Subgroups — C₆₁×#21465 #29524898

Order 15616.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#520	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#452	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₁×#440	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2323	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1878	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1877	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1872	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1863	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1862	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1852	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1788	C₂	1	1	yes	maximal, characteristic
13	C₆₁×#1763	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#102×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₆₁×#520	—	2	4	no	—
21	C₆₁×#520	—	2	4	no	—
22	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₆₁	—	2	1	no	—
26	C₂×C₄×D₄×C₆₁	—	2	1	no	—
27	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#117×C₆₁	—	2	1	no	—
30	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
32	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
33	C₆₁×#452	C₄	1	8	yes	complemented
34	C₆₁×#440	—	2	4	no	—
35	C₄×Q₁₆×C₆₁	—	2	4	no	—
36	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×#103×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×#102×C₆₁	C₂²	1	1	yes	characteristic
44	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
45	C₂×#102×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	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
50	C₆₁×#391	C₂²	1	1	yes	characteristic
51	C₆₁×#389	—	2	1	no	—
52	C₆₁×#389	C₂²	1	1	yes	characteristic
53	C₆₁×#388	—	2	1	no	—
54	C₆₁×#388	—	2	1	no	—
55	C₆₁×#387	—	2	1	no	—
56	C₆₁×#380	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₆₁	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×#340	C₂²	1	1	yes	characteristic
62	C₆₁×#336	C₂²	1	1	yes	characteristic
63	C₆₁×#336	C₂²	1	1	yes	characteristic
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	—	2	2	no	—
68	C₂×#41×C₆₁	—	2	2	no	—
69	C₂×#41×C₆₁	C₂×C₄	1	4	yes	—
70	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₆₁	—	2	1	no	—
73	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₆₁	—	2	1	no	—
75	C₂³×C₄×C₆₁	—	2	1	no	—
76	C₂³×C₄×C₆₁	—	2	1	no	—
77	C₂³×C₄×C₆₁	—	2	1	no	—
78	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
79	C₂×Q₁₆×C₆₁	—	2	2	no	—
80	C₂×Q₁₆×C₆₁	—	2	2	no	—
81	C₂×Q₁₆×C₆₁	C₂×C₄	1	4	yes	complemented
82	C₂×SD₁₆×C₆₁	—	2	2	no	—
83	C₂×SD₁₆×C₆₁	—	2	2	no	—
84	C₂×SD₁₆×C₆₁	C₂×C₄	1	4	yes	complemented
85	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
89	C₂²⋊Q₈×C₆₁	—	2	2	no	—
90	C₂²⋊Q₈×C₆₁	C₂×C₄	1	4	yes	complemented
91	C₄×Q₈×C₆₁	—	2	2	no	—
92	C₄×Q₈×C₆₁	—	2	2	no	—
93	C₄×Q₈×C₆₁	—	2	2	no	—
94	C₄×Q₈×C₆₁	—	2	2	no	—
95	C₄×Q₈×C₆₁	—	2	2	no	—
96	C₄×Q₈×C₆₁	D₄	1	4	yes	—
97	C₄×D₄×C₆₁	—	2	8	no	—
98	C₄×D₄×C₆₁	—	2	8	no	—
99	C₄×D₄×C₆₁	—	2	2	no	—
100	C₄×D₄×C₆₁	—	2	2	no	—
101	C₄×D₄×C₆₁	—	2	2	no	—
102	C₄×D₄×C₆₁	D₄	1	4	yes	—
103	#117×C₆₁	—	2	8	no	—
104	#117×C₆₁	—	2	2	no	—
105	#117×C₆₁	—	2	2	no	—
106	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
107	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
108	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
109	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
110	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
111	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
112	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
113	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
114	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
115	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
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×C₂²⋊C₄×C₆₁	—	2	1	no	—
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	D₄	1	1	yes	characteristic
127	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
128	C₂×C₄²×C₆₁	—	2	1	no	—
129	C₂×C₄²×C₆₁	—	2	1	no	—
130	C₂×C₄²×C₆₁	—	2	1	no	—
131	C₂×C₄²×C₆₁	—	2	1	no	—
132	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
134	#107×C₆₁	—	2	2	no	—
135	#107×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	C₂×C₄	1	4	yes	complemented
141	#102×C₆₁	—	2	2	no	—
142	#102×C₆₁	—	2	2	no	—
143	#102×C₆₁	C₂×C₄	1	4	yes	complemented
144	C₂²⋊C₈×C₆₁	—	2	2	no	—
145	C₂²⋊C₈×C₆₁	C₂×C₄	1	4	yes	complemented
146	#97×C₆₁	—	2	2	no	—
147	C₄×C₈×C₆₁	—	2	2	no	—
148	#95×C₆₁	—	2	1	no	—
149	#95×C₆₁	—	2	1	no	—
150	#95×C₆₁	—	2	1	no	—
151	#95×C₆₁	—	2	1	no	—
152	#95×C₆₁	—	2	1	no	—
153	C₂⁴×C₆₁	—	2	1	no	—
154	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
155	#41×C₆₁	—	2	8	no	—
156	#41×C₆₁	—	2	8	no	—
157	#41×C₆₁	—	2	8	no	—
158	#41×C₆₁	—	2	8	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	—	2	1	no	—
163	C₂×Q₈×C₆₁	—	2	1	no	—
164	C₂×Q₈×C₆₁	—	2	1	no	—
165	C₂×Q₈×C₆₁	—	2	1	no	—
166	C₂×Q₈×C₆₁	—	2	1	no	—
167	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
168	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
169	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
170	C₂×Q₈×C₆₁	#41	1	2	yes	—
171	C₂×D₄×C₆₁	—	2	4	no	—
172	C₂×D₄×C₆₁	—	2	4	no	—
173	C₂×D₄×C₆₁	—	2	4	no	—
174	C₂×D₄×C₆₁	—	2	1	no	—
175	C₂×D₄×C₆₁	—	2	1	no	—
176	C₂×D₄×C₆₁	—	2	1	no	—
177	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
178	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
179	C₂×D₄×C₆₁	#41	1	2	yes	—
180	C₂²×C₄×C₆₁	—	2	4	no	—
181	C₂²×C₄×C₆₁	—	2	4	no	—
182	C₂²×C₄×C₆₁	—	2	1	no	—
183	C₂²×C₄×C₆₁	—	2	4	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	—	2	1	no	—
189	C₂²×C₄×C₆₁	—	2	1	no	—
190	C₂²×C₄×C₆₁	—	2	1	no	—
191	C₂²×C₄×C₆₁	—	2	1	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	1	no	—
196	C₂²×C₄×C₆₁	—	2	1	no	—
197	C₂²×C₄×C₆₁	—	8	1	no	—
198	C₂²×C₄×C₆₁	—	8	1	no	—
199	C₂²×C₄×C₆₁	—	8	1	no	—
200	C₂²×C₄×C₆₁	—	8	1	no	—
201	C₂²×C₄×C₆₁	—	8	1	no	—
202	C₂²×C₄×C₆₁	—	8	1	no	—
203	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
204	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₆₁	#41	1	2	yes	—
210	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
211	Q₁₆×C₆₁	—	2	8	no	—
212	SD₁₆×C₆₁	—	2	8	no	—
213	C₂×C₈×C₆₁	—	2	1	no	—
214	C₂×C₈×C₆₁	—	2	1	no	—
215	C₂×C₈×C₆₁	—	2	1	no	—
216	C₂×C₈×C₆₁	—	2	1	no	—
217	C₂×C₈×C₆₁	—	2	1	no	—
218	C₂×C₈×C₆₁	—	2	1	no	—
219	C₂×C₈×C₆₁	—	2	1	no	—
220	C₂×C₈×C₆₁	—	2	1	no	—
221	C₂×C₈×C₆₁	—	2	1	no	—
222	C₂×C₈×C₆₁	—	2	1	no	—
223	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
224	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
225	C₄⋊C₄×C₆₁	—	2	4	no	—
226	C₄⋊C₄×C₆₁	—	2	4	no	—
227	C₄⋊C₄×C₆₁	—	2	4	no	—
228	C₄⋊C₄×C₆₁	—	2	2	no	—
229	C₄⋊C₄×C₆₁	—	2	4	no	—
230	C₄⋊C₄×C₆₁	—	2	2	no	—
231	C₄⋊C₄×C₆₁	—	2	1	no	—
232	C₄⋊C₄×C₆₁	—	2	1	no	—
233	C₄⋊C₄×C₆₁	—	2	1	no	—
234	C₄⋊C₄×C₆₁	—	2	1	no	—
235	C₄⋊C₄×C₆₁	—	2	1	no	—
236	C₄⋊C₄×C₆₁	—	2	1	no	—
237	C₄⋊C₄×C₆₁	—	2	1	no	—
238	C₄⋊C₄×C₆₁	—	4	2	no	—
239	C₄⋊C₄×C₆₁	—	8	1	no	—
240	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
241	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
242	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
243	C₂²⋊C₄×C₆₁	—	2	4	no	—
244	C₂²⋊C₄×C₆₁	—	2	4	no	—
245	C₂²⋊C₄×C₆₁	—	2	4	no	—
246	C₂²⋊C₄×C₆₁	—	2	2	no	—
247	C₂²⋊C₄×C₆₁	—	2	2	no	—
248	C₂²⋊C₄×C₆₁	—	8	1	no	—
249	C₄²×C₆₁	—	2	4	no	—
250	C₄²×C₆₁	—	2	4	no	—
251	C₄²×C₆₁	—	2	1	no	—
252	C₄²×C₆₁	—	2	1	no	—
253	C₄²×C₆₁	—	4	2	no	—
254	C₄²×C₆₁	—	8	1	no	—
255	C₄²×C₆₁	C₂×D₄	1	2	yes	—
256	C₄²×C₆₁	C₂×D₄	1	2	yes	—
257	C₂³×C₆₁	—	2	2	no	—
258	C₂³×C₆₁	—	2	1	no	—
259	C₂³×C₆₁	—	2	2	no	—
260	C₂³×C₆₁	—	2	1	no	—
261	C₂³×C₆₁	—	2	2	no	—
262	C₂³×C₆₁	—	2	1	no	—
263	C₂³×C₆₁	—	2	1	no	—
264	C₂³×C₆₁	—	2	1	no	—
265	C₂³×C₆₁	—	2	1	no	—
266	C₂³×C₆₁	—	4	1	no	—
267	C₂³×C₆₁	—	4	1	no	—
268	C₂³×C₆₁	—	4	1	no	—
269	C₂³×C₆₁	—	4	1	no	—
270	C₂³×C₆₁	C₄×D₄	1	2	yes	—
271	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
272	Q₈×C₆₁	—	2	2	no	—
273	Q₈×C₆₁	—	2	2	no	—
274	Q₈×C₆₁	—	2	2	no	—
275	Q₈×C₆₁	—	2	2	no	—
276	Q₈×C₆₁	—	2	2	no	—
277	Q₈×C₆₁	—	4	1	no	—
278	Q₈×C₆₁	—	4	1	no	—
279	Q₈×C₆₁	C₄×D₄	1	4	yes	—
280	D₄×C₆₁	—	2	16	no	—
281	D₄×C₆₁	—	2	2	no	—
282	D₄×C₆₁	—	2	2	no	—
283	D₄×C₆₁	—	2	2	no	—
284	D₄×C₆₁	C₄×D₄	1	4	yes	—
285	C₂×C₄×C₆₁	—	2	16	no	—
286	C₂×C₄×C₆₁	—	2	2	no	—
287	C₂×C₄×C₆₁	—	2	2	no	—
288	C₂×C₄×C₆₁	—	2	1	no	—
289	C₂×C₄×C₆₁	—	2	1	no	—
290	C₂×C₄×C₆₁	—	2	2	no	—
291	C₂×C₄×C₆₁	—	2	1	no	—
292	C₂×C₄×C₆₁	—	2	1	no	—
293	C₂×C₄×C₆₁	—	2	1	no	—
294	C₂×C₄×C₆₁	—	2	1	no	—
295	C₂×C₄×C₆₁	—	2	2	no	—
296	C₂×C₄×C₆₁	—	2	2	no	—
297	C₂×C₄×C₆₁	—	2	2	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	1	no	—
302	C₂×C₄×C₆₁	—	2	1	no	—
303	C₂×C₄×C₆₁	—	2	2	no	—
304	C₂×C₄×C₆₁	—	2	2	no	—
305	C₂×C₄×C₆₁	—	2	1	no	—
306	C₂×C₄×C₆₁	—	2	1	no	—
307	C₂×C₄×C₆₁	—	2	1	no	—
308	C₂×C₄×C₆₁	—	2	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	—	4	1	no	—
317	C₂×C₄×C₆₁	—	4	1	no	—
318	C₂×C₄×C₆₁	—	4	1	no	—
319	C₂×C₄×C₆₁	—	4	1	no	—
320	C₂×C₄×C₆₁	—	4	1	no	—
321	C₂×C₄×C₆₁	—	4	1	no	—
322	C₂×C₄×C₆₁	—	4	1	no	—
323	C₂×C₄×C₆₁	—	8	4	no	—
324	C₂×C₄×C₆₁	—	8	4	no	—
325	C₂×C₄×C₆₁	—	8	4	no	—
326	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
327	C₂×C₄×C₆₁	#120	1	2	yes	—
328	C₂×C₄×C₆₁	#120	1	2	yes	—
329	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
330	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
333	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
334	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
335	C₈×C₆₁	—	2	2	no	—
336	C₈×C₆₁	—	2	2	no	—
337	C₈×C₆₁	—	4	1	no	—
338	C₈×C₆₁	—	4	1	no	—
339	#21465	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
340	C₂²×C₆₁	—	2	2	no	—
341	C₂²×C₆₁	—	2	2	no	—
342	C₂²×C₆₁	—	2	2	no	—
343	C₂²×C₆₁	—	2	4	no	—
344	C₂²×C₆₁	—	4	1	no	—
345	C₂²×C₆₁	—	4	2	no	—
346	C₂²×C₆₁	—	4	1	no	—
347	C₂²×C₆₁	—	4	2	no	—
348	C₂²×C₆₁	—	4	2	no	—
349	C₂²×C₆₁	—	4	2	no	—
350	C₂²×C₆₁	—	4	1	no	—
351	C₂²×C₆₁	—	4	2	no	—
352	C₂²×C₆₁	—	4	1	no	—
353	C₂²×C₆₁	—	4	2	no	—
354	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
355	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
356	C₂²×C₆₁	#525	1	1	yes	characteristic
357	C₂²×C₆₁	#576	1	1	yes	characteristic
358	C₂²×C₆₁	#577	1	1	yes	characteristic
359	C₂²×C₆₁	#578	1	1	yes	characteristic
360	C₂²×C₆₁	#578	1	1	yes	characteristic
361	C₄×C₆₁	—	2	2	no	—
362	C₄×C₆₁	—	2	2	no	—
363	C₄×C₆₁	—	2	2	no	—
364	C₄×C₆₁	—	2	4	no	—
365	C₄×C₆₁	—	4	2	no	—
366	C₄×C₆₁	—	4	1	no	—
367	C₄×C₆₁	—	4	1	no	—
368	C₄×C₆₁	—	4	2	no	—
369	C₄×C₆₁	—	4	2	no	—
370	C₄×C₆₁	—	4	2	no	—
371	C₄×C₆₁	—	8	1	no	—
372	C₄×C₆₁	—	8	1	no	—
373	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
374	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
375	C₄×C₆₁	#525	1	1	yes	characteristic
376	C₄×C₆₁	#525	1	1	yes	characteristic
377	C₂×#520	C₂×C₆₁	1	1	yes	characteristic
378	C₂×#452	C₂×C₆₁	1	1	yes	characteristic
379	C₂×#440	C₂×C₆₁	1	1	yes	characteristic, complemented
380	C₂×C₄×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
381	#2323	C₂×C₆₁	1	1	yes	characteristic, complemented
382	#1878	C₂×C₆₁	1	1	yes	characteristic, complemented
383	#1877	C₂×C₆₁	1	1	yes	characteristic, complemented
384	#1872	C₂×C₆₁	1	1	yes	characteristic, complemented
385	#1863	C₂×C₆₁	1	1	yes	characteristic, complemented
386	#1862	C₂×C₆₁	1	1	yes	characteristic, complemented
387	#1852	C₂×C₆₁	1	1	yes	characteristic, complemented
388	#1788	C₂×C₆₁	1	1	yes	characteristic
389	#1763	C₂×C₆₁	1	1	yes	characteristic, complemented
390	C₄×#102	C₂×C₆₁	1	1	yes	characteristic, complemented
391	#1750	C₂×C₆₁	1	1	yes	characteristic, complemented
392	C₂×C₆₁	—	4	2	no	—
393	C₂×C₆₁	—	4	4	no	—
394	C₂×C₆₁	C₄×#120	1	1	yes	characteristic
395	C₂×C₆₁	#2947	1	1	yes	characteristic
396	C₂×C₆₁	#2951	1	1	yes	characteristic
397	C₂×C₆₁	#3011	1	1	yes	characteristic
398	C₂×C₆₁	#3012	1	1	yes	characteristic
399	C₂×C₆₁	#3120	1	1	yes	characteristic
400	C₂×C₆₁	#3124	1	1	yes	characteristic
401	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
402	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
403	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
404	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
405	#520	—	2	4	no	—
406	#520	—	2	4	no	—
407	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
408	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
409	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
410	C₂×C₄×D₄	—	2	1	no	—
411	C₂×C₄×D₄	—	2	1	no	—
412	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
413	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
414	C₂×#117	—	2	1	no	—
415	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
416	C₂²×C₄⋊C₄	—	2	1	no	—
417	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
418	#452	C₄×C₆₁	1	8	yes	complemented
419	#440	—	2	4	no	—
420	C₄×Q₁₆	—	2	4	no	—
421	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
422	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
423	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
424	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
425	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
426	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
427	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
428	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
429	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
430	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
431	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
432	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
433	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
434	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
435	#391	C₂²×C₆₁	1	1	yes	characteristic
436	#389	—	2	1	no	—
437	#389	C₂²×C₆₁	1	1	yes	characteristic
438	#388	—	2	1	no	—
439	#388	—	2	1	no	—
440	#387	—	2	1	no	—
441	#380	C₂²×C₆₁	1	1	yes	characteristic
442	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
443	#340	C₂²×C₆₁	1	1	yes	characteristic
444	#340	C₂²×C₆₁	1	1	yes	characteristic
445	#340	C₂²×C₆₁	1	1	yes	characteristic
446	#340	C₂²×C₆₁	1	1	yes	characteristic
447	#336	C₂²×C₆₁	1	1	yes	characteristic
448	#336	C₂²×C₆₁	1	1	yes	characteristic
449	C₆₁	#21465	1	1	yes	characteristic, direct product factor, Sylow
450	C₂×#41	—	2	2	no	—
451	C₂×#41	—	2	2	no	—
452	C₂×#41	—	2	2	no	—
453	C₂×#41	—	2	2	no	—
454	C₂×#41	—	2	2	no	—
455	C₂×#41	C₂×C₄×C₆₁	1	4	yes	—
456	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
457	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
458	C₂²×D₄	—	2	1	no	—
459	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
460	C₂³×C₄	—	2	1	no	—
461	C₂³×C₄	—	2	1	no	—
462	C₂³×C₄	—	2	1	no	—
463	C₂³×C₄	—	2	1	no	—
464	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
465	C₂×Q₁₆	—	2	2	no	—
466	C₂×Q₁₆	—	2	2	no	—
467	C₂×Q₁₆	C₂×C₄×C₆₁	1	4	yes	complemented
468	C₂×SD₁₆	—	2	2	no	—
469	C₂×SD₁₆	—	2	2	no	—
470	C₂×SD₁₆	C₂×C₄×C₆₁	1	4	yes	complemented
471	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
472	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
473	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
474	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
475	C₂²⋊Q₈	—	2	2	no	—
476	C₂²⋊Q₈	C₂×C₄×C₆₁	1	4	yes	complemented
477	C₄×Q₈	—	2	2	no	—
478	C₄×Q₈	—	2	2	no	—
479	C₄×Q₈	—	2	2	no	—
480	C₄×Q₈	—	2	2	no	—
481	C₄×Q₈	—	2	2	no	—
482	C₄×Q₈	D₄×C₆₁	1	4	yes	—
483	C₄×D₄	—	2	8	no	—
484	C₄×D₄	—	2	8	no	—
485	C₄×D₄	—	2	2	no	—
486	C₄×D₄	—	2	2	no	—
487	C₄×D₄	—	2	2	no	—
488	C₄×D₄	D₄×C₆₁	1	4	yes	—
489	#117	—	2	8	no	—
490	#117	—	2	2	no	—
491	#117	—	2	2	no	—
492	C₂×C₄⋊C₄	—	2	8	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	2	no	—
498	C₂×C₄⋊C₄	—	2	2	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
502	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
513	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
514	C₂×C₄²	—	2	1	no	—
515	C₂×C₄²	—	2	1	no	—
516	C₂×C₄²	—	2	1	no	—
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
519	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
520	#107	—	2	2	no	—
521	#107	—	2	2	no	—
522	#103	—	2	2	no	—
523	#103	—	2	2	no	—
524	#103	—	2	2	no	—
525	#103	—	2	2	no	—
526	#103	C₂×C₄×C₆₁	1	4	yes	complemented
527	#102	—	2	2	no	—
528	#102	—	2	2	no	—
529	#102	C₂×C₄×C₆₁	1	4	yes	complemented
530	C₂²⋊C₈	—	2	2	no	—
531	C₂²⋊C₈	C₂×C₄×C₆₁	1	4	yes	complemented
532	#97	—	2	2	no	—
533	C₄×C₈	—	2	2	no	—
534	#95	—	2	1	no	—
535	#95	—	2	1	no	—
536	#95	—	2	1	no	—
537	#95	—	2	1	no	—
538	#95	—	2	1	no	—
539	C₂⁴	—	2	1	no	—
540	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
541	#41	—	2	8	no	—
542	#41	—	2	8	no	—
543	#41	—	2	8	no	—
544	#41	—	2	8	no	—
545	C₂×Q₈	—	2	1	no	—
546	C₂×Q₈	—	2	1	no	—
547	C₂×Q₈	—	2	1	no	—
548	C₂×Q₈	—	2	1	no	—
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
554	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
555	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
556	C₂×Q₈	#41×C₆₁	1	2	yes	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	—	2	4	no	—
559	C₂×D₄	—	2	4	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
564	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
565	C₂×D₄	#41×C₆₁	1	2	yes	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	8	1	no	—
584	C₂²×C₄	—	8	1	no	—
585	C₂²×C₄	—	8	1	no	—
586	C₂²×C₄	—	8	1	no	—
587	C₂²×C₄	—	8	1	no	—
588	C₂²×C₄	—	8	1	no	—
589	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
590	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
591	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
592	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
595	C₂²×C₄	#41×C₆₁	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
597	Q₁₆	—	2	8	no	—
598	SD₁₆	—	2	8	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	2	1	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
610	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	4	2	no	—
625	C₄⋊C₄	—	8	1	no	—
626	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
627	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
628	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	8	1	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	2	4	no	—
637	C₄²	—	2	1	no	—
638	C₄²	—	2	1	no	—
639	C₄²	—	4	2	no	—
640	C₄²	—	8	1	no	—
641	C₄²	C₂×D₄×C₆₁	1	2	yes	—
642	C₄²	C₂×D₄×C₆₁	1	2	yes	—
643	C₂³	—	2	1	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	2	1	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	4	1	no	—
653	C₂³	—	4	1	no	—
654	C₂³	—	4	1	no	—
655	C₂³	—	4	1	no	—
656	C₂³	C₄×D₄×C₆₁	1	2	yes	—
657	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
658	Q₈	—	2	2	no	—
659	Q₈	—	2	2	no	—
660	Q₈	—	2	2	no	—
661	Q₈	—	2	2	no	—
662	Q₈	—	2	2	no	—
663	Q₈	—	4	1	no	—
664	Q₈	—	4	1	no	—
665	Q₈	C₄×D₄×C₆₁	1	4	yes	—
666	D₄	—	2	16	no	—
667	D₄	—	2	2	no	—
668	D₄	—	2	2	no	—
669	D₄	—	2	2	no	—
670	D₄	C₄×D₄×C₆₁	1	4	yes	—
671	C₂×C₄	—	2	16	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	8	4	no	—
710	C₂×C₄	—	8	4	no	—
711	C₂×C₄	—	8	4	no	—
712	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
713	C₂×C₄	#120×C₆₁	1	2	yes	—
714	C₂×C₄	#120×C₆₁	1	2	yes	—
715	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
716	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
717	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
718	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
719	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
720	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
721	C₈	—	2	2	no	—
722	C₈	—	2	2	no	—
723	C₈	—	4	1	no	—
724	C₈	—	4	1	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	2	no	—
739	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
740	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
741	C₂²	C₆₁×#525	1	1	yes	characteristic
742	C₂²	C₆₁×#576	1	1	yes	characteristic
743	C₂²	C₆₁×#577	1	1	yes	characteristic
744	C₂²	C₆₁×#578	1	1	yes	characteristic
745	C₂²	C₆₁×#578	1	1	yes	characteristic
746	C₄	—	2	2	no	—
747	C₄	—	2	4	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	8	1	no	—
757	C₄	—	8	1	no	—
758	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
759	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
760	C₄	C₆₁×#525	1	1	yes	characteristic
761	C₄	C₆₁×#525	1	1	yes	characteristic
762	C₂	—	4	2	no	—
763	C₂	—	4	4	no	—
764	C₂	C₄×#120×C₆₁	1	1	yes	characteristic
765	C₂	C₆₁×#2947	1	1	yes	characteristic
766	C₂	C₆₁×#2951	1	1	yes	characteristic
767	C₂	C₆₁×#3011	1	1	yes	characteristic
768	C₂	C₆₁×#3012	1	1	yes	characteristic
769	C₂	C₆₁×#3120	1	1	yes	characteristic
770	C₂	C₆₁×#3124	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂²×#41×C₆₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×#117×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₆₁×#440	C₂	semidirect
4. C₂×C₄×Q₁₆×C₆₁	C₂	semidirect
5. C₆₁×#2323	C₂	semidirect
6. C₆₁×#1878	C₂	semidirect
7. C₆₁×#1877	C₂	semidirect
8. C₆₁×#1872	C₂	semidirect
9. C₆₁×#1863	C₂	semidirect
10. C₆₁×#1862	C₂	semidirect
11. C₆₁×#1852	C₂	semidirect
13. C₆₁×#1763	C₂	semidirect
14. C₄×#102×C₆₁	C₂	semidirect
15. C₆₁×#1750	C₂	semidirect
33. C₆₁×#452	C₄	semidirect
81. C₂×Q₁₆×C₆₁	C₂×C₄	semidirect
84. C₂×SD₁₆×C₆₁	C₂×C₄	semidirect
90. C₂²⋊Q₈×C₆₁	C₂×C₄	semidirect
140. #103×C₆₁	C₂×C₄	semidirect
143. #102×C₆₁	C₂×C₄	semidirect
145. C₂²⋊C₈×C₆₁	C₂×C₄	semidirect
339. #21465	C₆₁	direct (N × H)
379. C₂×#440	C₂×C₆₁	semidirect
380. C₂×C₄×Q₁₆	C₂×C₆₁	semidirect
381. #2323	C₂×C₆₁	semidirect
382. #1878	C₂×C₆₁	semidirect
383. #1877	C₂×C₆₁	semidirect
384. #1872	C₂×C₆₁	semidirect
385. #1863	C₂×C₆₁	semidirect
386. #1862	C₂×C₆₁	semidirect
387. #1852	C₂×C₆₁	semidirect
389. #1763	C₂×C₆₁	semidirect
390. C₄×#102	C₂×C₆₁	semidirect
391. #1750	C₂×C₆₁	semidirect
418. #452	C₄×C₆₁	semidirect
449. C₆₁	#21465	direct (N × H)
467. C₂×Q₁₆	C₂×C₄×C₆₁	semidirect
470. C₂×SD₁₆	C₂×C₄×C₆₁	semidirect
476. C₂²⋊Q₈	C₂×C₄×C₆₁	semidirect
526. #103	C₂×C₄×C₆₁	semidirect
529. #102	C₂×C₄×C₆₁	semidirect
531. C₂²⋊C₈	C₂×C₄×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×#520	2
C₂×C₆₁×#452	2
C₂×C₆₁×#440	2
C₂×C₄×Q₁₆×C₆₁	2
C₆₁×#2323	2
C₆₁×#1878	2
C₆₁×#1877	2
C₆₁×#1872	2
C₆₁×#1863	2
C₆₁×#1862	2
C₆₁×#1852	2
C₆₁×#1788	2
C₆₁×#1763	2
C₄×#102×C₆₁	2
C₆₁×#1750	2
#21465	61

Subgroups — C61×#21465 #29524898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#21465 #29524898