Subgroups — C₆₁×#20493 #29523926

Order 15616.

1158 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#435	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#97×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2290	C₂	1	1	yes	maximal, characteristic
6	C₆₁×#1771	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1770	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1768	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1753	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1752	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1752	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈×C₂²⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#1750	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₂²⋊C₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1726	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×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	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
23	C₆₁×#435	C₄	1	8	yes	complemented
24	C₈×D₄×C₆₁	C₄	1	8	yes	complemented
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	C₆₁×#405	—	2	4	no	—
32	C₂×#97×C₆₁	—	2	4	no	—
33	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×#97×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×#97×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	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
45	C₆₁×#388	C₄	1	2	yes	—
46	C₆₁×#387	C₄	1	2	yes	—
47	C₆₁×#386	C₄	1	2	yes	—
48	C₆₁×#385	C₄	1	2	yes	—
49	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
50	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
51	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
52	C₆₁×#376	C₂²	1	1	yes	characteristic
53	C₆₁×#336	C₂²	1	1	yes	characteristic
54	C₆₁×#336	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	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₆₁	C₂×C₄	1	2	yes	—
61	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
63	C₂×M₁₆×C₆₁	—	2	2	no	—
64	C₂×M₁₆×C₆₁	—	2	2	no	—
65	C₂×M₁₆×C₆₁	C₂×C₄	1	4	yes	complemented
66	C₂²×C₈×C₆₁	—	2	2	no	—
67	C₂²×C₈×C₆₁	—	2	2	no	—
68	C₂²×C₈×C₆₁	—	2	2	no	—
69	C₂²×C₈×C₆₁	—	2	2	no	—
70	C₂²×C₈×C₆₁	—	2	2	no	—
71	C₂²×C₈×C₆₁	—	2	2	no	—
72	C₂²×C₈×C₆₁	C₂×C₄	1	4	yes	—
73	C₂²×C₈×C₆₁	C₂×C₄	1	4	yes	—
74	C₂²×C₈×C₆₁	C₂×C₄	1	4	yes	complemented
75	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
83	C₄×D₄×C₆₁	C₂×C₄	1	4	yes	—
84	C₄×D₄×C₆₁	C₂×C₄	1	4	yes	—
85	#117×C₆₁	—	2	2	no	—
86	#117×C₆₁	—	2	2	no	—
87	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
88	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
89	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
91	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
92	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
93	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₆₁	—	2	2	no	—
96	C₂×C₄²×C₆₁	—	2	2	no	—
97	C₂×C₄²×C₆₁	C₂×C₄	1	2	yes	—
98	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
103	C₄⋊C₈×C₆₁	C₂×C₄	1	4	yes	complemented
104	C₄⋊C₈×C₆₁	C₂×C₄	1	4	yes	complemented
105	C₂²⋊C₈×C₆₁	C₂×C₄	1	4	yes	—
106	C₂²⋊C₈×C₆₁	C₂×C₄	1	4	yes	—
107	C₂²⋊C₈×C₆₁	C₂×C₄	1	4	yes	complemented
108	C₂²⋊C₈×C₆₁	C₂×C₄	1	4	yes	complemented
109	#97×C₆₁	—	2	2	no	—
110	#97×C₆₁	—	2	2	no	—
111	#97×C₆₁	—	2	2	no	—
112	#97×C₆₁	—	2	2	no	—
113	#97×C₆₁	—	2	2	no	—
114	#97×C₆₁	C₂×C₄	1	4	yes	complemented
115	#97×C₆₁	D₄	1	4	yes	complemented
116	C₄×C₈×C₆₁	—	2	2	no	—
117	C₄×C₈×C₆₁	—	2	2	no	—
118	C₄×C₈×C₆₁	—	2	2	no	—
119	C₄×C₈×C₆₁	—	2	2	no	—
120	C₄×C₈×C₆₁	C₂×C₄	1	4	yes	complemented
121	#95×C₆₁	C₂×C₄	1	2	yes	—
122	#95×C₆₁	C₂×C₄	1	2	yes	—
123	#95×C₆₁	C₂×C₄	1	2	yes	—
124	#95×C₆₁	C₂×C₄	1	2	yes	—
125	#95×C₆₁	C₂×C₄	1	2	yes	—
126	C₂⁴×C₆₁	C₂²×C₄	1	1	yes	characteristic
127	C₂⁴×C₆₁	C₂²×C₄	1	1	yes	characteristic
128	C₂×D₄×C₆₁	—	2	4	no	—
129	C₂×D₄×C₆₁	C₄²	1	4	yes	—
130	C₂²×C₄×C₆₁	—	2	1	no	—
131	C₂²×C₄×C₆₁	—	2	1	no	—
132	C₂²×C₄×C₆₁	—	2	1	no	—
133	C₂²×C₄×C₆₁	—	2	1	no	—
134	C₂²×C₄×C₆₁	—	2	1	no	—
135	C₂²×C₄×C₆₁	—	2	1	no	—
136	C₂²×C₄×C₆₁	—	2	1	no	—
137	C₂²×C₄×C₆₁	—	2	1	no	—
138	C₂²×C₄×C₆₁	—	2	4	no	—
139	C₂²×C₄×C₆₁	—	2	4	no	—
140	C₂²×C₄×C₆₁	—	4	2	no	—
141	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
149	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
150	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
151	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
152	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
153	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
154	M₁₆×C₆₁	—	2	8	no	—
155	C₂×C₈×C₆₁	—	2	1	no	—
156	C₂×C₈×C₆₁	—	2	1	no	—
157	C₂×C₈×C₆₁	—	2	1	no	—
158	C₂×C₈×C₆₁	—	2	1	no	—
159	C₂×C₈×C₆₁	—	2	1	no	—
160	C₂×C₈×C₆₁	—	2	1	no	—
161	C₂×C₈×C₆₁	—	2	1	no	—
162	C₂×C₈×C₆₁	—	2	1	no	—
163	C₂×C₈×C₆₁	—	2	1	no	—
164	C₂×C₈×C₆₁	—	2	1	no	—
165	C₂×C₈×C₆₁	—	2	1	no	—
166	C₂×C₈×C₆₁	—	2	1	no	—
167	C₂×C₈×C₆₁	—	2	8	no	—
168	C₂×C₈×C₆₁	—	2	8	no	—
169	C₂×C₈×C₆₁	—	2	8	no	—
170	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
171	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
172	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
173	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
174	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
175	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
176	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
177	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
178	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
179	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
180	C₂×C₈×C₆₁	#41	1	2	yes	—
181	C₂×C₈×C₆₁	#41	1	2	yes	—
182	C₄⋊C₄×C₆₁	—	2	4	no	—
183	C₄⋊C₄×C₆₁	—	4	2	no	—
184	C₄⋊C₄×C₆₁	C₄²	1	4	yes	—
185	C₂²⋊C₄×C₆₁	—	2	4	no	—
186	C₂²⋊C₄×C₆₁	—	2	4	no	—
187	C₂²⋊C₄×C₆₁	—	4	2	no	—
188	C₂²⋊C₄×C₆₁	C₄²	1	4	yes	—
189	C₂²⋊C₄×C₆₁	C₄²	1	4	yes	—
190	C₄²×C₆₁	—	2	4	no	—
191	C₄²×C₆₁	—	2	1	no	—
192	C₄²×C₆₁	—	2	1	no	—
193	C₄²×C₆₁	—	2	1	no	—
194	C₄²×C₆₁	—	2	1	no	—
195	C₄²×C₆₁	—	2	1	no	—
196	C₄²×C₆₁	—	2	1	no	—
197	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
198	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
199	C₄²×C₆₁	C₂×D₄	1	2	yes	—
200	C₄²×C₆₁	#41	1	2	yes	—
201	C₂³×C₆₁	—	2	1	no	—
202	C₂³×C₆₁	—	2	1	no	—
203	C₂³×C₆₁	—	2	2	no	—
204	C₂³×C₆₁	—	2	1	no	—
205	C₂³×C₆₁	—	2	1	no	—
206	C₂³×C₆₁	—	2	2	no	—
207	C₂³×C₆₁	—	2	2	no	—
208	C₂³×C₆₁	C₂×C₄²	1	2	yes	—
209	C₂³×C₆₁	C₂×C₄²	1	2	yes	—
210	C₂³×C₆₁	#131	1	4	yes	—
211	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
212	D₄×C₆₁	—	2	8	no	—
213	C₂×C₄×C₆₁	—	2	1	no	—
214	C₂×C₄×C₆₁	—	2	1	no	—
215	C₂×C₄×C₆₁	—	2	1	no	—
216	C₂×C₄×C₆₁	—	2	1	no	—
217	C₂×C₄×C₆₁	—	2	2	no	—
218	C₂×C₄×C₆₁	—	2	2	no	—
219	C₂×C₄×C₆₁	—	2	2	no	—
220	C₂×C₄×C₆₁	—	2	2	no	—
221	C₂×C₄×C₆₁	—	2	2	no	—
222	C₂×C₄×C₆₁	—	2	2	no	—
223	C₂×C₄×C₆₁	—	2	2	no	—
224	C₂×C₄×C₆₁	—	2	2	no	—
225	C₂×C₄×C₆₁	—	2	2	no	—
226	C₂×C₄×C₆₁	—	2	2	no	—
227	C₂×C₄×C₆₁	—	2	2	no	—
228	C₂×C₄×C₆₁	—	2	2	no	—
229	C₂×C₄×C₆₁	—	2	2	no	—
230	C₂×C₄×C₆₁	—	2	2	no	—
231	C₂×C₄×C₆₁	—	2	2	no	—
232	C₂×C₄×C₆₁	—	2	2	no	—
233	C₂×C₄×C₆₁	—	2	2	no	—
234	C₂×C₄×C₆₁	—	2	2	no	—
235	C₂×C₄×C₆₁	—	2	2	no	—
236	C₂×C₄×C₆₁	—	2	2	no	—
237	C₂×C₄×C₆₁	—	2	2	no	—
238	C₂×C₄×C₆₁	—	4	8	no	—
239	C₂×C₄×C₆₁	C₂×C₄²	1	2	yes	—
240	C₂×C₄×C₆₁	C₂×C₄²	1	2	yes	—
241	C₂×C₄×C₆₁	C₂×C₄²	1	2	yes	—
242	C₂×C₄×C₆₁	C₂×C₄²	1	2	yes	—
243	C₂×C₄×C₆₁	C₄×D₄	1	4	yes	—
244	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
250	C₈×C₆₁	—	2	2	no	—
251	C₈×C₆₁	—	2	2	no	—
252	C₈×C₆₁	—	2	2	no	—
253	C₈×C₆₁	—	2	2	no	—
254	C₈×C₆₁	—	2	2	no	—
255	C₈×C₆₁	—	2	2	no	—
256	C₈×C₆₁	C₄×D₄	1	4	yes	—
257	C₈×C₆₁	C₄×D₄	1	4	yes	—
258	#20493	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₂²×C₆₁	—	2	2	no	—
260	C₂²×C₆₁	—	2	4	no	—
261	C₂²×C₆₁	—	2	4	no	—
262	C₂²×C₆₁	—	2	2	no	—
263	C₂²×C₆₁	—	2	2	no	—
264	C₂²×C₆₁	—	2	2	no	—
265	C₂²×C₆₁	—	2	2	no	—
266	C₂²×C₆₁	—	4	2	no	—
267	C₂²×C₆₁	—	4	2	no	—
268	C₂²×C₆₁	#405	1	4	yes	complemented
269	C₂²×C₆₁	C₂²×C₄²	1	1	yes	characteristic
270	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
271	C₂²×C₆₁	C₄×#41	1	1	yes	characteristic
272	C₂²×C₆₁	C₂×#131	1	2	yes	—
273	C₂²×C₆₁	#568	1	2	yes	—
274	C₄×C₆₁	—	2	2	no	—
275	C₄×C₆₁	—	2	2	no	—
276	C₄×C₆₁	—	2	4	no	—
277	C₄×C₆₁	—	2	2	no	—
278	C₄×C₆₁	—	2	2	no	—
279	C₄×C₆₁	—	4	2	no	—
280	C₄×C₆₁	—	4	2	no	—
281	C₄×C₆₁	—	4	2	no	—
282	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
283	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
284	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
285	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
286	C₂×#435	C₂×C₆₁	1	1	yes	characteristic
287	C₂×C₈×D₄	C₂×C₆₁	1	1	yes	characteristic
288	C₂×#405	C₂×C₆₁	1	1	yes	characteristic, complemented
289	C₂²×#97	C₂×C₆₁	1	1	yes	characteristic, complemented
290	#2290	C₂×C₆₁	1	1	yes	characteristic
291	#1771	C₂×C₆₁	1	1	yes	characteristic, complemented
292	#1770	C₂×C₆₁	1	1	yes	characteristic, complemented
293	#1768	C₂×C₆₁	1	1	yes	characteristic, complemented
294	#1753	C₂×C₆₁	1	1	yes	characteristic, complemented
295	#1752	C₂×C₆₁	1	1	yes	characteristic, complemented
296	#1752	C₂×C₆₁	1	1	yes	characteristic, complemented
297	C₈×C₂²⋊C₄	C₂×C₆₁	1	1	yes	characteristic, complemented
298	#1750	C₂×C₆₁	1	1	yes	characteristic, complemented
299	C₄×C₂²⋊C₈	C₂×C₆₁	1	1	yes	characteristic, complemented
300	#1726	C₂×C₆₁	1	1	yes	characteristic, complemented
301	C₂×C₆₁	—	2	4	no	—
302	C₂×C₆₁	—	4	2	no	—
303	C₂×C₆₁	C₄²×D₄	1	1	yes	characteristic
304	C₂×C₆₁	C₂×#405	1	1	yes	characteristic
305	C₂×C₆₁	#2875	1	1	yes	characteristic
306	C₂×C₆₁	#2933	1	2	yes	—
307	C₂×C₆₁	#2968	1	2	yes	—
308	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
309	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
310	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
311	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
312	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
313	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
314	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
315	#435	C₄×C₆₁	1	8	yes	complemented
316	C₈×D₄	C₄×C₆₁	1	8	yes	complemented
317	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
318	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
319	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
320	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
321	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
322	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
323	#405	—	2	4	no	—
324	C₂×#97	—	2	4	no	—
325	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
326	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
327	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
328	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
329	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
330	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
331	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
332	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
333	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
334	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
335	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
336	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
337	#388	C₄×C₆₁	1	2	yes	—
338	#387	C₄×C₆₁	1	2	yes	—
339	#386	C₄×C₆₁	1	2	yes	—
340	#385	C₄×C₆₁	1	2	yes	—
341	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
342	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
343	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
344	#376	C₂²×C₆₁	1	1	yes	characteristic
345	#336	C₂²×C₆₁	1	1	yes	characteristic
346	#336	C₂²×C₆₁	1	1	yes	characteristic
347	#336	C₂²×C₆₁	1	1	yes	characteristic
348	#336	C₂²×C₆₁	1	1	yes	characteristic
349	#336	C₂²×C₆₁	1	1	yes	characteristic
350	#336	C₂²×C₆₁	1	1	yes	characteristic
351	C₆₁	#20493	1	1	yes	characteristic, direct product factor, Sylow
352	C₂²×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
353	C₂³×C₄	C₂×C₄×C₆₁	1	2	yes	—
354	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
355	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
356	C₂×M₁₆	—	2	2	no	—
357	C₂×M₁₆	—	2	2	no	—
358	C₂×M₁₆	C₂×C₄×C₆₁	1	4	yes	complemented
359	C₂²×C₈	—	2	2	no	—
360	C₂²×C₈	—	2	2	no	—
361	C₂²×C₈	—	2	2	no	—
362	C₂²×C₈	—	2	2	no	—
363	C₂²×C₈	—	2	2	no	—
364	C₂²×C₈	—	2	2	no	—
365	C₂²×C₈	C₂×C₄×C₆₁	1	4	yes	—
366	C₂²×C₈	C₂×C₄×C₆₁	1	4	yes	—
367	C₂²×C₈	C₂×C₄×C₆₁	1	4	yes	complemented
368	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
369	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
370	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
373	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
374	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
375	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
376	C₄×D₄	C₂×C₄×C₆₁	1	4	yes	—
377	C₄×D₄	C₂×C₄×C₆₁	1	4	yes	—
378	#117	—	2	2	no	—
379	#117	—	2	2	no	—
380	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
381	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
382	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
383	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
384	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
385	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
386	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
388	C₂×C₄²	—	2	2	no	—
389	C₂×C₄²	—	2	2	no	—
390	C₂×C₄²	C₂×C₄×C₆₁	1	2	yes	—
391	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
394	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
396	C₄⋊C₈	C₂×C₄×C₆₁	1	4	yes	complemented
397	C₄⋊C₈	C₂×C₄×C₆₁	1	4	yes	complemented
398	C₂²⋊C₈	C₂×C₄×C₆₁	1	4	yes	—
399	C₂²⋊C₈	C₂×C₄×C₆₁	1	4	yes	—
400	C₂²⋊C₈	C₂×C₄×C₆₁	1	4	yes	complemented
401	C₂²⋊C₈	C₂×C₄×C₆₁	1	4	yes	complemented
402	#97	—	2	2	no	—
403	#97	—	2	2	no	—
404	#97	—	2	2	no	—
405	#97	—	2	2	no	—
406	#97	—	2	2	no	—
407	#97	C₂×C₄×C₆₁	1	4	yes	complemented
408	#97	D₄×C₆₁	1	4	yes	complemented
409	C₄×C₈	—	2	2	no	—
410	C₄×C₈	—	2	2	no	—
411	C₄×C₈	—	2	2	no	—
412	C₄×C₈	—	2	2	no	—
413	C₄×C₈	C₂×C₄×C₆₁	1	4	yes	complemented
414	#95	C₂×C₄×C₆₁	1	2	yes	—
415	#95	C₂×C₄×C₆₁	1	2	yes	—
416	#95	C₂×C₄×C₆₁	1	2	yes	—
417	#95	C₂×C₄×C₆₁	1	2	yes	—
418	#95	C₂×C₄×C₆₁	1	2	yes	—
419	C₂⁴	C₂²×C₄×C₆₁	1	1	yes	characteristic
420	C₂⁴	C₂²×C₄×C₆₁	1	1	yes	characteristic
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	C₄²×C₆₁	1	4	yes	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	4	2	no	—
434	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
435	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
436	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
437	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
438	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
439	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
440	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
441	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
442	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
443	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
444	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
445	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
447	M₁₆	—	2	8	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	8	no	—
461	C₂×C₈	—	2	8	no	—
462	C₂×C₈	—	2	8	no	—
463	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
464	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
465	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
466	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
467	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
468	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
469	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
470	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
471	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
472	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
473	C₂×C₈	#41×C₆₁	1	2	yes	—
474	C₂×C₈	#41×C₆₁	1	2	yes	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	4	2	no	—
477	C₄⋊C₄	C₄²×C₆₁	1	4	yes	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	4	2	no	—
481	C₂²⋊C₄	C₄²×C₆₁	1	4	yes	—
482	C₂²⋊C₄	C₄²×C₆₁	1	4	yes	—
483	C₄²	—	2	4	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
491	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
492	C₄²	C₂×D₄×C₆₁	1	2	yes	—
493	C₄²	#41×C₆₁	1	2	yes	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	C₂×C₄²×C₆₁	1	2	yes	—
502	C₂³	C₂×C₄²×C₆₁	1	2	yes	—
503	C₂³	#131×C₆₁	1	4	yes	—
504	C₂³	C₂³×C₄×C₆₁	1	1	yes	characteristic
505	D₄	—	2	8	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	4	8	no	—
532	C₂×C₄	C₂×C₄²×C₆₁	1	2	yes	—
533	C₂×C₄	C₂×C₄²×C₆₁	1	2	yes	—
534	C₂×C₄	C₂×C₄²×C₆₁	1	2	yes	—
535	C₂×C₄	C₂×C₄²×C₆₁	1	2	yes	—
536	C₂×C₄	C₄×D₄×C₆₁	1	4	yes	—
537	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
538	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
539	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
540	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
541	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
542	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
543	C₈	—	2	2	no	—
544	C₈	—	2	2	no	—
545	C₈	—	2	2	no	—
546	C₈	—	2	2	no	—
547	C₈	—	2	2	no	—
548	C₈	—	2	2	no	—
549	C₈	C₄×D₄×C₆₁	1	4	yes	—
550	C₈	C₄×D₄×C₆₁	1	4	yes	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	4	no	—
554	C₂²	—	2	4	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	C₆₁×#405	1	4	yes	complemented
561	C₂²	C₂²×C₄²×C₆₁	1	1	yes	characteristic
562	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
563	C₂²	C₄×#41×C₆₁	1	1	yes	characteristic
564	C₂²	C₂×#131×C₆₁	1	2	yes	—
565	C₂²	C₆₁×#568	1	2	yes	—
566	C₄	—	2	2	no	—
567	C₄	—	2	2	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	4	no	—
571	C₄	—	4	2	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	2	no	—
574	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
575	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
576	C₄	C₄×#41×C₆₁	1	1	yes	characteristic
577	C₄	C₄×#41×C₆₁	1	1	yes	characteristic
578	C₂	—	2	4	no	—
579	C₂	—	4	2	no	—
580	C₂	C₄²×D₄×C₆₁	1	1	yes	characteristic
581	C₂	C₂×C₆₁×#405	1	1	yes	characteristic
582	C₂	C₆₁×#2875	1	1	yes	characteristic
583	C₂	C₆₁×#2933	1	2	yes	—
584	C₂	C₆₁×#2968	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₁	C₂⁴
commutator	C₂²	C₂²×C₄²×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
socle	C₂³×C₆₁	C₂³×C₄
prime radical	C₂²×D₄×C₆₁	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₆₁×#405	C₂	semidirect
4. C₂²×#97×C₆₁	C₂	semidirect
6. C₆₁×#1771	C₂	semidirect
7. C₆₁×#1770	C₂	semidirect
8. C₆₁×#1768	C₂	semidirect
9. C₆₁×#1753	C₂	semidirect
10. C₆₁×#1752	C₂	semidirect
11. C₆₁×#1752	C₂	semidirect
12. C₈×C₂²⋊C₄×C₆₁	C₂	semidirect
13. C₆₁×#1750	C₂	semidirect
14. C₄×C₂²⋊C₈×C₆₁	C₂	semidirect
15. C₆₁×#1726	C₂	semidirect
23. C₆₁×#435	C₄	semidirect
24. C₈×D₄×C₆₁	C₄	semidirect
65. C₂×M₁₆×C₆₁	C₂×C₄	semidirect
74. C₂²×C₈×C₆₁	C₂×C₄	semidirect
103. C₄⋊C₈×C₆₁	C₂×C₄	semidirect
104. C₄⋊C₈×C₆₁	C₂×C₄	semidirect
107. C₂²⋊C₈×C₆₁	C₂×C₄	semidirect
108. C₂²⋊C₈×C₆₁	C₂×C₄	semidirect
114. #97×C₆₁	C₂×C₄	semidirect
115. #97×C₆₁	D₄	semidirect
120. C₄×C₈×C₆₁	C₂×C₄	semidirect
258. #20493	C₆₁	direct (N × H)
268. C₂²×C₆₁	#405	semidirect
288. C₂×#405	C₂×C₆₁	semidirect
289. C₂²×#97	C₂×C₆₁	semidirect
291. #1771	C₂×C₆₁	semidirect
292. #1770	C₂×C₆₁	semidirect
293. #1768	C₂×C₆₁	semidirect
294. #1753	C₂×C₆₁	semidirect
295. #1752	C₂×C₆₁	semidirect
296. #1752	C₂×C₆₁	semidirect
297. C₈×C₂²⋊C₄	C₂×C₆₁	semidirect
298. #1750	C₂×C₆₁	semidirect
299. C₄×C₂²⋊C₈	C₂×C₆₁	semidirect
300. #1726	C₂×C₆₁	semidirect
315. #435	C₄×C₆₁	semidirect
316. C₈×D₄	C₄×C₆₁	semidirect
351. C₆₁	#20493	direct (N × H)
358. C₂×M₁₆	C₂×C₄×C₆₁	semidirect
367. C₂²×C₈	C₂×C₄×C₆₁	semidirect
396. C₄⋊C₈	C₂×C₄×C₆₁	semidirect
397. C₄⋊C₈	C₂×C₄×C₆₁	semidirect
400. C₂²⋊C₈	C₂×C₄×C₆₁	semidirect
401. C₂²⋊C₈	C₂×C₄×C₆₁	semidirect
407. #97	C₂×C₄×C₆₁	semidirect
408. #97	D₄×C₆₁	semidirect
413. C₄×C₈	C₂×C₄×C₆₁	semidirect
560. C₂²	C₆₁×#405	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#435	2
C₂×C₈×D₄×C₆₁	2
C₂×C₆₁×#405	2
C₂²×#97×C₆₁	2
C₆₁×#2290	2
C₆₁×#1771	2
C₆₁×#1770	2
C₆₁×#1768	2
C₆₁×#1753	2
C₆₁×#1752	2
C₈×C₂²⋊C₄×C₆₁	2
C₆₁×#1750	2
C₄×C₂²⋊C₈×C₆₁	2
C₆₁×#1726	2
#20493	61

Subgroups — C61×#20493 #29523926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#20493 #29523926