Subgroups — C₆₁×#24555 #29527988

Order 15616.

1194 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#482	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊C₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2847	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2280	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2077	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2076	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2034	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1893	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1854	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#1825	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1808	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1807	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×#120×C₆₁	—	2	1	no	—
23	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
25	C₆₁×#482	—	2	4	no	—
26	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic, complemented
27	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic, complemented
28	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic, complemented
30	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic, complemented
31	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic, complemented
32	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic, complemented
33	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₂²⋊C₈×C₆₁	—	2	4	no	—
35	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
39	C₆₁×#386	—	2	1	no	—
40	C₆₁×#386	—	2	1	no	—
41	C₆₁×#386	—	2	1	no	—
42	C₆₁×#381	—	2	1	no	—
43	C₆₁×#380	C₂²	1	1	yes	characteristic
44	C₆₁×#380	C₂²	1	1	yes	characteristic
45	C₆₁×#380	C₂²	1	1	yes	characteristic
46	C₆₁×#380	C₂²	1	1	yes	characteristic
47	C₆₁×#380	C₂²	1	1	yes	characteristic
48	C₆₁×#380	C₂²	1	1	yes	characteristic
49	C₆₁×#380	C₂²	1	1	yes	characteristic
50	C₆₁×#379	—	2	1	no	—
51	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
52	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
53	C₆₁×#340	C₂²	1	1	yes	characteristic, complemented
54	C₆₁×#340	C₂²	1	1	yes	characteristic, complemented
55	C₆₁×#340	C₂²	1	1	yes	characteristic, complemented
56	C₆₁×#340	C₂²	1	1	yes	characteristic, complemented
57	C₆₁×#340	C₂²	1	1	yes	characteristic, complemented
58	C₆₁×#340	C₂²	1	1	yes	characteristic, complemented
59	C₆₁×#340	C₂²	1	1	yes	characteristic, complemented
60	C₆₁×#340	C₂²	1	1	yes	characteristic, complemented
61	C₂⁵×C₆₁	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₆₁	—	2	1	no	—
63	C₂²×D₄×C₆₁	—	2	1	no	—
64	C₂²×D₄×C₆₁	—	2	1	no	—
65	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₆₁	—	2	2	no	—
67	C₂³×C₄×C₆₁	—	2	2	no	—
68	C₂³×C₄×C₆₁	—	2	2	no	—
69	C₂³×C₄×C₆₁	—	2	2	no	—
70	C₂³×C₄×C₆₁	—	4	1	no	—
71	C₂³×C₄×C₆₁	—	4	1	no	—
72	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
73	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
74	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
75	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₆₁	—	2	2	no	—
79	C₂²×C₈×C₆₁	—	2	2	no	—
80	C₂²×C₈×C₆₁	—	2	2	no	—
81	C₂²×C₈×C₆₁	—	2	2	no	—
82	C₂²×C₈×C₆₁	—	4	1	no	—
83	C₂²×C₈×C₆₁	—	4	1	no	—
84	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
88	#121×C₆₁	—	2	2	no	—
89	#121×C₆₁	—	2	2	no	—
90	#121×C₆₁	—	2	2	no	—
91	#121×C₆₁	—	2	2	no	—
92	#121×C₆₁	—	4	1	no	—
93	#121×C₆₁	—	4	1	no	—
94	#120×C₆₁	—	4	4	no	—
95	#117×C₆₁	—	2	2	no	—
96	#117×C₆₁	—	2	2	no	—
97	#117×C₆₁	—	4	1	no	—
98	#117×C₆₁	—	4	1	no	—
99	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
118	C₂×C₄²×C₆₁	—	2	1	no	—
119	C₂×C₄²×C₆₁	—	2	1	no	—
120	#107×C₆₁	—	2	2	no	—
121	#107×C₆₁	—	4	1	no	—
122	#106×C₆₁	—	2	2	no	—
123	#106×C₆₁	—	4	1	no	—
124	#102×C₆₁	—	2	2	no	—
125	#102×C₆₁	—	2	2	no	—
126	#102×C₆₁	—	4	1	no	—
127	#102×C₆₁	—	4	1	no	—
128	C₂²⋊C₈×C₆₁	—	2	2	no	—
129	C₂²⋊C₈×C₆₁	—	2	2	no	—
130	C₂²⋊C₈×C₆₁	—	2	2	no	—
131	C₂²⋊C₈×C₆₁	D₄	1	4	yes	complemented
132	#95×C₆₁	—	2	1	no	—
133	#95×C₆₁	—	2	1	no	—
134	#95×C₆₁	—	2	1	no	—
135	#95×C₆₁	—	2	1	no	—
136	#95×C₆₁	—	2	1	no	—
137	#95×C₆₁	—	2	1	no	—
138	#95×C₆₁	—	2	1	no	—
139	C₂⁴×C₆₁	—	2	2	no	—
140	C₂⁴×C₆₁	—	2	2	no	—
141	C₂⁴×C₆₁	—	2	2	no	—
142	C₂⁴×C₆₁	—	2	2	no	—
143	C₂⁴×C₆₁	—	2	2	no	—
144	C₂⁴×C₆₁	—	2	1	no	—
145	C₂⁴×C₆₁	—	4	1	no	—
146	C₂⁴×C₆₁	—	4	1	no	—
147	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
148	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
149	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
150	C₂×D₄×C₆₁	—	2	1	no	—
151	C₂×D₄×C₆₁	—	2	1	no	—
152	C₂×D₄×C₆₁	—	2	1	no	—
153	C₂×D₄×C₆₁	—	2	1	no	—
154	C₂×D₄×C₆₁	—	2	1	no	—
155	C₂×D₄×C₆₁	—	2	1	no	—
156	C₂×D₄×C₆₁	—	4	2	no	—
157	C₂×D₄×C₆₁	—	4	2	no	—
158	C₂×D₄×C₆₁	—	4	2	no	—
159	C₂×D₄×C₆₁	—	4	2	no	—
160	C₂×D₄×C₆₁	—	4	2	no	—
161	C₂×D₄×C₆₁	—	4	2	no	—
162	C₂×D₄×C₆₁	—	4	2	no	—
163	C₂×D₄×C₆₁	—	4	2	no	—
164	C₂×D₄×C₆₁	—	4	2	no	—
165	C₂²×C₄×C₆₁	—	2	1	no	—
166	C₂²×C₄×C₆₁	—	2	1	no	—
167	C₂²×C₄×C₆₁	—	2	1	no	—
168	C₂²×C₄×C₆₁	—	2	1	no	—
169	C₂²×C₄×C₆₁	—	2	1	no	—
170	C₂²×C₄×C₆₁	—	2	1	no	—
171	C₂²×C₄×C₆₁	—	2	1	no	—
172	C₂²×C₄×C₆₁	—	2	1	no	—
173	C₂²×C₄×C₆₁	—	2	2	no	—
174	C₂²×C₄×C₆₁	—	2	2	no	—
175	C₂²×C₄×C₆₁	—	2	2	no	—
176	C₂²×C₄×C₆₁	—	2	2	no	—
177	C₂²×C₄×C₆₁	—	2	2	no	—
178	C₂²×C₄×C₆₁	—	2	2	no	—
179	C₂²×C₄×C₆₁	—	2	1	no	—
180	C₂²×C₄×C₆₁	—	2	1	no	—
181	C₂²×C₄×C₆₁	—	2	1	no	—
182	C₂²×C₄×C₆₁	—	2	1	no	—
183	C₂²×C₄×C₆₁	—	2	1	no	—
184	C₂²×C₄×C₆₁	—	2	1	no	—
185	C₂²×C₄×C₆₁	—	2	1	no	—
186	C₂²×C₄×C₆₁	—	2	1	no	—
187	C₂²×C₄×C₆₁	—	2	1	no	—
188	C₂²×C₄×C₆₁	—	2	1	no	—
189	C₂²×C₄×C₆₁	—	2	1	no	—
190	C₂²×C₄×C₆₁	—	2	1	no	—
191	C₂²×C₄×C₆₁	—	2	1	no	—
192	C₂²×C₄×C₆₁	—	4	1	no	—
193	C₂²×C₄×C₆₁	—	4	1	no	—
194	C₂²×C₄×C₆₁	—	4	1	no	—
195	C₂²×C₄×C₆₁	—	4	4	no	—
196	C₂²×C₄×C₆₁	—	4	4	no	—
197	C₂²×C₄×C₆₁	—	4	4	no	—
198	C₂²×C₄×C₆₁	—	4	4	no	—
199	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
202	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₆₁	#41	1	2	yes	—
204	C₂²×C₄×C₆₁	#41	1	2	yes	—
205	C₂²×C₄×C₆₁	#41	1	2	yes	—
206	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
207	C₂×C₈×C₆₁	—	2	1	no	—
208	C₂×C₈×C₆₁	—	2	1	no	—
209	C₂×C₈×C₆₁	—	2	1	no	—
210	C₂×C₈×C₆₁	—	2	1	no	—
211	C₂×C₈×C₆₁	—	2	1	no	—
212	C₂×C₈×C₆₁	—	2	1	no	—
213	C₂×C₈×C₆₁	—	2	1	no	—
214	C₂×C₈×C₆₁	—	2	1	no	—
215	C₂×C₈×C₆₁	—	2	1	no	—
216	C₂×C₈×C₆₁	—	2	1	no	—
217	C₂×C₈×C₆₁	—	4	4	no	—
218	C₂×C₈×C₆₁	—	4	4	no	—
219	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
220	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
221	C₄⋊C₄×C₆₁	—	2	1	no	—
222	C₄⋊C₄×C₆₁	—	2	1	no	—
223	C₄⋊C₄×C₆₁	—	2	1	no	—
224	C₄⋊C₄×C₆₁	—	2	1	no	—
225	C₄⋊C₄×C₆₁	—	2	1	no	—
226	C₄⋊C₄×C₆₁	—	2	1	no	—
227	C₄⋊C₄×C₆₁	—	2	1	no	—
228	C₄⋊C₄×C₆₁	—	2	1	no	—
229	C₄⋊C₄×C₆₁	—	2	1	no	—
230	C₄⋊C₄×C₆₁	—	2	1	no	—
231	C₄⋊C₄×C₆₁	—	2	1	no	—
232	C₄⋊C₄×C₆₁	—	2	1	no	—
233	C₄⋊C₄×C₆₁	—	2	1	no	—
234	C₄⋊C₄×C₆₁	—	2	1	no	—
235	C₂²⋊C₄×C₆₁	—	4	2	no	—
236	C₂²⋊C₄×C₆₁	—	4	2	no	—
237	C₂²⋊C₄×C₆₁	—	4	2	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	—	4	2	no	—
242	C₂²⋊C₄×C₆₁	—	4	2	no	—
243	C₂²⋊C₄×C₆₁	—	4	2	no	—
244	C₂²⋊C₄×C₆₁	—	4	2	no	—
245	C₂²⋊C₄×C₆₁	—	4	2	no	—
246	C₂²⋊C₄×C₆₁	—	4	2	no	—
247	C₄²×C₆₁	—	4	2	no	—
248	C₄²×C₆₁	—	4	2	no	—
249	C₂³×C₆₁	—	2	1	no	—
250	C₂³×C₆₁	—	2	1	no	—
251	C₂³×C₆₁	—	2	1	no	—
252	C₂³×C₆₁	—	2	1	no	—
253	C₂³×C₆₁	—	2	8	no	—
254	C₂³×C₆₁	—	2	1	no	—
255	C₂³×C₆₁	—	2	1	no	—
256	C₂³×C₆₁	—	2	1	no	—
257	C₂³×C₆₁	—	2	1	no	—
258	C₂³×C₆₁	—	2	1	no	—
259	C₂³×C₆₁	—	2	1	no	—
260	C₂³×C₆₁	—	2	1	no	—
261	C₂³×C₆₁	—	2	1	no	—
262	C₂³×C₆₁	—	2	1	no	—
263	C₂³×C₆₁	—	2	1	no	—
264	C₂³×C₆₁	—	2	1	no	—
265	C₂³×C₆₁	—	2	1	no	—
266	C₂³×C₆₁	—	4	4	no	—
267	C₂³×C₆₁	—	4	4	no	—
268	C₂³×C₆₁	—	4	4	no	—
269	C₂³×C₆₁	—	4	4	no	—
270	C₂³×C₆₁	—	4	4	no	—
271	C₂³×C₆₁	—	4	4	no	—
272	C₂³×C₆₁	—	4	1	no	—
273	C₂³×C₆₁	—	4	1	no	—
274	C₂³×C₆₁	—	4	1	no	—
275	C₂³×C₆₁	—	4	1	no	—
276	C₂³×C₆₁	—	4	1	no	—
277	C₂³×C₆₁	—	4	1	no	—
278	C₂³×C₆₁	—	4	1	no	—
279	C₂³×C₆₁	#121	1	2	yes	—
280	C₂³×C₆₁	#123	1	2	yes	—
281	C₂³×C₆₁	#135	1	2	yes	—
282	C₂³×C₆₁	#135	1	2	yes	—
283	C₂³×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
284	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
285	D₄×C₆₁	—	4	1	no	—
286	D₄×C₆₁	—	4	1	no	—
287	D₄×C₆₁	—	4	1	no	—
288	D₄×C₆₁	—	4	1	no	—
289	D₄×C₆₁	—	8	4	no	—
290	D₄×C₆₁	—	8	4	no	—
291	D₄×C₆₁	—	8	4	no	—
292	C₂×C₄×C₆₁	—	2	1	no	—
293	C₂×C₄×C₆₁	—	2	1	no	—
294	C₂×C₄×C₆₁	—	2	1	no	—
295	C₂×C₄×C₆₁	—	2	1	no	—
296	C₂×C₄×C₆₁	—	2	2	no	—
297	C₂×C₄×C₆₁	—	2	2	no	—
298	C₂×C₄×C₆₁	—	2	2	no	—
299	C₂×C₄×C₆₁	—	2	2	no	—
300	C₂×C₄×C₆₁	—	2	2	no	—
301	C₂×C₄×C₆₁	—	2	2	no	—
302	C₂×C₄×C₆₁	—	2	2	no	—
303	C₂×C₄×C₆₁	—	2	2	no	—
304	C₂×C₄×C₆₁	—	2	1	no	—
305	C₂×C₄×C₆₁	—	2	1	no	—
306	C₂×C₄×C₆₁	—	2	1	no	—
307	C₂×C₄×C₆₁	—	4	4	no	—
308	C₂×C₄×C₆₁	—	4	4	no	—
309	C₂×C₄×C₆₁	—	4	4	no	—
310	C₂×C₄×C₆₁	—	4	1	no	—
311	C₂×C₄×C₆₁	—	4	1	no	—
312	C₂×C₄×C₆₁	—	4	1	no	—
313	C₂×C₄×C₆₁	—	4	1	no	—
314	C₂×C₄×C₆₁	—	4	1	no	—
315	C₂×C₄×C₆₁	—	4	1	no	—
316	C₂×C₄×C₆₁	—	4	1	no	—
317	C₂×C₄×C₆₁	—	4	1	no	—
318	C₂×C₄×C₆₁	—	4	1	no	—
319	C₂×C₄×C₆₁	—	4	1	no	—
320	C₂×C₄×C₆₁	—	4	1	no	—
321	C₂×C₄×C₆₁	—	4	1	no	—
322	C₂×C₄×C₆₁	—	4	1	no	—
323	C₂×C₄×C₆₁	—	4	1	no	—
324	C₂×C₄×C₆₁	—	4	1	no	—
325	C₂×C₄×C₆₁	—	4	1	no	—
326	C₂×C₄×C₆₁	—	4	1	no	—
327	C₂×C₄×C₆₁	—	4	1	no	—
328	C₂×C₄×C₆₁	—	4	1	no	—
329	C₂×C₄×C₆₁	—	4	1	no	—
330	C₂×C₄×C₆₁	—	4	1	no	—
331	C₂×C₄×C₆₁	—	4	1	no	—
332	C₂×C₄×C₆₁	—	4	1	no	—
333	C₂×C₄×C₆₁	—	4	1	no	—
334	C₂×C₄×C₆₁	—	4	1	no	—
335	C₂×C₄×C₆₁	#121	1	2	yes	—
336	C₂×C₄×C₆₁	#123	1	2	yes	—
337	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
339	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
340	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
341	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
342	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
343	C₈×C₆₁	—	2	2	no	—
344	C₈×C₆₁	—	2	2	no	—
345	C₈×C₆₁	—	4	1	no	—
346	C₈×C₆₁	—	4	1	no	—
347	#24555	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
348	C₂²×C₆₁	—	2	2	no	—
349	C₂²×C₆₁	—	2	2	no	—
350	C₂²×C₆₁	—	2	2	no	—
351	C₂²×C₆₁	—	2	2	no	—
352	C₂²×C₆₁	—	2	2	no	—
353	C₂²×C₆₁	—	2	2	no	—
354	C₂²×C₆₁	—	2	2	no	—
355	C₂²×C₆₁	—	2	2	no	—
356	C₂²×C₆₁	—	2	2	no	—
357	C₂²×C₆₁	—	2	2	no	—
358	C₂²×C₆₁	—	2	2	no	—
359	C₂²×C₆₁	—	2	2	no	—
360	C₂²×C₆₁	—	4	16	no	—
361	C₂²×C₆₁	—	4	1	no	—
362	C₂²×C₆₁	—	4	1	no	—
363	C₂²×C₆₁	—	4	1	no	—
364	C₂²×C₆₁	—	4	1	no	—
365	C₂²×C₆₁	—	4	1	no	—
366	C₂²×C₆₁	—	4	1	no	—
367	C₂²×C₆₁	—	4	1	no	—
368	C₂²×C₆₁	—	4	1	no	—
369	C₂²×C₆₁	—	8	1	no	—
370	C₂²×C₆₁	—	8	1	no	—
371	C₂²×C₆₁	—	8	1	no	—
372	C₂²×C₆₁	—	8	1	no	—
373	C₂²×C₆₁	—	8	1	no	—
374	C₂²×C₆₁	—	8	1	no	—
375	C₂²×C₆₁	—	8	1	no	—
376	C₂²×C₆₁	#482	1	4	yes	complemented
377	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
378	C₂²×C₆₁	C₂×#123	1	1	yes	characteristic
379	C₂²×C₆₁	#534	1	1	yes	characteristic
380	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
381	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
382	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
383	C₂²×C₆₁	#575	1	1	yes	characteristic
384	C₄×C₆₁	—	2	2	no	—
385	C₄×C₆₁	—	2	2	no	—
386	C₄×C₆₁	—	4	1	no	—
387	C₄×C₆₁	—	8	1	no	—
388	C₄×C₆₁	—	8	1	no	—
389	C₄×C₆₁	—	8	1	no	—
390	C₄×C₆₁	—	8	1	no	—
391	C₄×C₆₁	—	8	1	no	—
392	C₄×C₆₁	—	8	1	no	—
393	C₄×C₆₁	—	8	1	no	—
394	C₄×C₆₁	#546	1	1	yes	characteristic
395	C₄×C₆₁	#546	1	1	yes	characteristic
396	C₄×C₆₁	#551	1	1	yes	characteristic
397	C₄×C₆₁	#551	1	1	yes	characteristic
398	C₂×#482	C₂×C₆₁	1	1	yes	characteristic, complemented
399	C₂²×C₂²⋊C₈	C₂×C₆₁	1	1	yes	characteristic, complemented
400	#2847	C₂×C₆₁	1	1	yes	characteristic
401	#2280	C₂×C₆₁	1	1	yes	characteristic, complemented
402	#2077	C₂×C₆₁	1	1	yes	characteristic, complemented
403	#2076	C₂×C₆₁	1	1	yes	characteristic, complemented
404	#2034	C₂×C₆₁	1	1	yes	characteristic, complemented
405	#2033	C₂×C₆₁	1	1	yes	characteristic, complemented
406	#1893	C₂×C₆₁	1	1	yes	characteristic, complemented
407	#1893	C₂×C₆₁	1	1	yes	characteristic, complemented
408	#1875	C₂×C₆₁	1	1	yes	characteristic, complemented
409	#1854	C₂×C₆₁	1	1	yes	characteristic, complemented
410	#1825	C₂×C₆₁	1	1	yes	characteristic, complemented
411	#1808	C₂×C₆₁	1	1	yes	characteristic, complemented
412	#1807	C₂×C₆₁	1	1	yes	characteristic, complemented
413	C₂×C₆₁	—	2	4	no	—
414	C₂×C₆₁	—	4	2	no	—
415	C₂×C₆₁	—	4	2	no	—
416	C₂×C₆₁	—	16	1	no	—
417	C₂×C₆₁	#2412	1	1	yes	characteristic
418	C₂×C₆₁	#3050	1	1	yes	characteristic
419	C₂×C₆₁	#3055	1	1	yes	characteristic
420	C₂×C₆₁	C₂×#482	1	1	yes	characteristic
421	C₂×C₆₁	#3091	1	1	yes	characteristic
422	C₂×C₆₁	#3188	1	1	yes	characteristic
423	C₂×C₆₁	#3191	1	1	yes	characteristic
424	C₂⁴×C₄	C₂²×C₆₁	1	1	yes	characteristic
425	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
426	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
427	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
428	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
429	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
430	C₂×#120	—	2	1	no	—
431	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
432	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
433	#482	—	2	4	no	—
434	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic, complemented
435	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic, complemented
436	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic, complemented
437	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic, complemented
438	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic, complemented
439	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic, complemented
440	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic, complemented
441	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic, complemented
442	C₂×C₂²⋊C₈	—	2	4	no	—
443	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
444	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
445	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
446	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
447	#386	—	2	1	no	—
448	#386	—	2	1	no	—
449	#386	—	2	1	no	—
450	#381	—	2	1	no	—
451	#380	C₂²×C₆₁	1	1	yes	characteristic
452	#380	C₂²×C₆₁	1	1	yes	characteristic
453	#380	C₂²×C₆₁	1	1	yes	characteristic
454	#380	C₂²×C₆₁	1	1	yes	characteristic
455	#380	C₂²×C₆₁	1	1	yes	characteristic
456	#380	C₂²×C₆₁	1	1	yes	characteristic
457	#380	C₂²×C₆₁	1	1	yes	characteristic
458	#379	—	2	1	no	—
459	C₄×C₂²⋊C₄	—	2	1	no	—
460	C₄×C₂²⋊C₄	—	2	1	no	—
461	#340	C₂²×C₆₁	1	1	yes	characteristic, complemented
462	#340	C₂²×C₆₁	1	1	yes	characteristic, complemented
463	#340	C₂²×C₆₁	1	1	yes	characteristic, complemented
464	#340	C₂²×C₆₁	1	1	yes	characteristic, complemented
465	#340	C₂²×C₆₁	1	1	yes	characteristic, complemented
466	#340	C₂²×C₆₁	1	1	yes	characteristic, complemented
467	#340	C₂²×C₆₁	1	1	yes	characteristic, complemented
468	#340	C₂²×C₆₁	1	1	yes	characteristic, complemented
469	C₆₁	#24555	1	1	yes	characteristic, direct product factor, Sylow
470	C₂⁵	D₄×C₆₁	1	1	yes	characteristic
471	C₂²×D₄	—	2	1	no	—
472	C₂²×D₄	—	2	1	no	—
473	C₂²×D₄	—	2	1	no	—
474	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
475	C₂³×C₄	—	2	2	no	—
476	C₂³×C₄	—	2	2	no	—
477	C₂³×C₄	—	2	2	no	—
478	C₂³×C₄	—	2	2	no	—
479	C₂³×C₄	—	4	1	no	—
480	C₂³×C₄	—	4	1	no	—
481	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
482	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
483	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
484	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
487	C₂²×C₈	—	2	2	no	—
488	C₂²×C₈	—	2	2	no	—
489	C₂²×C₈	—	2	2	no	—
490	C₂²×C₈	—	2	2	no	—
491	C₂²×C₈	—	4	1	no	—
492	C₂²×C₈	—	4	1	no	—
493	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
496	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
497	#121	—	2	2	no	—
498	#121	—	2	2	no	—
499	#121	—	2	2	no	—
500	#121	—	2	2	no	—
501	#121	—	4	1	no	—
502	#121	—	4	1	no	—
503	#120	—	4	4	no	—
504	#117	—	2	2	no	—
505	#117	—	2	2	no	—
506	#117	—	4	1	no	—
507	#117	—	4	1	no	—
508	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	—	2	1	no	—
527	C₂×C₄²	—	2	1	no	—
528	C₂×C₄²	—	2	1	no	—
529	#107	—	2	2	no	—
530	#107	—	4	1	no	—
531	#106	—	2	2	no	—
532	#106	—	4	1	no	—
533	#102	—	2	2	no	—
534	#102	—	2	2	no	—
535	#102	—	4	1	no	—
536	#102	—	4	1	no	—
537	C₂²⋊C₈	—	2	2	no	—
538	C₂²⋊C₈	—	2	2	no	—
539	C₂²⋊C₈	—	2	2	no	—
540	C₂²⋊C₈	D₄×C₆₁	1	4	yes	complemented
541	#95	—	2	1	no	—
542	#95	—	2	1	no	—
543	#95	—	2	1	no	—
544	#95	—	2	1	no	—
545	#95	—	2	1	no	—
546	#95	—	2	1	no	—
547	#95	—	2	1	no	—
548	C₂⁴	—	2	2	no	—
549	C₂⁴	—	2	2	no	—
550	C₂⁴	—	2	2	no	—
551	C₂⁴	—	2	2	no	—
552	C₂⁴	—	2	2	no	—
553	C₂⁴	—	2	1	no	—
554	C₂⁴	—	4	1	no	—
555	C₂⁴	—	4	1	no	—
556	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
557	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
558	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	4	2	no	—
566	C₂×D₄	—	4	2	no	—
567	C₂×D₄	—	4	2	no	—
568	C₂×D₄	—	4	2	no	—
569	C₂×D₄	—	4	2	no	—
570	C₂×D₄	—	4	2	no	—
571	C₂×D₄	—	4	2	no	—
572	C₂×D₄	—	4	2	no	—
573	C₂×D₄	—	4	2	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	4	1	no	—
602	C₂²×C₄	—	4	1	no	—
603	C₂²×C₄	—	4	1	no	—
604	C₂²×C₄	—	4	4	no	—
605	C₂²×C₄	—	4	4	no	—
606	C₂²×C₄	—	4	4	no	—
607	C₂²×C₄	—	4	4	no	—
608	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
609	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
610	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
611	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
612	C₂²×C₄	#41×C₆₁	1	2	yes	—
613	C₂²×C₄	#41×C₆₁	1	2	yes	—
614	C₂²×C₄	#41×C₆₁	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	4	4	no	—
627	C₂×C₈	—	4	4	no	—
628	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
629	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₂²⋊C₄	—	4	2	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	4	2	no	—
650	C₂²⋊C₄	—	4	2	no	—
651	C₂²⋊C₄	—	4	2	no	—
652	C₂²⋊C₄	—	4	2	no	—
653	C₂²⋊C₄	—	4	2	no	—
654	C₂²⋊C₄	—	4	2	no	—
655	C₂²⋊C₄	—	4	2	no	—
656	C₄²	—	4	2	no	—
657	C₄²	—	4	2	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	8	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	4	4	no	—
676	C₂³	—	4	4	no	—
677	C₂³	—	4	4	no	—
678	C₂³	—	4	4	no	—
679	C₂³	—	4	4	no	—
680	C₂³	—	4	4	no	—
681	C₂³	—	4	1	no	—
682	C₂³	—	4	1	no	—
683	C₂³	—	4	1	no	—
684	C₂³	—	4	1	no	—
685	C₂³	—	4	1	no	—
686	C₂³	—	4	1	no	—
687	C₂³	—	4	1	no	—
688	C₂³	#121×C₆₁	1	2	yes	—
689	C₂³	#123×C₆₁	1	2	yes	—
690	C₂³	#135×C₆₁	1	2	yes	—
691	C₂³	#135×C₆₁	1	2	yes	—
692	C₂³	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
693	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
694	D₄	—	4	1	no	—
695	D₄	—	4	1	no	—
696	D₄	—	4	1	no	—
697	D₄	—	4	1	no	—
698	D₄	—	8	4	no	—
699	D₄	—	8	4	no	—
700	D₄	—	8	4	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	#121×C₆₁	1	2	yes	—
745	C₂×C₄	#123×C₆₁	1	2	yes	—
746	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
747	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
748	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
749	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
750	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
751	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
752	C₈	—	2	2	no	—
753	C₈	—	2	2	no	—
754	C₈	—	4	1	no	—
755	C₈	—	4	1	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	2	2	no	—
759	C₂²	—	2	2	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	4	16	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	4	1	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	8	1	no	—
778	C₂²	—	8	1	no	—
779	C₂²	—	8	1	no	—
780	C₂²	—	8	1	no	—
781	C₂²	—	8	1	no	—
782	C₂²	—	8	1	no	—
783	C₂²	—	8	1	no	—
784	C₂²	C₆₁×#482	1	4	yes	complemented
785	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
786	C₂²	C₂×#123×C₆₁	1	1	yes	characteristic
787	C₂²	C₆₁×#534	1	1	yes	characteristic
788	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
789	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
790	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
791	C₂²	C₆₁×#575	1	1	yes	characteristic
792	C₄	—	2	2	no	—
793	C₄	—	2	2	no	—
794	C₄	—	4	1	no	—
795	C₄	—	8	1	no	—
796	C₄	—	8	1	no	—
797	C₄	—	8	1	no	—
798	C₄	—	8	1	no	—
799	C₄	—	8	1	no	—
800	C₄	—	8	1	no	—
801	C₄	—	8	1	no	—
802	C₄	C₆₁×#546	1	1	yes	characteristic
803	C₄	C₆₁×#546	1	1	yes	characteristic
804	C₄	C₆₁×#551	1	1	yes	characteristic
805	C₄	C₆₁×#551	1	1	yes	characteristic
806	C₂	—	2	4	no	—
807	C₂	—	4	2	no	—
808	C₂	—	4	2	no	—
809	C₂	—	16	1	no	—
810	C₂	C₆₁×#2412	1	1	yes	characteristic
811	C₂	C₆₁×#3050	1	1	yes	characteristic
812	C₂	C₆₁×#3055	1	1	yes	characteristic
813	C₂	C₂×C₆₁×#482	1	1	yes	characteristic
814	C₂	C₆₁×#3091	1	1	yes	characteristic
815	C₂	C₆₁×#3188	1	1	yes	characteristic
816	C₂	C₆₁×#3191	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×#2847	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂⁴×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#482	C₂	semidirect
2. C₂²×C₂²⋊C₈×C₆₁	C₂	semidirect
4. C₆₁×#2280	C₂	semidirect
5. C₆₁×#2077	C₂	semidirect
6. C₆₁×#2076	C₂	semidirect
7. C₆₁×#2034	C₂	semidirect
8. C₆₁×#2033	C₂	semidirect
9. C₆₁×#1893	C₂	semidirect
10. C₆₁×#1893	C₂	semidirect
11. C₆₁×#1875	C₂	semidirect
12. C₆₁×#1854	C₂	semidirect
13. C₆₁×#1825	C₂	semidirect
14. C₆₁×#1808	C₂	semidirect
15. C₆₁×#1807	C₂	semidirect
26. C₂×#107×C₆₁	C₂²	semidirect
27. C₂×#107×C₆₁	C₂²	semidirect
28. C₂×#106×C₆₁	C₂²	semidirect
29. C₂×#106×C₆₁	C₂²	semidirect
30. C₂×#102×C₆₁	C₂²	semidirect
31. C₂×#102×C₆₁	C₂²	semidirect
32. C₂×#102×C₆₁	C₂²	semidirect
33. C₂×#102×C₆₁	C₂²	semidirect
53. C₆₁×#340	C₂²	semidirect
54. C₆₁×#340	C₂²	semidirect
55. C₆₁×#340	C₂²	semidirect
56. C₆₁×#340	C₂²	semidirect
57. C₆₁×#340	C₂²	semidirect
58. C₆₁×#340	C₂²	semidirect
59. C₆₁×#340	C₂²	semidirect
60. C₆₁×#340	C₂²	semidirect
131. C₂²⋊C₈×C₆₁	D₄	semidirect
347. #24555	C₆₁	direct (N × H)
376. C₂²×C₆₁	#482	semidirect
398. C₂×#482	C₂×C₆₁	semidirect
399. C₂²×C₂²⋊C₈	C₂×C₆₁	semidirect
401. #2280	C₂×C₆₁	semidirect
402. #2077	C₂×C₆₁	semidirect
403. #2076	C₂×C₆₁	semidirect
404. #2034	C₂×C₆₁	semidirect
405. #2033	C₂×C₆₁	semidirect
406. #1893	C₂×C₆₁	semidirect
407. #1893	C₂×C₆₁	semidirect
408. #1875	C₂×C₆₁	semidirect
409. #1854	C₂×C₆₁	semidirect
410. #1825	C₂×C₆₁	semidirect
411. #1808	C₂×C₆₁	semidirect
412. #1807	C₂×C₆₁	semidirect
434. C₂×#107	C₂²×C₆₁	semidirect
435. C₂×#107	C₂²×C₆₁	semidirect
436. C₂×#106	C₂²×C₆₁	semidirect
437. C₂×#106	C₂²×C₆₁	semidirect
438. C₂×#102	C₂²×C₆₁	semidirect
439. C₂×#102	C₂²×C₆₁	semidirect
440. C₂×#102	C₂²×C₆₁	semidirect
441. C₂×#102	C₂²×C₆₁	semidirect
461. #340	C₂²×C₆₁	semidirect
462. #340	C₂²×C₆₁	semidirect
463. #340	C₂²×C₆₁	semidirect
464. #340	C₂²×C₆₁	semidirect
465. #340	C₂²×C₆₁	semidirect
466. #340	C₂²×C₆₁	semidirect
467. #340	C₂²×C₆₁	semidirect
468. #340	C₂²×C₆₁	semidirect
469. C₆₁	#24555	direct (N × H)
540. C₂²⋊C₈	D₄×C₆₁	semidirect
784. C₂²	C₆₁×#482	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#482	2
C₂²×C₂²⋊C₈×C₆₁	2
C₆₁×#2847	2
C₆₁×#2280	2
C₆₁×#2077	2
C₆₁×#2076	2
C₆₁×#2034	2
C₆₁×#2033	2
C₆₁×#1893	2
C₆₁×#1875	2
C₆₁×#1854	2
C₆₁×#1825	2
C₆₁×#1808	2
C₆₁×#1807	2
#24555	61

Subgroups — C61×#24555 #29527988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24555 #29527988