Subgroups — C₆₁×#36957 #29540390

Order 15616.

2586 conjugacy classes of subgroups.

The subgroup lattice has 754 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×#124×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2854	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2715	C₂	1	4	yes	maximal, complemented
6	C₆₁×#2712	C₂	1	4	yes	maximal, complemented
7	C₆₁×#2676	C₂	1	4	yes	maximal, complemented
8	C₆₁×#2672	C₂	1	4	yes	maximal, complemented
9	C₆₁×#2626	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#2617	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2534	C₂	1	2	yes	maximal, complemented
12	C₆₁×#2412	C₂	1	2	yes	maximal, complemented
13	C₆₁×#2410	C₂	1	2	yes	maximal, complemented
14	C₆₁×#2409	C₂	1	2	yes	maximal, complemented
15	C₆₁×#2315	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂³×D₄×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	—	2	8	no	—
21	C₂×#124×C₆₁	C₂²	1	4	yes	—
22	C₂×#124×C₆₁	C₂²	1	4	yes	—
23	C₂×#124×C₆₁	C₂²	1	2	yes	complemented
24	C₂×#123×C₆₁	C₂²	1	2	yes	—
25	C₂×#123×C₆₁	C₂²	1	2	yes	complemented
26	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	4	yes	complemented
28	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#121×C₆₁	C₂²	1	4	yes	—
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×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
38	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
40	C₆₁×#399	C₂²	1	2	yes	complemented
41	C₆₁×#397	C₂²	1	2	yes	complemented
42	C₆₁×#397	C₂²	1	4	yes	complemented
43	C₆₁×#396	C₂²	1	4	yes	complemented
44	C₆₁×#396	C₂²	1	4	yes	complemented
45	C₆₁×#395	C₂²	1	4	yes	complemented
46	C₆₁×#394	C₂²	1	4	yes	—
47	C₆₁×#394	C₂²	1	4	yes	complemented
48	C₆₁×#394	C₂²	1	4	yes	complemented
49	C₆₁×#394	C₂²	1	4	yes	complemented
50	C₆₁×#393	C₂²	1	2	yes	complemented
51	C₆₁×#393	C₂²	1	4	yes	complemented
52	C₆₁×#392	C₂²	1	4	yes	—
53	C₆₁×#392	C₂²	1	2	yes	complemented
54	C₆₁×#391	C₂²	1	2	yes	complemented
55	C₆₁×#391	C₂²	1	4	yes	complemented
56	C₆₁×#390	C₂²	1	2	yes	complemented
57	C₆₁×#389	C₂²	1	2	yes	complemented
58	C₆₁×#389	C₂²	1	2	yes	complemented
59	C₆₁×#388	C₂²	1	4	yes	complemented
60	C₆₁×#388	C₂²	1	4	yes	complemented
61	C₆₁×#387	C₂²	1	4	yes	complemented
62	C₆₁×#386	C₂²	1	2	yes	—
63	C₆₁×#386	C₂²	1	2	yes	—
64	C₆₁×#386	C₂²	1	4	yes	—
65	C₆₁×#386	C₂²	1	4	yes	complemented
66	C₆₁×#386	C₂²	1	4	yes	complemented
67	C₆₁×#385	C₂²	1	2	yes	—
68	C₆₁×#385	C₂²	1	2	yes	—
69	C₆₁×#385	C₂²	1	4	yes	complemented
70	C₆₁×#385	C₂²	1	4	yes	complemented
71	C₆₁×#381	C₂²	1	2	yes	—
72	C₆₁×#380	C₂²	1	2	yes	—
73	C₆₁×#380	C₂²	1	1	yes	characteristic
74	C₆₁×#380	C₂²	1	1	yes	characteristic
75	C₆₁×#380	C₂²	1	4	yes	complemented
76	C₆₁×#379	C₂²	1	2	yes	—
77	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
78	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₆₁	—	2	4	no	—
80	C₂²×Q₈×C₆₁	—	4	4	no	—
81	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
82	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₆₁	—	2	4	no	—
84	C₂²×D₄×C₆₁	—	4	4	no	—
85	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
86	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
87	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
88	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
90	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
91	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
95	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
96	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
98	#126×C₆₁	—	2	8	no	—
99	#124×C₆₁	—	2	8	no	—
100	#124×C₆₁	—	2	16	no	—
101	#124×C₆₁	—	2	16	no	—
102	#123×C₆₁	—	2	8	no	—
103	#123×C₆₁	—	4	4	no	—
104	C₂²⋊Q₈×C₆₁	—	2	4	no	—
105	C₂²⋊Q₈×C₆₁	—	4	8	no	—
106	#121×C₆₁	—	2	4	no	—
107	#121×C₆₁	—	2	8	no	—
108	#121×C₆₁	—	4	8	no	—
109	#120×C₆₁	—	2	8	no	—
110	#120×C₆₁	—	4	4	no	—
111	C₄×D₄×C₆₁	—	2	8	no	—
112	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
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	4	yes	—
120	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
123	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
124	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
125	C₂×C₂²⋊C₄×C₆₁	—	4	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	4	yes	—
132	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	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	2	yes	—
138	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	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	—	2	4	no	—
148	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
149	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
150	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
151	#95×C₆₁	C₂³	1	4	yes	—
152	#95×C₆₁	C₂³	1	2	yes	—
153	#95×C₆₁	C₂³	1	2	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	#95×C₆₁	C₂³	1	4	yes	—
160	C₂⁴×C₆₁	—	2	2	no	—
161	C₂⁴×C₆₁	—	2	2	no	—
162	C₂⁴×C₆₁	—	2	2	no	—
163	C₂⁴×C₆₁	—	2	2	no	—
164	C₂⁴×C₆₁	—	2	2	no	—
165	C₂⁴×C₆₁	—	4	2	no	—
166	C₂⁴×C₆₁	—	4	2	no	—
167	C₂⁴×C₆₁	—	4	2	no	—
168	C₂⁴×C₆₁	—	4	2	no	—
169	C₂⁴×C₆₁	C₂×D₄	1	4	yes	—
170	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
171	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
172	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
173	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
174	C₂×Q₈×C₆₁	—	2	8	no	—
175	C₂×Q₈×C₆₁	—	2	2	no	—
176	C₂×Q₈×C₆₁	—	2	8	no	—
177	C₂×Q₈×C₆₁	—	4	4	no	—
178	C₂×Q₈×C₆₁	—	4	2	no	—
179	C₂×Q₈×C₆₁	—	4	16	no	—
180	C₂×D₄×C₆₁	—	2	4	no	—
181	C₂×D₄×C₆₁	—	2	8	no	—
182	C₂×D₄×C₆₁	—	2	4	no	—
183	C₂×D₄×C₆₁	—	2	4	no	—
184	C₂×D₄×C₆₁	—	2	4	no	—
185	C₂×D₄×C₆₁	—	2	4	no	—
186	C₂×D₄×C₆₁	—	2	2	no	—
187	C₂×D₄×C₆₁	—	2	8	no	—
188	C₂×D₄×C₆₁	—	4	4	no	—
189	C₂×D₄×C₆₁	—	4	16	no	—
190	C₂×D₄×C₆₁	—	4	4	no	—
191	C₂×D₄×C₆₁	—	4	4	no	—
192	C₂×D₄×C₆₁	—	4	4	no	—
193	C₂×D₄×C₆₁	—	4	2	no	—
194	C₂×D₄×C₆₁	—	4	4	no	—
195	C₂×D₄×C₆₁	—	4	4	no	—
196	C₂²×C₄×C₆₁	—	2	2	no	—
197	C₂²×C₄×C₆₁	—	2	4	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	4	no	—
203	C₂²×C₄×C₆₁	—	4	2	no	—
204	C₂²×C₄×C₆₁	—	4	2	no	—
205	C₂²×C₄×C₆₁	—	4	2	no	—
206	C₂²×C₄×C₆₁	—	4	4	no	—
207	C₂²×C₄×C₆₁	—	4	4	no	—
208	C₂²×C₄×C₆₁	—	4	4	no	—
209	C₂²×C₄×C₆₁	—	4	4	no	—
210	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
211	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
212	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
223	C₄⋊C₄×C₆₁	—	2	4	no	—
224	C₄⋊C₄×C₆₁	—	2	4	no	—
225	C₄⋊C₄×C₆₁	—	2	2	no	—
226	C₄⋊C₄×C₆₁	—	2	2	no	—
227	C₄⋊C₄×C₆₁	—	2	8	no	—
228	C₄⋊C₄×C₆₁	—	4	2	no	—
229	C₄⋊C₄×C₆₁	—	4	2	no	—
230	C₄⋊C₄×C₆₁	—	4	4	no	—
231	C₄⋊C₄×C₆₁	—	4	4	no	—
232	C₄⋊C₄×C₆₁	—	4	4	no	—
233	C₂²⋊C₄×C₆₁	—	2	8	no	—
234	C₂²⋊C₄×C₆₁	—	2	4	no	—
235	C₂²⋊C₄×C₆₁	—	2	4	no	—
236	C₂²⋊C₄×C₆₁	—	2	4	no	—
237	C₂²⋊C₄×C₆₁	—	2	4	no	—
238	C₂²⋊C₄×C₆₁	—	2	4	no	—
239	C₂²⋊C₄×C₆₁	—	2	8	no	—
240	C₂²⋊C₄×C₆₁	—	2	4	no	—
241	C₂²⋊C₄×C₆₁	—	2	4	no	—
242	C₂²⋊C₄×C₆₁	—	2	4	no	—
243	C₂²⋊C₄×C₆₁	—	2	4	no	—
244	C₂²⋊C₄×C₆₁	—	2	8	no	—
245	C₂²⋊C₄×C₆₁	—	4	4	no	—
246	C₂²⋊C₄×C₆₁	—	4	4	no	—
247	C₂²⋊C₄×C₆₁	—	4	4	no	—
248	C₂²⋊C₄×C₆₁	—	4	4	no	—
249	C₂²⋊C₄×C₆₁	—	4	4	no	—
250	C₂²⋊C₄×C₆₁	—	4	4	no	—
251	C₂²⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
252	C₂²⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
253	C₄²×C₆₁	—	2	4	no	—
254	C₄²×C₆₁	—	2	4	no	—
255	C₄²×C₆₁	—	2	4	no	—
256	C₂³×C₆₁	—	2	2	no	—
257	C₂³×C₆₁	—	2	2	no	—
258	C₂³×C₆₁	—	2	2	no	—
259	C₂³×C₆₁	—	2	4	no	—
260	C₂³×C₆₁	—	2	2	no	—
261	C₂³×C₆₁	—	2	4	no	—
262	C₂³×C₆₁	—	2	8	no	—
263	C₂³×C₆₁	—	2	2	no	—
264	C₂³×C₆₁	—	2	2	no	—
265	C₂³×C₆₁	—	2	4	no	—
266	C₂³×C₆₁	—	2	2	no	—
267	C₂³×C₆₁	—	2	2	no	—
268	C₂³×C₆₁	—	2	4	no	—
269	C₂³×C₆₁	—	2	2	no	—
270	C₂³×C₆₁	—	2	2	no	—
271	C₂³×C₆₁	—	2	4	no	—
272	C₂³×C₆₁	—	2	4	no	—
273	C₂³×C₆₁	—	4	4	no	—
274	C₂³×C₆₁	—	4	4	no	—
275	C₂³×C₆₁	—	4	4	no	—
276	C₂³×C₆₁	—	4	4	no	—
277	C₂³×C₆₁	—	4	4	no	—
278	C₂³×C₆₁	—	8	4	no	—
279	C₂³×C₆₁	—	8	4	no	—
280	C₂³×C₆₁	—	8	4	no	—
281	C₂³×C₆₁	—	8	4	no	—
282	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
283	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
284	C₂³×C₆₁	H(5,𝔽₂)	1	2	yes	—
285	C₂³×C₆₁	2₋¹⁺⁴	1	2	yes	—
286	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
287	Q₈×C₆₁	—	4	16	no	—
288	Q₈×C₆₁	—	8	2	no	—
289	D₄×C₆₁	—	4	16	no	—
290	D₄×C₆₁	—	4	8	no	—
291	D₄×C₆₁	—	8	2	no	—
292	D₄×C₆₁	—	8	4	no	—
293	D₄×C₆₁	—	8	4	no	—
294	D₄×C₆₁	—	8	8	no	—
295	C₂×C₄×C₆₁	—	2	8	no	—
296	C₂×C₄×C₆₁	—	2	2	no	—
297	C₂×C₄×C₆₁	—	2	4	no	—
298	C₂×C₄×C₆₁	—	2	2	no	—
299	C₂×C₄×C₆₁	—	2	2	no	—
300	C₂×C₄×C₆₁	—	2	2	no	—
301	C₂×C₄×C₆₁	—	2	2	no	—
302	C₂×C₄×C₆₁	—	2	2	no	—
303	C₂×C₄×C₆₁	—	2	2	no	—
304	C₂×C₄×C₆₁	—	2	2	no	—
305	C₂×C₄×C₆₁	—	2	2	no	—
306	C₂×C₄×C₆₁	—	2	4	no	—
307	C₂×C₄×C₆₁	—	2	4	no	—
308	C₂×C₄×C₆₁	—	2	4	no	—
309	C₂×C₄×C₆₁	—	2	2	no	—
310	C₂×C₄×C₆₁	—	2	2	no	—
311	C₂×C₄×C₆₁	—	2	4	no	—
312	C₂×C₄×C₆₁	—	2	4	no	—
313	C₂×C₄×C₆₁	—	2	4	no	—
314	C₂×C₄×C₆₁	—	2	2	no	—
315	C₂×C₄×C₆₁	—	2	2	no	—
316	C₂×C₄×C₆₁	—	2	4	no	—
317	C₂×C₄×C₆₁	—	2	4	no	—
318	C₂×C₄×C₆₁	—	2	4	no	—
319	C₂×C₄×C₆₁	—	4	4	no	—
320	C₂×C₄×C₆₁	—	4	4	no	—
321	C₂×C₄×C₆₁	—	4	4	no	—
322	C₂×C₄×C₆₁	—	4	4	no	—
323	C₂×C₄×C₆₁	—	8	4	no	—
324	C₂×C₄×C₆₁	—	8	8	no	—
325	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
328	C₂×C₄×C₆₁	H(5,𝔽₂)	1	4	yes	—
329	#36957	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
330	C₂²×C₆₁	—	2	2	no	—
331	C₂²×C₆₁	—	2	2	no	—
332	C₂²×C₆₁	—	2	4	no	—
333	C₂²×C₆₁	—	2	4	no	—
334	C₂²×C₆₁	—	2	4	no	—
335	C₂²×C₆₁	—	2	4	no	—
336	C₂²×C₆₁	—	2	4	no	—
337	C₂²×C₆₁	—	4	4	no	—
338	C₂²×C₆₁	—	4	4	no	—
339	C₂²×C₆₁	—	4	2	no	—
340	C₂²×C₆₁	—	4	2	no	—
341	C₂²×C₆₁	—	4	2	no	—
342	C₂²×C₆₁	—	4	2	no	—
343	C₂²×C₆₁	—	4	2	no	—
344	C₂²×C₆₁	—	4	2	no	—
345	C₂²×C₆₁	—	4	4	no	—
346	C₂²×C₆₁	—	4	4	no	—
347	C₂²×C₆₁	—	4	4	no	—
348	C₂²×C₆₁	—	4	4	no	—
349	C₂²×C₆₁	—	8	8	no	—
350	C₂²×C₆₁	—	8	8	no	—
351	C₂²×C₆₁	#537	1	4	yes	—
352	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
353	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
355	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
356	C₂²×C₆₁	#585	1	2	yes	—
357	C₄×C₆₁	—	2	4	no	—
358	C₄×C₆₁	—	2	4	no	—
359	C₄×C₆₁	—	2	2	no	—
360	C₄×C₆₁	—	2	2	no	—
361	C₄×C₆₁	—	4	2	no	—
362	C₄×C₆₁	—	4	2	no	—
363	C₄×C₆₁	—	4	2	no	—
364	C₄×C₆₁	—	4	2	no	—
365	C₄×C₆₁	—	4	2	no	—
366	C₄×C₆₁	—	4	4	no	—
367	C₄×C₆₁	—	4	4	no	—
368	C₂×#538	C₂×C₆₁	1	1	yes	characteristic, complemented
369	C₂²×#124	C₂×C₆₁	1	1	yes	characteristic, complemented
370	#2855	C₂×C₆₁	1	1	yes	characteristic, complemented
371	#2854	C₂×C₆₁	1	1	yes	characteristic, complemented
372	#2715	C₂×C₆₁	1	4	yes	complemented
373	#2712	C₂×C₆₁	1	4	yes	complemented
374	#2676	C₂×C₆₁	1	4	yes	complemented
375	#2672	C₂×C₆₁	1	4	yes	complemented
376	#2626	C₂×C₆₁	1	1	yes	characteristic, complemented
377	#2617	C₂×C₆₁	1	1	yes	characteristic, complemented
378	#2534	C₂×C₆₁	1	2	yes	complemented
379	#2412	C₂×C₆₁	1	2	yes	complemented
380	#2410	C₂×C₆₁	1	2	yes	complemented
381	#2409	C₂×C₆₁	1	2	yes	complemented
382	#2315	C₂×C₆₁	1	1	yes	characteristic, complemented
383	C₂×C₆₁	—	2	4	no	—
384	C₂×C₆₁	—	4	4	no	—
385	C₂×C₆₁	—	8	2	no	—
386	C₂×C₆₁	—	8	2	no	—
387	C₂×C₆₁	C₂×#537	1	1	yes	characteristic
388	C₂×C₆₁	#3484	1	1	yes	characteristic
389	C₂×C₆₁	#3485	1	1	yes	characteristic
390	C₂×C₆₁	#3558	1	2	yes	—
391	C₂×C₆₁	#3561	1	2	yes	—
392	C₂³×Q₈	C₂²×C₆₁	1	1	yes	characteristic
393	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
394	#538	—	2	8	no	—
395	C₂×#126	C₂²×C₆₁	1	2	yes	complemented
396	C₂×#124	—	2	8	no	—
397	C₂×#124	C₂²×C₆₁	1	4	yes	—
398	C₂×#124	C₂²×C₆₁	1	4	yes	—
399	C₂×#124	C₂²×C₆₁	1	2	yes	complemented
400	C₂×#123	C₂²×C₆₁	1	2	yes	—
401	C₂×#123	C₂²×C₆₁	1	2	yes	complemented
402	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
403	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	4	yes	complemented
404	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
405	C₂×#121	C₂²×C₆₁	1	4	yes	—
406	C₂×#121	C₂²×C₆₁	1	2	yes	complemented
407	C₂×#120	C₂²×C₆₁	1	2	yes	—
408	C₂×#120	C₂²×C₆₁	1	2	yes	—
409	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
410	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
411	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
412	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
413	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
414	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
415	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
416	#399	C₂²×C₆₁	1	2	yes	complemented
417	#397	C₂²×C₆₁	1	2	yes	complemented
418	#397	C₂²×C₆₁	1	4	yes	complemented
419	#396	C₂²×C₆₁	1	4	yes	complemented
420	#396	C₂²×C₆₁	1	4	yes	complemented
421	#395	C₂²×C₆₁	1	4	yes	complemented
422	#394	C₂²×C₆₁	1	4	yes	—
423	#394	C₂²×C₆₁	1	4	yes	complemented
424	#394	C₂²×C₆₁	1	4	yes	complemented
425	#394	C₂²×C₆₁	1	4	yes	complemented
426	#393	C₂²×C₆₁	1	2	yes	complemented
427	#393	C₂²×C₆₁	1	4	yes	complemented
428	#392	C₂²×C₆₁	1	4	yes	—
429	#392	C₂²×C₆₁	1	2	yes	complemented
430	#391	C₂²×C₆₁	1	2	yes	complemented
431	#391	C₂²×C₆₁	1	4	yes	complemented
432	#390	C₂²×C₆₁	1	2	yes	complemented
433	#389	C₂²×C₆₁	1	2	yes	complemented
434	#389	C₂²×C₆₁	1	2	yes	complemented
435	#388	C₂²×C₆₁	1	4	yes	complemented
436	#388	C₂²×C₆₁	1	4	yes	complemented
437	#387	C₂²×C₆₁	1	4	yes	complemented
438	#386	C₂²×C₆₁	1	2	yes	—
439	#386	C₂²×C₆₁	1	2	yes	—
440	#386	C₂²×C₆₁	1	4	yes	—
441	#386	C₂²×C₆₁	1	4	yes	complemented
442	#386	C₂²×C₆₁	1	4	yes	complemented
443	#385	C₂²×C₆₁	1	2	yes	—
444	#385	C₂²×C₆₁	1	2	yes	—
445	#385	C₂²×C₆₁	1	4	yes	complemented
446	#385	C₂²×C₆₁	1	4	yes	complemented
447	#381	C₂²×C₆₁	1	2	yes	—
448	#380	C₂²×C₆₁	1	1	yes	characteristic
449	#380	C₂²×C₆₁	1	1	yes	characteristic
450	#380	C₂²×C₆₁	1	2	yes	—
451	#380	C₂²×C₆₁	1	4	yes	complemented
452	#379	C₂²×C₆₁	1	2	yes	—
453	C₆₁	#36957	1	1	yes	characteristic, direct product factor, Sylow
454	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
455	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
456	C₂²×Q₈	—	2	4	no	—
457	C₂²×Q₈	—	4	4	no	—
458	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
459	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
460	C₂²×D₄	—	2	4	no	—
461	C₂²×D₄	—	4	4	no	—
462	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
463	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
464	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
465	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
466	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
467	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
468	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
469	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
471	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
472	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
473	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
475	#126	—	2	8	no	—
476	#124	—	2	16	no	—
477	#124	—	2	16	no	—
478	#124	—	2	8	no	—
479	#123	—	2	8	no	—
480	#123	—	4	4	no	—
481	C₂²⋊Q₈	—	2	4	no	—
482	C₂²⋊Q₈	—	4	8	no	—
483	#121	—	2	4	no	—
484	#121	—	2	8	no	—
485	#121	—	4	8	no	—
486	#120	—	2	8	no	—
487	#120	—	4	4	no	—
488	C₄×D₄	—	2	8	no	—
489	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
491	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
495	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
496	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
497	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
499	C₂×C₂²⋊C₄	—	2	4	no	—
500	C₂×C₂²⋊C₄	—	2	4	no	—
501	C₂×C₂²⋊C₄	—	2	4	no	—
502	C₂×C₂²⋊C₄	—	4	4	no	—
503	C₂×C₂²⋊C₄	D₄×C₆₁	1	8	yes	complemented
504	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
524	C₂×C₄²	—	2	4	no	—
525	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
526	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
527	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
528	#95	C₂³×C₆₁	1	4	yes	—
529	#95	C₂³×C₆₁	1	2	yes	—
530	#95	C₂³×C₆₁	1	2	yes	—
531	#95	C₂³×C₆₁	1	4	yes	—
532	#95	C₂³×C₆₁	1	4	yes	—
533	#95	C₂³×C₆₁	1	4	yes	—
534	#95	C₂³×C₆₁	1	4	yes	—
535	#95	C₂³×C₆₁	1	4	yes	—
536	#95	C₂³×C₆₁	1	4	yes	—
537	C₂⁴	—	2	2	no	—
538	C₂⁴	—	2	2	no	—
539	C₂⁴	—	2	2	no	—
540	C₂⁴	—	2	2	no	—
541	C₂⁴	—	2	2	no	—
542	C₂⁴	—	4	2	no	—
543	C₂⁴	—	4	2	no	—
544	C₂⁴	—	4	2	no	—
545	C₂⁴	—	4	2	no	—
546	C₂⁴	C₂×D₄×C₆₁	1	4	yes	—
547	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
548	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
549	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
550	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
551	C₂×Q₈	—	2	8	no	—
552	C₂×Q₈	—	2	2	no	—
553	C₂×Q₈	—	2	8	no	—
554	C₂×Q₈	—	4	4	no	—
555	C₂×Q₈	—	4	2	no	—
556	C₂×Q₈	—	4	16	no	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	—	2	8	no	—
559	C₂×D₄	—	2	4	no	—
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	4	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	8	no	—
565	C₂×D₄	—	4	4	no	—
566	C₂×D₄	—	4	16	no	—
567	C₂×D₄	—	4	4	no	—
568	C₂×D₄	—	4	4	no	—
569	C₂×D₄	—	4	4	no	—
570	C₂×D₄	—	4	2	no	—
571	C₂×D₄	—	4	4	no	—
572	C₂×D₄	—	4	4	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	4	2	no	—
581	C₂²×C₄	—	4	2	no	—
582	C₂²×C₄	—	4	2	no	—
583	C₂²×C₄	—	4	4	no	—
584	C₂²×C₄	—	4	4	no	—
585	C₂²×C₄	—	4	4	no	—
586	C₂²×C₄	—	4	4	no	—
587	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
588	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
589	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
591	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
594	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
597	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
599	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	8	no	—
605	C₄⋊C₄	—	4	4	no	—
606	C₄⋊C₄	—	4	4	no	—
607	C₄⋊C₄	—	4	4	no	—
608	C₄⋊C₄	—	4	2	no	—
609	C₄⋊C₄	—	4	2	no	—
610	C₂²⋊C₄	—	2	8	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	8	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	8	no	—
622	C₂²⋊C₄	—	4	4	no	—
623	C₂²⋊C₄	—	4	4	no	—
624	C₂²⋊C₄	—	4	4	no	—
625	C₂²⋊C₄	—	4	4	no	—
626	C₂²⋊C₄	—	4	4	no	—
627	C₂²⋊C₄	—	4	4	no	—
628	C₂²⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
629	C₂²⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
630	C₄²	—	2	4	no	—
631	C₄²	—	2	4	no	—
632	C₄²	—	2	4	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	4	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	4	no	—
639	C₂³	—	2	8	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	4	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	4	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	4	no	—
649	C₂³	—	2	4	no	—
650	C₂³	—	4	4	no	—
651	C₂³	—	4	4	no	—
652	C₂³	—	4	4	no	—
653	C₂³	—	4	4	no	—
654	C₂³	—	4	4	no	—
655	C₂³	—	8	4	no	—
656	C₂³	—	8	4	no	—
657	C₂³	—	8	4	no	—
658	C₂³	—	8	4	no	—
659	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
660	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
661	C₂³	H(5,𝔽₂)×C₆₁	1	2	yes	—
662	C₂³	2₋¹⁺⁴×C₆₁	1	2	yes	—
663	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
664	Q₈	—	4	16	no	—
665	Q₈	—	8	2	no	—
666	D₄	—	4	16	no	—
667	D₄	—	4	8	no	—
668	D₄	—	8	2	no	—
669	D₄	—	8	4	no	—
670	D₄	—	8	4	no	—
671	D₄	—	8	8	no	—
672	C₂×C₄	—	2	8	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	4	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	4	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	8	4	no	—
701	C₂×C₄	—	8	8	no	—
702	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
704	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
705	C₂×C₄	H(5,𝔽₂)×C₆₁	1	4	yes	—
706	C₂²	—	2	4	no	—
707	C₂²	—	2	4	no	—
708	C₂²	—	2	2	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	4	no	—
711	C₂²	—	2	4	no	—
712	C₂²	—	2	4	no	—
713	C₂²	—	4	4	no	—
714	C₂²	—	4	4	no	—
715	C₂²	—	4	4	no	—
716	C₂²	—	4	4	no	—
717	C₂²	—	4	4	no	—
718	C₂²	—	4	4	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	8	8	no	—
726	C₂²	—	8	8	no	—
727	C₂²	C₆₁×#537	1	4	yes	—
728	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
729	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
730	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
731	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
732	C₂²	C₆₁×#585	1	2	yes	—
733	C₄	—	2	4	no	—
734	C₄	—	2	4	no	—
735	C₄	—	2	2	no	—
736	C₄	—	2	2	no	—
737	C₄	—	4	4	no	—
738	C₄	—	4	4	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	2	no	—
744	C₂	—	2	4	no	—
745	C₂	—	4	4	no	—
746	C₂	—	8	2	no	—
747	C₂	—	8	2	no	—
748	C₂	C₂×C₆₁×#537	1	1	yes	characteristic
749	C₂	C₆₁×#3484	1	1	yes	characteristic
750	C₂	C₆₁×#3485	1	1	yes	characteristic
751	C₂	C₆₁×#3558	1	2	yes	—
752	C₂	C₆₁×#3561	1	2	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×#124×C₆₁	C₂	semidirect
3. C₆₁×#2855	C₂	semidirect
4. C₆₁×#2854	C₂	semidirect
5. C₆₁×#2715	C₂	semidirect
6. C₆₁×#2712	C₂	semidirect
7. C₆₁×#2676	C₂	semidirect
8. C₆₁×#2672	C₂	semidirect
9. C₆₁×#2626	C₂	semidirect
10. C₆₁×#2617	C₂	semidirect
11. C₆₁×#2534	C₂	semidirect
12. C₆₁×#2412	C₂	semidirect
13. C₆₁×#2410	C₂	semidirect
14. C₆₁×#2409	C₂	semidirect
15. C₆₁×#2315	C₂	semidirect
19. C₂×#126×C₆₁	C₂²	semidirect
23. C₂×#124×C₆₁	C₂²	semidirect
25. C₂×#123×C₆₁	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
30. C₂×#121×C₆₁	C₂²	semidirect
40. C₆₁×#399	C₂²	semidirect
41. C₆₁×#397	C₂²	semidirect
42. C₆₁×#397	C₂²	semidirect
43. C₆₁×#396	C₂²	semidirect
44. C₆₁×#396	C₂²	semidirect
45. C₆₁×#395	C₂²	semidirect
47. C₆₁×#394	C₂²	semidirect
48. C₆₁×#394	C₂²	semidirect
49. C₆₁×#394	C₂²	semidirect
50. C₆₁×#393	C₂²	semidirect
51. C₆₁×#393	C₂²	semidirect
53. C₆₁×#392	C₂²	semidirect
54. C₆₁×#391	C₂²	semidirect
55. C₆₁×#391	C₂²	semidirect
56. C₆₁×#390	C₂²	semidirect
57. C₆₁×#389	C₂²	semidirect
58. C₆₁×#389	C₂²	semidirect
59. C₆₁×#388	C₂²	semidirect
60. C₆₁×#388	C₂²	semidirect
61. C₆₁×#387	C₂²	semidirect
65. C₆₁×#386	C₂²	semidirect
66. C₆₁×#386	C₂²	semidirect
69. C₆₁×#385	C₂²	semidirect
70. C₆₁×#385	C₂²	semidirect
75. C₆₁×#380	C₂²	semidirect
126. C₂×C₂²⋊C₄×C₆₁	D₄	semidirect
329. #36957	C₆₁	direct (N × H)
368. C₂×#538	C₂×C₆₁	semidirect
369. C₂²×#124	C₂×C₆₁	semidirect
370. #2855	C₂×C₆₁	semidirect
371. #2854	C₂×C₆₁	semidirect
372. #2715	C₂×C₆₁	semidirect
373. #2712	C₂×C₆₁	semidirect
374. #2676	C₂×C₆₁	semidirect
375. #2672	C₂×C₆₁	semidirect
376. #2626	C₂×C₆₁	semidirect
377. #2617	C₂×C₆₁	semidirect
378. #2534	C₂×C₆₁	semidirect
379. #2412	C₂×C₆₁	semidirect
380. #2410	C₂×C₆₁	semidirect
381. #2409	C₂×C₆₁	semidirect
382. #2315	C₂×C₆₁	semidirect
395. C₂×#126	C₂²×C₆₁	semidirect
399. C₂×#124	C₂²×C₆₁	semidirect
401. C₂×#123	C₂²×C₆₁	semidirect
403. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
406. C₂×#121	C₂²×C₆₁	semidirect
416. #399	C₂²×C₆₁	semidirect
417. #397	C₂²×C₆₁	semidirect
418. #397	C₂²×C₆₁	semidirect
419. #396	C₂²×C₆₁	semidirect
420. #396	C₂²×C₆₁	semidirect
421. #395	C₂²×C₆₁	semidirect
423. #394	C₂²×C₆₁	semidirect
424. #394	C₂²×C₆₁	semidirect
425. #394	C₂²×C₆₁	semidirect
426. #393	C₂²×C₆₁	semidirect
427. #393	C₂²×C₆₁	semidirect
429. #392	C₂²×C₆₁	semidirect
430. #391	C₂²×C₆₁	semidirect
431. #391	C₂²×C₆₁	semidirect
432. #390	C₂²×C₆₁	semidirect
433. #389	C₂²×C₆₁	semidirect
434. #389	C₂²×C₆₁	semidirect
435. #388	C₂²×C₆₁	semidirect
436. #388	C₂²×C₆₁	semidirect
437. #387	C₂²×C₆₁	semidirect
441. #386	C₂²×C₆₁	semidirect
442. #386	C₂²×C₆₁	semidirect
445. #385	C₂²×C₆₁	semidirect
446. #385	C₂²×C₆₁	semidirect
451. #380	C₂²×C₆₁	semidirect
453. C₆₁	#36957	direct (N × H)
503. 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×#124×C₆₁	2
C₆₁×#2855	2
C₆₁×#2854	2
C₆₁×#2715	2
C₆₁×#2712	2
C₆₁×#2676	2
C₆₁×#2672	2
C₆₁×#2626	2
C₆₁×#2617	2
C₆₁×#2534	2
C₆₁×#2412	2
C₆₁×#2410	2
C₆₁×#2409	2
C₆₁×#2315	2
#36957	61

Subgroups — C61×#36957 #29540390

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#36957 #29540390