Subgroups — C₆₁×#21459 #29524892

Order 15616.

1560 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#518	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#450	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₁×#440	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2323	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1877	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1877	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1873	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1864	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1862	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1854	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1786	C₂	1	1	yes	maximal, characteristic
13	C₆₁×#1762	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#102×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₆₁×#518	—	2	4	no	—
21	C₆₁×#518	—	2	4	no	—
22	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₄×D₄×C₆₁	—	2	1	no	—
24	C₂×C₄×D₄×C₆₁	—	2	1	no	—
25	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₆₁	—	2	1	no	—
32	C₂²×C₂²⋊C₄×C₆₁	—	2	1	no	—
33	C₆₁×#450	C₄	1	8	yes	complemented
34	C₆₁×#440	—	2	4	no	—
35	C₄×SD₁₆×C₆₁	—	2	4	no	—
36	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic, complemented
37	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic, complemented
38	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic, complemented
39	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic, complemented
40	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
41	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
43	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
44	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
45	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
48	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
50	C₆₁×#391	C₂²	1	1	yes	characteristic, complemented
51	C₆₁×#389	—	2	1	no	—
52	C₆₁×#389	C₂²	1	1	yes	characteristic, complemented
53	C₆₁×#388	—	2	1	no	—
54	C₆₁×#388	—	2	1	no	—
55	C₆₁×#387	—	2	1	no	—
56	C₆₁×#380	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₆₁	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	C₆₁×#340	C₂²	1	1	yes	characteristic, complemented
62	C₆₁×#336	C₂²	1	1	yes	characteristic, complemented
63	C₆₁×#336	C₂²	1	1	yes	characteristic, complemented
64	C₂⁵×C₆₁	—	2	1	no	—
65	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₆₁	—	2	2	no	—
67	C₂²×D₄×C₆₁	—	2	2	no	—
68	C₂²×D₄×C₆₁	—	2	2	no	—
69	C₂²×D₄×C₆₁	—	2	2	no	—
70	C₂²×D₄×C₆₁	—	2	1	no	—
71	C₂²×D₄×C₆₁	—	2	2	no	—
72	C₂²×D₄×C₆₁	C₂×C₄	1	4	yes	—
73	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₆₁	—	2	1	no	—
76	C₂³×C₄×C₆₁	—	2	1	no	—
77	C₂³×C₄×C₆₁	—	2	1	no	—
78	C₂³×C₄×C₆₁	—	2	1	no	—
79	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
80	C₂×SD₁₆×C₆₁	—	2	2	no	—
81	C₂×SD₁₆×C₆₁	—	2	2	no	—
82	C₂×SD₁₆×C₆₁	—	2	2	no	—
83	C₂×SD₁₆×C₆₁	—	2	2	no	—
84	C₂×SD₁₆×C₆₁	C₂×C₄	1	4	yes	complemented
85	C₂×SD₁₆×C₆₁	C₂×C₄	1	4	yes	complemented
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	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
90	C₂²⋊Q₈×C₆₁	—	2	2	no	—
91	C₂²⋊Q₈×C₆₁	C₂×C₄	1	4	yes	complemented
92	C₄×Q₈×C₆₁	—	2	2	no	—
93	C₄×Q₈×C₆₁	—	2	2	no	—
94	C₄×D₄×C₆₁	—	2	8	no	—
95	C₄×D₄×C₆₁	—	2	8	no	—
96	C₄×D₄×C₆₁	—	2	2	no	—
97	C₄×D₄×C₆₁	—	2	2	no	—
98	C₄×D₄×C₆₁	—	2	2	no	—
99	C₄×D₄×C₆₁	—	2	2	no	—
100	C₄×D₄×C₆₁	—	2	2	no	—
101	C₄×D₄×C₆₁	—	2	2	no	—
102	C₄×D₄×C₆₁	D₄	1	4	yes	—
103	C₄×D₄×C₆₁	D₄	1	4	yes	—
104	#117×C₆₁	—	2	2	no	—
105	#117×C₆₁	—	2	2	no	—
106	#117×C₆₁	—	2	2	no	—
107	#117×C₆₁	—	2	2	no	—
108	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
109	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
110	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
111	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
119	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
120	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
129	C₂×C₄²×C₆₁	—	2	1	no	—
130	C₂×C₄²×C₆₁	—	2	1	no	—
131	C₂×C₄²×C₆₁	—	2	1	no	—
132	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
134	#107×C₆₁	—	2	2	no	—
135	#106×C₆₁	—	2	2	no	—
136	#103×C₆₁	—	2	2	no	—
137	#103×C₆₁	—	2	2	no	—
138	#102×C₆₁	—	2	2	no	—
139	#102×C₆₁	—	2	2	no	—
140	#102×C₆₁	—	2	2	no	—
141	#102×C₆₁	—	2	2	no	—
142	#102×C₆₁	C₂×C₄	1	4	yes	complemented
143	#102×C₆₁	C₂×C₄	1	4	yes	complemented
144	C₂²⋊C₈×C₆₁	—	2	2	no	—
145	C₂²⋊C₈×C₆₁	C₂×C₄	1	4	yes	complemented
146	#97×C₆₁	—	2	2	no	—
147	C₄×C₈×C₆₁	—	2	2	no	—
148	#95×C₆₁	—	2	1	no	—
149	#95×C₆₁	—	2	1	no	—
150	#95×C₆₁	—	2	1	no	—
151	#95×C₆₁	—	2	1	no	—
152	#95×C₆₁	—	2	1	no	—
153	C₂⁴×C₆₁	—	2	4	no	—
154	C₂⁴×C₆₁	—	2	4	no	—
155	C₂⁴×C₆₁	—	2	1	no	—
156	C₂⁴×C₆₁	—	2	1	no	—
157	C₂⁴×C₆₁	—	2	4	no	—
158	C₂⁴×C₆₁	—	8	1	no	—
159	C₂⁴×C₆₁	—	8	1	no	—
160	C₂⁴×C₆₁	—	8	1	no	—
161	C₂⁴×C₆₁	—	8	1	no	—
162	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
163	C₂×Q₈×C₆₁	—	2	1	no	—
164	C₂×Q₈×C₆₁	—	2	1	no	—
165	C₂×Q₈×C₆₁	—	2	1	no	—
166	C₂×Q₈×C₆₁	—	2	1	no	—
167	C₂×Q₈×C₆₁	—	2	1	no	—
168	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
169	C₂×D₄×C₆₁	—	2	4	no	—
170	C₂×D₄×C₆₁	—	2	4	no	—
171	C₂×D₄×C₆₁	—	2	8	no	—
172	C₂×D₄×C₆₁	—	2	8	no	—
173	C₂×D₄×C₆₁	—	2	8	no	—
174	C₂×D₄×C₆₁	—	2	8	no	—
175	C₂×D₄×C₆₁	—	2	4	no	—
176	C₂×D₄×C₆₁	—	2	1	no	—
177	C₂×D₄×C₆₁	—	2	1	no	—
178	C₂×D₄×C₆₁	—	2	1	no	—
179	C₂×D₄×C₆₁	—	2	1	no	—
180	C₂×D₄×C₆₁	—	2	1	no	—
181	C₂×D₄×C₆₁	—	2	1	no	—
182	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
183	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
184	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
185	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
186	C₂×D₄×C₆₁	#41	1	2	yes	—
187	C₂×D₄×C₆₁	#41	1	2	yes	—
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	—	2	1	no	—
193	C₂²×C₄×C₆₁	—	2	1	no	—
194	C₂²×C₄×C₆₁	—	2	1	no	—
195	C₂²×C₄×C₆₁	—	2	1	no	—
196	C₂²×C₄×C₆₁	—	2	4	no	—
197	C₂²×C₄×C₆₁	—	2	4	no	—
198	C₂²×C₄×C₆₁	—	2	4	no	—
199	C₂²×C₄×C₆₁	—	2	4	no	—
200	C₂²×C₄×C₆₁	—	2	1	no	—
201	C₂²×C₄×C₆₁	—	2	1	no	—
202	C₂²×C₄×C₆₁	—	8	1	no	—
203	C₂²×C₄×C₆₁	—	8	1	no	—
204	C₂²×C₄×C₆₁	—	8	1	no	—
205	C₂²×C₄×C₆₁	—	8	1	no	—
206	C₂²×C₄×C₆₁	—	8	1	no	—
207	C₂²×C₄×C₆₁	—	8	1	no	—
208	C₂²×C₄×C₆₁	—	8	1	no	—
209	C₂²×C₄×C₆₁	—	8	1	no	—
210	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
211	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₆₁	#41	1	2	yes	—
217	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
218	SD₁₆×C₆₁	—	2	8	no	—
219	SD₁₆×C₆₁	—	2	8	no	—
220	C₂×C₈×C₆₁	—	2	1	no	—
221	C₂×C₈×C₆₁	—	2	1	no	—
222	C₂×C₈×C₆₁	—	2	1	no	—
223	C₂×C₈×C₆₁	—	2	1	no	—
224	C₂×C₈×C₆₁	—	2	1	no	—
225	C₂×C₈×C₆₁	—	2	1	no	—
226	C₂×C₈×C₆₁	—	2	1	no	—
227	C₂×C₈×C₆₁	—	2	1	no	—
228	C₂×C₈×C₆₁	—	2	1	no	—
229	C₂×C₈×C₆₁	—	2	1	no	—
230	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
231	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
232	C₄⋊C₄×C₆₁	—	2	4	no	—
233	C₄⋊C₄×C₆₁	—	2	2	no	—
234	C₄⋊C₄×C₆₁	—	2	2	no	—
235	C₄⋊C₄×C₆₁	—	2	1	no	—
236	C₄⋊C₄×C₆₁	—	2	1	no	—
237	C₄⋊C₄×C₆₁	—	2	1	no	—
238	C₄⋊C₄×C₆₁	—	2	1	no	—
239	C₄⋊C₄×C₆₁	—	2	1	no	—
240	C₄⋊C₄×C₆₁	—	2	1	no	—
241	C₄⋊C₄×C₆₁	—	2	1	no	—
242	C₄⋊C₄×C₆₁	—	4	2	no	—
243	C₄⋊C₄×C₆₁	—	8	1	no	—
244	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
245	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
246	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
247	C₂²⋊C₄×C₆₁	—	2	4	no	—
248	C₂²⋊C₄×C₆₁	—	2	4	no	—
249	C₂²⋊C₄×C₆₁	—	2	4	no	—
250	C₂²⋊C₄×C₆₁	—	2	4	no	—
251	C₂²⋊C₄×C₆₁	—	2	2	no	—
252	C₂²⋊C₄×C₆₁	—	2	2	no	—
253	C₂²⋊C₄×C₆₁	—	2	4	no	—
254	C₂²⋊C₄×C₆₁	—	2	4	no	—
255	C₂²⋊C₄×C₆₁	—	8	1	no	—
256	C₄²×C₆₁	—	2	4	no	—
257	C₄²×C₆₁	—	2	1	no	—
258	C₄²×C₆₁	—	2	1	no	—
259	C₄²×C₆₁	—	4	2	no	—
260	C₄²×C₆₁	—	8	1	no	—
261	C₄²×C₆₁	C₂×D₄	1	2	yes	—
262	C₄²×C₆₁	C₂×D₄	1	2	yes	—
263	C₂³×C₆₁	—	2	16	no	—
264	C₂³×C₆₁	—	2	2	no	—
265	C₂³×C₆₁	—	2	2	no	—
266	C₂³×C₆₁	—	2	1	no	—
267	C₂³×C₆₁	—	2	2	no	—
268	C₂³×C₆₁	—	2	2	no	—
269	C₂³×C₆₁	—	2	1	no	—
270	C₂³×C₆₁	—	2	2	no	—
271	C₂³×C₆₁	—	2	2	no	—
272	C₂³×C₆₁	—	2	1	no	—
273	C₂³×C₆₁	—	2	1	no	—
274	C₂³×C₆₁	—	2	1	no	—
275	C₂³×C₆₁	—	2	1	no	—
276	C₂³×C₆₁	—	4	1	no	—
277	C₂³×C₆₁	—	4	1	no	—
278	C₂³×C₆₁	—	4	1	no	—
279	C₂³×C₆₁	—	4	1	no	—
280	C₂³×C₆₁	—	4	1	no	—
281	C₂³×C₆₁	—	4	1	no	—
282	C₂³×C₆₁	—	4	1	no	—
283	C₂³×C₆₁	—	4	1	no	—
284	C₂³×C₆₁	—	8	4	no	—
285	C₂³×C₆₁	—	8	4	no	—
286	C₂³×C₆₁	—	8	4	no	—
287	C₂³×C₆₁	—	8	4	no	—
288	C₂³×C₆₁	—	8	4	no	—
289	C₂³×C₆₁	—	8	4	no	—
290	C₂³×C₆₁	C₄×D₄	1	2	yes	—
291	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
292	Q₈×C₆₁	—	2	2	no	—
293	Q₈×C₆₁	—	2	2	no	—
294	Q₈×C₆₁	—	4	1	no	—
295	Q₈×C₆₁	—	4	1	no	—
296	D₄×C₆₁	—	2	16	no	—
297	D₄×C₆₁	—	2	2	no	—
298	D₄×C₆₁	—	2	2	no	—
299	D₄×C₆₁	—	2	2	no	—
300	D₄×C₆₁	—	2	2	no	—
301	D₄×C₆₁	—	2	2	no	—
302	D₄×C₆₁	—	2	2	no	—
303	D₄×C₆₁	C₄×D₄	1	4	yes	—
304	D₄×C₆₁	C₄×D₄	1	4	yes	—
305	C₂×C₄×C₆₁	—	2	1	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	2	no	—
312	C₂×C₄×C₆₁	—	2	2	no	—
313	C₂×C₄×C₆₁	—	2	2	no	—
314	C₂×C₄×C₆₁	—	2	2	no	—
315	C₂×C₄×C₆₁	—	2	2	no	—
316	C₂×C₄×C₆₁	—	2	2	no	—
317	C₂×C₄×C₆₁	—	2	1	no	—
318	C₂×C₄×C₆₁	—	2	1	no	—
319	C₂×C₄×C₆₁	—	2	2	no	—
320	C₂×C₄×C₆₁	—	2	2	no	—
321	C₂×C₄×C₆₁	—	2	1	no	—
322	C₂×C₄×C₆₁	—	2	1	no	—
323	C₂×C₄×C₆₁	—	2	1	no	—
324	C₂×C₄×C₆₁	—	2	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	—	4	1	no	—
336	C₂×C₄×C₆₁	—	4	1	no	—
337	C₂×C₄×C₆₁	—	4	1	no	—
338	C₂×C₄×C₆₁	—	4	1	no	—
339	C₂×C₄×C₆₁	—	8	4	no	—
340	C₂×C₄×C₆₁	—	8	4	no	—
341	C₂×C₄×C₆₁	—	8	4	no	—
342	C₂×C₄×C₆₁	—	8	4	no	—
343	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
344	C₂×C₄×C₆₁	#120	1	2	yes	—
345	C₂×C₄×C₆₁	#120	1	2	yes	—
346	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
347	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
350	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
351	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
352	C₈×C₆₁	—	2	2	no	—
353	C₈×C₆₁	—	2	2	no	—
354	C₈×C₆₁	—	4	1	no	—
355	C₈×C₆₁	—	4	1	no	—
356	#21459	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
357	C₂²×C₆₁	—	2	2	no	—
358	C₂²×C₆₁	—	2	2	no	—
359	C₂²×C₆₁	—	2	2	no	—
360	C₂²×C₆₁	—	2	4	no	—
361	C₂²×C₆₁	—	2	4	no	—
362	C₂²×C₆₁	—	4	1	no	—
363	C₂²×C₆₁	—	4	2	no	—
364	C₂²×C₆₁	—	4	2	no	—
365	C₂²×C₆₁	—	4	1	no	—
366	C₂²×C₆₁	—	4	2	no	—
367	C₂²×C₆₁	—	4	2	no	—
368	C₂²×C₆₁	—	4	2	no	—
369	C₂²×C₆₁	—	4	2	no	—
370	C₂²×C₆₁	—	4	2	no	—
371	C₂²×C₆₁	—	4	2	no	—
372	C₂²×C₆₁	—	4	2	no	—
373	C₂²×C₆₁	—	4	2	no	—
374	C₂²×C₆₁	—	4	1	no	—
375	C₂²×C₆₁	—	4	2	no	—
376	C₂²×C₆₁	—	4	2	no	—
377	C₂²×C₆₁	—	4	1	no	—
378	C₂²×C₆₁	—	8	16	no	—
379	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
380	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
381	C₂²×C₆₁	#525	1	1	yes	characteristic
382	C₂²×C₆₁	#576	1	1	yes	characteristic
383	C₂²×C₆₁	#577	1	1	yes	characteristic
384	C₂²×C₆₁	#577	1	1	yes	characteristic
385	C₂²×C₆₁	#577	1	1	yes	characteristic
386	C₄×C₆₁	—	2	2	no	—
387	C₄×C₆₁	—	2	2	no	—
388	C₄×C₆₁	—	2	2	no	—
389	C₄×C₆₁	—	4	2	no	—
390	C₄×C₆₁	—	4	1	no	—
391	C₄×C₆₁	—	4	2	no	—
392	C₄×C₆₁	—	4	1	no	—
393	C₄×C₆₁	—	4	2	no	—
394	C₄×C₆₁	—	4	2	no	—
395	C₄×C₆₁	—	8	1	no	—
396	C₄×C₆₁	—	8	1	no	—
397	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
398	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
399	C₄×C₆₁	#525	1	1	yes	characteristic
400	C₄×C₆₁	#525	1	1	yes	characteristic
401	C₂×#518	C₂×C₆₁	1	1	yes	characteristic
402	C₂×#450	C₂×C₆₁	1	1	yes	characteristic
403	C₂×#440	C₂×C₆₁	1	1	yes	characteristic, complemented
404	C₂×C₄×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
405	#2323	C₂×C₆₁	1	1	yes	characteristic, complemented
406	#1877	C₂×C₆₁	1	1	yes	characteristic, complemented
407	#1877	C₂×C₆₁	1	1	yes	characteristic, complemented
408	#1873	C₂×C₆₁	1	1	yes	characteristic, complemented
409	#1864	C₂×C₆₁	1	1	yes	characteristic, complemented
410	#1862	C₂×C₆₁	1	1	yes	characteristic, complemented
411	#1854	C₂×C₆₁	1	1	yes	characteristic, complemented
412	#1786	C₂×C₆₁	1	1	yes	characteristic
413	#1762	C₂×C₆₁	1	1	yes	characteristic, complemented
414	C₄×#102	C₂×C₆₁	1	1	yes	characteristic, complemented
415	#1750	C₂×C₆₁	1	1	yes	characteristic, complemented
416	C₂×C₆₁	—	4	2	no	—
417	C₂×C₆₁	—	4	4	no	—
418	C₂×C₆₁	—	4	4	no	—
419	C₂×C₆₁	C₄×#120	1	1	yes	characteristic
420	C₂×C₆₁	#2946	1	1	yes	characteristic
421	C₂×C₆₁	#2949	1	1	yes	characteristic
422	C₂×C₆₁	#3009	1	1	yes	characteristic
423	C₂×C₆₁	#3012	1	1	yes	characteristic
424	C₂×C₆₁	#3118	1	1	yes	characteristic
425	C₂×C₆₁	#3123	1	1	yes	characteristic
426	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
427	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
428	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
429	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
430	#518	—	2	4	no	—
431	#518	—	2	4	no	—
432	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
433	C₂×C₄×D₄	—	2	1	no	—
434	C₂×C₄×D₄	—	2	1	no	—
435	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
436	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
437	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
438	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
439	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
440	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
441	C₂²×C₂²⋊C₄	—	2	1	no	—
442	C₂²×C₂²⋊C₄	—	2	1	no	—
443	#450	C₄×C₆₁	1	8	yes	complemented
444	#440	—	2	4	no	—
445	C₄×SD₁₆	—	2	4	no	—
446	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic, complemented
447	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic, complemented
448	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic, complemented
449	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic, complemented
450	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
451	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
452	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
453	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
454	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
455	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
456	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
457	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
458	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic, complemented
459	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
460	#391	C₂²×C₆₁	1	1	yes	characteristic, complemented
461	#389	—	2	1	no	—
462	#389	C₂²×C₆₁	1	1	yes	characteristic, complemented
463	#388	—	2	1	no	—
464	#388	—	2	1	no	—
465	#387	—	2	1	no	—
466	#380	C₂²×C₆₁	1	1	yes	characteristic
467	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
468	#340	C₂²×C₆₁	1	1	yes	characteristic, complemented
469	#340	C₂²×C₆₁	1	1	yes	characteristic, complemented
470	#340	C₂²×C₆₁	1	1	yes	characteristic, complemented
471	#340	C₂²×C₆₁	1	1	yes	characteristic, complemented
472	#336	C₂²×C₆₁	1	1	yes	characteristic, complemented
473	#336	C₂²×C₆₁	1	1	yes	characteristic, complemented
474	C₆₁	#21459	1	1	yes	characteristic, direct product factor, Sylow
475	C₂⁵	—	2	1	no	—
476	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
477	C₂²×D₄	—	2	2	no	—
478	C₂²×D₄	—	2	2	no	—
479	C₂²×D₄	—	2	2	no	—
480	C₂²×D₄	—	2	2	no	—
481	C₂²×D₄	—	2	1	no	—
482	C₂²×D₄	—	2	2	no	—
483	C₂²×D₄	C₂×C₄×C₆₁	1	4	yes	—
484	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
485	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
486	C₂³×C₄	—	2	1	no	—
487	C₂³×C₄	—	2	1	no	—
488	C₂³×C₄	—	2	1	no	—
489	C₂³×C₄	—	2	1	no	—
490	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
491	C₂×SD₁₆	—	2	2	no	—
492	C₂×SD₁₆	—	2	2	no	—
493	C₂×SD₁₆	—	2	2	no	—
494	C₂×SD₁₆	—	2	2	no	—
495	C₂×SD₁₆	C₂×C₄×C₆₁	1	4	yes	complemented
496	C₂×SD₁₆	C₂×C₄×C₆₁	1	4	yes	complemented
497	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
498	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
499	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
500	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	C₂×C₄×C₆₁	1	4	yes	complemented
503	C₄×Q₈	—	2	2	no	—
504	C₄×Q₈	—	2	2	no	—
505	C₄×D₄	—	2	8	no	—
506	C₄×D₄	—	2	8	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	D₄×C₆₁	1	4	yes	—
514	C₄×D₄	D₄×C₆₁	1	4	yes	—
515	#117	—	2	2	no	—
516	#117	—	2	2	no	—
517	#117	—	2	2	no	—
518	#117	—	2	2	no	—
519	C₂×C₄⋊C₄	—	2	1	no	—
520	C₂×C₄⋊C₄	—	2	1	no	—
521	C₂×C₄⋊C₄	—	2	1	no	—
522	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
523	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
529	C₂×C₂²⋊C₄	—	2	8	no	—
530	C₂×C₂²⋊C₄	—	2	8	no	—
531	C₂×C₂²⋊C₄	—	2	1	no	—
532	C₂×C₂²⋊C₄	—	2	1	no	—
533	C₂×C₂²⋊C₄	—	2	1	no	—
534	C₂×C₂²⋊C₄	—	2	1	no	—
535	C₂×C₂²⋊C₄	—	2	1	no	—
536	C₂×C₂²⋊C₄	—	2	1	no	—
537	C₂×C₂²⋊C₄	—	2	1	no	—
538	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
540	C₂×C₄²	—	2	1	no	—
541	C₂×C₄²	—	2	1	no	—
542	C₂×C₄²	—	2	1	no	—
543	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
545	#107	—	2	2	no	—
546	#106	—	2	2	no	—
547	#103	—	2	2	no	—
548	#103	—	2	2	no	—
549	#102	—	2	2	no	—
550	#102	—	2	2	no	—
551	#102	—	2	2	no	—
552	#102	—	2	2	no	—
553	#102	C₂×C₄×C₆₁	1	4	yes	complemented
554	#102	C₂×C₄×C₆₁	1	4	yes	complemented
555	C₂²⋊C₈	—	2	2	no	—
556	C₂²⋊C₈	C₂×C₄×C₆₁	1	4	yes	complemented
557	#97	—	2	2	no	—
558	C₄×C₈	—	2	2	no	—
559	#95	—	2	1	no	—
560	#95	—	2	1	no	—
561	#95	—	2	1	no	—
562	#95	—	2	1	no	—
563	#95	—	2	1	no	—
564	C₂⁴	—	2	4	no	—
565	C₂⁴	—	2	4	no	—
566	C₂⁴	—	2	1	no	—
567	C₂⁴	—	2	1	no	—
568	C₂⁴	—	2	4	no	—
569	C₂⁴	—	8	1	no	—
570	C₂⁴	—	8	1	no	—
571	C₂⁴	—	8	1	no	—
572	C₂⁴	—	8	1	no	—
573	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
574	C₂×Q₈	—	2	1	no	—
575	C₂×Q₈	—	2	1	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	8	no	—
583	C₂×D₄	—	2	8	no	—
584	C₂×D₄	—	2	8	no	—
585	C₂×D₄	—	2	8	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
594	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
595	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
596	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
597	C₂×D₄	#41×C₆₁	1	2	yes	—
598	C₂×D₄	#41×C₆₁	1	2	yes	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	8	1	no	—
614	C₂²×C₄	—	8	1	no	—
615	C₂²×C₄	—	8	1	no	—
616	C₂²×C₄	—	8	1	no	—
617	C₂²×C₄	—	8	1	no	—
618	C₂²×C₄	—	8	1	no	—
619	C₂²×C₄	—	8	1	no	—
620	C₂²×C₄	—	8	1	no	—
621	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
622	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
625	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
626	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
627	C₂²×C₄	#41×C₆₁	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
629	SD₁₆	—	2	8	no	—
630	SD₁₆	—	2	8	no	—
631	C₂×C₈	—	2	1	no	—
632	C₂×C₈	—	2	1	no	—
633	C₂×C₈	—	2	1	no	—
634	C₂×C₈	—	2	1	no	—
635	C₂×C₈	—	2	1	no	—
636	C₂×C₈	—	2	1	no	—
637	C₂×C₈	—	2	1	no	—
638	C₂×C₈	—	2	1	no	—
639	C₂×C₈	—	2	1	no	—
640	C₂×C₈	—	2	1	no	—
641	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
642	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	2	no	—
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	—	2	1	no	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	4	2	no	—
654	C₄⋊C₄	—	8	1	no	—
655	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
656	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
657	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	2	no	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	8	1	no	—
667	C₄²	—	2	4	no	—
668	C₄²	—	2	1	no	—
669	C₄²	—	2	1	no	—
670	C₄²	—	4	2	no	—
671	C₄²	—	8	1	no	—
672	C₄²	C₂×D₄×C₆₁	1	2	yes	—
673	C₄²	C₂×D₄×C₆₁	1	2	yes	—
674	C₂³	—	2	16	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	1	no	—
678	C₂³	—	2	1	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	1	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	4	1	no	—
688	C₂³	—	4	1	no	—
689	C₂³	—	4	1	no	—
690	C₂³	—	4	1	no	—
691	C₂³	—	4	1	no	—
692	C₂³	—	4	1	no	—
693	C₂³	—	4	1	no	—
694	C₂³	—	4	1	no	—
695	C₂³	—	8	4	no	—
696	C₂³	—	8	4	no	—
697	C₂³	—	8	4	no	—
698	C₂³	—	8	4	no	—
699	C₂³	—	8	4	no	—
700	C₂³	—	8	4	no	—
701	C₂³	C₄×D₄×C₆₁	1	2	yes	—
702	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
703	Q₈	—	2	2	no	—
704	Q₈	—	2	2	no	—
705	Q₈	—	4	1	no	—
706	Q₈	—	4	1	no	—
707	D₄	—	2	16	no	—
708	D₄	—	2	2	no	—
709	D₄	—	2	2	no	—
710	D₄	—	2	2	no	—
711	D₄	—	2	2	no	—
712	D₄	—	2	2	no	—
713	D₄	—	2	2	no	—
714	D₄	C₄×D₄×C₆₁	1	4	yes	—
715	D₄	C₄×D₄×C₆₁	1	4	yes	—
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	—	2	1	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	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	—	4	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	8	4	no	—
751	C₂×C₄	—	8	4	no	—
752	C₂×C₄	—	8	4	no	—
753	C₂×C₄	—	8	4	no	—
754	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
755	C₂×C₄	#120×C₆₁	1	2	yes	—
756	C₂×C₄	#120×C₆₁	1	2	yes	—
757	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
758	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
759	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
760	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
761	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
762	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
763	C₈	—	2	2	no	—
764	C₈	—	2	2	no	—
765	C₈	—	4	1	no	—
766	C₈	—	4	1	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	2	4	no	—
769	C₂²	—	2	4	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	1	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	8	16	no	—
789	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
790	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
791	C₂²	C₆₁×#525	1	1	yes	characteristic
792	C₂²	C₆₁×#576	1	1	yes	characteristic
793	C₂²	C₆₁×#577	1	1	yes	characteristic
794	C₂²	C₆₁×#577	1	1	yes	characteristic
795	C₂²	C₆₁×#577	1	1	yes	characteristic
796	C₄	—	2	2	no	—
797	C₄	—	2	2	no	—
798	C₄	—	2	2	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	1	no	—
802	C₄	—	4	2	no	—
803	C₄	—	4	1	no	—
804	C₄	—	4	2	no	—
805	C₄	—	8	1	no	—
806	C₄	—	8	1	no	—
807	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
808	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
809	C₄	C₆₁×#525	1	1	yes	characteristic
810	C₄	C₆₁×#525	1	1	yes	characteristic
811	C₂	—	4	2	no	—
812	C₂	—	4	4	no	—
813	C₂	—	4	4	no	—
814	C₂	C₄×#120×C₆₁	1	1	yes	characteristic
815	C₂	C₆₁×#2946	1	1	yes	characteristic
816	C₂	C₆₁×#2949	1	1	yes	characteristic
817	C₂	C₆₁×#3009	1	1	yes	characteristic
818	C₂	C₆₁×#3012	1	1	yes	characteristic
819	C₂	C₆₁×#3118	1	1	yes	characteristic
820	C₂	C₆₁×#3123	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂³×D₄×C₆₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×#117×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₆₁×#440	C₂	semidirect
4. C₂×C₄×SD₁₆×C₆₁	C₂	semidirect
5. C₆₁×#2323	C₂	semidirect
6. C₆₁×#1877	C₂	semidirect
7. C₆₁×#1877	C₂	semidirect
8. C₆₁×#1873	C₂	semidirect
9. C₆₁×#1864	C₂	semidirect
10. C₆₁×#1862	C₂	semidirect
11. C₆₁×#1854	C₂	semidirect
13. C₆₁×#1762	C₂	semidirect
14. C₄×#102×C₆₁	C₂	semidirect
15. C₆₁×#1750	C₂	semidirect
22. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
33. C₆₁×#450	C₄	semidirect
36. C₂×#107×C₆₁	C₂²	semidirect
37. C₂×#106×C₆₁	C₂²	semidirect
38. C₂×#103×C₆₁	C₂²	semidirect
39. C₂×#103×C₆₁	C₂²	semidirect
48. C₂×#97×C₆₁	C₂²	semidirect
49. C₂×C₄×C₈×C₆₁	C₂²	semidirect
50. C₆₁×#391	C₂²	semidirect
52. C₆₁×#389	C₂²	semidirect
57. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
58. C₆₁×#340	C₂²	semidirect
59. C₆₁×#340	C₂²	semidirect
60. C₆₁×#340	C₂²	semidirect
61. C₆₁×#340	C₂²	semidirect
62. C₆₁×#336	C₂²	semidirect
63. C₆₁×#336	C₂²	semidirect
84. C₂×SD₁₆×C₆₁	C₂×C₄	semidirect
85. C₂×SD₁₆×C₆₁	C₂×C₄	semidirect
91. C₂²⋊Q₈×C₆₁	C₂×C₄	semidirect
142. #102×C₆₁	C₂×C₄	semidirect
143. #102×C₆₁	C₂×C₄	semidirect
145. C₂²⋊C₈×C₆₁	C₂×C₄	semidirect
356. #21459	C₆₁	direct (N × H)
403. C₂×#440	C₂×C₆₁	semidirect
404. C₂×C₄×SD₁₆	C₂×C₆₁	semidirect
405. #2323	C₂×C₆₁	semidirect
406. #1877	C₂×C₆₁	semidirect
407. #1877	C₂×C₆₁	semidirect
408. #1873	C₂×C₆₁	semidirect
409. #1864	C₂×C₆₁	semidirect
410. #1862	C₂×C₆₁	semidirect
411. #1854	C₂×C₆₁	semidirect
413. #1762	C₂×C₆₁	semidirect
414. C₄×#102	C₂×C₆₁	semidirect
415. #1750	C₂×C₆₁	semidirect
432. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
443. #450	C₄×C₆₁	semidirect
446. C₂×#107	C₂²×C₆₁	semidirect
447. C₂×#106	C₂²×C₆₁	semidirect
448. C₂×#103	C₂²×C₆₁	semidirect
449. C₂×#103	C₂²×C₆₁	semidirect
458. C₂×#97	C₂²×C₆₁	semidirect
459. C₂×C₄×C₈	C₂²×C₆₁	semidirect
460. #391	C₂²×C₆₁	semidirect
462. #389	C₂²×C₆₁	semidirect
467. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
468. #340	C₂²×C₆₁	semidirect
469. #340	C₂²×C₆₁	semidirect
470. #340	C₂²×C₆₁	semidirect
471. #340	C₂²×C₆₁	semidirect
472. #336	C₂²×C₆₁	semidirect
473. #336	C₂²×C₆₁	semidirect
474. C₆₁	#21459	direct (N × H)
495. C₂×SD₁₆	C₂×C₄×C₆₁	semidirect
496. C₂×SD₁₆	C₂×C₄×C₆₁	semidirect
502. C₂²⋊Q₈	C₂×C₄×C₆₁	semidirect
553. #102	C₂×C₄×C₆₁	semidirect
554. #102	C₂×C₄×C₆₁	semidirect
556. C₂²⋊C₈	C₂×C₄×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#518	2
C₂×C₆₁×#450	2
C₂×C₆₁×#440	2
C₂×C₄×SD₁₆×C₆₁	2
C₆₁×#2323	2
C₆₁×#1877	2
C₆₁×#1873	2
C₆₁×#1864	2
C₆₁×#1862	2
C₆₁×#1854	2
C₆₁×#1786	2
C₆₁×#1762	2
C₄×#102×C₆₁	2
C₆₁×#1750	2
#21459	61

Subgroups — C61×#21459 #29524892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#21459 #29524892