	4	2	no	—
647	C₂×D₄	—	4	2	no	—
648	C₂×D₄	—	4	4	no	—
649	C₂×D₄	—	4	4	no	—
650	C₂×D₄	—	4	4	no	—
651	C₂×D₄	—	4	4	no	—
652	C₂×D₄	—	4	2	no	—
653	C₂×D₄	—	4	2	no	—
654	C₂×D₄	—	4	4	no	—
655	C₂×D₄	—	4	2	no	—
656	C₂×D₄	—	4	2	no	—
657	C₂×D₄	—	4	4	no	—
658	C₂×D₄	—	8	2	no	—
659	C₂×D₄	—	8	2	no	—
660	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
661	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
662	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	4	2	no	—
674	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
675	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
676	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
677	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
678	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
680	SD₁₆	—	2	8	no	—
681	SD₁₆	—	2	8	no	—
682	SD₁₆	—	4	4	no	—
683	SD₁₆	—	4	4	no	—
684	SD₁₆	—	4	4	no	—
685	SD₁₆	—	4	4	no	—
686	D₈	—	2	8	no	—
687	D₈	—	2	8	no	—
688	D₈	—	4	4	no	—
689	M₁₆	—	2	8	no	—
690	C₂×C₈	—	2	1	no	—
691	C₂×C₈	—	2	1	no	—
692	C₂×C₈	—	2	1	no	—
693	C₂×C₈	—	2	1	no	—
694	C₂×C₈	—	2	1	no	—
695	C₂×C₈	—	2	1	no	—
696	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
697	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
698	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
699	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
700	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
701	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	4	4	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	4	4	no	—
710	C₂²⋊C₄	—	4	4	no	—
711	C₂²⋊C₄	—	4	2	no	—
712	C₂²⋊C₄	—	4	2	no	—
713	C₂²⋊C₄	—	4	4	no	—
714	C₂²⋊C₄	—	4	4	no	—
715	C₄²	—	2	1	no	—
716	C₄²	—	2	1	no	—
717	C₄²	—	2	1	no	—
718	C₄²	—	2	1	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	4	8	no	—
727	C₂³	—	4	1	no	—
728	C₂³	—	4	1	no	—
729	C₂³	—	4	1	no	—
730	C₂³	—	4	1	no	—
731	C₂³	—	4	1	no	—
732	C₂³	—	4	1	no	—
733	C₂³	—	4	2	no	—
734	C₂³	—	4	2	no	—
735	C₂³	—	4	2	no	—
736	C₂³	—	4	2	no	—
737	C₂³	—	4	2	no	—
738	C₂³	—	4	2	no	—
739	C₂³	—	4	1	no	—
740	C₂³	—	4	1	no	—
741	C₂³	—	4	1	no	—
742	C₂³	—	4	2	no	—
743	C₂³	—	4	2	no	—
744	C₂³	—	8	4	no	—
745	C₂³	—	8	4	no	—
746	C₂³	—	8	8	no	—
747	C₂³	—	8	8	no	—
748	C₂³	#127×C₆₁	1	2	yes	—
749	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
750	Q₈	—	2	2	no	—
751	Q₈	—	2	2	no	—
752	Q₈	—	4	1	no	—
753	Q₈	—	4	1	no	—
754	Q₈	—	4	1	no	—
755	Q₈	—	4	1	no	—
756	Q₈	—	4	1	no	—
757	Q₈	—	4	1	no	—
758	D₄	—	2	2	no	—
759	D₄	—	2	2	no	—
760	D₄	—	2	2	no	—
761	D₄	—	2	2	no	—
762	D₄	—	2	2	no	—
763	D₄	—	2	2	no	—
764	D₄	—	4	8	no	—
765	D₄	—	4	8	no	—
766	D₄	—	4	1	no	—
767	D₄	—	4	1	no	—
768	D₄	—	4	1	no	—
769	D₄	—	4	1	no	—
770	D₄	—	4	1	no	—
771	D₄	—	4	1	no	—
772	D₄	—	4	1	no	—
773	D₄	—	4	1	no	—
774	D₄	—	4	1	no	—
775	D₄	—	4	1	no	—
776	D₄	—	8	8	no	—
777	D₄	—	8	8	no	—
778	D₄	—	8	4	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	4	8	no	—
792	C₂×C₄	—	4	1	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	1	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	4	1	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	4	1	no	—
799	C₂×C₄	—	4	2	no	—
800	C₂×C₄	—	4	2	no	—
801	C₂×C₄	#127×C₆₁	1	2	yes	—
802	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	4	yes	complemented
803	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
805	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
806	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
807	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
808	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
809	C₈	—	2	2	no	—
810	C₈	—	2	2	no	—
811	C₈	—	2	2	no	—
812	C₈	#120×C₆₁	1	4	yes	complemented
813	C₂²	—	2	2	no	—
814	C₂²	—	2	2	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	4	no	—
822	C₂²	—	4	4	no	—
823	C₂²	—	4	4	no	—
824	C₂²	—	8	16	no	—
825	C₂²	—	8	1	no	—
826	C₂²	—	8	1	no	—
827	C₂²	—	8	1	no	—
828	C₂²	—	8	1	no	—
829	C₂²	—	8	1	no	—
830	C₂²	—	8	1	no	—
831	C₂²	—	8	2	no	—
832	C₂²	—	8	2	no	—
833	C₂²	—	8	2	no	—
834	C₂²	—	8	1	no	—
835	C₂²	—	8	1	no	—
836	C₂²	—	8	1	no	—
837	C₂²	—	8	2	no	—
838	C₂²	—	8	2	no	—
839	C₂²	C₂×#127×C₆₁	1	1	yes	characteristic
840	C₂²	D₄²×C₆₁	1	1	yes	characteristic
841	C₂²	D₄²×C₆₁	1	1	yes	characteristic
842	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
843	C₂²	C₆₁×#577	1	2	yes	—
844	C₄	—	2	2	no	—
845	C₄	—	2	4	no	—
846	C₄	—	4	2	no	—
847	C₄	—	4	2	no	—
848	C₄	—	8	1	no	—
849	C₄	—	8	1	no	—
850	C₄	—	8	1	no	—
851	C₄	C₂×#120×C₆₁	1	1	yes	characteristic
852	C₄	C₆₁×#535	1	1	yes	characteristic
853	C₄	D₄²×C₆₁	1	1	yes	characteristic
854	C₄	D₄²×C₆₁	1	1	yes	characteristic
855	C₂	—	4	2	no	—
856	C₂	—	8	2	no	—
857	C₂	—	8	2	no	—
858	C₂	—	8	2	no	—
859	C₂	—	16	1	no	—
860	C₂	C₆₁×#2433	1	1	yes	characteristic
861	C₂	C₆₁×#3151	1	1	yes	characteristic
862	C₂	C₆₁×#3154	1	1	yes	characteristic
863	C₂	C₆₁×#3265	1	2	yes	—
864	C₂	C₆₁×#3272	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₄×C₂²⋊C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×AGL(1,ℤ/8)×C₆₁	C₂	semidirect
2. C₂×C₆₁×#496	C₂	semidirect
3. C₂×C₆₁×#492	C₂	semidirect
4. C₂×C₆₁×#468	C₂	semidirect
5. C₂×C₆₁×#449	C₂	semidirect
6. C₂×C₆₁×#450	C₂	semidirect
7. C₆₁×#2433	C₂	semidirect
8. C₆₁×#2432	C₂	semidirect
9. C₆₁×#2014	C₂	semidirect
10. C₆₁×#2013	C₂	semidirect
11. C₆₁×#2012	C₂	semidirect
12. C₆₁×#2011	C₂	semidirect
13. C₆₁×#1973	C₂	semidirect
14. C₆₁×#1970	C₂	semidirect
15. C₆₁×#1753	C₂	semidirect
25. C₂²×SD₁₆×C₆₁	C₂²	semidirect
26. C₂²×SD₁₆×C₆₁	C₂²	semidirect
29. C₂²×D₈×C₆₁	C₂²	semidirect
31. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
34. C₂×#124×C₆₁	C₂²	semidirect
43. C₂×#107×C₆₁	C₂²	semidirect
44. C₂×#103×C₆₁	C₂²	semidirect
45. C₂×#103×C₆₁	C₂²	semidirect
48. C₂×#102×C₆₁	C₂²	semidirect
49. C₂×#102×C₆₁	C₂²	semidirect
51. C₂×#97×C₆₁	C₂²	semidirect
52. C₂×C₄×C₈×C₆₁	C₂²	semidirect
55. C₆₁×#391	C₂²	semidirect
58. C₆₁×#390	C₂²	semidirect
61. C₆₁×#336	C₂²	semidirect
62. C₆₁×#336	C₂²	semidirect
107. C₂×SD₁₆×C₆₁	D₄	semidirect
116. C₂×D₈×C₆₁	D₄	semidirect
119. C₂×M₁₆×C₆₁	D₄	semidirect
157. C₂²⋊C₈×C₆₁	D₄	semidirect
369. C₂×C₄×C₆₁	AGL(1,ℤ/8)	semidirect
379. C₈×C₆₁	#120	semidirect
380. #25791	C₆₁	direct (N × H)
423. C₂²×AGL(1,ℤ/8)	C₂×C₆₁	semidirect
424. C₂×#496	C₂×C₆₁	semidirect
425. C₂×#492	C₂×C₆₁	semidirect
426. C₂×#468	C₂×C₆₁	semidirect
427. C₂×#449	C₂×C₆₁	semidirect
428. C₂×#450	C₂×C₆₁	semidirect
429. #2433	C₂×C₆₁	semidirect
430. #2432	C₂×C₆₁	semidirect
431. #2014	C₂×C₆₁	semidirect
432. #2013	C₂×C₆₁	semidirect
433. #2012	C₂×C₆₁	semidirect
434. #2011	C₂×C₆₁	semidirect
435. #1973	C₂×C₆₁	semidirect
436. #1970	C₂×C₆₁	semidirect
437. #1753	C₂×C₆₁	semidirect
457. C₂²×SD₁₆	C₂²×C₆₁	semidirect
458. C₂²×SD₁₆	C₂²×C₆₁	semidirect
461. C₂²×D₈	C₂²×C₆₁	semidirect
463. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
466. C₂×#124	C₂²×C₆₁	semidirect
475. C₂×#107	C₂²×C₆₁	semidirect
476. C₂×#103	C₂²×C₆₁	semidirect
477. C₂×#103	C₂²×C₆₁	semidirect
480. C₂×#102	C₂²×C₆₁	semidirect
481. C₂×#102	C₂²×C₆₁	semidirect
483. C₂×#97	C₂²×C₆₁	semidirect
484. C₂×C₄×C₈	C₂²×C₆₁	semidirect
487. #391	C₂²×C₆₁	semidirect
490. #390	C₂²×C₆₁	semidirect
493. #336	C₂²×C₆₁	semidirect
494. #336	C₂²×C₆₁	semidirect
495. C₆₁	#25791	direct (N × H)
540. C₂×SD₁₆	D₄×C₆₁	semidirect
549. C₂×D₈	D₄×C₆₁	semidirect
552. C₂×M₁₆	D₄×C₆₁	semidirect
590. C₂²⋊C₈	D₄×C₆₁	semidirect
802. C₂×C₄	AGL(1,ℤ/8)×C₆₁	semidirect
812. C₈	#120×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,ℤ/8)×C₆₁	2
C₂×C₆₁×#496	2
C₂×C₆₁×#492	2
C₂×C₆₁×#468	2
C₂×C₆₁×#449	2
C₂×C₆₁×#450	2
C₆₁×#2433	2
C₆₁×#2432	2
C₆₁×#2014	2
C₆₁×#2013	2
C₆₁×#2012	2
C₆₁×#2011	2
C₆₁×#1973	2
C₆₁×#1970	2
C₆₁×#1753	2
#25791	61

Subgroups — C61×#25791 #29529224

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25791 #29529224