Subgroups — C₆₁×#62071 #29565504

Order 15616.

1844 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3393	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3325	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3311	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3304	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3282	C₂	1	2	yes	maximal, complemented
12	D₄×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3271	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3263	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3224	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3121	C₂	1	2	yes	maximal, complemented
20	C₆₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3043	C₂	1	2	yes	maximal, complemented
22	C₆₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₆₁	C₂²	1	2	yes	complemented
25	C₂×#135×C₆₁	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
27	C₆₁×#560	—	2	2	no	—
28	Q₈²×C₆₁	C₂²	1	1	yes	characteristic, complemented
29	C₆₁×#556	—	2	2	no	—
30	C₆₁×#556	—	2	1	no	—
31	C₆₁×#556	C₂²	1	1	yes	characteristic
32	C₆₁×#556	C₂²	1	1	yes	characteristic, complemented
33	C₆₁×#556	C₂²	1	2	yes	complemented
34	C₆₁×#555	—	2	1	no	—
35	C₆₁×#555	C₂²	1	1	yes	characteristic
36	C₆₁×#553	—	2	1	no	—
37	C₆₁×#550	C₂²	1	2	yes	—
38	C₆₁×#550	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
40	C₆₁×#548	C₂²	1	2	yes	complemented
41	C₆₁×#547	C₂²	1	1	yes	characteristic
42	C₆₁×#546	—	2	1	no	—
43	C₆₁×#546	C₂²	1	2	yes	—
44	D₄²×C₆₁	C₂²	1	1	yes	characteristic
45	C₆₁×#542	—	2	2	no	—
46	C₆₁×#542	C₂²	1	2	yes	—
47	C₆₁×#542	C₂²	1	2	yes	complemented
48	C₆₁×#538	—	2	2	no	—
49	C₆₁×#537	—	2	1	no	—
50	C₆₁×#535	—	2	1	no	—
51	C₆₁×#535	C₂²	1	2	yes	—
52	C₆₁×#533	—	2	1	no	—
53	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
54	C₆₁×#532	C₂²	1	1	yes	characteristic
55	C₆₁×#532	C₂²	1	1	yes	characteristic
56	C₆₁×#529	—	2	1	no	—
57	C₆₁×#529	C₂²	1	1	yes	characteristic
58	C₆₁×#519	C₂²	1	2	yes	complemented
59	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic, complemented
60	C₆₁×#496	C₂²	1	2	yes	complemented
61	C₆₁×#495	C₂²	1	2	yes	—
62	C₆₁×#494	C₂²	1	1	yes	characteristic, complemented
63	C₆₁×#492	C₂²	1	1	yes	characteristic
64	C₆₁×#489	C₂²	1	2	yes	—
65	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
66	C₆₁×#486	C₂²	1	1	yes	characteristic
67	C₆₁×#486	C₂²	1	2	yes	complemented
68	C₆₁×#485	C₂²	1	2	yes	complemented
69	C₆₁×#482	C₂²	1	2	yes	—
70	C₆₁×#482	C₂²	1	1	yes	characteristic
71	C₆₁×#482	C₂²	1	1	yes	characteristic, complemented
72	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
73	C₆₁×#476	C₂²	1	1	yes	characteristic
74	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
75	C₆₁×#476	C₂²	1	2	yes	complemented
76	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
77	C₆₁×#475	C₂²	1	2	yes	complemented
78	C₆₁×#475	C₂²	1	2	yes	complemented
79	C₆₁×#470	C₂²	1	2	yes	complemented
80	C₆₁×#469	C₂²	1	2	yes	—
81	C₆₁×#465	C₂²	1	2	yes	—
82	C₆₁×#465	C₂²	1	2	yes	—
83	C₆₁×#465	C₂²	1	2	yes	complemented
84	C₆₁×#465	C₂²	1	2	yes	complemented
85	C₆₁×#464	C₂²	1	2	yes	—
86	C₆₁×#464	C₂²	1	2	yes	—
87	C₆₁×#464	C₂²	1	2	yes	complemented
88	C₆₁×#464	C₂²	1	2	yes	complemented
89	C₆₁×#464	C₂²	1	2	yes	complemented
90	C₆₁×#464	C₂²	1	2	yes	complemented
91	C₆₁×#463	C₂²	1	2	yes	complemented
92	C₆₁×#463	C₂²	1	2	yes	complemented
93	C₆₁×#462	C₂²	1	1	yes	characteristic, complemented
94	C₆₁×#461	C₂²	1	1	yes	characteristic
95	C₆₁×#461	C₂²	1	1	yes	characteristic, complemented
96	C₆₁×#461	C₂²	1	1	yes	characteristic, complemented
97	C₆₁×#460	C₂²	1	1	yes	characteristic
98	C₆₁×#460	C₂²	1	1	yes	characteristic
99	C₆₁×#460	C₂²	1	2	yes	—
100	C₆₁×#460	C₂²	1	2	yes	complemented
101	C₆₁×#460	C₂²	1	2	yes	complemented
102	C₆₁×#459	C₂²	1	1	yes	characteristic
103	C₆₁×#459	C₂²	1	1	yes	characteristic
104	C₆₁×#452	C₂²	1	2	yes	complemented
105	C₆₁×#452	C₂²	1	2	yes	complemented
106	C₆₁×#452	C₂²	1	2	yes	complemented
107	C₆₁×#451	C₂²	1	2	yes	complemented
108	C₆₁×#450	C₂²	1	2	yes	—
109	C₆₁×#449	C₂²	1	1	yes	characteristic
110	C₆₁×#449	C₂²	1	2	yes	complemented
111	C₆₁×#449	C₂²	1	1	yes	characteristic, complemented
112	C₆₁×#448	C₂²	1	2	yes	—
113	C₆₁×#447	C₂²	1	2	yes	—
114	C₆₁×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
116	C₆₁×#441	C₂²	1	2	yes	complemented
117	C₆₁×#440	C₂²	1	2	yes	complemented
118	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
119	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
121	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
122	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
123	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
124	C₆₁×#436	C₂²	1	1	yes	characteristic
125	C₆₁×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
127	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
128	C₆₁×#433	C₂²	1	2	yes	complemented
129	C₆₁×#431	C₂²	1	1	yes	characteristic, complemented
130	C₆₁×#424	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
132	C₆₁×#418	C₂²	1	2	yes	—
133	C₆₁×#416	C₂²	1	2	yes	complemented
134	C₆₁×#416	C₂²	1	2	yes	complemented
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	—	2	1	no	—
137	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
138	C₂×#41×C₆₁	C₂³	1	2	yes	—
139	C₂×#41×C₆₁	C₂³	1	2	yes	—
140	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
141	C₂²×D₄×C₆₁	—	2	1	no	—
142	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
143	#137×C₆₁	—	4	4	no	—
144	#135×C₆₁	—	4	4	no	—
145	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₆₁	—	4	4	no	—
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×SD₁₆×C₆₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
157	C₂×D₈×C₆₁	C₂³	1	2	yes	—
158	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
159	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
160	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
161	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
162	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₆₁	—	2	1	no	—
164	C₄⋊Q₈×C₆₁	—	2	1	no	—
165	C₄⋊Q₈×C₆₁	—	2	2	no	—
166	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
171	#127×C₆₁	—	2	2	no	—
172	#127×C₆₁	C₂³	1	1	yes	characteristic
173	#127×C₆₁	C₂³	1	1	yes	characteristic
174	#127×C₆₁	C₂³	1	2	yes	—
175	#126×C₆₁	—	2	2	no	—
176	#126×C₆₁	—	2	2	no	—
177	#126×C₆₁	—	2	2	no	—
178	#126×C₆₁	—	2	2	no	—
179	#126×C₆₁	—	2	2	no	—
180	#126×C₆₁	—	2	2	no	—
181	#126×C₆₁	D₄	1	2	yes	—
182	#125×C₆₁	—	2	1	no	—
183	#125×C₆₁	D₄	1	1	yes	characteristic
184	#124×C₆₁	—	2	2	no	—
185	#124×C₆₁	—	2	2	no	—
186	#124×C₆₁	—	2	2	no	—
187	#124×C₆₁	—	2	2	no	—
188	#124×C₆₁	—	2	2	no	—
189	#124×C₆₁	—	2	1	no	—
190	#124×C₆₁	D₄	1	1	yes	characteristic
191	#124×C₆₁	C₂³	1	2	yes	—
192	#124×C₆₁	C₂³	1	2	yes	—
193	#124×C₆₁	C₂³	1	2	yes	—
194	#123×C₆₁	—	2	2	no	—
195	#123×C₆₁	—	2	2	no	—
196	#123×C₆₁	—	2	2	no	—
197	#123×C₆₁	—	2	2	no	—
198	#123×C₆₁	D₄	1	2	yes	—
199	C₂²⋊Q₈×C₆₁	—	2	1	no	—
200	C₂²⋊Q₈×C₆₁	—	2	1	no	—
201	C₂²⋊Q₈×C₆₁	—	2	1	no	—
202	C₂²⋊Q₈×C₆₁	—	2	2	no	—
203	C₂²⋊Q₈×C₆₁	—	2	2	no	—
204	C₂²⋊Q₈×C₆₁	—	2	2	no	—
205	C₂²⋊Q₈×C₆₁	—	2	2	no	—
206	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
207	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
208	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
209	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
210	#121×C₆₁	—	2	1	no	—
211	#121×C₆₁	—	2	2	no	—
212	#121×C₆₁	—	2	1	no	—
213	#121×C₆₁	—	2	1	no	—
214	#121×C₆₁	—	2	1	no	—
215	#121×C₆₁	—	2	1	no	—
216	#121×C₆₁	—	2	1	no	—
217	#121×C₆₁	—	2	2	no	—
218	#121×C₆₁	—	2	2	no	—
219	#121×C₆₁	—	2	1	no	—
220	#121×C₆₁	—	2	2	no	—
221	#121×C₆₁	—	2	2	no	—
222	#121×C₆₁	—	2	2	no	—
223	#121×C₆₁	—	2	2	no	—
224	#121×C₆₁	D₄	1	1	yes	characteristic
225	#121×C₆₁	C₂³	1	1	yes	characteristic
226	#121×C₆₁	C₂³	1	1	yes	characteristic
227	#121×C₆₁	C₂³	1	2	yes	—
228	#121×C₆₁	C₂³	1	2	yes	—
229	#120×C₆₁	—	2	2	no	—
230	#120×C₆₁	—	2	2	no	—
231	#120×C₆₁	—	2	2	no	—
232	#120×C₆₁	—	2	2	no	—
233	C₄×Q₈×C₆₁	—	2	1	no	—
234	C₄×Q₈×C₆₁	—	2	2	no	—
235	C₄×Q₈×C₆₁	—	2	2	no	—
236	C₄×Q₈×C₆₁	—	2	2	no	—
237	C₄×Q₈×C₆₁	—	2	1	no	—
238	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
239	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
240	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
241	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
243	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₆₁	—	2	1	no	—
246	C₄×D₄×C₆₁	—	2	1	no	—
247	C₄×D₄×C₆₁	—	2	1	no	—
248	C₄×D₄×C₆₁	—	2	2	no	—
249	C₄×D₄×C₆₁	—	2	2	no	—
250	C₄×D₄×C₆₁	—	2	1	no	—
251	C₄×D₄×C₆₁	—	2	1	no	—
252	C₄×D₄×C₆₁	—	2	1	no	—
253	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₆₁	C₂³	1	2	yes	—
256	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₆₁	C₂³	1	2	yes	—
260	#117×C₆₁	—	2	1	no	—
261	#117×C₆₁	—	2	1	no	—
262	#117×C₆₁	—	2	1	no	—
263	#117×C₆₁	—	2	1	no	—
264	#117×C₆₁	—	2	2	no	—
265	#117×C₆₁	—	2	2	no	—
266	#117×C₆₁	—	2	1	no	—
267	#117×C₆₁	C₂³	1	2	yes	—
268	#117×C₆₁	C₂³	1	1	yes	characteristic
269	#117×C₆₁	C₂³	1	2	yes	—
270	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
271	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
272	C₂×C₄²×C₆₁	—	2	1	no	—
273	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
274	#107×C₆₁	C₂³	1	1	yes	characteristic
275	#107×C₆₁	C₂³	1	1	yes	characteristic
276	#106×C₆₁	C₂³	1	1	yes	characteristic
277	#106×C₆₁	C₂³	1	2	yes	—
278	#106×C₆₁	C₂³	1	1	yes	characteristic
279	#106×C₆₁	C₂³	1	2	yes	—
280	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
281	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
285	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
286	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
291	#103×C₆₁	C₂³	1	1	yes	characteristic
292	#103×C₆₁	C₂³	1	2	yes	—
293	#103×C₆₁	C₂³	1	2	yes	—
294	#103×C₆₁	C₂³	1	2	yes	—
295	#102×C₆₁	C₂³	1	1	yes	characteristic
296	#102×C₆₁	C₂³	1	2	yes	—
297	#102×C₆₁	C₂³	1	2	yes	—
298	#102×C₆₁	C₂³	1	2	yes	—
299	#102×C₆₁	C₂³	1	1	yes	characteristic
300	#102×C₆₁	C₂³	1	2	yes	—
301	#102×C₆₁	C₂³	1	2	yes	—
302	#102×C₆₁	C₂³	1	1	yes	characteristic
303	#102×C₆₁	C₂³	1	1	yes	characteristic
304	#102×C₆₁	C₂³	1	1	yes	characteristic
305	#102×C₆₁	C₂³	1	2	yes	—
306	#102×C₆₁	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
311	#97×C₆₁	C₂³	1	2	yes	—
312	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₆₁	C₂³	1	2	yes	—
315	C₂⁴×C₆₁	—	2	2	no	—
316	#41×C₆₁	—	2	2	no	—
317	#41×C₆₁	—	4	1	no	—
318	#41×C₆₁	—	4	2	no	—
319	#41×C₆₁	—	4	2	no	—
320	#41×C₆₁	—	4	2	no	—
321	#41×C₆₁	—	4	2	no	—
322	#41×C₆₁	—	8	2	no	—
323	#41×C₆₁	—	8	2	no	—
324	C₂×Q₈×C₆₁	—	2	2	no	—
325	C₂×Q₈×C₆₁	—	2	1	no	—
326	C₂×Q₈×C₆₁	—	2	2	no	—
327	C₂×Q₈×C₆₁	—	2	1	no	—
328	C₂×Q₈×C₆₁	—	2	4	no	—
329	C₂×Q₈×C₆₁	—	4	2	no	—
330	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₆₁	—	2	1	no	—
335	C₂×D₄×C₆₁	—	2	2	no	—
336	C₂×D₄×C₆₁	—	2	1	no	—
337	C₂×D₄×C₆₁	—	2	2	no	—
338	C₂×D₄×C₆₁	—	2	2	no	—
339	C₂×D₄×C₆₁	—	2	2	no	—
340	C₂×D₄×C₆₁	—	2	1	no	—
341	C₂×D₄×C₆₁	—	2	1	no	—
342	C₂×D₄×C₆₁	—	2	1	no	—
343	C₂×D₄×C₆₁	—	2	1	no	—
344	C₂×D₄×C₆₁	—	2	2	no	—
345	C₂×D₄×C₆₁	—	2	1	no	—
346	C₂×D₄×C₆₁	—	2	2	no	—
347	C₂×D₄×C₆₁	—	2	2	no	—
348	C₂×D₄×C₆₁	—	4	2	no	—
349	C₂×D₄×C₆₁	—	4	2	no	—
350	C₂×D₄×C₆₁	—	8	2	no	—
351	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
352	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
353	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
354	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
355	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
356	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₆₁	—	2	2	no	—
358	C₂²×C₄×C₆₁	—	2	1	no	—
359	C₂²×C₄×C₆₁	—	2	1	no	—
360	C₂²×C₄×C₆₁	—	2	1	no	—
361	C₂²×C₄×C₆₁	—	2	1	no	—
362	C₂²×C₄×C₆₁	—	2	1	no	—
363	C₂²×C₄×C₆₁	—	2	2	no	—
364	C₂²×C₄×C₆₁	—	2	2	no	—
365	C₂²×C₄×C₆₁	—	2	2	no	—
366	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
370	Q₁₆×C₆₁	—	2	4	no	—
371	Q₁₆×C₆₁	—	4	2	no	—
372	Q₁₆×C₆₁	—	4	2	no	—
373	SD₁₆×C₆₁	—	2	2	no	—
374	SD₁₆×C₆₁	—	2	4	no	—
375	SD₁₆×C₆₁	—	2	2	no	—
376	SD₁₆×C₆₁	—	4	2	no	—
377	SD₁₆×C₆₁	—	4	2	no	—
378	SD₁₆×C₆₁	—	4	2	no	—
379	SD₁₆×C₆₁	—	4	2	no	—
380	SD₁₆×C₆₁	—	4	2	no	—
381	D₈×C₆₁	—	4	1	no	—
382	D₈×C₆₁	—	4	1	no	—
383	D₈×C₆₁	—	4	2	no	—
384	M₁₆×C₆₁	—	4	2	no	—
385	C₂×C₈×C₆₁	—	4	2	no	—
386	C₂×C₈×C₆₁	—	4	2	no	—
387	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
392	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
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	1	no	—
397	C₄⋊C₄×C₆₁	—	2	1	no	—
398	C₄⋊C₄×C₆₁	—	2	1	no	—
399	C₄⋊C₄×C₆₁	—	2	2	no	—
400	C₄⋊C₄×C₆₁	—	2	2	no	—
401	C₄⋊C₄×C₆₁	—	2	2	no	—
402	C₄⋊C₄×C₆₁	—	2	2	no	—
403	C₄⋊C₄×C₆₁	—	2	1	no	—
404	C₄⋊C₄×C₆₁	—	2	1	no	—
405	C₄⋊C₄×C₆₁	—	2	1	no	—
406	C₄⋊C₄×C₆₁	—	2	2	no	—
407	C₄⋊C₄×C₆₁	—	2	2	no	—
408	C₄⋊C₄×C₆₁	—	2	2	no	—
409	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
411	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
414	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
417	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
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	2	no	—
425	C₂²⋊C₄×C₆₁	—	2	1	no	—
426	C₂²⋊C₄×C₆₁	—	2	2	no	—
427	C₂²⋊C₄×C₆₁	—	2	1	no	—
428	C₂²⋊C₄×C₆₁	—	2	1	no	—
429	C₂²⋊C₄×C₆₁	—	2	2	no	—
430	C₂²⋊C₄×C₆₁	—	2	2	no	—
431	C₂²⋊C₄×C₆₁	—	2	2	no	—
432	C₂²⋊C₄×C₆₁	—	2	1	no	—
433	C₂²⋊C₄×C₆₁	—	2	2	no	—
434	C₂²⋊C₄×C₆₁	—	2	2	no	—
435	C₂²⋊C₄×C₆₁	—	2	2	no	—
436	C₂²⋊C₄×C₆₁	—	2	2	no	—
437	C₂²⋊C₄×C₆₁	—	2	1	no	—
438	C₂²⋊C₄×C₆₁	—	2	2	no	—
439	C₂²⋊C₄×C₆₁	—	2	1	no	—
440	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
445	C₄²×C₆₁	—	2	1	no	—
446	C₄²×C₆₁	—	2	1	no	—
447	C₄²×C₆₁	—	2	1	no	—
448	C₄²×C₆₁	—	2	2	no	—
449	C₄²×C₆₁	—	2	2	no	—
450	C₄²×C₆₁	—	2	2	no	—
451	C₄²×C₆₁	—	2	2	no	—
452	C₄²×C₆₁	—	2	2	no	—
453	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
456	C₄²×C₆₁	C₂⁴	1	2	yes	—
457	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
458	C₂³×C₆₁	—	2	1	no	—
459	C₂³×C₆₁	—	2	1	no	—
460	C₂³×C₆₁	—	2	2	no	—
461	C₂³×C₆₁	—	2	1	no	—
462	C₂³×C₆₁	—	8	2	no	—
463	C₂³×C₆₁	—	8	2	no	—
464	C₂³×C₆₁	—	8	2	no	—
465	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
466	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
467	Q₈×C₆₁	—	2	2	no	—
468	Q₈×C₆₁	—	2	1	no	—
469	Q₈×C₆₁	—	2	2	no	—
470	Q₈×C₆₁	—	2	2	no	—
471	Q₈×C₆₁	—	2	2	no	—
472	Q₈×C₆₁	—	2	2	no	—
473	Q₈×C₆₁	—	4	4	no	—
474	Q₈×C₆₁	—	8	1	no	—
475	Q₈×C₆₁	—	8	2	no	—
476	Q₈×C₆₁	—	8	1	no	—
477	Q₈×C₆₁	H(5,𝔽₂)	1	2	yes	—
478	D₄×C₆₁	—	2	2	no	—
479	D₄×C₆₁	—	2	1	no	—
480	D₄×C₆₁	—	2	2	no	—
481	D₄×C₆₁	—	2	1	no	—
482	D₄×C₆₁	—	2	1	no	—
483	D₄×C₆₁	—	2	1	no	—
484	D₄×C₆₁	—	2	1	no	—
485	D₄×C₆₁	—	2	1	no	—
486	D₄×C₆₁	—	2	2	no	—
487	D₄×C₆₁	—	4	2	no	—
488	D₄×C₆₁	—	4	2	no	—
489	D₄×C₆₁	—	4	2	no	—
490	D₄×C₆₁	—	8	1	no	—
491	D₄×C₆₁	—	8	1	no	—
492	D₄×C₆₁	—	8	2	no	—
493	D₄×C₆₁	—	8	2	no	—
494	D₄×C₆₁	—	8	1	no	—
495	D₄×C₆₁	—	8	2	no	—
496	D₄×C₆₁	—	8	2	no	—
497	D₄×C₆₁	—	8	2	no	—
498	D₄×C₆₁	—	8	2	no	—
499	D₄×C₆₁	—	8	2	no	—
500	D₄×C₆₁	—	8	1	no	—
501	D₄×C₆₁	—	8	1	no	—
502	C₂×C₄×C₆₁	—	2	1	no	—
503	C₂×C₄×C₆₁	—	2	2	no	—
504	C₂×C₄×C₆₁	—	2	1	no	—
505	C₂×C₄×C₆₁	—	2	2	no	—
506	C₂×C₄×C₆₁	—	2	2	no	—
507	C₂×C₄×C₆₁	—	2	1	no	—
508	C₂×C₄×C₆₁	—	2	1	no	—
509	C₂×C₄×C₆₁	—	2	2	no	—
510	C₂×C₄×C₆₁	—	2	2	no	—
511	C₂×C₄×C₆₁	—	2	1	no	—
512	C₂×C₄×C₆₁	—	2	1	no	—
513	C₂×C₄×C₆₁	—	2	2	no	—
514	C₂×C₄×C₆₁	—	2	1	no	—
515	C₂×C₄×C₆₁	—	4	1	no	—
516	C₂×C₄×C₆₁	—	4	2	no	—
517	C₂×C₄×C₆₁	—	4	4	no	—
518	C₂×C₄×C₆₁	—	4	2	no	—
519	C₂×C₄×C₆₁	—	4	2	no	—
520	C₂×C₄×C₆₁	—	4	2	no	—
521	C₂×C₄×C₆₁	—	8	1	no	—
522	C₂×C₄×C₆₁	—	8	2	no	—
523	C₂×C₄×C₆₁	—	8	2	no	—
524	C₂×C₄×C₆₁	—	8	2	no	—
525	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
534	C₈×C₆₁	—	2	1	no	—
535	C₈×C₆₁	—	2	2	no	—
536	C₈×C₆₁	—	2	2	no	—
537	C₈×C₆₁	—	2	1	no	—
538	C₈×C₆₁	—	2	1	no	—
539	C₈×C₆₁	—	2	1	no	—
540	#62071	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
541	C₂²×C₆₁	—	2	1	no	—
542	C₂²×C₆₁	—	2	2	no	—
543	C₂²×C₆₁	—	2	2	no	—
544	C₂²×C₆₁	—	2	1	no	—
545	C₂²×C₆₁	—	2	1	no	—
546	C₂²×C₆₁	—	2	2	no	—
547	C₂²×C₆₁	—	4	1	no	—
548	C₂²×C₆₁	—	4	1	no	—
549	C₂²×C₆₁	—	4	2	no	—
550	C₂²×C₆₁	—	4	1	no	—
551	C₂²×C₆₁	—	4	1	no	—
552	C₂²×C₆₁	—	4	1	no	—
553	C₂²×C₆₁	—	4	2	no	—
554	C₂²×C₆₁	—	4	1	no	—
555	C₂²×C₆₁	—	4	1	no	—
556	C₂²×C₆₁	—	4	1	no	—
557	C₂²×C₆₁	—	4	1	no	—
558	C₂²×C₆₁	—	4	2	no	—
559	C₂²×C₆₁	—	16	4	no	—
560	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
561	C₄×C₆₁	—	2	1	no	—
562	C₄×C₆₁	—	2	1	no	—
563	C₄×C₆₁	—	2	2	no	—
564	C₄×C₆₁	—	2	1	no	—
565	C₄×C₆₁	—	2	2	no	—
566	C₄×C₆₁	—	2	2	no	—
567	C₄×C₆₁	—	2	1	no	—
568	C₄×C₆₁	—	2	2	no	—
569	C₄×C₆₁	—	4	1	no	—
570	C₄×C₆₁	—	4	2	no	—
571	C₄×C₆₁	—	4	2	no	—
572	C₄×C₆₁	—	4	2	no	—
573	C₄×C₆₁	—	4	1	no	—
574	C₄×C₆₁	—	4	1	no	—
575	C₄×C₆₁	—	4	1	no	—
576	C₄×C₆₁	#577	1	2	yes	—
577	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
578	C₄×C₆₁	#585	1	1	yes	characteristic
579	#3546	C₂×C₆₁	1	1	yes	characteristic, complemented
580	#3518	C₂×C₆₁	1	1	yes	characteristic, complemented
581	#3397	C₂×C₆₁	1	1	yes	characteristic, complemented
582	#3393	C₂×C₆₁	1	1	yes	characteristic, complemented
583	#3369	C₂×C₆₁	1	1	yes	characteristic, complemented
584	#3362	C₂×C₆₁	1	1	yes	characteristic, complemented
585	#3325	C₂×C₆₁	1	1	yes	characteristic, complemented
586	#3311	C₂×C₆₁	1	2	yes	complemented
587	#3304	C₂×C₆₁	1	2	yes	complemented
588	#3303	C₂×C₆₁	1	1	yes	characteristic, complemented
589	#3282	C₂×C₆₁	1	2	yes	complemented
590	D₄×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
591	#3276	C₂×C₆₁	1	1	yes	characteristic, complemented
592	#3271	C₂×C₆₁	1	2	yes	complemented
593	#3263	C₂×C₆₁	1	2	yes	complemented
594	#3246	C₂×C₆₁	1	1	yes	characteristic, complemented
595	#3224	C₂×C₆₁	1	2	yes	complemented
596	#3210	C₂×C₆₁	1	1	yes	characteristic, complemented
597	#3121	C₂×C₆₁	1	2	yes	complemented
598	#3106	C₂×C₆₁	1	1	yes	characteristic, complemented
599	#3043	C₂×C₆₁	1	2	yes	complemented
600	#3035	C₂×C₆₁	1	1	yes	characteristic, complemented
601	#2994	C₂×C₆₁	1	1	yes	characteristic, complemented
602	C₂×C₆₁	—	4	1	no	—
603	C₂×C₆₁	—	4	2	no	—
604	C₂×C₆₁	—	8	1	no	—
605	C₂×C₆₁	—	8	1	no	—
606	C₂×C₆₁	—	8	2	no	—
607	C₂×C₆₁	—	8	1	no	—
608	C₂×C₆₁	#3488	1	1	yes	characteristic
609	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
610	C₂×C₆₁	#3584	1	1	yes	characteristic
611	C₂×#137	C₂²×C₆₁	1	2	yes	complemented
612	C₂×#135	C₂²×C₆₁	1	2	yes	complemented
613	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
614	#560	—	2	2	no	—
615	Q₈²	C₂²×C₆₁	1	1	yes	characteristic, complemented
616	#556	—	2	2	no	—
617	#556	—	2	1	no	—
618	#556	C₂²×C₆₁	1	1	yes	characteristic
619	#556	C₂²×C₆₁	1	1	yes	characteristic, complemented
620	#556	C₂²×C₆₁	1	2	yes	complemented
621	#555	—	2	1	no	—
622	#555	C₂²×C₆₁	1	1	yes	characteristic
623	#553	—	2	1	no	—
624	#550	C₂²×C₆₁	1	2	yes	—
625	#550	C₂²×C₆₁	1	1	yes	characteristic
626	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
627	#548	C₂²×C₆₁	1	2	yes	complemented
628	#547	C₂²×C₆₁	1	1	yes	characteristic
629	#546	—	2	1	no	—
630	#546	C₂²×C₆₁	1	2	yes	—
631	D₄²	C₂²×C₆₁	1	1	yes	characteristic
632	#542	—	2	2	no	—
633	#542	C₂²×C₆₁	1	2	yes	—
634	#542	C₂²×C₆₁	1	2	yes	complemented
635	#538	—	2	2	no	—
636	#537	—	2	1	no	—
637	#535	—	2	1	no	—
638	#535	C₂²×C₆₁	1	2	yes	—
639	#533	—	2	1	no	—
640	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
641	#532	C₂²×C₆₁	1	1	yes	characteristic
642	#532	C₂²×C₆₁	1	1	yes	characteristic
643	#529	—	2	1	no	—
644	#529	C₂²×C₆₁	1	1	yes	characteristic
645	#519	C₂²×C₆₁	1	2	yes	complemented
646	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic, complemented
647	#496	C₂²×C₆₁	1	2	yes	complemented
648	#495	C₂²×C₆₁	1	2	yes	—
649	#494	C₂²×C₆₁	1	1	yes	characteristic, complemented
650	#492	C₂²×C₆₁	1	1	yes	characteristic
651	#489	C₂²×C₆₁	1	2	yes	—
652	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
653	#486	C₂²×C₆₁	1	1	yes	characteristic
654	#486	C₂²×C₆₁	1	2	yes	complemented
655	#485	C₂²×C₆₁	1	2	yes	complemented
656	#482	C₂²×C₆₁	1	1	yes	characteristic
657	#482	C₂²×C₆₁	1	2	yes	—
658	#482	C₂²×C₆₁	1	1	yes	characteristic, complemented
659	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
660	#476	C₂²×C₆₁	1	1	yes	characteristic
661	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
662	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
663	#476	C₂²×C₆₁	1	2	yes	complemented
664	#475	C₂²×C₆₁	1	2	yes	complemented
665	#475	C₂²×C₆₁	1	2	yes	complemented
666	#470	C₂²×C₆₁	1	2	yes	complemented
667	#469	C₂²×C₆₁	1	2	yes	—
668	#465	C₂²×C₆₁	1	2	yes	—
669	#465	C₂²×C₆₁	1	2	yes	—
670	#465	C₂²×C₆₁	1	2	yes	complemented
671	#465	C₂²×C₆₁	1	2	yes	complemented
672	#464	C₂²×C₆₁	1	2	yes	—
673	#464	C₂²×C₆₁	1	2	yes	—
674	#464	C₂²×C₆₁	1	2	yes	complemented
675	#464	C₂²×C₆₁	1	2	yes	complemented
676	#464	C₂²×C₆₁	1	2	yes	complemented
677	#464	C₂²×C₆₁	1	2	yes	complemented
678	#463	C₂²×C₆₁	1	2	yes	complemented
679	#463	C₂²×C₆₁	1	2	yes	complemented
680	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
681	#461	C₂²×C₆₁	1	1	yes	characteristic
682	#461	C₂²×C₆₁	1	1	yes	characteristic, complemented
683	#461	C₂²×C₆₁	1	1	yes	characteristic, complemented
684	#460	C₂²×C₆₁	1	1	yes	characteristic
685	#460	C₂²×C₆₁	1	1	yes	characteristic
686	#460	C₂²×C₆₁	1	2	yes	—
687	#460	C₂²×C₆₁	1	2	yes	complemented
688	#460	C₂²×C₆₁	1	2	yes	complemented
689	#459	C₂²×C₆₁	1	1	yes	characteristic
690	#459	C₂²×C₆₁	1	1	yes	characteristic
691	#452	C₂²×C₆₁	1	2	yes	complemented
692	#452	C₂²×C₆₁	1	2	yes	complemented
693	#452	C₂²×C₆₁	1	2	yes	complemented
694	#451	C₂²×C₆₁	1	2	yes	complemented
695	#450	C₂²×C₆₁	1	2	yes	—
696	#449	C₂²×C₆₁	1	1	yes	characteristic
697	#449	C₂²×C₆₁	1	1	yes	characteristic, complemented
698	#449	C₂²×C₆₁	1	2	yes	complemented
699	#448	C₂²×C₆₁	1	2	yes	—
700	#447	C₂²×C₆₁	1	2	yes	—
701	#446	C₂²×C₆₁	1	1	yes	characteristic, complemented
702	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
703	#441	C₂²×C₆₁	1	2	yes	complemented
704	#440	C₂²×C₆₁	1	2	yes	complemented
705	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
706	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
707	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
708	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
709	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
710	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
711	#436	C₂²×C₆₁	1	1	yes	characteristic
712	#435	C₂²×C₆₁	1	2	yes	complemented
713	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
714	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
715	#433	C₂²×C₆₁	1	2	yes	complemented
716	#431	C₂²×C₆₁	1	1	yes	characteristic, complemented
717	#424	C₂²×C₆₁	1	2	yes	complemented
718	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
719	#418	C₂²×C₆₁	1	2	yes	—
720	#416	C₂²×C₆₁	1	2	yes	complemented
721	#416	C₂²×C₆₁	1	2	yes	complemented
722	C₆₁	#62071	1	1	yes	characteristic, direct product factor, Sylow
723	C₂×#41	—	2	1	no	—
724	C₂×#41	—	2	1	no	—
725	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
726	C₂×#41	C₂³×C₆₁	1	2	yes	—
727	C₂×#41	C₂³×C₆₁	1	2	yes	—
728	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
729	C₂²×D₄	—	2	1	no	—
730	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
731	#137	—	4	4	no	—
732	#135	—	4	4	no	—
733	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
734	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
735	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
736	C₂×SD₁₆	—	4	4	no	—
737	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
738	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
739	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
740	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
742	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
743	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
744	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
745	C₂×D₈	C₂³×C₆₁	1	2	yes	—
746	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
747	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
748	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
749	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
750	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
751	C₄⋊Q₈	—	2	1	no	—
752	C₄⋊Q₈	—	2	1	no	—
753	C₄⋊Q₈	—	2	2	no	—
754	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
755	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
756	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
757	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
758	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
759	#127	—	2	2	no	—
760	#127	C₂³×C₆₁	1	1	yes	characteristic
761	#127	C₂³×C₆₁	1	1	yes	characteristic
762	#127	C₂³×C₆₁	1	2	yes	—
763	#126	—	2	2	no	—
764	#126	—	2	2	no	—
765	#126	—	2	2	no	—
766	#126	—	2	2	no	—
767	#126	—	2	2	no	—
768	#126	—	2	2	no	—
769	#126	D₄×C₆₁	1	2	yes	—
770	#125	—	2	1	no	—
771	#125	D₄×C₆₁	1	1	yes	characteristic
772	#124	—	2	2	no	—
773	#124	—	2	2	no	—
774	#124	—	2	2	no	—
775	#124	—	2	2	no	—
776	#124	—	2	2	no	—
777	#124	—	2	1	no	—
778	#124	D₄×C₆₁	1	1	yes	characteristic
779	#124	C₂³×C₆₁	1	2	yes	—
780	#124	C₂³×C₆₁	1	2	yes	—
781	#124	C₂³×C₆₁	1	2	yes	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	#123	D₄×C₆₁	1	2	yes	—
787	C₂²⋊Q₈	—	2	1	no	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
795	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
796	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
797	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
798	#121	—	2	1	no	—
799	#121	—	2	1	no	—
800	#121	—	2	2	no	—
801	#121	—	2	1	no	—
802	#121	—	2	1	no	—
803	#121	—	2	1	no	—
804	#121	—	2	1	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	—	2	1	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	D₄×C₆₁	1	1	yes	characteristic
813	#121	C₂³×C₆₁	1	1	yes	characteristic
814	#121	C₂³×C₆₁	1	1	yes	characteristic
815	#121	C₂³×C₆₁	1	2	yes	—
816	#121	C₂³×C₆₁	1	2	yes	—
817	#120	—	2	2	no	—
818	#120	—	2	2	no	—
819	#120	—	2	2	no	—
820	#120	—	2	2	no	—
821	C₄×Q₈	—	2	1	no	—
822	C₄×Q₈	—	2	2	no	—
823	C₄×Q₈	—	2	2	no	—
824	C₄×Q₈	—	2	2	no	—
825	C₄×Q₈	—	2	1	no	—
826	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
827	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
828	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
829	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
830	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
831	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
832	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	—	2	1	no	—
840	C₄×D₄	—	2	1	no	—
841	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
842	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
843	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
844	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
845	C₄×D₄	C₂³×C₆₁	1	2	yes	—
846	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
847	C₄×D₄	C₂³×C₆₁	1	2	yes	—
848	#117	—	2	1	no	—
849	#117	—	2	1	no	—
850	#117	—	2	1	no	—
851	#117	—	2	1	no	—
852	#117	—	2	2	no	—
853	#117	—	2	2	no	—
854	#117	—	2	1	no	—
855	#117	C₂³×C₆₁	1	1	yes	characteristic
856	#117	C₂³×C₆₁	1	2	yes	—
857	#117	C₂³×C₆₁	1	2	yes	—
858	C₂×C₄⋊C₄	—	2	1	no	—
859	C₂×C₂²⋊C₄	—	2	2	no	—
860	C₂×C₄²	—	2	1	no	—
861	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
862	#107	C₂³×C₆₁	1	1	yes	characteristic
863	#107	C₂³×C₆₁	1	1	yes	characteristic
864	#106	C₂³×C₆₁	1	1	yes	characteristic
865	#106	C₂³×C₆₁	1	2	yes	—
866	#106	C₂³×C₆₁	1	1	yes	characteristic
867	#106	C₂³×C₆₁	1	2	yes	—
868	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
869	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
870	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
871	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
872	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
873	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
874	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
875	#103	C₂³×C₆₁	1	2	yes	—
876	#103	C₂³×C₆₁	1	2	yes	—
877	#103	C₂³×C₆₁	1	2	yes	—
878	#103	C₂³×C₆₁	1	1	yes	characteristic
879	#103	C₂³×C₆₁	1	1	yes	characteristic
880	#103	C₂³×C₆₁	1	2	yes	—
881	#103	C₂³×C₆₁	1	2	yes	—
882	#103	C₂³×C₆₁	1	2	yes	—
883	#102	C₂³×C₆₁	1	1	yes	characteristic
884	#102	C₂³×C₆₁	1	2	yes	—
885	#102	C₂³×C₆₁	1	2	yes	—
886	#102	C₂³×C₆₁	1	2	yes	—
887	#102	C₂³×C₆₁	1	1	yes	characteristic
888	#102	C₂³×C₆₁	1	2	yes	—
889	#102	C₂³×C₆₁	1	2	yes	—
890	#102	C₂³×C₆₁	1	1	yes	characteristic
891	#102	C₂³×C₆₁	1	1	yes	characteristic
892	#102	C₂³×C₆₁	1	1	yes	characteristic
893	#102	C₂³×C₆₁	1	2	yes	—
894	#102	C₂³×C₆₁	1	1	yes	characteristic
895	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
896	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
897	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
898	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
899	#97	C₂³×C₆₁	1	2	yes	—
900	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
901	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
902	C₄×C₈	C₂³×C₆₁	1	2	yes	—
903	C₂⁴	—	2	2	no	—
904	#41	—	2	2	no	—
905	#41	—	4	1	no	—
906	#41	—	4	2	no	—
907	#41	—	4	2	no	—
908	#41	—	4	2	no	—
909	#41	—	4	2	no	—
910	#41	—	8	2	no	—
911	#41	—	8	2	no	—
912	C₂×Q₈	—	2	2	no	—
913	C₂×Q₈	—	2	1	no	—
914	C₂×Q₈	—	2	2	no	—
915	C₂×Q₈	—	2	1	no	—
916	C₂×Q₈	—	2	4	no	—
917	C₂×Q₈	—	4	2	no	—
918	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
919	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
920	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
921	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	1	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	1	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	4	2	no	—
937	C₂×D₄	—	4	2	no	—
938	C₂×D₄	—	8	2	no	—
939	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
940	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
941	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
942	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
943	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
944	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	2	no	—
952	C₂²×C₄	—	2	2	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
955	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
956	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
957	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
958	Q₁₆	—	2	4	no	—
959	Q₁₆	—	4	2	no	—
960	Q₁₆	—	4	2	no	—
961	SD₁₆	—	2	2	no	—
962	SD₁₆	—	2	4	no	—
963	SD₁₆	—	2	2	no	—
964	SD₁₆	—	4	2	no	—
965	SD₁₆	—	4	2	no	—
966	SD₁₆	—	4	2	no	—
967	SD₁₆	—	4	2	no	—
968	SD₁₆	—	4	2	no	—
969	D₈	—	4	1	no	—
970	D₈	—	4	1	no	—
971	D₈	—	4	2	no	—
972	M₁₆	—	4	2	no	—
973	C₂×C₈	—	4	2	no	—
974	C₂×C₈	—	4	2	no	—
975	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
976	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
977	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
978	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
979	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
980	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
998	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
999	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1000	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1001	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1002	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1003	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1004	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1005	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1006	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1007	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	1	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1029	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1030	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1031	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1032	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1033	C₄²	—	2	1	no	—
1034	C₄²	—	2	1	no	—
1035	C₄²	—	2	1	no	—
1036	C₄²	—	2	2	no	—
1037	C₄²	—	2	2	no	—
1038	C₄²	—	2	2	no	—
1039	C₄²	—	2	2	no	—
1040	C₄²	—	2	2	no	—
1041	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1042	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1043	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1044	C₄²	C₂⁴×C₆₁	1	2	yes	—
1045	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1046	C₂³	—	2	1	no	—
1047	C₂³	—	2	1	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	8	2	no	—
1051	C₂³	—	8	2	no	—
1052	C₂³	—	8	2	no	—
1053	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1054	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1055	Q₈	—	2	2	no	—
1056	Q₈	—	2	1	no	—
1057	Q₈	—	2	2	no	—
1058	Q₈	—	2	2	no	—
1059	Q₈	—	2	2	no	—
1060	Q₈	—	2	2	no	—
1061	Q₈	—	4	4	no	—
1062	Q₈	—	8	1	no	—
1063	Q₈	—	8	2	no	—
1064	Q₈	—	8	1	no	—
1065	Q₈	H(5,𝔽₂)×C₆₁	1	2	yes	—
1066	D₄	—	2	2	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	2	2	no	—
1069	D₄	—	2	1	no	—
1070	D₄	—	2	1	no	—
1071	D₄	—	2	1	no	—
1072	D₄	—	2	1	no	—
1073	D₄	—	2	1	no	—
1074	D₄	—	2	2	no	—
1075	D₄	—	4	2	no	—
1076	D₄	—	4	2	no	—
1077	D₄	—	4	2	no	—
1078	D₄	—	8	1	no	—
1079	D₄	—	8	1	no	—
1080	D₄	—	8	2	no	—
1081	D₄	—	8	2	no	—
1082	D₄	—	8	1	no	—
1083	D₄	—	8	2	no	—
1084	D₄	—	8	2	no	—
1085	D₄	—	8	2	no	—
1086	D₄	—	8	2	no	—
1087	D₄	—	8	2	no	—
1088	D₄	—	8	1	no	—
1089	D₄	—	8	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	4	1	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	4	4	no	—
1106	C₂×C₄	—	4	2	no	—
1107	C₂×C₄	—	4	2	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	8	1	no	—
1110	C₂×C₄	—	8	2	no	—
1111	C₂×C₄	—	8	2	no	—
1112	C₂×C₄	—	8	2	no	—
1113	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1114	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1115	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1116	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1117	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1118	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1119	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1120	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1121	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1122	C₈	—	2	1	no	—
1123	C₈	—	2	2	no	—
1124	C₈	—	2	2	no	—
1125	C₈	—	2	1	no	—
1126	C₈	—	2	1	no	—
1127	C₈	—	2	1	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	2	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	16	4	no	—
1147	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1148	C₄	—	2	1	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	2	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	4	1	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	2	no	—
1161	C₄	—	4	2	no	—
1162	C₄	—	4	2	no	—
1163	C₄	C₆₁×#577	1	2	yes	—
1164	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1165	C₄	C₆₁×#585	1	1	yes	characteristic
1166	C₂	—	4	2	no	—
1167	C₂	—	4	1	no	—
1168	C₂	—	8	1	no	—
1169	C₂	—	8	2	no	—
1170	C₂	—	8	1	no	—
1171	C₂	—	8	1	no	—
1172	C₂	C₆₁×#3488	1	1	yes	characteristic
1173	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
1174	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×#3546	C₂	semidirect
2. C₆₁×#3518	C₂	semidirect
3. C₆₁×#3397	C₂	semidirect
4. C₆₁×#3393	C₂	semidirect
5. C₆₁×#3369	C₂	semidirect
6. C₆₁×#3362	C₂	semidirect
7. C₆₁×#3325	C₂	semidirect
8. C₆₁×#3311	C₂	semidirect
9. C₆₁×#3304	C₂	semidirect
10. C₆₁×#3303	C₂	semidirect
11. C₆₁×#3282	C₂	semidirect
12. D₄×SD₁₆×C₆₁	C₂	semidirect
13. C₆₁×#3276	C₂	semidirect
14. C₆₁×#3271	C₂	semidirect
15. C₆₁×#3263	C₂	semidirect
16. C₆₁×#3246	C₂	semidirect
17. C₆₁×#3224	C₂	semidirect
18. C₆₁×#3210	C₂	semidirect
19. C₆₁×#3121	C₂	semidirect
20. C₆₁×#3106	C₂	semidirect
21. C₆₁×#3043	C₂	semidirect
22. C₆₁×#3035	C₂	semidirect
23. C₆₁×#2994	C₂	semidirect
24. C₂×#137×C₆₁	C₂²	semidirect
25. C₂×#135×C₆₁	C₂²	semidirect
28. Q₈²×C₆₁	C₂²	semidirect
32. C₆₁×#556	C₂²	semidirect
33. C₆₁×#556	C₂²	semidirect
40. C₆₁×#548	C₂²	semidirect
47. C₆₁×#542	C₂²	semidirect
53. C₆₁×#533	C₂²	semidirect
58. C₆₁×#519	C₂²	semidirect
59. C₄×#41×C₆₁	C₂²	semidirect
60. C₆₁×#496	C₂²	semidirect
62. C₆₁×#494	C₂²	semidirect
65. C₆₁×#487	C₂²	semidirect
67. C₆₁×#486	C₂²	semidirect
68. C₆₁×#485	C₂²	semidirect
71. C₆₁×#482	C₂²	semidirect
72. C₆₁×#477	C₂²	semidirect
74. C₆₁×#476	C₂²	semidirect
75. C₆₁×#476	C₂²	semidirect
76. C₆₁×#476	C₂²	semidirect
77. C₆₁×#475	C₂²	semidirect
78. C₆₁×#475	C₂²	semidirect
79. C₆₁×#470	C₂²	semidirect
83. C₆₁×#465	C₂²	semidirect
84. C₆₁×#465	C₂²	semidirect
87. C₆₁×#464	C₂²	semidirect
88. C₆₁×#464	C₂²	semidirect
89. C₆₁×#464	C₂²	semidirect
90. C₆₁×#464	C₂²	semidirect
91. C₆₁×#463	C₂²	semidirect
92. C₆₁×#463	C₂²	semidirect
93. C₆₁×#462	C₂²	semidirect
95. C₆₁×#461	C₂²	semidirect
96. C₆₁×#461	C₂²	semidirect
100. C₆₁×#460	C₂²	semidirect
101. C₆₁×#460	C₂²	semidirect
104. C₆₁×#452	C₂²	semidirect
105. C₆₁×#452	C₂²	semidirect
106. C₆₁×#452	C₂²	semidirect
107. C₆₁×#451	C₂²	semidirect
110. C₆₁×#449	C₂²	semidirect
111. C₆₁×#449	C₂²	semidirect
114. C₆₁×#446	C₂²	semidirect
115. C₈×Q₈×C₆₁	C₂²	semidirect
116. C₆₁×#441	C₂²	semidirect
117. C₆₁×#440	C₂²	semidirect
118. C₄×Q₁₆×C₆₁	C₂²	semidirect
120. C₄×SD₁₆×C₆₁	C₂²	semidirect
121. C₄×SD₁₆×C₆₁	C₂²	semidirect
123. C₄×D₈×C₆₁	C₂²	semidirect
125. C₆₁×#435	C₂²	semidirect
127. C₈×D₄×C₆₁	C₂²	semidirect
128. C₆₁×#433	C₂²	semidirect
129. C₆₁×#431	C₂²	semidirect
130. C₆₁×#424	C₂²	semidirect
131. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
133. C₆₁×#416	C₂²	semidirect
134. C₆₁×#416	C₂²	semidirect
540. #62071	C₆₁	direct (N × H)
579. #3546	C₂×C₆₁	semidirect
580. #3518	C₂×C₆₁	semidirect
581. #3397	C₂×C₆₁	semidirect
582. #3393	C₂×C₆₁	semidirect
583. #3369	C₂×C₆₁	semidirect
584. #3362	C₂×C₆₁	semidirect
585. #3325	C₂×C₆₁	semidirect
586. #3311	C₂×C₆₁	semidirect
587. #3304	C₂×C₆₁	semidirect
588. #3303	C₂×C₆₁	semidirect
589. #3282	C₂×C₆₁	semidirect
590. D₄×SD₁₆	C₂×C₆₁	semidirect
591. #3276	C₂×C₆₁	semidirect
592. #3271	C₂×C₆₁	semidirect
593. #3263	C₂×C₆₁	semidirect
594. #3246	C₂×C₆₁	semidirect
595. #3224	C₂×C₆₁	semidirect
596. #3210	C₂×C₆₁	semidirect
597. #3121	C₂×C₆₁	semidirect
598. #3106	C₂×C₆₁	semidirect
599. #3043	C₂×C₆₁	semidirect
600. #3035	C₂×C₆₁	semidirect
601. #2994	C₂×C₆₁	semidirect
611. C₂×#137	C₂²×C₆₁	semidirect
612. C₂×#135	C₂²×C₆₁	semidirect
615. Q₈²	C₂²×C₆₁	semidirect
619. #556	C₂²×C₆₁	semidirect
620. #556	C₂²×C₆₁	semidirect
627. #548	C₂²×C₆₁	semidirect
634. #542	C₂²×C₆₁	semidirect
640. #533	C₂²×C₆₁	semidirect
645. #519	C₂²×C₆₁	semidirect
646. C₄×#41	C₂²×C₆₁	semidirect
647. #496	C₂²×C₆₁	semidirect
649. #494	C₂²×C₆₁	semidirect
652. #487	C₂²×C₆₁	semidirect
654. #486	C₂²×C₆₁	semidirect
655. #485	C₂²×C₆₁	semidirect
658. #482	C₂²×C₆₁	semidirect
659. #477	C₂²×C₆₁	semidirect
661. #476	C₂²×C₆₁	semidirect
662. #476	C₂²×C₆₁	semidirect
663. #476	C₂²×C₆₁	semidirect
664. #475	C₂²×C₆₁	semidirect
665. #475	C₂²×C₆₁	semidirect
666. #470	C₂²×C₆₁	semidirect
670. #465	C₂²×C₆₁	semidirect
671. #465	C₂²×C₆₁	semidirect
674. #464	C₂²×C₆₁	semidirect
675. #464	C₂²×C₆₁	semidirect
676. #464	C₂²×C₆₁	semidirect
677. #464	C₂²×C₆₁	semidirect
678. #463	C₂²×C₆₁	semidirect
679. #463	C₂²×C₆₁	semidirect
680. #462	C₂²×C₆₁	semidirect
682. #461	C₂²×C₆₁	semidirect
683. #461	C₂²×C₆₁	semidirect
687. #460	C₂²×C₆₁	semidirect
688. #460	C₂²×C₆₁	semidirect
691. #452	C₂²×C₆₁	semidirect
692. #452	C₂²×C₆₁	semidirect
693. #452	C₂²×C₆₁	semidirect
694. #451	C₂²×C₆₁	semidirect
697. #449	C₂²×C₆₁	semidirect
698. #449	C₂²×C₆₁	semidirect
701. #446	C₂²×C₆₁	semidirect
702. C₈×Q₈	C₂²×C₆₁	semidirect
703. #441	C₂²×C₆₁	semidirect
704. #440	C₂²×C₆₁	semidirect
705. C₄×Q₁₆	C₂²×C₆₁	semidirect
707. C₄×SD₁₆	C₂²×C₆₁	semidirect
708. C₄×SD₁₆	C₂²×C₆₁	semidirect
710. C₄×D₈	C₂²×C₆₁	semidirect
712. #435	C₂²×C₆₁	semidirect
714. C₈×D₄	C₂²×C₆₁	semidirect
715. #433	C₂²×C₆₁	semidirect
716. #431	C₂²×C₆₁	semidirect
717. #424	C₂²×C₆₁	semidirect
718. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
720. #416	C₂²×C₆₁	semidirect
721. #416	C₂²×C₆₁	semidirect
722. C₆₁	#62071	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×#3546	2
C₆₁×#3518	2
C₆₁×#3397	2
C₆₁×#3393	2
C₆₁×#3369	2
C₆₁×#3362	2
C₆₁×#3325	2
C₆₁×#3311	2
C₆₁×#3304	2
C₆₁×#3303	2
C₆₁×#3282	2
D₄×SD₁₆×C₆₁	2
C₆₁×#3276	2
C₆₁×#3271	2
C₆₁×#3263	2
C₆₁×#3246	2
C₆₁×#3224	2
C₆₁×#3210	2
C₆₁×#3121	2
C₆₁×#3106	2
C₆₁×#3043	2
C₆₁×#3035	2
C₆₁×#2994	2
#62071	61

Subgroups — C61×#62071 #29565504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62071 #29565504