Subgroups — C₆₁×#34604 #29538037

Order 15616.

1536 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2666	C₂	1	2	yes	maximal, complemented
2	C₆₁×#2664	C₂	1	2	yes	maximal
3	C₆₁×#2655	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2655	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2654	C₂	1	2	yes	maximal
6	C₆₁×#2650	C₂	1	2	yes	maximal
7	C₆₁×#2637	C₂	1	2	yes	maximal
8	C₆₁×#2634	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2402	C₂	1	2	yes	maximal, complemented
10	C₆₁×#2402	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2401	C₂	1	2	yes	maximal
12	C₆₁×#2399	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#2396	C₂	1	1	yes	maximal, characteristic
14	C₆₁×#2396	C₂	1	1	yes	maximal, characteristic
15	C₄×#125×C₆₁	C₂	1	2	yes	maximal, complemented
16	C₄×#126×C₆₁	C₂	1	2	yes	maximal
17	C₆₁×#2298	C₂	1	1	yes	maximal, characteristic
18	C₆₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄²×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#126×C₆₁	C₂²	1	2	yes	—
21	C₂×#125×C₆₁	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#401	C₂²	1	2	yes	—
27	C₆₁×#400	C₂²	1	2	yes	—
28	C₆₁×#400	C₂²	1	2	yes	—
29	C₆₁×#400	C₂²	1	2	yes	—
30	C₆₁×#400	C₂²	1	2	yes	—
31	C₆₁×#400	C₂²	1	2	yes	—
32	C₆₁×#400	C₂²	1	2	yes	—
33	C₆₁×#400	C₂²	1	1	yes	characteristic
34	C₆₁×#400	C₂²	1	1	yes	characteristic
35	C₆₁×#400	C₂²	1	2	yes	—
36	C₆₁×#400	C₂²	1	2	yes	—
37	C₆₁×#400	C₂²	1	2	yes	—
38	C₆₁×#399	C₂²	1	1	yes	characteristic
39	C₆₁×#399	C₂²	1	1	yes	characteristic
40	C₆₁×#398	C₂²	1	2	yes	—
41	C₆₁×#398	C₂²	1	2	yes	—
42	C₆₁×#398	C₂²	1	2	yes	—
43	C₆₁×#398	C₂²	1	2	yes	—
44	C₆₁×#398	C₂²	1	2	yes	—
45	C₆₁×#398	C₂²	1	2	yes	—
46	C₆₁×#398	C₂²	1	2	yes	—
47	C₆₁×#398	C₂²	1	2	yes	—
48	C₆₁×#398	C₂²	1	2	yes	—
49	C₆₁×#398	C₂²	1	2	yes	—
50	C₆₁×#397	C₂²	1	2	yes	—
51	C₆₁×#397	C₂²	1	2	yes	—
52	C₆₁×#397	C₂²	1	2	yes	—
53	C₆₁×#396	C₂²	1	2	yes	—
54	C₆₁×#396	C₂²	1	2	yes	—
55	C₆₁×#396	C₂²	1	2	yes	—
56	C₆₁×#395	C₂²	1	1	yes	characteristic
57	C₆₁×#395	C₂²	1	2	yes	—
58	C₆₁×#395	C₂²	1	2	yes	—
59	C₆₁×#395	C₂²	1	1	yes	characteristic
60	C₆₁×#393	C₂²	1	1	yes	characteristic
61	C₆₁×#393	C₂²	1	1	yes	characteristic
62	C₆₁×#391	C₂²	1	2	yes	—
63	C₆₁×#389	C₂²	1	2	yes	—
64	C₆₁×#389	C₂²	1	2	yes	—
65	C₆₁×#389	C₂²	1	2	yes	—
66	C₆₁×#388	C₂²	1	2	yes	—
67	C₆₁×#388	C₂²	1	2	yes	—
68	C₆₁×#388	C₂²	1	2	yes	—
69	C₆₁×#388	C₂²	1	2	yes	—
70	C₆₁×#388	C₂²	1	2	yes	—
71	C₆₁×#387	C₂²	1	2	yes	—
72	C₆₁×#387	C₂²	1	2	yes	—
73	C₆₁×#387	C₂²	1	2	yes	—
74	C₆₁×#387	C₂²	1	2	yes	—
75	C₆₁×#387	C₂²	1	2	yes	—
76	C₆₁×#387	C₂²	1	2	yes	—
77	C₆₁×#387	C₂²	1	2	yes	—
78	C₆₁×#387	C₂²	1	2	yes	—
79	C₆₁×#387	C₂²	1	2	yes	—
80	C₆₁×#387	C₂²	1	2	yes	—
81	C₆₁×#387	C₂²	1	2	yes	—
82	C₆₁×#383	C₂²	1	2	yes	—
83	C₆₁×#382	C₂²	1	2	yes	—
84	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
85	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
86	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
87	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
88	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
89	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
91	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
92	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
93	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
103	C₆₁×#376	C₂²	1	2	yes	—
104	C₆₁×#376	C₂²	1	1	yes	characteristic
105	C₄³×C₆₁	C₂²	1	1	yes	characteristic
106	C₄³×C₆₁	C₂²	1	2	yes	—
107	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
110	#126×C₆₁	—	2	8	no	—
111	#125×C₆₁	—	2	8	no	—
112	C₄×Q₈×C₆₁	—	2	4	no	—
113	C₄×Q₈×C₆₁	—	2	4	no	—
114	C₄×Q₈×C₆₁	—	2	8	no	—
115	#117×C₆₁	—	2	4	no	—
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	2	yes	—
120	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
150	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
151	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
152	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
155	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
156	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
157	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
160	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
162	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
163	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
164	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
165	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
166	#95×C₆₁	C₂³	1	2	yes	—
167	#95×C₆₁	C₂³	1	2	yes	—
168	#95×C₆₁	C₂³	1	2	yes	—
169	#95×C₆₁	C₂³	1	2	yes	—
170	#95×C₆₁	C₂³	1	2	yes	—
171	#95×C₆₁	C₂³	1	2	yes	—
172	#95×C₆₁	C₂³	1	2	yes	—
173	#95×C₆₁	C₂³	1	2	yes	—
174	#95×C₆₁	C₂³	1	2	yes	—
175	#95×C₆₁	C₂³	1	2	yes	—
176	#95×C₆₁	C₂³	1	2	yes	—
177	#95×C₆₁	C₂³	1	2	yes	—
178	#95×C₆₁	C₂³	1	1	yes	characteristic
179	#95×C₆₁	C₂³	1	1	yes	characteristic
180	#95×C₆₁	C₂³	1	2	yes	—
181	#95×C₆₁	C₂³	1	2	yes	—
182	#95×C₆₁	C₂³	1	2	yes	—
183	#95×C₆₁	C₂³	1	2	yes	—
184	#95×C₆₁	C₂³	1	2	yes	—
185	#95×C₆₁	C₂³	1	2	yes	—
186	#95×C₆₁	C₂³	1	2	yes	—
187	#95×C₆₁	C₂³	1	2	yes	—
188	#95×C₆₁	C₂³	1	2	yes	—
189	#95×C₆₁	C₂³	1	1	yes	characteristic
190	#95×C₆₁	C₂³	1	2	yes	—
191	#95×C₆₁	C₂³	1	1	yes	characteristic
192	#95×C₆₁	C₂³	1	2	yes	—
193	#95×C₆₁	C₂³	1	2	yes	—
194	#95×C₆₁	C₂³	1	2	yes	—
195	#95×C₆₁	C₂³	1	2	yes	—
196	#95×C₆₁	C₂³	1	2	yes	—
197	#95×C₆₁	C₂³	1	2	yes	—
198	#95×C₆₁	C₂³	1	2	yes	—
199	#95×C₆₁	C₂³	1	2	yes	—
200	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
201	C₂×Q₈×C₆₁	—	2	2	no	—
202	C₂×Q₈×C₆₁	—	2	4	no	—
203	C₂×Q₈×C₆₁	—	2	2	no	—
204	C₂×Q₈×C₆₁	—	4	2	no	—
205	C₂²×C₄×C₆₁	—	2	2	no	—
206	C₂²×C₄×C₆₁	—	2	2	no	—
207	C₂²×C₄×C₆₁	—	2	2	no	—
208	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
226	C₄⋊C₄×C₆₁	—	2	2	no	—
227	C₄⋊C₄×C₆₁	—	2	2	no	—
228	C₄⋊C₄×C₆₁	—	2	4	no	—
229	C₄⋊C₄×C₆₁	—	2	4	no	—
230	C₄⋊C₄×C₆₁	—	2	4	no	—
231	C₄⋊C₄×C₆₁	—	2	4	no	—
232	C₄⋊C₄×C₆₁	—	2	2	no	—
233	C₄⋊C₄×C₆₁	—	2	2	no	—
234	C₄⋊C₄×C₆₁	—	2	4	no	—
235	C₄⋊C₄×C₆₁	—	2	4	no	—
236	C₄⋊C₄×C₆₁	—	2	4	no	—
237	C₄⋊C₄×C₆₁	—	2	4	no	—
238	C₄⋊C₄×C₆₁	—	2	4	no	—
239	C₄⋊C₄×C₆₁	—	2	4	no	—
240	C₄⋊C₄×C₆₁	—	2	4	no	—
241	C₄⋊C₄×C₆₁	—	2	4	no	—
242	C₄⋊C₄×C₆₁	—	2	4	no	—
243	C₄⋊C₄×C₆₁	—	2	4	no	—
244	C₄⋊C₄×C₆₁	—	4	2	no	—
245	C₄⋊C₄×C₆₁	—	4	2	no	—
246	C₄⋊C₄×C₆₁	—	4	2	no	—
247	C₄⋊C₄×C₆₁	—	4	2	no	—
248	C₄⋊C₄×C₆₁	—	4	2	no	—
249	C₄⋊C₄×C₆₁	—	4	2	no	—
250	C₄⋊C₄×C₆₁	—	4	2	no	—
251	C₄⋊C₄×C₆₁	—	4	2	no	—
252	C₂²⋊C₄×C₆₁	—	2	2	no	—
253	C₂²⋊C₄×C₆₁	—	2	2	no	—
254	C₂²⋊C₄×C₆₁	—	2	4	no	—
255	C₂²⋊C₄×C₆₁	—	2	4	no	—
256	C₂²⋊C₄×C₆₁	—	2	4	no	—
257	C₂²⋊C₄×C₆₁	—	4	2	no	—
258	C₂²⋊C₄×C₆₁	—	4	2	no	—
259	C₂²⋊C₄×C₆₁	—	4	2	no	—
260	C₄²×C₆₁	—	2	2	no	—
261	C₄²×C₆₁	—	2	4	no	—
262	C₄²×C₆₁	—	2	4	no	—
263	C₄²×C₆₁	—	2	4	no	—
264	C₄²×C₆₁	—	2	4	no	—
265	C₄²×C₆₁	—	2	2	no	—
266	C₄²×C₆₁	—	2	4	no	—
267	C₄²×C₆₁	—	2	2	no	—
268	C₄²×C₆₁	—	2	4	no	—
269	C₄²×C₆₁	—	2	2	no	—
270	C₄²×C₆₁	—	2	2	no	—
271	C₄²×C₆₁	—	4	2	no	—
272	C₄²×C₆₁	—	4	2	no	—
273	C₄²×C₆₁	—	4	2	no	—
274	C₄²×C₆₁	#41	1	4	yes	—
275	C₄²×C₆₁	#41	1	8	yes	—
276	C₂³×C₆₁	—	2	2	no	—
277	C₂³×C₆₁	—	2	1	no	—
278	C₂³×C₆₁	—	2	1	no	—
279	C₂³×C₆₁	—	2	1	no	—
280	C₂³×C₆₁	—	2	2	no	—
281	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
282	Q₈×C₆₁	—	2	8	no	—
283	Q₈×C₆₁	—	4	4	no	—
284	C₂×C₄×C₆₁	—	2	2	no	—
285	C₂×C₄×C₆₁	—	2	2	no	—
286	C₂×C₄×C₆₁	—	2	2	no	—
287	C₂×C₄×C₆₁	—	2	2	no	—
288	C₂×C₄×C₆₁	—	2	2	no	—
289	C₂×C₄×C₆₁	—	2	2	no	—
290	C₂×C₄×C₆₁	—	2	2	no	—
291	C₂×C₄×C₆₁	—	2	2	no	—
292	C₂×C₄×C₆₁	—	2	1	no	—
293	C₂×C₄×C₆₁	—	2	1	no	—
294	C₂×C₄×C₆₁	—	2	2	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	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	1	no	—
307	C₂×C₄×C₆₁	—	2	2	no	—
308	C₂×C₄×C₆₁	—	2	2	no	—
309	C₂×C₄×C₆₁	—	2	2	no	—
310	C₂×C₄×C₆₁	—	2	2	no	—
311	C₂×C₄×C₆₁	—	2	2	no	—
312	C₂×C₄×C₆₁	—	2	2	no	—
313	C₂×C₄×C₆₁	—	2	1	no	—
314	C₂×C₄×C₆₁	—	2	1	no	—
315	C₂×C₄×C₆₁	—	2	2	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	—	4	4	no	—
327	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
328	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
329	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
330	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
331	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
332	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
333	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
334	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
335	#34604	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
336	C₂²×C₆₁	—	4	1	no	—
337	C₂²×C₆₁	—	4	1	no	—
338	C₂²×C₆₁	—	4	1	no	—
339	C₂²×C₆₁	—	4	2	no	—
340	C₂²×C₆₁	—	4	2	no	—
341	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
342	C₂²×C₆₁	C₂²×#41	1	2	yes	—
343	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
344	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
345	C₂²×C₆₁	#585	1	2	yes	—
346	C₄×C₆₁	—	2	4	no	—
347	C₄×C₆₁	—	2	2	no	—
348	C₄×C₆₁	—	2	2	no	—
349	C₄×C₆₁	—	2	4	no	—
350	C₄×C₆₁	—	2	4	no	—
351	C₄×C₆₁	—	4	1	no	—
352	C₄×C₆₁	—	4	2	no	—
353	C₄×C₆₁	—	4	1	no	—
354	C₄×C₆₁	—	4	1	no	—
355	C₄×C₆₁	—	4	2	no	—
356	C₄×C₆₁	—	4	2	no	—
357	C₄×C₆₁	—	4	2	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	—	4	2	no	—
363	C₄×C₆₁	#541	1	4	yes	—
364	#2666	C₂×C₆₁	1	2	yes	complemented
365	#2664	C₂×C₆₁	1	2	yes	—
366	#2655	C₂×C₆₁	1	2	yes	complemented
367	#2655	C₂×C₆₁	1	2	yes	complemented
368	#2654	C₂×C₆₁	1	2	yes	—
369	#2650	C₂×C₆₁	1	2	yes	—
370	#2637	C₂×C₆₁	1	2	yes	—
371	#2634	C₂×C₆₁	1	2	yes	complemented
372	#2402	C₂×C₆₁	1	1	yes	characteristic, complemented
373	#2402	C₂×C₆₁	1	2	yes	complemented
374	#2401	C₂×C₆₁	1	2	yes	—
375	#2399	C₂×C₆₁	1	1	yes	characteristic, complemented
376	#2396	C₂×C₆₁	1	1	yes	characteristic
377	#2396	C₂×C₆₁	1	1	yes	characteristic
378	C₄×#125	C₂×C₆₁	1	2	yes	complemented
379	C₄×#126	C₂×C₆₁	1	2	yes	—
380	#2298	C₂×C₆₁	1	1	yes	characteristic
381	#2295	C₂×C₆₁	1	1	yes	characteristic, complemented
382	C₄²×Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
383	C₂×C₆₁	—	8	1	no	—
384	C₂×C₆₁	#3444	1	1	yes	characteristic
385	C₂×C₆₁	C₂×#541	1	1	yes	characteristic
386	C₂×C₆₁	#3455	1	1	yes	characteristic
387	C₂×C₆₁	#3461	1	2	yes	—
388	C₂×C₆₁	#3461	1	2	yes	—
389	C₂×#126	C₂²×C₆₁	1	2	yes	—
390	C₂×#125	C₂²×C₆₁	1	2	yes	—
391	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
392	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
393	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
394	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
395	#401	C₂²×C₆₁	1	2	yes	—
396	#400	C₂²×C₆₁	1	2	yes	—
397	#400	C₂²×C₆₁	1	2	yes	—
398	#400	C₂²×C₆₁	1	2	yes	—
399	#400	C₂²×C₆₁	1	2	yes	—
400	#400	C₂²×C₆₁	1	2	yes	—
401	#400	C₂²×C₆₁	1	2	yes	—
402	#400	C₂²×C₆₁	1	1	yes	characteristic
403	#400	C₂²×C₆₁	1	1	yes	characteristic
404	#400	C₂²×C₆₁	1	2	yes	—
405	#400	C₂²×C₆₁	1	2	yes	—
406	#400	C₂²×C₆₁	1	2	yes	—
407	#399	C₂²×C₆₁	1	1	yes	characteristic
408	#399	C₂²×C₆₁	1	1	yes	characteristic
409	#398	C₂²×C₆₁	1	2	yes	—
410	#398	C₂²×C₆₁	1	2	yes	—
411	#398	C₂²×C₆₁	1	2	yes	—
412	#398	C₂²×C₆₁	1	2	yes	—
413	#398	C₂²×C₆₁	1	2	yes	—
414	#398	C₂²×C₆₁	1	2	yes	—
415	#398	C₂²×C₆₁	1	2	yes	—
416	#398	C₂²×C₆₁	1	2	yes	—
417	#398	C₂²×C₆₁	1	2	yes	—
418	#398	C₂²×C₆₁	1	2	yes	—
419	#397	C₂²×C₆₁	1	2	yes	—
420	#397	C₂²×C₆₁	1	2	yes	—
421	#397	C₂²×C₆₁	1	2	yes	—
422	#396	C₂²×C₆₁	1	2	yes	—
423	#396	C₂²×C₆₁	1	2	yes	—
424	#396	C₂²×C₆₁	1	2	yes	—
425	#395	C₂²×C₆₁	1	1	yes	characteristic
426	#395	C₂²×C₆₁	1	2	yes	—
427	#395	C₂²×C₆₁	1	2	yes	—
428	#395	C₂²×C₆₁	1	1	yes	characteristic
429	#393	C₂²×C₆₁	1	1	yes	characteristic
430	#393	C₂²×C₆₁	1	1	yes	characteristic
431	#391	C₂²×C₆₁	1	2	yes	—
432	#389	C₂²×C₆₁	1	2	yes	—
433	#389	C₂²×C₆₁	1	2	yes	—
434	#389	C₂²×C₆₁	1	2	yes	—
435	#388	C₂²×C₆₁	1	2	yes	—
436	#388	C₂²×C₆₁	1	2	yes	—
437	#388	C₂²×C₆₁	1	2	yes	—
438	#388	C₂²×C₆₁	1	2	yes	—
439	#388	C₂²×C₆₁	1	2	yes	—
440	#387	C₂²×C₆₁	1	2	yes	—
441	#387	C₂²×C₆₁	1	2	yes	—
442	#387	C₂²×C₆₁	1	2	yes	—
443	#387	C₂²×C₆₁	1	2	yes	—
444	#387	C₂²×C₆₁	1	2	yes	—
445	#387	C₂²×C₆₁	1	2	yes	—
446	#387	C₂²×C₆₁	1	2	yes	—
447	#387	C₂²×C₆₁	1	2	yes	—
448	#387	C₂²×C₆₁	1	2	yes	—
449	#387	C₂²×C₆₁	1	2	yes	—
450	#387	C₂²×C₆₁	1	2	yes	—
451	#383	C₂²×C₆₁	1	2	yes	—
452	#382	C₂²×C₆₁	1	2	yes	—
453	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
454	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
455	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
456	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
457	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
458	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
459	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
460	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
461	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
462	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
463	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
464	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
465	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
466	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
467	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
468	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
469	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
470	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
471	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
472	#376	C₂²×C₆₁	1	1	yes	characteristic
473	#376	C₂²×C₆₁	1	2	yes	—
474	C₄³	C₂²×C₆₁	1	2	yes	—
475	C₄³	C₂²×C₆₁	1	1	yes	characteristic
476	C₆₁	#34604	1	1	yes	characteristic, direct product factor, Sylow
477	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
478	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
480	#126	—	2	8	no	—
481	#125	—	2	8	no	—
482	C₄×Q₈	—	2	4	no	—
483	C₄×Q₈	—	2	4	no	—
484	C₄×Q₈	—	2	8	no	—
485	#117	—	2	4	no	—
486	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
513	C₂×C₂²⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
514	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
520	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
521	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
522	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
523	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
524	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
525	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
526	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
528	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
531	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
532	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
533	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
534	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
535	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
536	#95	C₂³×C₆₁	1	2	yes	—
537	#95	C₂³×C₆₁	1	2	yes	—
538	#95	C₂³×C₆₁	1	2	yes	—
539	#95	C₂³×C₆₁	1	2	yes	—
540	#95	C₂³×C₆₁	1	2	yes	—
541	#95	C₂³×C₆₁	1	2	yes	—
542	#95	C₂³×C₆₁	1	2	yes	—
543	#95	C₂³×C₆₁	1	2	yes	—
544	#95	C₂³×C₆₁	1	2	yes	—
545	#95	C₂³×C₆₁	1	2	yes	—
546	#95	C₂³×C₆₁	1	2	yes	—
547	#95	C₂³×C₆₁	1	2	yes	—
548	#95	C₂³×C₆₁	1	1	yes	characteristic
549	#95	C₂³×C₆₁	1	1	yes	characteristic
550	#95	C₂³×C₆₁	1	2	yes	—
551	#95	C₂³×C₆₁	1	2	yes	—
552	#95	C₂³×C₆₁	1	2	yes	—
553	#95	C₂³×C₆₁	1	2	yes	—
554	#95	C₂³×C₆₁	1	2	yes	—
555	#95	C₂³×C₆₁	1	2	yes	—
556	#95	C₂³×C₆₁	1	2	yes	—
557	#95	C₂³×C₆₁	1	2	yes	—
558	#95	C₂³×C₆₁	1	2	yes	—
559	#95	C₂³×C₆₁	1	1	yes	characteristic
560	#95	C₂³×C₆₁	1	2	yes	—
561	#95	C₂³×C₆₁	1	1	yes	characteristic
562	#95	C₂³×C₆₁	1	2	yes	—
563	#95	C₂³×C₆₁	1	2	yes	—
564	#95	C₂³×C₆₁	1	2	yes	—
565	#95	C₂³×C₆₁	1	2	yes	—
566	#95	C₂³×C₆₁	1	2	yes	—
567	#95	C₂³×C₆₁	1	2	yes	—
568	#95	C₂³×C₆₁	1	2	yes	—
569	#95	C₂³×C₆₁	1	2	yes	—
570	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
571	C₂×Q₈	—	2	2	no	—
572	C₂×Q₈	—	2	4	no	—
573	C₂×Q₈	—	2	2	no	—
574	C₂×Q₈	—	4	2	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
593	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
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	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	4	2	no	—
615	C₄⋊C₄	—	4	2	no	—
616	C₄⋊C₄	—	4	2	no	—
617	C₄⋊C₄	—	4	2	no	—
618	C₄⋊C₄	—	4	2	no	—
619	C₄⋊C₄	—	4	2	no	—
620	C₄⋊C₄	—	4	2	no	—
621	C₄⋊C₄	—	4	2	no	—
622	C₂²⋊C₄	—	2	2	no	—
623	C₂²⋊C₄	—	2	2	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	4	2	no	—
628	C₂²⋊C₄	—	4	2	no	—
629	C₂²⋊C₄	—	4	2	no	—
630	C₄²	—	2	2	no	—
631	C₄²	—	2	4	no	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	4	no	—
635	C₄²	—	2	2	no	—
636	C₄²	—	2	4	no	—
637	C₄²	—	2	2	no	—
638	C₄²	—	2	2	no	—
639	C₄²	—	2	2	no	—
640	C₄²	—	2	4	no	—
641	C₄²	—	4	2	no	—
642	C₄²	—	4	2	no	—
643	C₄²	—	4	2	no	—
644	C₄²	#41×C₆₁	1	4	yes	—
645	C₄²	#41×C₆₁	1	8	yes	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	2	no	—
651	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
652	Q₈	—	2	8	no	—
653	Q₈	—	4	4	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	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	2	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	1	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	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
698	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
699	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
700	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
701	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
702	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
703	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
704	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
711	C₂²	C₂²×#41×C₆₁	1	2	yes	—
712	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
713	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
714	C₂²	C₆₁×#585	1	2	yes	—
715	C₄	—	2	4	no	—
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	4	no	—
719	C₄	—	2	4	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	1	no	—
723	C₄	—	4	1	no	—
724	C₄	—	4	2	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	C₆₁×#541	1	4	yes	—
733	C₂	—	8	1	no	—
734	C₂	C₆₁×#3444	1	1	yes	characteristic
735	C₂	C₂×C₆₁×#541	1	1	yes	characteristic
736	C₂	C₆₁×#3455	1	1	yes	characteristic
737	C₂	C₆₁×#3461	1	2	yes	—
738	C₂	C₆₁×#3461	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
socle	C₂³×C₆₁	C₂⁵
prime radical	C₂⁴×C₆₁	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#2666	C₂	semidirect
3. C₆₁×#2655	C₂	semidirect
4. C₆₁×#2655	C₂	semidirect
8. C₆₁×#2634	C₂	semidirect
9. C₆₁×#2402	C₂	semidirect
10. C₆₁×#2402	C₂	semidirect
12. C₆₁×#2399	C₂	semidirect
15. C₄×#125×C₆₁	C₂	semidirect
18. C₆₁×#2295	C₂	semidirect
19. C₄²×Q₈×C₆₁	C₂	semidirect
335. #34604	C₆₁	direct (N × H)
364. #2666	C₂×C₆₁	semidirect
366. #2655	C₂×C₆₁	semidirect
367. #2655	C₂×C₆₁	semidirect
371. #2634	C₂×C₆₁	semidirect
372. #2402	C₂×C₆₁	semidirect
373. #2402	C₂×C₆₁	semidirect
375. #2399	C₂×C₆₁	semidirect
378. C₄×#125	C₂×C₆₁	semidirect
381. #2295	C₂×C₆₁	semidirect
382. C₄²×Q₈	C₂×C₆₁	semidirect
476. C₆₁	#34604	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₁×#2666	2
C₆₁×#2664	2
C₆₁×#2655	2
C₆₁×#2654	2
C₆₁×#2650	2
C₆₁×#2637	2
C₆₁×#2634	2
C₆₁×#2402	2
C₆₁×#2401	2
C₆₁×#2399	2
C₆₁×#2396	2
C₄×#125×C₆₁	2
C₄×#126×C₆₁	2
C₆₁×#2298	2
C₆₁×#2295	2
C₄²×Q₈×C₆₁	2
#34604	61

Subgroups — C61×#34604 #29538037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#34604 #29538037