Subgroups — C₆₁×#61170 #29564603

Order 15616.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3321	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3317	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3313	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3309	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3305	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3304	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3301	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3300	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3136	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3096	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3093	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3062	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3050	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3045	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3005	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#2947	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#2929	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₁×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₆₁×#416	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#137×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#135×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
30	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₆₁×#556	—	2	1	no	—
32	C₆₁×#556	C₂²	1	2	yes	complemented
33	C₆₁×#555	—	2	1	no	—
34	C₆₁×#555	C₂²	1	2	yes	complemented
35	C₆₁×#553	—	2	1	no	—
36	C₆₁×#553	C₂²	1	2	yes	complemented
37	C₆₁×#552	—	2	1	no	—
38	C₆₁×#552	C₂²	1	2	yes	complemented
39	C₆₁×#550	—	2	1	no	—
40	C₆₁×#550	—	2	1	no	—
41	C₆₁×#550	C₂²	1	2	yes	—
42	C₆₁×#550	C₂²	1	2	yes	—
43	C₆₁×#548	—	2	1	no	—
44	C₆₁×#548	—	2	1	no	—
45	C₆₁×#548	C₂²	1	2	yes	—
46	C₆₁×#548	C₂²	1	2	yes	—
47	C₆₁×#544	C₂²	1	1	yes	characteristic
48	C₆₁×#538	—	2	2	no	—
49	C₆₁×#537	C₂²	1	1	yes	characteristic
50	C₆₁×#535	—	2	2	no	—
51	C₆₁×#535	C₂²	1	1	yes	characteristic
52	C₆₁×#535	C₂²	1	1	yes	characteristic
53	C₆₁×#529	—	2	2	no	—
54	C₆₁×#525	—	2	2	no	—
55	C₆₁×#525	C₂²	1	1	yes	characteristic
56	C₆₁×#525	C₂²	1	1	yes	characteristic
57	C₆₁×#525	C₂²	1	1	yes	characteristic
58	C₆₁×#520	C₂²	1	1	yes	characteristic
59	C₆₁×#520	C₂²	1	1	yes	characteristic
60	C₆₁×#519	C₂²	1	1	yes	characteristic
61	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
62	C₆₁×#490	C₂²	1	2	yes	complemented
63	C₆₁×#489	C₂²	1	2	yes	complemented
64	C₆₁×#488	C₂²	1	2	yes	complemented
65	C₆₁×#486	C₂²	1	2	yes	complemented
66	C₆₁×#485	C₂²	1	2	yes	complemented
67	C₆₁×#485	C₂²	1	2	yes	complemented
68	C₆₁×#482	C₂²	1	2	yes	complemented
69	C₆₁×#482	C₂²	1	2	yes	complemented
70	C₆₁×#482	C₂²	1	2	yes	complemented
71	C₆₁×#482	C₂²	1	2	yes	complemented
72	C₆₁×#481	C₂²	1	2	yes	complemented
73	C₆₁×#480	C₂²	1	2	yes	complemented
74	C₆₁×#479	C₂²	1	2	yes	complemented
75	C₆₁×#479	C₂²	1	2	yes	complemented
76	C₆₁×#477	C₂²	1	2	yes	complemented
77	C₆₁×#475	C₂²	1	2	yes	complemented
78	C₆₁×#469	C₂²	1	2	yes	complemented
79	C₆₁×#468	C₂²	1	2	yes	complemented
80	C₆₁×#467	C₂²	1	1	yes	characteristic, complemented
81	C₆₁×#467	C₂²	1	1	yes	characteristic, complemented
82	C₆₁×#466	C₂²	1	2	yes	complemented
83	C₆₁×#466	C₂²	1	1	yes	characteristic, complemented
84	C₆₁×#466	C₂²	1	1	yes	characteristic, complemented
85	C₆₁×#465	C₂²	1	2	yes	complemented
86	C₆₁×#465	C₂²	1	1	yes	characteristic, complemented
87	C₆₁×#465	C₂²	1	1	yes	characteristic, complemented
88	C₆₁×#465	C₂²	1	1	yes	characteristic, complemented
89	C₆₁×#465	C₂²	1	1	yes	characteristic, complemented
90	C₆₁×#464	C₂²	1	2	yes	complemented
91	C₆₁×#463	C₂²	1	2	yes	complemented
92	C₆₁×#460	C₂²	1	2	yes	complemented
93	C₆₁×#459	C₂²	1	2	yes	complemented
94	C₆₁×#452	C₂²	1	2	yes	—
95	C₆₁×#452	C₂²	1	2	yes	—
96	C₆₁×#452	C₂²	1	2	yes	complemented
97	C₆₁×#451	C₂²	1	2	yes	complemented
98	C₆₁×#449	C₂²	1	2	yes	—
99	C₆₁×#449	C₂²	1	2	yes	—
100	C₆₁×#449	C₂²	1	2	yes	complemented
101	C₆₁×#448	C₂²	1	2	yes	complemented
102	C₆₁×#441	C₂²	1	2	yes	complemented
103	C₆₁×#440	C₂²	1	2	yes	complemented
104	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
106	C₆₁×#435	C₂²	1	2	yes	complemented
107	C₆₁×#435	C₂²	1	2	yes	complemented
108	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
109	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
110	C₆₁×#428	C₂²	1	1	yes	characteristic
111	C₆₁×#428	C₂²	1	1	yes	characteristic
112	C₆₁×#427	C₂²	1	1	yes	characteristic
113	C₆₁×#424	C₂²	1	1	yes	characteristic
114	C₆₁×#419	C₂²	1	1	yes	characteristic
115	C₆₁×#419	C₂²	1	2	yes	complemented
116	C₆₁×#418	C₂²	1	1	yes	characteristic
117	C₆₁×#417	C₂²	1	1	yes	characteristic
118	C₆₁×#417	C₂²	1	1	yes	characteristic
119	C₆₁×#417	C₂²	1	2	yes	complemented
120	C₆₁×#416	C₂²	1	2	yes	—
121	C₆₁×#416	C₂²	1	2	yes	—
122	C₆₁×#416	C₂²	1	1	yes	characteristic
123	C₆₁×#416	C₂²	1	1	yes	characteristic
124	C₆₁×#416	C₂²	1	2	yes	—
125	C₆₁×#416	C₂²	1	2	yes	—
126	C₆₁×#416	C₂²	1	2	yes	complemented
127	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
128	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
129	C₂×#103×C₆₁	C₂²	1	2	yes	complemented
130	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
131	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
132	C₆₁×#408	C₂²	1	1	yes	characteristic
133	C₆₁×#407	C₂²	1	1	yes	characteristic
134	C₆₁×#405	C₂²	1	1	yes	characteristic
135	2₋¹⁺⁴×C₆₁	—	2	4	no	—
136	2₋¹⁺⁴×C₆₁	—	4	2	no	—
137	C₂×#41×C₆₁	—	2	2	no	—
138	C₂×#41×C₆₁	—	2	1	no	—
139	C₂×#41×C₆₁	—	2	1	no	—
140	C₂×#41×C₆₁	—	2	1	no	—
141	C₂×#41×C₆₁	—	2	4	no	—
142	C₂×#41×C₆₁	—	4	2	no	—
143	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
144	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
145	C₂×#41×C₆₁	C₂³	1	2	yes	—
146	C₂×#41×C₆₁	C₂³	1	2	yes	—
147	C₂×#41×C₆₁	C₂³	1	2	yes	—
148	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₆₁	—	2	1	no	—
150	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
151	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
152	C₂²×D₄×C₆₁	—	2	1	no	—
153	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
154	C₂³×C₄×C₆₁	—	2	1	no	—
155	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
156	#137×C₆₁	—	2	4	no	—
157	AGL(1,ℤ/8)×C₆₁	—	4	2	no	—
158	#135×C₆₁	—	4	2	no	—
159	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
160	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
163	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
164	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
165	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
166	C₂×D₈×C₆₁	C₂³	1	2	yes	—
167	#131×C₆₁	—	4	2	no	—
168	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
169	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
170	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
171	C₂²×C₈×C₆₁	—	4	2	no	—
172	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
173	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
174	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
179	C₄⋊Q₈×C₆₁	—	2	1	no	—
180	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
181	#127×C₆₁	—	2	2	no	—
182	#127×C₆₁	—	2	2	no	—
183	#127×C₆₁	—	2	1	no	—
184	#127×C₆₁	C₂³	1	2	yes	—
185	#126×C₆₁	—	2	2	no	—
186	#126×C₆₁	—	2	2	no	—
187	#126×C₆₁	—	2	2	no	—
188	#126×C₆₁	—	2	2	no	—
189	#125×C₆₁	—	2	1	no	—
190	#125×C₆₁	—	2	2	no	—
191	#125×C₆₁	C₂³	1	2	yes	—
192	#124×C₆₁	—	2	1	no	—
193	#124×C₆₁	—	2	2	no	—
194	#124×C₆₁	—	2	2	no	—
195	#124×C₆₁	—	2	2	no	—
196	#124×C₆₁	—	2	2	no	—
197	#124×C₆₁	—	2	2	no	—
198	#124×C₆₁	C₂³	1	2	yes	—
199	#123×C₆₁	—	2	2	no	—
200	#123×C₆₁	—	2	1	no	—
201	#123×C₆₁	—	2	1	no	—
202	#123×C₆₁	—	2	2	no	—
203	#123×C₆₁	D₄	1	2	yes	—
204	C₂²⋊Q₈×C₆₁	—	2	1	no	—
205	C₂²⋊Q₈×C₆₁	—	2	2	no	—
206	C₂²⋊Q₈×C₆₁	—	2	2	no	—
207	C₂²⋊Q₈×C₆₁	—	2	2	no	—
208	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
209	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
210	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
212	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
213	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
214	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
215	#121×C₆₁	—	2	2	no	—
216	#121×C₆₁	—	2	2	no	—
217	#121×C₆₁	—	2	2	no	—
218	#121×C₆₁	—	2	1	no	—
219	#121×C₆₁	—	2	2	no	—
220	#121×C₆₁	—	2	2	no	—
221	#121×C₆₁	—	2	1	no	—
222	#121×C₆₁	—	2	1	no	—
223	#121×C₆₁	—	2	2	no	—
224	#121×C₆₁	—	2	2	no	—
225	#121×C₆₁	—	2	2	no	—
226	#121×C₆₁	—	2	2	no	—
227	#121×C₆₁	D₄	1	1	yes	characteristic
228	#121×C₆₁	D₄	1	1	yes	characteristic
229	#121×C₆₁	C₂³	1	2	yes	—
230	#121×C₆₁	C₂³	1	2	yes	—
231	#121×C₆₁	C₂³	1	2	yes	—
232	#121×C₆₁	C₂³	1	1	yes	characteristic
233	#121×C₆₁	C₂³	1	1	yes	characteristic
234	#121×C₆₁	C₂³	1	1	yes	characteristic
235	#121×C₆₁	C₂³	1	1	yes	characteristic
236	#120×C₆₁	—	2	1	no	—
237	#120×C₆₁	—	2	1	no	—
238	#120×C₆₁	—	2	2	no	—
239	#120×C₆₁	—	2	2	no	—
240	#120×C₆₁	D₄	1	2	yes	—
241	C₄×Q₈×C₆₁	—	2	1	no	—
242	C₄×Q₈×C₆₁	—	2	1	no	—
243	C₄×Q₈×C₆₁	—	2	1	no	—
244	C₄×Q₈×C₆₁	—	2	2	no	—
245	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
246	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
247	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
248	C₄×D₄×C₆₁	—	2	2	no	—
249	C₄×D₄×C₆₁	—	2	1	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	—	2	1	no	—
254	C₄×D₄×C₆₁	—	2	2	no	—
255	C₄×D₄×C₆₁	—	2	2	no	—
256	C₄×D₄×C₆₁	—	2	2	no	—
257	C₄×D₄×C₆₁	—	2	2	no	—
258	C₄×D₄×C₆₁	—	2	2	no	—
259	C₄×D₄×C₆₁	—	2	2	no	—
260	C₄×D₄×C₆₁	C₂³	1	2	yes	—
261	C₄×D₄×C₆₁	C₂³	1	2	yes	—
262	C₄×D₄×C₆₁	C₂³	1	2	yes	—
263	#117×C₆₁	—	2	1	no	—
264	#117×C₆₁	—	2	1	no	—
265	#117×C₆₁	—	2	2	no	—
266	#117×C₆₁	—	2	1	no	—
267	#117×C₆₁	—	2	2	no	—
268	#117×C₆₁	—	2	2	no	—
269	#117×C₆₁	C₂³	1	1	yes	characteristic
270	#117×C₆₁	C₂³	1	1	yes	characteristic
271	#117×C₆₁	C₂³	1	2	yes	—
272	#117×C₆₁	C₂³	1	2	yes	—
273	#117×C₆₁	C₂³	1	2	yes	—
274	#117×C₆₁	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
276	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
277	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
278	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
280	C₂×C₄²×C₆₁	—	2	1	no	—
281	#107×C₆₁	C₂³	1	1	yes	characteristic
282	#107×C₆₁	C₂³	1	1	yes	characteristic
283	#107×C₆₁	C₂³	1	2	yes	—
284	#107×C₆₁	C₂³	1	2	yes	—
285	#106×C₆₁	C₂³	1	1	yes	characteristic
286	#106×C₆₁	C₂³	1	1	yes	characteristic
287	#106×C₆₁	C₂³	1	2	yes	—
288	#106×C₆₁	C₂³	1	2	yes	—
289	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
290	C₄⋊C₈×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	#103×C₆₁	C₂³	1	2	yes	—
295	#103×C₆₁	C₂³	1	1	yes	characteristic
296	#103×C₆₁	C₂³	1	2	yes	—
297	#103×C₆₁	C₂³	1	2	yes	—
298	#103×C₆₁	C₂³	1	1	yes	characteristic
299	#103×C₆₁	C₂³	1	1	yes	characteristic
300	#103×C₆₁	C₂³	1	1	yes	characteristic
301	#103×C₆₁	C₂³	1	2	yes	—
302	#103×C₆₁	C₂³	1	2	yes	—
303	#102×C₆₁	C₂³	1	2	yes	—
304	#102×C₆₁	C₂³	1	2	yes	—
305	#102×C₆₁	C₂³	1	2	yes	—
306	#102×C₆₁	C₂³	1	2	yes	—
307	#102×C₆₁	C₂³	1	1	yes	characteristic
308	#102×C₆₁	C₂³	1	1	yes	characteristic
309	#102×C₆₁	C₂³	1	1	yes	characteristic
310	#102×C₆₁	C₂³	1	1	yes	characteristic
311	#102×C₆₁	C₂³	1	2	yes	—
312	#102×C₆₁	C₂³	1	2	yes	—
313	#102×C₆₁	C₂³	1	2	yes	—
314	#102×C₆₁	C₂³	1	2	yes	—
315	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
316	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
317	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
318	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
319	#97×C₆₁	C₂³	1	2	yes	—
320	C₄×C₈×C₆₁	C₂³	1	2	yes	—
321	C₂⁴×C₆₁	—	2	1	no	—
322	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
323	#41×C₆₁	—	2	2	no	—
324	#41×C₆₁	—	2	2	no	—
325	#41×C₆₁	—	2	4	no	—
326	#41×C₆₁	—	2	4	no	—
327	#41×C₆₁	—	2	4	no	—
328	#41×C₆₁	—	2	2	no	—
329	#41×C₆₁	—	2	2	no	—
330	#41×C₆₁	—	2	2	no	—
331	#41×C₆₁	—	2	2	no	—
332	#41×C₆₁	—	4	2	no	—
333	#41×C₆₁	—	4	2	no	—
334	#41×C₆₁	—	4	2	no	—
335	#41×C₆₁	—	4	8	no	—
336	#41×C₆₁	—	4	4	no	—
337	#41×C₆₁	—	4	4	no	—
338	#41×C₆₁	—	4	4	no	—
339	C₂×Q₈×C₆₁	—	2	1	no	—
340	C₂×Q₈×C₆₁	—	2	2	no	—
341	C₂×Q₈×C₆₁	—	2	2	no	—
342	C₂×Q₈×C₆₁	—	2	2	no	—
343	C₂×Q₈×C₆₁	—	2	4	no	—
344	C₂×Q₈×C₆₁	—	4	2	no	—
345	C₂×Q₈×C₆₁	—	4	4	no	—
346	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
347	C₂×Q₈×C₆₁	#41	1	4	yes	—
348	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
349	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
350	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
351	C₂×D₄×C₆₁	—	2	1	no	—
352	C₂×D₄×C₆₁	—	2	1	no	—
353	C₂×D₄×C₆₁	—	2	2	no	—
354	C₂×D₄×C₆₁	—	2	2	no	—
355	C₂×D₄×C₆₁	—	2	2	no	—
356	C₂×D₄×C₆₁	—	2	1	no	—
357	C₂×D₄×C₆₁	—	2	1	no	—
358	C₂×D₄×C₆₁	—	2	2	no	—
359	C₂×D₄×C₆₁	—	2	2	no	—
360	C₂×D₄×C₆₁	—	2	1	no	—
361	C₂×D₄×C₆₁	—	2	1	no	—
362	C₂×D₄×C₆₁	—	2	2	no	—
363	C₂×D₄×C₆₁	—	2	1	no	—
364	C₂×D₄×C₆₁	—	2	2	no	—
365	C₂×D₄×C₆₁	—	2	2	no	—
366	C₂×D₄×C₆₁	—	2	2	no	—
367	C₂×D₄×C₆₁	—	2	2	no	—
368	C₂×D₄×C₆₁	—	4	4	no	—
369	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
370	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
371	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
372	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
373	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
374	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
375	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₆₁	—	2	1	no	—
377	C₂²×C₄×C₆₁	—	2	2	no	—
378	C₂²×C₄×C₆₁	—	2	2	no	—
379	C₂²×C₄×C₆₁	—	2	2	no	—
380	C₂²×C₄×C₆₁	—	2	1	no	—
381	C₂²×C₄×C₆₁	—	2	1	no	—
382	C₂²×C₄×C₆₁	—	2	2	no	—
383	C₂²×C₄×C₆₁	—	2	1	no	—
384	C₂²×C₄×C₆₁	—	2	2	no	—
385	C₂²×C₄×C₆₁	—	2	1	no	—
386	C₂²×C₄×C₆₁	—	2	2	no	—
387	C₂²×C₄×C₆₁	—	2	2	no	—
388	C₂²×C₄×C₆₁	—	2	2	no	—
389	C₂²×C₄×C₆₁	—	4	4	no	—
390	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
394	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
397	Q₁₆×C₆₁	—	2	4	no	—
398	Q₁₆×C₆₁	—	4	1	no	—
399	SD₁₆×C₆₁	—	2	4	no	—
400	SD₁₆×C₆₁	—	4	1	no	—
401	SD₁₆×C₆₁	—	4	1	no	—
402	SD₁₆×C₆₁	—	4	2	no	—
403	D₈×C₆₁	—	4	1	no	—
404	D₈×C₆₁	—	4	2	no	—
405	M₁₆×C₆₁	—	2	2	no	—
406	M₁₆×C₆₁	—	2	2	no	—
407	M₁₆×C₆₁	—	4	2	no	—
408	C₂×C₈×C₆₁	—	2	2	no	—
409	C₂×C₈×C₆₁	—	2	2	no	—
410	C₂×C₈×C₆₁	—	4	1	no	—
411	C₂×C₈×C₆₁	—	4	1	no	—
412	C₂×C₈×C₆₁	—	4	1	no	—
413	C₂×C₈×C₆₁	—	4	1	no	—
414	C₂×C₈×C₆₁	—	4	2	no	—
415	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
416	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
417	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
418	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
419	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
420	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
421	C₄⋊C₄×C₆₁	—	2	1	no	—
422	C₄⋊C₄×C₆₁	—	2	2	no	—
423	C₄⋊C₄×C₆₁	—	2	1	no	—
424	C₄⋊C₄×C₆₁	—	2	2	no	—
425	C₄⋊C₄×C₆₁	—	2	1	no	—
426	C₄⋊C₄×C₆₁	—	2	2	no	—
427	C₄⋊C₄×C₆₁	—	2	2	no	—
428	C₄⋊C₄×C₆₁	—	2	2	no	—
429	C₄⋊C₄×C₆₁	—	2	2	no	—
430	C₄⋊C₄×C₆₁	—	2	1	no	—
431	C₄⋊C₄×C₆₁	—	2	1	no	—
432	C₄⋊C₄×C₆₁	—	2	1	no	—
433	C₄⋊C₄×C₆₁	—	2	2	no	—
434	C₄⋊C₄×C₆₁	—	2	2	no	—
435	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
437	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
438	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
439	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
440	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
442	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
443	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
444	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
445	C₂²⋊C₄×C₆₁	—	2	2	no	—
446	C₂²⋊C₄×C₆₁	—	2	2	no	—
447	C₂²⋊C₄×C₆₁	—	2	1	no	—
448	C₂²⋊C₄×C₆₁	—	2	2	no	—
449	C₂²⋊C₄×C₆₁	—	2	1	no	—
450	C₂²⋊C₄×C₆₁	—	2	2	no	—
451	C₂²⋊C₄×C₆₁	—	2	1	no	—
452	C₂²⋊C₄×C₆₁	—	2	1	no	—
453	C₂²⋊C₄×C₆₁	—	2	1	no	—
454	C₂²⋊C₄×C₆₁	—	2	1	no	—
455	C₂²⋊C₄×C₆₁	—	2	1	no	—
456	C₂²⋊C₄×C₆₁	—	2	2	no	—
457	C₂²⋊C₄×C₆₁	—	2	2	no	—
458	C₂²⋊C₄×C₆₁	—	2	1	no	—
459	C₂²⋊C₄×C₆₁	—	2	1	no	—
460	C₂²⋊C₄×C₆₁	—	2	1	no	—
461	C₂²⋊C₄×C₆₁	—	2	2	no	—
462	C₂²⋊C₄×C₆₁	—	2	2	no	—
463	C₂²⋊C₄×C₆₁	—	2	2	no	—
464	C₂²⋊C₄×C₆₁	—	2	2	no	—
465	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
466	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
467	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
468	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
469	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
470	C₄²×C₆₁	—	2	2	no	—
471	C₄²×C₆₁	—	2	2	no	—
472	C₄²×C₆₁	—	2	2	no	—
473	C₄²×C₆₁	—	2	2	no	—
474	C₄²×C₆₁	—	2	2	no	—
475	C₄²×C₆₁	—	2	2	no	—
476	C₄²×C₆₁	—	2	1	no	—
477	C₄²×C₆₁	—	2	1	no	—
478	C₄²×C₆₁	C₂⁴	1	2	yes	—
479	C₂³×C₆₁	—	2	2	no	—
480	C₂³×C₆₁	—	2	1	no	—
481	C₂³×C₆₁	—	2	2	no	—
482	C₂³×C₆₁	—	2	1	no	—
483	C₂³×C₆₁	—	4	1	no	—
484	C₂³×C₆₁	—	4	1	no	—
485	C₂³×C₆₁	—	4	2	no	—
486	C₂³×C₆₁	—	8	1	no	—
487	C₂³×C₆₁	—	8	1	no	—
488	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
489	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
490	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
491	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
492	Q₈×C₆₁	—	2	4	no	—
493	Q₈×C₆₁	—	2	2	no	—
494	Q₈×C₆₁	—	2	2	no	—
495	Q₈×C₆₁	—	2	1	no	—
496	Q₈×C₆₁	—	2	1	no	—
497	Q₈×C₆₁	—	2	1	no	—
498	Q₈×C₆₁	—	2	1	no	—
499	Q₈×C₆₁	—	4	4	no	—
500	Q₈×C₆₁	—	8	2	no	—
501	Q₈×C₆₁	C₂×#41	1	4	yes	—
502	D₄×C₆₁	—	2	4	no	—
503	D₄×C₆₁	—	2	2	no	—
504	D₄×C₆₁	—	2	1	no	—
505	D₄×C₆₁	—	2	2	no	—
506	D₄×C₆₁	—	2	1	no	—
507	D₄×C₆₁	—	2	1	no	—
508	D₄×C₆₁	—	2	2	no	—
509	D₄×C₆₁	—	2	1	no	—
510	D₄×C₆₁	—	4	2	no	—
511	D₄×C₆₁	—	4	2	no	—
512	D₄×C₆₁	—	4	4	no	—
513	D₄×C₆₁	—	4	4	no	—
514	D₄×C₆₁	—	4	4	no	—
515	D₄×C₆₁	—	4	2	no	—
516	D₄×C₆₁	—	4	2	no	—
517	D₄×C₆₁	—	4	2	no	—
518	D₄×C₆₁	—	8	2	no	—
519	D₄×C₆₁	—	8	2	no	—
520	D₄×C₆₁	—	8	1	no	—
521	D₄×C₆₁	—	8	2	no	—
522	D₄×C₆₁	—	8	2	no	—
523	D₄×C₆₁	—	8	2	no	—
524	D₄×C₆₁	—	8	1	no	—
525	D₄×C₆₁	—	8	1	no	—
526	D₄×C₆₁	—	8	1	no	—
527	C₂×C₄×C₆₁	—	2	2	no	—
528	C₂×C₄×C₆₁	—	2	4	no	—
529	C₂×C₄×C₆₁	—	2	2	no	—
530	C₂×C₄×C₆₁	—	2	2	no	—
531	C₂×C₄×C₆₁	—	2	2	no	—
532	C₂×C₄×C₆₁	—	2	1	no	—
533	C₂×C₄×C₆₁	—	2	1	no	—
534	C₂×C₄×C₆₁	—	2	2	no	—
535	C₂×C₄×C₆₁	—	2	1	no	—
536	C₂×C₄×C₆₁	—	2	1	no	—
537	C₂×C₄×C₆₁	—	2	2	no	—
538	C₂×C₄×C₆₁	—	2	2	no	—
539	C₂×C₄×C₆₁	—	2	1	no	—
540	C₂×C₄×C₆₁	—	2	1	no	—
541	C₂×C₄×C₆₁	—	2	1	no	—
542	C₂×C₄×C₆₁	—	2	1	no	—
543	C₂×C₄×C₆₁	—	2	2	no	—
544	C₂×C₄×C₆₁	—	2	1	no	—
545	C₂×C₄×C₆₁	—	2	1	no	—
546	C₂×C₄×C₆₁	—	4	4	no	—
547	C₂×C₄×C₆₁	—	4	4	no	—
548	C₂×C₄×C₆₁	—	4	4	no	—
549	C₂×C₄×C₆₁	—	4	4	no	—
550	C₂×C₄×C₆₁	—	4	2	no	—
551	C₂×C₄×C₆₁	—	4	2	no	—
552	C₂×C₄×C₆₁	—	8	2	no	—
553	C₂×C₄×C₆₁	—	8	1	no	—
554	C₂×C₄×C₆₁	—	8	2	no	—
555	C₂×C₄×C₆₁	—	8	1	no	—
556	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
557	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
560	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
561	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
563	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
564	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
565	C₈×C₆₁	—	2	2	no	—
566	C₈×C₆₁	—	2	1	no	—
567	C₈×C₆₁	—	2	1	no	—
568	C₈×C₆₁	—	2	1	no	—
569	C₈×C₆₁	—	2	1	no	—
570	C₈×C₆₁	—	2	2	no	—
571	#61170	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
572	C₂²×C₆₁	—	2	1	no	—
573	C₂²×C₆₁	—	2	1	no	—
574	C₂²×C₆₁	—	2	2	no	—
575	C₂²×C₆₁	—	2	1	no	—
576	C₂²×C₆₁	—	2	1	no	—
577	C₂²×C₆₁	—	2	2	no	—
578	C₂²×C₆₁	—	2	1	no	—
579	C₂²×C₆₁	—	2	1	no	—
580	C₂²×C₆₁	—	2	1	no	—
581	C₂²×C₆₁	—	2	1	no	—
582	C₂²×C₆₁	—	2	2	no	—
583	C₂²×C₆₁	—	4	4	no	—
584	C₂²×C₆₁	—	4	1	no	—
585	C₂²×C₆₁	—	4	1	no	—
586	C₂²×C₆₁	—	4	1	no	—
587	C₂²×C₆₁	—	4	1	no	—
588	C₂²×C₆₁	—	4	2	no	—
589	C₂²×C₆₁	—	4	2	no	—
590	C₂²×C₆₁	—	4	1	no	—
591	C₂²×C₆₁	—	4	2	no	—
592	C₂²×C₆₁	—	4	1	no	—
593	C₂²×C₆₁	—	8	4	no	—
594	C₂²×C₆₁	#546	1	2	yes	—
595	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
596	C₄×C₆₁	—	2	2	no	—
597	C₄×C₆₁	—	2	2	no	—
598	C₄×C₆₁	—	2	1	no	—
599	C₄×C₆₁	—	2	1	no	—
600	C₄×C₆₁	—	2	4	no	—
601	C₄×C₆₁	—	2	2	no	—
602	C₄×C₆₁	—	4	2	no	—
603	C₄×C₆₁	—	4	1	no	—
604	C₄×C₆₁	—	4	2	no	—
605	C₄×C₆₁	—	4	1	no	—
606	C₄×C₆₁	—	4	1	no	—
607	C₄×C₆₁	—	4	1	no	—
608	C₄×C₆₁	—	4	1	no	—
609	C₄×C₆₁	—	4	1	no	—
610	C₄×C₆₁	#546	1	2	yes	—
611	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
612	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
613	#3493	C₂×C₆₁	1	1	yes	characteristic, complemented
614	#3487	C₂×C₆₁	1	1	yes	characteristic, complemented
615	#3321	C₂×C₆₁	1	2	yes	complemented
616	#3317	C₂×C₆₁	1	2	yes	complemented
617	#3313	C₂×C₆₁	1	2	yes	complemented
618	#3309	C₂×C₆₁	1	2	yes	complemented
619	#3305	C₂×C₆₁	1	2	yes	complemented
620	#3304	C₂×C₆₁	1	2	yes	complemented
621	#3301	C₂×C₆₁	1	2	yes	complemented
622	#3300	C₂×C₆₁	1	2	yes	complemented
623	#3136	C₂×C₆₁	1	1	yes	characteristic, complemented
624	#3096	C₂×C₆₁	1	1	yes	characteristic, complemented
625	#3093	C₂×C₆₁	1	1	yes	characteristic, complemented
626	#3082	C₂×C₆₁	1	1	yes	characteristic, complemented
627	#3062	C₂×C₆₁	1	1	yes	characteristic, complemented
628	#3050	C₂×C₆₁	1	1	yes	characteristic, complemented
629	#3045	C₂×C₆₁	1	1	yes	characteristic, complemented
630	#3013	C₂×C₆₁	1	1	yes	characteristic, complemented
631	#3005	C₂×C₆₁	1	1	yes	characteristic, complemented
632	#2947	C₂×C₆₁	1	1	yes	characteristic, complemented
633	#2929	C₂×C₆₁	1	1	yes	characteristic, complemented
634	#2898	C₂×C₆₁	1	1	yes	characteristic, complemented
635	C₂×#416	C₂×C₆₁	1	1	yes	characteristic, complemented
636	C₂×C₆₁	—	2	2	no	—
637	C₂×C₆₁	—	4	2	no	—
638	C₂×C₆₁	—	4	1	no	—
639	C₂×C₆₁	—	4	1	no	—
640	C₂×C₆₁	—	8	1	no	—
641	C₂×C₆₁	—	8	1	no	—
642	C₂×C₆₁	—	8	2	no	—
643	C₂×C₆₁	C₂×#546	1	1	yes	characteristic
644	C₂×C₆₁	#3584	1	1	yes	characteristic
645	C₂×C₆₁	#3584	1	1	yes	characteristic
646	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	1	yes	characteristic
647	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
648	C₂×#137	C₂²×C₆₁	1	1	yes	characteristic
649	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
650	C₂×#135	C₂²×C₆₁	1	1	yes	characteristic
651	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
652	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
653	#556	—	2	1	no	—
654	#556	C₂²×C₆₁	1	2	yes	complemented
655	#555	—	2	1	no	—
656	#555	C₂²×C₆₁	1	2	yes	complemented
657	#553	—	2	1	no	—
658	#553	C₂²×C₆₁	1	2	yes	complemented
659	#552	—	2	1	no	—
660	#552	C₂²×C₆₁	1	2	yes	complemented
661	#550	—	2	1	no	—
662	#550	—	2	1	no	—
663	#550	C₂²×C₆₁	1	2	yes	—
664	#550	C₂²×C₆₁	1	2	yes	—
665	#548	—	2	1	no	—
666	#548	—	2	1	no	—
667	#548	C₂²×C₆₁	1	2	yes	—
668	#548	C₂²×C₆₁	1	2	yes	—
669	#544	C₂²×C₆₁	1	1	yes	characteristic
670	#538	—	2	2	no	—
671	#537	C₂²×C₆₁	1	1	yes	characteristic
672	#535	—	2	2	no	—
673	#535	C₂²×C₆₁	1	1	yes	characteristic
674	#535	C₂²×C₆₁	1	1	yes	characteristic
675	#529	—	2	2	no	—
676	#525	—	2	2	no	—
677	#525	C₂²×C₆₁	1	1	yes	characteristic
678	#525	C₂²×C₆₁	1	1	yes	characteristic
679	#525	C₂²×C₆₁	1	1	yes	characteristic
680	#520	C₂²×C₆₁	1	1	yes	characteristic
681	#520	C₂²×C₆₁	1	1	yes	characteristic
682	#519	C₂²×C₆₁	1	1	yes	characteristic
683	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
684	#490	C₂²×C₆₁	1	2	yes	complemented
685	#489	C₂²×C₆₁	1	2	yes	complemented
686	#488	C₂²×C₆₁	1	2	yes	complemented
687	#486	C₂²×C₆₁	1	2	yes	complemented
688	#485	C₂²×C₆₁	1	2	yes	complemented
689	#485	C₂²×C₆₁	1	2	yes	complemented
690	#482	C₂²×C₆₁	1	2	yes	complemented
691	#482	C₂²×C₆₁	1	2	yes	complemented
692	#482	C₂²×C₆₁	1	2	yes	complemented
693	#482	C₂²×C₆₁	1	2	yes	complemented
694	#481	C₂²×C₆₁	1	2	yes	complemented
695	#480	C₂²×C₆₁	1	2	yes	complemented
696	#479	C₂²×C₆₁	1	2	yes	complemented
697	#479	C₂²×C₆₁	1	2	yes	complemented
698	#477	C₂²×C₆₁	1	2	yes	complemented
699	#475	C₂²×C₆₁	1	2	yes	complemented
700	#469	C₂²×C₆₁	1	2	yes	complemented
701	#468	C₂²×C₆₁	1	2	yes	complemented
702	#467	C₂²×C₆₁	1	1	yes	characteristic, complemented
703	#467	C₂²×C₆₁	1	1	yes	characteristic, complemented
704	#466	C₂²×C₆₁	1	2	yes	complemented
705	#466	C₂²×C₆₁	1	1	yes	characteristic, complemented
706	#466	C₂²×C₆₁	1	1	yes	characteristic, complemented
707	#465	C₂²×C₆₁	1	2	yes	complemented
708	#465	C₂²×C₆₁	1	1	yes	characteristic, complemented
709	#465	C₂²×C₆₁	1	1	yes	characteristic, complemented
710	#465	C₂²×C₆₁	1	1	yes	characteristic, complemented
711	#465	C₂²×C₆₁	1	1	yes	characteristic, complemented
712	#464	C₂²×C₆₁	1	2	yes	complemented
713	#463	C₂²×C₆₁	1	2	yes	complemented
714	#460	C₂²×C₆₁	1	2	yes	complemented
715	#459	C₂²×C₆₁	1	2	yes	complemented
716	#452	C₂²×C₆₁	1	2	yes	—
717	#452	C₂²×C₆₁	1	2	yes	—
718	#452	C₂²×C₆₁	1	2	yes	complemented
719	#451	C₂²×C₆₁	1	2	yes	complemented
720	#449	C₂²×C₆₁	1	2	yes	—
721	#449	C₂²×C₆₁	1	2	yes	—
722	#449	C₂²×C₆₁	1	2	yes	complemented
723	#448	C₂²×C₆₁	1	2	yes	complemented
724	#441	C₂²×C₆₁	1	2	yes	complemented
725	#440	C₂²×C₆₁	1	2	yes	complemented
726	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
727	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
728	#435	C₂²×C₆₁	1	2	yes	complemented
729	#435	C₂²×C₆₁	1	2	yes	complemented
730	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
731	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
732	#428	C₂²×C₆₁	1	1	yes	characteristic
733	#428	C₂²×C₆₁	1	1	yes	characteristic
734	#427	C₂²×C₆₁	1	1	yes	characteristic
735	#424	C₂²×C₆₁	1	1	yes	characteristic
736	#419	C₂²×C₆₁	1	1	yes	characteristic
737	#419	C₂²×C₆₁	1	2	yes	complemented
738	#418	C₂²×C₆₁	1	1	yes	characteristic
739	#417	C₂²×C₆₁	1	1	yes	characteristic
740	#417	C₂²×C₆₁	1	1	yes	characteristic
741	#417	C₂²×C₆₁	1	2	yes	complemented
742	#416	C₂²×C₆₁	1	1	yes	characteristic
743	#416	C₂²×C₆₁	1	2	yes	—
744	#416	C₂²×C₆₁	1	2	yes	—
745	#416	C₂²×C₆₁	1	2	yes	—
746	#416	C₂²×C₆₁	1	2	yes	—
747	#416	C₂²×C₆₁	1	1	yes	characteristic
748	#416	C₂²×C₆₁	1	2	yes	complemented
749	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
750	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
751	C₂×#103	C₂²×C₆₁	1	2	yes	complemented
752	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
753	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
754	#408	C₂²×C₆₁	1	1	yes	characteristic
755	#407	C₂²×C₆₁	1	1	yes	characteristic
756	#405	C₂²×C₆₁	1	1	yes	characteristic
757	C₆₁	#61170	1	1	yes	characteristic, direct product factor, Sylow
758	2₋¹⁺⁴	—	2	4	no	—
759	2₋¹⁺⁴	—	4	2	no	—
760	C₂×#41	—	2	2	no	—
761	C₂×#41	—	2	1	no	—
762	C₂×#41	—	2	1	no	—
763	C₂×#41	—	2	1	no	—
764	C₂×#41	—	2	4	no	—
765	C₂×#41	—	4	2	no	—
766	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
767	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
768	C₂×#41	C₂³×C₆₁	1	2	yes	—
769	C₂×#41	C₂³×C₆₁	1	2	yes	—
770	C₂×#41	C₂³×C₆₁	1	2	yes	—
771	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
772	C₂²×Q₈	—	2	1	no	—
773	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
774	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
775	C₂²×D₄	—	2	1	no	—
776	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
777	C₂³×C₄	—	2	1	no	—
778	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
779	#137	—	2	4	no	—
780	AGL(1,ℤ/8)	—	4	2	no	—
781	#135	—	4	2	no	—
782	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
783	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
784	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
785	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
786	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
787	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
788	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
789	C₂×D₈	C₂³×C₆₁	1	2	yes	—
790	#131	—	4	2	no	—
791	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
792	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
793	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
794	C₂²×C₈	—	4	2	no	—
795	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
796	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
797	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
798	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
799	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
800	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
801	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
802	C₄⋊Q₈	—	2	1	no	—
803	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
804	#127	—	2	2	no	—
805	#127	—	2	2	no	—
806	#127	—	2	1	no	—
807	#127	C₂³×C₆₁	1	2	yes	—
808	#126	—	2	2	no	—
809	#126	—	2	2	no	—
810	#126	—	2	2	no	—
811	#126	—	2	2	no	—
812	#125	—	2	2	no	—
813	#125	—	2	1	no	—
814	#125	C₂³×C₆₁	1	2	yes	—
815	#124	—	2	1	no	—
816	#124	—	2	2	no	—
817	#124	—	2	2	no	—
818	#124	—	2	2	no	—
819	#124	—	2	2	no	—
820	#124	—	2	2	no	—
821	#124	C₂³×C₆₁	1	2	yes	—
822	#123	—	2	2	no	—
823	#123	—	2	1	no	—
824	#123	—	2	1	no	—
825	#123	—	2	2	no	—
826	#123	D₄×C₆₁	1	2	yes	—
827	C₂²⋊Q₈	—	2	1	no	—
828	C₂²⋊Q₈	—	2	2	no	—
829	C₂²⋊Q₈	—	2	2	no	—
830	C₂²⋊Q₈	—	2	2	no	—
831	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
832	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
833	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
834	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
835	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
836	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
837	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
838	#121	—	2	2	no	—
839	#121	—	2	2	no	—
840	#121	—	2	2	no	—
841	#121	—	2	1	no	—
842	#121	—	2	2	no	—
843	#121	—	2	2	no	—
844	#121	—	2	1	no	—
845	#121	—	2	1	no	—
846	#121	—	2	2	no	—
847	#121	—	2	2	no	—
848	#121	—	2	2	no	—
849	#121	—	2	2	no	—
850	#121	D₄×C₆₁	1	1	yes	characteristic
851	#121	D₄×C₆₁	1	1	yes	characteristic
852	#121	C₂³×C₆₁	1	1	yes	characteristic
853	#121	C₂³×C₆₁	1	1	yes	characteristic
854	#121	C₂³×C₆₁	1	1	yes	characteristic
855	#121	C₂³×C₆₁	1	1	yes	characteristic
856	#121	C₂³×C₆₁	1	2	yes	—
857	#121	C₂³×C₆₁	1	2	yes	—
858	#121	C₂³×C₆₁	1	2	yes	—
859	#120	—	2	1	no	—
860	#120	—	2	1	no	—
861	#120	—	2	2	no	—
862	#120	—	2	2	no	—
863	#120	D₄×C₆₁	1	2	yes	—
864	C₄×Q₈	—	2	1	no	—
865	C₄×Q₈	—	2	1	no	—
866	C₄×Q₈	—	2	1	no	—
867	C₄×Q₈	—	2	2	no	—
868	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
869	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
870	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
871	C₄×D₄	—	2	2	no	—
872	C₄×D₄	—	2	1	no	—
873	C₄×D₄	—	2	1	no	—
874	C₄×D₄	—	2	1	no	—
875	C₄×D₄	—	2	1	no	—
876	C₄×D₄	—	2	1	no	—
877	C₄×D₄	—	2	2	no	—
878	C₄×D₄	—	2	2	no	—
879	C₄×D₄	—	2	2	no	—
880	C₄×D₄	—	2	2	no	—
881	C₄×D₄	—	2	2	no	—
882	C₄×D₄	—	2	2	no	—
883	C₄×D₄	C₂³×C₆₁	1	2	yes	—
884	C₄×D₄	C₂³×C₆₁	1	2	yes	—
885	C₄×D₄	C₂³×C₆₁	1	2	yes	—
886	#117	—	2	1	no	—
887	#117	—	2	1	no	—
888	#117	—	2	1	no	—
889	#117	—	2	2	no	—
890	#117	—	2	2	no	—
891	#117	—	2	2	no	—
892	#117	C₂³×C₆₁	1	2	yes	—
893	#117	C₂³×C₆₁	1	2	yes	—
894	#117	C₂³×C₆₁	1	1	yes	characteristic
895	#117	C₂³×C₆₁	1	1	yes	characteristic
896	#117	C₂³×C₆₁	1	2	yes	—
897	#117	C₂³×C₆₁	1	1	yes	characteristic
898	C₂×C₄⋊C₄	—	2	1	no	—
899	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
900	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
901	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
902	C₂×C₂²⋊C₄	—	2	1	no	—
903	C₂×C₄²	—	2	1	no	—
904	#107	C₂³×C₆₁	1	1	yes	characteristic
905	#107	C₂³×C₆₁	1	1	yes	characteristic
906	#107	C₂³×C₆₁	1	2	yes	—
907	#107	C₂³×C₆₁	1	2	yes	—
908	#106	C₂³×C₆₁	1	1	yes	characteristic
909	#106	C₂³×C₆₁	1	1	yes	characteristic
910	#106	C₂³×C₆₁	1	2	yes	—
911	#106	C₂³×C₆₁	1	2	yes	—
912	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
913	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
914	#103	C₂³×C₆₁	1	2	yes	—
915	#103	C₂³×C₆₁	1	2	yes	—
916	#103	C₂³×C₆₁	1	2	yes	—
917	#103	C₂³×C₆₁	1	2	yes	—
918	#103	C₂³×C₆₁	1	1	yes	characteristic
919	#103	C₂³×C₆₁	1	2	yes	—
920	#103	C₂³×C₆₁	1	2	yes	—
921	#103	C₂³×C₆₁	1	1	yes	characteristic
922	#103	C₂³×C₆₁	1	1	yes	characteristic
923	#103	C₂³×C₆₁	1	1	yes	characteristic
924	#103	C₂³×C₆₁	1	2	yes	—
925	#103	C₂³×C₆₁	1	2	yes	—
926	#102	C₂³×C₆₁	1	2	yes	—
927	#102	C₂³×C₆₁	1	2	yes	—
928	#102	C₂³×C₆₁	1	2	yes	—
929	#102	C₂³×C₆₁	1	2	yes	—
930	#102	C₂³×C₆₁	1	1	yes	characteristic
931	#102	C₂³×C₆₁	1	1	yes	characteristic
932	#102	C₂³×C₆₁	1	1	yes	characteristic
933	#102	C₂³×C₆₁	1	1	yes	characteristic
934	#102	C₂³×C₆₁	1	2	yes	—
935	#102	C₂³×C₆₁	1	2	yes	—
936	#102	C₂³×C₆₁	1	2	yes	—
937	#102	C₂³×C₆₁	1	2	yes	—
938	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
939	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
940	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
941	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
942	#97	C₂³×C₆₁	1	2	yes	—
943	C₄×C₈	C₂³×C₆₁	1	2	yes	—
944	C₂⁴	—	2	1	no	—
945	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
946	#41	—	2	2	no	—
947	#41	—	2	2	no	—
948	#41	—	2	4	no	—
949	#41	—	2	4	no	—
950	#41	—	2	4	no	—
951	#41	—	2	2	no	—
952	#41	—	2	2	no	—
953	#41	—	2	2	no	—
954	#41	—	2	2	no	—
955	#41	—	4	2	no	—
956	#41	—	4	2	no	—
957	#41	—	4	2	no	—
958	#41	—	4	8	no	—
959	#41	—	4	4	no	—
960	#41	—	4	4	no	—
961	#41	—	4	4	no	—
962	C₂×Q₈	—	2	1	no	—
963	C₂×Q₈	—	2	2	no	—
964	C₂×Q₈	—	2	2	no	—
965	C₂×Q₈	—	2	2	no	—
966	C₂×Q₈	—	2	4	no	—
967	C₂×Q₈	—	4	2	no	—
968	C₂×Q₈	—	4	4	no	—
969	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
970	C₂×Q₈	#41×C₆₁	1	4	yes	—
971	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
972	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
973	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
974	C₂×D₄	—	2	1	no	—
975	C₂×D₄	—	2	1	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	2	2	no	—
978	C₂×D₄	—	2	2	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	1	no	—
981	C₂×D₄	—	2	2	no	—
982	C₂×D₄	—	2	2	no	—
983	C₂×D₄	—	2	1	no	—
984	C₂×D₄	—	2	1	no	—
985	C₂×D₄	—	2	2	no	—
986	C₂×D₄	—	2	1	no	—
987	C₂×D₄	—	2	2	no	—
988	C₂×D₄	—	2	2	no	—
989	C₂×D₄	—	2	2	no	—
990	C₂×D₄	—	2	2	no	—
991	C₂×D₄	—	4	4	no	—
992	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
993	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
994	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
995	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
996	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
997	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
998	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	2	no	—
1001	C₂²×C₄	—	2	2	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	1	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	2	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	2	no	—
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	2	2	no	—
1010	C₂²×C₄	—	2	2	no	—
1011	C₂²×C₄	—	2	2	no	—
1012	C₂²×C₄	—	4	4	no	—
1013	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1014	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1015	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1016	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
1017	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1018	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1019	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1020	Q₁₆	—	2	4	no	—
1021	Q₁₆	—	4	1	no	—
1022	SD₁₆	—	2	4	no	—
1023	SD₁₆	—	4	1	no	—
1024	SD₁₆	—	4	1	no	—
1025	SD₁₆	—	4	2	no	—
1026	D₈	—	4	1	no	—
1027	D₈	—	4	2	no	—
1028	M₁₆	—	2	2	no	—
1029	M₁₆	—	2	2	no	—
1030	M₁₆	—	4	2	no	—
1031	C₂×C₈	—	2	2	no	—
1032	C₂×C₈	—	2	2	no	—
1033	C₂×C₈	—	4	1	no	—
1034	C₂×C₈	—	4	1	no	—
1035	C₂×C₈	—	4	1	no	—
1036	C₂×C₈	—	4	1	no	—
1037	C₂×C₈	—	4	2	no	—
1038	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
1039	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
1040	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
1041	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
1042	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
1043	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1059	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1060	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1061	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1062	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1063	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1064	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1065	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1066	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1067	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	1	no	—
1077	C₂²⋊C₄	—	2	1	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	2	no	—
1080	C₂²⋊C₄	—	2	2	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	2	no	—
1088	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1089	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1090	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1091	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1092	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1093	C₄²	—	2	2	no	—
1094	C₄²	—	2	2	no	—
1095	C₄²	—	2	2	no	—
1096	C₄²	—	2	2	no	—
1097	C₄²	—	2	2	no	—
1098	C₄²	—	2	2	no	—
1099	C₄²	—	2	1	no	—
1100	C₄²	—	2	1	no	—
1101	C₄²	C₂⁴×C₆₁	1	2	yes	—
1102	C₂³	—	2	2	no	—
1103	C₂³	—	2	1	no	—
1104	C₂³	—	2	2	no	—
1105	C₂³	—	2	1	no	—
1106	C₂³	—	4	1	no	—
1107	C₂³	—	4	1	no	—
1108	C₂³	—	4	2	no	—
1109	C₂³	—	8	1	no	—
1110	C₂³	—	8	1	no	—
1111	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1112	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1113	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1114	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1115	Q₈	—	2	4	no	—
1116	Q₈	—	2	2	no	—
1117	Q₈	—	2	2	no	—
1118	Q₈	—	2	1	no	—
1119	Q₈	—	2	1	no	—
1120	Q₈	—	2	1	no	—
1121	Q₈	—	2	1	no	—
1122	Q₈	—	4	4	no	—
1123	Q₈	—	8	2	no	—
1124	Q₈	C₂×#41×C₆₁	1	4	yes	—
1125	D₄	—	2	4	no	—
1126	D₄	—	2	2	no	—
1127	D₄	—	2	1	no	—
1128	D₄	—	2	2	no	—
1129	D₄	—	2	1	no	—
1130	D₄	—	2	1	no	—
1131	D₄	—	2	2	no	—
1132	D₄	—	2	1	no	—
1133	D₄	—	4	2	no	—
1134	D₄	—	4	2	no	—
1135	D₄	—	4	4	no	—
1136	D₄	—	4	4	no	—
1137	D₄	—	4	4	no	—
1138	D₄	—	4	2	no	—
1139	D₄	—	4	2	no	—
1140	D₄	—	4	2	no	—
1141	D₄	—	8	2	no	—
1142	D₄	—	8	2	no	—
1143	D₄	—	8	1	no	—
1144	D₄	—	8	2	no	—
1145	D₄	—	8	2	no	—
1146	D₄	—	8	2	no	—
1147	D₄	—	8	1	no	—
1148	D₄	—	8	1	no	—
1149	D₄	—	8	1	no	—
1150	C₂×C₄	—	2	2	no	—
1151	C₂×C₄	—	2	4	no	—
1152	C₂×C₄	—	2	2	no	—
1153	C₂×C₄	—	2	2	no	—
1154	C₂×C₄	—	2	2	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	2	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	2	2	no	—
1161	C₂×C₄	—	2	2	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	4	4	no	—
1170	C₂×C₄	—	4	4	no	—
1171	C₂×C₄	—	4	4	no	—
1172	C₂×C₄	—	4	4	no	—
1173	C₂×C₄	—	4	2	no	—
1174	C₂×C₄	—	4	2	no	—
1175	C₂×C₄	—	8	2	no	—
1176	C₂×C₄	—	8	1	no	—
1177	C₂×C₄	—	8	2	no	—
1178	C₂×C₄	—	8	1	no	—
1179	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1180	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1181	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1182	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1183	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1184	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1185	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1186	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
1187	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1188	C₈	—	2	2	no	—
1189	C₈	—	2	1	no	—
1190	C₈	—	2	1	no	—
1191	C₈	—	2	1	no	—
1192	C₈	—	2	1	no	—
1193	C₈	—	2	2	no	—
1194	C₂²	—	2	1	no	—
1195	C₂²	—	2	1	no	—
1196	C₂²	—	2	2	no	—
1197	C₂²	—	2	1	no	—
1198	C₂²	—	2	1	no	—
1199	C₂²	—	2	2	no	—
1200	C₂²	—	2	1	no	—
1201	C₂²	—	2	1	no	—
1202	C₂²	—	2	1	no	—
1203	C₂²	—	2	1	no	—
1204	C₂²	—	2	2	no	—
1205	C₂²	—	4	4	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	4	1	no	—
1209	C₂²	—	4	1	no	—
1210	C₂²	—	4	2	no	—
1211	C₂²	—	4	2	no	—
1212	C₂²	—	4	1	no	—
1213	C₂²	—	4	2	no	—
1214	C₂²	—	4	1	no	—
1215	C₂²	—	8	4	no	—
1216	C₂²	C₆₁×#546	1	2	yes	—
1217	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1218	C₄	—	2	2	no	—
1219	C₄	—	2	2	no	—
1220	C₄	—	2	1	no	—
1221	C₄	—	2	1	no	—
1222	C₄	—	2	4	no	—
1223	C₄	—	2	2	no	—
1224	C₄	—	4	2	no	—
1225	C₄	—	4	1	no	—
1226	C₄	—	4	2	no	—
1227	C₄	—	4	1	no	—
1228	C₄	—	4	1	no	—
1229	C₄	—	4	1	no	—
1230	C₄	—	4	1	no	—
1231	C₄	—	4	1	no	—
1232	C₄	C₆₁×#546	1	2	yes	—
1233	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
1234	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1235	C₂	—	2	2	no	—
1236	C₂	—	4	1	no	—
1237	C₂	—	4	1	no	—
1238	C₂	—	4	2	no	—
1239	C₂	—	8	2	no	—
1240	C₂	—	8	1	no	—
1241	C₂	—	8	1	no	—
1242	C₂	C₂×C₆₁×#546	1	1	yes	characteristic
1243	C₂	C₆₁×#3584	1	1	yes	characteristic
1244	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3493	C₂	semidirect
2. C₆₁×#3487	C₂	semidirect
3. C₆₁×#3321	C₂	semidirect
4. C₆₁×#3317	C₂	semidirect
5. C₆₁×#3313	C₂	semidirect
6. C₆₁×#3309	C₂	semidirect
7. C₆₁×#3305	C₂	semidirect
8. C₆₁×#3304	C₂	semidirect
9. C₆₁×#3301	C₂	semidirect
10. C₆₁×#3300	C₂	semidirect
11. C₆₁×#3136	C₂	semidirect
12. C₆₁×#3096	C₂	semidirect
13. C₆₁×#3093	C₂	semidirect
14. C₆₁×#3082	C₂	semidirect
15. C₆₁×#3062	C₂	semidirect
16. C₆₁×#3050	C₂	semidirect
17. C₆₁×#3045	C₂	semidirect
18. C₆₁×#3013	C₂	semidirect
19. C₆₁×#3005	C₂	semidirect
20. C₆₁×#2947	C₂	semidirect
21. C₆₁×#2929	C₂	semidirect
22. C₆₁×#2898	C₂	semidirect
23. C₂×C₆₁×#416	C₂	semidirect
32. C₆₁×#556	C₂²	semidirect
34. C₆₁×#555	C₂²	semidirect
36. C₆₁×#553	C₂²	semidirect
38. C₆₁×#552	C₂²	semidirect
62. C₆₁×#490	C₂²	semidirect
63. C₆₁×#489	C₂²	semidirect
64. C₆₁×#488	C₂²	semidirect
65. C₆₁×#486	C₂²	semidirect
66. C₆₁×#485	C₂²	semidirect
67. C₆₁×#485	C₂²	semidirect
68. C₆₁×#482	C₂²	semidirect
69. C₆₁×#482	C₂²	semidirect
70. C₆₁×#482	C₂²	semidirect
71. C₆₁×#482	C₂²	semidirect
72. C₆₁×#481	C₂²	semidirect
73. C₆₁×#480	C₂²	semidirect
74. C₆₁×#479	C₂²	semidirect
75. C₆₁×#479	C₂²	semidirect
76. C₆₁×#477	C₂²	semidirect
77. C₆₁×#475	C₂²	semidirect
78. C₆₁×#469	C₂²	semidirect
79. C₆₁×#468	C₂²	semidirect
80. C₆₁×#467	C₂²	semidirect
81. C₆₁×#467	C₂²	semidirect
82. C₆₁×#466	C₂²	semidirect
83. C₆₁×#466	C₂²	semidirect
84. C₆₁×#466	C₂²	semidirect
85. C₆₁×#465	C₂²	semidirect
86. C₆₁×#465	C₂²	semidirect
87. C₆₁×#465	C₂²	semidirect
88. C₆₁×#465	C₂²	semidirect
89. C₆₁×#465	C₂²	semidirect
90. C₆₁×#464	C₂²	semidirect
91. C₆₁×#463	C₂²	semidirect
92. C₆₁×#460	C₂²	semidirect
93. C₆₁×#459	C₂²	semidirect
96. C₆₁×#452	C₂²	semidirect
97. C₆₁×#451	C₂²	semidirect
100. C₆₁×#449	C₂²	semidirect
101. C₆₁×#448	C₂²	semidirect
102. C₆₁×#441	C₂²	semidirect
103. C₆₁×#440	C₂²	semidirect
104. C₄×Q₁₆×C₆₁	C₂²	semidirect
105. C₄×SD₁₆×C₆₁	C₂²	semidirect
106. C₆₁×#435	C₂²	semidirect
107. C₆₁×#435	C₂²	semidirect
108. C₈×D₄×C₆₁	C₂²	semidirect
109. C₈×D₄×C₆₁	C₂²	semidirect
115. C₆₁×#419	C₂²	semidirect
119. C₆₁×#417	C₂²	semidirect
126. C₆₁×#416	C₂²	semidirect
129. C₂×#103×C₆₁	C₂²	semidirect
571. #61170	C₆₁	direct (N × H)
613. #3493	C₂×C₆₁	semidirect
614. #3487	C₂×C₆₁	semidirect
615. #3321	C₂×C₆₁	semidirect
616. #3317	C₂×C₆₁	semidirect
617. #3313	C₂×C₆₁	semidirect
618. #3309	C₂×C₆₁	semidirect
619. #3305	C₂×C₆₁	semidirect
620. #3304	C₂×C₆₁	semidirect
621. #3301	C₂×C₆₁	semidirect
622. #3300	C₂×C₆₁	semidirect
623. #3136	C₂×C₆₁	semidirect
624. #3096	C₂×C₆₁	semidirect
625. #3093	C₂×C₆₁	semidirect
626. #3082	C₂×C₆₁	semidirect
627. #3062	C₂×C₆₁	semidirect
628. #3050	C₂×C₆₁	semidirect
629. #3045	C₂×C₆₁	semidirect
630. #3013	C₂×C₆₁	semidirect
631. #3005	C₂×C₆₁	semidirect
632. #2947	C₂×C₆₁	semidirect
633. #2929	C₂×C₆₁	semidirect
634. #2898	C₂×C₆₁	semidirect
635. C₂×#416	C₂×C₆₁	semidirect
654. #556	C₂²×C₆₁	semidirect
656. #555	C₂²×C₆₁	semidirect
658. #553	C₂²×C₆₁	semidirect
660. #552	C₂²×C₆₁	semidirect
684. #490	C₂²×C₆₁	semidirect
685. #489	C₂²×C₆₁	semidirect
686. #488	C₂²×C₆₁	semidirect
687. #486	C₂²×C₆₁	semidirect
688. #485	C₂²×C₆₁	semidirect
689. #485	C₂²×C₆₁	semidirect
690. #482	C₂²×C₆₁	semidirect
691. #482	C₂²×C₆₁	semidirect
692. #482	C₂²×C₆₁	semidirect
693. #482	C₂²×C₆₁	semidirect
694. #481	C₂²×C₆₁	semidirect
695. #480	C₂²×C₆₁	semidirect
696. #479	C₂²×C₆₁	semidirect
697. #479	C₂²×C₆₁	semidirect
698. #477	C₂²×C₆₁	semidirect
699. #475	C₂²×C₆₁	semidirect
700. #469	C₂²×C₆₁	semidirect
701. #468	C₂²×C₆₁	semidirect
702. #467	C₂²×C₆₁	semidirect
703. #467	C₂²×C₆₁	semidirect
704. #466	C₂²×C₆₁	semidirect
705. #466	C₂²×C₆₁	semidirect
706. #466	C₂²×C₆₁	semidirect
707. #465	C₂²×C₆₁	semidirect
708. #465	C₂²×C₆₁	semidirect
709. #465	C₂²×C₆₁	semidirect
710. #465	C₂²×C₆₁	semidirect
711. #465	C₂²×C₆₁	semidirect
712. #464	C₂²×C₆₁	semidirect
713. #463	C₂²×C₆₁	semidirect
714. #460	C₂²×C₆₁	semidirect
715. #459	C₂²×C₆₁	semidirect
718. #452	C₂²×C₆₁	semidirect
719. #451	C₂²×C₆₁	semidirect
722. #449	C₂²×C₆₁	semidirect
723. #448	C₂²×C₆₁	semidirect
724. #441	C₂²×C₆₁	semidirect
725. #440	C₂²×C₆₁	semidirect
726. C₄×Q₁₆	C₂²×C₆₁	semidirect
727. C₄×SD₁₆	C₂²×C₆₁	semidirect
728. #435	C₂²×C₆₁	semidirect
729. #435	C₂²×C₆₁	semidirect
730. C₈×D₄	C₂²×C₆₁	semidirect
731. C₈×D₄	C₂²×C₆₁	semidirect
737. #419	C₂²×C₆₁	semidirect
741. #417	C₂²×C₆₁	semidirect
748. #416	C₂²×C₆₁	semidirect
751. C₂×#103	C₂²×C₆₁	semidirect
757. C₆₁	#61170	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×#3493	2
C₆₁×#3487	2
C₆₁×#3321	2
C₆₁×#3317	2
C₆₁×#3313	2
C₆₁×#3309	2
C₆₁×#3305	2
C₆₁×#3304	2
C₆₁×#3301	2
C₆₁×#3300	2
C₆₁×#3136	2
C₆₁×#3096	2
C₆₁×#3093	2
C₆₁×#3082	2
C₆₁×#3062	2
C₆₁×#3050	2
C₆₁×#3045	2
C₆₁×#3013	2
C₆₁×#3005	2
C₆₁×#2947	2
C₆₁×#2929	2
C₆₁×#2898	2
C₂×C₆₁×#416	2
#61170	61

Subgroups — C61×#61170 #29564603

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61170 #29564603