Subgroups — C₆₁×#21272 #29524705

Order 15616.

868 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#433	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2290	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1955	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#1954	C₂	1	1	yes	maximal, characteristic
6	C₆₁×#1940	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1924	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1924	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1923	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1923	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1768	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#1750	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1749	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1726	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#433	—	2	4	no	—
20	C₆₁×#431	—	2	4	no	—
21	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
43	C₆₁×#388	C₄	1	1	yes	characteristic
44	C₆₁×#388	C₄	1	1	yes	characteristic
45	C₆₁×#387	C₄	1	1	yes	characteristic
46	C₆₁×#387	C₄	1	1	yes	characteristic
47	C₆₁×#386	C₄	1	1	yes	characteristic
48	C₆₁×#386	C₄	1	1	yes	characteristic
49	C₆₁×#385	C₄	1	1	yes	characteristic
50	C₆₁×#385	C₄	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
52	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
54	C₆₁×#376	C₂²	1	1	yes	characteristic
55	C₆₁×#336	C₂²	1	1	yes	characteristic
56	C₆₁×#336	C₂²	1	1	yes	characteristic
57	C₆₁×#336	C₂²	1	1	yes	characteristic
58	C₆₁×#336	C₂²	1	1	yes	characteristic
59	C₆₁×#336	C₂²	1	1	yes	characteristic
60	C₆₁×#336	C₂²	1	1	yes	characteristic
61	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
74	C₄×D₄×C₆₁	—	2	2	no	—
75	C₄×D₄×C₆₁	—	2	2	no	—
76	#117×C₆₁	—	2	2	no	—
77	#117×C₆₁	—	2	2	no	—
78	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₆₁	—	2	2	no	—
92	C₂×C₄²×C₆₁	—	2	2	no	—
93	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₆₁	—	2	2	no	—
101	C₄⋊C₈×C₆₁	—	2	2	no	—
102	C₄⋊C₈×C₆₁	—	2	2	no	—
103	C₄⋊C₈×C₆₁	—	2	2	no	—
104	C₄⋊C₈×C₆₁	—	2	2	no	—
105	C₄⋊C₈×C₆₁	—	2	2	no	—
106	C₂²⋊C₈×C₆₁	—	2	2	no	—
107	C₂²⋊C₈×C₆₁	—	2	2	no	—
108	C₂²⋊C₈×C₆₁	—	2	2	no	—
109	C₂²⋊C₈×C₆₁	—	2	2	no	—
110	C₂²⋊C₈×C₆₁	—	2	2	no	—
111	C₂²⋊C₈×C₆₁	—	2	2	no	—
112	C₂²⋊C₈×C₆₁	—	2	2	no	—
113	C₂²⋊C₈×C₆₁	—	2	2	no	—
114	#97×C₆₁	—	2	2	no	—
115	#97×C₆₁	—	2	2	no	—
116	#97×C₆₁	—	2	2	no	—
117	#97×C₆₁	—	2	2	no	—
118	C₄×C₈×C₆₁	—	2	2	no	—
119	C₄×C₈×C₆₁	—	2	2	no	—
120	C₄×C₈×C₆₁	—	2	2	no	—
121	C₄×C₈×C₆₁	D₄	1	4	yes	complemented
122	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
123	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
124	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
125	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
126	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
127	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
128	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
129	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
130	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
131	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
132	C₂⁴×C₆₁	C₂²×C₄	1	1	yes	characteristic
133	C₂⁴×C₆₁	C₂²×C₄	1	1	yes	characteristic
134	C₂×D₄×C₆₁	—	2	2	no	—
135	C₂×D₄×C₆₁	—	2	2	no	—
136	C₂×D₄×C₆₁	—	4	1	no	—
137	C₂²×C₄×C₆₁	—	2	2	no	—
138	C₂²×C₄×C₆₁	—	2	2	no	—
139	C₂²×C₄×C₆₁	—	2	2	no	—
140	C₂²×C₄×C₆₁	—	2	2	no	—
141	C₂²×C₄×C₆₁	—	2	1	no	—
142	C₂²×C₄×C₆₁	—	2	1	no	—
143	C₂²×C₄×C₆₁	—	2	1	no	—
144	C₂²×C₄×C₆₁	—	2	1	no	—
145	C₂²×C₄×C₆₁	—	2	1	no	—
146	C₂²×C₄×C₆₁	—	2	1	no	—
147	C₂²×C₄×C₆₁	—	2	1	no	—
148	C₂²×C₄×C₆₁	—	2	1	no	—
149	C₂²×C₄×C₆₁	—	2	1	no	—
150	C₂²×C₄×C₆₁	—	2	1	no	—
151	C₂²×C₄×C₆₁	—	2	1	no	—
152	C₂²×C₄×C₆₁	—	2	1	no	—
153	C₂²×C₄×C₆₁	—	4	1	no	—
154	C₂²×C₄×C₆₁	—	4	1	no	—
155	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
168	C₂×C₈×C₆₁	—	2	1	no	—
169	C₂×C₈×C₆₁	—	2	1	no	—
170	C₂×C₈×C₆₁	—	2	1	no	—
171	C₂×C₈×C₆₁	—	2	1	no	—
172	C₂×C₈×C₆₁	—	2	1	no	—
173	C₂×C₈×C₆₁	—	2	1	no	—
174	C₂×C₈×C₆₁	—	2	1	no	—
175	C₂×C₈×C₆₁	—	2	1	no	—
176	C₂×C₈×C₆₁	—	2	1	no	—
177	C₂×C₈×C₆₁	—	2	1	no	—
178	C₂×C₈×C₆₁	—	2	1	no	—
179	C₂×C₈×C₆₁	—	2	1	no	—
180	C₂×C₈×C₆₁	—	2	1	no	—
181	C₂×C₈×C₆₁	—	2	1	no	—
182	C₂×C₈×C₆₁	—	2	1	no	—
183	C₂×C₈×C₆₁	—	2	1	no	—
184	C₂×C₈×C₆₁	—	2	1	no	—
185	C₂×C₈×C₆₁	—	2	1	no	—
186	C₂×C₈×C₆₁	—	2	1	no	—
187	C₂×C₈×C₆₁	—	2	1	no	—
188	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
189	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
190	C₂×C₈×C₆₁	#41	1	2	yes	—
191	C₂×C₈×C₆₁	#41	1	2	yes	—
192	C₄⋊C₄×C₆₁	—	2	2	no	—
193	C₄⋊C₄×C₆₁	—	2	2	no	—
194	C₄⋊C₄×C₆₁	—	2	2	no	—
195	C₄⋊C₄×C₆₁	—	2	2	no	—
196	C₄⋊C₄×C₆₁	—	4	1	no	—
197	C₂²⋊C₄×C₆₁	—	2	2	no	—
198	C₂²⋊C₄×C₆₁	—	2	2	no	—
199	C₂²⋊C₄×C₆₁	—	2	2	no	—
200	C₂²⋊C₄×C₆₁	—	2	2	no	—
201	C₂²⋊C₄×C₆₁	—	2	2	no	—
202	C₂²⋊C₄×C₆₁	—	2	2	no	—
203	C₂²⋊C₄×C₆₁	—	4	1	no	—
204	C₂²⋊C₄×C₆₁	—	4	1	no	—
205	C₄²×C₆₁	—	2	2	no	—
206	C₄²×C₆₁	—	2	2	no	—
207	C₄²×C₆₁	—	2	1	no	—
208	C₄²×C₆₁	—	2	1	no	—
209	C₄²×C₆₁	—	2	1	no	—
210	C₄²×C₆₁	—	2	1	no	—
211	C₄²×C₆₁	—	2	1	no	—
212	C₄²×C₆₁	—	2	1	no	—
213	C₄²×C₆₁	C₂×D₄	1	2	yes	—
214	C₄²×C₆₁	#41	1	2	yes	—
215	C₄²×C₆₁	#41	1	2	yes	—
216	C₄²×C₆₁	#41	1	2	yes	—
217	C₂³×C₆₁	—	2	1	no	—
218	C₂³×C₆₁	—	2	1	no	—
219	C₂³×C₆₁	—	2	1	no	—
220	C₂³×C₆₁	—	2	1	no	—
221	C₂³×C₆₁	—	2	1	no	—
222	C₂³×C₆₁	—	2	1	no	—
223	C₂³×C₆₁	—	2	1	no	—
224	C₂³×C₆₁	—	2	1	no	—
225	C₂³×C₆₁	—	2	1	no	—
226	C₂³×C₆₁	—	2	1	no	—
227	C₂³×C₆₁	—	2	1	no	—
228	C₂³×C₆₁	—	2	1	no	—
229	C₂³×C₆₁	—	2	1	no	—
230	C₂³×C₆₁	#131	1	2	yes	—
231	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
232	D₄×C₆₁	—	4	4	no	—
233	C₂×C₄×C₆₁	—	2	8	no	—
234	C₂×C₄×C₆₁	—	2	1	no	—
235	C₂×C₄×C₆₁	—	2	1	no	—
236	C₂×C₄×C₆₁	—	2	1	no	—
237	C₂×C₄×C₆₁	—	2	1	no	—
238	C₂×C₄×C₆₁	—	2	1	no	—
239	C₂×C₄×C₆₁	—	2	1	no	—
240	C₂×C₄×C₆₁	—	2	1	no	—
241	C₂×C₄×C₆₁	—	2	1	no	—
242	C₂×C₄×C₆₁	—	2	1	no	—
243	C₂×C₄×C₆₁	—	2	1	no	—
244	C₂×C₄×C₆₁	—	2	1	no	—
245	C₂×C₄×C₆₁	—	2	1	no	—
246	C₂×C₄×C₆₁	—	2	1	no	—
247	C₂×C₄×C₆₁	—	2	1	no	—
248	C₂×C₄×C₆₁	—	2	1	no	—
249	C₂×C₄×C₆₁	—	2	1	no	—
250	C₂×C₄×C₆₁	—	2	1	no	—
251	C₂×C₄×C₆₁	—	2	1	no	—
252	C₂×C₄×C₆₁	—	2	1	no	—
253	C₂×C₄×C₆₁	—	2	1	no	—
254	C₂×C₄×C₆₁	—	2	1	no	—
255	C₂×C₄×C₆₁	—	2	1	no	—
256	C₂×C₄×C₆₁	—	2	1	no	—
257	C₂×C₄×C₆₁	—	2	1	no	—
258	C₂×C₄×C₆₁	—	2	1	no	—
259	C₂×C₄×C₆₁	—	2	1	no	—
260	C₂×C₄×C₆₁	—	2	1	no	—
261	C₂×C₄×C₆₁	—	2	1	no	—
262	C₂×C₄×C₆₁	—	2	1	no	—
263	C₂×C₄×C₆₁	—	2	1	no	—
264	C₂×C₄×C₆₁	—	2	1	no	—
265	C₂×C₄×C₆₁	—	4	4	no	—
266	C₂×C₄×C₆₁	—	4	1	no	—
267	C₂×C₄×C₆₁	—	4	1	no	—
268	C₂×C₄×C₆₁	—	4	1	no	—
269	C₂×C₄×C₆₁	—	4	1	no	—
270	C₂×C₄×C₆₁	—	4	1	no	—
271	C₂×C₄×C₆₁	—	4	1	no	—
272	C₂×C₄×C₆₁	—	4	1	no	—
273	C₂×C₄×C₆₁	—	4	1	no	—
274	C₂×C₄×C₆₁	#117	1	2	yes	—
275	C₂×C₄×C₆₁	#117	1	2	yes	—
276	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
277	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
278	C₂×C₄×C₆₁	#131	1	2	yes	—
279	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
281	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
282	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
283	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
285	C₈×C₆₁	—	2	2	no	—
286	C₈×C₆₁	—	2	2	no	—
287	C₈×C₆₁	—	2	2	no	—
288	C₈×C₆₁	—	2	2	no	—
289	C₈×C₆₁	—	4	1	no	—
290	C₈×C₆₁	—	4	1	no	—
291	C₈×C₆₁	—	4	1	no	—
292	C₈×C₆₁	—	4	1	no	—
293	#21272	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
294	C₂²×C₆₁	—	2	2	no	—
295	C₂²×C₆₁	—	2	2	no	—
296	C₂²×C₆₁	—	2	2	no	—
297	C₂²×C₆₁	—	4	1	no	—
298	C₂²×C₆₁	—	4	1	no	—
299	C₂²×C₆₁	—	4	1	no	—
300	C₂²×C₆₁	—	4	1	no	—
301	C₂²×C₆₁	—	4	1	no	—
302	C₂²×C₆₁	—	4	1	no	—
303	C₂²×C₆₁	—	4	1	no	—
304	C₂²×C₆₁	—	4	1	no	—
305	C₂²×C₆₁	—	4	1	no	—
306	C₂²×C₆₁	—	4	1	no	—
307	C₂²×C₆₁	—	4	1	no	—
308	C₂²×C₆₁	C₂×#117	1	1	yes	characteristic
309	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
310	C₂²×C₆₁	C₄×#41	1	1	yes	characteristic
311	C₂²×C₆₁	C₂×#131	1	1	yes	characteristic
312	C₂²×C₆₁	C₂×#131	1	1	yes	characteristic
313	C₂²×C₆₁	#568	1	1	yes	characteristic
314	C₂²×C₆₁	#568	1	1	yes	characteristic
315	C₄×C₆₁	—	2	2	no	—
316	C₄×C₆₁	—	2	2	no	—
317	C₄×C₆₁	—	2	2	no	—
318	C₄×C₆₁	—	2	2	no	—
319	C₄×C₆₁	—	2	2	no	—
320	C₄×C₆₁	—	4	1	no	—
321	C₄×C₆₁	—	4	1	no	—
322	C₄×C₆₁	—	4	1	no	—
323	C₄×C₆₁	—	4	1	no	—
324	C₄×C₆₁	—	4	1	no	—
325	C₄×C₆₁	—	4	1	no	—
326	C₄×C₆₁	—	4	1	no	—
327	C₄×C₆₁	#529	1	1	yes	characteristic
328	C₄×C₆₁	#529	1	1	yes	characteristic
329	C₄×C₆₁	#532	1	1	yes	characteristic
330	C₄×C₆₁	#532	1	1	yes	characteristic
331	C₂×#433	C₂×C₆₁	1	1	yes	characteristic, complemented
332	C₂×#431	C₂×C₆₁	1	1	yes	characteristic, complemented
333	#2290	C₂×C₆₁	1	1	yes	characteristic
334	#1955	C₂×C₆₁	1	1	yes	characteristic
335	#1954	C₂×C₆₁	1	1	yes	characteristic
336	#1940	C₂×C₆₁	1	1	yes	characteristic, complemented
337	#1939	C₂×C₆₁	1	1	yes	characteristic, complemented
338	#1924	C₂×C₆₁	1	1	yes	characteristic, complemented
339	#1924	C₂×C₆₁	1	1	yes	characteristic, complemented
340	#1923	C₂×C₆₁	1	1	yes	characteristic, complemented
341	#1923	C₂×C₆₁	1	1	yes	characteristic, complemented
342	#1768	C₂×C₆₁	1	1	yes	characteristic, complemented
343	#1750	C₂×C₆₁	1	1	yes	characteristic, complemented
344	#1749	C₂×C₆₁	1	1	yes	characteristic, complemented
345	#1726	C₂×C₆₁	1	1	yes	characteristic, complemented
346	C₂×C₆₁	—	4	2	no	—
347	C₂×C₆₁	—	8	1	no	—
348	C₂×C₆₁	#2293	1	1	yes	characteristic
349	C₂×C₆₁	#2924	1	1	yes	characteristic
350	C₂×C₆₁	#2925	1	1	yes	characteristic
351	C₂×C₆₁	#2929	1	1	yes	characteristic
352	C₂×C₆₁	#2930	1	1	yes	characteristic
353	C₂×C₆₁	#2968	1	1	yes	characteristic
354	C₂×C₆₁	#2969	1	1	yes	characteristic
355	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
356	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
357	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
358	#433	—	2	4	no	—
359	#431	—	2	4	no	—
360	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
361	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
362	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
363	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
364	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
365	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
366	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
367	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
368	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
369	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
370	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
371	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
372	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
373	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
374	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
375	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
376	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
377	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
378	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
379	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
380	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
381	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
382	#388	C₄×C₆₁	1	1	yes	characteristic
383	#388	C₄×C₆₁	1	1	yes	characteristic
384	#387	C₄×C₆₁	1	1	yes	characteristic
385	#387	C₄×C₆₁	1	1	yes	characteristic
386	#386	C₄×C₆₁	1	1	yes	characteristic
387	#386	C₄×C₆₁	1	1	yes	characteristic
388	#385	C₄×C₆₁	1	1	yes	characteristic
389	#385	C₄×C₆₁	1	1	yes	characteristic
390	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
391	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
392	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
393	#376	C₂²×C₆₁	1	1	yes	characteristic
394	#336	C₂²×C₆₁	1	1	yes	characteristic
395	#336	C₂²×C₆₁	1	1	yes	characteristic
396	#336	C₂²×C₆₁	1	1	yes	characteristic
397	#336	C₂²×C₆₁	1	1	yes	characteristic
398	#336	C₂²×C₆₁	1	1	yes	characteristic
399	#336	C₂²×C₆₁	1	1	yes	characteristic
400	C₆₁	#21272	1	1	yes	characteristic, direct product factor, Sylow
401	C₂²×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
402	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
403	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
404	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
405	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
406	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
407	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
408	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
409	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
411	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
412	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
413	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	—	2	2	no	—
416	#117	—	2	2	no	—
417	#117	—	2	2	no	—
418	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
424	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
427	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
428	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
429	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
431	C₂×C₄²	—	2	2	no	—
432	C₂×C₄²	—	2	2	no	—
433	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
434	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
436	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
437	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
438	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
439	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
440	C₄⋊C₈	—	2	2	no	—
441	C₄⋊C₈	—	2	2	no	—
442	C₄⋊C₈	—	2	2	no	—
443	C₄⋊C₈	—	2	2	no	—
444	C₄⋊C₈	—	2	2	no	—
445	C₄⋊C₈	—	2	2	no	—
446	C₂²⋊C₈	—	2	2	no	—
447	C₂²⋊C₈	—	2	2	no	—
448	C₂²⋊C₈	—	2	2	no	—
449	C₂²⋊C₈	—	2	2	no	—
450	C₂²⋊C₈	—	2	2	no	—
451	C₂²⋊C₈	—	2	2	no	—
452	C₂²⋊C₈	—	2	2	no	—
453	C₂²⋊C₈	—	2	2	no	—
454	#97	—	2	2	no	—
455	#97	—	2	2	no	—
456	#97	—	2	2	no	—
457	#97	—	2	2	no	—
458	C₄×C₈	—	2	2	no	—
459	C₄×C₈	—	2	2	no	—
460	C₄×C₈	—	2	2	no	—
461	C₄×C₈	D₄×C₆₁	1	4	yes	complemented
462	#95	C₂×C₄×C₆₁	1	1	yes	characteristic
463	#95	C₂×C₄×C₆₁	1	1	yes	characteristic
464	#95	C₂×C₄×C₆₁	1	1	yes	characteristic
465	#95	C₂×C₄×C₆₁	1	1	yes	characteristic
466	#95	C₂×C₄×C₆₁	1	1	yes	characteristic
467	#95	C₂×C₄×C₆₁	1	1	yes	characteristic
468	#95	C₂×C₄×C₆₁	1	1	yes	characteristic
469	#95	C₂×C₄×C₆₁	1	1	yes	characteristic
470	#95	C₂×C₄×C₆₁	1	1	yes	characteristic
471	#95	C₂×C₄×C₆₁	1	1	yes	characteristic
472	C₂⁴	C₂²×C₄×C₆₁	1	1	yes	characteristic
473	C₂⁴	C₂²×C₄×C₆₁	1	1	yes	characteristic
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	2	no	—
476	C₂×D₄	—	4	1	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	4	1	no	—
494	C₂²×C₄	—	4	1	no	—
495	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
496	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
497	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
498	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
499	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
500	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
501	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
502	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
503	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
504	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
505	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
506	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
507	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
529	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
530	C₂×C₈	#41×C₆₁	1	2	yes	—
531	C₂×C₈	#41×C₆₁	1	2	yes	—
532	C₄⋊C₄	—	2	2	no	—
533	C₄⋊C₄	—	2	2	no	—
534	C₄⋊C₄	—	2	2	no	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	4	1	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	2	2	no	—
542	C₂²⋊C₄	—	2	2	no	—
543	C₂²⋊C₄	—	4	1	no	—
544	C₂²⋊C₄	—	4	1	no	—
545	C₄²	—	2	2	no	—
546	C₄²	—	2	2	no	—
547	C₄²	—	2	1	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	2	1	no	—
553	C₄²	C₂×D₄×C₆₁	1	2	yes	—
554	C₄²	#41×C₆₁	1	2	yes	—
555	C₄²	#41×C₆₁	1	2	yes	—
556	C₄²	#41×C₆₁	1	2	yes	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	—	2	1	no	—
570	C₂³	#131×C₆₁	1	2	yes	—
571	C₂³	C₂³×C₄×C₆₁	1	1	yes	characteristic
572	D₄	—	4	4	no	—
573	C₂×C₄	—	2	8	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	4	4	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	#117×C₆₁	1	2	yes	—
615	C₂×C₄	#117×C₆₁	1	2	yes	—
616	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
617	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
618	C₂×C₄	#131×C₆₁	1	2	yes	—
619	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
620	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
621	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
622	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
623	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
624	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
625	C₈	—	2	2	no	—
626	C₈	—	2	2	no	—
627	C₈	—	2	2	no	—
628	C₈	—	2	2	no	—
629	C₈	—	4	1	no	—
630	C₈	—	4	1	no	—
631	C₈	—	4	1	no	—
632	C₈	—	4	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	1	no	—
641	C₂²	—	4	1	no	—
642	C₂²	—	4	1	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	1	no	—
647	C₂²	C₂×#117×C₆₁	1	1	yes	characteristic
648	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
649	C₂²	C₄×#41×C₆₁	1	1	yes	characteristic
650	C₂²	C₂×#131×C₆₁	1	1	yes	characteristic
651	C₂²	C₂×#131×C₆₁	1	1	yes	characteristic
652	C₂²	C₆₁×#568	1	1	yes	characteristic
653	C₂²	C₆₁×#568	1	1	yes	characteristic
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	4	1	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	1	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	1	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	1	no	—
666	C₄	C₆₁×#529	1	1	yes	characteristic
667	C₄	C₆₁×#529	1	1	yes	characteristic
668	C₄	C₆₁×#532	1	1	yes	characteristic
669	C₄	C₆₁×#532	1	1	yes	characteristic
670	C₂	—	4	2	no	—
671	C₂	—	8	1	no	—
672	C₂	C₆₁×#2293	1	1	yes	characteristic
673	C₂	C₆₁×#2924	1	1	yes	characteristic
674	C₂	C₆₁×#2925	1	1	yes	characteristic
675	C₂	C₆₁×#2929	1	1	yes	characteristic
676	C₂	C₆₁×#2930	1	1	yes	characteristic
677	C₂	C₆₁×#2968	1	1	yes	characteristic
678	C₂	C₆₁×#2969	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#433	C₂	semidirect
2. C₂×C₆₁×#431	C₂	semidirect
6. C₆₁×#1940	C₂	semidirect
7. C₆₁×#1939	C₂	semidirect
8. C₆₁×#1924	C₂	semidirect
9. C₆₁×#1924	C₂	semidirect
10. C₆₁×#1923	C₂	semidirect
11. C₆₁×#1923	C₂	semidirect
12. C₆₁×#1768	C₂	semidirect
13. C₆₁×#1750	C₂	semidirect
14. C₆₁×#1749	C₂	semidirect
15. C₆₁×#1726	C₂	semidirect
121. C₄×C₈×C₆₁	D₄	semidirect
293. #21272	C₆₁	direct (N × H)
331. C₂×#433	C₂×C₆₁	semidirect
332. C₂×#431	C₂×C₆₁	semidirect
336. #1940	C₂×C₆₁	semidirect
337. #1939	C₂×C₆₁	semidirect
338. #1924	C₂×C₆₁	semidirect
339. #1924	C₂×C₆₁	semidirect
340. #1923	C₂×C₆₁	semidirect
341. #1923	C₂×C₆₁	semidirect
342. #1768	C₂×C₆₁	semidirect
343. #1750	C₂×C₆₁	semidirect
344. #1749	C₂×C₆₁	semidirect
345. #1726	C₂×C₆₁	semidirect
400. C₆₁	#21272	direct (N × H)
461. C₄×C₈	D₄×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×#433	2
C₂×C₆₁×#431	2
C₆₁×#2290	2
C₆₁×#1955	2
C₆₁×#1954	2
C₆₁×#1940	2
C₆₁×#1939	2
C₆₁×#1924	2
C₆₁×#1923	2
C₆₁×#1768	2
C₆₁×#1750	2
C₆₁×#1749	2
C₆₁×#1726	2
#21272	61

Subgroups — C61×#21272 #29524705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#21272 #29524705