Subgroups — C₆₁×#62033 #29565466

Order 15616.

1896 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×#3543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3515	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3392	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3323	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3310	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3295	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3284	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3272	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3267	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3260	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3252	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3222	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3119	C₂	1	2	yes	maximal, complemented
20	C₆₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3045	C₂	1	2	yes	maximal, complemented
22	C₆₁×#3038	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	complemented
25	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	complemented
26	C₂×#135×C₆₁	C₂²	1	2	yes	complemented
27	C₆₁×#560	—	2	2	no	—
28	C₆₁×#559	C₂²	1	1	yes	characteristic
29	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
30	C₆₁×#554	C₂²	1	1	yes	characteristic, complemented
31	C₆₁×#554	C₂²	1	1	yes	characteristic, complemented
32	C₆₁×#553	—	2	1	no	—
33	C₆₁×#552	—	2	2	no	—
34	C₆₁×#552	—	2	1	no	—
35	C₆₁×#552	C₂²	1	2	yes	complemented
36	C₆₁×#550	C₂²	1	1	yes	characteristic
37	C₆₁×#550	C₂²	1	1	yes	characteristic
38	C₆₁×#547	C₂²	1	2	yes	complemented
39	C₆₁×#547	C₂²	1	1	yes	characteristic, complemented
40	C₆₁×#546	—	2	1	no	—
41	C₆₁×#546	C₂²	1	2	yes	—
42	D₄²×C₆₁	—	2	1	no	—
43	D₄²×C₆₁	C₂²	1	1	yes	characteristic
44	D₄²×C₆₁	C₂²	1	2	yes	—
45	C₆₁×#541	C₂²	1	2	yes	complemented
46	C₆₁×#540	—	2	1	no	—
47	C₆₁×#540	C₂²	1	2	yes	—
48	C₆₁×#539	—	2	2	no	—
49	C₆₁×#535	—	2	1	no	—
50	C₆₁×#535	C₂²	1	2	yes	—
51	C₆₁×#534	—	2	2	no	—
52	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
53	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
54	C₆₁×#529	—	2	1	no	—
55	C₆₁×#529	C₂²	1	1	yes	characteristic
56	C₆₁×#529	C₂²	1	1	yes	characteristic
57	C₂×#125×C₆₁	—	2	1	no	—
58	C₆₁×#520	C₂²	1	2	yes	complemented
59	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic, complemented
60	C₆₁×#497	C₂²	1	2	yes	complemented
61	C₆₁×#492	C₂²	1	1	yes	characteristic
62	C₆₁×#492	C₂²	1	1	yes	characteristic, complemented
63	C₆₁×#492	C₂²	1	2	yes	complemented
64	C₆₁×#490	C₂²	1	2	yes	complemented
65	C₆₁×#488	C₂²	1	2	yes	complemented
66	C₆₁×#486	C₂²	1	1	yes	characteristic
67	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
68	C₆₁×#485	C₂²	1	1	yes	characteristic, complemented
69	C₆₁×#482	C₂²	1	1	yes	characteristic
70	C₆₁×#481	C₂²	1	2	yes	complemented
71	C₆₁×#480	C₂²	1	2	yes	complemented
72	C₆₁×#479	C₂²	1	1	yes	characteristic, complemented
73	C₆₁×#479	C₂²	1	2	yes	complemented
74	C₆₁×#478	C₂²	1	2	yes	complemented
75	C₆₁×#478	C₂²	1	2	yes	complemented
76	C₆₁×#478	C₂²	1	1	yes	characteristic, complemented
77	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
78	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
79	C₆₁×#470	C₂²	1	2	yes	complemented
80	C₆₁×#468	C₂²	1	2	yes	—
81	C₆₁×#468	C₂²	1	2	yes	complemented
82	C₆₁×#468	C₂²	1	2	yes	complemented
83	C₆₁×#465	C₂²	1	2	yes	complemented
84	C₆₁×#465	C₂²	1	2	yes	complemented
85	C₆₁×#464	C₂²	1	2	yes	complemented
86	C₆₁×#464	C₂²	1	2	yes	complemented
87	C₆₁×#464	C₂²	1	1	yes	characteristic, complemented
88	C₆₁×#463	C₂²	1	1	yes	characteristic, complemented
89	C₆₁×#463	C₂²	1	2	yes	complemented
90	C₆₁×#462	C₂²	1	1	yes	characteristic, complemented
91	C₆₁×#461	C₂²	1	1	yes	characteristic, complemented
92	C₆₁×#461	C₂²	1	2	yes	complemented
93	C₆₁×#461	C₂²	1	2	yes	complemented
94	C₆₁×#460	C₂²	1	1	yes	characteristic
95	C₆₁×#460	C₂²	1	1	yes	characteristic, complemented
96	C₆₁×#460	C₂²	1	2	yes	complemented
97	C₆₁×#460	C₂²	1	2	yes	complemented
98	C₆₁×#460	C₂²	1	2	yes	complemented
99	C₆₁×#460	C₂²	1	2	yes	complemented
100	C₆₁×#459	C₂²	1	1	yes	characteristic
101	C₆₁×#459	C₂²	1	2	yes	complemented
102	C₆₁×#459	C₂²	1	1	yes	characteristic, complemented
103	C₆₁×#459	C₂²	1	2	yes	complemented
104	C₆₁×#452	C₂²	1	2	yes	complemented
105	C₆₁×#452	C₂²	1	2	yes	complemented
106	C₆₁×#452	C₂²	1	1	yes	characteristic, complemented
107	C₆₁×#450	C₂²	1	2	yes	complemented
108	C₆₁×#450	C₂²	1	2	yes	complemented
109	C₆₁×#450	C₂²	1	2	yes	complemented
110	C₆₁×#450	C₂²	1	2	yes	complemented
111	C₆₁×#449	C₂²	1	1	yes	characteristic
112	C₆₁×#449	C₂²	1	2	yes	complemented
113	C₆₁×#449	C₂²	1	2	yes	complemented
114	C₆₁×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
116	C₆₁×#442	C₂²	1	2	yes	complemented
117	C₆₁×#440	C₂²	1	2	yes	complemented
118	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
120	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
121	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₈×C₆₁	C₂²	1	2	yes	complemented
124	C₆₁×#436	C₂²	1	2	yes	complemented
125	C₆₁×#436	C₂²	1	1	yes	characteristic, complemented
126	C₆₁×#435	C₂²	1	2	yes	complemented
127	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
128	C₆₁×#433	C₂²	1	2	yes	complemented
129	C₆₁×#431	C₂²	1	1	yes	characteristic, complemented
130	C₆₁×#424	C₂²	1	2	yes	complemented
131	C₆₁×#423	C₂²	1	1	yes	characteristic, complemented
132	C₆₁×#418	C₂²	1	2	yes	complemented
133	C₆₁×#417	C₂²	1	2	yes	complemented
134	C₂×#102×C₆₁	C₂²	1	2	yes	complemented
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	C₂³	1	2	yes	—
137	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
138	C₂×#41×C₆₁	C₂³	1	2	yes	—
139	C₂²×D₄×C₆₁	—	2	2	no	—
140	C₂²×D₄×C₆₁	—	2	1	no	—
141	C₂²×D₄×C₆₁	—	2	1	no	—
142	C₂²×D₄×C₆₁	—	2	1	no	—
143	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
144	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
145	AGL(1,ℤ/8)×C₆₁	—	4	4	no	—
146	AGL(1,ℤ/8)×C₆₁	—	4	4	no	—
147	#135×C₆₁	—	4	4	no	—
148	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
157	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
159	C₂×D₈×C₆₁	C₂³	1	2	yes	—
160	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
161	C₂×D₈×C₆₁	C₂³	1	2	yes	—
162	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
163	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
164	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
167	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
168	#127×C₆₁	—	2	1	no	—
169	#127×C₆₁	—	2	1	no	—
170	#127×C₆₁	—	2	1	no	—
171	#127×C₆₁	C₂³	1	2	yes	—
172	#127×C₆₁	C₂³	1	1	yes	characteristic
173	#127×C₆₁	C₂³	1	1	yes	characteristic
174	#127×C₆₁	C₂³	1	2	yes	—
175	#126×C₆₁	—	2	2	no	—
176	#126×C₆₁	—	2	2	no	—
177	#126×C₆₁	—	2	2	no	—
178	#126×C₆₁	—	2	1	no	—
179	#126×C₆₁	D₄	1	2	yes	—
180	#125×C₆₁	—	2	2	no	—
181	#125×C₆₁	—	2	2	no	—
182	#125×C₆₁	—	2	2	no	—
183	#125×C₆₁	—	2	2	no	—
184	#125×C₆₁	—	2	1	no	—
185	#125×C₆₁	—	2	1	no	—
186	#125×C₆₁	—	2	1	no	—
187	#125×C₆₁	D₄	1	1	yes	characteristic
188	#125×C₆₁	C₂³	1	1	yes	characteristic
189	#125×C₆₁	C₂³	1	2	yes	—
190	#124×C₆₁	—	2	1	no	—
191	#124×C₆₁	D₄	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	1	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	#123×C₆₁	—	2	2	no	—
203	#123×C₆₁	D₄	1	2	yes	—
204	C₂²⋊Q₈×C₆₁	—	2	1	no	—
205	C₂²⋊Q₈×C₆₁	—	2	1	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	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
212	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
213	#121×C₆₁	—	2	2	no	—
214	#121×C₆₁	—	2	1	no	—
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	1	no	—
220	#121×C₆₁	—	2	2	no	—
221	#121×C₆₁	—	2	2	no	—
222	#121×C₆₁	—	2	2	no	—
223	#121×C₆₁	—	2	2	no	—
224	#121×C₆₁	—	2	2	no	—
225	#121×C₆₁	D₄	1	1	yes	characteristic
226	#121×C₆₁	C₂³	1	2	yes	—
227	#121×C₆₁	C₂³	1	2	yes	—
228	#121×C₆₁	C₂³	1	1	yes	characteristic
229	#120×C₆₁	—	2	2	no	—
230	#120×C₆₁	—	2	2	no	—
231	#120×C₆₁	—	2	2	no	—
232	#120×C₆₁	—	2	2	no	—
233	#120×C₆₁	—	2	2	no	—
234	#120×C₆₁	—	2	2	no	—
235	C₄×Q₈×C₆₁	—	2	1	no	—
236	C₄×Q₈×C₆₁	—	2	1	no	—
237	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
238	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
241	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₆₁	—	2	1	no	—
244	C₄×D₄×C₆₁	—	2	1	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	1	no	—
249	C₄×D₄×C₆₁	—	2	2	no	—
250	C₄×D₄×C₆₁	—	2	2	no	—
251	C₄×D₄×C₆₁	C₂³	1	2	yes	—
252	C₄×D₄×C₆₁	C₂³	1	2	yes	—
253	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₆₁	C₂³	1	2	yes	—
256	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₆₁	C₂³	1	2	yes	—
258	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
259	#117×C₆₁	—	2	1	no	—
260	#117×C₆₁	—	2	2	no	—
261	#117×C₆₁	—	2	2	no	—
262	#117×C₆₁	—	2	1	no	—
263	#117×C₆₁	—	2	1	no	—
264	#117×C₆₁	C₂³	1	1	yes	characteristic
265	#117×C₆₁	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
267	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
268	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
269	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
270	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
271	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
272	C₂×C₄²×C₆₁	—	2	1	no	—
273	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
274	#107×C₆₁	C₂³	1	2	yes	—
275	#107×C₆₁	C₂³	1	1	yes	characteristic
276	#107×C₆₁	C₂³	1	1	yes	characteristic
277	#106×C₆₁	C₂³	1	1	yes	characteristic
278	#106×C₆₁	C₂³	1	1	yes	characteristic
279	#106×C₆₁	C₂³	1	2	yes	—
280	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
281	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
285	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
286	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
287	#103×C₆₁	C₂³	1	1	yes	characteristic
288	#103×C₆₁	C₂³	1	2	yes	—
289	#103×C₆₁	C₂³	1	2	yes	—
290	#103×C₆₁	C₂³	1	1	yes	characteristic
291	#103×C₆₁	C₂³	1	1	yes	characteristic
292	#103×C₆₁	C₂³	1	1	yes	characteristic
293	#103×C₆₁	C₂³	1	2	yes	—
294	#102×C₆₁	C₂³	1	1	yes	characteristic
295	#102×C₆₁	C₂³	1	2	yes	—
296	#102×C₆₁	C₂³	1	2	yes	—
297	#102×C₆₁	C₂³	1	2	yes	—
298	#102×C₆₁	C₂³	1	2	yes	—
299	#102×C₆₁	C₂³	1	2	yes	—
300	#102×C₆₁	C₂³	1	2	yes	—
301	#102×C₆₁	C₂³	1	2	yes	—
302	#102×C₆₁	C₂³	1	1	yes	characteristic
303	#102×C₆₁	C₂³	1	1	yes	characteristic
304	#102×C₆₁	C₂³	1	2	yes	—
305	#102×C₆₁	C₂³	1	1	yes	characteristic
306	#102×C₆₁	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
311	#97×C₆₁	C₂³	1	2	yes	—
312	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₆₁	C₂³	1	2	yes	—
315	C₂⁴×C₆₁	—	2	2	no	—
316	C₂⁴×C₆₁	—	2	2	no	—
317	#41×C₆₁	—	2	4	no	—
318	#41×C₆₁	—	2	2	no	—
319	#41×C₆₁	—	4	1	no	—
320	#41×C₆₁	—	4	2	no	—
321	#41×C₆₁	—	4	2	no	—
322	#41×C₆₁	—	4	2	no	—
323	#41×C₆₁	—	8	2	no	—
324	C₂×Q₈×C₆₁	—	2	1	no	—
325	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
329	C₂×D₄×C₆₁	—	2	1	no	—
330	C₂×D₄×C₆₁	—	2	2	no	—
331	C₂×D₄×C₆₁	—	2	1	no	—
332	C₂×D₄×C₆₁	—	2	2	no	—
333	C₂×D₄×C₆₁	—	2	2	no	—
334	C₂×D₄×C₆₁	—	2	2	no	—
335	C₂×D₄×C₆₁	—	2	1	no	—
336	C₂×D₄×C₆₁	—	2	1	no	—
337	C₂×D₄×C₆₁	—	2	2	no	—
338	C₂×D₄×C₆₁	—	2	2	no	—
339	C₂×D₄×C₆₁	—	2	1	no	—
340	C₂×D₄×C₆₁	—	2	2	no	—
341	C₂×D₄×C₆₁	—	2	2	no	—
342	C₂×D₄×C₆₁	—	2	2	no	—
343	C₂×D₄×C₆₁	—	2	2	no	—
344	C₂×D₄×C₆₁	—	2	1	no	—
345	C₂×D₄×C₆₁	—	4	2	no	—
346	C₂×D₄×C₆₁	—	4	2	no	—
347	C₂×D₄×C₆₁	—	4	2	no	—
348	C₂×D₄×C₆₁	—	4	2	no	—
349	C₂×D₄×C₆₁	—	8	2	no	—
350	C₂×D₄×C₆₁	—	8	2	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	1	yes	characteristic
356	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
357	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
358	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₆₁	—	2	2	no	—
360	C₂²×C₄×C₆₁	—	2	1	no	—
361	C₂²×C₄×C₆₁	—	2	1	no	—
362	C₂²×C₄×C₆₁	—	2	2	no	—
363	C₂²×C₄×C₆₁	—	2	1	no	—
364	C₂²×C₄×C₆₁	—	2	1	no	—
365	C₂²×C₄×C₆₁	—	2	2	no	—
366	C₂²×C₄×C₆₁	—	2	2	no	—
367	C₂²×C₄×C₆₁	—	2	2	no	—
368	C₂²×C₄×C₆₁	—	2	2	no	—
369	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
371	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
373	Q₁₆×C₆₁	—	4	1	no	—
374	Q₁₆×C₆₁	—	4	2	no	—
375	SD₁₆×C₆₁	—	2	2	no	—
376	SD₁₆×C₆₁	—	4	1	no	—
377	SD₁₆×C₆₁	—	4	2	no	—
378	SD₁₆×C₆₁	—	4	2	no	—
379	SD₁₆×C₆₁	—	4	2	no	—
380	SD₁₆×C₆₁	—	4	2	no	—
381	SD₁₆×C₆₁	—	4	2	no	—
382	SD₁₆×C₆₁	—	4	2	no	—
383	SD₁₆×C₆₁	—	4	2	no	—
384	D₈×C₆₁	—	2	4	no	—
385	D₈×C₆₁	—	2	2	no	—
386	D₈×C₆₁	—	2	4	no	—
387	M₁₆×C₆₁	—	4	2	no	—
388	M₁₆×C₆₁	—	4	2	no	—
389	C₂×C₈×C₆₁	—	4	2	no	—
390	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
395	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
396	C₄⋊C₄×C₆₁	—	2	2	no	—
397	C₄⋊C₄×C₆₁	—	2	1	no	—
398	C₄⋊C₄×C₆₁	—	2	1	no	—
399	C₄⋊C₄×C₆₁	—	2	2	no	—
400	C₄⋊C₄×C₆₁	—	2	2	no	—
401	C₄⋊C₄×C₆₁	—	2	2	no	—
402	C₄⋊C₄×C₆₁	—	2	2	no	—
403	C₄⋊C₄×C₆₁	—	2	2	no	—
404	C₄⋊C₄×C₆₁	—	2	2	no	—
405	C₄⋊C₄×C₆₁	—	2	2	no	—
406	C₄⋊C₄×C₆₁	—	2	1	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	1	no	—
412	C₄⋊C₄×C₆₁	—	2	1	no	—
413	C₄⋊C₄×C₆₁	—	2	2	no	—
414	C₄⋊C₄×C₆₁	—	2	1	no	—
415	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
423	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
426	C₂²⋊C₄×C₆₁	—	2	1	no	—
427	C₂²⋊C₄×C₆₁	—	2	2	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	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	2	no	—
436	C₂²⋊C₄×C₆₁	—	2	1	no	—
437	C₂²⋊C₄×C₆₁	—	2	1	no	—
438	C₂²⋊C₄×C₆₁	—	2	1	no	—
439	C₂²⋊C₄×C₆₁	—	2	2	no	—
440	C₂²⋊C₄×C₆₁	—	2	2	no	—
441	C₂²⋊C₄×C₆₁	—	2	1	no	—
442	C₂²⋊C₄×C₆₁	—	2	2	no	—
443	C₂²⋊C₄×C₆₁	—	2	2	no	—
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	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
448	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
449	C₄²×C₆₁	—	2	1	no	—
450	C₄²×C₆₁	—	2	1	no	—
451	C₄²×C₆₁	—	2	1	no	—
452	C₄²×C₆₁	—	2	2	no	—
453	C₄²×C₆₁	—	2	2	no	—
454	C₄²×C₆₁	—	2	1	no	—
455	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
456	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
458	C₄²×C₆₁	C₂⁴	1	2	yes	—
459	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
460	C₂³×C₆₁	—	2	1	no	—
461	C₂³×C₆₁	—	2	2	no	—
462	C₂³×C₆₁	—	2	1	no	—
463	C₂³×C₆₁	—	2	2	no	—
464	C₂³×C₆₁	—	4	4	no	—
465	C₂³×C₆₁	—	8	2	no	—
466	C₂³×C₆₁	—	8	2	no	—
467	C₂³×C₆₁	—	8	2	no	—
468	C₂³×C₆₁	—	8	2	no	—
469	C₂³×C₆₁	—	8	2	no	—
470	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
471	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
472	Q₈×C₆₁	—	2	2	no	—
473	Q₈×C₆₁	—	2	1	no	—
474	Q₈×C₆₁	—	2	1	no	—
475	Q₈×C₆₁	—	2	2	no	—
476	Q₈×C₆₁	—	2	2	no	—
477	Q₈×C₆₁	—	2	1	no	—
478	Q₈×C₆₁	—	2	1	no	—
479	Q₈×C₆₁	—	8	1	no	—
480	D₄×C₆₁	—	2	2	no	—
481	D₄×C₆₁	—	2	1	no	—
482	D₄×C₆₁	—	2	2	no	—
483	D₄×C₆₁	—	2	2	no	—
484	D₄×C₆₁	—	2	1	no	—
485	D₄×C₆₁	—	2	1	no	—
486	D₄×C₆₁	—	2	2	no	—
487	D₄×C₆₁	—	2	2	no	—
488	D₄×C₆₁	—	4	2	no	—
489	D₄×C₆₁	—	4	4	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	2	no	—
495	D₄×C₆₁	—	8	2	no	—
496	D₄×C₆₁	—	8	2	no	—
497	D₄×C₆₁	—	8	1	no	—
498	D₄×C₆₁	—	8	1	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	—	8	2	no	—
505	D₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
506	C₂×C₄×C₆₁	—	2	2	no	—
507	C₂×C₄×C₆₁	—	2	2	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	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	1	no	—
516	C₂×C₄×C₆₁	—	2	1	no	—
517	C₂×C₄×C₆₁	—	2	2	no	—
518	C₂×C₄×C₆₁	—	2	1	no	—
519	C₂×C₄×C₆₁	—	4	1	no	—
520	C₂×C₄×C₆₁	—	4	4	no	—
521	C₂×C₄×C₆₁	—	4	2	no	—
522	C₂×C₄×C₆₁	—	4	2	no	—
523	C₂×C₄×C₆₁	—	4	2	no	—
524	C₂×C₄×C₆₁	—	8	1	no	—
525	C₂×C₄×C₆₁	—	8	2	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	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
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	C₂⁵	1	1	yes	characteristic
539	C₈×C₆₁	—	2	1	no	—
540	C₈×C₆₁	—	2	2	no	—
541	C₈×C₆₁	—	2	1	no	—
542	C₈×C₆₁	—	2	2	no	—
543	C₈×C₆₁	—	2	1	no	—
544	C₈×C₆₁	—	2	1	no	—
545	#62033	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
546	C₂²×C₆₁	—	2	1	no	—
547	C₂²×C₆₁	—	2	2	no	—
548	C₂²×C₆₁	—	2	2	no	—
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	—	4	1	no	—
554	C₂²×C₆₁	—	4	1	no	—
555	C₂²×C₆₁	—	4	2	no	—
556	C₂²×C₆₁	—	4	1	no	—
557	C₂²×C₆₁	—	4	2	no	—
558	C₂²×C₆₁	—	4	2	no	—
559	C₂²×C₆₁	—	4	2	no	—
560	C₂²×C₆₁	—	4	1	no	—
561	C₂²×C₆₁	—	4	1	no	—
562	C₂²×C₆₁	—	4	2	no	—
563	C₂²×C₆₁	—	4	2	no	—
564	C₂²×C₆₁	—	16	4	no	—
565	C₂²×C₆₁	—	16	4	no	—
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	2	no	—
571	C₄×C₆₁	—	2	1	no	—
572	C₄×C₆₁	—	2	1	no	—
573	C₄×C₆₁	—	2	2	no	—
574	C₄×C₆₁	—	4	1	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	#577	1	2	yes	—
583	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
584	C₄×C₆₁	#585	1	1	yes	characteristic
585	#3543	C₂×C₆₁	1	1	yes	characteristic, complemented
586	#3515	C₂×C₆₁	1	1	yes	characteristic, complemented
587	#3400	C₂×C₆₁	1	1	yes	characteristic, complemented
588	#3392	C₂×C₆₁	1	1	yes	characteristic, complemented
589	#3366	C₂×C₆₁	1	1	yes	characteristic, complemented
590	#3361	C₂×C₆₁	1	1	yes	characteristic, complemented
591	#3333	C₂×C₆₁	1	1	yes	characteristic, complemented
592	#3323	C₂×C₆₁	1	2	yes	complemented
593	#3310	C₂×C₆₁	1	2	yes	complemented
594	#3295	C₂×C₆₁	1	1	yes	characteristic, complemented
595	#3284	C₂×C₆₁	1	1	yes	characteristic, complemented
596	#3272	C₂×C₆₁	1	2	yes	complemented
597	#3272	C₂×C₆₁	1	1	yes	characteristic, complemented
598	#3267	C₂×C₆₁	1	2	yes	complemented
599	#3260	C₂×C₆₁	1	2	yes	complemented
600	#3252	C₂×C₆₁	1	1	yes	characteristic, complemented
601	#3222	C₂×C₆₁	1	2	yes	complemented
602	#3208	C₂×C₆₁	1	1	yes	characteristic, complemented
603	#3119	C₂×C₆₁	1	2	yes	complemented
604	#3102	C₂×C₆₁	1	1	yes	characteristic, complemented
605	#3045	C₂×C₆₁	1	2	yes	complemented
606	#3038	C₂×C₆₁	1	1	yes	characteristic, complemented
607	#2993	C₂×C₆₁	1	1	yes	characteristic, complemented
608	C₂×C₆₁	—	4	2	no	—
609	C₂×C₆₁	—	4	1	no	—
610	C₂×C₆₁	—	4	2	no	—
611	C₂×C₆₁	—	8	2	no	—
612	C₂×C₆₁	—	8	2	no	—
613	C₂×C₆₁	—	8	1	no	—
614	C₂×C₆₁	#3488	1	1	yes	characteristic
615	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
616	C₂×C₆₁	#3585	1	1	yes	characteristic
617	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	complemented
618	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	complemented
619	C₂×#135	C₂²×C₆₁	1	2	yes	complemented
620	#560	—	2	2	no	—
621	#559	C₂²×C₆₁	1	1	yes	characteristic
622	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
623	#554	C₂²×C₆₁	1	1	yes	characteristic, complemented
624	#554	C₂²×C₆₁	1	1	yes	characteristic, complemented
625	#553	—	2	1	no	—
626	#552	—	2	2	no	—
627	#552	—	2	1	no	—
628	#552	C₂²×C₆₁	1	2	yes	complemented
629	#550	C₂²×C₆₁	1	1	yes	characteristic
630	#550	C₂²×C₆₁	1	1	yes	characteristic
631	#547	C₂²×C₆₁	1	2	yes	complemented
632	#547	C₂²×C₆₁	1	1	yes	characteristic, complemented
633	#546	—	2	1	no	—
634	#546	C₂²×C₆₁	1	2	yes	—
635	D₄²	—	2	1	no	—
636	D₄²	C₂²×C₆₁	1	1	yes	characteristic
637	D₄²	C₂²×C₆₁	1	2	yes	—
638	#541	C₂²×C₆₁	1	2	yes	complemented
639	#540	—	2	1	no	—
640	#540	C₂²×C₆₁	1	2	yes	—
641	#539	—	2	2	no	—
642	#535	—	2	1	no	—
643	#535	C₂²×C₆₁	1	2	yes	—
644	#534	—	2	2	no	—
645	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
646	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
647	#529	—	2	1	no	—
648	#529	C₂²×C₆₁	1	1	yes	characteristic
649	#529	C₂²×C₆₁	1	1	yes	characteristic
650	C₂×#125	—	2	1	no	—
651	#520	C₂²×C₆₁	1	2	yes	complemented
652	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic, complemented
653	#497	C₂²×C₆₁	1	2	yes	complemented
654	#492	C₂²×C₆₁	1	1	yes	characteristic
655	#492	C₂²×C₆₁	1	1	yes	characteristic, complemented
656	#492	C₂²×C₆₁	1	2	yes	complemented
657	#490	C₂²×C₆₁	1	2	yes	complemented
658	#488	C₂²×C₆₁	1	2	yes	complemented
659	#486	C₂²×C₆₁	1	1	yes	characteristic
660	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
661	#485	C₂²×C₆₁	1	1	yes	characteristic, complemented
662	#482	C₂²×C₆₁	1	1	yes	characteristic
663	#481	C₂²×C₆₁	1	2	yes	complemented
664	#480	C₂²×C₆₁	1	2	yes	complemented
665	#479	C₂²×C₆₁	1	1	yes	characteristic, complemented
666	#479	C₂²×C₆₁	1	2	yes	complemented
667	#478	C₂²×C₆₁	1	1	yes	characteristic, complemented
668	#478	C₂²×C₆₁	1	2	yes	complemented
669	#478	C₂²×C₆₁	1	2	yes	complemented
670	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
671	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
672	#470	C₂²×C₆₁	1	2	yes	complemented
673	#468	C₂²×C₆₁	1	2	yes	—
674	#468	C₂²×C₆₁	1	2	yes	complemented
675	#468	C₂²×C₆₁	1	2	yes	complemented
676	#465	C₂²×C₆₁	1	2	yes	complemented
677	#465	C₂²×C₆₁	1	2	yes	complemented
678	#464	C₂²×C₆₁	1	1	yes	characteristic, complemented
679	#464	C₂²×C₆₁	1	2	yes	complemented
680	#464	C₂²×C₆₁	1	2	yes	complemented
681	#463	C₂²×C₆₁	1	1	yes	characteristic, complemented
682	#463	C₂²×C₆₁	1	2	yes	complemented
683	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
684	#461	C₂²×C₆₁	1	1	yes	characteristic, complemented
685	#461	C₂²×C₆₁	1	2	yes	complemented
686	#461	C₂²×C₆₁	1	2	yes	complemented
687	#460	C₂²×C₆₁	1	1	yes	characteristic
688	#460	C₂²×C₆₁	1	1	yes	characteristic, complemented
689	#460	C₂²×C₆₁	1	2	yes	complemented
690	#460	C₂²×C₆₁	1	2	yes	complemented
691	#460	C₂²×C₆₁	1	2	yes	complemented
692	#460	C₂²×C₆₁	1	2	yes	complemented
693	#459	C₂²×C₆₁	1	1	yes	characteristic
694	#459	C₂²×C₆₁	1	2	yes	complemented
695	#459	C₂²×C₆₁	1	1	yes	characteristic, complemented
696	#459	C₂²×C₆₁	1	2	yes	complemented
697	#452	C₂²×C₆₁	1	2	yes	complemented
698	#452	C₂²×C₆₁	1	1	yes	characteristic, complemented
699	#452	C₂²×C₆₁	1	2	yes	complemented
700	#450	C₂²×C₆₁	1	2	yes	complemented
701	#450	C₂²×C₆₁	1	2	yes	complemented
702	#450	C₂²×C₆₁	1	2	yes	complemented
703	#450	C₂²×C₆₁	1	2	yes	complemented
704	#449	C₂²×C₆₁	1	1	yes	characteristic
705	#449	C₂²×C₆₁	1	2	yes	complemented
706	#449	C₂²×C₆₁	1	2	yes	complemented
707	#446	C₂²×C₆₁	1	1	yes	characteristic, complemented
708	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
709	#442	C₂²×C₆₁	1	2	yes	complemented
710	#440	C₂²×C₆₁	1	2	yes	complemented
711	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
712	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
713	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
714	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
715	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
716	C₄×D₈	C₂²×C₆₁	1	2	yes	complemented
717	#436	C₂²×C₆₁	1	1	yes	characteristic, complemented
718	#436	C₂²×C₆₁	1	2	yes	complemented
719	#435	C₂²×C₆₁	1	2	yes	complemented
720	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
721	#433	C₂²×C₆₁	1	2	yes	complemented
722	#431	C₂²×C₆₁	1	1	yes	characteristic, complemented
723	#424	C₂²×C₆₁	1	2	yes	complemented
724	#423	C₂²×C₆₁	1	1	yes	characteristic, complemented
725	#418	C₂²×C₆₁	1	2	yes	complemented
726	#417	C₂²×C₆₁	1	2	yes	complemented
727	C₂×#102	C₂²×C₆₁	1	2	yes	complemented
728	C₆₁	#62033	1	1	yes	characteristic, direct product factor, Sylow
729	C₂×#41	—	2	1	no	—
730	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
731	C₂×#41	C₂³×C₆₁	1	2	yes	—
732	C₂×#41	C₂³×C₆₁	1	2	yes	—
733	C₂²×D₄	—	2	2	no	—
734	C₂²×D₄	—	2	1	no	—
735	C₂²×D₄	—	2	1	no	—
736	C₂²×D₄	—	2	1	no	—
737	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
738	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
739	AGL(1,ℤ/8)	—	4	4	no	—
740	AGL(1,ℤ/8)	—	4	4	no	—
741	#135	—	4	4	no	—
742	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
743	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
744	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
745	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
746	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
747	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
748	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
749	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
750	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
751	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
752	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
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×M₁₆	C₂³×C₆₁	1	2	yes	—
757	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
758	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
759	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
760	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
761	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
762	#127	—	2	1	no	—
763	#127	—	2	1	no	—
764	#127	—	2	1	no	—
765	#127	C₂³×C₆₁	1	2	yes	—
766	#127	C₂³×C₆₁	1	1	yes	characteristic
767	#127	C₂³×C₆₁	1	1	yes	characteristic
768	#127	C₂³×C₆₁	1	2	yes	—
769	#126	—	2	2	no	—
770	#126	—	2	2	no	—
771	#126	—	2	2	no	—
772	#126	—	2	1	no	—
773	#126	D₄×C₆₁	1	2	yes	—
774	#125	—	2	2	no	—
775	#125	—	2	2	no	—
776	#125	—	2	1	no	—
777	#125	—	2	1	no	—
778	#125	—	2	2	no	—
779	#125	—	2	2	no	—
780	#125	—	2	1	no	—
781	#125	D₄×C₆₁	1	1	yes	characteristic
782	#125	C₂³×C₆₁	1	1	yes	characteristic
783	#125	C₂³×C₆₁	1	2	yes	—
784	#124	—	2	1	no	—
785	#124	D₄×C₆₁	1	1	yes	characteristic
786	#124	C₂³×C₆₁	1	1	yes	characteristic
787	#124	C₂³×C₆₁	1	2	yes	—
788	#123	—	2	2	no	—
789	#123	—	2	1	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	#123	—	2	2	no	—
797	#123	D₄×C₆₁	1	2	yes	—
798	C₂²⋊Q₈	—	2	1	no	—
799	C₂²⋊Q₈	—	2	1	no	—
800	C₂²⋊Q₈	—	2	2	no	—
801	C₂²⋊Q₈	—	2	2	no	—
802	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
803	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
804	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
805	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
806	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
807	#121	—	2	1	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	—	2	1	no	—
813	#121	—	2	1	no	—
814	#121	—	2	2	no	—
815	#121	—	2	2	no	—
816	#121	—	2	2	no	—
817	#121	—	2	2	no	—
818	#121	—	2	2	no	—
819	#121	D₄×C₆₁	1	1	yes	characteristic
820	#121	C₂³×C₆₁	1	1	yes	characteristic
821	#121	C₂³×C₆₁	1	2	yes	—
822	#121	C₂³×C₆₁	1	2	yes	—
823	#120	—	2	2	no	—
824	#120	—	2	2	no	—
825	#120	—	2	2	no	—
826	#120	—	2	2	no	—
827	#120	—	2	2	no	—
828	#120	—	2	2	no	—
829	C₄×Q₈	—	2	1	no	—
830	C₄×Q₈	—	2	1	no	—
831	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
832	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
833	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
834	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
835	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
836	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
837	C₄×D₄	—	2	1	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	—	2	1	no	—
843	C₄×D₄	—	2	2	no	—
844	C₄×D₄	—	2	2	no	—
845	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
846	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
847	C₄×D₄	C₂³×C₆₁	1	2	yes	—
848	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
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	1	yes	characteristic
853	#117	—	2	1	no	—
854	#117	—	2	2	no	—
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	C₂×C₄⋊C₄	—	2	2	no	—
861	C₂×C₄⋊C₄	—	2	1	no	—
862	C₂×C₄⋊C₄	—	2	2	no	—
863	C₂×C₄⋊C₄	—	2	1	no	—
864	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
865	C₂×C₂²⋊C₄	—	2	2	no	—
866	C₂×C₄²	—	2	1	no	—
867	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
868	#107	C₂³×C₆₁	1	2	yes	—
869	#107	C₂³×C₆₁	1	1	yes	characteristic
870	#107	C₂³×C₆₁	1	1	yes	characteristic
871	#106	C₂³×C₆₁	1	1	yes	characteristic
872	#106	C₂³×C₆₁	1	1	yes	characteristic
873	#106	C₂³×C₆₁	1	2	yes	—
874	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
875	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
876	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
877	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
878	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
879	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
880	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
881	#103	C₂³×C₆₁	1	1	yes	characteristic
882	#103	C₂³×C₆₁	1	2	yes	—
883	#103	C₂³×C₆₁	1	2	yes	—
884	#103	C₂³×C₆₁	1	1	yes	characteristic
885	#103	C₂³×C₆₁	1	1	yes	characteristic
886	#103	C₂³×C₆₁	1	1	yes	characteristic
887	#103	C₂³×C₆₁	1	2	yes	—
888	#102	C₂³×C₆₁	1	1	yes	characteristic
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	2	yes	—
894	#102	C₂³×C₆₁	1	2	yes	—
895	#102	C₂³×C₆₁	1	2	yes	—
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	1	yes	characteristic
900	#102	C₂³×C₆₁	1	2	yes	—
901	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
902	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
903	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
904	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
905	#97	C₂³×C₆₁	1	2	yes	—
906	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
907	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
908	C₄×C₈	C₂³×C₆₁	1	2	yes	—
909	C₂⁴	—	2	2	no	—
910	C₂⁴	—	2	2	no	—
911	#41	—	2	4	no	—
912	#41	—	2	2	no	—
913	#41	—	4	1	no	—
914	#41	—	4	2	no	—
915	#41	—	4	2	no	—
916	#41	—	4	2	no	—
917	#41	—	8	2	no	—
918	C₂×Q₈	—	2	1	no	—
919	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
920	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
921	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
922	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	1	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	1	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	4	2	no	—
940	C₂×D₄	—	4	2	no	—
941	C₂×D₄	—	4	2	no	—
942	C₂×D₄	—	4	2	no	—
943	C₂×D₄	—	8	2	no	—
944	C₂×D₄	—	8	2	no	—
945	C₂×D₄	—	8	2	no	—
946	C₂×D₄	—	8	4	no	—
947	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
948	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
949	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
950	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
951	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
952	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	1	no	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	—	2	1	no	—
958	C₂²×C₄	—	2	1	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	—	2	2	no	—
963	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
964	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
965	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
966	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
967	Q₁₆	—	4	1	no	—
968	Q₁₆	—	4	2	no	—
969	SD₁₆	—	2	2	no	—
970	SD₁₆	—	4	1	no	—
971	SD₁₆	—	4	2	no	—
972	SD₁₆	—	4	2	no	—
973	SD₁₆	—	4	2	no	—
974	SD₁₆	—	4	2	no	—
975	SD₁₆	—	4	2	no	—
976	SD₁₆	—	4	2	no	—
977	SD₁₆	—	4	2	no	—
978	D₈	—	2	4	no	—
979	D₈	—	2	2	no	—
980	D₈	—	2	4	no	—
981	M₁₆	—	4	2	no	—
982	M₁₆	—	4	2	no	—
983	C₂×C₈	—	4	2	no	—
984	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
985	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
986	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
987	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
988	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
989	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	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	1	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	1	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1010	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1011	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1012	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1013	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1014	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1015	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1016	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1017	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1018	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1019	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	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	2	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1039	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1040	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1041	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1042	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	2	1	no	—
1045	C₄²	—	2	1	no	—
1046	C₄²	—	2	2	no	—
1047	C₄²	—	2	2	no	—
1048	C₄²	—	2	1	no	—
1049	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1050	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1051	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1052	C₄²	C₂⁴×C₆₁	1	2	yes	—
1053	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1054	C₂³	—	2	1	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	2	2	no	—
1058	C₂³	—	4	4	no	—
1059	C₂³	—	8	2	no	—
1060	C₂³	—	8	2	no	—
1061	C₂³	—	8	2	no	—
1062	C₂³	—	8	2	no	—
1063	C₂³	—	8	2	no	—
1064	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1065	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1066	Q₈	—	2	2	no	—
1067	Q₈	—	2	1	no	—
1068	Q₈	—	2	1	no	—
1069	Q₈	—	2	2	no	—
1070	Q₈	—	2	2	no	—
1071	Q₈	—	2	1	no	—
1072	Q₈	—	2	1	no	—
1073	Q₈	—	8	1	no	—
1074	D₄	—	2	2	no	—
1075	D₄	—	2	1	no	—
1076	D₄	—	2	2	no	—
1077	D₄	—	2	2	no	—
1078	D₄	—	2	1	no	—
1079	D₄	—	2	1	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	2	no	—
1082	D₄	—	4	2	no	—
1083	D₄	—	4	4	no	—
1084	D₄	—	4	2	no	—
1085	D₄	—	4	2	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	4	2	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	2	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	1	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	2	no	—
1099	D₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	4	1	no	—
1114	C₂×C₄	—	4	4	no	—
1115	C₂×C₄	—	4	2	no	—
1116	C₂×C₄	—	4	2	no	—
1117	C₂×C₄	—	4	2	no	—
1118	C₂×C₄	—	8	1	no	—
1119	C₂×C₄	—	8	2	no	—
1120	C₂×C₄	—	8	2	no	—
1121	C₂×C₄	—	8	2	no	—
1122	C₂×C₄	—	8	2	no	—
1123	C₂×C₄	—	8	2	no	—
1124	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1125	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1126	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1127	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1128	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1129	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1130	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1131	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1132	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1133	C₈	—	2	1	no	—
1134	C₈	—	2	2	no	—
1135	C₈	—	2	1	no	—
1136	C₈	—	2	2	no	—
1137	C₈	—	2	1	no	—
1138	C₈	—	2	1	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	1	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	1	no	—
1145	C₂²	—	2	2	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	4	1	no	—
1149	C₂²	—	4	2	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	4	2	no	—
1152	C₂²	—	4	1	no	—
1153	C₂²	—	4	2	no	—
1154	C₂²	—	4	2	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	2	no	—
1157	C₂²	—	16	4	no	—
1158	C₂²	—	16	4	no	—
1159	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1160	C₄	—	2	1	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	1	no	—
1163	C₄	—	2	1	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	2	2	no	—
1166	C₄	—	2	1	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	2	no	—
1172	C₄	—	4	1	no	—
1173	C₄	—	4	2	no	—
1174	C₄	—	4	1	no	—
1175	C₄	C₆₁×#577	1	2	yes	—
1176	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1177	C₄	C₆₁×#585	1	1	yes	characteristic
1178	C₂	—	4	1	no	—
1179	C₂	—	4	2	no	—
1180	C₂	—	4	2	no	—
1181	C₂	—	8	1	no	—
1182	C₂	—	8	2	no	—
1183	C₂	—	8	2	no	—
1184	C₂	C₆₁×#3488	1	1	yes	characteristic
1185	C₂	C₂×C₆₁×#577	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 ◁ C₆₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3543	C₂	semidirect
2. C₆₁×#3515	C₂	semidirect
3. C₆₁×#3400	C₂	semidirect
4. C₆₁×#3392	C₂	semidirect
5. C₆₁×#3366	C₂	semidirect
6. C₆₁×#3361	C₂	semidirect
7. C₆₁×#3333	C₂	semidirect
8. C₆₁×#3323	C₂	semidirect
9. C₆₁×#3310	C₂	semidirect
10. C₆₁×#3295	C₂	semidirect
11. C₆₁×#3284	C₂	semidirect
12. C₆₁×#3272	C₂	semidirect
13. C₆₁×#3272	C₂	semidirect
14. C₆₁×#3267	C₂	semidirect
15. C₆₁×#3260	C₂	semidirect
16. C₆₁×#3252	C₂	semidirect
17. C₆₁×#3222	C₂	semidirect
18. C₆₁×#3208	C₂	semidirect
19. C₆₁×#3119	C₂	semidirect
20. C₆₁×#3102	C₂	semidirect
21. C₆₁×#3045	C₂	semidirect
22. C₆₁×#3038	C₂	semidirect
23. C₆₁×#2993	C₂	semidirect
24. C₂×AGL(1,ℤ/8)×C₆₁	C₂²	semidirect
25. C₂×AGL(1,ℤ/8)×C₆₁	C₂²	semidirect
26. C₂×#135×C₆₁	C₂²	semidirect
29. C₆₁×#557	C₂²	semidirect
30. C₆₁×#554	C₂²	semidirect
31. C₆₁×#554	C₂²	semidirect
35. C₆₁×#552	C₂²	semidirect
38. C₆₁×#547	C₂²	semidirect
39. C₆₁×#547	C₂²	semidirect
45. C₆₁×#541	C₂²	semidirect
52. C₆₁×#533	C₂²	semidirect
58. C₆₁×#520	C₂²	semidirect
59. C₄×#41×C₆₁	C₂²	semidirect
60. C₆₁×#497	C₂²	semidirect
62. C₆₁×#492	C₂²	semidirect
63. C₆₁×#492	C₂²	semidirect
64. C₆₁×#490	C₂²	semidirect
65. C₆₁×#488	C₂²	semidirect
67. C₆₁×#486	C₂²	semidirect
68. C₆₁×#485	C₂²	semidirect
70. C₆₁×#481	C₂²	semidirect
71. C₆₁×#480	C₂²	semidirect
72. C₆₁×#479	C₂²	semidirect
73. C₆₁×#479	C₂²	semidirect
74. C₆₁×#478	C₂²	semidirect
75. C₆₁×#478	C₂²	semidirect
76. C₆₁×#478	C₂²	semidirect
77. C₆₁×#477	C₂²	semidirect
78. C₆₁×#476	C₂²	semidirect
79. C₆₁×#470	C₂²	semidirect
81. C₆₁×#468	C₂²	semidirect
82. C₆₁×#468	C₂²	semidirect
83. C₆₁×#465	C₂²	semidirect
84. C₆₁×#465	C₂²	semidirect
85. C₆₁×#464	C₂²	semidirect
86. C₆₁×#464	C₂²	semidirect
87. C₆₁×#464	C₂²	semidirect
88. C₆₁×#463	C₂²	semidirect
89. C₆₁×#463	C₂²	semidirect
90. C₆₁×#462	C₂²	semidirect
91. C₆₁×#461	C₂²	semidirect
92. C₆₁×#461	C₂²	semidirect
93. C₆₁×#461	C₂²	semidirect
95. C₆₁×#460	C₂²	semidirect
96. C₆₁×#460	C₂²	semidirect
97. C₆₁×#460	C₂²	semidirect
98. C₆₁×#460	C₂²	semidirect
99. C₆₁×#460	C₂²	semidirect
101. C₆₁×#459	C₂²	semidirect
102. C₆₁×#459	C₂²	semidirect
103. C₆₁×#459	C₂²	semidirect
104. C₆₁×#452	C₂²	semidirect
105. C₆₁×#452	C₂²	semidirect
106. C₆₁×#452	C₂²	semidirect
107. C₆₁×#450	C₂²	semidirect
108. C₆₁×#450	C₂²	semidirect
109. C₆₁×#450	C₂²	semidirect
110. C₆₁×#450	C₂²	semidirect
112. C₆₁×#449	C₂²	semidirect
113. C₆₁×#449	C₂²	semidirect
114. C₆₁×#446	C₂²	semidirect
115. C₈×Q₈×C₆₁	C₂²	semidirect
116. C₆₁×#442	C₂²	semidirect
117. C₆₁×#440	C₂²	semidirect
118. C₄×Q₁₆×C₆₁	C₂²	semidirect
119. C₄×SD₁₆×C₆₁	C₂²	semidirect
120. C₄×SD₁₆×C₆₁	C₂²	semidirect
121. C₄×SD₁₆×C₆₁	C₂²	semidirect
122. C₄×D₈×C₆₁	C₂²	semidirect
123. C₄×D₈×C₆₁	C₂²	semidirect
124. C₆₁×#436	C₂²	semidirect
125. C₆₁×#436	C₂²	semidirect
126. C₆₁×#435	C₂²	semidirect
127. C₈×D₄×C₆₁	C₂²	semidirect
128. C₆₁×#433	C₂²	semidirect
129. C₆₁×#431	C₂²	semidirect
130. C₆₁×#424	C₂²	semidirect
131. C₆₁×#423	C₂²	semidirect
132. C₆₁×#418	C₂²	semidirect
133. C₆₁×#417	C₂²	semidirect
134. C₂×#102×C₆₁	C₂²	semidirect
545. #62033	C₆₁	direct (N × H)
585. #3543	C₂×C₆₁	semidirect
586. #3515	C₂×C₆₁	semidirect
587. #3400	C₂×C₆₁	semidirect
588. #3392	C₂×C₆₁	semidirect
589. #3366	C₂×C₆₁	semidirect
590. #3361	C₂×C₆₁	semidirect
591. #3333	C₂×C₆₁	semidirect
592. #3323	C₂×C₆₁	semidirect
593. #3310	C₂×C₆₁	semidirect
594. #3295	C₂×C₆₁	semidirect
595. #3284	C₂×C₆₁	semidirect
596. #3272	C₂×C₆₁	semidirect
597. #3272	C₂×C₆₁	semidirect
598. #3267	C₂×C₆₁	semidirect
599. #3260	C₂×C₆₁	semidirect
600. #3252	C₂×C₆₁	semidirect
601. #3222	C₂×C₆₁	semidirect
602. #3208	C₂×C₆₁	semidirect
603. #3119	C₂×C₆₁	semidirect
604. #3102	C₂×C₆₁	semidirect
605. #3045	C₂×C₆₁	semidirect
606. #3038	C₂×C₆₁	semidirect
607. #2993	C₂×C₆₁	semidirect
617. C₂×AGL(1,ℤ/8)	C₂²×C₆₁	semidirect
618. C₂×AGL(1,ℤ/8)	C₂²×C₆₁	semidirect
619. C₂×#135	C₂²×C₆₁	semidirect
622. #557	C₂²×C₆₁	semidirect
623. #554	C₂²×C₆₁	semidirect
624. #554	C₂²×C₆₁	semidirect
628. #552	C₂²×C₆₁	semidirect
631. #547	C₂²×C₆₁	semidirect
632. #547	C₂²×C₆₁	semidirect
638. #541	C₂²×C₆₁	semidirect
645. #533	C₂²×C₆₁	semidirect
651. #520	C₂²×C₆₁	semidirect
652. C₄×#41	C₂²×C₆₁	semidirect
653. #497	C₂²×C₆₁	semidirect
655. #492	C₂²×C₆₁	semidirect
656. #492	C₂²×C₆₁	semidirect
657. #490	C₂²×C₆₁	semidirect
658. #488	C₂²×C₆₁	semidirect
660. #486	C₂²×C₆₁	semidirect
661. #485	C₂²×C₆₁	semidirect
663. #481	C₂²×C₆₁	semidirect
664. #480	C₂²×C₆₁	semidirect
665. #479	C₂²×C₆₁	semidirect
666. #479	C₂²×C₆₁	semidirect
667. #478	C₂²×C₆₁	semidirect
668. #478	C₂²×C₆₁	semidirect
669. #478	C₂²×C₆₁	semidirect
670. #477	C₂²×C₆₁	semidirect
671. #476	C₂²×C₆₁	semidirect
672. #470	C₂²×C₆₁	semidirect
674. #468	C₂²×C₆₁	semidirect
675. #468	C₂²×C₆₁	semidirect
676. #465	C₂²×C₆₁	semidirect
677. #465	C₂²×C₆₁	semidirect
678. #464	C₂²×C₆₁	semidirect
679. #464	C₂²×C₆₁	semidirect
680. #464	C₂²×C₆₁	semidirect
681. #463	C₂²×C₆₁	semidirect
682. #463	C₂²×C₆₁	semidirect
683. #462	C₂²×C₆₁	semidirect
684. #461	C₂²×C₆₁	semidirect
685. #461	C₂²×C₆₁	semidirect
686. #461	C₂²×C₆₁	semidirect
688. #460	C₂²×C₆₁	semidirect
689. #460	C₂²×C₆₁	semidirect
690. #460	C₂²×C₆₁	semidirect
691. #460	C₂²×C₆₁	semidirect
692. #460	C₂²×C₆₁	semidirect
694. #459	C₂²×C₆₁	semidirect
695. #459	C₂²×C₆₁	semidirect
696. #459	C₂²×C₆₁	semidirect
697. #452	C₂²×C₆₁	semidirect
698. #452	C₂²×C₆₁	semidirect
699. #452	C₂²×C₆₁	semidirect
700. #450	C₂²×C₆₁	semidirect
701. #450	C₂²×C₆₁	semidirect
702. #450	C₂²×C₆₁	semidirect
703. #450	C₂²×C₆₁	semidirect
705. #449	C₂²×C₆₁	semidirect
706. #449	C₂²×C₆₁	semidirect
707. #446	C₂²×C₆₁	semidirect
708. C₈×Q₈	C₂²×C₆₁	semidirect
709. #442	C₂²×C₆₁	semidirect
710. #440	C₂²×C₆₁	semidirect
711. C₄×Q₁₆	C₂²×C₆₁	semidirect
712. C₄×SD₁₆	C₂²×C₆₁	semidirect
713. C₄×SD₁₆	C₂²×C₆₁	semidirect
714. C₄×SD₁₆	C₂²×C₆₁	semidirect
715. C₄×D₈	C₂²×C₆₁	semidirect
716. C₄×D₈	C₂²×C₆₁	semidirect
717. #436	C₂²×C₆₁	semidirect
718. #436	C₂²×C₆₁	semidirect
719. #435	C₂²×C₆₁	semidirect
720. C₈×D₄	C₂²×C₆₁	semidirect
721. #433	C₂²×C₆₁	semidirect
722. #431	C₂²×C₆₁	semidirect
723. #424	C₂²×C₆₁	semidirect
724. #423	C₂²×C₆₁	semidirect
725. #418	C₂²×C₆₁	semidirect
726. #417	C₂²×C₆₁	semidirect
727. C₂×#102	C₂²×C₆₁	semidirect
728. C₆₁	#62033	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×#3543	2
C₆₁×#3515	2
C₆₁×#3400	2
C₆₁×#3392	2
C₆₁×#3366	2
C₆₁×#3361	2
C₆₁×#3333	2
C₆₁×#3323	2
C₆₁×#3310	2
C₆₁×#3295	2
C₆₁×#3284	2
C₆₁×#3272	2
C₆₁×#3267	2
C₆₁×#3260	2
C₆₁×#3252	2
C₆₁×#3222	2
C₆₁×#3208	2
C₆₁×#3119	2
C₆₁×#3102	2
C₆₁×#3045	2
C₆₁×#3038	2
C₆₁×#2993	2
#62033	61

Subgroups — C61×#62033 #29565466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62033 #29565466