Subgroups — C₆₁×#24539 #29527972

Order 15616.

1198 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#447	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#418	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2500	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₂²⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2073	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2071	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2054	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2054	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1895	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1879	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1851	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#1825	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1804	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1802	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₆₁	—	2	1	no	—
25	C₆₁×#447	—	2	4	no	—
26	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
28	C₆₁×#418	—	2	4	no	—
29	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic, complemented
36	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
38	C₆₁×#394	—	2	1	no	—
39	C₆₁×#394	—	2	1	no	—
40	C₆₁×#390	C₂²	1	1	yes	characteristic
41	C₆₁×#390	C₂²	1	1	yes	characteristic
42	C₆₁×#390	C₂²	1	1	yes	characteristic, complemented
43	C₆₁×#390	C₂²	1	1	yes	characteristic, complemented
44	C₆₁×#388	—	2	1	no	—
45	C₆₁×#388	—	2	1	no	—
46	C₆₁×#386	—	2	1	no	—
47	C₆₁×#386	—	2	1	no	—
48	C₆₁×#384	C₂²	1	1	yes	characteristic, complemented
49	C₆₁×#382	C₂²	1	1	yes	characteristic, complemented
50	C₆₁×#380	C₂²	1	1	yes	characteristic
51	C₆₁×#379	—	2	1	no	—
52	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
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×#336	C₂²	1	1	yes	characteristic, complemented
60	C₆₁×#336	C₂²	1	1	yes	characteristic, complemented
61	C₂⁵×C₆₁	—	2	1	no	—
62	C₂²×D₄×C₆₁	—	2	2	no	—
63	C₂²×D₄×C₆₁	—	2	2	no	—
64	C₂²×D₄×C₆₁	—	2	1	no	—
65	C₂²×D₄×C₆₁	—	2	1	no	—
66	C₂²×D₄×C₆₁	—	2	2	no	—
67	C₂²×D₄×C₆₁	—	4	1	no	—
68	C₂²×D₄×C₆₁	—	4	1	no	—
69	C₂²×D₄×C₆₁	D₄	1	4	yes	—
70	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₆₁	—	2	1	no	—
74	C₂³×C₄×C₆₁	—	2	1	no	—
75	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
76	C₂×D₈×C₆₁	—	2	2	no	—
77	C₂×D₈×C₆₁	—	2	2	no	—
78	C₂×D₈×C₆₁	—	2	2	no	—
79	C₂×D₈×C₆₁	—	2	2	no	—
80	C₂×D₈×C₆₁	—	4	1	no	—
81	C₂×D₈×C₆₁	—	4	1	no	—
82	C₂×M₁₆×C₆₁	—	2	2	no	—
83	C₂×M₁₆×C₆₁	—	4	1	no	—
84	C₂×M₁₆×C₆₁	—	4	1	no	—
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	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
89	#121×C₆₁	—	2	2	no	—
90	#121×C₆₁	—	2	2	no	—
91	C₄×D₄×C₆₁	—	2	2	no	—
92	C₄×D₄×C₆₁	—	2	2	no	—
93	C₄×D₄×C₆₁	—	4	1	no	—
94	C₄×D₄×C₆₁	—	4	1	no	—
95	#117×C₆₁	—	2	2	no	—
96	#117×C₆₁	—	2	2	no	—
97	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
98	C₂×C₄⋊C₄×C₆₁	—	2	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×C₂²⋊C₄×C₆₁	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
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	—	4	4	no	—
118	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
120	C₂×C₄²×C₆₁	—	2	1	no	—
121	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
123	C₄⋊C₈×C₆₁	—	4	1	no	—
124	C₄⋊C₈×C₆₁	—	4	1	no	—
125	#102×C₆₁	—	2	2	no	—
126	#102×C₆₁	—	2	2	no	—
127	#102×C₆₁	—	2	2	no	—
128	#102×C₆₁	—	2	2	no	—
129	#102×C₆₁	—	2	2	no	—
130	#102×C₆₁	—	2	2	no	—
131	#102×C₆₁	—	4	1	no	—
132	#102×C₆₁	—	4	1	no	—
133	C₂²⋊C₈×C₆₁	—	2	2	no	—
134	#95×C₆₁	—	2	1	no	—
135	#95×C₆₁	—	2	1	no	—
136	#95×C₆₁	—	2	1	no	—
137	#95×C₆₁	D₄	1	1	yes	characteristic
138	#95×C₆₁	D₄	1	1	yes	characteristic
139	C₂⁴×C₆₁	—	2	1	no	—
140	C₂⁴×C₆₁	—	2	1	no	—
141	C₂⁴×C₆₁	—	2	4	no	—
142	C₂⁴×C₆₁	—	2	1	no	—
143	C₂⁴×C₆₁	—	4	2	no	—
144	C₂⁴×C₆₁	—	4	2	no	—
145	C₂⁴×C₆₁	—	4	2	no	—
146	C₂⁴×C₆₁	—	4	2	no	—
147	C₂⁴×C₆₁	—	8	1	no	—
148	C₂⁴×C₆₁	—	8	1	no	—
149	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
150	C₂×D₄×C₆₁	—	2	8	no	—
151	C₂×D₄×C₆₁	—	2	4	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	—	2	1	no	—
157	C₂×D₄×C₆₁	—	2	1	no	—
158	C₂×D₄×C₆₁	—	2	1	no	—
159	C₂×D₄×C₆₁	—	2	1	no	—
160	C₂×D₄×C₆₁	—	2	1	no	—
161	C₂×D₄×C₆₁	—	2	1	no	—
162	C₂×D₄×C₆₁	—	2	1	no	—
163	C₂×D₄×C₆₁	—	2	1	no	—
164	C₂×D₄×C₆₁	—	2	1	no	—
165	C₂×D₄×C₆₁	—	2	1	no	—
166	C₂×D₄×C₆₁	—	4	4	no	—
167	C₂×D₄×C₆₁	—	4	4	no	—
168	C₂×D₄×C₆₁	—	4	4	no	—
169	C₂×D₄×C₆₁	—	4	2	no	—
170	C₂×D₄×C₆₁	—	4	2	no	—
171	C₂×D₄×C₆₁	—	4	2	no	—
172	C₂×D₄×C₆₁	—	8	1	no	—
173	C₂×D₄×C₆₁	—	8	1	no	—
174	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
175	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
176	C₂×D₄×C₆₁	#41	1	2	yes	—
177	C₂×D₄×C₆₁	#41	1	2	yes	—
178	C₂²×C₄×C₆₁	—	2	1	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	—	4	2	no	—
188	C₂²×C₄×C₆₁	—	4	2	no	—
189	C₂²×C₄×C₆₁	—	4	2	no	—
190	C₂²×C₄×C₆₁	—	4	2	no	—
191	C₂²×C₄×C₆₁	—	8	1	no	—
192	C₂²×C₄×C₆₁	—	8	1	no	—
193	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
198	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₆₁	#41	1	2	yes	—
200	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
201	D₈×C₆₁	—	4	4	no	—
202	D₈×C₆₁	—	4	4	no	—
203	M₁₆×C₆₁	—	4	4	no	—
204	C₂×C₈×C₆₁	—	2	1	no	—
205	C₂×C₈×C₆₁	—	2	1	no	—
206	C₂×C₈×C₆₁	—	2	1	no	—
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	C₄⋊C₄×C₆₁	—	2	1	no	—
217	C₄⋊C₄×C₆₁	—	2	1	no	—
218	C₄⋊C₄×C₆₁	—	2	1	no	—
219	C₄⋊C₄×C₆₁	—	2	1	no	—
220	C₄⋊C₄×C₆₁	—	2	1	no	—
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	—	8	1	no	—
227	C₄⋊C₄×C₆₁	—	8	1	no	—
228	C₂²⋊C₄×C₆₁	—	2	2	no	—
229	C₂²⋊C₄×C₆₁	—	4	1	no	—
230	C₂²⋊C₄×C₆₁	—	4	2	no	—
231	C₂²⋊C₄×C₆₁	—	4	2	no	—
232	C₂²⋊C₄×C₆₁	—	4	2	no	—
233	C₂²⋊C₄×C₆₁	—	4	2	no	—
234	C₂²⋊C₄×C₆₁	—	4	2	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	—	8	1	no	—
240	C₂²⋊C₄×C₆₁	—	8	1	no	—
241	C₂²⋊C₄×C₆₁	—	8	1	no	—
242	C₂²⋊C₄×C₆₁	—	8	1	no	—
243	C₄²×C₆₁	—	2	1	no	—
244	C₄²×C₆₁	—	2	1	no	—
245	C₄²×C₆₁	—	2	1	no	—
246	C₄²×C₆₁	—	2	1	no	—
247	C₄²×C₆₁	—	4	2	no	—
248	C₂³×C₆₁	—	2	2	no	—
249	C₂³×C₆₁	—	2	2	no	—
250	C₂³×C₆₁	—	2	2	no	—
251	C₂³×C₆₁	—	2	1	no	—
252	C₂³×C₆₁	—	2	1	no	—
253	C₂³×C₆₁	—	2	1	no	—
254	C₂³×C₆₁	—	2	1	no	—
255	C₂³×C₆₁	—	2	1	no	—
256	C₂³×C₆₁	—	2	1	no	—
257	C₂³×C₆₁	—	2	2	no	—
258	C₂³×C₆₁	—	4	8	no	—
259	C₂³×C₆₁	—	4	8	no	—
260	C₂³×C₆₁	—	4	1	no	—
261	C₂³×C₆₁	—	4	1	no	—
262	C₂³×C₆₁	—	4	1	no	—
263	C₂³×C₆₁	—	4	1	no	—
264	C₂³×C₆₁	—	4	1	no	—
265	C₂³×C₆₁	—	4	1	no	—
266	C₂³×C₆₁	—	4	1	no	—
267	C₂³×C₆₁	—	4	1	no	—
268	C₂³×C₆₁	—	4	1	no	—
269	C₂³×C₆₁	—	4	1	no	—
270	C₂³×C₆₁	—	4	1	no	—
271	C₂³×C₆₁	—	4	1	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	—	8	4	no	—
278	C₂³×C₆₁	—	8	4	no	—
279	C₂³×C₆₁	—	8	4	no	—
280	C₂³×C₆₁	—	8	4	no	—
281	C₂³×C₆₁	—	8	4	no	—
282	C₂³×C₆₁	#121	1	2	yes	—
283	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
284	D₄×C₆₁	—	2	2	no	—
285	D₄×C₆₁	—	2	2	no	—
286	D₄×C₆₁	—	2	2	no	—
287	D₄×C₆₁	—	2	2	no	—
288	D₄×C₆₁	—	2	2	no	—
289	D₄×C₆₁	—	4	8	no	—
290	D₄×C₆₁	—	4	1	no	—
291	D₄×C₆₁	—	4	1	no	—
292	D₄×C₆₁	—	4	1	no	—
293	D₄×C₆₁	—	4	1	no	—
294	D₄×C₆₁	—	4	1	no	—
295	D₄×C₆₁	—	4	1	no	—
296	D₄×C₆₁	—	8	4	no	—
297	D₄×C₆₁	#123	1	4	yes	—
298	C₂×C₄×C₆₁	—	2	1	no	—
299	C₂×C₄×C₆₁	—	2	1	no	—
300	C₂×C₄×C₆₁	—	2	1	no	—
301	C₂×C₄×C₆₁	—	2	1	no	—
302	C₂×C₄×C₆₁	—	2	2	no	—
303	C₂×C₄×C₆₁	—	2	2	no	—
304	C₂×C₄×C₆₁	—	2	2	no	—
305	C₂×C₄×C₆₁	—	2	2	no	—
306	C₂×C₄×C₆₁	—	2	1	no	—
307	C₂×C₄×C₆₁	—	2	1	no	—
308	C₂×C₄×C₆₁	—	2	1	no	—
309	C₂×C₄×C₆₁	—	2	1	no	—
310	C₂×C₄×C₆₁	—	2	1	no	—
311	C₂×C₄×C₆₁	—	2	1	no	—
312	C₂×C₄×C₆₁	—	2	1	no	—
313	C₂×C₄×C₆₁	—	2	1	no	—
314	C₂×C₄×C₆₁	—	2	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	—	8	4	no	—
331	C₂×C₄×C₆₁	—	8	4	no	—
332	C₂×C₄×C₆₁	#121	1	2	yes	—
333	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
334	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
336	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
337	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
338	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
340	C₈×C₆₁	—	4	1	no	—
341	C₈×C₆₁	—	4	1	no	—
342	C₈×C₆₁	—	4	1	no	—
343	C₈×C₆₁	—	4	1	no	—
344	#24539	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
345	C₂²×C₆₁	—	2	2	no	—
346	C₂²×C₆₁	—	2	4	no	—
347	C₂²×C₆₁	—	2	2	no	—
348	C₂²×C₆₁	—	2	2	no	—
349	C₂²×C₆₁	—	4	2	no	—
350	C₂²×C₆₁	—	4	2	no	—
351	C₂²×C₆₁	—	4	2	no	—
352	C₂²×C₆₁	—	4	1	no	—
353	C₂²×C₆₁	—	4	1	no	—
354	C₂²×C₆₁	—	4	2	no	—
355	C₂²×C₆₁	—	4	1	no	—
356	C₂²×C₆₁	—	4	2	no	—
357	C₂²×C₆₁	—	4	2	no	—
358	C₂²×C₆₁	—	4	1	no	—
359	C₂²×C₆₁	—	4	2	no	—
360	C₂²×C₆₁	—	4	2	no	—
361	C₂²×C₆₁	—	4	2	no	—
362	C₂²×C₆₁	—	8	16	no	—
363	C₂²×C₆₁	—	8	1	no	—
364	C₂²×C₆₁	—	8	1	no	—
365	C₂²×C₆₁	—	8	1	no	—
366	C₂²×C₆₁	—	8	1	no	—
367	C₂²×C₆₁	—	8	1	no	—
368	C₂²×C₆₁	—	8	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	C₂×#121	1	1	yes	characteristic
375	C₂²×C₆₁	#546	1	1	yes	characteristic
376	C₂²×C₆₁	#546	1	1	yes	characteristic
377	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
378	C₂²×C₆₁	#575	1	1	yes	characteristic
379	C₂²×C₆₁	#576	1	1	yes	characteristic
380	C₂²×C₆₁	#576	1	1	yes	characteristic
381	C₄×C₆₁	—	2	2	no	—
382	C₄×C₆₁	—	2	2	no	—
383	C₄×C₆₁	—	4	1	no	—
384	C₄×C₆₁	—	4	1	no	—
385	C₄×C₆₁	—	4	1	no	—
386	C₄×C₆₁	—	8	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	C₂×#123	1	1	yes	characteristic
392	C₄×C₆₁	#534	1	1	yes	characteristic
393	C₄×C₆₁	#551	1	1	yes	characteristic
394	C₄×C₆₁	#551	1	1	yes	characteristic
395	C₂×#447	C₂×C₆₁	1	1	yes	characteristic
396	C₂×#418	C₂×C₆₁	1	1	yes	characteristic, complemented
397	#2500	C₂×C₆₁	1	1	yes	characteristic, complemented
398	D₄×C₂²⋊C₄	C₂×C₆₁	1	1	yes	characteristic, complemented
399	#2073	C₂×C₆₁	1	1	yes	characteristic, complemented
400	#2071	C₂×C₆₁	1	1	yes	characteristic, complemented
401	#2054	C₂×C₆₁	1	1	yes	characteristic, complemented
402	#2054	C₂×C₆₁	1	1	yes	characteristic, complemented
403	#1895	C₂×C₆₁	1	1	yes	characteristic, complemented
404	#1879	C₂×C₆₁	1	1	yes	characteristic, complemented
405	#1879	C₂×C₆₁	1	1	yes	characteristic, complemented
406	#1851	C₂×C₆₁	1	1	yes	characteristic, complemented
407	#1825	C₂×C₆₁	1	1	yes	characteristic, complemented
408	#1804	C₂×C₆₁	1	1	yes	characteristic, complemented
409	#1802	C₂×C₆₁	1	1	yes	characteristic, complemented
410	C₂×C₆₁	—	4	2	no	—
411	C₂×C₆₁	—	4	4	no	—
412	C₂×C₆₁	—	8	2	no	—
413	C₂×C₆₁	—	16	1	no	—
414	C₂×C₆₁	#2412	1	1	yes	characteristic
415	C₂×C₆₁	#3036	1	1	yes	characteristic
416	C₂×C₆₁	#3041	1	1	yes	characteristic
417	C₂×C₆₁	#3318	1	1	yes	characteristic
418	C₂×C₆₁	#3319	1	1	yes	characteristic
419	C₂×C₆₁	#3322	1	1	yes	characteristic
420	C₂×C₆₁	#3325	1	1	yes	characteristic
421	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
422	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
423	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
424	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
425	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
426	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
427	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
428	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
429	C₂²×C₂²⋊C₄	—	2	1	no	—
430	#447	—	2	4	no	—
431	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
432	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
433	#418	—	2	4	no	—
434	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
435	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
436	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
437	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
438	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
439	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
440	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic, complemented
441	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic, complemented
442	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
443	#394	—	2	1	no	—
444	#394	—	2	1	no	—
445	#390	C₂²×C₆₁	1	1	yes	characteristic
446	#390	C₂²×C₆₁	1	1	yes	characteristic
447	#390	C₂²×C₆₁	1	1	yes	characteristic, complemented
448	#390	C₂²×C₆₁	1	1	yes	characteristic, complemented
449	#388	—	2	1	no	—
450	#388	—	2	1	no	—
451	#386	—	2	1	no	—
452	#386	—	2	1	no	—
453	#384	C₂²×C₆₁	1	1	yes	characteristic, complemented
454	#382	C₂²×C₆₁	1	1	yes	characteristic, complemented
455	#380	C₂²×C₆₁	1	1	yes	characteristic
456	#379	—	2	1	no	—
457	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
458	#340	C₂²×C₆₁	1	1	yes	characteristic, complemented
459	#340	C₂²×C₆₁	1	1	yes	characteristic, complemented
460	#340	C₂²×C₆₁	1	1	yes	characteristic, complemented
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	#336	C₂²×C₆₁	1	1	yes	characteristic, complemented
465	#336	C₂²×C₆₁	1	1	yes	characteristic, complemented
466	C₆₁	#24539	1	1	yes	characteristic, direct product factor, Sylow
467	C₂⁵	—	2	1	no	—
468	C₂²×D₄	—	2	2	no	—
469	C₂²×D₄	—	2	2	no	—
470	C₂²×D₄	—	2	1	no	—
471	C₂²×D₄	—	2	1	no	—
472	C₂²×D₄	—	2	2	no	—
473	C₂²×D₄	—	4	1	no	—
474	C₂²×D₄	—	4	1	no	—
475	C₂²×D₄	D₄×C₆₁	1	4	yes	—
476	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
477	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
478	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
479	C₂³×C₄	—	2	1	no	—
480	C₂³×C₄	—	2	1	no	—
481	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
482	C₂×D₈	—	2	2	no	—
483	C₂×D₈	—	2	2	no	—
484	C₂×D₈	—	2	2	no	—
485	C₂×D₈	—	2	2	no	—
486	C₂×D₈	—	4	1	no	—
487	C₂×D₈	—	4	1	no	—
488	C₂×M₁₆	—	2	2	no	—
489	C₂×M₁₆	—	4	1	no	—
490	C₂×M₁₆	—	4	1	no	—
491	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
495	#121	—	2	2	no	—
496	#121	—	2	2	no	—
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	—	4	1	no	—
500	C₄×D₄	—	4	1	no	—
501	#117	—	2	2	no	—
502	#117	—	2	2	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
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	—	4	4	no	—
524	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
525	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
526	C₂×C₄²	—	2	1	no	—
527	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
529	C₄⋊C₈	—	4	1	no	—
530	C₄⋊C₈	—	4	1	no	—
531	#102	—	2	2	no	—
532	#102	—	2	2	no	—
533	#102	—	2	2	no	—
534	#102	—	2	2	no	—
535	#102	—	2	2	no	—
536	#102	—	2	2	no	—
537	#102	—	4	1	no	—
538	#102	—	4	1	no	—
539	C₂²⋊C₈	—	2	2	no	—
540	#95	—	2	1	no	—
541	#95	—	2	1	no	—
542	#95	—	2	1	no	—
543	#95	D₄×C₆₁	1	1	yes	characteristic
544	#95	D₄×C₆₁	1	1	yes	characteristic
545	C₂⁴	—	2	1	no	—
546	C₂⁴	—	2	1	no	—
547	C₂⁴	—	2	4	no	—
548	C₂⁴	—	2	1	no	—
549	C₂⁴	—	4	2	no	—
550	C₂⁴	—	4	2	no	—
551	C₂⁴	—	4	2	no	—
552	C₂⁴	—	4	2	no	—
553	C₂⁴	—	8	1	no	—
554	C₂⁴	—	8	1	no	—
555	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
556	C₂×D₄	—	2	8	no	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	—	2	1	no	—
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	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	4	4	no	—
573	C₂×D₄	—	4	4	no	—
574	C₂×D₄	—	4	4	no	—
575	C₂×D₄	—	4	2	no	—
576	C₂×D₄	—	4	2	no	—
577	C₂×D₄	—	4	2	no	—
578	C₂×D₄	—	8	1	no	—
579	C₂×D₄	—	8	1	no	—
580	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
581	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
582	C₂×D₄	#41×C₆₁	1	2	yes	—
583	C₂×D₄	#41×C₆₁	1	2	yes	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	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	—	4	2	no	—
594	C₂²×C₄	—	4	2	no	—
595	C₂²×C₄	—	4	2	no	—
596	C₂²×C₄	—	4	2	no	—
597	C₂²×C₄	—	8	1	no	—
598	C₂²×C₄	—	8	1	no	—
599	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
601	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
602	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
603	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
604	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
605	C₂²×C₄	#41×C₆₁	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
607	D₈	—	4	4	no	—
608	D₈	—	4	4	no	—
609	M₁₆	—	4	4	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	2	1	no	—
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	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	8	1	no	—
633	C₄⋊C₄	—	8	1	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	4	1	no	—
636	C₂²⋊C₄	—	4	2	no	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₂²⋊C₄	—	4	2	no	—
639	C₂²⋊C₄	—	4	2	no	—
640	C₂²⋊C₄	—	4	2	no	—
641	C₂²⋊C₄	—	4	2	no	—
642	C₂²⋊C₄	—	4	2	no	—
643	C₂²⋊C₄	—	4	2	no	—
644	C₂²⋊C₄	—	4	2	no	—
645	C₂²⋊C₄	—	8	1	no	—
646	C₂²⋊C₄	—	8	1	no	—
647	C₂²⋊C₄	—	8	1	no	—
648	C₂²⋊C₄	—	8	1	no	—
649	C₄²	—	2	1	no	—
650	C₄²	—	2	1	no	—
651	C₄²	—	2	1	no	—
652	C₄²	—	2	1	no	—
653	C₄²	—	4	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	1	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	4	8	no	—
665	C₂³	—	4	8	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	4	1	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	—	4	1	no	—
678	C₂³	—	4	1	no	—
679	C₂³	—	4	1	no	—
680	C₂³	—	4	1	no	—
681	C₂³	—	4	1	no	—
682	C₂³	—	4	1	no	—
683	C₂³	—	8	4	no	—
684	C₂³	—	8	4	no	—
685	C₂³	—	8	4	no	—
686	C₂³	—	8	4	no	—
687	C₂³	—	8	4	no	—
688	C₂³	#121×C₆₁	1	2	yes	—
689	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
690	D₄	—	2	2	no	—
691	D₄	—	2	2	no	—
692	D₄	—	2	2	no	—
693	D₄	—	2	2	no	—
694	D₄	—	2	2	no	—
695	D₄	—	4	8	no	—
696	D₄	—	4	1	no	—
697	D₄	—	4	1	no	—
698	D₄	—	4	1	no	—
699	D₄	—	4	1	no	—
700	D₄	—	4	1	no	—
701	D₄	—	4	1	no	—
702	D₄	—	8	4	no	—
703	D₄	#123×C₆₁	1	4	yes	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	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	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	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	—	8	4	no	—
737	C₂×C₄	—	8	4	no	—
738	C₂×C₄	#121×C₆₁	1	2	yes	—
739	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
740	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
741	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
742	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
743	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
744	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
745	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
746	C₈	—	4	1	no	—
747	C₈	—	4	1	no	—
748	C₈	—	4	1	no	—
749	C₈	—	4	1	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	8	16	no	—
768	C₂²	—	8	1	no	—
769	C₂²	—	8	1	no	—
770	C₂²	—	8	1	no	—
771	C₂²	—	8	1	no	—
772	C₂²	—	8	1	no	—
773	C₂²	—	8	1	no	—
774	C₂²	—	8	1	no	—
775	C₂²	—	8	1	no	—
776	C₂²	—	8	1	no	—
777	C₂²	—	8	1	no	—
778	C₂²	—	8	1	no	—
779	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
780	C₂²	C₆₁×#546	1	1	yes	characteristic
781	C₂²	C₆₁×#546	1	1	yes	characteristic
782	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
783	C₂²	C₆₁×#575	1	1	yes	characteristic
784	C₂²	C₆₁×#576	1	1	yes	characteristic
785	C₂²	C₆₁×#576	1	1	yes	characteristic
786	C₄	—	2	2	no	—
787	C₄	—	2	2	no	—
788	C₄	—	4	1	no	—
789	C₄	—	4	1	no	—
790	C₄	—	4	1	no	—
791	C₄	—	8	1	no	—
792	C₄	—	8	1	no	—
793	C₄	—	8	1	no	—
794	C₄	—	8	1	no	—
795	C₄	—	8	1	no	—
796	C₄	C₂×#123×C₆₁	1	1	yes	characteristic
797	C₄	C₆₁×#534	1	1	yes	characteristic
798	C₄	C₆₁×#551	1	1	yes	characteristic
799	C₄	C₆₁×#551	1	1	yes	characteristic
800	C₂	—	4	2	no	—
801	C₂	—	4	4	no	—
802	C₂	—	8	2	no	—
803	C₂	—	16	1	no	—
804	C₂	C₆₁×#2412	1	1	yes	characteristic
805	C₂	C₆₁×#3036	1	1	yes	characteristic
806	C₂	C₆₁×#3041	1	1	yes	characteristic
807	C₂	C₆₁×#3318	1	1	yes	characteristic
808	C₂	C₆₁×#3319	1	1	yes	characteristic
809	C₂	C₆₁×#3322	1	1	yes	characteristic
810	C₂	C₆₁×#3325	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×C₆₁×#447	C₂
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
2. C₂×C₆₁×#418	C₂	semidirect
3. C₆₁×#2500	C₂	semidirect
4. D₄×C₂²⋊C₄×C₆₁	C₂	semidirect
5. C₆₁×#2073	C₂	semidirect
6. C₆₁×#2071	C₂	semidirect
7. C₆₁×#2054	C₂	semidirect
8. C₆₁×#2054	C₂	semidirect
9. C₆₁×#1895	C₂	semidirect
10. C₆₁×#1879	C₂	semidirect
11. C₆₁×#1879	C₂	semidirect
12. C₆₁×#1851	C₂	semidirect
13. C₆₁×#1825	C₂	semidirect
14. C₆₁×#1804	C₂	semidirect
15. C₆₁×#1802	C₂	semidirect
26. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
27. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
35. C₂×#102×C₆₁	C₂²	semidirect
36. C₂×#102×C₆₁	C₂²	semidirect
42. C₆₁×#390	C₂²	semidirect
43. C₆₁×#390	C₂²	semidirect
48. C₆₁×#384	C₂²	semidirect
49. C₆₁×#382	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×#336	C₂²	semidirect
60. C₆₁×#336	C₂²	semidirect
344. #24539	C₆₁	direct (N × H)
396. C₂×#418	C₂×C₆₁	semidirect
397. #2500	C₂×C₆₁	semidirect
398. D₄×C₂²⋊C₄	C₂×C₆₁	semidirect
399. #2073	C₂×C₆₁	semidirect
400. #2071	C₂×C₆₁	semidirect
401. #2054	C₂×C₆₁	semidirect
402. #2054	C₂×C₆₁	semidirect
403. #1895	C₂×C₆₁	semidirect
404. #1879	C₂×C₆₁	semidirect
405. #1879	C₂×C₆₁	semidirect
406. #1851	C₂×C₆₁	semidirect
407. #1825	C₂×C₆₁	semidirect
408. #1804	C₂×C₆₁	semidirect
409. #1802	C₂×C₆₁	semidirect
431. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
432. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
440. C₂×#102	C₂²×C₆₁	semidirect
441. C₂×#102	C₂²×C₆₁	semidirect
447. #390	C₂²×C₆₁	semidirect
448. #390	C₂²×C₆₁	semidirect
453. #384	C₂²×C₆₁	semidirect
454. #382	C₂²×C₆₁	semidirect
458. #340	C₂²×C₆₁	semidirect
459. #340	C₂²×C₆₁	semidirect
460. #340	C₂²×C₆₁	semidirect
461. #340	C₂²×C₆₁	semidirect
462. #340	C₂²×C₆₁	semidirect
463. #340	C₂²×C₆₁	semidirect
464. #336	C₂²×C₆₁	semidirect
465. #336	C₂²×C₆₁	semidirect
466. C₆₁	#24539	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#447	2
C₂×C₆₁×#418	2
C₆₁×#2500	2
D₄×C₂²⋊C₄×C₆₁	2
C₆₁×#2073	2
C₆₁×#2071	2
C₆₁×#2054	2
C₆₁×#1895	2
C₆₁×#1879	2
C₆₁×#1851	2
C₆₁×#1825	2
C₆₁×#1804	2
C₆₁×#1802	2
#24539	61

Subgroups — C61×#24539 #29527972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24539 #29527972