Subgroups — C₆₁×#25545 #29528978

Order 15616.

1158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#554	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#484	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#467	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2417	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2057	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2036	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2024	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2001	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1878	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1872	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1872	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1869	C₂	1	1	yes	maximal, characteristic
13	C₆₁×#1863	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1852	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₆₁×#340	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₆₁×#554	—	2	4	no	—
19	C₆₁×#554	—	2	4	no	—
20	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#125×C₆₁	—	2	1	no	—
22	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
23	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
24	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₆₁	—	2	1	no	—
30	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#484	—	2	4	no	—
35	C₆₁×#467	—	2	4	no	—
36	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
40	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
41	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
43	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
44	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
48	C₆₁×#398	—	2	1	no	—
49	C₆₁×#396	—	2	1	no	—
50	C₆₁×#391	C₂²	1	1	yes	characteristic
51	C₆₁×#389	C₂²	1	1	yes	characteristic
52	C₆₁×#386	—	2	1	no	—
53	C₆₁×#380	—	2	1	no	—
54	C₆₁×#380	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×#340	C₂²	1	1	yes	characteristic
59	C₆₁×#340	C₂²	1	1	yes	characteristic
60	C₆₁×#340	C₂²	1	1	yes	characteristic
61	C₆₁×#336	C₂²	1	1	yes	characteristic
62	C₆₁×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₆₁	—	2	1	no	—
64	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
65	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
67	C₂³×C₄×C₆₁	—	2	1	no	—
68	C₂³×C₄×C₆₁	—	2	1	no	—
69	C₂³×C₄×C₆₁	—	2	1	no	—
70	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
72	C₂×Q₁₆×C₆₁	—	2	2	no	—
73	C₂×Q₁₆×C₆₁	—	2	2	no	—
74	C₂×Q₁₆×C₆₁	—	4	1	no	—
75	C₂²×C₈×C₆₁	—	2	2	no	—
76	C₂²×C₈×C₆₁	—	2	2	no	—
77	C₂²×C₈×C₆₁	—	4	1	no	—
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	C₄⋊Q₈×C₆₁	—	2	2	no	—
83	C₄⋊Q₈×C₆₁	—	2	2	no	—
84	#125×C₆₁	—	2	8	no	—
85	C₂²⋊Q₈×C₆₁	—	2	8	no	—
86	C₂²⋊Q₈×C₆₁	—	2	8	no	—
87	C₂²⋊Q₈×C₆₁	—	2	2	no	—
88	C₂²⋊Q₈×C₆₁	—	2	2	no	—
89	C₂²⋊Q₈×C₆₁	—	2	2	no	—
90	C₂²⋊Q₈×C₆₁	—	2	2	no	—
91	C₂²⋊Q₈×C₆₁	—	2	2	no	—
92	C₂²⋊Q₈×C₆₁	—	2	2	no	—
93	C₂²⋊Q₈×C₆₁	—	4	1	no	—
94	C₂²⋊Q₈×C₆₁	D₄	1	4	yes	—
95	C₄×Q₈×C₆₁	—	2	2	no	—
96	C₄×Q₈×C₆₁	—	2	2	no	—
97	C₄×D₄×C₆₁	—	2	8	no	—
98	C₄×D₄×C₆₁	—	2	2	no	—
99	C₄×D₄×C₆₁	—	2	2	no	—
100	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
101	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
102	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
103	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
104	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
105	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
106	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
107	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
108	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
109	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
110	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
111	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
112	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
113	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
114	C₂×C₄⋊C₄×C₆₁	—	4	1	no	—
115	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₆₁	D₄	1	4	yes	—
117	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
130	C₂×C₄²×C₆₁	—	2	1	no	—
131	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
132	#107×C₆₁	—	2	2	no	—
133	#107×C₆₁	—	2	2	no	—
134	#107×C₆₁	—	2	2	no	—
135	#103×C₆₁	—	2	2	no	—
136	#103×C₆₁	—	2	2	no	—
137	#103×C₆₁	—	2	2	no	—
138	#103×C₆₁	—	2	2	no	—
139	#103×C₆₁	—	2	2	no	—
140	#103×C₆₁	—	4	1	no	—
141	C₂²⋊C₈×C₆₁	—	2	2	no	—
142	C₂²⋊C₈×C₆₁	—	2	2	no	—
143	C₂²⋊C₈×C₆₁	—	4	1	no	—
144	#95×C₆₁	—	2	1	no	—
145	#95×C₆₁	—	2	1	no	—
146	#95×C₆₁	—	2	1	no	—
147	#95×C₆₁	—	2	1	no	—
148	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
149	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
150	C₂×Q₈×C₆₁	—	2	4	no	—
151	C₂×Q₈×C₆₁	—	2	1	no	—
152	C₂×Q₈×C₆₁	—	2	1	no	—
153	C₂×Q₈×C₆₁	—	2	1	no	—
154	C₂×Q₈×C₆₁	—	2	1	no	—
155	C₂×Q₈×C₆₁	—	2	1	no	—
156	C₂×Q₈×C₆₁	—	2	1	no	—
157	C₂×Q₈×C₆₁	—	2	1	no	—
158	C₂×Q₈×C₆₁	—	2	1	no	—
159	C₂×Q₈×C₆₁	—	2	1	no	—
160	C₂×Q₈×C₆₁	—	2	1	no	—
161	C₂×Q₈×C₆₁	—	2	1	no	—
162	C₂×Q₈×C₆₁	—	8	1	no	—
163	C₂×Q₈×C₆₁	—	8	1	no	—
164	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
165	C₂×D₄×C₆₁	—	2	2	no	—
166	C₂×D₄×C₆₁	—	2	2	no	—
167	C₂×D₄×C₆₁	Q₁₆	1	4	yes	complemented
168	C₂²×C₄×C₆₁	—	2	1	no	—
169	C₂²×C₄×C₆₁	—	2	1	no	—
170	C₂²×C₄×C₆₁	—	2	1	no	—
171	C₂²×C₄×C₆₁	—	2	1	no	—
172	C₂²×C₄×C₆₁	—	2	1	no	—
173	C₂²×C₄×C₆₁	—	2	1	no	—
174	C₂²×C₄×C₆₁	—	2	1	no	—
175	C₂²×C₄×C₆₁	—	2	1	no	—
176	C₂²×C₄×C₆₁	—	2	1	no	—
177	C₂²×C₄×C₆₁	—	2	4	no	—
178	C₂²×C₄×C₆₁	—	2	4	no	—
179	C₂²×C₄×C₆₁	—	2	1	no	—
180	C₂²×C₄×C₆₁	—	2	1	no	—
181	C₂²×C₄×C₆₁	—	2	1	no	—
182	C₂²×C₄×C₆₁	—	2	1	no	—
183	C₂²×C₄×C₆₁	—	2	1	no	—
184	C₂²×C₄×C₆₁	—	2	1	no	—
185	C₂²×C₄×C₆₁	—	2	1	no	—
186	C₂²×C₄×C₆₁	—	2	1	no	—
187	C₂²×C₄×C₆₁	—	2	1	no	—
188	C₂²×C₄×C₆₁	—	4	2	no	—
189	C₂²×C₄×C₆₁	—	4	2	no	—
190	C₂²×C₄×C₆₁	—	8	1	no	—
191	C₂²×C₄×C₆₁	—	8	1	no	—
192	C₂²×C₄×C₆₁	—	8	1	no	—
193	C₂²×C₄×C₆₁	—	8	1	no	—
194	C₂²×C₄×C₆₁	—	8	1	no	—
195	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
199	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
200	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
202	Q₁₆×C₆₁	—	4	4	no	—
203	C₂×C₈×C₆₁	—	2	1	no	—
204	C₂×C₈×C₆₁	—	2	1	no	—
205	C₂×C₈×C₆₁	—	2	1	no	—
206	C₂×C₈×C₆₁	—	2	1	no	—
207	C₂×C₈×C₆₁	—	2	1	no	—
208	C₂×C₈×C₆₁	—	2	1	no	—
209	C₂×C₈×C₆₁	—	2	1	no	—
210	C₂×C₈×C₆₁	—	2	1	no	—
211	C₂×C₈×C₆₁	—	2	1	no	—
212	C₂×C₈×C₆₁	—	2	1	no	—
213	C₂×C₈×C₆₁	—	2	1	no	—
214	C₂×C₈×C₆₁	—	4	4	no	—
215	C₂×C₈×C₆₁	#41	1	2	yes	—
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	4	no	—
220	C₄⋊C₄×C₆₁	—	2	4	no	—
221	C₄⋊C₄×C₆₁	—	2	4	no	—
222	C₄⋊C₄×C₆₁	—	2	2	no	—
223	C₄⋊C₄×C₆₁	—	2	1	no	—
224	C₄⋊C₄×C₆₁	—	2	1	no	—
225	C₄⋊C₄×C₆₁	—	2	1	no	—
226	C₄⋊C₄×C₆₁	—	2	1	no	—
227	C₄⋊C₄×C₆₁	—	2	1	no	—
228	C₄⋊C₄×C₆₁	—	2	1	no	—
229	C₄⋊C₄×C₆₁	—	2	1	no	—
230	C₄⋊C₄×C₆₁	—	2	1	no	—
231	C₄⋊C₄×C₆₁	—	4	2	no	—
232	C₄⋊C₄×C₆₁	—	4	2	no	—
233	C₄⋊C₄×C₆₁	—	4	2	no	—
234	C₄⋊C₄×C₆₁	—	8	1	no	—
235	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
236	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
237	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
238	C₄⋊C₄×C₆₁	#41	1	2	yes	—
239	C₂²⋊C₄×C₆₁	—	2	4	no	—
240	C₂²⋊C₄×C₆₁	—	2	4	no	—
241	C₂²⋊C₄×C₆₁	—	2	2	no	—
242	C₂²⋊C₄×C₆₁	—	2	2	no	—
243	C₂²⋊C₄×C₆₁	—	4	2	no	—
244	C₂²⋊C₄×C₆₁	—	4	2	no	—
245	C₂²⋊C₄×C₆₁	—	8	1	no	—
246	C₄²×C₆₁	—	2	4	no	—
247	C₄²×C₆₁	—	2	1	no	—
248	C₄²×C₆₁	—	2	1	no	—
249	C₂³×C₆₁	—	2	1	no	—
250	C₂³×C₆₁	—	2	1	no	—
251	C₂³×C₆₁	—	2	1	no	—
252	C₂³×C₆₁	—	2	1	no	—
253	C₂³×C₆₁	—	2	1	no	—
254	C₂³×C₆₁	—	2	1	no	—
255	C₂³×C₆₁	—	2	1	no	—
256	C₂³×C₆₁	—	2	1	no	—
257	C₂³×C₆₁	—	2	1	no	—
258	C₂³×C₆₁	—	2	1	no	—
259	C₂³×C₆₁	#120	1	2	yes	—
260	C₂³×C₆₁	C₂×Q₁₆	1	2	yes	—
261	C₂³×C₆₁	C₂×Q₁₆	1	2	yes	—
262	C₂³×C₆₁	#137	1	2	yes	—
263	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
264	Q₈×C₆₁	—	2	2	no	—
265	Q₈×C₆₁	—	2	2	no	—
266	Q₈×C₆₁	—	4	1	no	—
267	Q₈×C₆₁	—	4	1	no	—
268	Q₈×C₆₁	—	4	1	no	—
269	Q₈×C₆₁	—	4	1	no	—
270	Q₈×C₆₁	—	4	1	no	—
271	Q₈×C₆₁	—	4	1	no	—
272	Q₈×C₆₁	—	8	4	no	—
273	D₄×C₆₁	—	2	8	no	—
274	C₂×C₄×C₆₁	—	2	1	no	—
275	C₂×C₄×C₆₁	—	2	1	no	—
276	C₂×C₄×C₆₁	—	2	1	no	—
277	C₂×C₄×C₆₁	—	2	1	no	—
278	C₂×C₄×C₆₁	—	2	2	no	—
279	C₂×C₄×C₆₁	—	2	2	no	—
280	C₂×C₄×C₆₁	—	2	2	no	—
281	C₂×C₄×C₆₁	—	2	2	no	—
282	C₂×C₄×C₆₁	—	2	2	no	—
283	C₂×C₄×C₆₁	—	2	1	no	—
284	C₂×C₄×C₆₁	—	2	2	no	—
285	C₂×C₄×C₆₁	—	2	1	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	1	no	—
290	C₂×C₄×C₆₁	—	2	1	no	—
291	C₂×C₄×C₆₁	—	2	1	no	—
292	C₂×C₄×C₆₁	—	2	1	no	—
293	C₂×C₄×C₆₁	—	4	1	no	—
294	C₂×C₄×C₆₁	—	4	1	no	—
295	C₂×C₄×C₆₁	—	4	1	no	—
296	C₂×C₄×C₆₁	—	4	1	no	—
297	C₂×C₄×C₆₁	—	4	1	no	—
298	C₂×C₄×C₆₁	—	4	1	no	—
299	C₂×C₄×C₆₁	—	4	1	no	—
300	C₂×C₄×C₆₁	—	4	1	no	—
301	C₂×C₄×C₆₁	—	4	1	no	—
302	C₂×C₄×C₆₁	—	4	1	no	—
303	C₂×C₄×C₆₁	—	4	1	no	—
304	C₂×C₄×C₆₁	—	4	1	no	—
305	C₂×C₄×C₆₁	—	4	1	no	—
306	C₂×C₄×C₆₁	—	4	1	no	—
307	C₂×C₄×C₆₁	—	4	1	no	—
308	C₂×C₄×C₆₁	—	4	1	no	—
309	C₂×C₄×C₆₁	—	4	1	no	—
310	C₂×C₄×C₆₁	—	4	1	no	—
311	C₂×C₄×C₆₁	—	4	1	no	—
312	C₂×C₄×C₆₁	—	4	1	no	—
313	C₂×C₄×C₆₁	—	4	1	no	—
314	C₂×C₄×C₆₁	—	4	1	no	—
315	C₂×C₄×C₆₁	—	4	1	no	—
316	C₂×C₄×C₆₁	—	8	4	no	—
317	C₂×C₄×C₆₁	—	8	4	no	—
318	C₂×C₄×C₆₁	—	8	4	no	—
319	C₂×C₄×C₆₁	#120	1	2	yes	—
320	C₂×C₄×C₆₁	C₂×Q₁₆	1	2	yes	—
321	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
324	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
325	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
326	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
327	C₈×C₆₁	—	2	2	no	—
328	C₈×C₆₁	—	4	1	no	—
329	C₈×C₆₁	—	4	1	no	—
330	C₈×C₆₁	—	4	1	no	—
331	#25545	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
332	C₂²×C₆₁	—	2	2	no	—
333	C₂²×C₆₁	—	2	2	no	—
334	C₂²×C₆₁	—	2	2	no	—
335	C₂²×C₆₁	—	2	2	no	—
336	C₂²×C₆₁	—	2	2	no	—
337	C₂²×C₆₁	—	2	2	no	—
338	C₂²×C₆₁	—	2	2	no	—
339	C₂²×C₆₁	—	2	2	no	—
340	C₂²×C₆₁	—	2	2	no	—
341	C₂²×C₆₁	—	4	1	no	—
342	C₂²×C₆₁	—	4	1	no	—
343	C₂²×C₆₁	—	4	1	no	—
344	C₂²×C₆₁	—	4	1	no	—
345	C₂²×C₆₁	#451	1	4	yes	—
346	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
347	C₂²×C₆₁	#546	1	1	yes	characteristic
348	C₂²×C₆₁	#547	1	1	yes	characteristic
349	C₂²×C₆₁	C₂²×Q₁₆	1	1	yes	characteristic
350	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
351	C₂²×C₆₁	#576	1	1	yes	characteristic
352	C₂²×C₆₁	#577	1	1	yes	characteristic
353	C₄×C₆₁	—	2	2	no	—
354	C₄×C₆₁	—	2	2	no	—
355	C₄×C₆₁	—	4	1	no	—
356	C₄×C₆₁	—	4	2	no	—
357	C₄×C₆₁	—	4	1	no	—
358	C₄×C₆₁	—	4	2	no	—
359	C₄×C₆₁	—	4	2	no	—
360	C₄×C₆₁	—	4	2	no	—
361	C₄×C₆₁	—	4	2	no	—
362	C₄×C₆₁	—	8	1	no	—
363	C₄×C₆₁	—	8	1	no	—
364	C₄×C₆₁	—	8	1	no	—
365	C₄×C₆₁	#532	1	1	yes	characteristic
366	C₄×C₆₁	#537	1	1	yes	characteristic
367	C₄×C₆₁	#546	1	1	yes	characteristic
368	C₄×C₆₁	#547	1	1	yes	characteristic
369	C₂×#554	C₂×C₆₁	1	1	yes	characteristic
370	C₂×#484	C₂×C₆₁	1	1	yes	characteristic, complemented
371	C₂×#467	C₂×C₆₁	1	1	yes	characteristic, complemented
372	#2417	C₂×C₆₁	1	1	yes	characteristic
373	#2057	C₂×C₆₁	1	1	yes	characteristic, complemented
374	#2036	C₂×C₆₁	1	1	yes	characteristic, complemented
375	#2024	C₂×C₆₁	1	1	yes	characteristic, complemented
376	#2001	C₂×C₆₁	1	1	yes	characteristic, complemented
377	#1878	C₂×C₆₁	1	1	yes	characteristic, complemented
378	#1872	C₂×C₆₁	1	1	yes	characteristic, complemented
379	#1872	C₂×C₆₁	1	1	yes	characteristic, complemented
380	#1869	C₂×C₆₁	1	1	yes	characteristic
381	#1863	C₂×C₆₁	1	1	yes	characteristic, complemented
382	#1852	C₂×C₆₁	1	1	yes	characteristic, complemented
383	C₂×#340	C₂×C₆₁	1	1	yes	characteristic, complemented
384	C₂×C₆₁	—	2	4	no	—
385	C₂×C₆₁	—	4	2	no	—
386	C₂×C₆₁	#2430	1	1	yes	characteristic
387	C₂×C₆₁	C₂×#451	1	1	yes	characteristic
388	C₂×C₆₁	#3012	1	1	yes	characteristic
389	C₂×C₆₁	#3299	1	1	yes	characteristic
390	C₂×C₆₁	#3314	1	1	yes	characteristic
391	C₂×C₆₁	#3338	1	1	yes	characteristic
392	C₂×C₆₁	#3344	1	1	yes	characteristic
393	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
394	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
395	#554	—	2	4	no	—
396	#554	—	2	4	no	—
397	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
398	C₂×#125	—	2	1	no	—
399	C₂×C₂²⋊Q₈	—	2	1	no	—
400	C₂×C₂²⋊Q₈	—	2	1	no	—
401	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
402	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
403	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
404	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
405	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
406	C₂×C₄×D₄	—	2	1	no	—
407	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
408	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
409	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
410	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
411	#484	—	2	4	no	—
412	#467	—	2	4	no	—
413	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
414	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
415	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
416	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
417	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
418	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
419	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
420	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
421	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
422	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
423	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
424	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
425	#398	—	2	1	no	—
426	#396	—	2	1	no	—
427	#391	C₂²×C₆₁	1	1	yes	characteristic
428	#389	C₂²×C₆₁	1	1	yes	characteristic
429	#386	—	2	1	no	—
430	#380	—	2	1	no	—
431	#380	C₂²×C₆₁	1	1	yes	characteristic
432	#340	C₂²×C₆₁	1	1	yes	characteristic
433	#340	C₂²×C₆₁	1	1	yes	characteristic
434	#340	C₂²×C₆₁	1	1	yes	characteristic
435	#340	C₂²×C₆₁	1	1	yes	characteristic
436	#340	C₂²×C₆₁	1	1	yes	characteristic
437	#340	C₂²×C₆₁	1	1	yes	characteristic
438	#336	C₂²×C₆₁	1	1	yes	characteristic
439	#336	C₂²×C₆₁	1	1	yes	characteristic
440	C₆₁	#25545	1	1	yes	characteristic, direct product factor, Sylow
441	C₂²×Q₈	—	2	1	no	—
442	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
443	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
444	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
445	C₂³×C₄	—	2	1	no	—
446	C₂³×C₄	—	2	1	no	—
447	C₂³×C₄	—	2	1	no	—
448	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
449	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
450	C₂×Q₁₆	—	2	2	no	—
451	C₂×Q₁₆	—	2	2	no	—
452	C₂×Q₁₆	—	4	1	no	—
453	C₂²×C₈	—	2	2	no	—
454	C₂²×C₈	—	2	2	no	—
455	C₂²×C₈	—	4	1	no	—
456	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
457	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
458	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
459	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
460	C₄⋊Q₈	—	2	2	no	—
461	C₄⋊Q₈	—	2	2	no	—
462	#125	—	2	8	no	—
463	C₂²⋊Q₈	—	2	8	no	—
464	C₂²⋊Q₈	—	2	8	no	—
465	C₂²⋊Q₈	—	2	2	no	—
466	C₂²⋊Q₈	—	2	2	no	—
467	C₂²⋊Q₈	—	2	2	no	—
468	C₂²⋊Q₈	—	2	2	no	—
469	C₂²⋊Q₈	—	2	2	no	—
470	C₂²⋊Q₈	—	2	2	no	—
471	C₂²⋊Q₈	—	4	1	no	—
472	C₂²⋊Q₈	D₄×C₆₁	1	4	yes	—
473	C₄×Q₈	—	2	2	no	—
474	C₄×Q₈	—	2	2	no	—
475	C₄×D₄	—	2	8	no	—
476	C₄×D₄	—	2	2	no	—
477	C₄×D₄	—	2	2	no	—
478	C₂×C₄⋊C₄	—	2	1	no	—
479	C₂×C₄⋊C₄	—	2	1	no	—
480	C₂×C₄⋊C₄	—	2	2	no	—
481	C₂×C₄⋊C₄	—	2	1	no	—
482	C₂×C₄⋊C₄	—	2	1	no	—
483	C₂×C₄⋊C₄	—	2	1	no	—
484	C₂×C₄⋊C₄	—	2	1	no	—
485	C₂×C₄⋊C₄	—	2	2	no	—
486	C₂×C₄⋊C₄	—	2	2	no	—
487	C₂×C₄⋊C₄	—	2	2	no	—
488	C₂×C₄⋊C₄	—	2	1	no	—
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	—	2	1	no	—
492	C₂×C₄⋊C₄	—	4	1	no	—
493	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
494	C₂×C₄⋊C₄	D₄×C₆₁	1	4	yes	—
495	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₂²⋊C₄	—	2	1	no	—
504	C₂×C₂²⋊C₄	—	2	1	no	—
505	C₂×C₂²⋊C₄	—	2	1	no	—
506	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
507	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
508	C₂×C₄²	—	2	1	no	—
509	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
510	#107	—	2	2	no	—
511	#107	—	2	2	no	—
512	#107	—	2	2	no	—
513	#103	—	2	2	no	—
514	#103	—	2	2	no	—
515	#103	—	2	2	no	—
516	#103	—	2	2	no	—
517	#103	—	2	2	no	—
518	#103	—	4	1	no	—
519	C₂²⋊C₈	—	2	2	no	—
520	C₂²⋊C₈	—	2	2	no	—
521	C₂²⋊C₈	—	4	1	no	—
522	#95	—	2	1	no	—
523	#95	—	2	1	no	—
524	#95	—	2	1	no	—
525	#95	—	2	1	no	—
526	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
527	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
528	C₂×Q₈	—	2	4	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	—	2	1	no	—
534	C₂×Q₈	—	2	1	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	—	8	1	no	—
541	C₂×Q₈	—	8	1	no	—
542	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	Q₁₆×C₆₁	1	4	yes	complemented
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	4	no	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	—	8	1	no	—
569	C₂²×C₄	—	8	1	no	—
570	C₂²×C₄	—	8	1	no	—
571	C₂²×C₄	—	8	1	no	—
572	C₂²×C₄	—	8	1	no	—
573	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
574	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
575	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
576	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
577	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
578	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
580	Q₁₆	—	4	4	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	4	4	no	—
593	C₂×C₈	#41×C₆₁	1	2	yes	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	4	2	no	—
610	C₄⋊C₄	—	4	2	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	—	8	1	no	—
613	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
614	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
615	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
616	C₄⋊C₄	#41×C₆₁	1	2	yes	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	2	no	—
620	C₂²⋊C₄	—	2	2	no	—
621	C₂²⋊C₄	—	4	2	no	—
622	C₂²⋊C₄	—	4	2	no	—
623	C₂²⋊C₄	—	8	1	no	—
624	C₄²	—	2	4	no	—
625	C₄²	—	2	1	no	—
626	C₄²	—	2	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	2	1	no	—
630	C₂³	—	2	1	no	—
631	C₂³	—	2	1	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	#120×C₆₁	1	2	yes	—
638	C₂³	C₂×Q₁₆×C₆₁	1	2	yes	—
639	C₂³	C₂×Q₁₆×C₆₁	1	2	yes	—
640	C₂³	#137×C₆₁	1	2	yes	—
641	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
642	Q₈	—	2	2	no	—
643	Q₈	—	2	2	no	—
644	Q₈	—	4	1	no	—
645	Q₈	—	4	1	no	—
646	Q₈	—	4	1	no	—
647	Q₈	—	4	1	no	—
648	Q₈	—	4	1	no	—
649	Q₈	—	4	1	no	—
650	Q₈	—	8	4	no	—
651	D₄	—	2	8	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	8	4	no	—
695	C₂×C₄	—	8	4	no	—
696	C₂×C₄	—	8	4	no	—
697	C₂×C₄	#120×C₆₁	1	2	yes	—
698	C₂×C₄	C₂×Q₁₆×C₆₁	1	2	yes	—
699	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
700	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
701	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
702	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
703	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
704	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
705	C₈	—	2	2	no	—
706	C₈	—	4	1	no	—
707	C₈	—	4	1	no	—
708	C₈	—	4	1	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	2	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	2	2	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	4	1	no	—
722	C₂²	C₆₁×#451	1	4	yes	—
723	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
724	C₂²	C₆₁×#546	1	1	yes	characteristic
725	C₂²	C₆₁×#547	1	1	yes	characteristic
726	C₂²	C₂²×Q₁₆×C₆₁	1	1	yes	characteristic
727	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
728	C₂²	C₆₁×#576	1	1	yes	characteristic
729	C₂²	C₆₁×#577	1	1	yes	characteristic
730	C₄	—	2	2	no	—
731	C₄	—	2	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	1	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	1	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	8	1	no	—
740	C₄	—	8	1	no	—
741	C₄	—	8	1	no	—
742	C₄	C₆₁×#532	1	1	yes	characteristic
743	C₄	C₆₁×#537	1	1	yes	characteristic
744	C₄	C₆₁×#546	1	1	yes	characteristic
745	C₄	C₆₁×#547	1	1	yes	characteristic
746	C₂	—	2	4	no	—
747	C₂	—	4	2	no	—
748	C₂	C₆₁×#2430	1	1	yes	characteristic
749	C₂	C₂×C₆₁×#451	1	1	yes	characteristic
750	C₂	C₆₁×#3012	1	1	yes	characteristic
751	C₂	C₆₁×#3299	1	1	yes	characteristic
752	C₂	C₆₁×#3314	1	1	yes	characteristic
753	C₂	C₆₁×#3338	1	1	yes	characteristic
754	C₂	C₆₁×#3344	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#484	C₂	semidirect
3. C₂×C₆₁×#467	C₂	semidirect
5. C₆₁×#2057	C₂	semidirect
6. C₆₁×#2036	C₂	semidirect
7. C₆₁×#2024	C₂	semidirect
8. C₆₁×#2001	C₂	semidirect
9. C₆₁×#1878	C₂	semidirect
10. C₆₁×#1872	C₂	semidirect
11. C₆₁×#1872	C₂	semidirect
13. C₆₁×#1863	C₂	semidirect
14. C₆₁×#1852	C₂	semidirect
15. C₂×C₆₁×#340	C₂	semidirect
167. C₂×D₄×C₆₁	Q₁₆	semidirect
331. #25545	C₆₁	direct (N × H)
370. C₂×#484	C₂×C₆₁	semidirect
371. C₂×#467	C₂×C₆₁	semidirect
373. #2057	C₂×C₆₁	semidirect
374. #2036	C₂×C₆₁	semidirect
375. #2024	C₂×C₆₁	semidirect
376. #2001	C₂×C₆₁	semidirect
377. #1878	C₂×C₆₁	semidirect
378. #1872	C₂×C₆₁	semidirect
379. #1872	C₂×C₆₁	semidirect
381. #1863	C₂×C₆₁	semidirect
382. #1852	C₂×C₆₁	semidirect
383. C₂×#340	C₂×C₆₁	semidirect
440. C₆₁	#25545	direct (N × H)
545. C₂×D₄	Q₁₆×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×#554	2
C₂×C₆₁×#484	2
C₂×C₆₁×#467	2
C₆₁×#2417	2
C₆₁×#2057	2
C₆₁×#2036	2
C₆₁×#2024	2
C₆₁×#2001	2
C₆₁×#1878	2
C₆₁×#1872	2
C₆₁×#1869	2
C₆₁×#1863	2
C₆₁×#1852	2
C₂×C₆₁×#340	2
#25545	61

Subgroups — C61×#25545 #29528978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25545 #29528978