Subgroups — C₆₁×#36956 #29540389

Order 15616.

2518 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#123×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2849	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2718	C₂	1	4	yes	maximal, complemented
5	C₆₁×#2710	C₂	1	4	yes	maximal, complemented
6	C₆₁×#2706	C₂	1	4	yes	maximal, complemented
7	C₆₁×#2703	C₂	1	4	yes	maximal, complemented
8	C₆₁×#2613	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2561	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#2539	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2534	C₂	1	2	yes	maximal, complemented
12	C₆₁×#2503	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#2501	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#2486	C₂	1	2	yes	maximal, complemented
15	C₆₁×#2312	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
18	C₆₁×#538	—	2	8	no	—
19	C₂×#126×C₆₁	C₂²	1	2	yes	complemented
20	C₂×#124×C₆₁	C₂²	1	2	yes	complemented
21	C₂×#123×C₆₁	—	2	8	no	—
22	C₂×#123×C₆₁	C₂²	1	4	yes	—
23	C₂×#123×C₆₁	C₂²	1	4	yes	—
24	C₂×#123×C₆₁	C₂²	1	2	yes	—
25	C₂×#123×C₆₁	C₂²	1	2	yes	—
26	C₂×#123×C₆₁	C₂²	1	2	yes	—
27	C₂×#123×C₆₁	C₂²	1	2	yes	complemented
28	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#121×C₆₁	C₂²	1	2	yes	complemented
31	C₂×#120×C₆₁	C₂²	1	2	yes	—
32	C₂×#120×C₆₁	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
39	C₆₁×#400	C₂²	1	4	yes	complemented
40	C₆₁×#399	C₂²	1	2	yes	complemented
41	C₆₁×#399	C₂²	1	4	yes	complemented
42	C₆₁×#398	C₂²	1	4	yes	complemented
43	C₆₁×#397	C₂²	1	2	yes	complemented
44	C₆₁×#397	C₂²	1	4	yes	complemented
45	C₆₁×#396	C₂²	1	4	yes	complemented
46	C₆₁×#394	C₂²	1	4	yes	—
47	C₆₁×#394	C₂²	1	4	yes	—
48	C₆₁×#394	C₂²	1	4	yes	complemented
49	C₆₁×#393	C₂²	1	2	yes	complemented
50	C₆₁×#392	C₂²	1	4	yes	—
51	C₆₁×#392	C₂²	1	4	yes	—
52	C₆₁×#392	C₂²	1	2	yes	complemented
53	C₆₁×#391	C₂²	1	2	yes	complemented
54	C₆₁×#390	C₂²	1	4	yes	complemented
55	C₆₁×#390	C₂²	1	2	yes	complemented
56	C₆₁×#389	C₂²	1	4	yes	complemented
57	C₆₁×#388	C₂²	1	4	yes	complemented
58	C₆₁×#388	C₂²	1	4	yes	complemented
59	C₆₁×#388	C₂²	1	4	yes	complemented
60	C₆₁×#388	C₂²	1	4	yes	complemented
61	C₆₁×#386	C₂²	1	4	yes	complemented
62	C₆₁×#386	C₂²	1	4	yes	complemented
63	C₆₁×#386	C₂²	1	4	yes	complemented
64	C₆₁×#385	C₂²	1	4	yes	complemented
65	C₆₁×#385	C₂²	1	4	yes	complemented
66	C₆₁×#384	C₂²	1	2	yes	complemented
67	C₆₁×#382	C₂²	1	2	yes	complemented
68	C₆₁×#381	C₂²	1	2	yes	—
69	C₆₁×#381	C₂²	1	2	yes	—
70	C₆₁×#381	C₂²	1	2	yes	—
71	C₆₁×#380	C₂²	1	2	yes	—
72	C₆₁×#380	C₂²	1	4	yes	complemented
73	C₆₁×#379	C₂²	1	2	yes	—
74	C₆₁×#379	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
77	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
78	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₆₁	—	2	4	no	—
81	C₂²×D₄×C₆₁	—	4	4	no	—
82	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
83	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
84	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
85	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
86	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
88	C₂³×C₄×C₆₁	—	2	4	no	—
89	C₂³×C₄×C₆₁	—	4	4	no	—
90	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
94	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
95	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
97	#126×C₆₁	—	2	8	no	—
98	#124×C₆₁	—	2	8	no	—
99	#123×C₆₁	—	2	8	no	—
100	#123×C₆₁	—	2	16	no	—
101	#123×C₆₁	—	2	16	no	—
102	#123×C₆₁	—	4	4	no	—
103	#123×C₆₁	—	4	4	no	—
104	#123×C₆₁	—	4	4	no	—
105	C₂²⋊Q₈×C₆₁	—	2	4	no	—
106	#121×C₆₁	—	2	4	no	—
107	#121×C₆₁	—	2	8	no	—
108	#120×C₆₁	—	2	8	no	—
109	#120×C₆₁	—	4	4	no	—
110	C₄×D₄×C₆₁	—	2	8	no	—
111	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
112	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
113	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
125	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
126	C₂×C₂²⋊C₄×C₆₁	D₄	1	8	yes	complemented
127	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
147	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
148	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
149	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
150	#95×C₆₁	C₂³	1	2	yes	—
151	#95×C₆₁	C₂³	1	2	yes	—
152	#95×C₆₁	C₂³	1	4	yes	—
153	#95×C₆₁	C₂³	1	4	yes	—
154	#95×C₆₁	C₂³	1	4	yes	—
155	#95×C₆₁	C₂³	1	4	yes	—
156	#95×C₆₁	C₂³	1	4	yes	—
157	#95×C₆₁	C₂³	1	4	yes	—
158	#95×C₆₁	C₂³	1	4	yes	—
159	C₂⁴×C₆₁	—	2	4	no	—
160	C₂⁴×C₆₁	—	2	2	no	—
161	C₂⁴×C₆₁	—	2	4	no	—
162	C₂⁴×C₆₁	—	4	2	no	—
163	C₂⁴×C₆₁	—	4	2	no	—
164	C₂⁴×C₆₁	—	4	2	no	—
165	C₂⁴×C₆₁	—	4	2	no	—
166	C₂⁴×C₆₁	C₂×D₄	1	4	yes	—
167	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
168	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
169	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
170	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
171	C₂×Q₈×C₆₁	—	2	2	no	—
172	C₂×Q₈×C₆₁	—	4	2	no	—
173	C₂×D₄×C₆₁	—	2	4	no	—
174	C₂×D₄×C₆₁	—	2	8	no	—
175	C₂×D₄×C₆₁	—	2	4	no	—
176	C₂×D₄×C₆₁	—	2	4	no	—
177	C₂×D₄×C₆₁	—	2	4	no	—
178	C₂×D₄×C₆₁	—	2	4	no	—
179	C₂×D₄×C₆₁	—	2	2	no	—
180	C₂×D₄×C₆₁	—	4	8	no	—
181	C₂×D₄×C₆₁	—	4	4	no	—
182	C₂×D₄×C₆₁	—	4	2	no	—
183	C₂×D₄×C₆₁	—	4	4	no	—
184	C₂×D₄×C₆₁	—	4	4	no	—
185	C₂×D₄×C₆₁	—	4	4	no	—
186	C₂×D₄×C₆₁	—	4	4	no	—
187	C₂×D₄×C₆₁	—	4	16	no	—
188	C₂²×C₄×C₆₁	—	2	2	no	—
189	C₂²×C₄×C₆₁	—	2	2	no	—
190	C₂²×C₄×C₆₁	—	2	2	no	—
191	C₂²×C₄×C₆₁	—	2	8	no	—
192	C₂²×C₄×C₆₁	—	2	4	no	—
193	C₂²×C₄×C₆₁	—	2	4	no	—
194	C₂²×C₄×C₆₁	—	2	4	no	—
195	C₂²×C₄×C₆₁	—	2	4	no	—
196	C₂²×C₄×C₆₁	—	4	8	no	—
197	C₂²×C₄×C₆₁	—	4	2	no	—
198	C₂²×C₄×C₆₁	—	4	2	no	—
199	C₂²×C₄×C₆₁	—	4	4	no	—
200	C₂²×C₄×C₆₁	—	4	16	no	—
201	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
202	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
203	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
214	C₄⋊C₄×C₆₁	—	2	8	no	—
215	C₄⋊C₄×C₆₁	—	2	4	no	—
216	C₄⋊C₄×C₆₁	—	2	4	no	—
217	C₄⋊C₄×C₆₁	—	2	4	no	—
218	C₄⋊C₄×C₆₁	—	2	4	no	—
219	C₄⋊C₄×C₆₁	—	2	2	no	—
220	C₄⋊C₄×C₆₁	—	2	2	no	—
221	C₄⋊C₄×C₆₁	—	4	4	no	—
222	C₄⋊C₄×C₆₁	—	4	4	no	—
223	C₄⋊C₄×C₆₁	—	4	4	no	—
224	C₄⋊C₄×C₆₁	—	4	4	no	—
225	C₂²⋊C₄×C₆₁	—	2	4	no	—
226	C₂²⋊C₄×C₆₁	—	2	4	no	—
227	C₂²⋊C₄×C₆₁	—	2	4	no	—
228	C₂²⋊C₄×C₆₁	—	2	4	no	—
229	C₂²⋊C₄×C₆₁	—	2	4	no	—
230	C₂²⋊C₄×C₆₁	—	2	8	no	—
231	C₂²⋊C₄×C₆₁	—	2	4	no	—
232	C₂²⋊C₄×C₆₁	—	2	4	no	—
233	C₂²⋊C₄×C₆₁	—	2	4	no	—
234	C₂²⋊C₄×C₆₁	—	2	4	no	—
235	C₂²⋊C₄×C₆₁	—	4	4	no	—
236	C₂²⋊C₄×C₆₁	—	4	4	no	—
237	C₂²⋊C₄×C₆₁	—	4	4	no	—
238	C₂²⋊C₄×C₆₁	—	4	4	no	—
239	C₂²⋊C₄×C₆₁	—	4	4	no	—
240	C₂²⋊C₄×C₆₁	—	4	4	no	—
241	C₂²⋊C₄×C₆₁	—	4	4	no	—
242	C₂²⋊C₄×C₆₁	—	4	4	no	—
243	C₂²⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
244	C₂²⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
245	C₄²×C₆₁	—	2	4	no	—
246	C₄²×C₆₁	—	4	2	no	—
247	C₄²×C₆₁	—	4	2	no	—
248	C₂³×C₆₁	—	2	2	no	—
249	C₂³×C₆₁	—	2	2	no	—
250	C₂³×C₆₁	—	2	8	no	—
251	C₂³×C₆₁	—	2	4	no	—
252	C₂³×C₆₁	—	2	4	no	—
253	C₂³×C₆₁	—	2	4	no	—
254	C₂³×C₆₁	—	2	2	no	—
255	C₂³×C₆₁	—	2	2	no	—
256	C₂³×C₆₁	—	2	2	no	—
257	C₂³×C₆₁	—	2	2	no	—
258	C₂³×C₆₁	—	2	4	no	—
259	C₂³×C₆₁	—	2	2	no	—
260	C₂³×C₆₁	—	2	4	no	—
261	C₂³×C₆₁	—	2	4	no	—
262	C₂³×C₆₁	—	2	4	no	—
263	C₂³×C₆₁	—	2	2	no	—
264	C₂³×C₆₁	—	4	4	no	—
265	C₂³×C₆₁	—	4	4	no	—
266	C₂³×C₆₁	—	4	16	no	—
267	C₂³×C₆₁	—	4	4	no	—
268	C₂³×C₆₁	—	4	4	no	—
269	C₂³×C₆₁	—	4	4	no	—
270	C₂³×C₆₁	—	8	8	no	—
271	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
272	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
273	C₂³×C₆₁	H(5,𝔽₂)	1	4	yes	—
274	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
275	Q₈×C₆₁	—	8	2	no	—
276	D₄×C₆₁	—	4	16	no	—
277	D₄×C₆₁	—	4	8	no	—
278	D₄×C₆₁	—	8	2	no	—
279	D₄×C₆₁	—	8	4	no	—
280	D₄×C₆₁	—	8	4	no	—
281	D₄×C₆₁	—	8	8	no	—
282	C₂×C₄×C₆₁	—	2	2	no	—
283	C₂×C₄×C₆₁	—	2	2	no	—
284	C₂×C₄×C₆₁	—	2	4	no	—
285	C₂×C₄×C₆₁	—	2	2	no	—
286	C₂×C₄×C₆₁	—	2	2	no	—
287	C₂×C₄×C₆₁	—	2	2	no	—
288	C₂×C₄×C₆₁	—	2	2	no	—
289	C₂×C₄×C₆₁	—	2	2	no	—
290	C₂×C₄×C₆₁	—	2	2	no	—
291	C₂×C₄×C₆₁	—	2	4	no	—
292	C₂×C₄×C₆₁	—	2	4	no	—
293	C₂×C₄×C₆₁	—	2	2	no	—
294	C₂×C₄×C₆₁	—	2	4	no	—
295	C₂×C₄×C₆₁	—	2	4	no	—
296	C₂×C₄×C₆₁	—	2	4	no	—
297	C₂×C₄×C₆₁	—	2	2	no	—
298	C₂×C₄×C₆₁	—	2	4	no	—
299	C₂×C₄×C₆₁	—	2	4	no	—
300	C₂×C₄×C₆₁	—	2	4	no	—
301	C₂×C₄×C₆₁	—	2	4	no	—
302	C₂×C₄×C₆₁	—	2	4	no	—
303	C₂×C₄×C₆₁	—	2	4	no	—
304	C₂×C₄×C₆₁	—	4	4	no	—
305	C₂×C₄×C₆₁	—	4	4	no	—
306	C₂×C₄×C₆₁	—	4	16	no	—
307	C₂×C₄×C₆₁	—	4	4	no	—
308	C₂×C₄×C₆₁	—	4	4	no	—
309	C₂×C₄×C₆₁	—	4	4	no	—
310	C₂×C₄×C₆₁	—	8	4	no	—
311	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
312	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
314	#36956	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
315	C₂²×C₆₁	—	2	2	no	—
316	C₂²×C₆₁	—	2	2	no	—
317	C₂²×C₆₁	—	2	8	no	—
318	C₂²×C₆₁	—	2	4	no	—
319	C₂²×C₆₁	—	2	4	no	—
320	C₂²×C₆₁	—	2	4	no	—
321	C₂²×C₆₁	—	4	16	no	—
322	C₂²×C₆₁	—	4	8	no	—
323	C₂²×C₆₁	—	4	2	no	—
324	C₂²×C₆₁	—	4	2	no	—
325	C₂²×C₆₁	—	4	2	no	—
326	C₂²×C₆₁	—	4	2	no	—
327	C₂²×C₆₁	—	4	2	no	—
328	C₂²×C₆₁	—	4	2	no	—
329	C₂²×C₆₁	—	4	4	no	—
330	C₂²×C₆₁	—	4	4	no	—
331	C₂²×C₆₁	—	4	4	no	—
332	C₂²×C₆₁	—	4	4	no	—
333	C₂²×C₆₁	—	8	8	no	—
334	C₂²×C₆₁	#535	1	4	yes	—
335	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
336	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
337	C₂²×C₆₁	#585	1	2	yes	—
338	C₂²×C₆₁	#585	1	2	yes	—
339	C₄×C₆₁	—	2	4	no	—
340	C₄×C₆₁	—	2	2	no	—
341	C₄×C₆₁	—	2	2	no	—
342	C₄×C₆₁	—	4	2	no	—
343	C₄×C₆₁	—	4	2	no	—
344	C₄×C₆₁	—	4	2	no	—
345	C₄×C₆₁	—	4	2	no	—
346	C₄×C₆₁	—	4	2	no	—
347	C₄×C₆₁	—	4	2	no	—
348	C₄×C₆₁	—	4	4	no	—
349	C₄×C₆₁	—	4	4	no	—
350	C₂×#538	C₂×C₆₁	1	1	yes	characteristic, complemented
351	C₂²×#123	C₂×C₆₁	1	1	yes	characteristic, complemented
352	#2849	C₂×C₆₁	1	2	yes	complemented
353	#2718	C₂×C₆₁	1	4	yes	complemented
354	#2710	C₂×C₆₁	1	4	yes	complemented
355	#2706	C₂×C₆₁	1	4	yes	complemented
356	#2703	C₂×C₆₁	1	4	yes	complemented
357	#2613	C₂×C₆₁	1	2	yes	complemented
358	#2561	C₂×C₆₁	1	1	yes	characteristic, complemented
359	#2539	C₂×C₆₁	1	1	yes	characteristic, complemented
360	#2534	C₂×C₆₁	1	2	yes	complemented
361	#2503	C₂×C₆₁	1	1	yes	characteristic, complemented
362	#2501	C₂×C₆₁	1	1	yes	characteristic, complemented
363	#2486	C₂×C₆₁	1	2	yes	complemented
364	#2312	C₂×C₆₁	1	1	yes	characteristic, complemented
365	C₂×C₆₁	—	2	4	no	—
366	C₂×C₆₁	—	4	4	no	—
367	C₂×C₆₁	—	8	2	no	—
368	C₂×C₆₁	—	8	2	no	—
369	C₂×C₆₁	C₂×#535	1	1	yes	characteristic
370	C₂×C₆₁	#3485	1	1	yes	characteristic
371	C₂×C₆₁	#3485	1	1	yes	characteristic
372	C₂×C₆₁	#3533	1	4	yes	—
373	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
374	C₂⁴×C₄	C₂²×C₆₁	1	1	yes	characteristic
375	#538	—	2	8	no	—
376	C₂×#126	C₂²×C₆₁	1	2	yes	complemented
377	C₂×#124	C₂²×C₆₁	1	2	yes	complemented
378	C₂×#123	—	2	8	no	—
379	C₂×#123	C₂²×C₆₁	1	4	yes	—
380	C₂×#123	C₂²×C₆₁	1	4	yes	—
381	C₂×#123	C₂²×C₆₁	1	2	yes	—
382	C₂×#123	C₂²×C₆₁	1	2	yes	—
383	C₂×#123	C₂²×C₆₁	1	2	yes	—
384	C₂×#123	C₂²×C₆₁	1	2	yes	complemented
385	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
386	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
387	C₂×#121	C₂²×C₆₁	1	2	yes	complemented
388	C₂×#120	C₂²×C₆₁	1	2	yes	—
389	C₂×#120	C₂²×C₆₁	1	2	yes	—
390	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
391	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
392	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
393	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
394	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
395	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
396	#400	C₂²×C₆₁	1	4	yes	complemented
397	#399	C₂²×C₆₁	1	4	yes	complemented
398	#399	C₂²×C₆₁	1	2	yes	complemented
399	#398	C₂²×C₆₁	1	4	yes	complemented
400	#397	C₂²×C₆₁	1	2	yes	complemented
401	#397	C₂²×C₆₁	1	4	yes	complemented
402	#396	C₂²×C₆₁	1	4	yes	complemented
403	#394	C₂²×C₆₁	1	4	yes	—
404	#394	C₂²×C₆₁	1	4	yes	—
405	#394	C₂²×C₆₁	1	4	yes	complemented
406	#393	C₂²×C₆₁	1	2	yes	complemented
407	#392	C₂²×C₆₁	1	4	yes	—
408	#392	C₂²×C₆₁	1	4	yes	—
409	#392	C₂²×C₆₁	1	2	yes	complemented
410	#391	C₂²×C₆₁	1	2	yes	complemented
411	#390	C₂²×C₆₁	1	2	yes	complemented
412	#390	C₂²×C₆₁	1	4	yes	complemented
413	#389	C₂²×C₆₁	1	4	yes	complemented
414	#388	C₂²×C₆₁	1	4	yes	complemented
415	#388	C₂²×C₆₁	1	4	yes	complemented
416	#388	C₂²×C₆₁	1	4	yes	complemented
417	#388	C₂²×C₆₁	1	4	yes	complemented
418	#386	C₂²×C₆₁	1	4	yes	complemented
419	#386	C₂²×C₆₁	1	4	yes	complemented
420	#386	C₂²×C₆₁	1	4	yes	complemented
421	#385	C₂²×C₆₁	1	4	yes	complemented
422	#385	C₂²×C₆₁	1	4	yes	complemented
423	#384	C₂²×C₆₁	1	2	yes	complemented
424	#382	C₂²×C₆₁	1	2	yes	complemented
425	#381	C₂²×C₆₁	1	2	yes	—
426	#381	C₂²×C₆₁	1	2	yes	—
427	#381	C₂²×C₆₁	1	2	yes	—
428	#380	C₂²×C₆₁	1	2	yes	—
429	#380	C₂²×C₆₁	1	4	yes	complemented
430	#379	C₂²×C₆₁	1	2	yes	—
431	#379	C₂²×C₆₁	1	2	yes	—
432	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
433	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
434	C₆₁	#36956	1	1	yes	characteristic, direct product factor, Sylow
435	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
436	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
437	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
438	C₂²×D₄	—	2	4	no	—
439	C₂²×D₄	—	4	4	no	—
440	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
441	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
442	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
443	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
444	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
445	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
446	C₂³×C₄	—	2	4	no	—
447	C₂³×C₄	—	4	4	no	—
448	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
449	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
450	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
451	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
452	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
453	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
455	#126	—	2	8	no	—
456	#124	—	2	8	no	—
457	#123	—	2	16	no	—
458	#123	—	2	16	no	—
459	#123	—	2	8	no	—
460	#123	—	4	4	no	—
461	#123	—	4	4	no	—
462	#123	—	4	4	no	—
463	C₂²⋊Q₈	—	2	4	no	—
464	#121	—	2	4	no	—
465	#121	—	2	8	no	—
466	#120	—	2	8	no	—
467	#120	—	4	4	no	—
468	C₄×D₄	—	2	8	no	—
469	C₂×C₄⋊C₄	—	2	4	no	—
470	C₂×C₄⋊C₄	—	2	4	no	—
471	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
472	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
478	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
479	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
480	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
481	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
482	C₂×C₂²⋊C₄	—	2	4	no	—
483	C₂×C₂²⋊C₄	—	2	4	no	—
484	C₂×C₂²⋊C₄	D₄×C₆₁	1	8	yes	complemented
485	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
505	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
506	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
507	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
508	#95	C₂³×C₆₁	1	2	yes	—
509	#95	C₂³×C₆₁	1	2	yes	—
510	#95	C₂³×C₆₁	1	4	yes	—
511	#95	C₂³×C₆₁	1	4	yes	—
512	#95	C₂³×C₆₁	1	4	yes	—
513	#95	C₂³×C₆₁	1	4	yes	—
514	#95	C₂³×C₆₁	1	4	yes	—
515	#95	C₂³×C₆₁	1	4	yes	—
516	#95	C₂³×C₆₁	1	4	yes	—
517	C₂⁴	—	2	4	no	—
518	C₂⁴	—	2	2	no	—
519	C₂⁴	—	2	4	no	—
520	C₂⁴	—	4	2	no	—
521	C₂⁴	—	4	2	no	—
522	C₂⁴	—	4	2	no	—
523	C₂⁴	—	4	2	no	—
524	C₂⁴	C₂×D₄×C₆₁	1	4	yes	—
525	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
526	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
527	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
528	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
529	C₂×Q₈	—	2	2	no	—
530	C₂×Q₈	—	4	2	no	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	2	8	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	4	8	no	—
539	C₂×D₄	—	4	4	no	—
540	C₂×D₄	—	4	2	no	—
541	C₂×D₄	—	4	4	no	—
542	C₂×D₄	—	4	4	no	—
543	C₂×D₄	—	4	4	no	—
544	C₂×D₄	—	4	4	no	—
545	C₂×D₄	—	4	16	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	8	no	—
550	C₂²×C₄	—	2	4	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	2	4	no	—
554	C₂²×C₄	—	4	8	no	—
555	C₂²×C₄	—	4	2	no	—
556	C₂²×C₄	—	4	2	no	—
557	C₂²×C₄	—	4	4	no	—
558	C₂²×C₄	—	4	16	no	—
559	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
560	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
561	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
562	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
563	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
564	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
565	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
570	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
571	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
572	C₄⋊C₄	—	2	8	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	4	4	no	—
580	C₄⋊C₄	—	4	4	no	—
581	C₄⋊C₄	—	4	4	no	—
582	C₄⋊C₄	—	4	4	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	2	8	no	—
589	C₂²⋊C₄	—	2	4	no	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	4	4	no	—
594	C₂²⋊C₄	—	4	4	no	—
595	C₂²⋊C₄	—	4	4	no	—
596	C₂²⋊C₄	—	4	4	no	—
597	C₂²⋊C₄	—	4	4	no	—
598	C₂²⋊C₄	—	4	4	no	—
599	C₂²⋊C₄	—	4	4	no	—
600	C₂²⋊C₄	—	4	4	no	—
601	C₂²⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
602	C₂²⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
603	C₄²	—	2	4	no	—
604	C₄²	—	4	2	no	—
605	C₄²	—	4	2	no	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	8	no	—
609	C₂³	—	2	4	no	—
610	C₂³	—	2	4	no	—
611	C₂³	—	2	4	no	—
612	C₂³	—	2	2	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	2	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	2	4	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	4	no	—
619	C₂³	—	2	4	no	—
620	C₂³	—	2	4	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	4	4	no	—
623	C₂³	—	4	4	no	—
624	C₂³	—	4	16	no	—
625	C₂³	—	4	4	no	—
626	C₂³	—	4	4	no	—
627	C₂³	—	4	4	no	—
628	C₂³	—	8	8	no	—
629	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
630	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
631	C₂³	H(5,𝔽₂)×C₆₁	1	4	yes	—
632	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
633	Q₈	—	8	2	no	—
634	D₄	—	4	16	no	—
635	D₄	—	4	8	no	—
636	D₄	—	8	2	no	—
637	D₄	—	8	4	no	—
638	D₄	—	8	4	no	—
639	D₄	—	8	8	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	4	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	4	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	16	no	—
665	C₂×C₄	—	4	4	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	4	4	no	—
668	C₂×C₄	—	8	4	no	—
669	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
670	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
671	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	8	no	—
675	C₂²	—	2	4	no	—
676	C₂²	—	2	4	no	—
677	C₂²	—	2	4	no	—
678	C₂²	—	4	16	no	—
679	C₂²	—	4	8	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	4	2	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	4	4	no	—
687	C₂²	—	4	4	no	—
688	C₂²	—	4	4	no	—
689	C₂²	—	4	4	no	—
690	C₂²	—	8	8	no	—
691	C₂²	C₆₁×#535	1	4	yes	—
692	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
693	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
694	C₂²	C₆₁×#585	1	2	yes	—
695	C₂²	C₆₁×#585	1	2	yes	—
696	C₄	—	2	4	no	—
697	C₄	—	2	2	no	—
698	C₄	—	2	2	no	—
699	C₄	—	4	2	no	—
700	C₄	—	4	2	no	—
701	C₄	—	4	2	no	—
702	C₄	—	4	2	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	2	no	—
705	C₄	—	4	4	no	—
706	C₄	—	4	4	no	—
707	C₂	—	2	4	no	—
708	C₂	—	4	4	no	—
709	C₂	—	8	2	no	—
710	C₂	—	8	2	no	—
711	C₂	C₂×C₆₁×#535	1	1	yes	characteristic
712	C₂	C₆₁×#3485	1	1	yes	characteristic
713	C₂	C₆₁×#3485	1	1	yes	characteristic
714	C₂	C₆₁×#3533	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#538	C₂	semidirect
2. C₂²×#123×C₆₁	C₂	semidirect
3. C₆₁×#2849	C₂	semidirect
4. C₆₁×#2718	C₂	semidirect
5. C₆₁×#2710	C₂	semidirect
6. C₆₁×#2706	C₂	semidirect
7. C₆₁×#2703	C₂	semidirect
8. C₆₁×#2613	C₂	semidirect
9. C₆₁×#2561	C₂	semidirect
10. C₆₁×#2539	C₂	semidirect
11. C₆₁×#2534	C₂	semidirect
12. C₆₁×#2503	C₂	semidirect
13. C₆₁×#2501	C₂	semidirect
14. C₆₁×#2486	C₂	semidirect
15. C₆₁×#2312	C₂	semidirect
19. C₂×#126×C₆₁	C₂²	semidirect
20. C₂×#124×C₆₁	C₂²	semidirect
27. C₂×#123×C₆₁	C₂²	semidirect
30. C₂×#121×C₆₁	C₂²	semidirect
39. C₆₁×#400	C₂²	semidirect
40. C₆₁×#399	C₂²	semidirect
41. C₆₁×#399	C₂²	semidirect
42. C₆₁×#398	C₂²	semidirect
43. C₆₁×#397	C₂²	semidirect
44. C₆₁×#397	C₂²	semidirect
45. C₆₁×#396	C₂²	semidirect
48. C₆₁×#394	C₂²	semidirect
49. C₆₁×#393	C₂²	semidirect
52. C₆₁×#392	C₂²	semidirect
53. C₆₁×#391	C₂²	semidirect
54. C₆₁×#390	C₂²	semidirect
55. C₆₁×#390	C₂²	semidirect
56. C₆₁×#389	C₂²	semidirect
57. C₆₁×#388	C₂²	semidirect
58. C₆₁×#388	C₂²	semidirect
59. C₆₁×#388	C₂²	semidirect
60. C₆₁×#388	C₂²	semidirect
61. C₆₁×#386	C₂²	semidirect
62. C₆₁×#386	C₂²	semidirect
63. C₆₁×#386	C₂²	semidirect
64. C₆₁×#385	C₂²	semidirect
65. C₆₁×#385	C₂²	semidirect
66. C₆₁×#384	C₂²	semidirect
67. C₆₁×#382	C₂²	semidirect
72. C₆₁×#380	C₂²	semidirect
126. C₂×C₂²⋊C₄×C₆₁	D₄	semidirect
314. #36956	C₆₁	direct (N × H)
350. C₂×#538	C₂×C₆₁	semidirect
351. C₂²×#123	C₂×C₆₁	semidirect
352. #2849	C₂×C₆₁	semidirect
353. #2718	C₂×C₆₁	semidirect
354. #2710	C₂×C₆₁	semidirect
355. #2706	C₂×C₆₁	semidirect
356. #2703	C₂×C₆₁	semidirect
357. #2613	C₂×C₆₁	semidirect
358. #2561	C₂×C₆₁	semidirect
359. #2539	C₂×C₆₁	semidirect
360. #2534	C₂×C₆₁	semidirect
361. #2503	C₂×C₆₁	semidirect
362. #2501	C₂×C₆₁	semidirect
363. #2486	C₂×C₆₁	semidirect
364. #2312	C₂×C₆₁	semidirect
376. C₂×#126	C₂²×C₆₁	semidirect
377. C₂×#124	C₂²×C₆₁	semidirect
384. C₂×#123	C₂²×C₆₁	semidirect
387. C₂×#121	C₂²×C₆₁	semidirect
396. #400	C₂²×C₆₁	semidirect
397. #399	C₂²×C₆₁	semidirect
398. #399	C₂²×C₆₁	semidirect
399. #398	C₂²×C₆₁	semidirect
400. #397	C₂²×C₆₁	semidirect
401. #397	C₂²×C₆₁	semidirect
402. #396	C₂²×C₆₁	semidirect
405. #394	C₂²×C₆₁	semidirect
406. #393	C₂²×C₆₁	semidirect
409. #392	C₂²×C₆₁	semidirect
410. #391	C₂²×C₆₁	semidirect
411. #390	C₂²×C₆₁	semidirect
412. #390	C₂²×C₆₁	semidirect
413. #389	C₂²×C₆₁	semidirect
414. #388	C₂²×C₆₁	semidirect
415. #388	C₂²×C₆₁	semidirect
416. #388	C₂²×C₆₁	semidirect
417. #388	C₂²×C₆₁	semidirect
418. #386	C₂²×C₆₁	semidirect
419. #386	C₂²×C₆₁	semidirect
420. #386	C₂²×C₆₁	semidirect
421. #385	C₂²×C₆₁	semidirect
422. #385	C₂²×C₆₁	semidirect
423. #384	C₂²×C₆₁	semidirect
424. #382	C₂²×C₆₁	semidirect
429. #380	C₂²×C₆₁	semidirect
434. C₆₁	#36956	direct (N × H)
484. C₂×C₂²⋊C₄	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×#538	2
C₂²×#123×C₆₁	2
C₆₁×#2849	2
C₆₁×#2718	2
C₆₁×#2710	2
C₆₁×#2706	2
C₆₁×#2703	2
C₆₁×#2613	2
C₆₁×#2561	2
C₆₁×#2539	2
C₆₁×#2534	2
C₆₁×#2503	2
C₆₁×#2501	2
C₆₁×#2486	2
C₆₁×#2312	2
#36956	61

Subgroups — C61×#36956 #29540389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#36956 #29540389