Subgroups — C₆₁×#22780 #29526213

Order 15616.

942 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#442	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2354	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2349	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#1936	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1934	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1920	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1919	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1879	C₂	1	1	yes	maximal, characteristic
9	C₆₁×#1879	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#1836	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1804	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1802	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#1771	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1762	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#102×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#117×C₆₁	—	2	1	no	—
22	C₆₁×#442	C₄	1	8	yes	complemented
23	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#390	C₂²	1	1	yes	characteristic
35	C₆₁×#390	C₂²	1	1	yes	characteristic
36	C₆₁×#389	C₂²	1	1	yes	characteristic
37	C₆₁×#389	C₂²	1	1	yes	characteristic
38	C₆₁×#388	—	2	1	no	—
39	C₆₁×#388	—	2	1	no	—
40	C₆₁×#385	—	2	1	no	—
41	C₆₁×#385	—	2	1	no	—
42	C₆₁×#384	C₂²	1	1	yes	characteristic
43	C₆₁×#382	C₂²	1	1	yes	characteristic
44	C₆₁×#380	—	2	1	no	—
45	C₆₁×#380	—	2	1	no	—
46	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
49	C₂×#95×C₆₁	—	2	1	no	—
50	C₆₁×#340	C₂²	1	1	yes	characteristic
51	C₆₁×#340	C₂²	1	1	yes	characteristic
52	C₆₁×#340	C₂²	1	1	yes	characteristic
53	C₆₁×#340	C₂²	1	1	yes	characteristic
54	C₆₁×#340	C₂²	1	1	yes	characteristic
55	C₆₁×#340	C₂²	1	1	yes	characteristic
56	C₆₁×#340	C₂²	1	1	yes	characteristic
57	C₆₁×#340	C₂²	1	1	yes	characteristic
58	C₆₁×#336	C₂²	1	1	yes	characteristic
59	C₆₁×#336	C₂²	1	1	yes	characteristic
60	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₆₁	—	2	1	no	—
63	C₂³×C₄×C₆₁	—	2	1	no	—
64	C₂³×C₄×C₆₁	—	2	1	no	—
65	C₂³×C₄×C₆₁	—	2	1	no	—
66	C₂×D₈×C₆₁	—	2	2	no	—
67	C₂×D₈×C₆₁	—	2	2	no	—
68	C₂×D₈×C₆₁	C₂×C₄	1	4	yes	—
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	C₄×D₄×C₆₁	—	2	2	no	—
74	C₄×D₄×C₆₁	—	2	2	no	—
75	C₄×D₄×C₆₁	—	2	2	no	—
76	C₄×D₄×C₆₁	—	2	2	no	—
77	C₄×D₄×C₆₁	—	4	1	no	—
78	C₄×D₄×C₆₁	—	4	1	no	—
79	C₄×D₄×C₆₁	C₂×C₄	1	4	yes	—
80	C₄×D₄×C₆₁	C₂×C₄	1	4	yes	complemented
81	#117×C₆₁	—	4	4	no	—
82	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
83	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
84	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
85	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
86	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
102	C₂×C₄²×C₆₁	—	2	1	no	—
103	C₂×C₄²×C₆₁	—	2	1	no	—
104	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
107	#106×C₆₁	C₂×C₄	1	4	yes	complemented
108	C₄⋊C₈×C₆₁	—	2	2	no	—
109	#102×C₆₁	—	2	2	no	—
110	#102×C₆₁	—	2	2	no	—
111	#102×C₆₁	—	4	1	no	—
112	#102×C₆₁	—	4	1	no	—
113	#102×C₆₁	C₂×C₄	1	4	yes	—
114	#102×C₆₁	C₂×C₄	1	4	yes	complemented
115	#97×C₆₁	—	4	1	no	—
116	#97×C₆₁	C₂×C₄	1	4	yes	complemented
117	C₄×C₈×C₆₁	—	4	1	no	—
118	#95×C₆₁	—	2	1	no	—
119	#95×C₆₁	—	2	1	no	—
120	#95×C₆₁	—	2	1	no	—
121	#95×C₆₁	—	2	1	no	—
122	#95×C₆₁	—	2	1	no	—
123	#95×C₆₁	—	2	1	no	—
124	#95×C₆₁	D₄	1	1	yes	characteristic
125	#95×C₆₁	D₄	1	1	yes	characteristic
126	C₂⁴×C₆₁	—	2	1	no	—
127	C₂⁴×C₆₁	—	2	1	no	—
128	C₂×D₄×C₆₁	—	2	1	no	—
129	C₂×D₄×C₆₁	—	2	1	no	—
130	C₂×D₄×C₆₁	—	2	1	no	—
131	C₂×D₄×C₆₁	—	2	1	no	—
132	C₂×D₄×C₆₁	—	2	1	no	—
133	C₂×D₄×C₆₁	—	2	1	no	—
134	C₂×D₄×C₆₁	—	2	1	no	—
135	C₂×D₄×C₆₁	—	2	1	no	—
136	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
137	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
138	C₂×D₄×C₆₁	#41	1	2	yes	—
139	C₂×D₄×C₆₁	#41	1	2	yes	—
140	C₂²×C₄×C₆₁	—	2	1	no	—
141	C₂²×C₄×C₆₁	—	2	1	no	—
142	C₂²×C₄×C₆₁	—	2	4	no	—
143	C₂²×C₄×C₆₁	—	2	4	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	—	4	2	no	—
149	C₂²×C₄×C₆₁	—	4	2	no	—
150	C₂²×C₄×C₆₁	—	4	2	no	—
151	C₂²×C₄×C₆₁	—	4	2	no	—
152	C₂²×C₄×C₆₁	—	4	2	no	—
153	C₂²×C₄×C₆₁	—	4	2	no	—
154	C₂²×C₄×C₆₁	—	8	1	no	—
155	C₂²×C₄×C₆₁	—	8	1	no	—
156	C₂²×C₄×C₆₁	—	8	1	no	—
157	C₂²×C₄×C₆₁	—	8	1	no	—
158	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
165	D₈×C₆₁	—	2	8	no	—
166	C₂×C₈×C₆₁	—	2	1	no	—
167	C₂×C₈×C₆₁	—	2	1	no	—
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	C₂²×C₄	1	2	yes	—
177	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
178	C₄⋊C₄×C₆₁	—	2	2	no	—
179	C₄⋊C₄×C₆₁	—	2	1	no	—
180	C₄⋊C₄×C₆₁	—	2	1	no	—
181	C₄⋊C₄×C₆₁	—	2	1	no	—
182	C₄⋊C₄×C₆₁	—	2	1	no	—
183	C₄⋊C₄×C₆₁	—	2	1	no	—
184	C₄⋊C₄×C₆₁	—	2	1	no	—
185	C₄⋊C₄×C₆₁	—	2	1	no	—
186	C₄⋊C₄×C₆₁	—	2	1	no	—
187	C₄⋊C₄×C₆₁	—	2	1	no	—
188	C₄⋊C₄×C₆₁	—	2	1	no	—
189	C₄⋊C₄×C₆₁	—	4	1	no	—
190	C₄⋊C₄×C₆₁	—	4	2	no	—
191	C₄⋊C₄×C₆₁	—	8	1	no	—
192	C₄⋊C₄×C₆₁	—	8	1	no	—
193	C₄⋊C₄×C₆₁	—	8	1	no	—
194	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
195	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
196	C₂²⋊C₄×C₆₁	—	2	4	no	—
197	C₂²⋊C₄×C₆₁	—	2	4	no	—
198	C₂²⋊C₄×C₆₁	—	4	2	no	—
199	C₂²⋊C₄×C₆₁	—	4	2	no	—
200	C₂²⋊C₄×C₆₁	—	4	2	no	—
201	C₂²⋊C₄×C₆₁	—	4	2	no	—
202	C₂²⋊C₄×C₆₁	—	8	1	no	—
203	C₂²⋊C₄×C₆₁	—	8	1	no	—
204	C₄²×C₆₁	—	2	1	no	—
205	C₄²×C₆₁	—	2	1	no	—
206	C₄²×C₆₁	—	2	1	no	—
207	C₄²×C₆₁	—	2	1	no	—
208	C₄²×C₆₁	—	4	2	no	—
209	C₄²×C₆₁	—	4	2	no	—
210	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
211	C₄²×C₆₁	#41	1	2	yes	—
212	C₂³×C₆₁	—	2	2	no	—
213	C₂³×C₆₁	—	2	2	no	—
214	C₂³×C₆₁	—	2	2	no	—
215	C₂³×C₆₁	—	2	2	no	—
216	C₂³×C₆₁	—	4	1	no	—
217	C₂³×C₆₁	—	4	1	no	—
218	C₂³×C₆₁	—	4	1	no	—
219	C₂³×C₆₁	—	4	1	no	—
220	C₂³×C₆₁	—	4	1	no	—
221	C₂³×C₆₁	—	4	1	no	—
222	C₂³×C₆₁	—	4	1	no	—
223	C₂³×C₆₁	—	4	1	no	—
224	C₂³×C₆₁	—	4	1	no	—
225	C₂³×C₆₁	—	4	1	no	—
226	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
227	D₄×C₆₁	—	2	2	no	—
228	D₄×C₆₁	—	2	2	no	—
229	D₄×C₆₁	—	2	2	no	—
230	D₄×C₆₁	—	2	2	no	—
231	D₄×C₆₁	—	2	2	no	—
232	D₄×C₆₁	—	4	1	no	—
233	D₄×C₆₁	—	4	1	no	—
234	D₄×C₆₁	#117	1	4	yes	complemented
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	2	no	—
242	C₂×C₄×C₆₁	—	2	2	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	—	4	8	no	—
253	C₂×C₄×C₆₁	—	4	1	no	—
254	C₂×C₄×C₆₁	—	4	1	no	—
255	C₂×C₄×C₆₁	—	4	1	no	—
256	C₂×C₄×C₆₁	—	4	1	no	—
257	C₂×C₄×C₆₁	—	4	1	no	—
258	C₂×C₄×C₆₁	—	4	1	no	—
259	C₂×C₄×C₆₁	—	4	1	no	—
260	C₂×C₄×C₆₁	—	4	1	no	—
261	C₂×C₄×C₆₁	—	4	1	no	—
262	C₂×C₄×C₆₁	—	4	1	no	—
263	C₂×C₄×C₆₁	—	4	1	no	—
264	C₂×C₄×C₆₁	—	4	1	no	—
265	C₂×C₄×C₆₁	—	4	1	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	—	8	4	no	—
270	C₂×C₄×C₆₁	—	8	4	no	—
271	C₂×C₄×C₆₁	—	8	4	no	—
272	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
273	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
274	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
275	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
276	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
277	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
278	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
279	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
280	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
281	C₈×C₆₁	—	2	2	no	—
282	C₈×C₆₁	—	2	2	no	—
283	C₈×C₆₁	—	4	1	no	—
284	C₈×C₆₁	—	4	1	no	—
285	#22780	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
286	C₂²×C₆₁	—	2	4	no	—
287	C₂²×C₆₁	—	4	2	no	—
288	C₂²×C₆₁	—	4	2	no	—
289	C₂²×C₆₁	—	4	2	no	—
290	C₂²×C₆₁	—	4	2	no	—
291	C₂²×C₆₁	—	4	2	no	—
292	C₂²×C₆₁	—	4	2	no	—
293	C₂²×C₆₁	—	4	2	no	—
294	C₂²×C₆₁	—	4	2	no	—
295	C₂²×C₆₁	—	4	2	no	—
296	C₂²×C₆₁	—	8	1	no	—
297	C₂²×C₆₁	—	8	1	no	—
298	C₂²×C₆₁	—	8	1	no	—
299	C₂²×C₆₁	—	8	1	no	—
300	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
301	C₂²×C₆₁	#546	1	1	yes	characteristic
302	C₂²×C₆₁	#548	1	1	yes	characteristic
303	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
304	C₂²×C₆₁	#575	1	1	yes	characteristic
305	C₂²×C₆₁	#576	1	1	yes	characteristic
306	C₂²×C₆₁	#577	1	1	yes	characteristic
307	C₄×C₆₁	—	2	2	no	—
308	C₄×C₆₁	—	2	2	no	—
309	C₄×C₆₁	—	2	2	no	—
310	C₄×C₆₁	—	4	2	no	—
311	C₄×C₆₁	—	4	2	no	—
312	C₄×C₆₁	—	4	1	no	—
313	C₄×C₆₁	—	4	1	no	—
314	C₄×C₆₁	—	4	1	no	—
315	C₄×C₆₁	—	8	1	no	—
316	C₄×C₆₁	—	8	1	no	—
317	C₄×C₆₁	—	8	1	no	—
318	C₄×C₆₁	—	8	1	no	—
319	C₄×C₆₁	C₂×#117	1	1	yes	characteristic
320	C₄×C₆₁	#520	1	1	yes	characteristic
321	C₄×C₆₁	#552	1	1	yes	characteristic
322	C₄×C₆₁	#553	1	1	yes	characteristic
323	C₂×#442	C₂×C₆₁	1	1	yes	characteristic
324	#2354	C₂×C₆₁	1	1	yes	characteristic, complemented
325	#2349	C₂×C₆₁	1	1	yes	characteristic, complemented
326	#1936	C₂×C₆₁	1	1	yes	characteristic, complemented
327	#1934	C₂×C₆₁	1	1	yes	characteristic, complemented
328	#1920	C₂×C₆₁	1	1	yes	characteristic, complemented
329	#1919	C₂×C₆₁	1	1	yes	characteristic, complemented
330	#1879	C₂×C₆₁	1	1	yes	characteristic
331	#1879	C₂×C₆₁	1	1	yes	characteristic
332	#1836	C₂×C₆₁	1	1	yes	characteristic, complemented
333	#1804	C₂×C₆₁	1	1	yes	characteristic, complemented
334	#1802	C₂×C₆₁	1	1	yes	characteristic, complemented
335	#1771	C₂×C₆₁	1	1	yes	characteristic, complemented
336	#1762	C₂×C₆₁	1	1	yes	characteristic, complemented
337	C₄×#102	C₂×C₆₁	1	1	yes	characteristic, complemented
338	C₂×C₆₁	—	4	4	no	—
339	C₂×C₆₁	—	8	2	no	—
340	C₂×C₆₁	#2352	1	1	yes	characteristic
341	C₂×C₆₁	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
342	C₂×C₆₁	#2946	1	1	yes	characteristic
343	C₂×C₆₁	#3306	1	1	yes	characteristic
344	C₂×C₆₁	#3319	1	1	yes	characteristic
345	C₂×C₆₁	#3366	1	1	yes	characteristic
346	C₂×C₆₁	#3376	1	1	yes	characteristic
347	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
348	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
349	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
350	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
351	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
352	C₂×#117	—	2	1	no	—
353	#442	C₄×C₆₁	1	8	yes	complemented
354	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
355	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
356	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
357	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
358	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
359	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
360	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
361	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
362	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
363	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
364	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
365	#390	C₂²×C₆₁	1	1	yes	characteristic
366	#390	C₂²×C₆₁	1	1	yes	characteristic
367	#389	C₂²×C₆₁	1	1	yes	characteristic
368	#389	C₂²×C₆₁	1	1	yes	characteristic
369	#388	—	2	1	no	—
370	#388	—	2	1	no	—
371	#385	—	2	1	no	—
372	#385	—	2	1	no	—
373	#384	C₂²×C₆₁	1	1	yes	characteristic
374	#382	C₂²×C₆₁	1	1	yes	characteristic
375	#380	—	2	1	no	—
376	#380	—	2	1	no	—
377	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
378	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
379	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
380	C₂×#95	—	2	1	no	—
381	#340	C₂²×C₆₁	1	1	yes	characteristic
382	#340	C₂²×C₆₁	1	1	yes	characteristic
383	#340	C₂²×C₆₁	1	1	yes	characteristic
384	#340	C₂²×C₆₁	1	1	yes	characteristic
385	#340	C₂²×C₆₁	1	1	yes	characteristic
386	#340	C₂²×C₆₁	1	1	yes	characteristic
387	#340	C₂²×C₆₁	1	1	yes	characteristic
388	#340	C₂²×C₆₁	1	1	yes	characteristic
389	#336	C₂²×C₆₁	1	1	yes	characteristic
390	#336	C₂²×C₆₁	1	1	yes	characteristic
391	C₆₁	#22780	1	1	yes	characteristic, direct product factor, Sylow
392	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
393	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
394	C₂³×C₄	—	2	1	no	—
395	C₂³×C₄	—	2	1	no	—
396	C₂³×C₄	—	2	1	no	—
397	C₂³×C₄	—	2	1	no	—
398	C₂×D₈	—	2	2	no	—
399	C₂×D₈	—	2	2	no	—
400	C₂×D₈	C₂×C₄×C₆₁	1	4	yes	—
401	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
402	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
403	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
404	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	4	1	no	—
410	C₄×D₄	—	4	1	no	—
411	C₄×D₄	C₂×C₄×C₆₁	1	4	yes	—
412	C₄×D₄	C₂×C₄×C₆₁	1	4	yes	complemented
413	#117	—	4	4	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
419	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₄²	—	2	1	no	—
435	C₂×C₄²	—	2	1	no	—
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	#106	C₂×C₄×C₆₁	1	4	yes	complemented
440	C₄⋊C₈	—	2	2	no	—
441	#102	—	2	2	no	—
442	#102	—	2	2	no	—
443	#102	—	4	1	no	—
444	#102	—	4	1	no	—
445	#102	C₂×C₄×C₆₁	1	4	yes	—
446	#102	C₂×C₄×C₆₁	1	4	yes	complemented
447	#97	—	4	1	no	—
448	#97	C₂×C₄×C₆₁	1	4	yes	complemented
449	C₄×C₈	—	4	1	no	—
450	#95	—	2	1	no	—
451	#95	—	2	1	no	—
452	#95	—	2	1	no	—
453	#95	—	2	1	no	—
454	#95	—	2	1	no	—
455	#95	—	2	1	no	—
456	#95	D₄×C₆₁	1	1	yes	characteristic
457	#95	D₄×C₆₁	1	1	yes	characteristic
458	C₂⁴	—	2	1	no	—
459	C₂⁴	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
469	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
470	C₂×D₄	#41×C₆₁	1	2	yes	—
471	C₂×D₄	#41×C₆₁	1	2	yes	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	4	2	no	—
481	C₂²×C₄	—	4	2	no	—
482	C₂²×C₄	—	4	2	no	—
483	C₂²×C₄	—	4	2	no	—
484	C₂²×C₄	—	4	2	no	—
485	C₂²×C₄	—	4	2	no	—
486	C₂²×C₄	—	8	1	no	—
487	C₂²×C₄	—	8	1	no	—
488	C₂²×C₄	—	8	1	no	—
489	C₂²×C₄	—	8	1	no	—
490	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
491	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
492	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
496	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
497	D₈	—	2	8	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
509	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	4	1	no	—
522	C₄⋊C₄	—	4	2	no	—
523	C₄⋊C₄	—	8	1	no	—
524	C₄⋊C₄	—	8	1	no	—
525	C₄⋊C₄	—	8	1	no	—
526	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
527	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
528	C₂²⋊C₄	—	2	4	no	—
529	C₂²⋊C₄	—	2	4	no	—
530	C₂²⋊C₄	—	4	2	no	—
531	C₂²⋊C₄	—	4	2	no	—
532	C₂²⋊C₄	—	4	2	no	—
533	C₂²⋊C₄	—	4	2	no	—
534	C₂²⋊C₄	—	8	1	no	—
535	C₂²⋊C₄	—	8	1	no	—
536	C₄²	—	2	1	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	1	no	—
540	C₄²	—	4	2	no	—
541	C₄²	—	4	2	no	—
542	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
543	C₄²	#41×C₆₁	1	2	yes	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	4	1	no	—
550	C₂³	—	4	1	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	4	1	no	—
554	C₂³	—	4	1	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
559	D₄	—	2	2	no	—
560	D₄	—	2	2	no	—
561	D₄	—	2	2	no	—
562	D₄	—	2	2	no	—
563	D₄	—	2	2	no	—
564	D₄	—	4	1	no	—
565	D₄	—	4	1	no	—
566	D₄	#117×C₆₁	1	4	yes	complemented
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	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	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	4	8	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	8	4	no	—
602	C₂×C₄	—	8	4	no	—
603	C₂×C₄	—	8	4	no	—
604	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
605	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
606	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
607	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
608	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
609	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
610	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
611	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
612	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
613	C₈	—	2	2	no	—
614	C₈	—	2	2	no	—
615	C₈	—	4	1	no	—
616	C₈	—	4	1	no	—
617	C₂²	—	2	4	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	4	2	no	—
626	C₂²	—	4	2	no	—
627	C₂²	—	8	1	no	—
628	C₂²	—	8	1	no	—
629	C₂²	—	8	1	no	—
630	C₂²	—	8	1	no	—
631	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
632	C₂²	C₆₁×#546	1	1	yes	characteristic
633	C₂²	C₆₁×#548	1	1	yes	characteristic
634	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
635	C₂²	C₆₁×#575	1	1	yes	characteristic
636	C₂²	C₆₁×#576	1	1	yes	characteristic
637	C₂²	C₆₁×#577	1	1	yes	characteristic
638	C₄	—	2	2	no	—
639	C₄	—	2	2	no	—
640	C₄	—	2	2	no	—
641	C₄	—	4	1	no	—
642	C₄	—	4	1	no	—
643	C₄	—	4	1	no	—
644	C₄	—	4	2	no	—
645	C₄	—	4	2	no	—
646	C₄	—	8	1	no	—
647	C₄	—	8	1	no	—
648	C₄	—	8	1	no	—
649	C₄	—	8	1	no	—
650	C₄	C₂×#117×C₆₁	1	1	yes	characteristic
651	C₄	C₆₁×#520	1	1	yes	characteristic
652	C₄	C₆₁×#552	1	1	yes	characteristic
653	C₄	C₆₁×#553	1	1	yes	characteristic
654	C₂	—	4	4	no	—
655	C₂	—	8	2	no	—
656	C₂	C₆₁×#2352	1	1	yes	characteristic
657	C₂	C₄×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
658	C₂	C₆₁×#2946	1	1	yes	characteristic
659	C₂	C₆₁×#3306	1	1	yes	characteristic
660	C₂	C₆₁×#3319	1	1	yes	characteristic
661	C₂	C₆₁×#3366	1	1	yes	characteristic
662	C₂	C₆₁×#3376	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	C₂²×D₈×C₆₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₄×C₄⋊C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#2354	C₂	semidirect
3. C₆₁×#2349	C₂	semidirect
4. C₆₁×#1936	C₂	semidirect
5. C₆₁×#1934	C₂	semidirect
6. C₆₁×#1920	C₂	semidirect
7. C₆₁×#1919	C₂	semidirect
10. C₆₁×#1836	C₂	semidirect
11. C₆₁×#1804	C₂	semidirect
12. C₆₁×#1802	C₂	semidirect
13. C₆₁×#1771	C₂	semidirect
14. C₆₁×#1762	C₂	semidirect
15. C₄×#102×C₆₁	C₂	semidirect
22. C₆₁×#442	C₄	semidirect
80. C₄×D₄×C₆₁	C₂×C₄	semidirect
107. #106×C₆₁	C₂×C₄	semidirect
114. #102×C₆₁	C₂×C₄	semidirect
116. #97×C₆₁	C₂×C₄	semidirect
234. D₄×C₆₁	#117	semidirect
285. #22780	C₆₁	direct (N × H)
324. #2354	C₂×C₆₁	semidirect
325. #2349	C₂×C₆₁	semidirect
326. #1936	C₂×C₆₁	semidirect
327. #1934	C₂×C₆₁	semidirect
328. #1920	C₂×C₆₁	semidirect
329. #1919	C₂×C₆₁	semidirect
332. #1836	C₂×C₆₁	semidirect
333. #1804	C₂×C₆₁	semidirect
334. #1802	C₂×C₆₁	semidirect
335. #1771	C₂×C₆₁	semidirect
336. #1762	C₂×C₆₁	semidirect
337. C₄×#102	C₂×C₆₁	semidirect
353. #442	C₄×C₆₁	semidirect
391. C₆₁	#22780	direct (N × H)
412. C₄×D₄	C₂×C₄×C₆₁	semidirect
439. #106	C₂×C₄×C₆₁	semidirect
446. #102	C₂×C₄×C₆₁	semidirect
448. #97	C₂×C₄×C₆₁	semidirect
566. D₄	#117×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×#442	2
C₆₁×#2354	2
C₆₁×#2349	2
C₆₁×#1936	2
C₆₁×#1934	2
C₆₁×#1920	2
C₆₁×#1919	2
C₆₁×#1879	2
C₆₁×#1836	2
C₆₁×#1804	2
C₆₁×#1802	2
C₆₁×#1771	2
C₆₁×#1762	2
C₄×#102×C₆₁	2
#22780	61

Subgroups — C61×#22780 #29526213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#22780 #29526213