Subgroups — C₆₁×#61555 #29564988

Order 15616.

1940 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3517	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3391	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3355	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3318	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3309	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3305	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3274	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3184	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3176	C₂	1	2	yes	maximal, complemented
17	C₆₁×#3122	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3119	C₂	1	2	yes	maximal, complemented
19	C₆₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#2969	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₁×#2946	C₂	1	2	yes	maximal, complemented
23	C₄×AGL(1,ℤ/8)×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
26	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
27	C₆₁×#555	C₂²	1	1	yes	characteristic
28	C₆₁×#554	C₂²	1	1	yes	characteristic
29	C₆₁×#553	—	2	2	no	—
30	C₆₁×#553	—	2	1	no	—
31	C₆₁×#553	C₂²	1	2	yes	—
32	C₆₁×#553	C₂²	1	2	yes	complemented
33	C₆₁×#550	—	2	1	no	—
34	C₆₁×#550	C₂²	1	1	yes	characteristic
35	C₆₁×#550	C₂²	1	1	yes	characteristic, complemented
36	C₆₁×#550	C₂²	1	2	yes	complemented
37	C₆₁×#550	C₂²	1	1	yes	characteristic, complemented
38	C₆₁×#547	—	2	1	no	—
39	C₆₁×#547	C₂²	1	1	yes	characteristic, complemented
40	C₆₁×#546	—	2	1	no	—
41	C₆₁×#546	—	2	2	no	—
42	D₄²×C₆₁	C₂²	1	1	yes	characteristic
43	D₄²×C₆₁	C₂²	1	2	yes	—
44	C₆₁×#540	—	2	2	no	—
45	C₆₁×#540	C₂²	1	2	yes	—
46	C₆₁×#540	C₂²	1	2	yes	complemented
47	C₆₁×#538	—	2	2	no	—
48	C₆₁×#532	—	2	1	no	—
49	C₆₁×#532	C₂²	1	1	yes	characteristic
50	C₆₁×#532	C₂²	1	1	yes	characteristic, complemented
51	C₆₁×#529	—	2	1	no	—
52	C₆₁×#529	C₂²	1	1	yes	characteristic
53	C₆₁×#525	—	2	1	no	—
54	C₂×#121×C₆₁	—	2	1	no	—
55	C₆₁×#520	C₂²	1	2	yes	complemented
56	C₆₁×#518	C₂²	1	2	yes	—
57	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
59	C₆₁×#499	C₂²	1	2	yes	complemented
60	C₆₁×#498	C₂²	1	1	yes	characteristic, complemented
61	C₆₁×#493	C₂²	1	2	yes	complemented
62	C₆₁×#493	C₂²	1	1	yes	characteristic, complemented
63	C₆₁×#490	C₂²	1	2	yes	complemented
64	C₆₁×#490	C₂²	1	2	yes	complemented
65	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
66	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
67	C₆₁×#482	C₂²	1	2	yes	complemented
68	C₆₁×#482	C₂²	1	2	yes	complemented
69	C₆₁×#482	C₂²	1	2	yes	complemented
70	C₆₁×#481	C₂²	1	2	yes	complemented
71	C₆₁×#480	C₂²	1	2	yes	complemented
72	C₆₁×#480	C₂²	1	2	yes	complemented
73	C₆₁×#479	C₂²	1	2	yes	complemented
74	C₆₁×#478	C₂²	1	2	yes	—
75	C₆₁×#478	C₂²	1	2	yes	complemented
76	C₆₁×#478	C₂²	1	2	yes	complemented
77	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
78	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
79	C₆₁×#474	C₂²	1	1	yes	characteristic
80	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
81	C₆₁×#469	C₂²	1	2	yes	complemented
82	C₆₁×#469	C₂²	1	2	yes	complemented
83	C₆₁×#469	C₂²	1	2	yes	complemented
84	C₆₁×#469	C₂²	1	2	yes	complemented
85	C₆₁×#466	C₂²	1	2	yes	complemented
86	C₆₁×#466	C₂²	1	2	yes	complemented
87	C₆₁×#460	C₂²	1	1	yes	characteristic, complemented
88	C₆₁×#460	C₂²	1	2	yes	complemented
89	C₆₁×#459	C₂²	1	1	yes	characteristic
90	C₆₁×#459	C₂²	1	2	yes	—
91	C₆₁×#459	C₂²	1	1	yes	characteristic, complemented
92	C₆₁×#459	C₂²	1	1	yes	characteristic, complemented
93	C₆₁×#459	C₂²	1	2	yes	complemented
94	C₆₁×#459	C₂²	1	2	yes	complemented
95	C₆₁×#449	C₂²	1	2	yes	complemented
96	C₆₁×#449	C₂²	1	2	yes	complemented
97	C₆₁×#449	C₂²	1	2	yes	complemented
98	C₆₁×#447	C₂²	1	2	yes	—
99	C₆₁×#447	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	—
104	C₆₁×#442	C₂²	1	1	yes	characteristic
105	C₆₁×#442	C₂²	1	2	yes	complemented
106	C₆₁×#442	C₂²	1	1	yes	characteristic, complemented
107	C₆₁×#442	C₂²	1	2	yes	complemented
108	C₆₁×#440	C₂²	1	1	yes	characteristic
109	C₆₁×#440	C₂²	1	2	yes	complemented
110	C₆₁×#440	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, complemented
114	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
115	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
116	C₄×D₈×C₆₁	C₂²	1	2	yes	—
117	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₈×C₆₁	C₂²	1	2	yes	complemented
119	C₄×D₈×C₆₁	C₂²	1	2	yes	complemented
120	C₄×D₈×C₆₁	C₂²	1	2	yes	complemented
121	C₆₁×#436	C₂²	1	1	yes	characteristic, complemented
122	C₆₁×#436	C₂²	1	2	yes	complemented
123	C₆₁×#435	C₂²	1	2	yes	complemented
124	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
125	C₆₁×#433	C₂²	1	2	yes	complemented
126	C₆₁×#431	C₂²	1	1	yes	characteristic, complemented
127	C₆₁×#428	C₂²	1	2	yes	complemented
128	C₆₁×#428	C₂²	1	1	yes	characteristic, complemented
129	C₆₁×#418	C₂²	1	1	yes	characteristic
130	C₆₁×#417	C₂²	1	1	yes	characteristic, complemented
131	C₆₁×#416	C₂²	1	2	yes	complemented
132	C₂×#102×C₆₁	C₂²	1	2	yes	—
133	C₆₁×#405	C₂²	1	2	yes	complemented
134	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	—	2	1	no	—
137	C₂×#41×C₆₁	—	2	1	no	—
138	C₂×#41×C₆₁	—	2	1	no	—
139	C₂×#41×C₆₁	—	2	1	no	—
140	C₂×#41×C₆₁	C₂³	1	2	yes	—
141	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₆₁	—	2	1	no	—
143	C₂²×D₄×C₆₁	—	2	2	no	—
144	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
145	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₆₁	—	2	1	no	—
147	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
148	AGL(1,ℤ/8)×C₆₁	—	2	8	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×D₈×C₆₁	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₆₁	C₂³	1	2	yes	—
154	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
155	C₂×D₈×C₆₁	C₂³	1	2	yes	—
156	C₂×D₈×C₆₁	C₂³	1	2	yes	—
157	C₂×D₈×C₆₁	C₂³	1	2	yes	—
158	C₂×D₈×C₆₁	C₂³	1	2	yes	—
159	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
160	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
161	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
162	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₆₁	—	2	1	no	—
164	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
166	#127×C₆₁	—	2	1	no	—
167	#127×C₆₁	—	2	2	no	—
168	#127×C₆₁	C₂³	1	1	yes	characteristic
169	#127×C₆₁	C₂³	1	1	yes	characteristic
170	#127×C₆₁	C₂³	1	2	yes	—
171	#127×C₆₁	C₂³	1	2	yes	—
172	#126×C₆₁	—	2	2	no	—
173	#126×C₆₁	—	2	2	no	—
174	#126×C₆₁	D₄	1	2	yes	—
175	#125×C₆₁	—	2	2	no	—
176	#125×C₆₁	D₄	1	1	yes	characteristic
177	#125×C₆₁	C₂³	1	2	yes	—
178	#125×C₆₁	C₂³	1	2	yes	—
179	#124×C₆₁	—	2	2	no	—
180	#124×C₆₁	—	2	1	no	—
181	#124×C₆₁	—	2	1	no	—
182	#124×C₆₁	D₄	1	1	yes	characteristic
183	#123×C₆₁	—	2	2	no	—
184	#123×C₆₁	—	2	2	no	—
185	#123×C₆₁	—	2	2	no	—
186	#123×C₆₁	—	2	2	no	—
187	#123×C₆₁	—	2	2	no	—
188	#123×C₆₁	—	2	2	no	—
189	#123×C₆₁	—	2	2	no	—
190	#123×C₆₁	D₄	1	2	yes	—
191	C₂²⋊Q₈×C₆₁	—	2	1	no	—
192	C₂²⋊Q₈×C₆₁	—	2	2	no	—
193	C₂²⋊Q₈×C₆₁	—	2	1	no	—
194	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
195	#121×C₆₁	—	2	2	no	—
196	#121×C₆₁	—	2	2	no	—
197	#121×C₆₁	—	2	1	no	—
198	#121×C₆₁	—	2	1	no	—
199	#121×C₆₁	—	2	1	no	—
200	#121×C₆₁	—	2	2	no	—
201	#121×C₆₁	—	2	2	no	—
202	#121×C₆₁	—	2	2	no	—
203	#121×C₆₁	—	2	1	no	—
204	#121×C₆₁	—	2	1	no	—
205	#121×C₆₁	—	2	1	no	—
206	#121×C₆₁	—	2	2	no	—
207	#121×C₆₁	—	2	2	no	—
208	#121×C₆₁	—	2	2	no	—
209	#121×C₆₁	—	2	2	no	—
210	#121×C₆₁	—	2	2	no	—
211	#121×C₆₁	—	2	2	no	—
212	#121×C₆₁	—	2	2	no	—
213	#121×C₆₁	D₄	1	1	yes	characteristic
214	#121×C₆₁	C₂³	1	2	yes	—
215	#121×C₆₁	C₂³	1	2	yes	—
216	#121×C₆₁	C₂³	1	2	yes	—
217	#121×C₆₁	C₂³	1	2	yes	—
218	#121×C₆₁	C₂³	1	2	yes	—
219	#121×C₆₁	C₂³	1	2	yes	—
220	#120×C₆₁	—	2	2	no	—
221	#120×C₆₁	—	2	2	no	—
222	#120×C₆₁	—	2	2	no	—
223	C₄×Q₈×C₆₁	—	2	1	no	—
224	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
226	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₆₁	—	2	1	no	—
229	C₄×D₄×C₆₁	—	2	1	no	—
230	C₄×D₄×C₆₁	—	2	2	no	—
231	C₄×D₄×C₆₁	—	2	2	no	—
232	C₄×D₄×C₆₁	—	2	1	no	—
233	C₄×D₄×C₆₁	—	2	2	no	—
234	C₄×D₄×C₆₁	—	2	2	no	—
235	C₄×D₄×C₆₁	—	2	2	no	—
236	C₄×D₄×C₆₁	—	2	2	no	—
237	C₄×D₄×C₆₁	—	2	2	no	—
238	C₄×D₄×C₆₁	—	2	1	no	—
239	C₄×D₄×C₆₁	—	2	1	no	—
240	C₄×D₄×C₆₁	—	2	1	no	—
241	C₄×D₄×C₆₁	—	2	1	no	—
242	C₄×D₄×C₆₁	C₂³	1	2	yes	—
243	C₄×D₄×C₆₁	C₂³	1	2	yes	—
244	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
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	2	yes	—
250	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₆₁	C₂³	1	2	yes	—
252	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₆₁	C₂³	1	2	yes	—
255	#117×C₆₁	—	2	2	no	—
256	#117×C₆₁	—	2	1	no	—
257	#117×C₆₁	—	2	1	no	—
258	#117×C₆₁	C₂³	1	2	yes	—
259	#117×C₆₁	C₂³	1	1	yes	characteristic
260	#117×C₆₁	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
262	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
263	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
266	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₆₁	—	2	2	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	2	yes	—
272	#107×C₆₁	C₂³	1	1	yes	characteristic
273	#107×C₆₁	C₂³	1	2	yes	—
274	#107×C₆₁	C₂³	1	2	yes	—
275	#106×C₆₁	C₂³	1	2	yes	—
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	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	2	yes	—
286	#103×C₆₁	C₂³	1	1	yes	characteristic
287	#102×C₆₁	C₂³	1	1	yes	characteristic
288	#102×C₆₁	C₂³	1	2	yes	—
289	#102×C₆₁	C₂³	1	2	yes	—
290	#102×C₆₁	C₂³	1	2	yes	—
291	#102×C₆₁	C₂³	1	2	yes	—
292	#102×C₆₁	C₂³	1	2	yes	—
293	#102×C₆₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
308	#97×C₆₁	C₂³	1	1	yes	characteristic
309	#97×C₆₁	C₂³	1	2	yes	—
310	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₆₁	C₂³	1	2	yes	—
313	C₄×C₈×C₆₁	C₂³	1	2	yes	—
314	C₂⁴×C₆₁	—	2	1	no	—
315	C₂⁴×C₆₁	—	2	2	no	—
316	#41×C₆₁	—	2	4	no	—
317	#41×C₆₁	—	2	2	no	—
318	#41×C₆₁	—	4	2	no	—
319	#41×C₆₁	—	4	1	no	—
320	#41×C₆₁	—	8	2	no	—
321	#41×C₆₁	—	8	2	no	—
322	#41×C₆₁	—	8	2	no	—
323	#41×C₆₁	—	8	2	no	—
324	#41×C₆₁	—	8	2	no	—
325	C₂×Q₈×C₆₁	—	2	1	no	—
326	C₂×Q₈×C₆₁	—	2	1	no	—
327	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₆₁	—	2	2	no	—
330	C₂×D₄×C₆₁	—	2	4	no	—
331	C₂×D₄×C₆₁	—	2	2	no	—
332	C₂×D₄×C₆₁	—	2	1	no	—
333	C₂×D₄×C₆₁	—	2	2	no	—
334	C₂×D₄×C₆₁	—	2	2	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	2	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	2	no	—
346	C₂×D₄×C₆₁	—	2	1	no	—
347	C₂×D₄×C₆₁	—	2	2	no	—
348	C₂×D₄×C₆₁	—	2	2	no	—
349	C₂×D₄×C₆₁	—	4	2	no	—
350	C₂×D₄×C₆₁	—	4	1	no	—
351	C₂×D₄×C₆₁	—	8	2	no	—
352	C₂×D₄×C₆₁	—	8	4	no	—
353	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
354	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
355	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
356	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
357	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
358	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
359	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₆₁	—	2	1	no	—
361	C₂²×C₄×C₆₁	—	2	2	no	—
362	C₂²×C₄×C₆₁	—	2	1	no	—
363	C₂²×C₄×C₆₁	—	2	1	no	—
364	C₂²×C₄×C₆₁	—	2	2	no	—
365	C₂²×C₄×C₆₁	—	2	1	no	—
366	C₂²×C₄×C₆₁	—	2	1	no	—
367	C₂²×C₄×C₆₁	—	2	1	no	—
368	C₂²×C₄×C₆₁	—	2	1	no	—
369	C₂²×C₄×C₆₁	—	2	2	no	—
370	C₂²×C₄×C₆₁	—	2	2	no	—
371	C₂²×C₄×C₆₁	—	2	2	no	—
372	C₂²×C₄×C₆₁	—	2	2	no	—
373	C₂²×C₄×C₆₁	—	2	2	no	—
374	C₂²×C₄×C₆₁	—	2	1	no	—
375	C₂²×C₄×C₆₁	—	8	2	no	—
376	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
378	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
380	SD₁₆×C₆₁	—	2	2	no	—
381	SD₁₆×C₆₁	—	2	4	no	—
382	SD₁₆×C₆₁	#41	1	4	yes	complemented
383	D₈×C₆₁	—	2	2	no	—
384	D₈×C₆₁	—	2	4	no	—
385	D₈×C₆₁	—	2	2	no	—
386	D₈×C₆₁	—	2	4	no	—
387	D₈×C₆₁	—	4	2	no	—
388	D₈×C₆₁	—	4	2	no	—
389	D₈×C₆₁	—	4	2	no	—
390	M₁₆×C₆₁	—	2	2	no	—
391	M₁₆×C₆₁	—	2	4	no	—
392	M₁₆×C₆₁	—	4	1	no	—
393	C₂×C₈×C₆₁	—	4	2	no	—
394	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
395	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
397	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
398	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
399	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₆₁	—	2	1	no	—
401	C₄⋊C₄×C₆₁	—	2	2	no	—
402	C₄⋊C₄×C₆₁	—	2	1	no	—
403	C₄⋊C₄×C₆₁	—	2	2	no	—
404	C₄⋊C₄×C₆₁	—	2	2	no	—
405	C₄⋊C₄×C₆₁	—	2	1	no	—
406	C₄⋊C₄×C₆₁	—	2	1	no	—
407	C₄⋊C₄×C₆₁	—	2	2	no	—
408	C₄⋊C₄×C₆₁	—	2	1	no	—
409	C₄⋊C₄×C₆₁	—	2	2	no	—
410	C₄⋊C₄×C₆₁	—	2	2	no	—
411	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
413	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
414	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
415	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
419	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
421	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
423	C₂²⋊C₄×C₆₁	—	2	2	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	1	no	—
428	C₂²⋊C₄×C₆₁	—	2	2	no	—
429	C₂²⋊C₄×C₆₁	—	2	1	no	—
430	C₂²⋊C₄×C₆₁	—	2	2	no	—
431	C₂²⋊C₄×C₆₁	—	2	1	no	—
432	C₂²⋊C₄×C₆₁	—	2	2	no	—
433	C₂²⋊C₄×C₆₁	—	2	1	no	—
434	C₂²⋊C₄×C₆₁	—	2	1	no	—
435	C₂²⋊C₄×C₆₁	—	2	2	no	—
436	C₂²⋊C₄×C₆₁	—	2	2	no	—
437	C₂²⋊C₄×C₆₁	—	2	2	no	—
438	C₂²⋊C₄×C₆₁	—	2	2	no	—
439	C₂²⋊C₄×C₆₁	—	2	2	no	—
440	C₂²⋊C₄×C₆₁	—	2	2	no	—
441	C₂²⋊C₄×C₆₁	—	2	2	no	—
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	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
447	C₄²×C₆₁	—	2	1	no	—
448	C₄²×C₆₁	—	2	1	no	—
449	C₄²×C₆₁	—	2	1	no	—
450	C₄²×C₆₁	—	2	2	no	—
451	C₄²×C₆₁	—	2	2	no	—
452	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
455	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
456	C₄²×C₆₁	C₂⁴	1	2	yes	—
457	C₂³×C₆₁	—	2	1	no	—
458	C₂³×C₆₁	—	2	1	no	—
459	C₂³×C₆₁	—	2	2	no	—
460	C₂³×C₆₁	—	2	2	no	—
461	C₂³×C₆₁	—	2	1	no	—
462	C₂³×C₆₁	—	4	2	no	—
463	C₂³×C₆₁	—	4	4	no	—
464	C₂³×C₆₁	—	4	2	no	—
465	C₂³×C₆₁	—	8	1	no	—
466	C₂³×C₆₁	—	8	2	no	—
467	C₂³×C₆₁	—	8	2	no	—
468	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
469	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
470	Q₈×C₆₁	—	2	2	no	—
471	Q₈×C₆₁	—	2	1	no	—
472	Q₈×C₆₁	—	4	2	no	—
473	Q₈×C₆₁	—	8	1	no	—
474	Q₈×C₆₁	C₂×#41	1	2	yes	—
475	D₄×C₆₁	—	2	2	no	—
476	D₄×C₆₁	—	2	2	no	—
477	D₄×C₆₁	—	2	1	no	—
478	D₄×C₆₁	—	2	1	no	—
479	D₄×C₆₁	—	2	2	no	—
480	D₄×C₆₁	—	2	1	no	—
481	D₄×C₆₁	—	2	1	no	—
482	D₄×C₆₁	—	2	2	no	—
483	D₄×C₆₁	—	2	1	no	—
484	D₄×C₆₁	—	2	2	no	—
485	D₄×C₆₁	—	4	2	no	—
486	D₄×C₆₁	—	4	4	no	—
487	D₄×C₆₁	—	4	2	no	—
488	D₄×C₆₁	—	4	2	no	—
489	D₄×C₆₁	—	4	4	no	—
490	D₄×C₆₁	—	4	4	no	—
491	D₄×C₆₁	—	4	2	no	—
492	D₄×C₆₁	—	4	2	no	—
493	D₄×C₆₁	—	8	1	no	—
494	D₄×C₆₁	—	8	2	no	—
495	D₄×C₆₁	—	8	2	no	—
496	D₄×C₆₁	—	8	1	no	—
497	D₄×C₆₁	—	8	2	no	—
498	D₄×C₆₁	—	8	2	no	—
499	D₄×C₆₁	—	8	2	no	—
500	D₄×C₆₁	—	8	2	no	—
501	D₄×C₆₁	—	8	2	no	—
502	D₄×C₆₁	—	8	2	no	—
503	D₄×C₆₁	—	8	2	no	—
504	D₄×C₆₁	C₂×#41	1	2	yes	—
505	C₂×C₄×C₆₁	—	2	1	no	—
506	C₂×C₄×C₆₁	—	2	2	no	—
507	C₂×C₄×C₆₁	—	2	1	no	—
508	C₂×C₄×C₆₁	—	2	2	no	—
509	C₂×C₄×C₆₁	—	2	2	no	—
510	C₂×C₄×C₆₁	—	2	1	no	—
511	C₂×C₄×C₆₁	—	2	1	no	—
512	C₂×C₄×C₆₁	—	2	1	no	—
513	C₂×C₄×C₆₁	—	2	1	no	—
514	C₂×C₄×C₆₁	—	2	2	no	—
515	C₂×C₄×C₆₁	—	2	2	no	—
516	C₂×C₄×C₆₁	—	2	1	no	—
517	C₂×C₄×C₆₁	—	4	1	no	—
518	C₂×C₄×C₆₁	—	4	2	no	—
519	C₂×C₄×C₆₁	—	4	4	no	—
520	C₂×C₄×C₆₁	—	4	2	no	—
521	C₂×C₄×C₆₁	—	4	2	no	—
522	C₂×C₄×C₆₁	—	4	2	no	—
523	C₂×C₄×C₆₁	—	8	1	no	—
524	C₂×C₄×C₆₁	—	8	1	no	—
525	C₂×C₄×C₆₁	—	8	1	no	—
526	C₂×C₄×C₆₁	—	8	2	no	—
527	C₂×C₄×C₆₁	—	8	2	no	—
528	C₂×C₄×C₆₁	—	8	2	no	—
529	C₂×C₄×C₆₁	—	8	2	no	—
530	C₂×C₄×C₆₁	—	8	2	no	—
531	C₂×C₄×C₆₁	—	8	1	no	—
532	C₂×C₄×C₆₁	—	8	2	no	—
533	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
536	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
537	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
540	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
542	C₈×C₆₁	—	2	1	no	—
543	C₈×C₆₁	—	2	2	no	—
544	C₈×C₆₁	—	2	1	no	—
545	C₈×C₆₁	—	2	2	no	—
546	C₈×C₆₁	—	2	1	no	—
547	C₈×C₆₁	C₂×#41	1	2	yes	—
548	#61555	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
549	C₂²×C₆₁	—	2	1	no	—
550	C₂²×C₆₁	—	2	2	no	—
551	C₂²×C₆₁	—	2	1	no	—
552	C₂²×C₆₁	—	2	2	no	—
553	C₂²×C₆₁	—	2	2	no	—
554	C₂²×C₆₁	—	2	1	no	—
555	C₂²×C₆₁	—	2	2	no	—
556	C₂²×C₆₁	—	4	1	no	—
557	C₂²×C₆₁	—	4	1	no	—
558	C₂²×C₆₁	—	4	2	no	—
559	C₂²×C₆₁	—	4	1	no	—
560	C₂²×C₆₁	—	4	1	no	—
561	C₂²×C₆₁	—	4	2	no	—
562	C₂²×C₆₁	—	4	1	no	—
563	C₂²×C₆₁	—	4	2	no	—
564	C₂²×C₆₁	—	4	1	no	—
565	C₂²×C₆₁	—	4	2	no	—
566	C₂²×C₆₁	—	4	1	no	—
567	C₂²×C₆₁	—	4	1	no	—
568	C₂²×C₆₁	—	4	2	no	—
569	C₂²×C₆₁	—	4	2	no	—
570	C₂²×C₆₁	—	8	4	no	—
571	C₂²×C₆₁	—	16	4	no	—
572	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
573	C₄×C₆₁	—	2	1	no	—
574	C₄×C₆₁	—	2	1	no	—
575	C₄×C₆₁	—	2	2	no	—
576	C₄×C₆₁	—	2	2	no	—
577	C₄×C₆₁	—	2	1	no	—
578	C₄×C₆₁	—	2	2	no	—
579	C₄×C₆₁	—	2	1	no	—
580	C₄×C₆₁	—	2	2	no	—
581	C₄×C₆₁	—	4	2	no	—
582	C₄×C₆₁	—	4	1	no	—
583	C₄×C₆₁	—	4	1	no	—
584	C₄×C₆₁	—	4	1	no	—
585	C₄×C₆₁	—	4	1	no	—
586	C₄×C₆₁	—	4	2	no	—
587	C₄×C₆₁	#576	1	2	yes	—
588	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
589	C₄×C₆₁	#585	1	1	yes	characteristic
590	#3519	C₂×C₆₁	1	1	yes	characteristic, complemented
591	#3517	C₂×C₆₁	1	1	yes	characteristic, complemented
592	#3391	C₂×C₆₁	1	1	yes	characteristic, complemented
593	#3381	C₂×C₆₁	1	1	yes	characteristic, complemented
594	#3368	C₂×C₆₁	1	1	yes	characteristic, complemented
595	#3366	C₂×C₆₁	1	1	yes	characteristic, complemented
596	#3355	C₂×C₆₁	1	2	yes	complemented
597	#3354	C₂×C₆₁	1	1	yes	characteristic, complemented
598	#3318	C₂×C₆₁	1	2	yes	complemented
599	#3309	C₂×C₆₁	1	2	yes	complemented
600	#3305	C₂×C₆₁	1	1	yes	characteristic, complemented
601	#3294	C₂×C₆₁	1	1	yes	characteristic, complemented
602	#3274	C₂×C₆₁	1	1	yes	characteristic, complemented
603	#3274	C₂×C₆₁	1	2	yes	complemented
604	#3184	C₂×C₆₁	1	1	yes	characteristic, complemented
605	#3176	C₂×C₆₁	1	2	yes	complemented
606	#3122	C₂×C₆₁	1	2	yes	complemented
607	#3119	C₂×C₆₁	1	2	yes	complemented
608	#3106	C₂×C₆₁	1	1	yes	characteristic, complemented
609	#3100	C₂×C₆₁	1	1	yes	characteristic, complemented
610	#2969	C₂×C₆₁	1	1	yes	characteristic, complemented
611	#2946	C₂×C₆₁	1	2	yes	complemented
612	C₄×AGL(1,ℤ/8)	C₂×C₆₁	1	1	yes	characteristic, complemented
613	C₂×C₆₁	—	4	1	no	—
614	C₂×C₆₁	—	4	2	no	—
615	C₂×C₆₁	—	4	2	no	—
616	C₂×C₆₁	—	8	1	no	—
617	C₂×C₆₁	—	8	2	no	—
618	C₂×C₆₁	—	8	1	no	—
619	C₂×C₆₁	—	8	2	no	—
620	C₂×C₆₁	D₄×#41	1	1	yes	characteristic
621	C₂×C₆₁	C₂×#576	1	1	yes	characteristic
622	C₂×C₆₁	#3585	1	1	yes	characteristic
623	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
624	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
625	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
626	#555	C₂²×C₆₁	1	1	yes	characteristic
627	#554	C₂²×C₆₁	1	1	yes	characteristic
628	#553	—	2	2	no	—
629	#553	—	2	1	no	—
630	#553	C₂²×C₆₁	1	2	yes	—
631	#553	C₂²×C₆₁	1	2	yes	complemented
632	#550	—	2	1	no	—
633	#550	C₂²×C₆₁	1	1	yes	characteristic
634	#550	C₂²×C₆₁	1	1	yes	characteristic, complemented
635	#550	C₂²×C₆₁	1	2	yes	complemented
636	#550	C₂²×C₆₁	1	1	yes	characteristic, complemented
637	#547	—	2	1	no	—
638	#547	C₂²×C₆₁	1	1	yes	characteristic, complemented
639	#546	—	2	1	no	—
640	#546	—	2	2	no	—
641	D₄²	C₂²×C₆₁	1	1	yes	characteristic
642	D₄²	C₂²×C₆₁	1	2	yes	—
643	#540	—	2	2	no	—
644	#540	C₂²×C₆₁	1	2	yes	—
645	#540	C₂²×C₆₁	1	2	yes	complemented
646	#538	—	2	2	no	—
647	#532	—	2	1	no	—
648	#532	C₂²×C₆₁	1	1	yes	characteristic
649	#532	C₂²×C₆₁	1	1	yes	characteristic, complemented
650	#529	—	2	1	no	—
651	#529	C₂²×C₆₁	1	1	yes	characteristic
652	#525	—	2	1	no	—
653	C₂×#121	—	2	1	no	—
654	#520	C₂²×C₆₁	1	2	yes	complemented
655	#518	C₂²×C₆₁	1	2	yes	—
656	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic, complemented
657	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
658	#499	C₂²×C₆₁	1	2	yes	complemented
659	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
660	#493	C₂²×C₆₁	1	2	yes	complemented
661	#493	C₂²×C₆₁	1	1	yes	characteristic, complemented
662	#490	C₂²×C₆₁	1	2	yes	complemented
663	#490	C₂²×C₆₁	1	2	yes	complemented
664	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
665	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
666	#482	C₂²×C₆₁	1	2	yes	complemented
667	#482	C₂²×C₆₁	1	2	yes	complemented
668	#482	C₂²×C₆₁	1	2	yes	complemented
669	#481	C₂²×C₆₁	1	2	yes	complemented
670	#480	C₂²×C₆₁	1	2	yes	complemented
671	#480	C₂²×C₆₁	1	2	yes	complemented
672	#479	C₂²×C₆₁	1	2	yes	complemented
673	#478	C₂²×C₆₁	1	2	yes	—
674	#478	C₂²×C₆₁	1	2	yes	complemented
675	#478	C₂²×C₆₁	1	2	yes	complemented
676	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
677	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
678	#474	C₂²×C₆₁	1	1	yes	characteristic
679	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
680	#469	C₂²×C₆₁	1	2	yes	complemented
681	#469	C₂²×C₆₁	1	2	yes	complemented
682	#469	C₂²×C₆₁	1	2	yes	complemented
683	#469	C₂²×C₆₁	1	2	yes	complemented
684	#466	C₂²×C₆₁	1	2	yes	complemented
685	#466	C₂²×C₆₁	1	2	yes	complemented
686	#460	C₂²×C₆₁	1	1	yes	characteristic, complemented
687	#460	C₂²×C₆₁	1	2	yes	complemented
688	#459	C₂²×C₆₁	1	1	yes	characteristic
689	#459	C₂²×C₆₁	1	2	yes	—
690	#459	C₂²×C₆₁	1	1	yes	characteristic, complemented
691	#459	C₂²×C₆₁	1	1	yes	characteristic, complemented
692	#459	C₂²×C₆₁	1	2	yes	complemented
693	#459	C₂²×C₆₁	1	2	yes	complemented
694	#449	C₂²×C₆₁	1	2	yes	complemented
695	#449	C₂²×C₆₁	1	2	yes	complemented
696	#449	C₂²×C₆₁	1	2	yes	complemented
697	#447	C₂²×C₆₁	1	2	yes	—
698	#447	C₂²×C₆₁	1	2	yes	—
699	#447	C₂²×C₆₁	1	2	yes	—
700	#446	C₂²×C₆₁	1	1	yes	characteristic, complemented
701	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
702	#442	C₂²×C₆₁	1	2	yes	—
703	#442	C₂²×C₆₁	1	1	yes	characteristic
704	#442	C₂²×C₆₁	1	2	yes	complemented
705	#442	C₂²×C₆₁	1	1	yes	characteristic, complemented
706	#442	C₂²×C₆₁	1	2	yes	complemented
707	#440	C₂²×C₆₁	1	1	yes	characteristic
708	#440	C₂²×C₆₁	1	2	yes	complemented
709	#440	C₂²×C₆₁	1	1	yes	characteristic, complemented
710	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
711	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
712	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
713	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
714	C₄×D₈	C₂²×C₆₁	1	2	yes	—
715	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
716	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
717	C₄×D₈	C₂²×C₆₁	1	2	yes	complemented
718	C₄×D₈	C₂²×C₆₁	1	2	yes	complemented
719	C₄×D₈	C₂²×C₆₁	1	2	yes	complemented
720	#436	C₂²×C₆₁	1	1	yes	characteristic, complemented
721	#436	C₂²×C₆₁	1	2	yes	complemented
722	#435	C₂²×C₆₁	1	2	yes	complemented
723	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
724	#433	C₂²×C₆₁	1	2	yes	complemented
725	#431	C₂²×C₆₁	1	1	yes	characteristic, complemented
726	#428	C₂²×C₆₁	1	2	yes	complemented
727	#428	C₂²×C₆₁	1	1	yes	characteristic, complemented
728	#418	C₂²×C₆₁	1	1	yes	characteristic
729	#417	C₂²×C₆₁	1	1	yes	characteristic, complemented
730	#416	C₂²×C₆₁	1	2	yes	complemented
731	C₂×#102	C₂²×C₆₁	1	2	yes	—
732	#405	C₂²×C₆₁	1	2	yes	complemented
733	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
734	C₆₁	#61555	1	1	yes	characteristic, direct product factor, Sylow
735	C₂×#41	—	2	1	no	—
736	C₂×#41	—	2	1	no	—
737	C₂×#41	—	2	1	no	—
738	C₂×#41	—	2	1	no	—
739	C₂×#41	—	2	1	no	—
740	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
741	C₂×#41	C₂³×C₆₁	1	2	yes	—
742	C₂²×D₄	—	2	1	no	—
743	C₂²×D₄	—	2	2	no	—
744	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
745	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
746	C₂³×C₄	—	2	1	no	—
747	AGL(1,ℤ/8)	—	2	4	no	—
748	AGL(1,ℤ/8)	—	2	8	no	—
749	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
750	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
751	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
752	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
753	C₂×D₈	C₂³×C₆₁	1	2	yes	—
754	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
755	C₂×D₈	C₂³×C₆₁	1	2	yes	—
756	C₂×D₈	C₂³×C₆₁	1	2	yes	—
757	C₂×D₈	C₂³×C₆₁	1	2	yes	—
758	C₂×D₈	C₂³×C₆₁	1	2	yes	—
759	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
760	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
761	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
762	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
763	C₄⋊Q₈	—	2	1	no	—
764	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
765	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
766	#127	—	2	1	no	—
767	#127	—	2	2	no	—
768	#127	C₂³×C₆₁	1	1	yes	characteristic
769	#127	C₂³×C₆₁	1	1	yes	characteristic
770	#127	C₂³×C₆₁	1	2	yes	—
771	#127	C₂³×C₆₁	1	2	yes	—
772	#126	—	2	2	no	—
773	#126	—	2	2	no	—
774	#126	D₄×C₆₁	1	2	yes	—
775	#125	—	2	2	no	—
776	#125	D₄×C₆₁	1	1	yes	characteristic
777	#125	C₂³×C₆₁	1	2	yes	—
778	#125	C₂³×C₆₁	1	2	yes	—
779	#124	—	2	2	no	—
780	#124	—	2	1	no	—
781	#124	—	2	1	no	—
782	#124	D₄×C₆₁	1	1	yes	characteristic
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	#123	D₄×C₆₁	1	2	yes	—
791	C₂²⋊Q₈	—	2	1	no	—
792	C₂²⋊Q₈	—	2	1	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
795	#121	—	2	2	no	—
796	#121	—	2	1	no	—
797	#121	—	2	2	no	—
798	#121	—	2	1	no	—
799	#121	—	2	1	no	—
800	#121	—	2	1	no	—
801	#121	—	2	1	no	—
802	#121	—	2	1	no	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	—	2	2	no	—
813	#121	D₄×C₆₁	1	1	yes	characteristic
814	#121	C₂³×C₆₁	1	2	yes	—
815	#121	C₂³×C₆₁	1	2	yes	—
816	#121	C₂³×C₆₁	1	2	yes	—
817	#121	C₂³×C₆₁	1	2	yes	—
818	#121	C₂³×C₆₁	1	2	yes	—
819	#121	C₂³×C₆₁	1	2	yes	—
820	#120	—	2	2	no	—
821	#120	—	2	2	no	—
822	#120	—	2	2	no	—
823	C₄×Q₈	—	2	1	no	—
824	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
825	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
826	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
827	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	2	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	—	2	1	no	—
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	1	yes	characteristic
846	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
847	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
848	C₄×D₄	C₂³×C₆₁	1	2	yes	—
849	C₄×D₄	C₂³×C₆₁	1	2	yes	—
850	C₄×D₄	C₂³×C₆₁	1	2	yes	—
851	C₄×D₄	C₂³×C₆₁	1	2	yes	—
852	C₄×D₄	C₂³×C₆₁	1	2	yes	—
853	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
854	C₄×D₄	C₂³×C₆₁	1	2	yes	—
855	#117	—	2	2	no	—
856	#117	—	2	1	no	—
857	#117	—	2	1	no	—
858	#117	C₂³×C₆₁	1	1	yes	characteristic
859	#117	C₂³×C₆₁	1	2	yes	—
860	#117	C₂³×C₆₁	1	2	yes	—
861	C₂×C₄⋊C₄	—	2	2	no	—
862	C₂×C₄⋊C₄	—	2	1	no	—
863	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
864	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
865	C₂×C₂²⋊C₄	—	2	1	no	—
866	C₂×C₂²⋊C₄	—	2	2	no	—
867	C₂×C₂²⋊C₄	—	2	2	no	—
868	C₂×C₄²	—	2	1	no	—
869	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
870	#107	C₂³×C₆₁	1	1	yes	characteristic
871	#107	C₂³×C₆₁	1	2	yes	—
872	#107	C₂³×C₆₁	1	1	yes	characteristic
873	#107	C₂³×C₆₁	1	2	yes	—
874	#107	C₂³×C₆₁	1	2	yes	—
875	#106	C₂³×C₆₁	1	2	yes	—
876	#106	C₂³×C₆₁	1	1	yes	characteristic
877	#106	C₂³×C₆₁	1	2	yes	—
878	#106	C₂³×C₆₁	1	1	yes	characteristic
879	#106	C₂³×C₆₁	1	2	yes	—
880	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
881	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
882	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
883	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
884	#103	C₂³×C₆₁	1	1	yes	characteristic
885	#103	C₂³×C₆₁	1	2	yes	—
886	#103	C₂³×C₆₁	1	1	yes	characteristic
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	2	yes	—
891	#102	C₂³×C₆₁	1	2	yes	—
892	#102	C₂³×C₆₁	1	2	yes	—
893	#102	C₂³×C₆₁	1	1	yes	characteristic
894	#102	C₂³×C₆₁	1	1	yes	characteristic
895	#102	C₂³×C₆₁	1	1	yes	characteristic
896	#102	C₂³×C₆₁	1	1	yes	characteristic
897	#102	C₂³×C₆₁	1	1	yes	characteristic
898	#102	C₂³×C₆₁	1	2	yes	—
899	#102	C₂³×C₆₁	1	2	yes	—
900	#102	C₂³×C₆₁	1	2	yes	—
901	#102	C₂³×C₆₁	1	2	yes	—
902	#102	C₂³×C₆₁	1	2	yes	—
903	#102	C₂³×C₆₁	1	2	yes	—
904	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
905	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
906	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
907	#97	C₂³×C₆₁	1	1	yes	characteristic
908	#97	C₂³×C₆₁	1	1	yes	characteristic
909	#97	C₂³×C₆₁	1	2	yes	—
910	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
911	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
912	C₄×C₈	C₂³×C₆₁	1	2	yes	—
913	C₄×C₈	C₂³×C₆₁	1	2	yes	—
914	C₂⁴	—	2	1	no	—
915	C₂⁴	—	2	2	no	—
916	#41	—	2	2	no	—
917	#41	—	2	4	no	—
918	#41	—	4	2	no	—
919	#41	—	4	1	no	—
920	#41	—	8	2	no	—
921	#41	—	8	2	no	—
922	#41	—	8	2	no	—
923	#41	—	8	2	no	—
924	#41	—	8	2	no	—
925	C₂×Q₈	—	2	1	no	—
926	C₂×Q₈	—	2	1	no	—
927	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
928	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	4	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	1	no	—
942	C₂×D₄	—	2	1	no	—
943	C₂×D₄	—	2	1	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	1	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	2	no	—
949	C₂×D₄	—	4	2	no	—
950	C₂×D₄	—	4	1	no	—
951	C₂×D₄	—	8	2	no	—
952	C₂×D₄	—	8	4	no	—
953	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
954	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
955	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
956	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
957	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
958	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
959	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
960	C₂²×C₄	—	2	1	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	1	no	—
964	C₂²×C₄	—	2	2	no	—
965	C₂²×C₄	—	2	1	no	—
966	C₂²×C₄	—	2	1	no	—
967	C₂²×C₄	—	2	1	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	2	no	—
971	C₂²×C₄	—	2	2	no	—
972	C₂²×C₄	—	2	2	no	—
973	C₂²×C₄	—	2	2	no	—
974	C₂²×C₄	—	2	1	no	—
975	C₂²×C₄	—	8	2	no	—
976	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
977	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
978	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
979	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
980	SD₁₆	—	2	2	no	—
981	SD₁₆	—	2	4	no	—
982	SD₁₆	#41×C₆₁	1	4	yes	complemented
983	D₈	—	2	2	no	—
984	D₈	—	2	4	no	—
985	D₈	—	2	2	no	—
986	D₈	—	2	4	no	—
987	D₈	—	4	2	no	—
988	D₈	—	4	2	no	—
989	D₈	—	4	2	no	—
990	M₁₆	—	2	2	no	—
991	M₁₆	—	2	4	no	—
992	M₁₆	—	4	1	no	—
993	C₂×C₈	—	4	2	no	—
994	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
995	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
996	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
997	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
998	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
999	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	2	1	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1012	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1013	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1014	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1015	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1016	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1017	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1018	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1019	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1020	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1021	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1022	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	1	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	1	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1043	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1044	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1045	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1046	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	2	1	no	—
1049	C₄²	—	2	1	no	—
1050	C₄²	—	2	2	no	—
1051	C₄²	—	2	2	no	—
1052	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1053	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1054	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1055	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1056	C₄²	C₂⁴×C₆₁	1	2	yes	—
1057	C₂³	—	2	1	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	2	no	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	2	2	no	—
1062	C₂³	—	4	2	no	—
1063	C₂³	—	4	4	no	—
1064	C₂³	—	4	2	no	—
1065	C₂³	—	8	1	no	—
1066	C₂³	—	8	2	no	—
1067	C₂³	—	8	2	no	—
1068	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1069	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1070	Q₈	—	2	2	no	—
1071	Q₈	—	2	1	no	—
1072	Q₈	—	4	2	no	—
1073	Q₈	—	8	1	no	—
1074	Q₈	C₂×#41×C₆₁	1	2	yes	—
1075	D₄	—	2	2	no	—
1076	D₄	—	2	2	no	—
1077	D₄	—	2	1	no	—
1078	D₄	—	2	1	no	—
1079	D₄	—	2	2	no	—
1080	D₄	—	2	1	no	—
1081	D₄	—	2	1	no	—
1082	D₄	—	2	2	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	2	2	no	—
1085	D₄	—	4	2	no	—
1086	D₄	—	4	4	no	—
1087	D₄	—	4	2	no	—
1088	D₄	—	4	2	no	—
1089	D₄	—	4	4	no	—
1090	D₄	—	4	4	no	—
1091	D₄	—	4	2	no	—
1092	D₄	—	4	2	no	—
1093	D₄	—	8	1	no	—
1094	D₄	—	8	2	no	—
1095	D₄	—	8	2	no	—
1096	D₄	—	8	2	no	—
1097	D₄	—	8	2	no	—
1098	D₄	—	8	1	no	—
1099	D₄	—	8	2	no	—
1100	D₄	—	8	2	no	—
1101	D₄	—	8	2	no	—
1102	D₄	—	8	2	no	—
1103	D₄	—	8	2	no	—
1104	D₄	C₂×#41×C₆₁	1	2	yes	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	2	no	—
1116	C₂×C₄	—	2	1	no	—
1117	C₂×C₄	—	4	1	no	—
1118	C₂×C₄	—	4	2	no	—
1119	C₂×C₄	—	4	4	no	—
1120	C₂×C₄	—	4	2	no	—
1121	C₂×C₄	—	4	2	no	—
1122	C₂×C₄	—	4	2	no	—
1123	C₂×C₄	—	8	1	no	—
1124	C₂×C₄	—	8	1	no	—
1125	C₂×C₄	—	8	1	no	—
1126	C₂×C₄	—	8	2	no	—
1127	C₂×C₄	—	8	2	no	—
1128	C₂×C₄	—	8	2	no	—
1129	C₂×C₄	—	8	2	no	—
1130	C₂×C₄	—	8	2	no	—
1131	C₂×C₄	—	8	1	no	—
1132	C₂×C₄	—	8	2	no	—
1133	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1134	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1135	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1136	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1137	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1138	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1139	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1140	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1141	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1142	C₈	—	2	1	no	—
1143	C₈	—	2	2	no	—
1144	C₈	—	2	1	no	—
1145	C₈	—	2	2	no	—
1146	C₈	—	2	1	no	—
1147	C₈	C₂×#41×C₆₁	1	2	yes	—
1148	C₂²	—	2	1	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	1	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	2	1	no	—
1153	C₂²	—	2	2	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	1	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	2	no	—
1160	C₂²	—	4	2	no	—
1161	C₂²	—	4	2	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	—	4	1	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	1	no	—
1168	C₂²	—	4	2	no	—
1169	C₂²	—	8	4	no	—
1170	C₂²	—	16	4	no	—
1171	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1172	C₄	—	2	1	no	—
1173	C₄	—	2	2	no	—
1174	C₄	—	2	1	no	—
1175	C₄	—	2	1	no	—
1176	C₄	—	2	2	no	—
1177	C₄	—	2	2	no	—
1178	C₄	—	2	1	no	—
1179	C₄	—	2	2	no	—
1180	C₄	—	4	1	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	2	no	—
1184	C₄	—	4	2	no	—
1185	C₄	—	4	1	no	—
1186	C₄	C₆₁×#576	1	2	yes	—
1187	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
1188	C₄	C₆₁×#585	1	1	yes	characteristic
1189	C₂	—	4	1	no	—
1190	C₂	—	4	2	no	—
1191	C₂	—	4	2	no	—
1192	C₂	—	8	1	no	—
1193	C₂	—	8	2	no	—
1194	C₂	—	8	1	no	—
1195	C₂	—	8	2	no	—
1196	C₂	D₄×#41×C₆₁	1	1	yes	characteristic
1197	C₂	C₂×C₆₁×#576	1	1	yes	characteristic
1198	C₂	C₆₁×#3585	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×#3519	C₂	semidirect
2. C₆₁×#3517	C₂	semidirect
3. C₆₁×#3391	C₂	semidirect
4. C₆₁×#3381	C₂	semidirect
5. C₆₁×#3368	C₂	semidirect
6. C₆₁×#3366	C₂	semidirect
7. C₆₁×#3355	C₂	semidirect
8. C₆₁×#3354	C₂	semidirect
9. C₆₁×#3318	C₂	semidirect
10. C₆₁×#3309	C₂	semidirect
11. C₆₁×#3305	C₂	semidirect
12. C₆₁×#3294	C₂	semidirect
13. C₆₁×#3274	C₂	semidirect
14. C₆₁×#3274	C₂	semidirect
15. C₆₁×#3184	C₂	semidirect
16. C₆₁×#3176	C₂	semidirect
17. C₆₁×#3122	C₂	semidirect
18. C₆₁×#3119	C₂	semidirect
19. C₆₁×#3106	C₂	semidirect
20. C₆₁×#3100	C₂	semidirect
21. C₆₁×#2969	C₂	semidirect
22. C₆₁×#2946	C₂	semidirect
23. C₄×AGL(1,ℤ/8)×C₆₁	C₂	semidirect
26. C₆₁×#557	C₂²	semidirect
32. C₆₁×#553	C₂²	semidirect
35. C₆₁×#550	C₂²	semidirect
36. C₆₁×#550	C₂²	semidirect
37. C₆₁×#550	C₂²	semidirect
39. C₆₁×#547	C₂²	semidirect
46. C₆₁×#540	C₂²	semidirect
50. C₆₁×#532	C₂²	semidirect
55. C₆₁×#520	C₂²	semidirect
57. C₄×#41×C₆₁	C₂²	semidirect
59. C₆₁×#499	C₂²	semidirect
60. C₆₁×#498	C₂²	semidirect
61. C₆₁×#493	C₂²	semidirect
62. C₆₁×#493	C₂²	semidirect
63. C₆₁×#490	C₂²	semidirect
64. C₆₁×#490	C₂²	semidirect
65. C₆₁×#486	C₂²	semidirect
66. C₆₁×#486	C₂²	semidirect
67. C₆₁×#482	C₂²	semidirect
68. C₆₁×#482	C₂²	semidirect
69. C₆₁×#482	C₂²	semidirect
70. C₆₁×#481	C₂²	semidirect
71. C₆₁×#480	C₂²	semidirect
72. C₆₁×#480	C₂²	semidirect
73. C₆₁×#479	C₂²	semidirect
75. C₆₁×#478	C₂²	semidirect
76. C₆₁×#478	C₂²	semidirect
77. C₆₁×#477	C₂²	semidirect
78. C₆₁×#476	C₂²	semidirect
80. C₆₁×#474	C₂²	semidirect
81. C₆₁×#469	C₂²	semidirect
82. C₆₁×#469	C₂²	semidirect
83. C₆₁×#469	C₂²	semidirect
84. C₆₁×#469	C₂²	semidirect
85. C₆₁×#466	C₂²	semidirect
86. C₆₁×#466	C₂²	semidirect
87. C₆₁×#460	C₂²	semidirect
88. C₆₁×#460	C₂²	semidirect
91. C₆₁×#459	C₂²	semidirect
92. C₆₁×#459	C₂²	semidirect
93. C₆₁×#459	C₂²	semidirect
94. C₆₁×#459	C₂²	semidirect
95. C₆₁×#449	C₂²	semidirect
96. C₆₁×#449	C₂²	semidirect
97. C₆₁×#449	C₂²	semidirect
101. C₆₁×#446	C₂²	semidirect
102. C₈×Q₈×C₆₁	C₂²	semidirect
105. C₆₁×#442	C₂²	semidirect
106. C₆₁×#442	C₂²	semidirect
107. C₆₁×#442	C₂²	semidirect
109. C₆₁×#440	C₂²	semidirect
110. C₆₁×#440	C₂²	semidirect
113. C₄×SD₁₆×C₆₁	C₂²	semidirect
114. C₄×SD₁₆×C₆₁	C₂²	semidirect
117. C₄×D₈×C₆₁	C₂²	semidirect
118. C₄×D₈×C₆₁	C₂²	semidirect
119. C₄×D₈×C₆₁	C₂²	semidirect
120. C₄×D₈×C₆₁	C₂²	semidirect
121. C₆₁×#436	C₂²	semidirect
122. C₆₁×#436	C₂²	semidirect
123. C₆₁×#435	C₂²	semidirect
124. C₈×D₄×C₆₁	C₂²	semidirect
125. C₆₁×#433	C₂²	semidirect
126. C₆₁×#431	C₂²	semidirect
127. C₆₁×#428	C₂²	semidirect
128. C₆₁×#428	C₂²	semidirect
130. C₆₁×#417	C₂²	semidirect
131. C₆₁×#416	C₂²	semidirect
133. C₆₁×#405	C₂²	semidirect
134. C₄×M₁₆×C₆₁	C₂²	semidirect
382. SD₁₆×C₆₁	#41	semidirect
548. #61555	C₆₁	direct (N × H)
590. #3519	C₂×C₆₁	semidirect
591. #3517	C₂×C₆₁	semidirect
592. #3391	C₂×C₆₁	semidirect
593. #3381	C₂×C₆₁	semidirect
594. #3368	C₂×C₆₁	semidirect
595. #3366	C₂×C₆₁	semidirect
596. #3355	C₂×C₆₁	semidirect
597. #3354	C₂×C₆₁	semidirect
598. #3318	C₂×C₆₁	semidirect
599. #3309	C₂×C₆₁	semidirect
600. #3305	C₂×C₆₁	semidirect
601. #3294	C₂×C₆₁	semidirect
602. #3274	C₂×C₆₁	semidirect
603. #3274	C₂×C₆₁	semidirect
604. #3184	C₂×C₆₁	semidirect
605. #3176	C₂×C₆₁	semidirect
606. #3122	C₂×C₆₁	semidirect
607. #3119	C₂×C₆₁	semidirect
608. #3106	C₂×C₆₁	semidirect
609. #3100	C₂×C₆₁	semidirect
610. #2969	C₂×C₆₁	semidirect
611. #2946	C₂×C₆₁	semidirect
612. C₄×AGL(1,ℤ/8)	C₂×C₆₁	semidirect
625. #557	C₂²×C₆₁	semidirect
631. #553	C₂²×C₆₁	semidirect
634. #550	C₂²×C₆₁	semidirect
635. #550	C₂²×C₆₁	semidirect
636. #550	C₂²×C₆₁	semidirect
638. #547	C₂²×C₆₁	semidirect
645. #540	C₂²×C₆₁	semidirect
649. #532	C₂²×C₆₁	semidirect
654. #520	C₂²×C₆₁	semidirect
656. C₄×#41	C₂²×C₆₁	semidirect
658. #499	C₂²×C₆₁	semidirect
659. #498	C₂²×C₆₁	semidirect
660. #493	C₂²×C₆₁	semidirect
661. #493	C₂²×C₆₁	semidirect
662. #490	C₂²×C₆₁	semidirect
663. #490	C₂²×C₆₁	semidirect
664. #486	C₂²×C₆₁	semidirect
665. #486	C₂²×C₆₁	semidirect
666. #482	C₂²×C₆₁	semidirect
667. #482	C₂²×C₆₁	semidirect
668. #482	C₂²×C₆₁	semidirect
669. #481	C₂²×C₆₁	semidirect
670. #480	C₂²×C₆₁	semidirect
671. #480	C₂²×C₆₁	semidirect
672. #479	C₂²×C₆₁	semidirect
674. #478	C₂²×C₆₁	semidirect
675. #478	C₂²×C₆₁	semidirect
676. #477	C₂²×C₆₁	semidirect
677. #476	C₂²×C₆₁	semidirect
679. #474	C₂²×C₆₁	semidirect
680. #469	C₂²×C₆₁	semidirect
681. #469	C₂²×C₆₁	semidirect
682. #469	C₂²×C₆₁	semidirect
683. #469	C₂²×C₆₁	semidirect
684. #466	C₂²×C₆₁	semidirect
685. #466	C₂²×C₆₁	semidirect
686. #460	C₂²×C₆₁	semidirect
687. #460	C₂²×C₆₁	semidirect
690. #459	C₂²×C₆₁	semidirect
691. #459	C₂²×C₆₁	semidirect
692. #459	C₂²×C₆₁	semidirect
693. #459	C₂²×C₆₁	semidirect
694. #449	C₂²×C₆₁	semidirect
695. #449	C₂²×C₆₁	semidirect
696. #449	C₂²×C₆₁	semidirect
700. #446	C₂²×C₆₁	semidirect
701. C₈×Q₈	C₂²×C₆₁	semidirect
704. #442	C₂²×C₆₁	semidirect
705. #442	C₂²×C₆₁	semidirect
706. #442	C₂²×C₆₁	semidirect
708. #440	C₂²×C₆₁	semidirect
709. #440	C₂²×C₆₁	semidirect
712. C₄×SD₁₆	C₂²×C₆₁	semidirect
713. C₄×SD₁₆	C₂²×C₆₁	semidirect
716. C₄×D₈	C₂²×C₆₁	semidirect
717. C₄×D₈	C₂²×C₆₁	semidirect
718. C₄×D₈	C₂²×C₆₁	semidirect
719. C₄×D₈	C₂²×C₆₁	semidirect
720. #436	C₂²×C₆₁	semidirect
721. #436	C₂²×C₆₁	semidirect
722. #435	C₂²×C₆₁	semidirect
723. C₈×D₄	C₂²×C₆₁	semidirect
724. #433	C₂²×C₆₁	semidirect
725. #431	C₂²×C₆₁	semidirect
726. #428	C₂²×C₆₁	semidirect
727. #428	C₂²×C₆₁	semidirect
729. #417	C₂²×C₆₁	semidirect
730. #416	C₂²×C₆₁	semidirect
732. #405	C₂²×C₆₁	semidirect
733. C₄×M₁₆	C₂²×C₆₁	semidirect
734. C₆₁	#61555	direct (N × H)
982. 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×#3519	2
C₆₁×#3517	2
C₆₁×#3391	2
C₆₁×#3381	2
C₆₁×#3368	2
C₆₁×#3366	2
C₆₁×#3355	2
C₆₁×#3354	2
C₆₁×#3318	2
C₆₁×#3309	2
C₆₁×#3305	2
C₆₁×#3294	2
C₆₁×#3274	2
C₆₁×#3184	2
C₆₁×#3176	2
C₆₁×#3122	2
C₆₁×#3119	2
C₆₁×#3106	2
C₆₁×#3100	2
C₆₁×#2969	2
C₆₁×#2946	2
C₄×AGL(1,ℤ/8)×C₆₁	2
#61555	61

Subgroups — C61×#61555 #29564988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61555 #29564988