Subgroups — C₆₁×#60933 #29564366

Order 15616.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3260	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3259	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3258	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3257	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3256	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3251	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3250	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3247	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3084	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3083	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3080	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₆₁×#478	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3062	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3062	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3061	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#3060	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3045	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#3045	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3036	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#2906	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	1	yes	characteristic
26	C₂×#135×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#135×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
30	C₆₁×#553	—	2	2	no	—
31	C₆₁×#553	—	2	2	no	—
32	C₆₁×#553	—	2	1	no	—
33	C₆₁×#553	—	2	1	no	—
34	C₆₁×#552	—	2	1	no	—
35	C₆₁×#552	—	2	1	no	—
36	C₆₁×#544	C₂²	1	1	yes	characteristic
37	C₆₁×#542	—	2	1	no	—
38	C₆₁×#542	C₂²	1	2	yes	—
39	C₆₁×#541	C₂²	1	2	yes	complemented
40	C₆₁×#540	—	2	1	no	—
41	C₆₁×#540	C₂²	1	2	yes	—
42	C₆₁×#540	C₂²	1	2	yes	complemented
43	C₆₁×#538	—	2	2	no	—
44	C₆₁×#537	C₂²	1	1	yes	characteristic
45	C₆₁×#537	C₂²	1	1	yes	characteristic
46	C₆₁×#537	C₂²	1	1	yes	characteristic
47	C₆₁×#535	C₂²	1	1	yes	characteristic
48	C₆₁×#535	C₂²	1	1	yes	characteristic
49	C₆₁×#532	—	2	1	no	—
50	C₆₁×#532	C₂²	1	1	yes	characteristic
51	C₆₁×#532	C₂²	1	2	yes	—
52	C₆₁×#529	—	2	1	no	—
53	C₆₁×#529	C₂²	1	2	yes	—
54	C₆₁×#529	C₂²	1	2	yes	complemented
55	C₆₁×#529	C₂²	1	2	yes	complemented
56	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
57	C₆₁×#525	—	2	2	no	—
58	C₆₁×#520	C₂²	1	1	yes	characteristic
59	C₆₁×#520	C₂²	1	1	yes	characteristic
60	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
61	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
62	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
63	C₆₁×#479	C₂²	1	2	yes	complemented
64	C₆₁×#479	C₂²	1	2	yes	complemented
65	C₆₁×#479	C₂²	1	2	yes	complemented
66	C₆₁×#479	C₂²	1	2	yes	complemented
67	C₆₁×#478	C₂²	1	2	yes	—
68	C₆₁×#478	C₂²	1	2	yes	—
69	C₆₁×#478	C₂²	1	2	yes	—
70	C₆₁×#478	C₂²	1	2	yes	—
71	C₆₁×#478	C₂²	1	2	yes	complemented
72	C₆₁×#478	C₂²	1	2	yes	complemented
73	C₆₁×#478	C₂²	1	2	yes	complemented
74	C₆₁×#478	C₂²	1	2	yes	complemented
75	C₆₁×#477	C₂²	1	2	yes	complemented
76	C₆₁×#476	C₂²	1	2	yes	complemented
77	C₆₁×#475	C₂²	1	2	yes	complemented
78	C₆₁×#474	C₂²	1	2	yes	complemented
79	C₆₁×#470	C₂²	1	2	yes	complemented
80	C₆₁×#469	C₂²	1	2	yes	—
81	C₆₁×#469	C₂²	1	2	yes	—
82	C₆₁×#469	C₂²	1	2	yes	complemented
83	C₆₁×#468	C₂²	1	2	yes	—
84	C₆₁×#468	C₂²	1	2	yes	—
85	C₆₁×#468	C₂²	1	2	yes	complemented
86	C₆₁×#468	C₂²	1	2	yes	complemented
87	C₆₁×#467	C₂²	1	2	yes	complemented
88	C₆₁×#466	C₂²	1	2	yes	—
89	C₆₁×#466	C₂²	1	2	yes	—
90	C₆₁×#466	C₂²	1	2	yes	complemented
91	C₆₁×#465	C₂²	1	2	yes	—
92	C₆₁×#465	C₂²	1	2	yes	—
93	C₆₁×#465	C₂²	1	2	yes	complemented
94	C₆₁×#465	C₂²	1	2	yes	complemented
95	C₆₁×#464	C₂²	1	2	yes	—
96	C₆₁×#464	C₂²	1	2	yes	—
97	C₆₁×#464	C₂²	1	1	yes	characteristic, complemented
98	C₆₁×#464	C₂²	1	1	yes	characteristic, complemented
99	C₆₁×#463	C₂²	1	2	yes	—
100	C₆₁×#463	C₂²	1	2	yes	—
101	C₆₁×#463	C₂²	1	2	yes	—
102	C₆₁×#463	C₂²	1	2	yes	—
103	C₆₁×#463	C₂²	1	1	yes	characteristic, complemented
104	C₆₁×#463	C₂²	1	1	yes	characteristic, complemented
105	C₆₁×#462	C₂²	1	1	yes	characteristic, complemented
106	C₆₁×#461	C₂²	1	2	yes	—
107	C₆₁×#461	C₂²	1	1	yes	characteristic, complemented
108	C₆₁×#460	C₂²	1	2	yes	—
109	C₆₁×#460	C₂²	1	2	yes	—
110	C₆₁×#460	C₂²	1	1	yes	characteristic, complemented
111	C₆₁×#459	C₂²	1	2	yes	—
112	C₆₁×#459	C₂²	1	2	yes	—
113	C₆₁×#459	C₂²	1	2	yes	—
114	C₆₁×#459	C₂²	1	1	yes	characteristic, complemented
115	C₆₁×#428	C₂²	1	1	yes	characteristic
116	C₆₁×#428	C₂²	1	1	yes	characteristic
117	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
118	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
119	C₆₁×#424	C₂²	1	1	yes	characteristic
120	C₆₁×#424	C₂²	1	1	yes	characteristic
121	C₆₁×#424	C₂²	1	2	yes	complemented
122	C₆₁×#424	C₂²	1	2	yes	complemented
123	C₆₁×#423	C₂²	1	1	yes	characteristic
124	C₆₁×#423	C₂²	1	2	yes	complemented
125	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
126	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	complemented
127	C₆₁×#417	C₂²	1	1	yes	characteristic
128	C₆₁×#417	C₂²	1	1	yes	characteristic
129	C₆₁×#417	C₂²	1	1	yes	characteristic
130	C₆₁×#417	C₂²	1	1	yes	characteristic
131	C₆₁×#416	C₂²	1	1	yes	characteristic
132	C₆₁×#416	C₂²	1	1	yes	characteristic
133	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
134	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₁	—	2	2	no	—
136	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
137	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
138	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
139	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₆₁	—	2	1	no	—
142	AGL(1,ℤ/8)×C₆₁	—	4	2	no	—
143	AGL(1,ℤ/8)×C₆₁	—	4	2	no	—
144	#135×C₆₁	—	4	2	no	—
145	#135×C₆₁	—	4	2	no	—
146	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
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×D₈×C₆₁	C₂³	1	1	yes	characteristic
155	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
156	C₂×D₈×C₆₁	C₂³	1	2	yes	—
157	C₂×D₈×C₆₁	C₂³	1	2	yes	—
158	#131×C₆₁	—	4	2	no	—
159	#131×C₆₁	—	4	2	no	—
160	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
161	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
162	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
163	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
164	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
165	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
167	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
168	C₄⋊Q₈×C₆₁	—	2	1	no	—
169	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
171	#127×C₆₁	—	2	1	no	—
172	#127×C₆₁	C₂³	1	2	yes	—
173	#127×C₆₁	C₂³	1	1	yes	characteristic
174	#126×C₆₁	—	2	2	no	—
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	#125×C₆₁	—	2	1	no	—
181	#125×C₆₁	—	2	2	no	—
182	#125×C₆₁	—	2	2	no	—
183	#125×C₆₁	—	2	1	no	—
184	#125×C₆₁	—	2	1	no	—
185	#125×C₆₁	C₂³	1	2	yes	—
186	#125×C₆₁	C₂³	1	2	yes	—
187	#125×C₆₁	C₂³	1	2	yes	—
188	#124×C₆₁	—	2	1	no	—
189	#124×C₆₁	—	2	2	no	—
190	#124×C₆₁	—	2	2	no	—
191	#124×C₆₁	C₂³	1	1	yes	characteristic
192	#124×C₆₁	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
199	#123×C₆₁	—	2	2	no	—
200	#123×C₆₁	—	2	2	no	—
201	#123×C₆₁	—	2	2	no	—
202	C₂²⋊Q₈×C₆₁	—	2	1	no	—
203	C₂²⋊Q₈×C₆₁	—	2	1	no	—
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	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	2	no	—
215	#121×C₆₁	—	2	2	no	—
216	#121×C₆₁	—	2	2	no	—
217	#121×C₆₁	—	2	1	no	—
218	#121×C₆₁	—	2	1	no	—
219	#121×C₆₁	—	2	1	no	—
220	#121×C₆₁	—	2	1	no	—
221	#121×C₆₁	—	2	2	no	—
222	#121×C₆₁	—	2	2	no	—
223	#121×C₆₁	—	2	2	no	—
224	#121×C₆₁	—	2	2	no	—
225	#121×C₆₁	C₂³	1	2	yes	—
226	#121×C₆₁	C₂³	1	2	yes	—
227	#121×C₆₁	C₂³	1	2	yes	—
228	#121×C₆₁	C₂³	1	2	yes	—
229	#121×C₆₁	C₂³	1	2	yes	—
230	#120×C₆₁	—	2	2	no	—
231	#120×C₆₁	—	2	2	no	—
232	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
233	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
234	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
235	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
236	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₆₁	—	2	2	no	—
239	C₄×D₄×C₆₁	—	2	1	no	—
240	C₄×D₄×C₆₁	—	2	2	no	—
241	C₄×D₄×C₆₁	—	2	2	no	—
242	C₄×D₄×C₆₁	—	2	1	no	—
243	C₄×D₄×C₆₁	—	2	2	no	—
244	C₄×D₄×C₆₁	—	2	2	no	—
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	1	no	—
250	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
251	C₄×D₄×C₆₁	D₄	1	2	yes	—
252	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
253	C₄×D₄×C₆₁	D₄	1	2	yes	—
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	2	yes	—
258	C₄×D₄×C₆₁	C₂³	1	2	yes	—
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	2	no	—
264	#117×C₆₁	—	2	2	no	—
265	#117×C₆₁	—	2	2	no	—
266	#117×C₆₁	C₂³	1	1	yes	characteristic
267	#117×C₆₁	C₂³	1	1	yes	characteristic
268	#117×C₆₁	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
270	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
271	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
272	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
273	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
277	C₂×C₄²×C₆₁	—	2	1	no	—
278	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
279	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
280	#107×C₆₁	C₂³	1	2	yes	—
281	#107×C₆₁	C₂³	1	2	yes	—
282	#107×C₆₁	C₂³	1	2	yes	—
283	#107×C₆₁	C₂³	1	2	yes	—
284	#106×C₆₁	C₂³	1	2	yes	—
285	#106×C₆₁	C₂³	1	2	yes	—
286	#106×C₆₁	C₂³	1	2	yes	—
287	#106×C₆₁	C₂³	1	2	yes	—
288	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
289	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
290	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
291	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
292	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
293	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
294	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
295	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
296	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
297	C₄⋊C₈×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	1	yes	characteristic
302	#103×C₆₁	C₂³	1	2	yes	—
303	#103×C₆₁	C₂³	1	2	yes	—
304	#103×C₆₁	C₂³	1	2	yes	—
305	#103×C₆₁	C₂³	1	2	yes	—
306	#102×C₆₁	C₂³	1	2	yes	—
307	#102×C₆₁	C₂³	1	2	yes	—
308	#102×C₆₁	C₂³	1	2	yes	—
309	#102×C₆₁	C₂³	1	2	yes	—
310	#102×C₆₁	C₂³	1	1	yes	characteristic
311	#102×C₆₁	C₂³	1	1	yes	characteristic
312	#102×C₆₁	C₂³	1	1	yes	characteristic
313	#102×C₆₁	C₂³	1	1	yes	characteristic
314	#102×C₆₁	C₂³	1	2	yes	—
315	#102×C₆₁	C₂³	1	2	yes	—
316	#102×C₆₁	C₂³	1	2	yes	—
317	#102×C₆₁	C₂³	1	2	yes	—
318	C₂⁴×C₆₁	—	2	1	no	—
319	#41×C₆₁	—	2	2	no	—
320	#41×C₆₁	—	2	2	no	—
321	#41×C₆₁	—	2	2	no	—
322	#41×C₆₁	—	2	2	no	—
323	#41×C₆₁	—	2	2	no	—
324	#41×C₆₁	—	2	2	no	—
325	#41×C₆₁	—	2	2	no	—
326	#41×C₆₁	—	2	2	no	—
327	#41×C₆₁	—	8	4	no	—
328	C₂×Q₈×C₆₁	—	2	2	no	—
329	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₆₁	—	2	1	no	—
334	C₂×D₄×C₆₁	—	2	1	no	—
335	C₂×D₄×C₆₁	—	2	1	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	2	no	—
340	C₂×D₄×C₆₁	—	2	2	no	—
341	C₂×D₄×C₆₁	—	2	1	no	—
342	C₂×D₄×C₆₁	—	2	2	no	—
343	C₂×D₄×C₆₁	—	2	1	no	—
344	C₂×D₄×C₆₁	—	2	1	no	—
345	C₂×D₄×C₆₁	—	2	2	no	—
346	C₂×D₄×C₆₁	—	2	2	no	—
347	C₂×D₄×C₆₁	—	2	2	no	—
348	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
353	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₆₁	—	2	1	no	—
355	C₂²×C₄×C₆₁	—	2	1	no	—
356	C₂²×C₄×C₆₁	—	2	1	no	—
357	C₂²×C₄×C₆₁	—	2	1	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	2	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	—	8	2	no	—
367	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
370	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
371	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
372	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
373	Q₁₆×C₆₁	—	4	1	no	—
374	Q₁₆×C₆₁	—	4	1	no	—
375	SD₁₆×C₆₁	—	4	1	no	—
376	SD₁₆×C₆₁	—	4	1	no	—
377	SD₁₆×C₆₁	—	4	1	no	—
378	SD₁₆×C₆₁	—	4	1	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	D₈×C₆₁	—	4	2	no	—
385	M₁₆×C₆₁	—	2	2	no	—
386	M₁₆×C₆₁	—	2	2	no	—
387	M₁₆×C₆₁	—	4	2	no	—
388	M₁₆×C₆₁	—	4	2	no	—
389	C₂×C₈×C₆₁	—	2	2	no	—
390	C₂×C₈×C₆₁	—	2	2	no	—
391	C₂×C₈×C₆₁	—	4	2	no	—
392	C₂×C₈×C₆₁	—	4	2	no	—
393	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
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	2	yes	—
399	C₄⋊C₄×C₆₁	—	2	1	no	—
400	C₄⋊C₄×C₆₁	—	2	1	no	—
401	C₄⋊C₄×C₆₁	—	2	2	no	—
402	C₄⋊C₄×C₆₁	—	2	2	no	—
403	C₄⋊C₄×C₆₁	—	2	2	no	—
404	C₄⋊C₄×C₆₁	—	2	2	no	—
405	C₄⋊C₄×C₆₁	—	2	2	no	—
406	C₄⋊C₄×C₆₁	—	2	2	no	—
407	C₄⋊C₄×C₆₁	—	2	1	no	—
408	C₄⋊C₄×C₆₁	—	2	1	no	—
409	C₄⋊C₄×C₆₁	—	2	1	no	—
410	C₄⋊C₄×C₆₁	—	2	2	no	—
411	C₄⋊C₄×C₆₁	—	2	2	no	—
412	C₄⋊C₄×C₆₁	—	2	2	no	—
413	C₄⋊C₄×C₆₁	—	2	2	no	—
414	C₄⋊C₄×C₆₁	—	2	2	no	—
415	C₄⋊C₄×C₆₁	—	2	2	no	—
416	C₄⋊C₄×C₆₁	—	2	1	no	—
417	C₄⋊C₄×C₆₁	—	2	1	no	—
418	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
420	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
423	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
424	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
427	C₂²⋊C₄×C₆₁	—	2	1	no	—
428	C₂²⋊C₄×C₆₁	—	2	2	no	—
429	C₂²⋊C₄×C₆₁	—	2	2	no	—
430	C₂²⋊C₄×C₆₁	—	2	2	no	—
431	C₂²⋊C₄×C₆₁	—	2	2	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	1	no	—
436	C₂²⋊C₄×C₆₁	—	2	1	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	—	2	2	no	—
443	C₂²⋊C₄×C₆₁	—	2	1	no	—
444	C₂²⋊C₄×C₆₁	—	2	1	no	—
445	C₂²⋊C₄×C₆₁	—	2	2	no	—
446	C₂²⋊C₄×C₆₁	—	2	2	no	—
447	C₂²⋊C₄×C₆₁	—	2	2	no	—
448	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
451	C₄²×C₆₁	—	2	1	no	—
452	C₄²×C₆₁	—	2	1	no	—
453	C₄²×C₆₁	—	2	1	no	—
454	C₄²×C₆₁	—	2	2	no	—
455	C₄²×C₆₁	—	2	2	no	—
456	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₆₁	C₂×D₄	1	2	yes	—
458	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₆₁	C₂×D₄	1	2	yes	—
460	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
461	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
462	C₄²×C₆₁	C₂⁴	1	2	yes	—
463	C₂³×C₆₁	—	2	1	no	—
464	C₂³×C₆₁	—	2	1	no	—
465	C₂³×C₆₁	—	2	2	no	—
466	C₂³×C₆₁	—	2	1	no	—
467	C₂³×C₆₁	—	4	2	no	—
468	C₂³×C₆₁	—	8	1	no	—
469	C₂³×C₆₁	—	8	1	no	—
470	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
471	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
472	Q₈×C₆₁	—	2	2	no	—
473	Q₈×C₆₁	—	2	1	no	—
474	Q₈×C₆₁	—	2	1	no	—
475	Q₈×C₆₁	—	2	1	no	—
476	Q₈×C₆₁	—	2	1	no	—
477	Q₈×C₆₁	—	2	1	no	—
478	Q₈×C₆₁	—	2	1	no	—
479	Q₈×C₆₁	—	8	2	no	—
480	D₄×C₆₁	—	2	4	no	—
481	D₄×C₆₁	—	2	2	no	—
482	D₄×C₆₁	—	2	1	no	—
483	D₄×C₆₁	—	2	1	no	—
484	D₄×C₆₁	—	2	2	no	—
485	D₄×C₆₁	—	2	1	no	—
486	D₄×C₆₁	—	2	2	no	—
487	D₄×C₆₁	—	2	1	no	—
488	D₄×C₆₁	—	2	1	no	—
489	D₄×C₆₁	—	2	1	no	—
490	D₄×C₆₁	—	4	2	no	—
491	D₄×C₆₁	—	4	2	no	—
492	D₄×C₆₁	—	4	2	no	—
493	D₄×C₆₁	—	4	2	no	—
494	D₄×C₆₁	—	8	1	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	C₂×C₄×C₆₁	—	2	2	no	—
504	C₂×C₄×C₆₁	—	2	2	no	—
505	C₂×C₄×C₆₁	—	2	1	no	—
506	C₂×C₄×C₆₁	—	2	1	no	—
507	C₂×C₄×C₆₁	—	2	1	no	—
508	C₂×C₄×C₆₁	—	2	1	no	—
509	C₂×C₄×C₆₁	—	2	1	no	—
510	C₂×C₄×C₆₁	—	2	2	no	—
511	C₂×C₄×C₆₁	—	2	2	no	—
512	C₂×C₄×C₆₁	—	2	2	no	—
513	C₂×C₄×C₆₁	—	4	1	no	—
514	C₂×C₄×C₆₁	—	4	1	no	—
515	C₂×C₄×C₆₁	—	4	2	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	—	4	2	no	—
522	C₂×C₄×C₆₁	—	8	2	no	—
523	C₂×C₄×C₆₁	—	8	1	no	—
524	C₂×C₄×C₆₁	—	8	2	no	—
525	C₂×C₄×C₆₁	—	8	2	no	—
526	C₂×C₄×C₆₁	—	8	1	no	—
527	C₂×C₄×C₆₁	—	8	1	no	—
528	C₂×C₄×C₆₁	—	8	1	no	—
529	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
535	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
538	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
539	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
540	C₈×C₆₁	—	2	1	no	—
541	C₈×C₆₁	—	2	1	no	—
542	C₈×C₆₁	—	2	1	no	—
543	C₈×C₆₁	—	2	1	no	—
544	C₈×C₆₁	—	2	2	no	—
545	C₈×C₆₁	—	2	2	no	—
546	#60933	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
547	C₂²×C₆₁	—	2	1	no	—
548	C₂²×C₆₁	—	2	1	no	—
549	C₂²×C₆₁	—	2	2	no	—
550	C₂²×C₆₁	—	2	2	no	—
551	C₂²×C₆₁	—	2	2	no	—
552	C₂²×C₆₁	—	4	1	no	—
553	C₂²×C₆₁	—	4	1	no	—
554	C₂²×C₆₁	—	4	1	no	—
555	C₂²×C₆₁	—	4	2	no	—
556	C₂²×C₆₁	—	4	2	no	—
557	C₂²×C₆₁	—	4	1	no	—
558	C₂²×C₆₁	—	4	1	no	—
559	C₂²×C₆₁	—	4	1	no	—
560	C₂²×C₆₁	—	4	1	no	—
561	C₂²×C₆₁	—	4	1	no	—
562	C₂²×C₆₁	—	4	1	no	—
563	C₂²×C₆₁	—	4	2	no	—
564	C₂²×C₆₁	—	8	4	no	—
565	C₂²×C₆₁	#537	1	2	yes	—
566	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
567	C₄×C₆₁	—	2	1	no	—
568	C₄×C₆₁	—	2	1	no	—
569	C₄×C₆₁	—	2	2	no	—
570	C₄×C₆₁	—	2	1	no	—
571	C₄×C₆₁	—	2	1	no	—
572	C₄×C₆₁	—	2	2	no	—
573	C₄×C₆₁	—	2	2	no	—
574	C₄×C₆₁	—	4	2	no	—
575	C₄×C₆₁	—	4	1	no	—
576	C₄×C₆₁	—	4	2	no	—
577	C₄×C₆₁	—	4	1	no	—
578	C₄×C₆₁	—	4	2	no	—
579	C₄×C₆₁	—	4	1	no	—
580	C₄×C₆₁	—	4	1	no	—
581	C₄×C₆₁	—	4	1	no	—
582	C₄×C₆₁	#537	1	2	yes	—
583	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
584	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
585	#3512	C₂×C₆₁	1	1	yes	characteristic, complemented
586	#3460	C₂×C₆₁	1	1	yes	characteristic, complemented
587	#3260	C₂×C₆₁	1	2	yes	complemented
588	#3259	C₂×C₆₁	1	2	yes	complemented
589	#3258	C₂×C₆₁	1	2	yes	complemented
590	#3257	C₂×C₆₁	1	2	yes	complemented
591	#3256	C₂×C₆₁	1	2	yes	complemented
592	#3251	C₂×C₆₁	1	2	yes	complemented
593	#3250	C₂×C₆₁	1	2	yes	complemented
594	#3247	C₂×C₆₁	1	2	yes	complemented
595	#3084	C₂×C₆₁	1	1	yes	characteristic, complemented
596	#3083	C₂×C₆₁	1	1	yes	characteristic, complemented
597	#3080	C₂×C₆₁	1	1	yes	characteristic, complemented
598	C₂×#478	C₂×C₆₁	1	1	yes	characteristic, complemented
599	#3062	C₂×C₆₁	1	1	yes	characteristic, complemented
600	#3062	C₂×C₆₁	1	1	yes	characteristic, complemented
601	#3061	C₂×C₆₁	1	1	yes	characteristic, complemented
602	#3060	C₂×C₆₁	1	1	yes	characteristic, complemented
603	#3045	C₂×C₆₁	1	1	yes	characteristic, complemented
604	#3045	C₂×C₆₁	1	1	yes	characteristic, complemented
605	#3036	C₂×C₆₁	1	1	yes	characteristic, complemented
606	#3035	C₂×C₆₁	1	1	yes	characteristic, complemented
607	#2906	C₂×C₆₁	1	1	yes	characteristic, complemented
608	C₂×C₆₁	—	2	2	no	—
609	C₂×C₆₁	—	4	2	no	—
610	C₂×C₆₁	—	8	1	no	—
611	C₂×C₆₁	—	8	1	no	—
612	C₂×C₆₁	—	8	1	no	—
613	C₂×C₆₁	—	8	2	no	—
614	C₂×C₆₁	C₂×#537	1	1	yes	characteristic
615	C₂×C₆₁	#3584	1	1	yes	characteristic
616	C₂×C₆₁	#3585	1	1	yes	characteristic
617	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
618	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
619	C₂×#135	C₂²×C₆₁	1	1	yes	characteristic
620	C₂×#135	C₂²×C₆₁	1	1	yes	characteristic
621	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
622	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
623	#553	—	2	2	no	—
624	#553	—	2	2	no	—
625	#553	—	2	1	no	—
626	#553	—	2	1	no	—
627	#552	—	2	1	no	—
628	#552	—	2	1	no	—
629	#544	C₂²×C₆₁	1	1	yes	characteristic
630	#542	—	2	1	no	—
631	#542	C₂²×C₆₁	1	2	yes	—
632	#541	C₂²×C₆₁	1	2	yes	complemented
633	#540	—	2	1	no	—
634	#540	C₂²×C₆₁	1	2	yes	—
635	#540	C₂²×C₆₁	1	2	yes	complemented
636	#538	—	2	2	no	—
637	#537	C₂²×C₆₁	1	1	yes	characteristic
638	#537	C₂²×C₆₁	1	1	yes	characteristic
639	#537	C₂²×C₆₁	1	1	yes	characteristic
640	#535	C₂²×C₆₁	1	1	yes	characteristic
641	#535	C₂²×C₆₁	1	1	yes	characteristic
642	#532	—	2	1	no	—
643	#532	C₂²×C₆₁	1	1	yes	characteristic
644	#532	C₂²×C₆₁	1	2	yes	—
645	#529	—	2	1	no	—
646	#529	C₂²×C₆₁	1	2	yes	—
647	#529	C₂²×C₆₁	1	2	yes	complemented
648	#529	C₂²×C₆₁	1	2	yes	complemented
649	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
650	#525	—	2	2	no	—
651	#520	C₂²×C₆₁	1	1	yes	characteristic
652	#520	C₂²×C₆₁	1	1	yes	characteristic
653	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
654	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
655	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
656	#479	C₂²×C₆₁	1	2	yes	complemented
657	#479	C₂²×C₆₁	1	2	yes	complemented
658	#479	C₂²×C₆₁	1	2	yes	complemented
659	#479	C₂²×C₆₁	1	2	yes	complemented
660	#478	C₂²×C₆₁	1	2	yes	—
661	#478	C₂²×C₆₁	1	2	yes	—
662	#478	C₂²×C₆₁	1	2	yes	—
663	#478	C₂²×C₆₁	1	2	yes	—
664	#478	C₂²×C₆₁	1	2	yes	complemented
665	#478	C₂²×C₆₁	1	2	yes	complemented
666	#478	C₂²×C₆₁	1	2	yes	complemented
667	#478	C₂²×C₆₁	1	2	yes	complemented
668	#477	C₂²×C₆₁	1	2	yes	complemented
669	#476	C₂²×C₆₁	1	2	yes	complemented
670	#475	C₂²×C₆₁	1	2	yes	complemented
671	#474	C₂²×C₆₁	1	2	yes	complemented
672	#470	C₂²×C₆₁	1	2	yes	complemented
673	#469	C₂²×C₆₁	1	2	yes	—
674	#469	C₂²×C₆₁	1	2	yes	—
675	#469	C₂²×C₆₁	1	2	yes	complemented
676	#468	C₂²×C₆₁	1	2	yes	—
677	#468	C₂²×C₆₁	1	2	yes	—
678	#468	C₂²×C₆₁	1	2	yes	complemented
679	#468	C₂²×C₆₁	1	2	yes	complemented
680	#467	C₂²×C₆₁	1	2	yes	complemented
681	#466	C₂²×C₆₁	1	2	yes	—
682	#466	C₂²×C₆₁	1	2	yes	—
683	#466	C₂²×C₆₁	1	2	yes	complemented
684	#465	C₂²×C₆₁	1	2	yes	—
685	#465	C₂²×C₆₁	1	2	yes	—
686	#465	C₂²×C₆₁	1	2	yes	complemented
687	#465	C₂²×C₆₁	1	2	yes	complemented
688	#464	C₂²×C₆₁	1	2	yes	—
689	#464	C₂²×C₆₁	1	2	yes	—
690	#464	C₂²×C₆₁	1	1	yes	characteristic, complemented
691	#464	C₂²×C₆₁	1	1	yes	characteristic, complemented
692	#463	C₂²×C₆₁	1	2	yes	—
693	#463	C₂²×C₆₁	1	2	yes	—
694	#463	C₂²×C₆₁	1	2	yes	—
695	#463	C₂²×C₆₁	1	2	yes	—
696	#463	C₂²×C₆₁	1	1	yes	characteristic, complemented
697	#463	C₂²×C₆₁	1	1	yes	characteristic, complemented
698	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
699	#461	C₂²×C₆₁	1	2	yes	—
700	#461	C₂²×C₆₁	1	1	yes	characteristic, complemented
701	#460	C₂²×C₆₁	1	2	yes	—
702	#460	C₂²×C₆₁	1	2	yes	—
703	#460	C₂²×C₆₁	1	1	yes	characteristic, complemented
704	#459	C₂²×C₆₁	1	2	yes	—
705	#459	C₂²×C₆₁	1	2	yes	—
706	#459	C₂²×C₆₁	1	2	yes	—
707	#459	C₂²×C₆₁	1	1	yes	characteristic, complemented
708	#428	C₂²×C₆₁	1	1	yes	characteristic
709	#428	C₂²×C₆₁	1	1	yes	characteristic
710	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
711	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
712	#424	C₂²×C₆₁	1	1	yes	characteristic
713	#424	C₂²×C₆₁	1	1	yes	characteristic
714	#424	C₂²×C₆₁	1	2	yes	complemented
715	#424	C₂²×C₆₁	1	2	yes	complemented
716	#423	C₂²×C₆₁	1	1	yes	characteristic
717	#423	C₂²×C₆₁	1	2	yes	complemented
718	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
719	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	complemented
720	#417	C₂²×C₆₁	1	1	yes	characteristic
721	#417	C₂²×C₆₁	1	1	yes	characteristic
722	#417	C₂²×C₆₁	1	1	yes	characteristic
723	#417	C₂²×C₆₁	1	1	yes	characteristic
724	#416	C₂²×C₆₁	1	1	yes	characteristic
725	#416	C₂²×C₆₁	1	1	yes	characteristic
726	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
727	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
728	C₆₁	#60933	1	1	yes	characteristic, direct product factor, Sylow
729	C₂×#41	—	2	2	no	—
730	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
731	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
732	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
733	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
734	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
735	C₂³×C₄	—	2	1	no	—
736	AGL(1,ℤ/8)	—	4	2	no	—
737	AGL(1,ℤ/8)	—	4	2	no	—
738	#135	—	4	2	no	—
739	#135	—	4	2	no	—
740	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
741	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
742	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
743	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
744	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
745	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
746	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
747	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
748	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
749	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
750	C₂×D₈	C₂³×C₆₁	1	2	yes	—
751	C₂×D₈	C₂³×C₆₁	1	2	yes	—
752	#131	—	4	2	no	—
753	#131	—	4	2	no	—
754	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
755	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
756	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
757	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
758	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
759	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
760	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
761	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
762	C₄⋊Q₈	—	2	1	no	—
763	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
764	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
765	#127	—	2	1	no	—
766	#127	C₂³×C₆₁	1	2	yes	—
767	#127	C₂³×C₆₁	1	1	yes	characteristic
768	#126	—	2	2	no	—
769	#126	—	2	2	no	—
770	#126	—	2	2	no	—
771	#126	—	2	2	no	—
772	#126	—	2	2	no	—
773	#126	—	2	2	no	—
774	#125	—	2	1	no	—
775	#125	—	2	2	no	—
776	#125	—	2	2	no	—
777	#125	—	2	1	no	—
778	#125	—	2	1	no	—
779	#125	C₂³×C₆₁	1	2	yes	—
780	#125	C₂³×C₆₁	1	2	yes	—
781	#125	C₂³×C₆₁	1	2	yes	—
782	#124	—	2	1	no	—
783	#124	—	2	2	no	—
784	#124	—	2	2	no	—
785	#124	C₂³×C₆₁	1	2	yes	—
786	#124	C₂³×C₆₁	1	1	yes	characteristic
787	#124	C₂³×C₆₁	1	1	yes	characteristic
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	#123	—	2	2	no	—
792	#123	—	2	2	no	—
793	#123	—	2	2	no	—
794	#123	—	2	2	no	—
795	#123	—	2	2	no	—
796	C₂²⋊Q₈	—	2	1	no	—
797	C₂²⋊Q₈	—	2	1	no	—
798	C₂²⋊Q₈	—	2	1	no	—
799	C₂²⋊Q₈	—	2	2	no	—
800	C₂²⋊Q₈	—	2	2	no	—
801	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
802	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
803	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
804	#121	—	2	2	no	—
805	#121	—	2	1	no	—
806	#121	—	2	1	no	—
807	#121	—	2	1	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	—	2	1	no	—
812	#121	—	2	1	no	—
813	#121	—	2	1	no	—
814	#121	—	2	1	no	—
815	#121	—	2	2	no	—
816	#121	—	2	2	no	—
817	#121	—	2	2	no	—
818	#121	—	2	2	no	—
819	#121	C₂³×C₆₁	1	2	yes	—
820	#121	C₂³×C₆₁	1	2	yes	—
821	#121	C₂³×C₆₁	1	2	yes	—
822	#121	C₂³×C₆₁	1	2	yes	—
823	#121	C₂³×C₆₁	1	2	yes	—
824	#120	—	2	2	no	—
825	#120	—	2	2	no	—
826	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
827	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
828	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
829	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
830	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
831	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	1	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	2	no	—
839	C₄×D₄	—	2	1	no	—
840	C₄×D₄	—	2	1	no	—
841	C₄×D₄	—	2	2	no	—
842	C₄×D₄	—	2	1	no	—
843	C₄×D₄	—	2	1	no	—
844	C₄×D₄	D₄×C₆₁	1	2	yes	—
845	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
846	C₄×D₄	D₄×C₆₁	1	2	yes	—
847	C₄×D₄	D₄×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	1	yes	characteristic
851	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
852	C₄×D₄	C₂³×C₆₁	1	2	yes	—
853	C₄×D₄	C₂³×C₆₁	1	2	yes	—
854	#117	—	2	1	no	—
855	#117	—	2	1	no	—
856	#117	—	2	1	no	—
857	#117	—	2	2	no	—
858	#117	—	2	2	no	—
859	#117	—	2	2	no	—
860	#117	C₂³×C₆₁	1	1	yes	characteristic
861	#117	C₂³×C₆₁	1	1	yes	characteristic
862	#117	C₂³×C₆₁	1	2	yes	—
863	C₂×C₄⋊C₄	—	2	1	no	—
864	C₂×C₄⋊C₄	—	2	1	no	—
865	C₂×C₄⋊C₄	—	2	1	no	—
866	C₂×C₄⋊C₄	—	2	1	no	—
867	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
868	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
869	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
870	C₂×C₂²⋊C₄	—	2	1	no	—
871	C₂×C₄²	—	2	1	no	—
872	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
873	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
874	#107	C₂³×C₆₁	1	2	yes	—
875	#107	C₂³×C₆₁	1	2	yes	—
876	#107	C₂³×C₆₁	1	2	yes	—
877	#107	C₂³×C₆₁	1	2	yes	—
878	#106	C₂³×C₆₁	1	2	yes	—
879	#106	C₂³×C₆₁	1	2	yes	—
880	#106	C₂³×C₆₁	1	2	yes	—
881	#106	C₂³×C₆₁	1	2	yes	—
882	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
883	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
884	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
885	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
886	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
887	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
888	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
889	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
890	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
891	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
892	#103	C₂³×C₆₁	1	1	yes	characteristic
893	#103	C₂³×C₆₁	1	1	yes	characteristic
894	#103	C₂³×C₆₁	1	1	yes	characteristic
895	#103	C₂³×C₆₁	1	1	yes	characteristic
896	#103	C₂³×C₆₁	1	2	yes	—
897	#103	C₂³×C₆₁	1	2	yes	—
898	#103	C₂³×C₆₁	1	2	yes	—
899	#103	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	#102	C₂³×C₆₁	1	1	yes	characteristic
905	#102	C₂³×C₆₁	1	1	yes	characteristic
906	#102	C₂³×C₆₁	1	1	yes	characteristic
907	#102	C₂³×C₆₁	1	1	yes	characteristic
908	#102	C₂³×C₆₁	1	2	yes	—
909	#102	C₂³×C₆₁	1	2	yes	—
910	#102	C₂³×C₆₁	1	2	yes	—
911	#102	C₂³×C₆₁	1	2	yes	—
912	C₂⁴	—	2	1	no	—
913	#41	—	2	2	no	—
914	#41	—	2	2	no	—
915	#41	—	2	2	no	—
916	#41	—	2	2	no	—
917	#41	—	2	2	no	—
918	#41	—	2	2	no	—
919	#41	—	2	2	no	—
920	#41	—	2	2	no	—
921	#41	—	8	4	no	—
922	C₂×Q₈	—	2	2	no	—
923	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
924	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
925	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
926	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
943	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
944	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
945	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
946	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
947	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	1	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	8	2	no	—
961	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
962	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
963	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
964	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
965	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
966	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
967	Q₁₆	—	4	1	no	—
968	Q₁₆	—	4	1	no	—
969	SD₁₆	—	4	1	no	—
970	SD₁₆	—	4	1	no	—
971	SD₁₆	—	4	1	no	—
972	SD₁₆	—	4	1	no	—
973	SD₁₆	—	4	2	no	—
974	SD₁₆	—	4	2	no	—
975	D₈	—	4	1	no	—
976	D₈	—	4	1	no	—
977	D₈	—	4	2	no	—
978	D₈	—	4	2	no	—
979	M₁₆	—	2	2	no	—
980	M₁₆	—	2	2	no	—
981	M₁₆	—	4	2	no	—
982	M₁₆	—	4	2	no	—
983	C₂×C₈	—	2	2	no	—
984	C₂×C₈	—	2	2	no	—
985	C₂×C₈	—	4	2	no	—
986	C₂×C₈	—	4	2	no	—
987	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
988	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
989	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
990	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
991	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
992	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	1	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1013	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1014	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1015	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1016	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1017	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1018	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1019	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1020	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	1	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	1	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	C₄²	—	2	1	no	—
1046	C₄²	—	2	1	no	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	2	2	no	—
1049	C₄²	—	2	2	no	—
1050	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1051	C₄²	C₂×D₄×C₆₁	1	2	yes	—
1052	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1053	C₄²	C₂×D₄×C₆₁	1	2	yes	—
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	—	4	2	no	—
1062	C₂³	—	8	1	no	—
1063	C₂³	—	8	1	no	—
1064	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1065	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1066	Q₈	—	2	2	no	—
1067	Q₈	—	2	1	no	—
1068	Q₈	—	2	1	no	—
1069	Q₈	—	2	1	no	—
1070	Q₈	—	2	1	no	—
1071	Q₈	—	2	1	no	—
1072	Q₈	—	2	1	no	—
1073	Q₈	—	8	2	no	—
1074	D₄	—	2	4	no	—
1075	D₄	—	2	2	no	—
1076	D₄	—	2	1	no	—
1077	D₄	—	2	1	no	—
1078	D₄	—	2	2	no	—
1079	D₄	—	2	1	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	1	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	4	2	no	—
1085	D₄	—	4	2	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	4	2	no	—
1088	D₄	—	8	1	no	—
1089	D₄	—	8	2	no	—
1090	D₄	—	8	1	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	2	no	—
1093	D₄	—	8	2	no	—
1094	D₄	—	8	2	no	—
1095	D₄	—	8	2	no	—
1096	D₄	—	8	2	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	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	4	1	no	—
1108	C₂×C₄	—	4	1	no	—
1109	C₂×C₄	—	4	2	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	4	4	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	4	2	no	—
1114	C₂×C₄	—	4	2	no	—
1115	C₂×C₄	—	4	2	no	—
1116	C₂×C₄	—	8	2	no	—
1117	C₂×C₄	—	8	1	no	—
1118	C₂×C₄	—	8	2	no	—
1119	C₂×C₄	—	8	2	no	—
1120	C₂×C₄	—	8	1	no	—
1121	C₂×C₄	—	8	1	no	—
1122	C₂×C₄	—	8	1	no	—
1123	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1124	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1125	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1126	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1127	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1128	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1129	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1130	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1131	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
1132	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
1133	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1134	C₈	—	2	1	no	—
1135	C₈	—	2	1	no	—
1136	C₈	—	2	1	no	—
1137	C₈	—	2	1	no	—
1138	C₈	—	2	2	no	—
1139	C₈	—	2	2	no	—
1140	C₂²	—	2	1	no	—
1141	C₂²	—	2	1	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	2	no	—
1150	C₂²	—	4	1	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	1	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	4	1	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	2	no	—
1157	C₂²	—	8	4	no	—
1158	C₂²	C₆₁×#537	1	2	yes	—
1159	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1160	C₄	—	2	1	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	1	no	—
1164	C₄	—	2	1	no	—
1165	C₄	—	2	2	no	—
1166	C₄	—	2	2	no	—
1167	C₄	—	4	2	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	2	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	2	no	—
1172	C₄	—	4	1	no	—
1173	C₄	—	4	1	no	—
1174	C₄	—	4	1	no	—
1175	C₄	C₆₁×#537	1	2	yes	—
1176	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1177	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1178	C₂	—	2	2	no	—
1179	C₂	—	4	2	no	—
1180	C₂	—	8	2	no	—
1181	C₂	—	8	1	no	—
1182	C₂	—	8	1	no	—
1183	C₂	—	8	1	no	—
1184	C₂	C₂×C₆₁×#537	1	1	yes	characteristic
1185	C₂	C₆₁×#3584	1	1	yes	characteristic
1186	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 ◁ C₄×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3512	C₂	semidirect
2. C₆₁×#3460	C₂	semidirect
3. C₆₁×#3260	C₂	semidirect
4. C₆₁×#3259	C₂	semidirect
5. C₆₁×#3258	C₂	semidirect
6. C₆₁×#3257	C₂	semidirect
7. C₆₁×#3256	C₂	semidirect
8. C₆₁×#3251	C₂	semidirect
9. C₆₁×#3250	C₂	semidirect
10. C₆₁×#3247	C₂	semidirect
11. C₆₁×#3084	C₂	semidirect
12. C₆₁×#3083	C₂	semidirect
13. C₆₁×#3080	C₂	semidirect
14. C₂×C₆₁×#478	C₂	semidirect
15. C₆₁×#3062	C₂	semidirect
16. C₆₁×#3062	C₂	semidirect
17. C₆₁×#3061	C₂	semidirect
18. C₆₁×#3060	C₂	semidirect
19. C₆₁×#3045	C₂	semidirect
20. C₆₁×#3045	C₂	semidirect
21. C₆₁×#3036	C₂	semidirect
22. C₆₁×#3035	C₂	semidirect
23. C₆₁×#2906	C₂	semidirect
39. C₆₁×#541	C₂²	semidirect
42. C₆₁×#540	C₂²	semidirect
54. C₆₁×#529	C₂²	semidirect
55. C₆₁×#529	C₂²	semidirect
63. C₆₁×#479	C₂²	semidirect
64. C₆₁×#479	C₂²	semidirect
65. C₆₁×#479	C₂²	semidirect
66. C₆₁×#479	C₂²	semidirect
71. C₆₁×#478	C₂²	semidirect
72. C₆₁×#478	C₂²	semidirect
73. C₆₁×#478	C₂²	semidirect
74. C₆₁×#478	C₂²	semidirect
75. C₆₁×#477	C₂²	semidirect
76. C₆₁×#476	C₂²	semidirect
77. C₆₁×#475	C₂²	semidirect
78. C₆₁×#474	C₂²	semidirect
79. C₆₁×#470	C₂²	semidirect
82. C₆₁×#469	C₂²	semidirect
85. C₆₁×#468	C₂²	semidirect
86. C₆₁×#468	C₂²	semidirect
87. C₆₁×#467	C₂²	semidirect
90. C₆₁×#466	C₂²	semidirect
93. C₆₁×#465	C₂²	semidirect
94. C₆₁×#465	C₂²	semidirect
97. C₆₁×#464	C₂²	semidirect
98. C₆₁×#464	C₂²	semidirect
103. C₆₁×#463	C₂²	semidirect
104. C₆₁×#463	C₂²	semidirect
105. C₆₁×#462	C₂²	semidirect
107. C₆₁×#461	C₂²	semidirect
110. C₆₁×#460	C₂²	semidirect
114. C₆₁×#459	C₂²	semidirect
121. C₆₁×#424	C₂²	semidirect
122. C₆₁×#424	C₂²	semidirect
124. C₆₁×#423	C₂²	semidirect
126. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
546. #60933	C₆₁	direct (N × H)
585. #3512	C₂×C₆₁	semidirect
586. #3460	C₂×C₆₁	semidirect
587. #3260	C₂×C₆₁	semidirect
588. #3259	C₂×C₆₁	semidirect
589. #3258	C₂×C₆₁	semidirect
590. #3257	C₂×C₆₁	semidirect
591. #3256	C₂×C₆₁	semidirect
592. #3251	C₂×C₆₁	semidirect
593. #3250	C₂×C₆₁	semidirect
594. #3247	C₂×C₆₁	semidirect
595. #3084	C₂×C₆₁	semidirect
596. #3083	C₂×C₆₁	semidirect
597. #3080	C₂×C₆₁	semidirect
598. C₂×#478	C₂×C₆₁	semidirect
599. #3062	C₂×C₆₁	semidirect
600. #3062	C₂×C₆₁	semidirect
601. #3061	C₂×C₆₁	semidirect
602. #3060	C₂×C₆₁	semidirect
603. #3045	C₂×C₆₁	semidirect
604. #3045	C₂×C₆₁	semidirect
605. #3036	C₂×C₆₁	semidirect
606. #3035	C₂×C₆₁	semidirect
607. #2906	C₂×C₆₁	semidirect
632. #541	C₂²×C₆₁	semidirect
635. #540	C₂²×C₆₁	semidirect
647. #529	C₂²×C₆₁	semidirect
648. #529	C₂²×C₆₁	semidirect
656. #479	C₂²×C₆₁	semidirect
657. #479	C₂²×C₆₁	semidirect
658. #479	C₂²×C₆₁	semidirect
659. #479	C₂²×C₆₁	semidirect
664. #478	C₂²×C₆₁	semidirect
665. #478	C₂²×C₆₁	semidirect
666. #478	C₂²×C₆₁	semidirect
667. #478	C₂²×C₆₁	semidirect
668. #477	C₂²×C₆₁	semidirect
669. #476	C₂²×C₆₁	semidirect
670. #475	C₂²×C₆₁	semidirect
671. #474	C₂²×C₆₁	semidirect
672. #470	C₂²×C₆₁	semidirect
675. #469	C₂²×C₆₁	semidirect
678. #468	C₂²×C₆₁	semidirect
679. #468	C₂²×C₆₁	semidirect
680. #467	C₂²×C₆₁	semidirect
683. #466	C₂²×C₆₁	semidirect
686. #465	C₂²×C₆₁	semidirect
687. #465	C₂²×C₆₁	semidirect
690. #464	C₂²×C₆₁	semidirect
691. #464	C₂²×C₆₁	semidirect
696. #463	C₂²×C₆₁	semidirect
697. #463	C₂²×C₆₁	semidirect
698. #462	C₂²×C₆₁	semidirect
700. #461	C₂²×C₆₁	semidirect
703. #460	C₂²×C₆₁	semidirect
707. #459	C₂²×C₆₁	semidirect
714. #424	C₂²×C₆₁	semidirect
715. #424	C₂²×C₆₁	semidirect
717. #423	C₂²×C₆₁	semidirect
719. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
728. C₆₁	#60933	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×#3512	2
C₆₁×#3460	2
C₆₁×#3260	2
C₆₁×#3259	2
C₆₁×#3258	2
C₆₁×#3257	2
C₆₁×#3256	2
C₆₁×#3251	2
C₆₁×#3250	2
C₆₁×#3247	2
C₆₁×#3084	2
C₆₁×#3083	2
C₆₁×#3080	2
C₂×C₆₁×#478	2
C₆₁×#3062	2
C₆₁×#3061	2
C₆₁×#3060	2
C₆₁×#3045	2
C₆₁×#3036	2
C₆₁×#3035	2
C₆₁×#2906	2
#60933	61

Subgroups — C61×#60933 #29564366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#60933 #29564366