Subgroups — C₆₁×#61839 #29565272

Order 15616.

1688 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×#41×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3390	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3388	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3385	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3384	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3381	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3380	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3371	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3370	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3360	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3240	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3233	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#3111	C₂	1	2	yes	maximal, complemented
21	C₆₁×#3106	C₂	1	1	yes	maximal, characteristic
22	C₆₁×#3102	C₂	1	2	yes	maximal, complemented
23	C₆₁×#2984	C₂	1	1	yes	maximal, characteristic, complemented
24	C₆₁×#559	C₂²	1	2	yes	—
25	Q₈²×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#557	C₂²	1	1	yes	characteristic
27	C₆₁×#557	C₂²	1	2	yes	—
28	C₆₁×#557	C₂²	1	2	yes	—
29	C₆₁×#556	—	2	2	no	—
30	C₆₁×#556	C₂²	1	1	yes	characteristic
31	C₆₁×#556	C₂²	1	1	yes	characteristic
32	C₆₁×#554	—	2	2	no	—
33	C₆₁×#554	—	2	1	no	—
34	C₆₁×#554	C₂²	1	1	yes	characteristic
35	C₆₁×#554	C₂²	1	2	yes	—
36	C₆₁×#554	C₂²	1	1	yes	characteristic
37	C₆₁×#554	C₂²	1	1	yes	characteristic
38	C₆₁×#552	—	2	1	no	—
39	C₆₁×#552	—	2	1	no	—
40	D₄×Q₈×C₆₁	—	2	1	no	—
41	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
42	C₆₁×#539	—	2	2	no	—
43	C₆₁×#536	—	2	1	no	—
44	C₆₁×#533	—	2	1	no	—
45	C₆₁×#533	—	2	2	no	—
46	C₆₁×#533	C₂²	1	1	yes	characteristic
47	C₆₁×#533	C₂²	1	1	yes	characteristic
48	C₆₁×#533	C₂²	1	2	yes	—
49	C₆₁×#532	C₂²	1	1	yes	characteristic
50	C₆₁×#529	C₂²	1	2	yes	—
51	C₆₁×#529	C₂²	1	2	yes	—
52	C₆₁×#520	—	2	1	no	—
53	C₄×#41×C₆₁	C₂²	1	2	yes	—
54	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
55	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
56	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
57	C₆₁×#501	C₂²	1	2	yes	—
58	C₆₁×#501	C₂²	1	2	yes	—
59	C₆₁×#501	C₂²	1	2	yes	—
60	C₆₁×#500	C₂²	1	1	yes	characteristic
61	C₆₁×#499	C₂²	1	2	yes	—
62	C₆₁×#499	C₂²	1	2	yes	—
63	C₆₁×#498	C₂²	1	1	yes	characteristic
64	C₆₁×#490	C₂²	1	2	yes	—
65	C₆₁×#489	C₂²	1	2	yes	—
66	C₆₁×#489	C₂²	1	2	yes	—
67	C₆₁×#488	C₂²	1	2	yes	—
68	C₆₁×#488	C₂²	1	2	yes	—
69	C₆₁×#487	C₂²	1	1	yes	characteristic
70	C₆₁×#487	C₂²	1	1	yes	characteristic
71	C₆₁×#485	C₂²	1	2	yes	—
72	C₆₁×#485	C₂²	1	2	yes	—
73	C₆₁×#485	C₂²	1	2	yes	—
74	C₆₁×#482	C₂²	1	2	yes	—
75	C₆₁×#482	C₂²	1	1	yes	characteristic
76	C₆₁×#482	C₂²	1	1	yes	characteristic
77	C₆₁×#482	C₂²	1	2	yes	—
78	C₆₁×#479	C₂²	1	2	yes	—
79	C₆₁×#479	C₂²	1	2	yes	—
80	C₆₁×#479	C₂²	1	2	yes	—
81	C₆₁×#479	C₂²	1	2	yes	—
82	C₆₁×#479	C₂²	1	2	yes	—
83	C₆₁×#479	C₂²	1	2	yes	—
84	C₆₁×#478	C₂²	1	2	yes	—
85	C₆₁×#478	C₂²	1	2	yes	—
86	C₆₁×#478	C₂²	1	2	yes	—
87	C₆₁×#478	C₂²	1	2	yes	—
88	C₆₁×#477	C₂²	1	1	yes	characteristic
89	C₆₁×#477	C₂²	1	2	yes	—
90	C₆₁×#477	C₂²	1	1	yes	characteristic
91	C₆₁×#476	C₂²	1	1	yes	characteristic
92	C₆₁×#476	C₂²	1	1	yes	characteristic
93	C₆₁×#476	C₂²	1	1	yes	characteristic
94	C₆₁×#476	C₂²	1	2	yes	—
95	C₆₁×#476	C₂²	1	1	yes	characteristic
96	C₆₁×#475	C₂²	1	2	yes	—
97	C₆₁×#474	C₂²	1	1	yes	characteristic
98	C₆₁×#474	C₂²	1	1	yes	characteristic
99	C₆₁×#474	C₂²	1	2	yes	—
100	C₆₁×#464	C₂²	1	2	yes	—
101	C₆₁×#464	C₂²	1	2	yes	—
102	C₆₁×#463	C₂²	1	2	yes	—
103	C₆₁×#463	C₂²	1	2	yes	—
104	C₆₁×#462	C₂²	1	1	yes	characteristic
105	C₆₁×#461	C₂²	1	1	yes	characteristic
106	C₆₁×#460	C₂²	1	1	yes	characteristic
107	C₆₁×#459	C₂²	1	1	yes	characteristic
108	C₆₁×#452	C₂²	1	2	yes	—
109	C₆₁×#449	C₂²	1	1	yes	characteristic
110	C₆₁×#449	C₂²	1	1	yes	characteristic
111	C₆₁×#446	C₂²	1	1	yes	characteristic
112	C₆₁×#446	C₂²	1	1	yes	characteristic
113	C₆₁×#446	C₂²	1	2	yes	—
114	C₆₁×#446	C₂²	1	2	yes	—
115	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
116	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
117	C₆₁×#442	C₂²	1	2	yes	—
118	C₆₁×#441	C₂²	1	2	yes	—
119	C₆₁×#441	C₂²	1	2	yes	—
120	C₆₁×#440	C₂²	1	2	yes	—
121	C₆₁×#440	C₂²	1	2	yes	—
122	C₆₁×#440	C₂²	1	2	yes	—
123	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
124	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
125	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
126	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
127	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
128	C₄×D₈×C₆₁	C₂²	1	2	yes	—
129	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
131	C₆₁×#432	C₂²	1	2	yes	—
132	C₆₁×#432	C₂²	1	1	yes	characteristic
133	C₆₁×#431	C₂²	1	2	yes	—
134	C₆₁×#431	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₆₁	—	2	1	no	—
138	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
139	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
140	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
141	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
143	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
144	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
145	C₄⋊Q₈×C₆₁	—	2	1	no	—
146	C₄⋊Q₈×C₆₁	—	2	2	no	—
147	C₄⋊Q₈×C₆₁	—	2	2	no	—
148	C₄⋊Q₈×C₆₁	—	2	1	no	—
149	C₄⋊Q₈×C₆₁	—	2	2	no	—
150	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
151	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
154	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
155	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
156	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
157	#127×C₆₁	C₂³	1	1	yes	characteristic
158	#126×C₆₁	—	2	2	no	—
159	#126×C₆₁	—	2	2	no	—
160	#126×C₆₁	—	2	2	no	—
161	#126×C₆₁	—	2	2	no	—
162	#125×C₆₁	—	2	2	no	—
163	#125×C₆₁	—	2	2	no	—
164	#125×C₆₁	—	2	2	no	—
165	#125×C₆₁	—	2	2	no	—
166	#125×C₆₁	—	2	2	no	—
167	#125×C₆₁	—	2	1	no	—
168	#125×C₆₁	C₂³	1	2	yes	—
169	#125×C₆₁	C₂³	1	2	yes	—
170	#125×C₆₁	C₂³	1	2	yes	—
171	#125×C₆₁	C₂³	1	2	yes	—
172	#125×C₆₁	C₂³	1	2	yes	—
173	#124×C₆₁	—	2	2	no	—
174	#124×C₆₁	—	2	1	no	—
175	#124×C₆₁	C₂³	1	2	yes	—
176	#124×C₆₁	C₂³	1	2	yes	—
177	#123×C₆₁	—	2	2	no	—
178	#123×C₆₁	—	2	2	no	—
179	#123×C₆₁	—	2	2	no	—
180	#123×C₆₁	—	2	2	no	—
181	C₂²⋊Q₈×C₆₁	—	2	1	no	—
182	C₂²⋊Q₈×C₆₁	—	2	2	no	—
183	C₂²⋊Q₈×C₆₁	—	2	1	no	—
184	C₂²⋊Q₈×C₆₁	—	2	1	no	—
185	C₂²⋊Q₈×C₆₁	—	2	1	no	—
186	C₂²⋊Q₈×C₆₁	—	2	1	no	—
187	C₂²⋊Q₈×C₆₁	—	2	1	no	—
188	C₂²⋊Q₈×C₆₁	—	2	1	no	—
189	C₂²⋊Q₈×C₆₁	—	2	2	no	—
190	C₂²⋊Q₈×C₆₁	—	2	2	no	—
191	C₂²⋊Q₈×C₆₁	—	2	1	no	—
192	C₂²⋊Q₈×C₆₁	—	2	1	no	—
193	C₂²⋊Q₈×C₆₁	—	2	2	no	—
194	C₂²⋊Q₈×C₆₁	—	2	2	no	—
195	C₂²⋊Q₈×C₆₁	—	2	2	no	—
196	C₂²⋊Q₈×C₆₁	—	2	2	no	—
197	C₂²⋊Q₈×C₆₁	—	2	2	no	—
198	C₂²⋊Q₈×C₆₁	—	2	2	no	—
199	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
200	#121×C₆₁	—	2	1	no	—
201	#121×C₆₁	C₂³	1	1	yes	characteristic
202	#121×C₆₁	C₂³	1	1	yes	characteristic
203	C₄×Q₈×C₆₁	—	2	1	no	—
204	C₄×Q₈×C₆₁	—	2	1	no	—
205	C₄×Q₈×C₆₁	—	2	2	no	—
206	C₄×Q₈×C₆₁	—	2	2	no	—
207	C₄×Q₈×C₆₁	—	2	2	no	—
208	C₄×Q₈×C₆₁	—	2	1	no	—
209	C₄×Q₈×C₆₁	—	2	2	no	—
210	C₄×Q₈×C₆₁	—	2	1	no	—
211	C₄×Q₈×C₆₁	—	2	1	no	—
212	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
213	C₄×Q₈×C₆₁	D₄	1	2	yes	—
214	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
215	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
216	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
217	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
218	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
222	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
225	C₄×D₄×C₆₁	—	2	2	no	—
226	C₄×D₄×C₆₁	—	2	2	no	—
227	C₄×D₄×C₆₁	—	2	1	no	—
228	C₄×D₄×C₆₁	—	2	2	no	—
229	C₄×D₄×C₆₁	—	2	2	no	—
230	C₄×D₄×C₆₁	—	2	1	no	—
231	C₄×D₄×C₆₁	—	2	2	no	—
232	C₄×D₄×C₆₁	—	2	1	no	—
233	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₆₁	C₂³	1	2	yes	—
237	C₄×D₄×C₆₁	C₂³	1	2	yes	—
238	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₆₁	C₂³	1	2	yes	—
240	C₄×D₄×C₆₁	C₂³	1	2	yes	—
241	#117×C₆₁	—	2	1	no	—
242	#117×C₆₁	—	2	1	no	—
243	#117×C₆₁	—	2	1	no	—
244	#117×C₆₁	—	2	2	no	—
245	#117×C₆₁	—	2	1	no	—
246	#117×C₆₁	—	2	2	no	—
247	#117×C₆₁	—	2	2	no	—
248	#117×C₆₁	C₂³	1	2	yes	—
249	#117×C₆₁	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
251	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
252	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
253	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
254	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
255	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
256	C₂×C₄²×C₆₁	—	2	2	no	—
257	C₂×C₄²×C₆₁	—	2	1	no	—
258	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
259	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
260	#107×C₆₁	C₂³	1	2	yes	—
261	#107×C₆₁	C₂³	1	1	yes	characteristic
262	#107×C₆₁	C₂³	1	1	yes	characteristic
263	#107×C₆₁	C₂³	1	2	yes	—
264	#107×C₆₁	C₂³	1	2	yes	—
265	#107×C₆₁	C₂³	1	2	yes	—
266	#107×C₆₁	C₂³	1	2	yes	—
267	#106×C₆₁	C₂³	1	1	yes	characteristic
268	#106×C₆₁	C₂³	1	2	yes	—
269	#106×C₆₁	C₂³	1	2	yes	—
270	#106×C₆₁	C₂³	1	1	yes	characteristic
271	#106×C₆₁	C₂³	1	2	yes	—
272	#106×C₆₁	C₂³	1	2	yes	—
273	#106×C₆₁	C₂³	1	2	yes	—
274	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
277	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
278	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
281	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
282	#103×C₆₁	C₂³	1	1	yes	characteristic
283	#103×C₆₁	C₂³	1	2	yes	—
284	#103×C₆₁	C₂³	1	1	yes	characteristic
285	#103×C₆₁	C₂³	1	2	yes	—
286	#103×C₆₁	C₂³	1	2	yes	—
287	#103×C₆₁	C₂³	1	2	yes	—
288	#103×C₆₁	C₂³	1	2	yes	—
289	#103×C₆₁	C₂³	1	2	yes	—
290	#103×C₆₁	C₂³	1	2	yes	—
291	#102×C₆₁	C₂³	1	1	yes	characteristic
292	#102×C₆₁	C₂³	1	1	yes	characteristic
293	#102×C₆₁	C₂³	1	2	yes	—
294	#102×C₆₁	C₂³	1	1	yes	characteristic
295	#102×C₆₁	C₂³	1	1	yes	characteristic
296	#102×C₆₁	C₂³	1	2	yes	—
297	#102×C₆₁	C₂³	1	1	yes	characteristic
298	#102×C₆₁	C₂³	1	1	yes	characteristic
299	#102×C₆₁	C₂³	1	2	yes	—
300	#102×C₆₁	C₂³	1	2	yes	—
301	#102×C₆₁	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
305	#97×C₆₁	C₂³	1	2	yes	—
306	#97×C₆₁	C₂³	1	2	yes	—
307	#97×C₆₁	C₂³	1	2	yes	—
308	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₁	C₂³	1	2	yes	—
311	C₄×C₈×C₆₁	C₂³	1	2	yes	—
312	#41×C₆₁	—	2	2	no	—
313	#41×C₆₁	—	2	2	no	—
314	#41×C₆₁	—	4	4	no	—
315	C₂×Q₈×C₆₁	—	2	2	no	—
316	C₂×Q₈×C₆₁	—	2	1	no	—
317	C₂×Q₈×C₆₁	—	2	1	no	—
318	C₂×Q₈×C₆₁	—	2	1	no	—
319	C₂×Q₈×C₆₁	—	2	2	no	—
320	C₂×Q₈×C₆₁	—	2	1	no	—
321	C₂×Q₈×C₆₁	—	4	2	no	—
322	C₂×Q₈×C₆₁	—	4	4	no	—
323	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
326	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
327	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₆₁	—	2	1	no	—
329	C₂×D₄×C₆₁	—	2	1	no	—
330	C₂×D₄×C₆₁	—	2	1	no	—
331	C₂×D₄×C₆₁	—	2	1	no	—
332	C₂×D₄×C₆₁	—	2	1	no	—
333	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₆₁	—	2	1	no	—
337	C₂²×C₄×C₆₁	—	2	2	no	—
338	C₂²×C₄×C₆₁	—	2	1	no	—
339	C₂²×C₄×C₆₁	—	2	1	no	—
340	C₂²×C₄×C₆₁	—	2	1	no	—
341	C₂²×C₄×C₆₁	—	2	2	no	—
342	C₂²×C₄×C₆₁	—	2	1	no	—
343	C₂²×C₄×C₆₁	—	2	2	no	—
344	C₂²×C₄×C₆₁	—	2	2	no	—
345	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
346	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
347	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
349	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
350	Q₁₆×C₆₁	—	2	4	no	—
351	SD₁₆×C₆₁	—	2	2	no	—
352	SD₁₆×C₆₁	—	2	2	no	—
353	SD₁₆×C₆₁	—	2	4	no	—
354	D₈×C₆₁	—	2	2	no	—
355	D₈×C₆₁	—	2	2	no	—
356	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
357	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
359	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
361	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
362	C₄⋊C₄×C₆₁	—	2	1	no	—
363	C₄⋊C₄×C₆₁	—	2	2	no	—
364	C₄⋊C₄×C₆₁	—	2	2	no	—
365	C₄⋊C₄×C₆₁	—	2	2	no	—
366	C₄⋊C₄×C₆₁	—	2	2	no	—
367	C₄⋊C₄×C₆₁	—	2	2	no	—
368	C₄⋊C₄×C₆₁	—	2	2	no	—
369	C₄⋊C₄×C₆₁	—	2	1	no	—
370	C₄⋊C₄×C₆₁	—	2	1	no	—
371	C₄⋊C₄×C₆₁	—	2	2	no	—
372	C₄⋊C₄×C₆₁	—	2	1	no	—
373	C₄⋊C₄×C₆₁	—	2	2	no	—
374	C₄⋊C₄×C₆₁	—	2	2	no	—
375	C₄⋊C₄×C₆₁	—	2	1	no	—
376	C₄⋊C₄×C₆₁	—	2	2	no	—
377	C₄⋊C₄×C₆₁	—	2	2	no	—
378	C₄⋊C₄×C₆₁	—	2	1	no	—
379	C₄⋊C₄×C₆₁	—	2	2	no	—
380	C₄⋊C₄×C₆₁	—	2	1	no	—
381	C₄⋊C₄×C₆₁	—	2	2	no	—
382	C₄⋊C₄×C₆₁	—	2	2	no	—
383	C₄⋊C₄×C₆₁	—	2	2	no	—
384	C₄⋊C₄×C₆₁	—	2	1	no	—
385	C₄⋊C₄×C₆₁	—	2	2	no	—
386	C₄⋊C₄×C₆₁	—	2	2	no	—
387	C₄⋊C₄×C₆₁	—	2	2	no	—
388	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
389	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
390	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
391	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
392	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
393	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
397	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
402	C₂²⋊C₄×C₆₁	—	2	2	no	—
403	C₂²⋊C₄×C₆₁	—	2	2	no	—
404	C₂²⋊C₄×C₆₁	—	2	1	no	—
405	C₂²⋊C₄×C₆₁	—	2	1	no	—
406	C₂²⋊C₄×C₆₁	—	2	1	no	—
407	C₂²⋊C₄×C₆₁	—	2	2	no	—
408	C₂²⋊C₄×C₆₁	—	2	2	no	—
409	C₂²⋊C₄×C₆₁	—	2	1	no	—
410	C₂²⋊C₄×C₆₁	—	2	2	no	—
411	C₂²⋊C₄×C₆₁	—	2	2	no	—
412	C₂²⋊C₄×C₆₁	—	2	1	no	—
413	C₂²⋊C₄×C₆₁	—	2	2	no	—
414	C₂²⋊C₄×C₆₁	—	2	2	no	—
415	C₂²⋊C₄×C₆₁	—	2	1	no	—
416	C₂²⋊C₄×C₆₁	—	2	1	no	—
417	C₂²⋊C₄×C₆₁	—	2	2	no	—
418	C₂²⋊C₄×C₆₁	—	2	2	no	—
419	C₄²×C₆₁	—	2	2	no	—
420	C₄²×C₆₁	—	2	1	no	—
421	C₄²×C₆₁	—	2	2	no	—
422	C₄²×C₆₁	—	2	1	no	—
423	C₄²×C₆₁	—	2	2	no	—
424	C₄²×C₆₁	—	2	1	no	—
425	C₄²×C₆₁	—	2	2	no	—
426	C₄²×C₆₁	—	2	2	no	—
427	C₄²×C₆₁	—	2	2	no	—
428	C₄²×C₆₁	C₂×D₄	1	2	yes	—
429	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
430	C₄²×C₆₁	C₂×D₄	1	2	yes	—
431	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
432	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
433	C₄²×C₆₁	C₂⁴	1	2	yes	—
434	C₄²×C₆₁	C₂⁴	1	2	yes	—
435	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
436	C₂³×C₆₁	—	2	1	no	—
437	C₂³×C₆₁	—	2	1	no	—
438	C₂³×C₆₁	—	2	1	no	—
439	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
440	Q₈×C₆₁	—	2	2	no	—
441	Q₈×C₆₁	—	2	2	no	—
442	Q₈×C₆₁	—	2	1	no	—
443	Q₈×C₆₁	—	2	2	no	—
444	Q₈×C₆₁	—	2	2	no	—
445	Q₈×C₆₁	—	4	2	no	—
446	Q₈×C₆₁	—	4	4	no	—
447	Q₈×C₆₁	—	4	2	no	—
448	Q₈×C₆₁	—	4	2	no	—
449	Q₈×C₆₁	—	8	2	no	—
450	Q₈×C₆₁	—	8	1	no	—
451	Q₈×C₆₁	—	8	1	no	—
452	Q₈×C₆₁	2₋¹⁺⁴	1	2	yes	—
453	D₄×C₆₁	—	2	4	no	—
454	D₄×C₆₁	—	2	1	no	—
455	D₄×C₆₁	—	2	1	no	—
456	D₄×C₆₁	—	2	1	no	—
457	D₄×C₆₁	—	2	1	no	—
458	D₄×C₆₁	—	2	1	no	—
459	D₄×C₆₁	—	4	2	no	—
460	D₄×C₆₁	—	4	2	no	—
461	D₄×C₆₁	—	4	2	no	—
462	D₄×C₆₁	—	8	1	no	—
463	D₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
464	C₂×C₄×C₆₁	—	2	4	no	—
465	C₂×C₄×C₆₁	—	2	1	no	—
466	C₂×C₄×C₆₁	—	2	2	no	—
467	C₂×C₄×C₆₁	—	2	1	no	—
468	C₂×C₄×C₆₁	—	2	1	no	—
469	C₂×C₄×C₆₁	—	2	2	no	—
470	C₂×C₄×C₆₁	—	2	1	no	—
471	C₂×C₄×C₆₁	—	2	1	no	—
472	C₂×C₄×C₆₁	—	2	2	no	—
473	C₂×C₄×C₆₁	—	2	1	no	—
474	C₂×C₄×C₆₁	—	2	2	no	—
475	C₂×C₄×C₆₁	—	2	1	no	—
476	C₂×C₄×C₆₁	—	2	2	no	—
477	C₂×C₄×C₆₁	—	4	2	no	—
478	C₂×C₄×C₆₁	—	4	1	no	—
479	C₂×C₄×C₆₁	—	4	2	no	—
480	C₂×C₄×C₆₁	—	4	4	no	—
481	C₂×C₄×C₆₁	—	4	2	no	—
482	C₂×C₄×C₆₁	—	4	2	no	—
483	C₂×C₄×C₆₁	—	4	2	no	—
484	C₂×C₄×C₆₁	—	8	2	no	—
485	C₂×C₄×C₆₁	—	8	2	no	—
486	C₂×C₄×C₆₁	—	8	1	no	—
487	C₂×C₄×C₆₁	—	8	2	no	—
488	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
498	C₈×C₆₁	—	2	1	no	—
499	C₈×C₆₁	—	2	1	no	—
500	C₈×C₆₁	—	2	1	no	—
501	C₈×C₆₁	—	2	1	no	—
502	C₈×C₆₁	—	2	2	no	—
503	C₈×C₆₁	—	2	2	no	—
504	#61839	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
505	C₂²×C₆₁	—	2	1	no	—
506	C₂²×C₆₁	—	2	1	no	—
507	C₂²×C₆₁	—	2	2	no	—
508	C₂²×C₆₁	—	2	1	no	—
509	C₂²×C₆₁	—	4	1	no	—
510	C₂²×C₆₁	—	4	1	no	—
511	C₂²×C₆₁	—	4	1	no	—
512	C₂²×C₆₁	—	4	1	no	—
513	C₂²×C₆₁	—	4	1	no	—
514	C₂²×C₆₁	—	4	1	no	—
515	C₂²×C₆₁	—	4	1	no	—
516	C₂²×C₆₁	—	4	1	no	—
517	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
518	C₄×C₆₁	—	2	2	no	—
519	C₄×C₆₁	—	2	1	no	—
520	C₄×C₆₁	—	2	2	no	—
521	C₄×C₆₁	—	2	1	no	—
522	C₄×C₆₁	—	2	1	no	—
523	C₄×C₆₁	—	2	2	no	—
524	C₄×C₆₁	—	2	1	no	—
525	C₄×C₆₁	—	2	2	no	—
526	C₄×C₆₁	—	2	2	no	—
527	C₄×C₆₁	—	4	2	no	—
528	C₄×C₆₁	—	4	2	no	—
529	C₄×C₆₁	—	4	1	no	—
530	C₄×C₆₁	—	4	2	no	—
531	C₄×C₆₁	—	4	1	no	—
532	C₄×C₆₁	—	4	1	no	—
533	C₄×C₆₁	—	4	2	no	—
534	C₄×C₆₁	—	4	1	no	—
535	C₄×C₆₁	#575	1	2	yes	—
536	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
537	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
538	#3507	C₂×C₆₁	1	1	yes	characteristic, complemented
539	Q₈×#41	C₂×C₆₁	1	1	yes	characteristic, complemented
540	#3390	C₂×C₆₁	1	2	yes	complemented
541	#3388	C₂×C₆₁	1	2	yes	complemented
542	#3385	C₂×C₆₁	1	1	yes	characteristic, complemented
543	#3384	C₂×C₆₁	1	1	yes	characteristic, complemented
544	#3381	C₂×C₆₁	1	1	yes	characteristic, complemented
545	#3380	C₂×C₆₁	1	1	yes	characteristic, complemented
546	#3371	C₂×C₆₁	1	2	yes	complemented
547	#3370	C₂×C₆₁	1	2	yes	complemented
548	#3369	C₂×C₆₁	1	1	yes	characteristic, complemented
549	#3367	C₂×C₆₁	1	1	yes	characteristic, complemented
550	#3364	C₂×C₆₁	1	1	yes	characteristic, complemented
551	#3360	C₂×C₆₁	1	1	yes	characteristic, complemented
552	#3240	C₂×C₆₁	1	2	yes	complemented
553	#3235	C₂×C₆₁	1	1	yes	characteristic, complemented
554	#3233	C₂×C₆₁	1	2	yes	complemented
555	#3231	C₂×C₆₁	1	1	yes	characteristic, complemented
556	#3116	C₂×C₆₁	1	1	yes	characteristic, complemented
557	#3111	C₂×C₆₁	1	2	yes	complemented
558	#3106	C₂×C₆₁	1	1	yes	characteristic
559	#3102	C₂×C₆₁	1	2	yes	complemented
560	#2984	C₂×C₆₁	1	1	yes	characteristic, complemented
561	C₂×C₆₁	—	4	1	no	—
562	C₂×C₆₁	—	4	2	no	—
563	C₂×C₆₁	—	8	1	no	—
564	C₂×C₆₁	—	8	1	no	—
565	C₂×C₆₁	#3486	1	1	yes	characteristic
566	C₂×C₆₁	C₂×#575	1	1	yes	characteristic
567	C₂×C₆₁	#3584	1	1	yes	characteristic
568	#559	C₂²×C₆₁	1	2	yes	—
569	Q₈²	C₂²×C₆₁	1	1	yes	characteristic
570	#557	C₂²×C₆₁	1	1	yes	characteristic
571	#557	C₂²×C₆₁	1	2	yes	—
572	#557	C₂²×C₆₁	1	2	yes	—
573	#556	—	2	2	no	—
574	#556	C₂²×C₆₁	1	1	yes	characteristic
575	#556	C₂²×C₆₁	1	1	yes	characteristic
576	#554	—	2	1	no	—
577	#554	—	2	2	no	—
578	#554	C₂²×C₆₁	1	1	yes	characteristic
579	#554	C₂²×C₆₁	1	2	yes	—
580	#554	C₂²×C₆₁	1	1	yes	characteristic
581	#554	C₂²×C₆₁	1	1	yes	characteristic
582	#552	—	2	1	no	—
583	#552	—	2	1	no	—
584	D₄×Q₈	—	2	1	no	—
585	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
586	#539	—	2	2	no	—
587	#536	—	2	1	no	—
588	#533	—	2	1	no	—
589	#533	—	2	2	no	—
590	#533	C₂²×C₆₁	1	1	yes	characteristic
591	#533	C₂²×C₆₁	1	1	yes	characteristic
592	#533	C₂²×C₆₁	1	2	yes	—
593	#532	C₂²×C₆₁	1	1	yes	characteristic
594	#529	C₂²×C₆₁	1	2	yes	—
595	#529	C₂²×C₆₁	1	2	yes	—
596	#520	—	2	1	no	—
597	C₄×#41	C₂²×C₆₁	1	2	yes	—
598	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
599	C₂×C₄×Q₈	—	2	1	no	—
600	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
601	#501	C₂²×C₆₁	1	2	yes	—
602	#501	C₂²×C₆₁	1	2	yes	—
603	#501	C₂²×C₆₁	1	2	yes	—
604	#500	C₂²×C₆₁	1	1	yes	characteristic
605	#499	C₂²×C₆₁	1	2	yes	—
606	#499	C₂²×C₆₁	1	2	yes	—
607	#498	C₂²×C₆₁	1	1	yes	characteristic
608	#490	C₂²×C₆₁	1	2	yes	—
609	#489	C₂²×C₆₁	1	2	yes	—
610	#489	C₂²×C₆₁	1	2	yes	—
611	#488	C₂²×C₆₁	1	2	yes	—
612	#488	C₂²×C₆₁	1	2	yes	—
613	#487	C₂²×C₆₁	1	1	yes	characteristic
614	#487	C₂²×C₆₁	1	1	yes	characteristic
615	#485	C₂²×C₆₁	1	2	yes	—
616	#485	C₂²×C₆₁	1	2	yes	—
617	#485	C₂²×C₆₁	1	2	yes	—
618	#482	C₂²×C₆₁	1	2	yes	—
619	#482	C₂²×C₆₁	1	1	yes	characteristic
620	#482	C₂²×C₆₁	1	1	yes	characteristic
621	#482	C₂²×C₆₁	1	2	yes	—
622	#479	C₂²×C₆₁	1	2	yes	—
623	#479	C₂²×C₆₁	1	2	yes	—
624	#479	C₂²×C₆₁	1	2	yes	—
625	#479	C₂²×C₆₁	1	2	yes	—
626	#479	C₂²×C₆₁	1	2	yes	—
627	#479	C₂²×C₆₁	1	2	yes	—
628	#478	C₂²×C₆₁	1	2	yes	—
629	#478	C₂²×C₆₁	1	2	yes	—
630	#478	C₂²×C₆₁	1	2	yes	—
631	#478	C₂²×C₆₁	1	2	yes	—
632	#477	C₂²×C₆₁	1	1	yes	characteristic
633	#477	C₂²×C₆₁	1	2	yes	—
634	#477	C₂²×C₆₁	1	1	yes	characteristic
635	#476	C₂²×C₆₁	1	1	yes	characteristic
636	#476	C₂²×C₆₁	1	1	yes	characteristic
637	#476	C₂²×C₆₁	1	1	yes	characteristic
638	#476	C₂²×C₆₁	1	2	yes	—
639	#476	C₂²×C₆₁	1	1	yes	characteristic
640	#475	C₂²×C₆₁	1	2	yes	—
641	#474	C₂²×C₆₁	1	1	yes	characteristic
642	#474	C₂²×C₆₁	1	1	yes	characteristic
643	#474	C₂²×C₆₁	1	2	yes	—
644	#464	C₂²×C₆₁	1	2	yes	—
645	#464	C₂²×C₆₁	1	2	yes	—
646	#463	C₂²×C₆₁	1	2	yes	—
647	#463	C₂²×C₆₁	1	2	yes	—
648	#462	C₂²×C₆₁	1	1	yes	characteristic
649	#461	C₂²×C₆₁	1	1	yes	characteristic
650	#460	C₂²×C₆₁	1	1	yes	characteristic
651	#459	C₂²×C₆₁	1	1	yes	characteristic
652	#452	C₂²×C₆₁	1	2	yes	—
653	#449	C₂²×C₆₁	1	1	yes	characteristic
654	#449	C₂²×C₆₁	1	1	yes	characteristic
655	#446	C₂²×C₆₁	1	1	yes	characteristic
656	#446	C₂²×C₆₁	1	1	yes	characteristic
657	#446	C₂²×C₆₁	1	2	yes	—
658	#446	C₂²×C₆₁	1	2	yes	—
659	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
660	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
661	#442	C₂²×C₆₁	1	2	yes	—
662	#441	C₂²×C₆₁	1	2	yes	—
663	#441	C₂²×C₆₁	1	2	yes	—
664	#440	C₂²×C₆₁	1	2	yes	—
665	#440	C₂²×C₆₁	1	2	yes	—
666	#440	C₂²×C₆₁	1	2	yes	—
667	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
668	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
669	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
670	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
671	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
672	C₄×D₈	C₂²×C₆₁	1	2	yes	—
673	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
674	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
675	#432	C₂²×C₆₁	1	2	yes	—
676	#432	C₂²×C₆₁	1	1	yes	characteristic
677	#431	C₂²×C₆₁	1	2	yes	—
678	#431	C₂²×C₆₁	1	1	yes	characteristic
679	C₆₁	#61839	1	1	yes	characteristic, direct product factor, Sylow
680	C₂×#41	—	2	1	no	—
681	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
682	C₂²×Q₈	—	2	1	no	—
683	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
684	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
685	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
686	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
687	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
688	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
689	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
690	C₄⋊Q₈	—	2	1	no	—
691	C₄⋊Q₈	—	2	2	no	—
692	C₄⋊Q₈	—	2	2	no	—
693	C₄⋊Q₈	—	2	1	no	—
694	C₄⋊Q₈	—	2	2	no	—
695	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
696	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
697	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
698	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
699	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
700	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
701	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
702	#127	C₂³×C₆₁	1	1	yes	characteristic
703	#126	—	2	2	no	—
704	#126	—	2	2	no	—
705	#126	—	2	2	no	—
706	#126	—	2	2	no	—
707	#125	—	2	2	no	—
708	#125	—	2	2	no	—
709	#125	—	2	2	no	—
710	#125	—	2	2	no	—
711	#125	—	2	2	no	—
712	#125	—	2	1	no	—
713	#125	C₂³×C₆₁	1	2	yes	—
714	#125	C₂³×C₆₁	1	2	yes	—
715	#125	C₂³×C₆₁	1	2	yes	—
716	#125	C₂³×C₆₁	1	2	yes	—
717	#125	C₂³×C₆₁	1	2	yes	—
718	#124	—	2	2	no	—
719	#124	—	2	1	no	—
720	#124	C₂³×C₆₁	1	2	yes	—
721	#124	C₂³×C₆₁	1	2	yes	—
722	#123	—	2	2	no	—
723	#123	—	2	2	no	—
724	#123	—	2	2	no	—
725	#123	—	2	2	no	—
726	C₂²⋊Q₈	—	2	1	no	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	2	1	no	—
729	C₂²⋊Q₈	—	2	1	no	—
730	C₂²⋊Q₈	—	2	1	no	—
731	C₂²⋊Q₈	—	2	1	no	—
732	C₂²⋊Q₈	—	2	1	no	—
733	C₂²⋊Q₈	—	2	1	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	1	no	—
737	C₂²⋊Q₈	—	2	1	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
745	#121	—	2	1	no	—
746	#121	C₂³×C₆₁	1	1	yes	characteristic
747	#121	C₂³×C₆₁	1	1	yes	characteristic
748	C₄×Q₈	—	2	1	no	—
749	C₄×Q₈	—	2	1	no	—
750	C₄×Q₈	—	2	2	no	—
751	C₄×Q₈	—	2	2	no	—
752	C₄×Q₈	—	2	2	no	—
753	C₄×Q₈	—	2	1	no	—
754	C₄×Q₈	—	2	2	no	—
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	—	2	1	no	—
757	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
758	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
759	C₄×Q₈	D₄×C₆₁	1	2	yes	—
760	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
761	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
762	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
763	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
764	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
765	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
766	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
767	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
768	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
769	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
770	C₄×D₄	—	2	1	no	—
771	C₄×D₄	—	2	2	no	—
772	C₄×D₄	—	2	2	no	—
773	C₄×D₄	—	2	1	no	—
774	C₄×D₄	—	2	2	no	—
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	—	2	1	no	—
778	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
779	C₄×D₄	C₂³×C₆₁	1	2	yes	—
780	C₄×D₄	C₂³×C₆₁	1	2	yes	—
781	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
782	C₄×D₄	C₂³×C₆₁	1	2	yes	—
783	C₄×D₄	C₂³×C₆₁	1	2	yes	—
784	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
785	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
786	#117	—	2	1	no	—
787	#117	—	2	1	no	—
788	#117	—	2	1	no	—
789	#117	—	2	2	no	—
790	#117	—	2	1	no	—
791	#117	—	2	2	no	—
792	#117	—	2	2	no	—
793	#117	C₂³×C₆₁	1	2	yes	—
794	#117	C₂³×C₆₁	1	1	yes	characteristic
795	C₂×C₄⋊C₄	—	2	1	no	—
796	C₂×C₄⋊C₄	—	2	2	no	—
797	C₂×C₄⋊C₄	—	2	1	no	—
798	C₂×C₄⋊C₄	—	2	1	no	—
799	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
800	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
801	C₂×C₄²	—	2	2	no	—
802	C₂×C₄²	—	2	1	no	—
803	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
804	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
805	#107	C₂³×C₆₁	1	2	yes	—
806	#107	C₂³×C₆₁	1	1	yes	characteristic
807	#107	C₂³×C₆₁	1	1	yes	characteristic
808	#107	C₂³×C₆₁	1	2	yes	—
809	#107	C₂³×C₆₁	1	2	yes	—
810	#107	C₂³×C₆₁	1	2	yes	—
811	#107	C₂³×C₆₁	1	2	yes	—
812	#106	C₂³×C₆₁	1	1	yes	characteristic
813	#106	C₂³×C₆₁	1	2	yes	—
814	#106	C₂³×C₆₁	1	2	yes	—
815	#106	C₂³×C₆₁	1	1	yes	characteristic
816	#106	C₂³×C₆₁	1	2	yes	—
817	#106	C₂³×C₆₁	1	2	yes	—
818	#106	C₂³×C₆₁	1	2	yes	—
819	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
820	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
821	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
822	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
823	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
824	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
825	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
826	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
827	#103	C₂³×C₆₁	1	1	yes	characteristic
828	#103	C₂³×C₆₁	1	2	yes	—
829	#103	C₂³×C₆₁	1	1	yes	characteristic
830	#103	C₂³×C₆₁	1	2	yes	—
831	#103	C₂³×C₆₁	1	2	yes	—
832	#103	C₂³×C₆₁	1	2	yes	—
833	#103	C₂³×C₆₁	1	2	yes	—
834	#103	C₂³×C₆₁	1	2	yes	—
835	#103	C₂³×C₆₁	1	2	yes	—
836	#102	C₂³×C₆₁	1	1	yes	characteristic
837	#102	C₂³×C₆₁	1	1	yes	characteristic
838	#102	C₂³×C₆₁	1	2	yes	—
839	#102	C₂³×C₆₁	1	1	yes	characteristic
840	#102	C₂³×C₆₁	1	1	yes	characteristic
841	#102	C₂³×C₆₁	1	2	yes	—
842	#102	C₂³×C₆₁	1	1	yes	characteristic
843	#102	C₂³×C₆₁	1	1	yes	characteristic
844	#102	C₂³×C₆₁	1	2	yes	—
845	#102	C₂³×C₆₁	1	2	yes	—
846	#102	C₂³×C₆₁	1	2	yes	—
847	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
848	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
849	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
850	#97	C₂³×C₆₁	1	2	yes	—
851	#97	C₂³×C₆₁	1	2	yes	—
852	#97	C₂³×C₆₁	1	2	yes	—
853	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
854	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
855	C₄×C₈	C₂³×C₆₁	1	2	yes	—
856	C₄×C₈	C₂³×C₆₁	1	2	yes	—
857	#41	—	2	2	no	—
858	#41	—	2	2	no	—
859	#41	—	4	4	no	—
860	C₂×Q₈	—	2	2	no	—
861	C₂×Q₈	—	2	1	no	—
862	C₂×Q₈	—	2	1	no	—
863	C₂×Q₈	—	2	1	no	—
864	C₂×Q₈	—	2	2	no	—
865	C₂×Q₈	—	2	1	no	—
866	C₂×Q₈	—	4	2	no	—
867	C₂×Q₈	—	4	4	no	—
868	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
869	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
870	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
871	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
872	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
873	C₂×D₄	—	2	1	no	—
874	C₂×D₄	—	2	1	no	—
875	C₂×D₄	—	2	1	no	—
876	C₂×D₄	—	2	1	no	—
877	C₂×D₄	—	2	1	no	—
878	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
879	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
880	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	1	no	—
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	2	1	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	1	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
891	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
892	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
893	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
894	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
895	Q₁₆	—	2	4	no	—
896	SD₁₆	—	2	2	no	—
897	SD₁₆	—	2	2	no	—
898	SD₁₆	—	2	4	no	—
899	D₈	—	2	2	no	—
900	D₈	—	2	2	no	—
901	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
902	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
903	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
904	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
905	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
906	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
934	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
935	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
936	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
937	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
938	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
939	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
940	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
941	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
942	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
943	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
944	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
945	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
946	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	1	no	—
950	C₂²⋊C₄	—	2	1	no	—
951	C₂²⋊C₄	—	2	1	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	1	no	—
961	C₂²⋊C₄	—	2	1	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₄²	—	2	2	no	—
965	C₄²	—	2	1	no	—
966	C₄²	—	2	2	no	—
967	C₄²	—	2	1	no	—
968	C₄²	—	2	2	no	—
969	C₄²	—	2	1	no	—
970	C₄²	—	2	2	no	—
971	C₄²	—	2	2	no	—
972	C₄²	—	2	2	no	—
973	C₄²	C₂×D₄×C₆₁	1	2	yes	—
974	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
975	C₄²	C₂×D₄×C₆₁	1	2	yes	—
976	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
977	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
978	C₄²	C₂⁴×C₆₁	1	2	yes	—
979	C₄²	C₂⁴×C₆₁	1	2	yes	—
980	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
981	C₂³	—	2	1	no	—
982	C₂³	—	2	1	no	—
983	C₂³	—	2	1	no	—
984	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
985	Q₈	—	2	2	no	—
986	Q₈	—	2	2	no	—
987	Q₈	—	2	1	no	—
988	Q₈	—	2	2	no	—
989	Q₈	—	2	2	no	—
990	Q₈	—	4	2	no	—
991	Q₈	—	4	4	no	—
992	Q₈	—	4	2	no	—
993	Q₈	—	4	2	no	—
994	Q₈	—	8	2	no	—
995	Q₈	—	8	1	no	—
996	Q₈	—	8	1	no	—
997	Q₈	2₋¹⁺⁴×C₆₁	1	2	yes	—
998	D₄	—	2	4	no	—
999	D₄	—	2	1	no	—
1000	D₄	—	2	1	no	—
1001	D₄	—	2	1	no	—
1002	D₄	—	2	1	no	—
1003	D₄	—	2	1	no	—
1004	D₄	—	4	2	no	—
1005	D₄	—	4	2	no	—
1006	D₄	—	4	2	no	—
1007	D₄	—	8	1	no	—
1008	D₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
1009	C₂×C₄	—	2	4	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	4	2	no	—
1023	C₂×C₄	—	4	1	no	—
1024	C₂×C₄	—	4	2	no	—
1025	C₂×C₄	—	4	4	no	—
1026	C₂×C₄	—	4	2	no	—
1027	C₂×C₄	—	4	2	no	—
1028	C₂×C₄	—	4	2	no	—
1029	C₂×C₄	—	8	2	no	—
1030	C₂×C₄	—	8	2	no	—
1031	C₂×C₄	—	8	1	no	—
1032	C₂×C₄	—	8	2	no	—
1033	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1034	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1035	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1036	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1037	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1038	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1039	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1040	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1041	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1042	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1043	C₈	—	2	1	no	—
1044	C₈	—	2	1	no	—
1045	C₈	—	2	1	no	—
1046	C₈	—	2	1	no	—
1047	C₈	—	2	2	no	—
1048	C₈	—	2	2	no	—
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	1	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	1	no	—
1058	C₂²	—	4	1	no	—
1059	C₂²	—	4	1	no	—
1060	C₂²	—	4	1	no	—
1061	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1062	C₄	—	2	1	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	2	2	no	—
1066	C₄	—	2	1	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	2	1	no	—
1070	C₄	—	2	2	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	2	no	—
1074	C₄	—	4	1	no	—
1075	C₄	—	4	2	no	—
1076	C₄	—	4	2	no	—
1077	C₄	—	4	1	no	—
1078	C₄	—	4	2	no	—
1079	C₄	C₆₁×#575	1	2	yes	—
1080	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1081	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1082	C₂	—	4	1	no	—
1083	C₂	—	4	2	no	—
1084	C₂	—	8	1	no	—
1085	C₂	—	8	1	no	—
1086	C₂	C₆₁×#3486	1	1	yes	characteristic
1087	C₂	C₂×C₆₁×#575	1	1	yes	characteristic
1088	C₂	C₆₁×#3584	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 ◁ C₂×C₄×Q₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3507	C₂	semidirect
2. Q₈×#41×C₆₁	C₂	semidirect
3. C₆₁×#3390	C₂	semidirect
4. C₆₁×#3388	C₂	semidirect
5. C₆₁×#3385	C₂	semidirect
6. C₆₁×#3384	C₂	semidirect
7. C₆₁×#3381	C₂	semidirect
8. C₆₁×#3380	C₂	semidirect
9. C₆₁×#3371	C₂	semidirect
10. C₆₁×#3370	C₂	semidirect
11. C₆₁×#3369	C₂	semidirect
12. C₆₁×#3367	C₂	semidirect
13. C₆₁×#3364	C₂	semidirect
14. C₆₁×#3360	C₂	semidirect
15. C₆₁×#3240	C₂	semidirect
16. C₆₁×#3235	C₂	semidirect
17. C₆₁×#3233	C₂	semidirect
18. C₆₁×#3231	C₂	semidirect
19. C₆₁×#3116	C₂	semidirect
20. C₆₁×#3111	C₂	semidirect
22. C₆₁×#3102	C₂	semidirect
23. C₆₁×#2984	C₂	semidirect
504. #61839	C₆₁	direct (N × H)
538. #3507	C₂×C₆₁	semidirect
539. Q₈×#41	C₂×C₆₁	semidirect
540. #3390	C₂×C₆₁	semidirect
541. #3388	C₂×C₆₁	semidirect
542. #3385	C₂×C₆₁	semidirect
543. #3384	C₂×C₆₁	semidirect
544. #3381	C₂×C₆₁	semidirect
545. #3380	C₂×C₆₁	semidirect
546. #3371	C₂×C₆₁	semidirect
547. #3370	C₂×C₆₁	semidirect
548. #3369	C₂×C₆₁	semidirect
549. #3367	C₂×C₆₁	semidirect
550. #3364	C₂×C₆₁	semidirect
551. #3360	C₂×C₆₁	semidirect
552. #3240	C₂×C₆₁	semidirect
553. #3235	C₂×C₆₁	semidirect
554. #3233	C₂×C₆₁	semidirect
555. #3231	C₂×C₆₁	semidirect
556. #3116	C₂×C₆₁	semidirect
557. #3111	C₂×C₆₁	semidirect
559. #3102	C₂×C₆₁	semidirect
560. #2984	C₂×C₆₁	semidirect
679. C₆₁	#61839	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×#3507	2
Q₈×#41×C₆₁	2
C₆₁×#3390	2
C₆₁×#3388	2
C₆₁×#3385	2
C₆₁×#3384	2
C₆₁×#3381	2
C₆₁×#3380	2
C₆₁×#3371	2
C₆₁×#3370	2
C₆₁×#3369	2
C₆₁×#3367	2
C₆₁×#3364	2
C₆₁×#3360	2
C₆₁×#3240	2
C₆₁×#3235	2
C₆₁×#3233	2
C₆₁×#3231	2
C₆₁×#3116	2
C₆₁×#3111	2
C₆₁×#3106	2
C₆₁×#3102	2
C₆₁×#2984	2
#61839	61

Subgroups — C61×#61839 #29565272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61839 #29565272