Subgroups — C₆₁×#61934 #29565367

Order 15616.

1690 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3400	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3398	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3394	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3393	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3369	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3367	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3363	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3359	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3225	C₂	1	4	yes	maximal, complemented
12	C₆₁×#3209	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3206	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3121	C₂	1	4	yes	maximal, complemented
15	C₆₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3106	C₂	1	1	yes	maximal, characteristic
17	C₆₁×#2986	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#563	—	2	2	no	—
19	C₆₁×#559	C₂²	1	2	yes	—
20	Q₈²×C₆₁	C₂²	1	2	yes	—
21	C₆₁×#557	C₂²	1	2	yes	—
22	C₆₁×#557	C₂²	1	2	yes	—
23	C₆₁×#556	—	2	1	no	—
24	C₆₁×#556	C₂²	1	2	yes	—
25	C₆₁×#556	C₂²	1	2	yes	—
26	C₆₁×#556	C₂²	1	2	yes	—
27	C₆₁×#552	—	2	2	no	—
28	C₆₁×#552	—	2	2	no	—
29	D₄×Q₈×C₆₁	—	2	1	no	—
30	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
31	C₆₁×#542	—	2	2	no	—
32	C₆₁×#542	C₂²	1	4	yes	—
33	C₆₁×#541	—	2	2	no	—
34	C₆₁×#536	—	2	2	no	—
35	C₆₁×#536	C₂²	1	2	yes	—
36	C₆₁×#533	—	2	1	no	—
37	C₆₁×#533	—	2	1	no	—
38	C₆₁×#533	C₂²	1	1	yes	characteristic
39	C₆₁×#533	C₂²	1	1	yes	characteristic
40	C₆₁×#532	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
42	C₆₁×#519	C₂²	1	2	yes	—
43	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
44	C₆₁×#497	C₂²	1	4	yes	—
45	C₆₁×#495	C₂²	1	4	yes	—
46	C₆₁×#494	C₂²	1	2	yes	—
47	C₆₁×#492	C₂²	1	2	yes	—
48	C₆₁×#489	C₂²	1	4	yes	—
49	C₆₁×#487	C₂²	1	4	yes	—
50	C₆₁×#487	C₂²	1	2	yes	—
51	C₆₁×#487	C₂²	1	2	yes	—
52	C₆₁×#485	C₂²	1	2	yes	—
53	C₆₁×#482	C₂²	1	2	yes	—
54	C₆₁×#477	C₂²	1	1	yes	characteristic
55	C₆₁×#477	C₂²	1	4	yes	—
56	C₆₁×#476	C₂²	1	1	yes	characteristic
57	C₆₁×#475	C₂²	1	1	yes	characteristic
58	C₆₁×#475	C₂²	1	4	yes	—
59	C₆₁×#474	C₂²	1	1	yes	characteristic
60	C₆₁×#464	C₂²	1	4	yes	—
61	C₆₁×#464	C₂²	1	4	yes	—
62	C₆₁×#464	C₂²	1	4	yes	—
63	C₆₁×#463	C₂²	1	4	yes	—
64	C₆₁×#462	C₂²	1	1	yes	characteristic
65	C₆₁×#462	C₂²	1	2	yes	—
66	C₆₁×#462	C₂²	1	4	yes	—
67	C₆₁×#462	C₂²	1	2	yes	—
68	C₆₁×#461	C₂²	1	2	yes	—
69	C₆₁×#461	C₂²	1	4	yes	—
70	C₆₁×#461	C₂²	1	1	yes	characteristic
71	C₆₁×#461	C₂²	1	2	yes	—
72	C₆₁×#460	C₂²	1	1	yes	characteristic
73	C₆₁×#459	C₂²	1	1	yes	characteristic
74	C₆₁×#452	C₂²	1	2	yes	—
75	C₆₁×#451	C₂²	1	4	yes	—
76	C₆₁×#449	C₂²	1	2	yes	—
77	C₆₁×#448	C₂²	1	4	yes	—
78	C₆₁×#446	C₂²	1	2	yes	—
79	C₆₁×#446	C₂²	1	2	yes	—
80	C₈×Q₈×C₆₁	C₂²	1	2	yes	—
81	C₈×Q₈×C₆₁	C₂²	1	2	yes	—
82	C₆₁×#441	C₂²	1	4	yes	—
83	C₆₁×#440	C₂²	1	4	yes	—
84	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
85	C₄×Q₁₆×C₆₁	C₂²	1	4	yes	—
86	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
87	C₄×SD₁₆×C₆₁	C₂²	1	4	yes	—
88	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
89	C₄×D₈×C₆₁	C₂²	1	2	yes	—
90	C₆₁×#433	C₂²	1	4	yes	—
91	C₆₁×#431	C₂²	1	1	yes	characteristic
92	C₆₁×#431	C₂²	1	1	yes	characteristic
93	C₂×#41×C₆₁	—	2	1	no	—
94	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₆₁	—	2	2	no	—
96	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
97	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
98	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
99	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₆₁	C₂³	1	4	yes	—
104	C₂×D₈×C₆₁	C₂³	1	2	yes	—
105	C₄⋊Q₈×C₆₁	—	2	4	no	—
106	C₄⋊Q₈×C₆₁	—	2	2	no	—
107	C₄⋊Q₈×C₆₁	—	2	1	no	—
108	C₄⋊Q₈×C₆₁	—	2	1	no	—
109	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
110	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
111	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
113	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
115	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
117	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
118	#127×C₆₁	C₂³	1	1	yes	characteristic
119	#126×C₆₁	—	2	4	no	—
120	#126×C₆₁	—	2	4	no	—
121	#126×C₆₁	—	2	4	no	—
122	#126×C₆₁	—	2	4	no	—
123	#125×C₆₁	—	2	2	no	—
124	#125×C₆₁	—	2	2	no	—
125	#125×C₆₁	—	2	4	no	—
126	#125×C₆₁	—	2	4	no	—
127	#125×C₆₁	—	2	1	no	—
128	#125×C₆₁	D₄	1	2	yes	—
129	#124×C₆₁	—	2	2	no	—
130	#124×C₆₁	—	2	4	no	—
131	#124×C₆₁	—	2	1	no	—
132	#124×C₆₁	C₂³	1	4	yes	—
133	#124×C₆₁	C₂³	1	4	yes	—
134	#123×C₆₁	—	2	4	no	—
135	#123×C₆₁	—	2	4	no	—
136	#123×C₆₁	—	2	4	no	—
137	C₂²⋊Q₈×C₆₁	—	2	2	no	—
138	C₂²⋊Q₈×C₆₁	—	2	2	no	—
139	C₂²⋊Q₈×C₆₁	—	2	2	no	—
140	C₂²⋊Q₈×C₆₁	—	2	1	no	—
141	C₂²⋊Q₈×C₆₁	—	2	2	no	—
142	C₂²⋊Q₈×C₆₁	—	2	2	no	—
143	C₂²⋊Q₈×C₆₁	—	2	2	no	—
144	C₂²⋊Q₈×C₆₁	—	2	4	no	—
145	C₂²⋊Q₈×C₆₁	—	2	4	no	—
146	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
147	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
148	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
149	#121×C₆₁	—	2	1	no	—
150	#121×C₆₁	C₂³	1	2	yes	—
151	C₄×Q₈×C₆₁	—	2	2	no	—
152	C₄×Q₈×C₆₁	—	2	2	no	—
153	C₄×Q₈×C₆₁	—	2	2	no	—
154	C₄×Q₈×C₆₁	—	2	2	no	—
155	C₄×Q₈×C₆₁	—	2	2	no	—
156	C₄×Q₈×C₆₁	—	2	1	no	—
157	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
158	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
159	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
160	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
161	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
162	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
164	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
165	C₄×D₄×C₆₁	—	2	1	no	—
166	C₄×D₄×C₆₁	—	2	1	no	—
167	C₄×D₄×C₆₁	—	2	2	no	—
168	C₄×D₄×C₆₁	—	2	1	no	—
169	C₄×D₄×C₆₁	C₂³	1	2	yes	—
170	C₄×D₄×C₆₁	C₂³	1	4	yes	—
171	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
173	#117×C₆₁	—	2	1	no	—
174	#117×C₆₁	—	2	2	no	—
175	#117×C₆₁	—	2	2	no	—
176	#117×C₆₁	—	2	2	no	—
177	#117×C₆₁	—	2	4	no	—
178	#117×C₆₁	—	2	1	no	—
179	#117×C₆₁	C₂³	1	1	yes	characteristic
180	#117×C₆₁	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
182	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
183	C₂×C₄²×C₆₁	—	2	1	no	—
184	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
185	#107×C₆₁	C₂³	1	2	yes	—
186	#107×C₆₁	C₂³	1	2	yes	—
187	#106×C₆₁	C₂³	1	2	yes	—
188	#106×C₆₁	C₂³	1	2	yes	—
189	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
190	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
191	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
192	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
193	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
194	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
195	#103×C₆₁	C₂³	1	2	yes	—
196	#103×C₆₁	C₂³	1	2	yes	—
197	#103×C₆₁	C₂³	1	4	yes	—
198	#103×C₆₁	C₂³	1	2	yes	—
199	#103×C₆₁	C₂³	1	4	yes	—
200	#103×C₆₁	C₂³	1	2	yes	—
201	#103×C₆₁	C₂³	1	4	yes	—
202	#103×C₆₁	C₂³	1	4	yes	—
203	#102×C₆₁	C₂³	1	2	yes	—
204	#102×C₆₁	C₂³	1	2	yes	—
205	#102×C₆₁	C₂³	1	2	yes	—
206	#102×C₆₁	C₂³	1	2	yes	—
207	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
208	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
209	#97×C₆₁	C₂³	1	4	yes	—
210	C₄×C₈×C₆₁	C₂³	1	2	yes	—
211	C₄×C₈×C₆₁	C₂³	1	2	yes	—
212	C₄×C₈×C₆₁	C₂³	1	4	yes	—
213	#41×C₆₁	—	4	1	no	—
214	#41×C₆₁	—	4	1	no	—
215	#41×C₆₁	—	8	2	no	—
216	C₂×Q₈×C₆₁	—	2	2	no	—
217	C₂×Q₈×C₆₁	—	2	1	no	—
218	C₂×Q₈×C₆₁	—	2	4	no	—
219	C₂×Q₈×C₆₁	—	2	1	no	—
220	C₂×Q₈×C₆₁	—	4	2	no	—
221	C₂×Q₈×C₆₁	—	4	2	no	—
222	C₂×Q₈×C₆₁	—	8	4	no	—
223	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
224	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
225	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
226	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
227	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
228	C₂×D₄×C₆₁	—	2	1	no	—
229	C₂×D₄×C₆₁	—	2	2	no	—
230	C₂×D₄×C₆₁	—	2	1	no	—
231	C₂×D₄×C₆₁	—	2	1	no	—
232	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
233	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₆₁	—	2	2	no	—
235	C₂²×C₄×C₆₁	—	2	1	no	—
236	C₂²×C₄×C₆₁	—	2	1	no	—
237	C₂²×C₄×C₆₁	—	2	1	no	—
238	C₂²×C₄×C₆₁	—	2	2	no	—
239	C₂²×C₄×C₆₁	—	2	4	no	—
240	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
243	Q₁₆×C₆₁	—	4	4	no	—
244	Q₁₆×C₆₁	—	4	2	no	—
245	Q₁₆×C₆₁	—	4	4	no	—
246	SD₁₆×C₆₁	—	4	4	no	—
247	SD₁₆×C₆₁	—	4	2	no	—
248	SD₁₆×C₆₁	—	4	4	no	—
249	SD₁₆×C₆₁	—	4	2	no	—
250	D₈×C₆₁	—	4	2	no	—
251	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
252	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
253	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
254	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
255	C₄⋊C₄×C₆₁	—	2	2	no	—
256	C₄⋊C₄×C₆₁	—	2	2	no	—
257	C₄⋊C₄×C₆₁	—	2	2	no	—
258	C₄⋊C₄×C₆₁	—	2	2	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	—	2	4	no	—
263	C₄⋊C₄×C₆₁	—	2	4	no	—
264	C₄⋊C₄×C₆₁	—	2	1	no	—
265	C₄⋊C₄×C₆₁	—	2	1	no	—
266	C₄⋊C₄×C₆₁	—	2	1	no	—
267	C₄⋊C₄×C₆₁	—	2	2	no	—
268	C₄⋊C₄×C₆₁	—	2	4	no	—
269	C₄⋊C₄×C₆₁	—	2	4	no	—
270	C₄⋊C₄×C₆₁	—	2	4	no	—
271	C₄⋊C₄×C₆₁	—	2	4	no	—
272	C₄⋊C₄×C₆₁	—	2	2	no	—
273	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
274	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
275	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
277	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
278	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
279	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
280	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
281	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
283	C₂²⋊C₄×C₆₁	—	2	1	no	—
284	C₂²⋊C₄×C₆₁	—	2	2	no	—
285	C₂²⋊C₄×C₆₁	—	2	1	no	—
286	C₂²⋊C₄×C₆₁	—	2	1	no	—
287	C₂²⋊C₄×C₆₁	—	2	4	no	—
288	C₂²⋊C₄×C₆₁	—	2	4	no	—
289	C₂²⋊C₄×C₆₁	—	2	4	no	—
290	C₂²⋊C₄×C₆₁	—	2	2	no	—
291	C₂²⋊C₄×C₆₁	—	2	4	no	—
292	C₂²⋊C₄×C₆₁	—	2	2	no	—
293	C₂²⋊C₄×C₆₁	—	2	4	no	—
294	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
295	C₄²×C₆₁	—	2	1	no	—
296	C₄²×C₆₁	—	2	1	no	—
297	C₄²×C₆₁	—	2	1	no	—
298	C₄²×C₆₁	—	2	4	no	—
299	C₄²×C₆₁	—	2	4	no	—
300	C₄²×C₆₁	—	2	2	no	—
301	C₄²×C₆₁	—	2	4	no	—
302	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
305	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
306	C₄²×C₆₁	C₂⁴	1	4	yes	—
307	C₂³×C₆₁	—	2	1	no	—
308	C₂³×C₆₁	—	2	2	no	—
309	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
310	Q₈×C₆₁	—	2	4	no	—
311	Q₈×C₆₁	—	2	4	no	—
312	Q₈×C₆₁	—	2	1	no	—
313	Q₈×C₆₁	—	2	2	no	—
314	Q₈×C₆₁	—	2	4	no	—
315	Q₈×C₆₁	—	2	4	no	—
316	Q₈×C₆₁	—	2	2	no	—
317	Q₈×C₆₁	—	2	1	no	—
318	Q₈×C₆₁	—	4	4	no	—
319	Q₈×C₆₁	—	4	2	no	—
320	Q₈×C₆₁	—	8	4	no	—
321	Q₈×C₆₁	—	8	1	no	—
322	D₄×C₆₁	—	2	1	no	—
323	D₄×C₆₁	—	2	2	no	—
324	D₄×C₆₁	—	2	2	no	—
325	D₄×C₆₁	—	2	1	no	—
326	D₄×C₆₁	—	4	2	no	—
327	D₄×C₆₁	—	4	2	no	—
328	D₄×C₆₁	—	8	1	no	—
329	D₄×C₆₁	—	8	2	no	—
330	C₂×C₄×C₆₁	—	2	2	no	—
331	C₂×C₄×C₆₁	—	2	2	no	—
332	C₂×C₄×C₆₁	—	2	1	no	—
333	C₂×C₄×C₆₁	—	2	1	no	—
334	C₂×C₄×C₆₁	—	2	1	no	—
335	C₂×C₄×C₆₁	—	2	1	no	—
336	C₂×C₄×C₆₁	—	2	2	no	—
337	C₂×C₄×C₆₁	—	2	4	no	—
338	C₂×C₄×C₆₁	—	2	2	no	—
339	C₂×C₄×C₆₁	—	2	1	no	—
340	C₂×C₄×C₆₁	—	2	2	no	—
341	C₂×C₄×C₆₁	—	4	2	no	—
342	C₂×C₄×C₆₁	—	4	4	no	—
343	C₂×C₄×C₆₁	—	4	2	no	—
344	C₂×C₄×C₆₁	—	4	4	no	—
345	C₂×C₄×C₆₁	—	4	2	no	—
346	C₂×C₄×C₆₁	—	8	4	no	—
347	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
348	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
350	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
355	C₈×C₆₁	—	2	2	no	—
356	C₈×C₆₁	—	2	2	no	—
357	C₈×C₆₁	—	2	2	no	—
358	C₈×C₆₁	—	2	2	no	—
359	#61934	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
360	C₂²×C₆₁	—	2	1	no	—
361	C₂²×C₆₁	—	2	1	no	—
362	C₂²×C₆₁	—	2	1	no	—
363	C₂²×C₆₁	—	4	1	no	—
364	C₂²×C₆₁	—	4	2	no	—
365	C₂²×C₆₁	—	4	2	no	—
366	C₂²×C₆₁	—	4	1	no	—
367	C₂²×C₆₁	—	4	1	no	—
368	C₂²×C₆₁	—	4	2	no	—
369	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
370	C₄×C₆₁	—	2	1	no	—
371	C₄×C₆₁	—	2	1	no	—
372	C₄×C₆₁	—	2	4	no	—
373	C₄×C₆₁	—	2	1	no	—
374	C₄×C₆₁	—	2	4	no	—
375	C₄×C₆₁	—	4	1	no	—
376	C₄×C₆₁	—	4	4	no	—
377	C₄×C₆₁	—	4	2	no	—
378	C₄×C₆₁	—	4	1	no	—
379	C₄×C₆₁	—	4	2	no	—
380	C₄×C₆₁	—	4	2	no	—
381	C₄×C₆₁	—	4	1	no	—
382	C₄×C₆₁	#577	1	2	yes	—
383	C₄×C₆₁	#578	1	2	yes	—
384	C₄×C₆₁	#585	1	1	yes	characteristic
385	C₄×C₆₁	#585	1	1	yes	characteristic
386	#3550	C₂×C₆₁	1	1	yes	characteristic, complemented
387	#3509	C₂×C₆₁	1	1	yes	characteristic, complemented
388	#3400	C₂×C₆₁	1	2	yes	complemented
389	#3398	C₂×C₆₁	1	2	yes	complemented
390	#3394	C₂×C₆₁	1	2	yes	complemented
391	#3393	C₂×C₆₁	1	2	yes	complemented
392	#3369	C₂×C₆₁	1	2	yes	complemented
393	#3367	C₂×C₆₁	1	2	yes	complemented
394	#3363	C₂×C₆₁	1	2	yes	complemented
395	#3359	C₂×C₆₁	1	2	yes	complemented
396	#3225	C₂×C₆₁	1	4	yes	complemented
397	#3209	C₂×C₆₁	1	1	yes	characteristic, complemented
398	#3206	C₂×C₆₁	1	1	yes	characteristic, complemented
399	#3121	C₂×C₆₁	1	4	yes	complemented
400	#3107	C₂×C₆₁	1	1	yes	characteristic, complemented
401	#3106	C₂×C₆₁	1	1	yes	characteristic
402	#2986	C₂×C₆₁	1	1	yes	characteristic, complemented
403	C₂×C₆₁	—	4	1	no	—
404	C₂×C₆₁	—	8	1	no	—
405	C₂×C₆₁	—	8	2	no	—
406	C₂×C₆₁	#3487	1	1	yes	characteristic
407	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
408	C₂×C₆₁	C₂×#578	1	1	yes	characteristic
409	#563	—	2	2	no	—
410	#559	C₂²×C₆₁	1	2	yes	—
411	Q₈²	C₂²×C₆₁	1	2	yes	—
412	#557	C₂²×C₆₁	1	2	yes	—
413	#557	C₂²×C₆₁	1	2	yes	—
414	#556	—	2	1	no	—
415	#556	C₂²×C₆₁	1	2	yes	—
416	#556	C₂²×C₆₁	1	2	yes	—
417	#556	C₂²×C₆₁	1	2	yes	—
418	#552	—	2	2	no	—
419	#552	—	2	2	no	—
420	D₄×Q₈	—	2	1	no	—
421	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
422	#542	—	2	2	no	—
423	#542	C₂²×C₆₁	1	4	yes	—
424	#541	—	2	2	no	—
425	#536	—	2	2	no	—
426	#536	C₂²×C₆₁	1	2	yes	—
427	#533	—	2	1	no	—
428	#533	—	2	1	no	—
429	#533	C₂²×C₆₁	1	1	yes	characteristic
430	#533	C₂²×C₆₁	1	1	yes	characteristic
431	#532	C₂²×C₆₁	1	1	yes	characteristic
432	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
433	#519	C₂²×C₆₁	1	2	yes	—
434	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
435	#497	C₂²×C₆₁	1	4	yes	—
436	#495	C₂²×C₆₁	1	4	yes	—
437	#494	C₂²×C₆₁	1	2	yes	—
438	#492	C₂²×C₆₁	1	2	yes	—
439	#489	C₂²×C₆₁	1	4	yes	—
440	#487	C₂²×C₆₁	1	4	yes	—
441	#487	C₂²×C₆₁	1	2	yes	—
442	#487	C₂²×C₆₁	1	2	yes	—
443	#485	C₂²×C₆₁	1	2	yes	—
444	#482	C₂²×C₆₁	1	2	yes	—
445	#477	C₂²×C₆₁	1	1	yes	characteristic
446	#477	C₂²×C₆₁	1	4	yes	—
447	#476	C₂²×C₆₁	1	1	yes	characteristic
448	#475	C₂²×C₆₁	1	1	yes	characteristic
449	#475	C₂²×C₆₁	1	4	yes	—
450	#474	C₂²×C₆₁	1	1	yes	characteristic
451	#464	C₂²×C₆₁	1	4	yes	—
452	#464	C₂²×C₆₁	1	4	yes	—
453	#464	C₂²×C₆₁	1	4	yes	—
454	#463	C₂²×C₆₁	1	4	yes	—
455	#462	C₂²×C₆₁	1	1	yes	characteristic
456	#462	C₂²×C₆₁	1	2	yes	—
457	#462	C₂²×C₆₁	1	4	yes	—
458	#462	C₂²×C₆₁	1	2	yes	—
459	#461	C₂²×C₆₁	1	2	yes	—
460	#461	C₂²×C₆₁	1	4	yes	—
461	#461	C₂²×C₆₁	1	1	yes	characteristic
462	#461	C₂²×C₆₁	1	2	yes	—
463	#460	C₂²×C₆₁	1	1	yes	characteristic
464	#459	C₂²×C₆₁	1	1	yes	characteristic
465	#452	C₂²×C₆₁	1	2	yes	—
466	#451	C₂²×C₆₁	1	4	yes	—
467	#449	C₂²×C₆₁	1	2	yes	—
468	#448	C₂²×C₆₁	1	4	yes	—
469	#446	C₂²×C₆₁	1	2	yes	—
470	#446	C₂²×C₆₁	1	2	yes	—
471	C₈×Q₈	C₂²×C₆₁	1	2	yes	—
472	C₈×Q₈	C₂²×C₆₁	1	2	yes	—
473	#441	C₂²×C₆₁	1	4	yes	—
474	#440	C₂²×C₆₁	1	4	yes	—
475	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
476	C₄×Q₁₆	C₂²×C₆₁	1	4	yes	—
477	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
478	C₄×SD₁₆	C₂²×C₆₁	1	4	yes	—
479	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
480	C₄×D₈	C₂²×C₆₁	1	2	yes	—
481	#433	C₂²×C₆₁	1	4	yes	—
482	#431	C₂²×C₆₁	1	1	yes	characteristic
483	#431	C₂²×C₆₁	1	1	yes	characteristic
484	C₆₁	#61934	1	1	yes	characteristic, direct product factor, Sylow
485	C₂×#41	—	2	1	no	—
486	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
487	C₂²×Q₈	—	2	2	no	—
488	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
489	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
490	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
491	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
492	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
493	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
494	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
495	C₂×SD₁₆	C₂³×C₆₁	1	4	yes	—
496	C₂×D₈	C₂³×C₆₁	1	2	yes	—
497	C₄⋊Q₈	—	2	4	no	—
498	C₄⋊Q₈	—	2	2	no	—
499	C₄⋊Q₈	—	2	1	no	—
500	C₄⋊Q₈	—	2	1	no	—
501	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
502	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
503	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
504	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
505	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
506	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
507	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
508	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
509	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
510	#127	C₂³×C₆₁	1	1	yes	characteristic
511	#126	—	2	4	no	—
512	#126	—	2	4	no	—
513	#126	—	2	4	no	—
514	#126	—	2	4	no	—
515	#125	—	2	2	no	—
516	#125	—	2	2	no	—
517	#125	—	2	4	no	—
518	#125	—	2	4	no	—
519	#125	—	2	1	no	—
520	#125	D₄×C₆₁	1	2	yes	—
521	#124	—	2	2	no	—
522	#124	—	2	4	no	—
523	#124	—	2	1	no	—
524	#124	C₂³×C₆₁	1	4	yes	—
525	#124	C₂³×C₆₁	1	4	yes	—
526	#123	—	2	4	no	—
527	#123	—	2	4	no	—
528	#123	—	2	4	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	2	2	no	—
532	C₂²⋊Q₈	—	2	1	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	4	no	—
537	C₂²⋊Q₈	—	2	4	no	—
538	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
539	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
540	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
541	#121	—	2	1	no	—
542	#121	C₂³×C₆₁	1	2	yes	—
543	C₄×Q₈	—	2	2	no	—
544	C₄×Q₈	—	2	2	no	—
545	C₄×Q₈	—	2	2	no	—
546	C₄×Q₈	—	2	2	no	—
547	C₄×Q₈	—	2	2	no	—
548	C₄×Q₈	—	2	1	no	—
549	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
550	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
551	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
552	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
553	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
554	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
555	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
556	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
557	C₄×D₄	—	2	1	no	—
558	C₄×D₄	—	2	1	no	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	1	no	—
561	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
562	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
563	C₄×D₄	C₂³×C₆₁	1	2	yes	—
564	C₄×D₄	C₂³×C₆₁	1	4	yes	—
565	#117	—	2	1	no	—
566	#117	—	2	2	no	—
567	#117	—	2	2	no	—
568	#117	—	2	2	no	—
569	#117	—	2	4	no	—
570	#117	—	2	1	no	—
571	#117	C₂³×C₆₁	1	1	yes	characteristic
572	#117	C₂³×C₆₁	1	2	yes	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄²	—	2	1	no	—
576	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
577	#107	C₂³×C₆₁	1	2	yes	—
578	#107	C₂³×C₆₁	1	2	yes	—
579	#106	C₂³×C₆₁	1	2	yes	—
580	#106	C₂³×C₆₁	1	2	yes	—
581	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
582	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
583	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
584	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
585	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
586	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
587	#103	C₂³×C₆₁	1	2	yes	—
588	#103	C₂³×C₆₁	1	2	yes	—
589	#103	C₂³×C₆₁	1	4	yes	—
590	#103	C₂³×C₆₁	1	2	yes	—
591	#103	C₂³×C₆₁	1	4	yes	—
592	#103	C₂³×C₆₁	1	2	yes	—
593	#103	C₂³×C₆₁	1	4	yes	—
594	#103	C₂³×C₆₁	1	4	yes	—
595	#102	C₂³×C₆₁	1	2	yes	—
596	#102	C₂³×C₆₁	1	2	yes	—
597	#102	C₂³×C₆₁	1	2	yes	—
598	#102	C₂³×C₆₁	1	2	yes	—
599	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
600	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
601	#97	C₂³×C₆₁	1	4	yes	—
602	C₄×C₈	C₂³×C₆₁	1	2	yes	—
603	C₄×C₈	C₂³×C₆₁	1	2	yes	—
604	C₄×C₈	C₂³×C₆₁	1	4	yes	—
605	#41	—	4	1	no	—
606	#41	—	4	1	no	—
607	#41	—	8	2	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	2	1	no	—
610	C₂×Q₈	—	2	4	no	—
611	C₂×Q₈	—	2	1	no	—
612	C₂×Q₈	—	4	2	no	—
613	C₂×Q₈	—	4	2	no	—
614	C₂×Q₈	—	8	4	no	—
615	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
616	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
617	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
618	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
619	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	2	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
625	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
633	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
634	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
635	Q₁₆	—	4	4	no	—
636	Q₁₆	—	4	2	no	—
637	Q₁₆	—	4	4	no	—
638	SD₁₆	—	4	4	no	—
639	SD₁₆	—	4	2	no	—
640	SD₁₆	—	4	4	no	—
641	SD₁₆	—	4	2	no	—
642	D₈	—	4	2	no	—
643	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
644	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
645	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
646	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
647	C₄⋊C₄	—	2	2	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	2	no	—
650	C₄⋊C₄	—	2	2	no	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
666	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
667	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
668	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
669	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
670	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
671	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
672	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
673	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
674	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
675	C₂²⋊C₄	—	2	1	no	—
676	C₂²⋊C₄	—	2	2	no	—
677	C₂²⋊C₄	—	2	1	no	—
678	C₂²⋊C₄	—	2	1	no	—
679	C₂²⋊C₄	—	2	4	no	—
680	C₂²⋊C₄	—	2	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	2	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
687	C₄²	—	2	1	no	—
688	C₄²	—	2	1	no	—
689	C₄²	—	2	1	no	—
690	C₄²	—	2	4	no	—
691	C₄²	—	2	4	no	—
692	C₄²	—	2	2	no	—
693	C₄²	—	2	4	no	—
694	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
695	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
696	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
697	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
698	C₄²	C₂⁴×C₆₁	1	4	yes	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	2	no	—
701	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
702	Q₈	—	2	4	no	—
703	Q₈	—	2	4	no	—
704	Q₈	—	2	1	no	—
705	Q₈	—	2	2	no	—
706	Q₈	—	2	4	no	—
707	Q₈	—	2	4	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	2	1	no	—
710	Q₈	—	4	4	no	—
711	Q₈	—	4	2	no	—
712	Q₈	—	8	4	no	—
713	Q₈	—	8	1	no	—
714	D₄	—	2	1	no	—
715	D₄	—	2	2	no	—
716	D₄	—	2	2	no	—
717	D₄	—	2	1	no	—
718	D₄	—	4	2	no	—
719	D₄	—	4	2	no	—
720	D₄	—	8	1	no	—
721	D₄	—	8	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	4	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	4	4	no	—
735	C₂×C₄	—	4	2	no	—
736	C₂×C₄	—	4	4	no	—
737	C₂×C₄	—	4	2	no	—
738	C₂×C₄	—	8	4	no	—
739	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
740	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
741	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
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	C₂²×D₄×C₆₁	1	1	yes	characteristic
746	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
747	C₈	—	2	2	no	—
748	C₈	—	2	2	no	—
749	C₈	—	2	2	no	—
750	C₈	—	2	2	no	—
751	C₂²	—	2	1	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	2	1	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	2	no	—
760	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
761	C₄	—	2	1	no	—
762	C₄	—	2	4	no	—
763	C₄	—	2	1	no	—
764	C₄	—	2	4	no	—
765	C₄	—	2	1	no	—
766	C₄	—	4	1	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	1	no	—
770	C₄	—	4	1	no	—
771	C₄	—	4	4	no	—
772	C₄	—	4	2	no	—
773	C₄	C₆₁×#577	1	2	yes	—
774	C₄	C₆₁×#578	1	2	yes	—
775	C₄	C₆₁×#585	1	1	yes	characteristic
776	C₄	C₆₁×#585	1	1	yes	characteristic
777	C₂	—	4	1	no	—
778	C₂	—	8	2	no	—
779	C₂	—	8	1	no	—
780	C₂	C₆₁×#3487	1	1	yes	characteristic
781	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
782	C₂	C₂×C₆₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3106	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3550	C₂	semidirect
2. C₆₁×#3509	C₂	semidirect
3. C₆₁×#3400	C₂	semidirect
4. C₆₁×#3398	C₂	semidirect
5. C₆₁×#3394	C₂	semidirect
6. C₆₁×#3393	C₂	semidirect
7. C₆₁×#3369	C₂	semidirect
8. C₆₁×#3367	C₂	semidirect
9. C₆₁×#3363	C₂	semidirect
10. C₆₁×#3359	C₂	semidirect
11. C₆₁×#3225	C₂	semidirect
12. C₆₁×#3209	C₂	semidirect
13. C₆₁×#3206	C₂	semidirect
14. C₆₁×#3121	C₂	semidirect
15. C₆₁×#3107	C₂	semidirect
17. C₆₁×#2986	C₂	semidirect
359. #61934	C₆₁	direct (N × H)
386. #3550	C₂×C₆₁	semidirect
387. #3509	C₂×C₆₁	semidirect
388. #3400	C₂×C₆₁	semidirect
389. #3398	C₂×C₆₁	semidirect
390. #3394	C₂×C₆₁	semidirect
391. #3393	C₂×C₆₁	semidirect
392. #3369	C₂×C₆₁	semidirect
393. #3367	C₂×C₆₁	semidirect
394. #3363	C₂×C₆₁	semidirect
395. #3359	C₂×C₆₁	semidirect
396. #3225	C₂×C₆₁	semidirect
397. #3209	C₂×C₆₁	semidirect
398. #3206	C₂×C₆₁	semidirect
399. #3121	C₂×C₆₁	semidirect
400. #3107	C₂×C₆₁	semidirect
402. #2986	C₂×C₆₁	semidirect
484. C₆₁	#61934	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×#3550	2
C₆₁×#3509	2
C₆₁×#3400	2
C₆₁×#3398	2
C₆₁×#3394	2
C₆₁×#3393	2
C₆₁×#3369	2
C₆₁×#3367	2
C₆₁×#3363	2
C₆₁×#3359	2
C₆₁×#3225	2
C₆₁×#3209	2
C₆₁×#3206	2
C₆₁×#3121	2
C₆₁×#3107	2
C₆₁×#3106	2
C₆₁×#2986	2
#61934	61

Subgroups — C61×#61934 #29565367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61934 #29565367