Subgroups — C₆₁×#25795 #29529228

Order 15616.

1486 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#494	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#470	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₆₁×#452	C₂	1	1	yes	maximal, characteristic
6	C₂×C₆₁×#451	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2434	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2432	C₂	1	1	yes	maximal, characteristic
9	C₆₁×#2016	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#2016	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2015	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#2013	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#1971	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1968	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×#137×C₆₁	—	2	4	no	—
19	C₂×#137×C₆₁	—	2	4	no	—
20	C₂×#137×C₆₁	—	2	4	no	—
21	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
22	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
23	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
24	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
25	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
26	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
29	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
37	C₆₁×#497	—	2	4	no	—
38	C₆₁×#494	—	2	4	no	—
39	C₆₁×#470	—	2	4	no	—
40	C₆₁×#452	—	2	4	no	—
41	C₆₁×#451	—	2	4	no	—
42	C₂×#106×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×#103×C₆₁	C₂²	1	1	yes	characteristic
46	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
47	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
48	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
50	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
52	C₆₁×#395	—	2	2	no	—
53	C₆₁×#394	—	2	2	no	—
54	C₆₁×#391	C₂²	1	1	yes	characteristic
55	C₆₁×#391	C₂²	1	1	yes	characteristic
56	C₆₁×#391	C₂²	1	1	yes	characteristic
57	C₆₁×#390	C₂²	1	1	yes	characteristic
58	C₆₁×#385	—	2	2	no	—
59	C₆₁×#385	—	2	2	no	—
60	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
61	C₆₁×#336	C₂²	1	1	yes	characteristic
62	C₆₁×#336	C₂²	1	1	yes	characteristic
63	C₂×#41×C₆₁	—	2	2	no	—
64	C₂×#41×C₆₁	—	2	2	no	—
65	C₂×#41×C₆₁	—	2	2	no	—
66	C₂×#41×C₆₁	—	2	2	no	—
67	C₂×#41×C₆₁	—	4	1	no	—
68	C₂×#41×C₆₁	—	4	1	no	—
69	C₂²×Q₈×C₆₁	—	2	1	no	—
70	C₂²×Q₈×C₆₁	—	2	2	no	—
71	C₂²×Q₈×C₆₁	—	2	2	no	—
72	C₂²×Q₈×C₆₁	—	2	2	no	—
73	C₂²×Q₈×C₆₁	—	2	2	no	—
74	C₂²×Q₈×C₆₁	—	4	1	no	—
75	C₂²×Q₈×C₆₁	—	4	1	no	—
76	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
77	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₆₁	—	2	1	no	—
82	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₆₁	—	2	1	no	—
84	C₂³×C₄×C₆₁	—	2	1	no	—
85	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
86	#137×C₆₁	—	2	32	no	—
87	C₂×Q₁₆×C₆₁	—	2	2	no	—
88	C₂×Q₁₆×C₆₁	—	2	2	no	—
89	C₂×Q₁₆×C₆₁	—	2	2	no	—
90	C₂×Q₁₆×C₆₁	—	2	2	no	—
91	C₂×Q₁₆×C₆₁	—	2	2	no	—
92	C₂×Q₁₆×C₆₁	—	2	2	no	—
93	C₂×Q₁₆×C₆₁	—	2	2	no	—
94	C₂×Q₁₆×C₆₁	—	2	2	no	—
95	C₂×Q₁₆×C₆₁	—	2	2	no	—
96	C₂×Q₁₆×C₆₁	—	2	2	no	—
97	C₂×Q₁₆×C₆₁	—	2	2	no	—
98	C₂×Q₁₆×C₆₁	—	2	2	no	—
99	C₂×Q₁₆×C₆₁	—	2	2	no	—
100	C₂×Q₁₆×C₆₁	—	2	2	no	—
101	C₂×Q₁₆×C₆₁	—	4	1	no	—
102	C₂×Q₁₆×C₆₁	—	4	1	no	—
103	C₂×Q₁₆×C₆₁	—	4	1	no	—
104	C₂×Q₁₆×C₆₁	D₄	1	4	yes	—
105	C₂×SD₁₆×C₆₁	—	2	2	no	—
106	C₂×SD₁₆×C₆₁	—	2	2	no	—
107	C₂×SD₁₆×C₆₁	—	2	2	no	—
108	C₂×SD₁₆×C₆₁	—	2	2	no	—
109	C₂×SD₁₆×C₆₁	—	2	2	no	—
110	C₂×SD₁₆×C₆₁	—	2	2	no	—
111	C₂×SD₁₆×C₆₁	—	2	2	no	—
112	C₂×SD₁₆×C₆₁	—	4	1	no	—
113	C₂×SD₁₆×C₆₁	D₄	1	4	yes	—
114	C₂×M₁₆×C₆₁	—	2	2	no	—
115	C₂×M₁₆×C₆₁	—	2	2	no	—
116	C₂×M₁₆×C₆₁	D₄	1	4	yes	—
117	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
118	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
121	C₄⋊Q₈×C₆₁	—	2	2	no	—
122	C₄⋊Q₈×C₆₁	—	2	2	no	—
123	C₄⋊Q₈×C₆₁	—	2	2	no	—
124	C₄⋊Q₈×C₆₁	—	4	1	no	—
125	C₄⋊Q₈×C₆₁	—	4	1	no	—
126	C₄⋊Q₈×C₆₁	—	4	1	no	—
127	#124×C₆₁	—	2	2	no	—
128	#124×C₆₁	—	4	1	no	—
129	C₂²⋊Q₈×C₆₁	—	2	2	no	—
130	C₂²⋊Q₈×C₆₁	—	2	2	no	—
131	C₂²⋊Q₈×C₆₁	—	2	2	no	—
132	C₂²⋊Q₈×C₆₁	—	2	2	no	—
133	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
134	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
135	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
136	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
137	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
138	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
141	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
143	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
144	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
145	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
147	#106×C₆₁	—	2	2	no	—
148	#103×C₆₁	—	2	2	no	—
149	#103×C₆₁	—	2	2	no	—
150	#103×C₆₁	—	2	2	no	—
151	#103×C₆₁	—	2	2	no	—
152	#103×C₆₁	—	2	2	no	—
153	#102×C₆₁	—	2	2	no	—
154	C₂²⋊C₈×C₆₁	D₄	1	4	yes	—
155	#97×C₆₁	—	2	2	no	—
156	C₄×C₈×C₆₁	—	2	2	no	—
157	#95×C₆₁	—	2	2	no	—
158	#95×C₆₁	—	2	2	no	—
159	#95×C₆₁	—	2	2	no	—
160	#95×C₆₁	D₄	1	2	yes	—
161	C₂⁴×C₆₁	—	2	1	no	—
162	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
163	#41×C₆₁	—	2	8	no	—
164	#41×C₆₁	—	4	4	no	—
165	#41×C₆₁	—	4	4	no	—
166	#41×C₆₁	—	4	4	no	—
167	C₂×Q₈×C₆₁	—	2	1	no	—
168	C₂×Q₈×C₆₁	—	2	1	no	—
169	C₂×Q₈×C₆₁	—	2	1	no	—
170	C₂×Q₈×C₆₁	—	2	8	no	—
171	C₂×Q₈×C₆₁	—	2	1	no	—
172	C₂×Q₈×C₆₁	—	2	1	no	—
173	C₂×Q₈×C₆₁	—	2	1	no	—
174	C₂×Q₈×C₆₁	—	2	1	no	—
175	C₂×Q₈×C₆₁	—	2	1	no	—
176	C₂×Q₈×C₆₁	—	2	1	no	—
177	C₂×Q₈×C₆₁	—	2	1	no	—
178	C₂×Q₈×C₆₁	—	2	1	no	—
179	C₂×Q₈×C₆₁	—	2	1	no	—
180	C₂×Q₈×C₆₁	—	2	1	no	—
181	C₂×Q₈×C₆₁	—	2	1	no	—
182	C₂×Q₈×C₆₁	—	2	1	no	—
183	C₂×Q₈×C₆₁	—	2	1	no	—
184	C₂×Q₈×C₆₁	—	2	1	no	—
185	C₂×Q₈×C₆₁	—	2	1	no	—
186	C₂×Q₈×C₆₁	—	2	1	no	—
187	C₂×Q₈×C₆₁	—	2	1	no	—
188	C₂×Q₈×C₆₁	—	2	1	no	—
189	C₂×Q₈×C₆₁	—	2	1	no	—
190	C₂×Q₈×C₆₁	—	2	1	no	—
191	C₂×Q₈×C₆₁	—	2	1	no	—
192	C₂×Q₈×C₆₁	—	2	1	no	—
193	C₂×Q₈×C₆₁	—	2	1	no	—
194	C₂×Q₈×C₆₁	—	2	1	no	—
195	C₂×Q₈×C₆₁	—	4	2	no	—
196	C₂×Q₈×C₆₁	—	4	2	no	—
197	C₂×Q₈×C₆₁	—	4	4	no	—
198	C₂×Q₈×C₆₁	—	4	4	no	—
199	C₂×Q₈×C₆₁	—	4	4	no	—
200	C₂×Q₈×C₆₁	—	4	2	no	—
201	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
202	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
203	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
204	C₂×D₄×C₆₁	—	2	1	no	—
205	C₂×D₄×C₆₁	—	2	1	no	—
206	C₂×D₄×C₆₁	—	2	1	no	—
207	C₂×D₄×C₆₁	—	2	1	no	—
208	C₂×D₄×C₆₁	—	2	1	no	—
209	C₂×D₄×C₆₁	—	4	2	no	—
210	C₂×D₄×C₆₁	—	4	2	no	—
211	C₂×D₄×C₆₁	—	4	2	no	—
212	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
213	C₂²×C₄×C₆₁	—	2	1	no	—
214	C₂²×C₄×C₆₁	—	2	1	no	—
215	C₂²×C₄×C₆₁	—	2	1	no	—
216	C₂²×C₄×C₆₁	—	2	1	no	—
217	C₂²×C₄×C₆₁	—	2	1	no	—
218	C₂²×C₄×C₆₁	—	2	1	no	—
219	C₂²×C₄×C₆₁	—	2	1	no	—
220	C₂²×C₄×C₆₁	—	2	1	no	—
221	C₂²×C₄×C₆₁	—	2	1	no	—
222	C₂²×C₄×C₆₁	—	2	1	no	—
223	C₂²×C₄×C₆₁	—	2	1	no	—
224	C₂²×C₄×C₆₁	—	4	2	no	—
225	C₂²×C₄×C₆₁	—	4	2	no	—
226	C₂²×C₄×C₆₁	—	4	2	no	—
227	C₂²×C₄×C₆₁	—	4	2	no	—
228	C₂²×C₄×C₆₁	—	4	2	no	—
229	C₂²×C₄×C₆₁	—	4	2	no	—
230	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
231	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
233	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
234	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
235	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
236	Q₁₆×C₆₁	—	2	8	no	—
237	Q₁₆×C₆₁	—	2	8	no	—
238	Q₁₆×C₆₁	—	4	4	no	—
239	Q₁₆×C₆₁	—	4	4	no	—
240	Q₁₆×C₆₁	—	4	4	no	—
241	Q₁₆×C₆₁	—	4	4	no	—
242	SD₁₆×C₆₁	—	2	8	no	—
243	SD₁₆×C₆₁	—	2	8	no	—
244	SD₁₆×C₆₁	—	4	4	no	—
245	M₁₆×C₆₁	—	2	8	no	—
246	C₂×C₈×C₆₁	—	2	1	no	—
247	C₂×C₈×C₆₁	—	2	1	no	—
248	C₂×C₈×C₆₁	—	2	1	no	—
249	C₂×C₈×C₆₁	—	2	1	no	—
250	C₂×C₈×C₆₁	—	2	1	no	—
251	C₂×C₈×C₆₁	—	2	1	no	—
252	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
253	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
254	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
255	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
256	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
257	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₆₁	—	2	1	no	—
259	C₄⋊C₄×C₆₁	—	2	1	no	—
260	C₄⋊C₄×C₆₁	—	2	1	no	—
261	C₄⋊C₄×C₆₁	—	2	1	no	—
262	C₄⋊C₄×C₆₁	—	4	4	no	—
263	C₄⋊C₄×C₆₁	—	4	4	no	—
264	C₄⋊C₄×C₆₁	—	4	4	no	—
265	C₄⋊C₄×C₆₁	—	4	2	no	—
266	C₄⋊C₄×C₆₁	—	4	2	no	—
267	C₂²⋊C₄×C₆₁	—	2	4	no	—
268	C₂²⋊C₄×C₆₁	—	4	4	no	—
269	C₂²⋊C₄×C₆₁	—	4	2	no	—
270	C₂²⋊C₄×C₆₁	—	4	2	no	—
271	C₂²⋊C₄×C₆₁	—	4	4	no	—
272	C₄²×C₆₁	—	2	1	no	—
273	C₄²×C₆₁	—	2	1	no	—
274	C₄²×C₆₁	—	2	1	no	—
275	C₄²×C₆₁	—	2	1	no	—
276	C₂³×C₆₁	—	2	1	no	—
277	C₂³×C₆₁	—	2	1	no	—
278	C₂³×C₆₁	—	2	2	no	—
279	C₂³×C₆₁	—	2	2	no	—
280	C₂³×C₆₁	—	2	2	no	—
281	C₂³×C₆₁	—	4	1	no	—
282	C₂³×C₆₁	—	4	1	no	—
283	C₂³×C₆₁	—	4	2	no	—
284	C₂³×C₆₁	—	4	2	no	—
285	C₂³×C₆₁	#127	1	2	yes	—
286	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
287	Q₈×C₆₁	—	2	2	no	—
288	Q₈×C₆₁	—	2	2	no	—
289	Q₈×C₆₁	—	2	2	no	—
290	Q₈×C₆₁	—	2	2	no	—
291	Q₈×C₆₁	—	2	2	no	—
292	Q₈×C₆₁	—	2	2	no	—
293	Q₈×C₆₁	—	4	8	no	—
294	Q₈×C₆₁	—	4	1	no	—
295	Q₈×C₆₁	—	4	1	no	—
296	Q₈×C₆₁	—	4	1	no	—
297	Q₈×C₆₁	—	4	1	no	—
298	Q₈×C₆₁	—	4	1	no	—
299	Q₈×C₆₁	—	4	1	no	—
300	Q₈×C₆₁	—	4	1	no	—
301	Q₈×C₆₁	—	4	1	no	—
302	Q₈×C₆₁	—	4	1	no	—
303	Q₈×C₆₁	—	4	1	no	—
304	Q₈×C₆₁	—	4	1	no	—
305	Q₈×C₆₁	—	4	1	no	—
306	Q₈×C₆₁	—	4	1	no	—
307	Q₈×C₆₁	—	4	1	no	—
308	D₄×C₆₁	—	2	2	no	—
309	D₄×C₆₁	—	2	2	no	—
310	D₄×C₆₁	—	4	8	no	—
311	D₄×C₆₁	—	4	1	no	—
312	D₄×C₆₁	—	4	1	no	—
313	C₂×C₄×C₆₁	—	2	2	no	—
314	C₂×C₄×C₆₁	—	2	1	no	—
315	C₂×C₄×C₆₁	—	2	1	no	—
316	C₂×C₄×C₆₁	—	2	2	no	—
317	C₂×C₄×C₆₁	—	2	2	no	—
318	C₂×C₄×C₆₁	—	2	2	no	—
319	C₂×C₄×C₆₁	—	2	2	no	—
320	C₂×C₄×C₆₁	—	2	2	no	—
321	C₂×C₄×C₆₁	—	2	2	no	—
322	C₂×C₄×C₆₁	—	2	2	no	—
323	C₂×C₄×C₆₁	—	2	2	no	—
324	C₂×C₄×C₆₁	—	2	2	no	—
325	C₂×C₄×C₆₁	—	2	2	no	—
326	C₂×C₄×C₆₁	—	2	2	no	—
327	C₂×C₄×C₆₁	—	4	8	no	—
328	C₂×C₄×C₆₁	—	4	8	no	—
329	C₂×C₄×C₆₁	—	4	1	no	—
330	C₂×C₄×C₆₁	—	4	1	no	—
331	C₂×C₄×C₆₁	—	4	1	no	—
332	C₂×C₄×C₆₁	—	4	1	no	—
333	C₂×C₄×C₆₁	—	4	1	no	—
334	C₂×C₄×C₆₁	—	4	1	no	—
335	C₂×C₄×C₆₁	—	4	1	no	—
336	C₂×C₄×C₆₁	—	4	1	no	—
337	C₂×C₄×C₆₁	—	4	1	no	—
338	C₂×C₄×C₆₁	—	4	1	no	—
339	C₂×C₄×C₆₁	—	4	1	no	—
340	C₂×C₄×C₆₁	—	4	1	no	—
341	C₂×C₄×C₆₁	—	4	1	no	—
342	C₂×C₄×C₆₁	—	4	1	no	—
343	C₂×C₄×C₆₁	—	4	2	no	—
344	C₂×C₄×C₆₁	—	4	2	no	—
345	C₂×C₄×C₆₁	#127	1	2	yes	—
346	C₂×C₄×C₆₁	#137	1	4	yes	complemented
347	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
352	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
353	C₈×C₆₁	—	2	2	no	—
354	C₈×C₆₁	—	2	2	no	—
355	C₈×C₆₁	—	2	2	no	—
356	C₈×C₆₁	#120	1	4	yes	—
357	#25795	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
358	C₂²×C₆₁	—	2	2	no	—
359	C₂²×C₆₁	—	2	2	no	—
360	C₂²×C₆₁	—	2	2	no	—
361	C₂²×C₆₁	—	4	2	no	—
362	C₂²×C₆₁	—	4	2	no	—
363	C₂²×C₆₁	—	4	2	no	—
364	C₂²×C₆₁	—	4	4	no	—
365	C₂²×C₆₁	—	8	1	no	—
366	C₂²×C₆₁	—	8	1	no	—
367	C₂²×C₆₁	—	8	2	no	—
368	C₂²×C₆₁	C₂×#127	1	1	yes	characteristic
369	C₂²×C₆₁	D₄²	1	1	yes	characteristic
370	C₂²×C₆₁	D₄²	1	1	yes	characteristic
371	C₂²×C₆₁	C₂×#137	1	2	yes	—
372	C₂²×C₆₁	#578	1	2	yes	—
373	C₄×C₆₁	—	2	2	no	—
374	C₄×C₆₁	—	2	4	no	—
375	C₄×C₆₁	—	4	2	no	—
376	C₄×C₆₁	—	4	2	no	—
377	C₄×C₆₁	—	4	2	no	—
378	C₄×C₆₁	—	4	2	no	—
379	C₄×C₆₁	—	8	1	no	—
380	C₄×C₆₁	—	8	1	no	—
381	C₄×C₆₁	—	8	1	no	—
382	C₄×C₆₁	—	8	1	no	—
383	C₄×C₆₁	C₂×#120	1	1	yes	characteristic
384	C₄×C₆₁	#535	1	1	yes	characteristic
385	C₄×C₆₁	D₄²	1	1	yes	characteristic
386	C₄×C₆₁	D₄²	1	1	yes	characteristic
387	C₂²×#137	C₂×C₆₁	1	1	yes	characteristic
388	C₂×#497	C₂×C₆₁	1	1	yes	characteristic, complemented
389	C₂×#494	C₂×C₆₁	1	1	yes	characteristic, complemented
390	C₂×#470	C₂×C₆₁	1	1	yes	characteristic, complemented
391	C₂×#452	C₂×C₆₁	1	1	yes	characteristic
392	C₂×#451	C₂×C₆₁	1	1	yes	characteristic, complemented
393	#2434	C₂×C₆₁	1	1	yes	characteristic, complemented
394	#2432	C₂×C₆₁	1	1	yes	characteristic
395	#2016	C₂×C₆₁	1	1	yes	characteristic, complemented
396	#2016	C₂×C₆₁	1	1	yes	characteristic, complemented
397	#2015	C₂×C₆₁	1	1	yes	characteristic, complemented
398	#2013	C₂×C₆₁	1	1	yes	characteristic, complemented
399	#1971	C₂×C₆₁	1	1	yes	characteristic, complemented
400	#1968	C₂×C₆₁	1	1	yes	characteristic, complemented
401	#1753	C₂×C₆₁	1	1	yes	characteristic, complemented
402	C₂×C₆₁	—	4	2	no	—
403	C₂×C₆₁	—	8	2	no	—
404	C₂×C₆₁	#2433	1	1	yes	characteristic
405	C₂×C₆₁	#3152	1	1	yes	characteristic
406	C₂×C₆₁	#3156	1	1	yes	characteristic
407	C₂×C₆₁	#3270	1	2	yes	—
408	C₂×C₆₁	#3276	1	2	yes	—
409	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
410	C₂³×Q₈	C₂²×C₆₁	1	1	yes	characteristic
411	C₂×#137	—	2	4	no	—
412	C₂×#137	—	2	4	no	—
413	C₂×#137	—	2	4	no	—
414	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
415	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
416	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
417	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
418	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
419	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
420	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
421	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
422	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
423	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
424	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
425	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
426	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
427	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
428	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
429	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
430	#497	—	2	4	no	—
431	#494	—	2	4	no	—
432	#470	—	2	4	no	—
433	#452	—	2	4	no	—
434	#451	—	2	4	no	—
435	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
436	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
437	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
438	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
439	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
440	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
441	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
442	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
443	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
444	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
445	#395	—	2	2	no	—
446	#394	—	2	2	no	—
447	#391	C₂²×C₆₁	1	1	yes	characteristic
448	#391	C₂²×C₆₁	1	1	yes	characteristic
449	#391	C₂²×C₆₁	1	1	yes	characteristic
450	#390	C₂²×C₆₁	1	1	yes	characteristic
451	#385	—	2	2	no	—
452	#385	—	2	2	no	—
453	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
454	#336	C₂²×C₆₁	1	1	yes	characteristic
455	#336	C₂²×C₆₁	1	1	yes	characteristic
456	C₆₁	#25795	1	1	yes	characteristic, direct product factor, Sylow
457	C₂×#41	—	2	2	no	—
458	C₂×#41	—	2	2	no	—
459	C₂×#41	—	2	2	no	—
460	C₂×#41	—	2	2	no	—
461	C₂×#41	—	4	1	no	—
462	C₂×#41	—	4	1	no	—
463	C₂²×Q₈	—	2	1	no	—
464	C₂²×Q₈	—	2	2	no	—
465	C₂²×Q₈	—	2	2	no	—
466	C₂²×Q₈	—	2	2	no	—
467	C₂²×Q₈	—	2	2	no	—
468	C₂²×Q₈	—	4	1	no	—
469	C₂²×Q₈	—	4	1	no	—
470	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
471	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
472	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
473	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
474	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
475	C₂²×D₄	—	2	1	no	—
476	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
477	C₂³×C₄	—	2	1	no	—
478	C₂³×C₄	—	2	1	no	—
479	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
480	#137	—	2	32	no	—
481	C₂×Q₁₆	—	2	2	no	—
482	C₂×Q₁₆	—	2	2	no	—
483	C₂×Q₁₆	—	2	2	no	—
484	C₂×Q₁₆	—	2	2	no	—
485	C₂×Q₁₆	—	2	2	no	—
486	C₂×Q₁₆	—	2	2	no	—
487	C₂×Q₁₆	—	2	2	no	—
488	C₂×Q₁₆	—	2	2	no	—
489	C₂×Q₁₆	—	2	2	no	—
490	C₂×Q₁₆	—	2	2	no	—
491	C₂×Q₁₆	—	2	2	no	—
492	C₂×Q₁₆	—	2	2	no	—
493	C₂×Q₁₆	—	2	2	no	—
494	C₂×Q₁₆	—	2	2	no	—
495	C₂×Q₁₆	—	4	1	no	—
496	C₂×Q₁₆	—	4	1	no	—
497	C₂×Q₁₆	—	4	1	no	—
498	C₂×Q₁₆	D₄×C₆₁	1	4	yes	—
499	C₂×SD₁₆	—	2	2	no	—
500	C₂×SD₁₆	—	2	2	no	—
501	C₂×SD₁₆	—	2	2	no	—
502	C₂×SD₁₆	—	2	2	no	—
503	C₂×SD₁₆	—	2	2	no	—
504	C₂×SD₁₆	—	2	2	no	—
505	C₂×SD₁₆	—	2	2	no	—
506	C₂×SD₁₆	—	4	1	no	—
507	C₂×SD₁₆	D₄×C₆₁	1	4	yes	—
508	C₂×M₁₆	—	2	2	no	—
509	C₂×M₁₆	—	2	2	no	—
510	C₂×M₁₆	D₄×C₆₁	1	4	yes	—
511	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
512	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
513	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
514	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
515	C₄⋊Q₈	—	2	2	no	—
516	C₄⋊Q₈	—	2	2	no	—
517	C₄⋊Q₈	—	2	2	no	—
518	C₄⋊Q₈	—	4	1	no	—
519	C₄⋊Q₈	—	4	1	no	—
520	C₄⋊Q₈	—	4	1	no	—
521	#124	—	2	2	no	—
522	#124	—	4	1	no	—
523	C₂²⋊Q₈	—	2	2	no	—
524	C₂²⋊Q₈	—	2	2	no	—
525	C₂²⋊Q₈	—	2	2	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂×C₄⋊C₄	—	2	1	no	—
528	C₂×C₄⋊C₄	—	2	1	no	—
529	C₂×C₄⋊C₄	—	2	2	no	—
530	C₂×C₄⋊C₄	—	2	2	no	—
531	C₂×C₄⋊C₄	—	2	2	no	—
532	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	—	2	1	no	—
535	C₂×C₂²⋊C₄	—	2	1	no	—
536	C₂×C₂²⋊C₄	—	2	2	no	—
537	C₂×C₂²⋊C₄	—	2	2	no	—
538	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
539	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
541	#106	—	2	2	no	—
542	#103	—	2	2	no	—
543	#103	—	2	2	no	—
544	#103	—	2	2	no	—
545	#103	—	2	2	no	—
546	#103	—	2	2	no	—
547	#102	—	2	2	no	—
548	C₂²⋊C₈	D₄×C₆₁	1	4	yes	—
549	#97	—	2	2	no	—
550	C₄×C₈	—	2	2	no	—
551	#95	—	2	2	no	—
552	#95	—	2	2	no	—
553	#95	—	2	2	no	—
554	#95	D₄×C₆₁	1	2	yes	—
555	C₂⁴	—	2	1	no	—
556	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
557	#41	—	2	8	no	—
558	#41	—	4	4	no	—
559	#41	—	4	4	no	—
560	#41	—	4	4	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	8	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	1	no	—
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	—	2	1	no	—
569	C₂×Q₈	—	2	1	no	—
570	C₂×Q₈	—	2	1	no	—
571	C₂×Q₈	—	2	1	no	—
572	C₂×Q₈	—	2	1	no	—
573	C₂×Q₈	—	2	1	no	—
574	C₂×Q₈	—	2	1	no	—
575	C₂×Q₈	—	2	1	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	1	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	—	2	1	no	—
585	C₂×Q₈	—	2	1	no	—
586	C₂×Q₈	—	2	1	no	—
587	C₂×Q₈	—	2	1	no	—
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	4	2	no	—
590	C₂×Q₈	—	4	2	no	—
591	C₂×Q₈	—	4	4	no	—
592	C₂×Q₈	—	4	4	no	—
593	C₂×Q₈	—	4	4	no	—
594	C₂×Q₈	—	4	2	no	—
595	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
596	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
597	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
598	C₂×D₄	—	2	1	no	—
599	C₂×D₄	—	2	1	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	4	2	no	—
604	C₂×D₄	—	4	2	no	—
605	C₂×D₄	—	4	2	no	—
606	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	4	2	no	—
619	C₂²×C₄	—	4	2	no	—
620	C₂²×C₄	—	4	2	no	—
621	C₂²×C₄	—	4	2	no	—
622	C₂²×C₄	—	4	2	no	—
623	C₂²×C₄	—	4	2	no	—
624	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
625	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
626	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
627	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
628	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
630	Q₁₆	—	2	8	no	—
631	Q₁₆	—	2	8	no	—
632	Q₁₆	—	4	4	no	—
633	Q₁₆	—	4	4	no	—
634	Q₁₆	—	4	4	no	—
635	Q₁₆	—	4	4	no	—
636	SD₁₆	—	2	8	no	—
637	SD₁₆	—	2	8	no	—
638	SD₁₆	—	4	4	no	—
639	M₁₆	—	2	8	no	—
640	C₂×C₈	—	2	1	no	—
641	C₂×C₈	—	2	1	no	—
642	C₂×C₈	—	2	1	no	—
643	C₂×C₈	—	2	1	no	—
644	C₂×C₈	—	2	1	no	—
645	C₂×C₈	—	2	1	no	—
646	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
647	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
648	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
649	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
650	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
651	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	4	4	no	—
657	C₄⋊C₄	—	4	4	no	—
658	C₄⋊C₄	—	4	4	no	—
659	C₄⋊C₄	—	4	2	no	—
660	C₄⋊C₄	—	4	2	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	4	4	no	—
663	C₂²⋊C₄	—	4	2	no	—
664	C₂²⋊C₄	—	4	2	no	—
665	C₂²⋊C₄	—	4	4	no	—
666	C₄²	—	2	1	no	—
667	C₄²	—	2	1	no	—
668	C₄²	—	2	1	no	—
669	C₄²	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	—	4	2	no	—
678	C₂³	—	4	2	no	—
679	C₂³	#127×C₆₁	1	2	yes	—
680	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
681	Q₈	—	2	2	no	—
682	Q₈	—	2	2	no	—
683	Q₈	—	2	2	no	—
684	Q₈	—	2	2	no	—
685	Q₈	—	2	2	no	—
686	Q₈	—	2	2	no	—
687	Q₈	—	4	8	no	—
688	Q₈	—	4	1	no	—
689	Q₈	—	4	1	no	—
690	Q₈	—	4	1	no	—
691	Q₈	—	4	1	no	—
692	Q₈	—	4	1	no	—
693	Q₈	—	4	1	no	—
694	Q₈	—	4	1	no	—
695	Q₈	—	4	1	no	—
696	Q₈	—	4	1	no	—
697	Q₈	—	4	1	no	—
698	Q₈	—	4	1	no	—
699	Q₈	—	4	1	no	—
700	Q₈	—	4	1	no	—
701	Q₈	—	4	1	no	—
702	D₄	—	2	2	no	—
703	D₄	—	2	2	no	—
704	D₄	—	4	8	no	—
705	D₄	—	4	1	no	—
706	D₄	—	4	1	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	4	8	no	—
722	C₂×C₄	—	4	8	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	2	no	—
738	C₂×C₄	—	4	2	no	—
739	C₂×C₄	#127×C₆₁	1	2	yes	—
740	C₂×C₄	#137×C₆₁	1	4	yes	complemented
741	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
742	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
743	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
745	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
746	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
747	C₈	—	2	2	no	—
748	C₈	—	2	2	no	—
749	C₈	—	2	2	no	—
750	C₈	#120×C₆₁	1	4	yes	—
751	C₂²	—	2	2	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	4	no	—
758	C₂²	—	8	1	no	—
759	C₂²	—	8	1	no	—
760	C₂²	—	8	2	no	—
761	C₂²	C₂×#127×C₆₁	1	1	yes	characteristic
762	C₂²	D₄²×C₆₁	1	1	yes	characteristic
763	C₂²	D₄²×C₆₁	1	1	yes	characteristic
764	C₂²	C₂×#137×C₆₁	1	2	yes	—
765	C₂²	C₆₁×#578	1	2	yes	—
766	C₄	—	2	2	no	—
767	C₄	—	2	4	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	8	1	no	—
773	C₄	—	8	1	no	—
774	C₄	—	8	1	no	—
775	C₄	—	8	1	no	—
776	C₄	C₂×#120×C₆₁	1	1	yes	characteristic
777	C₄	C₆₁×#535	1	1	yes	characteristic
778	C₄	D₄²×C₆₁	1	1	yes	characteristic
779	C₄	D₄²×C₆₁	1	1	yes	characteristic
780	C₂	—	4	2	no	—
781	C₂	—	8	2	no	—
782	C₂	C₆₁×#2433	1	1	yes	characteristic
783	C₂	C₆₁×#3152	1	1	yes	characteristic
784	C₂	C₆₁×#3156	1	1	yes	characteristic
785	C₂	C₆₁×#3270	1	2	yes	—
786	C₂	C₆₁×#3276	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂²×#41×C₆₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₄×C₂²⋊C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#497	C₂	semidirect
3. C₂×C₆₁×#494	C₂	semidirect
4. C₂×C₆₁×#470	C₂	semidirect
6. C₂×C₆₁×#451	C₂	semidirect
7. C₆₁×#2434	C₂	semidirect
9. C₆₁×#2016	C₂	semidirect
10. C₆₁×#2016	C₂	semidirect
11. C₆₁×#2015	C₂	semidirect
12. C₆₁×#2013	C₂	semidirect
13. C₆₁×#1971	C₂	semidirect
14. C₆₁×#1968	C₂	semidirect
15. C₆₁×#1753	C₂	semidirect
346. C₂×C₄×C₆₁	#137	semidirect
357. #25795	C₆₁	direct (N × H)
388. C₂×#497	C₂×C₆₁	semidirect
389. C₂×#494	C₂×C₆₁	semidirect
390. C₂×#470	C₂×C₆₁	semidirect
392. C₂×#451	C₂×C₆₁	semidirect
393. #2434	C₂×C₆₁	semidirect
395. #2016	C₂×C₆₁	semidirect
396. #2016	C₂×C₆₁	semidirect
397. #2015	C₂×C₆₁	semidirect
398. #2013	C₂×C₆₁	semidirect
399. #1971	C₂×C₆₁	semidirect
400. #1968	C₂×C₆₁	semidirect
401. #1753	C₂×C₆₁	semidirect
456. C₆₁	#25795	direct (N × H)
740. C₂×C₄	#137×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#137×C₆₁	2
C₂×C₆₁×#497	2
C₂×C₆₁×#494	2
C₂×C₆₁×#470	2
C₂×C₆₁×#452	2
C₂×C₆₁×#451	2
C₆₁×#2434	2
C₆₁×#2432	2
C₆₁×#2016	2
C₆₁×#2015	2
C₆₁×#2013	2
C₆₁×#1971	2
C₆₁×#1968	2
C₆₁×#1753	2
#25795	61

Subgroups — C61×#25795 #29529228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25795 #29529228