Subgroups — C₆₁×#61474 #29564907

Order 15616.

1834 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3394	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3340	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3340	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3328	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3325	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3321	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3311	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3282	C₂	1	2	yes	maximal, complemented
14	D₄×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3173	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3121	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3118	C₂	1	2	yes	maximal, complemented
19	C₆₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#3115	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₁×#2949	C₂	1	2	yes	maximal, complemented
23	C₄×#135×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#135×C₆₁	C₂²	1	1	yes	characteristic
25	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
26	C₆₁×#559	C₂²	1	1	yes	characteristic
27	Q₈²×C₆₁	C₂²	1	1	yes	characteristic, complemented
28	C₆₁×#556	—	2	2	no	—
29	C₆₁×#556	—	2	1	no	—
30	C₆₁×#556	C₂²	1	1	yes	characteristic
31	C₆₁×#556	C₂²	1	1	yes	characteristic, complemented
32	C₆₁×#556	C₂²	1	2	yes	complemented
33	C₆₁×#555	—	2	1	no	—
34	C₆₁×#555	C₂²	1	2	yes	—
35	C₆₁×#555	C₂²	1	1	yes	characteristic
36	C₆₁×#551	—	2	2	no	—
37	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
39	C₆₁×#548	—	2	1	no	—
40	C₆₁×#548	C₂²	1	2	yes	complemented
41	C₆₁×#546	—	2	1	no	—
42	C₆₁×#546	C₂²	1	2	yes	—
43	D₄²×C₆₁	C₂²	1	1	yes	characteristic
44	C₆₁×#542	—	2	2	no	—
45	C₆₁×#542	C₂²	1	2	yes	—
46	C₆₁×#542	C₂²	1	2	yes	complemented
47	C₆₁×#538	—	2	2	no	—
48	C₆₁×#533	—	2	1	no	—
49	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
50	C₆₁×#532	C₂²	1	1	yes	characteristic
51	C₆₁×#529	—	2	1	no	—
52	C₆₁×#529	—	2	1	no	—
53	C₆₁×#529	C₂²	1	1	yes	characteristic
54	C₂×#124×C₆₁	—	2	1	no	—
55	C₆₁×#519	C₂²	1	2	yes	complemented
56	C₆₁×#518	C₂²	1	2	yes	—
57	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
58	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic, complemented
59	C₆₁×#498	C₂²	1	1	yes	characteristic, complemented
60	C₆₁×#498	C₂²	1	2	yes	complemented
61	C₆₁×#495	C₂²	1	2	yes	complemented
62	C₆₁×#492	C₂²	1	1	yes	characteristic
63	C₆₁×#489	C₂²	1	2	yes	complemented
64	C₆₁×#489	C₂²	1	2	yes	complemented
65	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
66	C₆₁×#486	C₂²	1	1	yes	characteristic
67	C₆₁×#485	C₂²	1	2	yes	complemented
68	C₆₁×#485	C₂²	1	2	yes	complemented
69	C₆₁×#485	C₂²	1	2	yes	complemented
70	C₆₁×#482	C₂²	1	2	yes	—
71	C₆₁×#482	C₂²	1	2	yes	complemented
72	C₆₁×#482	C₂²	1	2	yes	complemented
73	C₆₁×#477	C₂²	1	2	yes	complemented
74	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
75	C₆₁×#476	C₂²	1	2	yes	—
76	C₆₁×#476	C₂²	1	1	yes	characteristic
77	C₆₁×#475	C₂²	1	2	yes	complemented
78	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
79	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
80	C₆₁×#474	C₂²	1	2	yes	complemented
81	C₆₁×#470	C₂²	1	2	yes	complemented
82	C₆₁×#469	C₂²	1	2	yes	—
83	C₆₁×#465	C₂²	1	2	yes	—
84	C₆₁×#465	C₂²	1	2	yes	complemented
85	C₆₁×#465	C₂²	1	2	yes	complemented
86	C₆₁×#465	C₂²	1	2	yes	complemented
87	C₆₁×#464	C₂²	1	2	yes	complemented
88	C₆₁×#464	C₂²	1	2	yes	complemented
89	C₆₁×#463	C₂²	1	2	yes	—
90	C₆₁×#463	C₂²	1	2	yes	complemented
91	C₆₁×#462	C₂²	1	1	yes	characteristic, complemented
92	C₆₁×#461	C₂²	1	1	yes	characteristic
93	C₆₁×#460	C₂²	1	1	yes	characteristic
94	C₆₁×#459	C₂²	1	1	yes	characteristic
95	C₆₁×#452	C₂²	1	2	yes	—
96	C₆₁×#451	C₂²	1	2	yes	complemented
97	C₆₁×#450	C₂²	1	2	yes	—
98	C₆₁×#449	C₂²	1	2	yes	complemented
99	C₆₁×#448	C₂²	1	2	yes	—
100	C₆₁×#447	C₂²	1	2	yes	—
101	C₆₁×#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
103	C₆₁×#442	C₂²	1	2	yes	complemented
104	C₆₁×#441	C₂²	1	2	yes	complemented
105	C₆₁×#440	C₂²	1	2	yes	—
106	C₆₁×#440	C₂²	1	2	yes	—
107	C₆₁×#440	C₂²	1	2	yes	complemented
108	C₆₁×#440	C₂²	1	2	yes	complemented
109	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
110	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
111	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
113	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
114	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
116	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
118	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
121	C₆₁×#436	C₂²	1	1	yes	characteristic
122	C₆₁×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
125	C₆₁×#433	C₂²	1	2	yes	complemented
126	C₆₁×#432	C₂²	1	1	yes	characteristic, complemented
127	C₆₁×#427	C₂²	1	1	yes	characteristic, complemented
128	C₆₁×#427	C₂²	1	2	yes	complemented
129	C₆₁×#419	C₂²	1	2	yes	complemented
130	C₆₁×#418	C₂²	1	2	yes	—
131	C₆₁×#416	C₂²	1	1	yes	characteristic
132	C₆₁×#416	C₂²	1	1	yes	characteristic, complemented
133	C₆₁×#405	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
137	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₆₁	—	2	1	no	—
139	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
140	C₂²×D₄×C₆₁	—	2	1	no	—
141	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
142	#135×C₆₁	—	2	4	no	—
143	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
144	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₆₁	—	2	8	no	—
146	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
152	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₆₁	C₂³	1	2	yes	—
154	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
155	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
156	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
158	C₄⋊Q₈×C₆₁	—	2	1	no	—
159	C₄⋊Q₈×C₆₁	—	2	1	no	—
160	C₄⋊Q₈×C₆₁	—	2	2	no	—
161	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
166	#127×C₆₁	C₂³	1	1	yes	characteristic
167	#126×C₆₁	—	2	2	no	—
168	#126×C₆₁	—	2	2	no	—
169	#126×C₆₁	—	2	2	no	—
170	#126×C₆₁	—	2	2	no	—
171	#126×C₆₁	—	2	2	no	—
172	#126×C₆₁	—	2	2	no	—
173	#126×C₆₁	D₄	1	2	yes	—
174	#125×C₆₁	—	2	1	no	—
175	#125×C₆₁	D₄	1	1	yes	characteristic
176	#124×C₆₁	—	2	1	no	—
177	#124×C₆₁	—	2	2	no	—
178	#124×C₆₁	—	2	1	no	—
179	#124×C₆₁	—	2	2	no	—
180	#124×C₆₁	—	2	2	no	—
181	#124×C₆₁	—	2	2	no	—
182	#124×C₆₁	—	2	2	no	—
183	#124×C₆₁	—	2	2	no	—
184	#124×C₆₁	—	2	2	no	—
185	#124×C₆₁	—	2	1	no	—
186	#124×C₆₁	D₄	1	1	yes	characteristic
187	#124×C₆₁	C₂³	1	2	yes	—
188	#124×C₆₁	C₂³	1	2	yes	—
189	#123×C₆₁	—	2	2	no	—
190	#123×C₆₁	—	2	2	no	—
191	#123×C₆₁	—	2	2	no	—
192	#123×C₆₁	—	2	2	no	—
193	#123×C₆₁	D₄	1	2	yes	—
194	C₂²⋊Q₈×C₆₁	—	2	1	no	—
195	C₂²⋊Q₈×C₆₁	—	2	1	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	—	2	2	no	—
200	C₂²⋊Q₈×C₆₁	—	2	1	no	—
201	C₂²⋊Q₈×C₆₁	—	2	2	no	—
202	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
203	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
204	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
205	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
206	#121×C₆₁	—	2	2	no	—
207	#121×C₆₁	—	2	2	no	—
208	#121×C₆₁	—	2	1	no	—
209	#121×C₆₁	—	2	1	no	—
210	#121×C₆₁	—	2	1	no	—
211	#121×C₆₁	—	2	2	no	—
212	#121×C₆₁	D₄	1	1	yes	characteristic
213	#121×C₆₁	C₂³	1	2	yes	—
214	#121×C₆₁	C₂³	1	2	yes	—
215	#121×C₆₁	C₂³	1	2	yes	—
216	#120×C₆₁	—	2	2	no	—
217	#120×C₆₁	—	2	2	no	—
218	C₄×Q₈×C₆₁	—	2	1	no	—
219	C₄×Q₈×C₆₁	—	2	2	no	—
220	C₄×Q₈×C₆₁	—	2	2	no	—
221	C₄×Q₈×C₆₁	—	2	1	no	—
222	C₄×Q₈×C₆₁	—	2	2	no	—
223	C₄×Q₈×C₆₁	—	2	1	no	—
224	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
225	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
230	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₆₁	—	2	1	no	—
233	C₄×D₄×C₆₁	—	2	1	no	—
234	C₄×D₄×C₆₁	—	2	1	no	—
235	C₄×D₄×C₆₁	—	2	1	no	—
236	C₄×D₄×C₆₁	—	2	1	no	—
237	C₄×D₄×C₆₁	—	2	2	no	—
238	C₄×D₄×C₆₁	—	2	1	no	—
239	C₄×D₄×C₆₁	—	2	2	no	—
240	C₄×D₄×C₆₁	—	2	2	no	—
241	C₄×D₄×C₆₁	—	2	1	no	—
242	C₄×D₄×C₆₁	C₂³	1	2	yes	—
243	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₆₁	C₂³	1	2	yes	—
246	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₆₁	C₂³	1	2	yes	—
248	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₆₁	C₂³	1	2	yes	—
251	#117×C₆₁	—	2	1	no	—
252	#117×C₆₁	—	2	1	no	—
253	#117×C₆₁	—	2	1	no	—
254	#117×C₆₁	—	2	2	no	—
255	#117×C₆₁	—	2	2	no	—
256	#117×C₆₁	—	2	2	no	—
257	#117×C₆₁	—	2	1	no	—
258	#117×C₆₁	—	2	1	no	—
259	#117×C₆₁	C₂³	1	1	yes	characteristic
260	#117×C₆₁	C₂³	1	2	yes	—
261	#117×C₆₁	C₂³	1	2	yes	—
262	#117×C₆₁	C₂³	1	1	yes	characteristic
263	#117×C₆₁	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
266	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
267	C₂×C₄²×C₆₁	—	2	1	no	—
268	C₂×C₄²×C₆₁	—	2	1	no	—
269	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
270	#107×C₆₁	C₂³	1	1	yes	characteristic
271	#107×C₆₁	C₂³	1	1	yes	characteristic
272	#107×C₆₁	C₂³	1	2	yes	—
273	#107×C₆₁	C₂³	1	2	yes	—
274	#106×C₆₁	C₂³	1	1	yes	characteristic
275	#106×C₆₁	C₂³	1	1	yes	characteristic
276	#106×C₆₁	C₂³	1	2	yes	—
277	#106×C₆₁	C₂³	1	2	yes	—
278	#106×C₆₁	C₂³	1	2	yes	—
279	#106×C₆₁	C₂³	1	2	yes	—
280	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
283	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
284	#103×C₆₁	C₂³	1	1	yes	characteristic
285	#103×C₆₁	C₂³	1	1	yes	characteristic
286	#103×C₆₁	C₂³	1	1	yes	characteristic
287	#103×C₆₁	C₂³	1	1	yes	characteristic
288	#103×C₆₁	C₂³	1	2	yes	—
289	#103×C₆₁	C₂³	1	2	yes	—
290	#103×C₆₁	C₂³	1	2	yes	—
291	#103×C₆₁	C₂³	1	2	yes	—
292	#103×C₆₁	C₂³	1	2	yes	—
293	#103×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	1	yes	characteristic
297	#102×C₆₁	C₂³	1	1	yes	characteristic
298	#102×C₆₁	C₂³	1	2	yes	—
299	#102×C₆₁	C₂³	1	2	yes	—
300	#102×C₆₁	C₂³	1	2	yes	—
301	#102×C₆₁	C₂³	1	2	yes	—
302	#102×C₆₁	C₂³	1	2	yes	—
303	#102×C₆₁	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
307	#97×C₆₁	C₂³	1	2	yes	—
308	#97×C₆₁	C₂³	1	2	yes	—
309	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₆₁	C₂³	1	2	yes	—
314	C₂⁴×C₆₁	—	2	2	no	—
315	#41×C₆₁	—	2	2	no	—
316	#41×C₆₁	—	2	2	no	—
317	#41×C₆₁	—	4	1	no	—
318	#41×C₆₁	—	4	1	no	—
319	#41×C₆₁	—	8	2	no	—
320	C₂×Q₈×C₆₁	—	2	2	no	—
321	C₂×Q₈×C₆₁	—	2	1	no	—
322	C₂×Q₈×C₆₁	—	2	1	no	—
323	C₂×Q₈×C₆₁	—	2	2	no	—
324	C₂×Q₈×C₆₁	—	2	2	no	—
325	C₂×Q₈×C₆₁	—	2	4	no	—
326	C₂×Q₈×C₆₁	—	4	2	no	—
327	C₂×Q₈×C₆₁	—	8	2	no	—
328	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₆₁	—	2	4	no	—
333	C₂×D₄×C₆₁	—	2	1	no	—
334	C₂×D₄×C₆₁	—	2	1	no	—
335	C₂×D₄×C₆₁	—	2	2	no	—
336	C₂×D₄×C₆₁	—	2	2	no	—
337	C₂×D₄×C₆₁	—	2	2	no	—
338	C₂×D₄×C₆₁	—	2	2	no	—
339	C₂×D₄×C₆₁	—	2	1	no	—
340	C₂×D₄×C₆₁	—	2	1	no	—
341	C₂×D₄×C₆₁	—	4	2	no	—
342	C₂×D₄×C₆₁	—	8	2	no	—
343	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
344	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
345	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
347	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
348	C₂²×C₄×C₆₁	—	2	2	no	—
349	C₂²×C₄×C₆₁	—	2	1	no	—
350	C₂²×C₄×C₆₁	—	2	1	no	—
351	C₂²×C₄×C₆₁	—	2	1	no	—
352	C₂²×C₄×C₆₁	—	2	1	no	—
353	C₂²×C₄×C₆₁	—	2	1	no	—
354	C₂²×C₄×C₆₁	—	2	1	no	—
355	C₂²×C₄×C₆₁	—	2	2	no	—
356	C₂²×C₄×C₆₁	—	2	2	no	—
357	C₂²×C₄×C₆₁	—	2	2	no	—
358	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
362	Q₁₆×C₆₁	—	2	2	no	—
363	Q₁₆×C₆₁	—	4	2	no	—
364	SD₁₆×C₆₁	—	2	4	no	—
365	SD₁₆×C₆₁	—	2	4	no	—
366	SD₁₆×C₆₁	—	2	4	no	—
367	SD₁₆×C₆₁	—	2	2	no	—
368	SD₁₆×C₆₁	—	4	2	no	—
369	SD₁₆×C₆₁	#41	1	4	yes	complemented
370	D₈×C₆₁	—	2	2	no	—
371	D₈×C₆₁	—	4	2	no	—
372	M₁₆×C₆₁	—	4	2	no	—
373	C₂×C₈×C₆₁	—	2	4	no	—
374	C₂×C₈×C₆₁	—	2	2	no	—
375	C₂×C₈×C₆₁	—	4	1	no	—
376	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
380	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
381	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
382	C₄⋊C₄×C₆₁	—	2	1	no	—
383	C₄⋊C₄×C₆₁	—	2	1	no	—
384	C₄⋊C₄×C₆₁	—	2	1	no	—
385	C₄⋊C₄×C₆₁	—	2	1	no	—
386	C₄⋊C₄×C₆₁	—	2	1	no	—
387	C₄⋊C₄×C₆₁	—	2	1	no	—
388	C₄⋊C₄×C₆₁	—	2	2	no	—
389	C₄⋊C₄×C₆₁	—	2	2	no	—
390	C₄⋊C₄×C₆₁	—	2	2	no	—
391	C₄⋊C₄×C₆₁	—	2	2	no	—
392	C₄⋊C₄×C₆₁	—	2	2	no	—
393	C₄⋊C₄×C₆₁	—	2	1	no	—
394	C₄⋊C₄×C₆₁	—	2	2	no	—
395	C₄⋊C₄×C₆₁	—	2	1	no	—
396	C₄⋊C₄×C₆₁	—	2	2	no	—
397	C₄⋊C₄×C₆₁	—	2	2	no	—
398	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
406	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
408	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
410	C₂²⋊C₄×C₆₁	—	2	2	no	—
411	C₂²⋊C₄×C₆₁	—	2	2	no	—
412	C₂²⋊C₄×C₆₁	—	2	2	no	—
413	C₂²⋊C₄×C₆₁	—	2	2	no	—
414	C₂²⋊C₄×C₆₁	—	2	1	no	—
415	C₂²⋊C₄×C₆₁	—	2	1	no	—
416	C₂²⋊C₄×C₆₁	—	2	2	no	—
417	C₂²⋊C₄×C₆₁	—	2	1	no	—
418	C₂²⋊C₄×C₆₁	—	2	2	no	—
419	C₂²⋊C₄×C₆₁	—	2	2	no	—
420	C₂²⋊C₄×C₆₁	—	2	2	no	—
421	C₂²⋊C₄×C₆₁	—	2	2	no	—
422	C₂²⋊C₄×C₆₁	—	2	2	no	—
423	C₂²⋊C₄×C₆₁	—	2	1	no	—
424	C₂²⋊C₄×C₆₁	—	2	1	no	—
425	C₂²⋊C₄×C₆₁	—	2	1	no	—
426	C₂²⋊C₄×C₆₁	—	2	2	no	—
427	C₂²⋊C₄×C₆₁	—	2	2	no	—
428	C₂²⋊C₄×C₆₁	—	2	2	no	—
429	C₂²⋊C₄×C₆₁	—	2	2	no	—
430	C₂²⋊C₄×C₆₁	—	2	2	no	—
431	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
436	C₄²×C₆₁	—	2	1	no	—
437	C₄²×C₆₁	—	2	1	no	—
438	C₄²×C₆₁	—	2	1	no	—
439	C₄²×C₆₁	—	2	1	no	—
440	C₄²×C₆₁	—	2	1	no	—
441	C₄²×C₆₁	—	2	1	no	—
442	C₄²×C₆₁	—	2	2	no	—
443	C₄²×C₆₁	—	2	2	no	—
444	C₄²×C₆₁	—	2	2	no	—
445	C₄²×C₆₁	—	2	2	no	—
446	C₄²×C₆₁	—	2	2	no	—
447	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
450	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
451	C₄²×C₆₁	C₂⁴	1	2	yes	—
452	C₂³×C₆₁	—	2	1	no	—
453	C₂³×C₆₁	—	2	1	no	—
454	C₂³×C₆₁	—	2	2	no	—
455	C₂³×C₆₁	—	4	4	no	—
456	C₂³×C₆₁	—	8	2	no	—
457	C₂³×C₆₁	—	8	2	no	—
458	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
459	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
460	Q₈×C₆₁	—	2	2	no	—
461	Q₈×C₆₁	—	2	1	no	—
462	Q₈×C₆₁	—	2	2	no	—
463	Q₈×C₆₁	—	2	1	no	—
464	Q₈×C₆₁	—	2	2	no	—
465	Q₈×C₆₁	—	2	1	no	—
466	Q₈×C₆₁	—	4	4	no	—
467	Q₈×C₆₁	—	4	2	no	—
468	Q₈×C₆₁	—	8	1	no	—
469	Q₈×C₆₁	—	8	2	no	—
470	Q₈×C₆₁	—	8	2	no	—
471	Q₈×C₆₁	C₂×#41	1	2	yes	—
472	D₄×C₆₁	—	2	2	no	—
473	D₄×C₆₁	—	2	1	no	—
474	D₄×C₆₁	—	2	2	no	—
475	D₄×C₆₁	—	2	1	no	—
476	D₄×C₆₁	—	2	1	no	—
477	D₄×C₆₁	—	2	2	no	—
478	D₄×C₆₁	—	4	2	no	—
479	D₄×C₆₁	—	4	4	no	—
480	D₄×C₆₁	—	4	2	no	—
481	D₄×C₆₁	—	4	2	no	—
482	D₄×C₆₁	—	4	2	no	—
483	D₄×C₆₁	—	8	1	no	—
484	D₄×C₆₁	—	8	2	no	—
485	D₄×C₆₁	—	8	2	no	—
486	D₄×C₆₁	—	8	2	no	—
487	D₄×C₆₁	C₂×#41	1	2	yes	—
488	C₂×C₄×C₆₁	—	2	1	no	—
489	C₂×C₄×C₆₁	—	2	2	no	—
490	C₂×C₄×C₆₁	—	2	2	no	—
491	C₂×C₄×C₆₁	—	2	1	no	—
492	C₂×C₄×C₆₁	—	2	1	no	—
493	C₂×C₄×C₆₁	—	2	2	no	—
494	C₂×C₄×C₆₁	—	2	1	no	—
495	C₂×C₄×C₆₁	—	2	1	no	—
496	C₂×C₄×C₆₁	—	2	2	no	—
497	C₂×C₄×C₆₁	—	2	1	no	—
498	C₂×C₄×C₆₁	—	2	2	no	—
499	C₂×C₄×C₆₁	—	2	1	no	—
500	C₂×C₄×C₆₁	—	2	1	no	—
501	C₂×C₄×C₆₁	—	2	2	no	—
502	C₂×C₄×C₆₁	—	4	1	no	—
503	C₂×C₄×C₆₁	—	4	2	no	—
504	C₂×C₄×C₆₁	—	4	4	no	—
505	C₂×C₄×C₆₁	—	4	2	no	—
506	C₂×C₄×C₆₁	—	4	2	no	—
507	C₂×C₄×C₆₁	—	4	2	no	—
508	C₂×C₄×C₆₁	—	8	1	no	—
509	C₂×C₄×C₆₁	—	8	1	no	—
510	C₂×C₄×C₆₁	—	8	2	no	—
511	C₂×C₄×C₆₁	—	8	2	no	—
512	C₂×C₄×C₆₁	—	8	2	no	—
513	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
519	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
522	C₈×C₆₁	—	2	1	no	—
523	C₈×C₆₁	—	2	2	no	—
524	C₈×C₆₁	—	2	1	no	—
525	C₈×C₆₁	—	2	1	no	—
526	C₈×C₆₁	—	2	2	no	—
527	C₈×C₆₁	C₂×#41	1	2	yes	—
528	#61474	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
529	C₂²×C₆₁	—	2	1	no	—
530	C₂²×C₆₁	—	2	2	no	—
531	C₂²×C₆₁	—	2	2	no	—
532	C₂²×C₆₁	—	2	1	no	—
533	C₂²×C₆₁	—	2	2	no	—
534	C₂²×C₆₁	—	2	1	no	—
535	C₂²×C₆₁	—	2	2	no	—
536	C₂²×C₆₁	—	4	1	no	—
537	C₂²×C₆₁	—	4	1	no	—
538	C₂²×C₆₁	—	4	1	no	—
539	C₂²×C₆₁	—	4	2	no	—
540	C₂²×C₆₁	—	4	1	no	—
541	C₂²×C₆₁	—	4	2	no	—
542	C₂²×C₆₁	—	4	1	no	—
543	C₂²×C₆₁	—	4	2	no	—
544	C₂²×C₆₁	—	16	4	no	—
545	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
546	C₄×C₆₁	—	2	1	no	—
547	C₄×C₆₁	—	2	1	no	—
548	C₄×C₆₁	—	2	2	no	—
549	C₄×C₆₁	—	2	1	no	—
550	C₄×C₆₁	—	2	2	no	—
551	C₄×C₆₁	—	2	2	no	—
552	C₄×C₆₁	—	2	1	no	—
553	C₄×C₆₁	—	2	2	no	—
554	C₄×C₆₁	—	4	1	no	—
555	C₄×C₆₁	—	4	1	no	—
556	C₄×C₆₁	—	4	2	no	—
557	C₄×C₆₁	—	4	1	no	—
558	C₄×C₆₁	—	4	2	no	—
559	C₄×C₆₁	—	4	1	no	—
560	C₄×C₆₁	—	4	1	no	—
561	C₄×C₆₁	—	4	2	no	—
562	C₄×C₆₁	#577	1	2	yes	—
563	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
564	C₄×C₆₁	#585	1	1	yes	characteristic
565	#3518	C₂×C₆₁	1	1	yes	characteristic, complemented
566	#3514	C₂×C₆₁	1	1	yes	characteristic, complemented
567	#3394	C₂×C₆₁	1	1	yes	characteristic, complemented
568	Q₈×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
569	#3375	C₂×C₆₁	1	1	yes	characteristic, complemented
570	#3367	C₂×C₆₁	1	1	yes	characteristic, complemented
571	#3340	C₂×C₆₁	1	1	yes	characteristic, complemented
572	#3340	C₂×C₆₁	1	2	yes	complemented
573	#3328	C₂×C₆₁	1	1	yes	characteristic, complemented
574	#3325	C₂×C₆₁	1	1	yes	characteristic, complemented
575	#3321	C₂×C₆₁	1	2	yes	complemented
576	#3311	C₂×C₆₁	1	2	yes	complemented
577	#3282	C₂×C₆₁	1	2	yes	complemented
578	D₄×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
579	#3173	C₂×C₆₁	1	2	yes	complemented
580	#3167	C₂×C₆₁	1	1	yes	characteristic, complemented
581	#3121	C₂×C₆₁	1	2	yes	complemented
582	#3118	C₂×C₆₁	1	2	yes	complemented
583	#3116	C₂×C₆₁	1	1	yes	characteristic, complemented
584	#3115	C₂×C₆₁	1	1	yes	characteristic, complemented
585	#2966	C₂×C₆₁	1	1	yes	characteristic, complemented
586	#2949	C₂×C₆₁	1	2	yes	complemented
587	C₄×#135	C₂×C₆₁	1	1	yes	characteristic, complemented
588	C₂×C₆₁	—	4	1	no	—
589	C₂×C₆₁	—	4	2	no	—
590	C₂×C₆₁	—	4	2	no	—
591	C₂×C₆₁	—	8	1	no	—
592	C₂×C₆₁	—	8	2	no	—
593	C₂×C₆₁	D₄×#41	1	1	yes	characteristic
594	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
595	C₂×C₆₁	#3584	1	1	yes	characteristic
596	C₂×#135	C₂²×C₆₁	1	1	yes	characteristic
597	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
598	#559	C₂²×C₆₁	1	1	yes	characteristic
599	Q₈²	C₂²×C₆₁	1	1	yes	characteristic, complemented
600	#556	—	2	2	no	—
601	#556	—	2	1	no	—
602	#556	C₂²×C₆₁	1	1	yes	characteristic
603	#556	C₂²×C₆₁	1	1	yes	characteristic, complemented
604	#556	C₂²×C₆₁	1	2	yes	complemented
605	#555	—	2	1	no	—
606	#555	C₂²×C₆₁	1	2	yes	—
607	#555	C₂²×C₆₁	1	1	yes	characteristic
608	#551	—	2	2	no	—
609	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
610	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
611	#548	—	2	1	no	—
612	#548	C₂²×C₆₁	1	2	yes	complemented
613	#546	—	2	1	no	—
614	#546	C₂²×C₆₁	1	2	yes	—
615	D₄²	C₂²×C₆₁	1	1	yes	characteristic
616	#542	—	2	2	no	—
617	#542	C₂²×C₆₁	1	2	yes	—
618	#542	C₂²×C₆₁	1	2	yes	complemented
619	#538	—	2	2	no	—
620	#533	—	2	1	no	—
621	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
622	#532	C₂²×C₆₁	1	1	yes	characteristic
623	#529	—	2	1	no	—
624	#529	—	2	1	no	—
625	#529	C₂²×C₆₁	1	1	yes	characteristic
626	C₂×#124	—	2	1	no	—
627	#519	C₂²×C₆₁	1	2	yes	complemented
628	#518	C₂²×C₆₁	1	2	yes	—
629	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
630	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic, complemented
631	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
632	#498	C₂²×C₆₁	1	2	yes	complemented
633	#495	C₂²×C₆₁	1	2	yes	complemented
634	#492	C₂²×C₆₁	1	1	yes	characteristic
635	#489	C₂²×C₆₁	1	2	yes	complemented
636	#489	C₂²×C₆₁	1	2	yes	complemented
637	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
638	#486	C₂²×C₆₁	1	1	yes	characteristic
639	#485	C₂²×C₆₁	1	2	yes	complemented
640	#485	C₂²×C₆₁	1	2	yes	complemented
641	#485	C₂²×C₆₁	1	2	yes	complemented
642	#482	C₂²×C₆₁	1	2	yes	—
643	#482	C₂²×C₆₁	1	2	yes	complemented
644	#482	C₂²×C₆₁	1	2	yes	complemented
645	#477	C₂²×C₆₁	1	2	yes	complemented
646	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
647	#476	C₂²×C₆₁	1	1	yes	characteristic
648	#476	C₂²×C₆₁	1	2	yes	—
649	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
650	#475	C₂²×C₆₁	1	2	yes	complemented
651	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
652	#474	C₂²×C₆₁	1	2	yes	complemented
653	#470	C₂²×C₆₁	1	2	yes	complemented
654	#469	C₂²×C₆₁	1	2	yes	—
655	#465	C₂²×C₆₁	1	2	yes	—
656	#465	C₂²×C₆₁	1	2	yes	complemented
657	#465	C₂²×C₆₁	1	2	yes	complemented
658	#465	C₂²×C₆₁	1	2	yes	complemented
659	#464	C₂²×C₆₁	1	2	yes	complemented
660	#464	C₂²×C₆₁	1	2	yes	complemented
661	#463	C₂²×C₆₁	1	2	yes	—
662	#463	C₂²×C₆₁	1	2	yes	complemented
663	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
664	#461	C₂²×C₆₁	1	1	yes	characteristic
665	#460	C₂²×C₆₁	1	1	yes	characteristic
666	#459	C₂²×C₆₁	1	1	yes	characteristic
667	#452	C₂²×C₆₁	1	2	yes	—
668	#451	C₂²×C₆₁	1	2	yes	complemented
669	#450	C₂²×C₆₁	1	2	yes	—
670	#449	C₂²×C₆₁	1	2	yes	complemented
671	#448	C₂²×C₆₁	1	2	yes	—
672	#447	C₂²×C₆₁	1	2	yes	—
673	#446	C₂²×C₆₁	1	1	yes	characteristic, complemented
674	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
675	#442	C₂²×C₆₁	1	2	yes	complemented
676	#441	C₂²×C₆₁	1	2	yes	complemented
677	#440	C₂²×C₆₁	1	2	yes	—
678	#440	C₂²×C₆₁	1	2	yes	—
679	#440	C₂²×C₆₁	1	2	yes	complemented
680	#440	C₂²×C₆₁	1	2	yes	complemented
681	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
682	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
683	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
684	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
685	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
686	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
687	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
688	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
689	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
690	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
691	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
692	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
693	#436	C₂²×C₆₁	1	1	yes	characteristic
694	#435	C₂²×C₆₁	1	2	yes	complemented
695	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
696	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
697	#433	C₂²×C₆₁	1	2	yes	complemented
698	#432	C₂²×C₆₁	1	1	yes	characteristic, complemented
699	#427	C₂²×C₆₁	1	1	yes	characteristic, complemented
700	#427	C₂²×C₆₁	1	2	yes	complemented
701	#419	C₂²×C₆₁	1	2	yes	complemented
702	#418	C₂²×C₆₁	1	2	yes	—
703	#416	C₂²×C₆₁	1	1	yes	characteristic
704	#416	C₂²×C₆₁	1	1	yes	characteristic, complemented
705	#405	C₂²×C₆₁	1	2	yes	complemented
706	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
707	C₆₁	#61474	1	1	yes	characteristic, direct product factor, Sylow
708	C₂×#41	—	2	1	no	—
709	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
710	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
711	C₂²×Q₈	—	2	1	no	—
712	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
713	C₂²×D₄	—	2	1	no	—
714	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
715	#135	—	2	4	no	—
716	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
717	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
718	C₂×SD₁₆	—	2	8	no	—
719	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
720	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
723	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
724	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
725	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
726	C₂×D₈	C₂³×C₆₁	1	2	yes	—
727	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
728	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
729	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
730	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
731	C₄⋊Q₈	—	2	1	no	—
732	C₄⋊Q₈	—	2	1	no	—
733	C₄⋊Q₈	—	2	2	no	—
734	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
735	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
736	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
737	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
738	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
739	#127	C₂³×C₆₁	1	1	yes	characteristic
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	D₄×C₆₁	1	2	yes	—
747	#125	—	2	1	no	—
748	#125	D₄×C₆₁	1	1	yes	characteristic
749	#124	—	2	1	no	—
750	#124	—	2	1	no	—
751	#124	—	2	2	no	—
752	#124	—	2	2	no	—
753	#124	—	2	2	no	—
754	#124	—	2	2	no	—
755	#124	—	2	2	no	—
756	#124	—	2	2	no	—
757	#124	—	2	2	no	—
758	#124	—	2	1	no	—
759	#124	D₄×C₆₁	1	1	yes	characteristic
760	#124	C₂³×C₆₁	1	2	yes	—
761	#124	C₂³×C₆₁	1	2	yes	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	D₄×C₆₁	1	2	yes	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
776	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
777	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
778	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
779	#121	—	2	1	no	—
780	#121	—	2	2	no	—
781	#121	—	2	2	no	—
782	#121	—	2	1	no	—
783	#121	—	2	1	no	—
784	#121	—	2	2	no	—
785	#121	D₄×C₆₁	1	1	yes	characteristic
786	#121	C₂³×C₆₁	1	2	yes	—
787	#121	C₂³×C₆₁	1	2	yes	—
788	#121	C₂³×C₆₁	1	2	yes	—
789	#120	—	2	2	no	—
790	#120	—	2	2	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	2	no	—
793	C₄×Q₈	—	2	2	no	—
794	C₄×Q₈	—	2	1	no	—
795	C₄×Q₈	—	2	2	no	—
796	C₄×Q₈	—	2	1	no	—
797	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
799	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
800	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
802	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
803	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
804	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
817	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₆₁	1	2	yes	—
820	C₄×D₄	C₂³×C₆₁	1	2	yes	—
821	C₄×D₄	C₂³×C₆₁	1	2	yes	—
822	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
823	C₄×D₄	C₂³×C₆₁	1	2	yes	—
824	#117	—	2	1	no	—
825	#117	—	2	2	no	—
826	#117	—	2	1	no	—
827	#117	—	2	1	no	—
828	#117	—	2	2	no	—
829	#117	—	2	2	no	—
830	#117	—	2	1	no	—
831	#117	—	2	1	no	—
832	#117	C₂³×C₆₁	1	1	yes	characteristic
833	#117	C₂³×C₆₁	1	1	yes	characteristic
834	#117	C₂³×C₆₁	1	2	yes	—
835	#117	C₂³×C₆₁	1	2	yes	—
836	#117	C₂³×C₆₁	1	2	yes	—
837	C₂×C₂²⋊C₄	—	2	2	no	—
838	C₂×C₂²⋊C₄	—	2	2	no	—
839	C₂×C₂²⋊C₄	—	2	2	no	—
840	C₂×C₄²	—	2	1	no	—
841	C₂×C₄²	—	2	1	no	—
842	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
843	#107	C₂³×C₆₁	1	1	yes	characteristic
844	#107	C₂³×C₆₁	1	1	yes	characteristic
845	#107	C₂³×C₆₁	1	2	yes	—
846	#107	C₂³×C₆₁	1	2	yes	—
847	#106	C₂³×C₆₁	1	1	yes	characteristic
848	#106	C₂³×C₆₁	1	1	yes	characteristic
849	#106	C₂³×C₆₁	1	2	yes	—
850	#106	C₂³×C₆₁	1	2	yes	—
851	#106	C₂³×C₆₁	1	2	yes	—
852	#106	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	#103	C₂³×C₆₁	1	1	yes	characteristic
858	#103	C₂³×C₆₁	1	1	yes	characteristic
859	#103	C₂³×C₆₁	1	1	yes	characteristic
860	#103	C₂³×C₆₁	1	1	yes	characteristic
861	#103	C₂³×C₆₁	1	2	yes	—
862	#103	C₂³×C₆₁	1	2	yes	—
863	#103	C₂³×C₆₁	1	2	yes	—
864	#103	C₂³×C₆₁	1	2	yes	—
865	#103	C₂³×C₆₁	1	2	yes	—
866	#103	C₂³×C₆₁	1	2	yes	—
867	#102	C₂³×C₆₁	1	1	yes	characteristic
868	#102	C₂³×C₆₁	1	1	yes	characteristic
869	#102	C₂³×C₆₁	1	1	yes	characteristic
870	#102	C₂³×C₆₁	1	1	yes	characteristic
871	#102	C₂³×C₆₁	1	2	yes	—
872	#102	C₂³×C₆₁	1	2	yes	—
873	#102	C₂³×C₆₁	1	2	yes	—
874	#102	C₂³×C₆₁	1	2	yes	—
875	#102	C₂³×C₆₁	1	2	yes	—
876	#102	C₂³×C₆₁	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
880	#97	C₂³×C₆₁	1	2	yes	—
881	#97	C₂³×C₆₁	1	2	yes	—
882	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
883	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
884	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
885	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
886	C₄×C₈	C₂³×C₆₁	1	2	yes	—
887	C₂⁴	—	2	2	no	—
888	#41	—	2	2	no	—
889	#41	—	2	2	no	—
890	#41	—	4	1	no	—
891	#41	—	4	1	no	—
892	#41	—	8	2	no	—
893	C₂×Q₈	—	2	2	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	2	2	no	—
897	C₂×Q₈	—	2	2	no	—
898	C₂×Q₈	—	2	4	no	—
899	C₂×Q₈	—	4	2	no	—
900	C₂×Q₈	—	8	2	no	—
901	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
902	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
903	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
904	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
905	C₂×D₄	—	2	4	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	1	no	—
914	C₂×D₄	—	4	2	no	—
915	C₂×D₄	—	8	2	no	—
916	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
917	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
918	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
919	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
920	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
932	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
933	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
934	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
935	Q₁₆	—	2	2	no	—
936	Q₁₆	—	4	2	no	—
937	SD₁₆	—	2	4	no	—
938	SD₁₆	—	2	4	no	—
939	SD₁₆	—	2	4	no	—
940	SD₁₆	—	2	2	no	—
941	SD₁₆	—	4	2	no	—
942	SD₁₆	#41×C₆₁	1	4	yes	complemented
943	D₈	—	2	2	no	—
944	D₈	—	4	2	no	—
945	M₁₆	—	4	2	no	—
946	C₂×C₈	—	2	4	no	—
947	C₂×C₈	—	2	2	no	—
948	C₂×C₈	—	4	1	no	—
949	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
950	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
951	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
952	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
953	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
954	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
972	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
973	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
974	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
975	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
976	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
977	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
978	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
979	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
980	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
981	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
982	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1005	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1006	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1007	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1008	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	—	2	2	no	—
1020	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1021	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1022	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1023	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1024	C₄²	C₂⁴×C₆₁	1	2	yes	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	2	2	no	—
1028	C₂³	—	4	4	no	—
1029	C₂³	—	8	2	no	—
1030	C₂³	—	8	2	no	—
1031	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1032	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1033	Q₈	—	2	2	no	—
1034	Q₈	—	2	1	no	—
1035	Q₈	—	2	2	no	—
1036	Q₈	—	2	1	no	—
1037	Q₈	—	2	2	no	—
1038	Q₈	—	2	1	no	—
1039	Q₈	—	4	4	no	—
1040	Q₈	—	4	2	no	—
1041	Q₈	—	8	1	no	—
1042	Q₈	—	8	2	no	—
1043	Q₈	—	8	2	no	—
1044	Q₈	C₂×#41×C₆₁	1	2	yes	—
1045	D₄	—	2	2	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	2	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	2	2	no	—
1051	D₄	—	4	2	no	—
1052	D₄	—	4	4	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	4	2	no	—
1055	D₄	—	4	2	no	—
1056	D₄	—	8	1	no	—
1057	D₄	—	8	2	no	—
1058	D₄	—	8	2	no	—
1059	D₄	—	8	2	no	—
1060	D₄	C₂×#41×C₆₁	1	2	yes	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	4	1	no	—
1076	C₂×C₄	—	4	2	no	—
1077	C₂×C₄	—	4	4	no	—
1078	C₂×C₄	—	4	2	no	—
1079	C₂×C₄	—	4	2	no	—
1080	C₂×C₄	—	4	2	no	—
1081	C₂×C₄	—	8	1	no	—
1082	C₂×C₄	—	8	1	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	2	no	—
1085	C₂×C₄	—	8	2	no	—
1086	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1087	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1088	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1089	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1090	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1091	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1092	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1093	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1094	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1095	C₈	—	2	1	no	—
1096	C₈	—	2	2	no	—
1097	C₈	—	2	1	no	—
1098	C₈	—	2	1	no	—
1099	C₈	—	2	2	no	—
1100	C₈	C₂×#41×C₆₁	1	2	yes	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	1	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	2	no	—
1114	C₂²	—	4	1	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	16	4	no	—
1117	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1118	C₄	—	2	1	no	—
1119	C₄	—	2	2	no	—
1120	C₄	—	2	1	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	2	no	—
1125	C₄	—	2	2	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	2	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	2	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	4	2	no	—
1134	C₄	C₆₁×#577	1	2	yes	—
1135	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
1136	C₄	C₆₁×#585	1	1	yes	characteristic
1137	C₂	—	4	2	no	—
1138	C₂	—	4	1	no	—
1139	C₂	—	4	2	no	—
1140	C₂	—	8	2	no	—
1141	C₂	—	8	1	no	—
1142	C₂	D₄×#41×C₆₁	1	1	yes	characteristic
1143	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
1144	C₂	C₆₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3518	C₂	semidirect
2. C₆₁×#3514	C₂	semidirect
3. C₆₁×#3394	C₂	semidirect
4. Q₈×SD₁₆×C₆₁	C₂	semidirect
5. C₆₁×#3375	C₂	semidirect
6. C₆₁×#3367	C₂	semidirect
7. C₆₁×#3340	C₂	semidirect
8. C₆₁×#3340	C₂	semidirect
9. C₆₁×#3328	C₂	semidirect
10. C₆₁×#3325	C₂	semidirect
11. C₆₁×#3321	C₂	semidirect
12. C₆₁×#3311	C₂	semidirect
13. C₆₁×#3282	C₂	semidirect
14. D₄×SD₁₆×C₆₁	C₂	semidirect
15. C₆₁×#3173	C₂	semidirect
16. C₆₁×#3167	C₂	semidirect
17. C₆₁×#3121	C₂	semidirect
18. C₆₁×#3118	C₂	semidirect
19. C₆₁×#3116	C₂	semidirect
20. C₆₁×#3115	C₂	semidirect
21. C₆₁×#2966	C₂	semidirect
22. C₆₁×#2949	C₂	semidirect
23. C₄×#135×C₆₁	C₂	semidirect
27. Q₈²×C₆₁	C₂²	semidirect
31. C₆₁×#556	C₂²	semidirect
32. C₆₁×#556	C₂²	semidirect
40. C₆₁×#548	C₂²	semidirect
46. C₆₁×#542	C₂²	semidirect
49. C₆₁×#533	C₂²	semidirect
55. C₆₁×#519	C₂²	semidirect
58. C₄×#41×C₆₁	C₂²	semidirect
59. C₆₁×#498	C₂²	semidirect
60. C₆₁×#498	C₂²	semidirect
61. C₆₁×#495	C₂²	semidirect
63. C₆₁×#489	C₂²	semidirect
64. C₆₁×#489	C₂²	semidirect
65. C₆₁×#487	C₂²	semidirect
67. C₆₁×#485	C₂²	semidirect
68. C₆₁×#485	C₂²	semidirect
69. C₆₁×#485	C₂²	semidirect
71. C₆₁×#482	C₂²	semidirect
72. C₆₁×#482	C₂²	semidirect
73. C₆₁×#477	C₂²	semidirect
74. C₆₁×#477	C₂²	semidirect
77. C₆₁×#475	C₂²	semidirect
78. C₆₁×#475	C₂²	semidirect
79. C₆₁×#474	C₂²	semidirect
80. C₆₁×#474	C₂²	semidirect
81. C₆₁×#470	C₂²	semidirect
84. C₆₁×#465	C₂²	semidirect
85. C₆₁×#465	C₂²	semidirect
86. C₆₁×#465	C₂²	semidirect
87. C₆₁×#464	C₂²	semidirect
88. C₆₁×#464	C₂²	semidirect
90. C₆₁×#463	C₂²	semidirect
91. C₆₁×#462	C₂²	semidirect
96. C₆₁×#451	C₂²	semidirect
98. C₆₁×#449	C₂²	semidirect
101. C₆₁×#446	C₂²	semidirect
102. C₈×Q₈×C₆₁	C₂²	semidirect
103. C₆₁×#442	C₂²	semidirect
104. C₆₁×#441	C₂²	semidirect
107. C₆₁×#440	C₂²	semidirect
108. C₆₁×#440	C₂²	semidirect
109. C₄×Q₁₆×C₆₁	C₂²	semidirect
110. C₄×Q₁₆×C₆₁	C₂²	semidirect
114. C₄×SD₁₆×C₆₁	C₂²	semidirect
115. C₄×SD₁₆×C₆₁	C₂²	semidirect
116. C₄×SD₁₆×C₆₁	C₂²	semidirect
117. C₄×SD₁₆×C₆₁	C₂²	semidirect
118. C₄×SD₁₆×C₆₁	C₂²	semidirect
122. C₆₁×#435	C₂²	semidirect
124. C₈×D₄×C₆₁	C₂²	semidirect
125. C₆₁×#433	C₂²	semidirect
126. C₆₁×#432	C₂²	semidirect
127. C₆₁×#427	C₂²	semidirect
128. C₆₁×#427	C₂²	semidirect
129. C₆₁×#419	C₂²	semidirect
132. C₆₁×#416	C₂²	semidirect
133. C₆₁×#405	C₂²	semidirect
134. C₂×C₄×C₈×C₆₁	C₂²	semidirect
369. SD₁₆×C₆₁	#41	semidirect
528. #61474	C₆₁	direct (N × H)
565. #3518	C₂×C₆₁	semidirect
566. #3514	C₂×C₆₁	semidirect
567. #3394	C₂×C₆₁	semidirect
568. Q₈×SD₁₆	C₂×C₆₁	semidirect
569. #3375	C₂×C₆₁	semidirect
570. #3367	C₂×C₆₁	semidirect
571. #3340	C₂×C₆₁	semidirect
572. #3340	C₂×C₆₁	semidirect
573. #3328	C₂×C₆₁	semidirect
574. #3325	C₂×C₆₁	semidirect
575. #3321	C₂×C₆₁	semidirect
576. #3311	C₂×C₆₁	semidirect
577. #3282	C₂×C₆₁	semidirect
578. D₄×SD₁₆	C₂×C₆₁	semidirect
579. #3173	C₂×C₆₁	semidirect
580. #3167	C₂×C₆₁	semidirect
581. #3121	C₂×C₆₁	semidirect
582. #3118	C₂×C₆₁	semidirect
583. #3116	C₂×C₆₁	semidirect
584. #3115	C₂×C₆₁	semidirect
585. #2966	C₂×C₆₁	semidirect
586. #2949	C₂×C₆₁	semidirect
587. C₄×#135	C₂×C₆₁	semidirect
599. Q₈²	C₂²×C₆₁	semidirect
603. #556	C₂²×C₆₁	semidirect
604. #556	C₂²×C₆₁	semidirect
612. #548	C₂²×C₆₁	semidirect
618. #542	C₂²×C₆₁	semidirect
621. #533	C₂²×C₆₁	semidirect
627. #519	C₂²×C₆₁	semidirect
630. C₄×#41	C₂²×C₆₁	semidirect
631. #498	C₂²×C₆₁	semidirect
632. #498	C₂²×C₆₁	semidirect
633. #495	C₂²×C₆₁	semidirect
635. #489	C₂²×C₆₁	semidirect
636. #489	C₂²×C₆₁	semidirect
637. #487	C₂²×C₆₁	semidirect
639. #485	C₂²×C₆₁	semidirect
640. #485	C₂²×C₆₁	semidirect
641. #485	C₂²×C₆₁	semidirect
643. #482	C₂²×C₆₁	semidirect
644. #482	C₂²×C₆₁	semidirect
645. #477	C₂²×C₆₁	semidirect
646. #477	C₂²×C₆₁	semidirect
649. #475	C₂²×C₆₁	semidirect
650. #475	C₂²×C₆₁	semidirect
651. #474	C₂²×C₆₁	semidirect
652. #474	C₂²×C₆₁	semidirect
653. #470	C₂²×C₆₁	semidirect
656. #465	C₂²×C₆₁	semidirect
657. #465	C₂²×C₆₁	semidirect
658. #465	C₂²×C₆₁	semidirect
659. #464	C₂²×C₆₁	semidirect
660. #464	C₂²×C₆₁	semidirect
662. #463	C₂²×C₆₁	semidirect
663. #462	C₂²×C₆₁	semidirect
668. #451	C₂²×C₆₁	semidirect
670. #449	C₂²×C₆₁	semidirect
673. #446	C₂²×C₆₁	semidirect
674. C₈×Q₈	C₂²×C₆₁	semidirect
675. #442	C₂²×C₆₁	semidirect
676. #441	C₂²×C₆₁	semidirect
679. #440	C₂²×C₆₁	semidirect
680. #440	C₂²×C₆₁	semidirect
681. C₄×Q₁₆	C₂²×C₆₁	semidirect
682. C₄×Q₁₆	C₂²×C₆₁	semidirect
686. C₄×SD₁₆	C₂²×C₆₁	semidirect
687. C₄×SD₁₆	C₂²×C₆₁	semidirect
688. C₄×SD₁₆	C₂²×C₆₁	semidirect
689. C₄×SD₁₆	C₂²×C₆₁	semidirect
690. C₄×SD₁₆	C₂²×C₆₁	semidirect
694. #435	C₂²×C₆₁	semidirect
696. C₈×D₄	C₂²×C₆₁	semidirect
697. #433	C₂²×C₆₁	semidirect
698. #432	C₂²×C₆₁	semidirect
699. #427	C₂²×C₆₁	semidirect
700. #427	C₂²×C₆₁	semidirect
701. #419	C₂²×C₆₁	semidirect
704. #416	C₂²×C₆₁	semidirect
705. #405	C₂²×C₆₁	semidirect
706. C₂×C₄×C₈	C₂²×C₆₁	semidirect
707. C₆₁	#61474	direct (N × H)
942. SD₁₆	#41×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3518	2
C₆₁×#3514	2
C₆₁×#3394	2
Q₈×SD₁₆×C₆₁	2
C₆₁×#3375	2
C₆₁×#3367	2
C₆₁×#3340	2
C₆₁×#3328	2
C₆₁×#3325	2
C₆₁×#3321	2
C₆₁×#3311	2
C₆₁×#3282	2
D₄×SD₁₆×C₆₁	2
C₆₁×#3173	2
C₆₁×#3167	2
C₆₁×#3121	2
C₆₁×#3118	2
C₆₁×#3116	2
C₆₁×#3115	2
C₆₁×#2966	2
C₆₁×#2949	2
C₄×#135×C₆₁	2
#61474	61

Subgroups — C61×#61474 #29564907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61474 #29564907