Subgroups — C₆₁×#22393 #29525826

Order 15616.

762 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#124×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#1985	C₂	1	2	yes	maximal, complemented
3	C₆₁×#1924	C₂	1	2	yes	maximal, complemented
4	C₆₁×#1923	C₂	1	2	yes	maximal, complemented
5	C₆₁×#1870	C₂	1	2	yes	maximal
6	C₆₁×#1851	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1839	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₄⋊C₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1753	C₂	1	2	yes	maximal, complemented
10	C₂²×M₁₆×C₆₁	C₂²	1	2	yes	—
11	C₂×#124×C₆₁	C₄	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
15	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
17	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
18	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
19	C₂×#97×C₆₁	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₆₁×#391	C₄	1	1	yes	characteristic
23	C₆₁×#390	C₄	1	1	yes	characteristic
24	C₆₁×#388	C₄	1	2	yes	—
25	C₆₁×#388	C₄	1	2	yes	—
26	C₆₁×#382	C₄	1	1	yes	characteristic
27	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
28	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
29	C₄³×C₆₁	C₂²	1	1	yes	characteristic
30	C₆₁×#336	C₂²	1	2	yes	—
31	C₆₁×#336	C₂²	1	2	yes	—
32	C₆₁×#336	C₂²	1	2	yes	—
33	C₆₁×#336	C₂²	1	1	yes	characteristic
34	C₆₁×#336	C₂²	1	2	yes	—
35	C₆₁×#336	C₂²	1	1	yes	characteristic
36	C₆₁×#336	C₂²	1	2	yes	—
37	C₂²×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
40	C₂×M₁₆×C₆₁	—	2	4	no	—
41	C₂×M₁₆×C₆₁	—	4	2	no	—
42	C₂×M₁₆×C₆₁	—	4	2	no	—
43	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
47	#124×C₆₁	—	2	4	no	—
48	C₄×Q₈×C₆₁	—	4	2	no	—
49	C₄×D₄×C₆₁	—	4	2	no	—
50	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
54	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
56	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
57	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
66	C₄⋊C₈×C₆₁	—	2	4	no	—
67	C₄⋊C₈×C₆₁	—	4	2	no	—
68	C₂²⋊C₈×C₆₁	—	2	4	no	—
69	C₂²⋊C₈×C₆₁	—	4	2	no	—
70	C₂²⋊C₈×C₆₁	—	4	2	no	—
71	#97×C₆₁	—	4	2	no	—
72	C₄×C₈×C₆₁	—	4	1	no	—
73	C₄×C₈×C₆₁	—	4	1	no	—
74	#95×C₆₁	C₂×C₄	1	2	yes	—
75	#95×C₆₁	C₂×C₄	1	2	yes	—
76	#95×C₆₁	C₂×C₄	1	2	yes	—
77	#95×C₆₁	C₂×C₄	1	2	yes	—
78	C₂⁴×C₆₁	C₂²×C₄	1	2	yes	—
79	C₂×Q₈×C₆₁	—	2	2	no	—
80	C₂×Q₈×C₆₁	—	4	1	no	—
81	C₂×Q₈×C₆₁	—	4	1	no	—
82	C₂×D₄×C₆₁	—	2	2	no	—
83	C₂×D₄×C₆₁	—	4	1	no	—
84	C₂×D₄×C₆₁	—	4	1	no	—
85	C₂²×C₄×C₆₁	—	2	2	no	—
86	C₂²×C₄×C₆₁	—	2	2	no	—
87	C₂²×C₄×C₆₁	—	2	2	no	—
88	C₂²×C₄×C₆₁	—	2	2	no	—
89	C₂²×C₄×C₆₁	—	2	2	no	—
90	C₂²×C₄×C₆₁	—	2	2	no	—
91	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
101	M₁₆×C₆₁	—	4	8	no	—
102	C₂×C₈×C₆₁	—	2	2	no	—
103	C₂×C₈×C₆₁	—	2	2	no	—
104	C₂×C₈×C₆₁	—	2	2	no	—
105	C₂×C₈×C₆₁	—	2	2	no	—
106	C₂×C₈×C₆₁	—	2	2	no	—
107	C₂×C₈×C₆₁	—	2	2	no	—
108	C₂×C₈×C₆₁	—	2	2	no	—
109	C₂×C₈×C₆₁	—	2	2	no	—
110	C₂×C₈×C₆₁	—	2	2	no	—
111	C₂×C₈×C₆₁	—	2	2	no	—
112	C₂×C₈×C₆₁	—	2	2	no	—
113	C₂×C₈×C₆₁	#41	1	4	yes	—
114	C₄⋊C₄×C₆₁	—	4	1	no	—
115	C₄⋊C₄×C₆₁	—	4	1	no	—
116	C₄⋊C₄×C₆₁	—	4	2	no	—
117	C₂²⋊C₄×C₆₁	—	2	4	no	—
118	C₂²⋊C₄×C₆₁	—	2	4	no	—
119	C₂²⋊C₄×C₆₁	—	2	4	no	—
120	C₂²⋊C₄×C₆₁	—	4	2	no	—
121	C₂²⋊C₄×C₆₁	—	4	2	no	—
122	C₄²×C₆₁	—	2	2	no	—
123	C₄²×C₆₁	—	2	2	no	—
124	C₄²×C₆₁	—	2	1	no	—
125	C₄²×C₆₁	—	2	2	no	—
126	C₄²×C₆₁	—	2	2	no	—
127	C₄²×C₆₁	—	2	2	no	—
128	C₄²×C₆₁	—	2	1	no	—
129	C₄²×C₆₁	—	4	1	no	—
130	C₄²×C₆₁	—	4	1	no	—
131	C₄²×C₆₁	M₁₆	1	4	yes	complemented
132	C₂³×C₆₁	—	2	2	no	—
133	C₂³×C₆₁	—	2	2	no	—
134	C₂³×C₆₁	—	2	2	no	—
135	C₂³×C₆₁	—	2	2	no	—
136	C₂³×C₆₁	—	2	2	no	—
137	C₂³×C₆₁	—	2	2	no	—
138	C₂³×C₆₁	—	2	2	no	—
139	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
140	Q₈×C₆₁	—	4	4	no	—
141	D₄×C₆₁	—	4	4	no	—
142	C₂×C₄×C₆₁	—	2	1	no	—
143	C₂×C₄×C₆₁	—	2	1	no	—
144	C₂×C₄×C₆₁	—	2	1	no	—
145	C₂×C₄×C₆₁	—	2	1	no	—
146	C₂×C₄×C₆₁	—	2	1	no	—
147	C₂×C₄×C₆₁	—	2	1	no	—
148	C₂×C₄×C₆₁	—	2	1	no	—
149	C₂×C₄×C₆₁	—	2	1	no	—
150	C₂×C₄×C₆₁	—	2	1	no	—
151	C₂×C₄×C₆₁	—	2	2	no	—
152	C₂×C₄×C₆₁	—	2	1	no	—
153	C₂×C₄×C₆₁	—	2	2	no	—
154	C₂×C₄×C₆₁	—	2	2	no	—
155	C₂×C₄×C₆₁	—	2	2	no	—
156	C₂×C₄×C₆₁	—	2	2	no	—
157	C₂×C₄×C₆₁	—	2	2	no	—
158	C₂×C₄×C₆₁	—	2	1	no	—
159	C₂×C₄×C₆₁	—	2	2	no	—
160	C₂×C₄×C₆₁	—	2	1	no	—
161	C₂×C₄×C₆₁	—	2	1	no	—
162	C₂×C₄×C₆₁	—	2	1	no	—
163	C₂×C₄×C₆₁	—	2	2	no	—
164	C₂×C₄×C₆₁	—	2	2	no	—
165	C₂×C₄×C₆₁	—	4	2	no	—
166	C₂×C₄×C₆₁	—	4	2	no	—
167	C₂×C₄×C₆₁	—	4	2	no	—
168	C₂×C₄×C₆₁	—	4	2	no	—
169	C₂×C₄×C₆₁	C₂×M₁₆	1	2	yes	—
170	C₂×C₄×C₆₁	C₂×M₁₆	1	2	yes	—
171	C₂×C₄×C₆₁	C₂×M₁₆	1	2	yes	—
172	C₂×C₄×C₆₁	#131	1	2	yes	—
173	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
174	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
176	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
177	C₈×C₆₁	—	2	4	no	—
178	C₈×C₆₁	—	4	2	no	—
179	C₈×C₆₁	—	4	2	no	—
180	C₈×C₆₁	—	4	2	no	—
181	#22393	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂²×C₆₁	—	4	2	no	—
183	C₂²×C₆₁	—	4	2	no	—
184	C₂²×C₆₁	—	4	2	no	—
185	C₂²×C₆₁	—	4	2	no	—
186	C₂²×C₆₁	—	4	2	no	—
187	C₂²×C₆₁	—	4	2	no	—
188	C₂²×C₆₁	—	4	2	no	—
189	C₂²×C₆₁	C₄×#41	1	1	yes	characteristic
190	C₂²×C₆₁	#518	1	1	yes	characteristic
191	C₂²×C₆₁	#520	1	1	yes	characteristic
192	C₂²×C₆₁	C₂²×M₁₆	1	1	yes	characteristic
193	C₂²×C₆₁	C₂×#131	1	1	yes	characteristic
194	C₂²×C₆₁	#568	1	1	yes	characteristic
195	C₂²×C₆₁	#568	1	1	yes	characteristic
196	C₄×C₆₁	—	2	2	no	—
197	C₄×C₆₁	—	2	2	no	—
198	C₄×C₆₁	—	2	2	no	—
199	C₄×C₆₁	—	2	2	no	—
200	C₄×C₆₁	—	4	2	no	—
201	C₄×C₆₁	—	4	1	no	—
202	C₄×C₆₁	—	4	2	no	—
203	C₄×C₆₁	—	4	1	no	—
204	C₄×C₆₁	—	4	2	no	—
205	C₄×C₆₁	#538	1	2	yes	—
206	C₄×C₆₁	#542	1	2	yes	—
207	C₄×#124	C₂×C₆₁	1	1	yes	characteristic
208	#1985	C₂×C₆₁	1	2	yes	complemented
209	#1924	C₂×C₆₁	1	2	yes	complemented
210	#1923	C₂×C₆₁	1	2	yes	complemented
211	#1870	C₂×C₆₁	1	2	yes	—
212	#1851	C₂×C₆₁	1	2	yes	complemented
213	#1839	C₂×C₆₁	1	1	yes	characteristic, complemented
214	C₄×C₄⋊C₈	C₂×C₆₁	1	1	yes	characteristic, complemented
215	#1753	C₂×C₆₁	1	2	yes	complemented
216	C₂×C₆₁	—	8	2	no	—
217	C₂×C₆₁	#2337	1	1	yes	characteristic
218	C₂×C₆₁	#2965	1	1	yes	characteristic
219	C₂×C₆₁	#2967	1	1	yes	characteristic
220	C₂×C₆₁	#2975	1	1	yes	characteristic
221	C₂×C₆₁	#2981	1	1	yes	characteristic
222	C₂×C₆₁	#2989	1	1	yes	characteristic
223	C₂×C₆₁	#2992	1	1	yes	characteristic
224	C₂²×M₁₆	C₂²×C₆₁	1	2	yes	—
225	C₂×#124	C₄×C₆₁	1	1	yes	characteristic
226	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
227	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
228	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
229	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
230	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
231	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
232	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
233	C₂×#97	C₂²×C₆₁	1	2	yes	—
234	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
235	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
236	#391	C₄×C₆₁	1	1	yes	characteristic
237	#390	C₄×C₆₁	1	1	yes	characteristic
238	#388	C₄×C₆₁	1	2	yes	—
239	#388	C₄×C₆₁	1	2	yes	—
240	#382	C₄×C₆₁	1	1	yes	characteristic
241	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
242	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
243	C₄³	C₂²×C₆₁	1	1	yes	characteristic
244	#336	C₂²×C₆₁	1	1	yes	characteristic
245	#336	C₂²×C₆₁	1	2	yes	—
246	#336	C₂²×C₆₁	1	2	yes	—
247	#336	C₂²×C₆₁	1	1	yes	characteristic
248	#336	C₂²×C₆₁	1	2	yes	—
249	#336	C₂²×C₆₁	1	2	yes	—
250	#336	C₂²×C₆₁	1	2	yes	—
251	C₆₁	#22393	1	1	yes	characteristic, direct product factor, Sylow
252	C₂²×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
253	C₂²×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
254	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
255	C₂×M₁₆	—	2	4	no	—
256	C₂×M₁₆	—	4	2	no	—
257	C₂×M₁₆	—	4	2	no	—
258	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
259	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
260	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
261	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
262	#124	—	2	4	no	—
263	C₄×Q₈	—	4	2	no	—
264	C₄×D₄	—	4	2	no	—
265	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
268	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
269	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
270	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
271	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
272	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
273	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
274	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
275	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
276	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
279	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
280	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
281	C₄⋊C₈	—	2	4	no	—
282	C₄⋊C₈	—	4	2	no	—
283	C₂²⋊C₈	—	2	4	no	—
284	C₂²⋊C₈	—	4	2	no	—
285	C₂²⋊C₈	—	4	2	no	—
286	#97	—	4	2	no	—
287	C₄×C₈	—	4	1	no	—
288	C₄×C₈	—	4	1	no	—
289	#95	C₂×C₄×C₆₁	1	2	yes	—
290	#95	C₂×C₄×C₆₁	1	2	yes	—
291	#95	C₂×C₄×C₆₁	1	2	yes	—
292	#95	C₂×C₄×C₆₁	1	2	yes	—
293	C₂⁴	C₂²×C₄×C₆₁	1	2	yes	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×Q₈	—	4	1	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
307	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
308	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
309	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
310	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
311	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
312	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
313	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
314	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
315	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
316	M₁₆	—	4	8	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	#41×C₆₁	1	4	yes	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₂²⋊C₄	—	2	4	no	—
333	C₂²⋊C₄	—	2	4	no	—
334	C₂²⋊C₄	—	2	4	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	4	1	no	—
345	C₄²	—	4	1	no	—
346	C₄²	M₁₆×C₆₁	1	4	yes	complemented
347	C₂³	—	2	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	C₂³×C₄×C₆₁	1	1	yes	characteristic
355	Q₈	—	4	4	no	—
356	D₄	—	4	4	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	C₂×M₁₆×C₆₁	1	2	yes	—
385	C₂×C₄	C₂×M₁₆×C₆₁	1	2	yes	—
386	C₂×C₄	C₂×M₁₆×C₆₁	1	2	yes	—
387	C₂×C₄	#131×C₆₁	1	2	yes	—
388	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
389	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
390	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
391	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
392	C₈	—	2	4	no	—
393	C₈	—	4	2	no	—
394	C₈	—	4	2	no	—
395	C₈	—	4	2	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	C₄×#41×C₆₁	1	1	yes	characteristic
404	C₂²	C₆₁×#518	1	1	yes	characteristic
405	C₂²	C₆₁×#520	1	1	yes	characteristic
406	C₂²	C₂²×M₁₆×C₆₁	1	1	yes	characteristic
407	C₂²	C₂×#131×C₆₁	1	1	yes	characteristic
408	C₂²	C₆₁×#568	1	1	yes	characteristic
409	C₂²	C₆₁×#568	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	1	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	2	no	—
419	C₄	C₆₁×#538	1	2	yes	—
420	C₄	C₆₁×#542	1	2	yes	—
421	C₂	—	8	2	no	—
422	C₂	C₆₁×#2337	1	1	yes	characteristic
423	C₂	C₆₁×#2965	1	1	yes	characteristic
424	C₂	C₆₁×#2967	1	1	yes	characteristic
425	C₂	C₆₁×#2975	1	1	yes	characteristic
426	C₂	C₆₁×#2981	1	1	yes	characteristic
427	C₂	C₆₁×#2989	1	1	yes	characteristic
428	C₂	C₆₁×#2992	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
2. C₆₁×#1985	C₂	semidirect
3. C₆₁×#1924	C₂	semidirect
4. C₆₁×#1923	C₂	semidirect
6. C₆₁×#1851	C₂	semidirect
7. C₆₁×#1839	C₂	semidirect
8. C₄×C₄⋊C₈×C₆₁	C₂	semidirect
9. C₆₁×#1753	C₂	semidirect
131. C₄²×C₆₁	M₁₆	semidirect
181. #22393	C₆₁	direct (N × H)
208. #1985	C₂×C₆₁	semidirect
209. #1924	C₂×C₆₁	semidirect
210. #1923	C₂×C₆₁	semidirect
212. #1851	C₂×C₆₁	semidirect
213. #1839	C₂×C₆₁	semidirect
214. C₄×C₄⋊C₈	C₂×C₆₁	semidirect
215. #1753	C₂×C₆₁	semidirect
251. C₆₁	#22393	direct (N × H)
346. C₄²	M₁₆×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₄×#124×C₆₁	2
C₆₁×#1985	2
C₆₁×#1924	2
C₆₁×#1923	2
C₆₁×#1870	2
C₆₁×#1851	2
C₆₁×#1839	2
C₄×C₄⋊C₈×C₆₁	2
C₆₁×#1753	2
#22393	61

Subgroups — C61×#22393 #29525826

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#22393 #29525826