Subgroups — C₆₁×#62126 #29565559

Order 15616.

1776 conjugacy classes of subgroups.

The subgroup lattice has 1284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3481	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#3388	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3371	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3350	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3344	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3337	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3311	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3310	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3296	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3252	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3248	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3246	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3238	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3233	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3076	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₆₁×#476	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₆₁×#559	C₂²	1	1	yes	characteristic
25	C₆₁×#557	—	2	1	no	—
26	C₆₁×#557	C₂²	1	2	yes	complemented
27	C₆₁×#556	—	2	1	no	—
28	C₆₁×#556	C₂²	1	2	yes	complemented
29	C₆₁×#554	C₂²	1	1	yes	characteristic
30	C₆₁×#554	C₂²	1	1	yes	characteristic
31	C₆₁×#553	—	2	1	no	—
32	C₆₁×#553	C₂²	1	1	yes	characteristic
33	C₆₁×#553	C₂²	1	1	yes	characteristic
34	C₆₁×#552	—	2	1	no	—
35	C₆₁×#552	—	2	1	no	—
36	C₆₁×#552	C₂²	1	2	yes	—
37	C₆₁×#552	C₂²	1	2	yes	complemented
38	C₆₁×#551	—	2	1	no	—
39	C₆₁×#551	—	2	1	no	—
40	C₆₁×#546	—	2	1	no	—
41	C₆₁×#546	C₂²	1	1	yes	characteristic
42	C₆₁×#546	C₂²	1	1	yes	characteristic
43	D₄²×C₆₁	C₂²	1	1	yes	characteristic
44	C₆₁×#541	—	2	1	no	—
45	C₆₁×#541	—	2	1	no	—
46	C₆₁×#536	—	2	1	no	—
47	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
48	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
49	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
50	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
51	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
52	C₆₁×#532	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
54	C₆₁×#529	—	2	1	no	—
55	C₆₁×#529	C₂²	1	1	yes	characteristic
56	C₆₁×#529	C₂²	1	1	yes	characteristic
57	C₆₁×#525	—	2	1	no	—
58	C₆₁×#525	—	2	1	no	—
59	C₆₁×#519	—	2	1	no	—
60	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
61	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
62	C₂×C₄×D₄×C₆₁	—	2	1	no	—
63	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
64	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
65	C₆₁×#501	C₂²	1	2	yes	complemented
66	C₆₁×#501	C₂²	1	2	yes	complemented
67	C₆₁×#499	C₂²	1	2	yes	complemented
68	C₆₁×#490	C₂²	1	2	yes	—
69	C₆₁×#489	C₂²	1	2	yes	complemented
70	C₆₁×#488	C₂²	1	2	yes	complemented
71	C₆₁×#485	C₂²	1	2	yes	complemented
72	C₆₁×#485	C₂²	1	2	yes	complemented
73	C₆₁×#484	C₂²	1	2	yes	complemented
74	C₆₁×#483	C₂²	1	2	yes	complemented
75	C₆₁×#483	C₂²	1	2	yes	complemented
76	C₆₁×#482	C₂²	1	2	yes	—
77	C₆₁×#482	C₂²	1	2	yes	complemented
78	C₆₁×#482	C₂²	1	2	yes	complemented
79	C₆₁×#480	C₂²	1	2	yes	—
80	C₆₁×#479	C₂²	1	2	yes	complemented
81	C₆₁×#479	C₂²	1	2	yes	complemented
82	C₆₁×#479	C₂²	1	2	yes	complemented
83	C₆₁×#478	C₂²	1	2	yes	—
84	C₆₁×#478	C₂²	1	2	yes	—
85	C₆₁×#478	C₂²	1	2	yes	complemented
86	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
87	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
88	C₆₁×#476	C₂²	1	2	yes	—
89	C₆₁×#476	C₂²	1	1	yes	characteristic
90	C₆₁×#476	C₂²	1	1	yes	characteristic
91	C₆₁×#476	C₂²	1	2	yes	complemented
92	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
93	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
94	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
95	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
96	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
97	C₆₁×#475	C₂²	1	2	yes	complemented
98	C₆₁×#474	C₂²	1	1	yes	characteristic
99	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
100	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
101	C₆₁×#470	C₂²	1	2	yes	complemented
102	C₆₁×#468	C₂²	1	2	yes	—
103	C₆₁×#467	C₂²	1	2	yes	complemented
104	C₆₁×#465	C₂²	1	2	yes	—
105	C₆₁×#465	C₂²	1	2	yes	complemented
106	C₆₁×#465	C₂²	1	2	yes	complemented
107	C₆₁×#464	C₂²	1	2	yes	complemented
108	C₆₁×#464	C₂²	1	2	yes	complemented
109	C₆₁×#462	C₂²	1	1	yes	characteristic, complemented
110	C₆₁×#461	C₂²	1	1	yes	characteristic
111	C₆₁×#461	C₂²	1	1	yes	characteristic, complemented
112	C₆₁×#461	C₂²	1	1	yes	characteristic, complemented
113	C₆₁×#460	C₂²	1	2	yes	—
114	C₆₁×#452	C₂²	1	2	yes	—
115	C₆₁×#450	C₂²	1	2	yes	—
116	C₆₁×#450	C₂²	1	2	yes	—
117	C₆₁×#446	C₂²	1	2	yes	complemented
118	C₆₁×#441	C₂²	1	2	yes	complemented
119	C₆₁×#440	C₂²	1	2	yes	—
120	C₆₁×#440	C₂²	1	2	yes	—
121	C₆₁×#440	C₂²	1	2	yes	complemented
122	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
123	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
124	C₆₁×#435	C₂²	1	2	yes	—
125	C₆₁×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
127	C₆₁×#432	C₂²	1	1	yes	characteristic, complemented
128	C₆₁×#432	C₂²	1	1	yes	characteristic, complemented
129	C₆₁×#431	C₂²	1	1	yes	characteristic, complemented
130	C₆₁×#428	C₂²	1	2	yes	complemented
131	C₆₁×#427	C₂²	1	2	yes	complemented
132	C₂×#106×C₆₁	C₂²	1	2	yes	complemented
133	C₆₁×#423	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
136	C₆₁×#418	C₂²	1	2	yes	—
137	C₆₁×#416	C₂²	1	2	yes	—
138	C₂×#102×C₆₁	C₂²	1	2	yes	—
139	C₂×#41×C₆₁	—	2	1	no	—
140	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
141	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₆₁	—	2	1	no	—
143	C₂²×D₄×C₆₁	—	2	1	no	—
144	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
145	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₆₁	—	2	1	no	—
147	C₂³×C₄×C₆₁	—	2	1	no	—
148	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
152	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
153	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
154	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
155	C₄⋊Q₈×C₆₁	—	2	2	no	—
156	C₄⋊Q₈×C₆₁	—	2	1	no	—
157	C₄⋊Q₈×C₆₁	—	2	1	no	—
158	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
159	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
160	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
161	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
164	#127×C₆₁	C₂³	1	1	yes	characteristic
165	#126×C₆₁	—	2	1	no	—
166	#126×C₆₁	—	2	1	no	—
167	#126×C₆₁	—	2	2	no	—
168	#126×C₆₁	—	2	2	no	—
169	#126×C₆₁	—	2	2	no	—
170	#126×C₆₁	—	2	2	no	—
171	#126×C₆₁	—	2	1	no	—
172	#126×C₆₁	—	2	1	no	—
173	#125×C₆₁	—	2	2	no	—
174	#125×C₆₁	—	2	2	no	—
175	#125×C₆₁	—	2	2	no	—
176	#125×C₆₁	—	2	2	no	—
177	#125×C₆₁	—	2	1	no	—
178	#125×C₆₁	—	2	1	no	—
179	#125×C₆₁	—	2	1	no	—
180	#125×C₆₁	—	2	1	no	—
181	#125×C₆₁	C₂³	1	2	yes	—
182	#125×C₆₁	C₂³	1	2	yes	—
183	#125×C₆₁	C₂³	1	1	yes	characteristic
184	#125×C₆₁	C₂³	1	1	yes	characteristic
185	#124×C₆₁	—	2	1	no	—
186	#124×C₆₁	—	2	2	no	—
187	#124×C₆₁	—	2	1	no	—
188	#124×C₆₁	C₂³	1	1	yes	characteristic
189	#124×C₆₁	C₂³	1	1	yes	characteristic
190	#123×C₆₁	—	2	2	no	—
191	#123×C₆₁	—	2	2	no	—
192	#123×C₆₁	—	2	1	no	—
193	#123×C₆₁	—	2	1	no	—
194	#123×C₆₁	—	2	1	no	—
195	#123×C₆₁	—	2	1	no	—
196	#123×C₆₁	—	2	1	no	—
197	#123×C₆₁	—	2	1	no	—
198	#123×C₆₁	—	2	1	no	—
199	#123×C₆₁	—	2	1	no	—
200	C₂²⋊Q₈×C₆₁	—	2	1	no	—
201	C₂²⋊Q₈×C₆₁	—	2	1	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	1	no	—
206	C₂²⋊Q₈×C₆₁	—	2	1	no	—
207	C₂²⋊Q₈×C₆₁	—	2	1	no	—
208	C₂²⋊Q₈×C₆₁	—	2	1	no	—
209	C₂²⋊Q₈×C₆₁	—	2	1	no	—
210	C₂²⋊Q₈×C₆₁	—	2	1	no	—
211	C₂²⋊Q₈×C₆₁	—	2	1	no	—
212	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
213	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
214	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
215	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
216	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
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	1	no	—
222	#121×C₆₁	—	2	1	no	—
223	#121×C₆₁	C₂³	1	1	yes	characteristic
224	#121×C₆₁	C₂³	1	1	yes	characteristic
225	#121×C₆₁	C₂³	1	1	yes	characteristic
226	#121×C₆₁	C₂³	1	1	yes	characteristic
227	#120×C₆₁	—	2	1	no	—
228	#120×C₆₁	—	2	1	no	—
229	#120×C₆₁	—	2	1	no	—
230	#120×C₆₁	—	2	1	no	—
231	C₄×Q₈×C₆₁	—	2	2	no	—
232	C₄×Q₈×C₆₁	—	2	2	no	—
233	C₄×Q₈×C₆₁	—	2	1	no	—
234	C₄×Q₈×C₆₁	—	2	1	no	—
235	C₄×Q₈×C₆₁	—	2	1	no	—
236	C₄×Q₈×C₆₁	—	2	1	no	—
237	C₄×Q₈×C₆₁	—	2	1	no	—
238	C₄×Q₈×C₆₁	—	2	1	no	—
239	C₄×Q₈×C₆₁	—	2	1	no	—
240	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
241	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
242	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
243	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
244	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
245	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
246	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₆₁	—	2	1	no	—
248	C₄×D₄×C₆₁	—	2	1	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	1	no	—
255	C₄×D₄×C₆₁	—	2	1	no	—
256	C₄×D₄×C₆₁	—	2	1	no	—
257	C₄×D₄×C₆₁	—	2	1	no	—
258	C₄×D₄×C₆₁	—	2	1	no	—
259	C₄×D₄×C₆₁	—	2	1	no	—
260	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
261	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
262	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
263	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
266	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
267	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
268	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
269	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
270	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
271	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
272	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
273	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
274	#117×C₆₁	—	2	1	no	—
275	#117×C₆₁	—	2	1	no	—
276	#117×C₆₁	—	2	1	no	—
277	#117×C₆₁	—	2	2	no	—
278	#117×C₆₁	—	2	2	no	—
279	#117×C₆₁	—	2	1	no	—
280	#117×C₆₁	—	2	1	no	—
281	#117×C₆₁	—	2	1	no	—
282	#117×C₆₁	D₄	1	1	yes	characteristic
283	#117×C₆₁	D₄	1	1	yes	characteristic
284	#117×C₆₁	D₄	1	1	yes	characteristic
285	#117×C₆₁	C₂³	1	2	yes	—
286	#117×C₆₁	C₂³	1	2	yes	—
287	#117×C₆₁	C₂³	1	1	yes	characteristic
288	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
289	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
290	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
291	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
294	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
295	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
296	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
297	C₂×C₄²×C₆₁	—	2	1	no	—
298	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
300	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
301	#107×C₆₁	C₂³	1	2	yes	—
302	#107×C₆₁	C₂³	1	2	yes	—
303	#107×C₆₁	C₂³	1	2	yes	—
304	#107×C₆₁	C₂³	1	2	yes	—
305	#107×C₆₁	C₂³	1	2	yes	—
306	#106×C₆₁	C₂³	1	2	yes	—
307	#106×C₆₁	C₂³	1	2	yes	—
308	#106×C₆₁	C₂³	1	2	yes	—
309	#106×C₆₁	C₂³	1	2	yes	—
310	#106×C₆₁	C₂³	1	2	yes	—
311	#106×C₆₁	C₂³	1	2	yes	—
312	#106×C₆₁	C₂³	1	2	yes	—
313	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
314	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
315	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
316	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
317	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
318	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
319	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
320	#103×C₆₁	C₂³	1	2	yes	—
321	#103×C₆₁	C₂³	1	2	yes	—
322	#103×C₆₁	C₂³	1	2	yes	—
323	#103×C₆₁	C₂³	1	2	yes	—
324	#103×C₆₁	C₂³	1	2	yes	—
325	#103×C₆₁	C₂³	1	2	yes	—
326	#103×C₆₁	C₂³	1	2	yes	—
327	#102×C₆₁	C₂³	1	2	yes	—
328	#102×C₆₁	C₂³	1	2	yes	—
329	#102×C₆₁	C₂³	1	2	yes	—
330	#102×C₆₁	C₂³	1	2	yes	—
331	#102×C₆₁	C₂³	1	2	yes	—
332	#102×C₆₁	C₂³	1	2	yes	—
333	#102×C₆₁	C₂³	1	2	yes	—
334	#102×C₆₁	C₂³	1	2	yes	—
335	#102×C₆₁	C₂³	1	2	yes	—
336	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
337	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
338	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
339	#97×C₆₁	C₂³	1	2	yes	—
340	#97×C₆₁	C₂³	1	2	yes	—
341	C₄×C₈×C₆₁	C₂³	1	2	yes	—
342	C₂⁴×C₆₁	—	2	1	no	—
343	C₂⁴×C₆₁	—	2	1	no	—
344	#41×C₆₁	—	2	2	no	—
345	#41×C₆₁	—	4	2	no	—
346	#41×C₆₁	—	4	1	no	—
347	#41×C₆₁	—	8	2	no	—
348	C₂×Q₈×C₆₁	—	2	1	no	—
349	C₂×Q₈×C₆₁	—	2	1	no	—
350	C₂×Q₈×C₆₁	—	2	1	no	—
351	C₂×Q₈×C₆₁	—	2	2	no	—
352	C₂×Q₈×C₆₁	—	2	1	no	—
353	C₂×Q₈×C₆₁	—	4	4	no	—
354	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
355	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
357	C₂×D₄×C₆₁	—	2	2	no	—
358	C₂×D₄×C₆₁	—	2	2	no	—
359	C₂×D₄×C₆₁	—	2	1	no	—
360	C₂×D₄×C₆₁	—	2	1	no	—
361	C₂×D₄×C₆₁	—	2	1	no	—
362	C₂×D₄×C₆₁	—	2	1	no	—
363	C₂×D₄×C₆₁	—	2	1	no	—
364	C₂×D₄×C₆₁	—	2	1	no	—
365	C₂×D₄×C₆₁	—	2	1	no	—
366	C₂×D₄×C₆₁	—	2	1	no	—
367	C₂×D₄×C₆₁	—	2	1	no	—
368	C₂×D₄×C₆₁	—	4	1	no	—
369	C₂×D₄×C₆₁	—	4	1	no	—
370	C₂×D₄×C₆₁	—	4	4	no	—
371	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
372	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
373	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
374	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
375	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
376	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₆₁	—	2	2	no	—
378	C₂²×C₄×C₆₁	—	2	1	no	—
379	C₂²×C₄×C₆₁	—	2	1	no	—
380	C₂²×C₄×C₆₁	—	2	1	no	—
381	C₂²×C₄×C₆₁	—	2	1	no	—
382	C₂²×C₄×C₆₁	—	2	1	no	—
383	C₂²×C₄×C₆₁	—	2	1	no	—
384	C₂²×C₄×C₆₁	—	2	1	no	—
385	C₂²×C₄×C₆₁	—	2	1	no	—
386	C₂²×C₄×C₆₁	—	2	1	no	—
387	C₂²×C₄×C₆₁	—	2	1	no	—
388	C₂²×C₄×C₆₁	—	2	1	no	—
389	C₂²×C₄×C₆₁	—	8	2	no	—
390	C₂²×C₄×C₆₁	—	8	2	no	—
391	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
397	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
400	Q₁₆×C₆₁	—	4	2	no	—
401	SD₁₆×C₆₁	—	2	4	no	—
402	SD₁₆×C₆₁	—	4	2	no	—
403	SD₁₆×C₆₁	—	4	2	no	—
404	M₁₆×C₆₁	—	4	2	no	—
405	C₂×C₈×C₆₁	—	4	2	no	—
406	C₂×C₈×C₆₁	—	4	2	no	—
407	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
408	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
409	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
410	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₆₁	—	2	1	no	—
412	C₄⋊C₄×C₆₁	—	2	1	no	—
413	C₄⋊C₄×C₆₁	—	2	1	no	—
414	C₄⋊C₄×C₆₁	—	2	1	no	—
415	C₄⋊C₄×C₆₁	—	2	1	no	—
416	C₄⋊C₄×C₆₁	—	2	2	no	—
417	C₄⋊C₄×C₆₁	—	2	1	no	—
418	C₄⋊C₄×C₆₁	—	2	1	no	—
419	C₄⋊C₄×C₆₁	—	2	2	no	—
420	C₄⋊C₄×C₆₁	—	2	1	no	—
421	C₄⋊C₄×C₆₁	—	2	1	no	—
422	C₄⋊C₄×C₆₁	—	2	1	no	—
423	C₄⋊C₄×C₆₁	—	2	1	no	—
424	C₄⋊C₄×C₆₁	—	2	1	no	—
425	C₄⋊C₄×C₆₁	—	2	2	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	1	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	—	2	2	no	—
436	C₄⋊C₄×C₆₁	—	2	2	no	—
437	C₄⋊C₄×C₆₁	—	2	2	no	—
438	C₄⋊C₄×C₆₁	—	2	2	no	—
439	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
440	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
441	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
445	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
446	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
447	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
448	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
451	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
452	C₂²⋊C₄×C₆₁	—	2	1	no	—
453	C₂²⋊C₄×C₆₁	—	2	1	no	—
454	C₂²⋊C₄×C₆₁	—	2	2	no	—
455	C₂²⋊C₄×C₆₁	—	2	2	no	—
456	C₂²⋊C₄×C₆₁	—	2	2	no	—
457	C₂²⋊C₄×C₆₁	—	2	1	no	—
458	C₂²⋊C₄×C₆₁	—	2	2	no	—
459	C₂²⋊C₄×C₆₁	—	2	2	no	—
460	C₂²⋊C₄×C₆₁	—	2	1	no	—
461	C₂²⋊C₄×C₆₁	—	2	1	no	—
462	C₂²⋊C₄×C₆₁	—	2	1	no	—
463	C₂²⋊C₄×C₆₁	—	2	1	no	—
464	C₂²⋊C₄×C₆₁	—	2	1	no	—
465	C₂²⋊C₄×C₆₁	—	2	1	no	—
466	C₂²⋊C₄×C₆₁	—	2	1	no	—
467	C₂²⋊C₄×C₆₁	—	2	1	no	—
468	C₂²⋊C₄×C₆₁	—	2	1	no	—
469	C₂²⋊C₄×C₆₁	—	2	1	no	—
470	C₂²⋊C₄×C₆₁	—	2	1	no	—
471	C₂²⋊C₄×C₆₁	—	2	1	no	—
472	C₂²⋊C₄×C₆₁	—	2	1	no	—
473	C₂²⋊C₄×C₆₁	—	2	1	no	—
474	C₂²⋊C₄×C₆₁	—	2	1	no	—
475	C₂²⋊C₄×C₆₁	—	2	1	no	—
476	C₂²⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
477	C₂²⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
478	C₂²⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
479	C₂²⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
480	C₂²⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
481	C₂²⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
482	C₄²×C₆₁	—	2	1	no	—
483	C₄²×C₆₁	—	2	1	no	—
484	C₄²×C₆₁	—	2	1	no	—
485	C₄²×C₆₁	—	2	2	no	—
486	C₄²×C₆₁	—	2	2	no	—
487	C₄²×C₆₁	—	2	2	no	—
488	C₄²×C₆₁	—	2	2	no	—
489	C₄²×C₆₁	—	2	2	no	—
490	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
491	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
492	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
493	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
494	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
495	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
496	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
497	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
498	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
499	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
500	C₂³×C₆₁	—	2	1	no	—
501	C₂³×C₆₁	—	2	1	no	—
502	C₂³×C₆₁	—	2	1	no	—
503	C₂³×C₆₁	—	4	2	no	—
504	C₂³×C₆₁	—	4	2	no	—
505	C₂³×C₆₁	—	4	2	no	—
506	C₂³×C₆₁	—	4	2	no	—
507	C₂³×C₆₁	—	8	1	no	—
508	C₂³×C₆₁	—	8	1	no	—
509	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
510	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
511	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
512	Q₈×C₆₁	—	2	2	no	—
513	Q₈×C₆₁	—	2	1	no	—
514	Q₈×C₆₁	—	2	2	no	—
515	Q₈×C₆₁	—	2	1	no	—
516	Q₈×C₆₁	—	4	1	no	—
517	Q₈×C₆₁	—	4	2	no	—
518	Q₈×C₆₁	—	4	2	no	—
519	Q₈×C₆₁	—	4	4	no	—
520	Q₈×C₆₁	—	4	2	no	—
521	Q₈×C₆₁	—	8	1	no	—
522	D₄×C₆₁	—	2	2	no	—
523	D₄×C₆₁	—	2	2	no	—
524	D₄×C₆₁	—	2	1	no	—
525	D₄×C₆₁	—	2	1	no	—
526	D₄×C₆₁	—	2	1	no	—
527	D₄×C₆₁	—	2	1	no	—
528	D₄×C₆₁	—	2	1	no	—
529	D₄×C₆₁	—	4	1	no	—
530	D₄×C₆₁	—	4	2	no	—
531	D₄×C₆₁	—	4	2	no	—
532	D₄×C₆₁	—	4	2	no	—
533	D₄×C₆₁	—	4	2	no	—
534	D₄×C₆₁	—	4	2	no	—
535	D₄×C₆₁	—	4	2	no	—
536	D₄×C₆₁	—	8	1	no	—
537	D₄×C₆₁	—	8	1	no	—
538	D₄×C₆₁	—	8	1	no	—
539	D₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
540	C₂×C₄×C₆₁	—	2	2	no	—
541	C₂×C₄×C₆₁	—	2	2	no	—
542	C₂×C₄×C₆₁	—	2	2	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	—	2	1	no	—
547	C₂×C₄×C₆₁	—	2	1	no	—
548	C₂×C₄×C₆₁	—	2	1	no	—
549	C₂×C₄×C₆₁	—	2	1	no	—
550	C₂×C₄×C₆₁	—	2	2	no	—
551	C₂×C₄×C₆₁	—	2	2	no	—
552	C₂×C₄×C₆₁	—	2	1	no	—
553	C₂×C₄×C₆₁	—	2	1	no	—
554	C₂×C₄×C₆₁	—	2	1	no	—
555	C₂×C₄×C₆₁	—	2	2	no	—
556	C₂×C₄×C₆₁	—	2	2	no	—
557	C₂×C₄×C₆₁	—	2	1	no	—
558	C₂×C₄×C₆₁	—	2	1	no	—
559	C₂×C₄×C₆₁	—	4	1	no	—
560	C₂×C₄×C₆₁	—	4	1	no	—
561	C₂×C₄×C₆₁	—	4	2	no	—
562	C₂×C₄×C₆₁	—	4	2	no	—
563	C₂×C₄×C₆₁	—	4	4	no	—
564	C₂×C₄×C₆₁	—	4	2	no	—
565	C₂×C₄×C₆₁	—	4	2	no	—
566	C₂×C₄×C₆₁	—	4	2	no	—
567	C₂×C₄×C₆₁	—	8	1	no	—
568	C₂×C₄×C₆₁	—	8	1	no	—
569	C₂×C₄×C₆₁	—	8	1	no	—
570	C₂×C₄×C₆₁	—	8	1	no	—
571	C₂×C₄×C₆₁	—	8	1	no	—
572	C₂×C₄×C₆₁	—	8	1	no	—
573	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
574	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
575	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
576	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
577	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
578	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
579	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
580	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
581	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
582	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
583	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
584	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
585	C₈×C₆₁	—	2	2	no	—
586	C₈×C₆₁	—	2	2	no	—
587	C₈×C₆₁	—	2	2	no	—
588	C₈×C₆₁	—	2	2	no	—
589	#62126	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
590	C₂²×C₆₁	—	2	1	no	—
591	C₂²×C₆₁	—	2	1	no	—
592	C₂²×C₆₁	—	2	1	no	—
593	C₂²×C₆₁	—	2	1	no	—
594	C₂²×C₆₁	—	2	2	no	—
595	C₂²×C₆₁	—	2	1	no	—
596	C₂²×C₆₁	—	2	1	no	—
597	C₂²×C₆₁	—	2	1	no	—
598	C₂²×C₆₁	—	2	1	no	—
599	C₂²×C₆₁	—	4	1	no	—
600	C₂²×C₆₁	—	4	1	no	—
601	C₂²×C₆₁	—	4	1	no	—
602	C₂²×C₆₁	—	4	1	no	—
603	C₂²×C₆₁	—	4	1	no	—
604	C₂²×C₆₁	—	4	1	no	—
605	C₂²×C₆₁	—	4	1	no	—
606	C₂²×C₆₁	—	4	1	no	—
607	C₂²×C₆₁	—	8	4	no	—
608	C₂²×C₆₁	—	8	4	no	—
609	C₂²×C₆₁	#575	1	2	yes	—
610	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
611	C₄×C₆₁	—	2	1	no	—
612	C₄×C₆₁	—	2	1	no	—
613	C₄×C₆₁	—	2	1	no	—
614	C₄×C₆₁	—	2	1	no	—
615	C₄×C₆₁	—	2	1	no	—
616	C₄×C₆₁	—	2	1	no	—
617	C₄×C₆₁	—	2	1	no	—
618	C₄×C₆₁	—	2	1	no	—
619	C₄×C₆₁	—	2	1	no	—
620	C₄×C₆₁	—	2	1	no	—
621	C₄×C₆₁	—	4	1	no	—
622	C₄×C₆₁	—	4	2	no	—
623	C₄×C₆₁	—	4	1	no	—
624	C₄×C₆₁	—	4	2	no	—
625	C₄×C₆₁	—	4	2	no	—
626	C₄×C₆₁	—	4	1	no	—
627	C₄×C₆₁	—	4	1	no	—
628	C₄×C₆₁	—	4	1	no	—
629	C₄×C₆₁	—	4	2	no	—
630	C₄×C₆₁	#577	1	2	yes	—
631	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
632	C₄×C₆₁	#585	1	1	yes	characteristic
633	#3509	C₂×C₆₁	1	1	yes	characteristic, complemented
634	#3481	C₂×C₆₁	1	1	yes	characteristic
635	#3388	C₂×C₆₁	1	2	yes	complemented
636	#3371	C₂×C₆₁	1	2	yes	complemented
637	#3350	C₂×C₆₁	1	2	yes	complemented
638	#3344	C₂×C₆₁	1	2	yes	complemented
639	#3337	C₂×C₆₁	1	2	yes	complemented
640	#3311	C₂×C₆₁	1	2	yes	complemented
641	#3310	C₂×C₆₁	1	2	yes	complemented
642	#3296	C₂×C₆₁	1	2	yes	complemented
643	#3252	C₂×C₆₁	1	1	yes	characteristic, complemented
644	#3248	C₂×C₆₁	1	1	yes	characteristic, complemented
645	#3246	C₂×C₆₁	1	1	yes	characteristic, complemented
646	#3238	C₂×C₆₁	1	1	yes	characteristic, complemented
647	#3235	C₂×C₆₁	1	1	yes	characteristic, complemented
648	#3233	C₂×C₆₁	1	1	yes	characteristic, complemented
649	#3116	C₂×C₆₁	1	1	yes	characteristic, complemented
650	#3110	C₂×C₆₁	1	1	yes	characteristic, complemented
651	#3101	C₂×C₆₁	1	1	yes	characteristic, complemented
652	#3077	C₂×C₆₁	1	1	yes	characteristic, complemented
653	#3076	C₂×C₆₁	1	1	yes	characteristic, complemented
654	C₂×#476	C₂×C₆₁	1	1	yes	characteristic, complemented
655	#2990	C₂×C₆₁	1	1	yes	characteristic, complemented
656	C₂×C₆₁	—	2	2	no	—
657	C₂×C₆₁	—	4	1	no	—
658	C₂×C₆₁	—	4	1	no	—
659	C₂×C₆₁	—	4	2	no	—
660	C₂×C₆₁	—	8	1	no	—
661	C₂×C₆₁	—	8	1	no	—
662	C₂×C₆₁	#3489	1	1	yes	characteristic
663	C₂×C₆₁	C₂×#575	1	1	yes	characteristic
664	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
665	#559	C₂²×C₆₁	1	1	yes	characteristic
666	#557	—	2	1	no	—
667	#557	C₂²×C₆₁	1	2	yes	complemented
668	#556	—	2	1	no	—
669	#556	C₂²×C₆₁	1	2	yes	complemented
670	#554	C₂²×C₆₁	1	1	yes	characteristic
671	#554	C₂²×C₆₁	1	1	yes	characteristic
672	#553	—	2	1	no	—
673	#553	C₂²×C₆₁	1	1	yes	characteristic
674	#553	C₂²×C₆₁	1	1	yes	characteristic
675	#552	—	2	1	no	—
676	#552	—	2	1	no	—
677	#552	C₂²×C₆₁	1	2	yes	—
678	#552	C₂²×C₆₁	1	2	yes	complemented
679	#551	—	2	1	no	—
680	#551	—	2	1	no	—
681	#546	—	2	1	no	—
682	#546	C₂²×C₆₁	1	1	yes	characteristic
683	#546	C₂²×C₆₁	1	1	yes	characteristic
684	D₄²	C₂²×C₆₁	1	1	yes	characteristic
685	#541	—	2	1	no	—
686	#541	—	2	1	no	—
687	#536	—	2	1	no	—
688	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
689	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
690	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
691	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
692	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
693	#532	C₂²×C₆₁	1	1	yes	characteristic
694	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
695	#529	—	2	1	no	—
696	#529	C₂²×C₆₁	1	1	yes	characteristic
697	#529	C₂²×C₆₁	1	1	yes	characteristic
698	#525	—	2	1	no	—
699	#525	—	2	1	no	—
700	#519	—	2	1	no	—
701	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
702	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
703	C₂×C₄×D₄	—	2	1	no	—
704	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
705	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
706	#501	C₂²×C₆₁	1	2	yes	complemented
707	#501	C₂²×C₆₁	1	2	yes	complemented
708	#499	C₂²×C₆₁	1	2	yes	complemented
709	#490	C₂²×C₆₁	1	2	yes	—
710	#489	C₂²×C₆₁	1	2	yes	complemented
711	#488	C₂²×C₆₁	1	2	yes	complemented
712	#485	C₂²×C₆₁	1	2	yes	complemented
713	#485	C₂²×C₆₁	1	2	yes	complemented
714	#484	C₂²×C₆₁	1	2	yes	complemented
715	#483	C₂²×C₆₁	1	2	yes	complemented
716	#483	C₂²×C₆₁	1	2	yes	complemented
717	#482	C₂²×C₆₁	1	2	yes	—
718	#482	C₂²×C₆₁	1	2	yes	complemented
719	#482	C₂²×C₆₁	1	2	yes	complemented
720	#480	C₂²×C₆₁	1	2	yes	—
721	#479	C₂²×C₆₁	1	2	yes	complemented
722	#479	C₂²×C₆₁	1	2	yes	complemented
723	#479	C₂²×C₆₁	1	2	yes	complemented
724	#478	C₂²×C₆₁	1	2	yes	—
725	#478	C₂²×C₆₁	1	2	yes	—
726	#478	C₂²×C₆₁	1	2	yes	complemented
727	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
728	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
729	#476	C₂²×C₆₁	1	1	yes	characteristic
730	#476	C₂²×C₆₁	1	1	yes	characteristic
731	#476	C₂²×C₆₁	1	2	yes	—
732	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
733	#476	C₂²×C₆₁	1	2	yes	complemented
734	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
735	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
736	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
737	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
738	#475	C₂²×C₆₁	1	2	yes	complemented
739	#474	C₂²×C₆₁	1	1	yes	characteristic
740	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
741	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
742	#470	C₂²×C₆₁	1	2	yes	complemented
743	#468	C₂²×C₆₁	1	2	yes	—
744	#467	C₂²×C₆₁	1	2	yes	complemented
745	#465	C₂²×C₆₁	1	2	yes	—
746	#465	C₂²×C₆₁	1	2	yes	complemented
747	#465	C₂²×C₆₁	1	2	yes	complemented
748	#464	C₂²×C₆₁	1	2	yes	complemented
749	#464	C₂²×C₆₁	1	2	yes	complemented
750	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
751	#461	C₂²×C₆₁	1	1	yes	characteristic
752	#461	C₂²×C₆₁	1	1	yes	characteristic, complemented
753	#461	C₂²×C₆₁	1	1	yes	characteristic, complemented
754	#460	C₂²×C₆₁	1	2	yes	—
755	#452	C₂²×C₆₁	1	2	yes	—
756	#450	C₂²×C₆₁	1	2	yes	—
757	#450	C₂²×C₆₁	1	2	yes	—
758	#446	C₂²×C₆₁	1	2	yes	complemented
759	#441	C₂²×C₆₁	1	2	yes	complemented
760	#440	C₂²×C₆₁	1	2	yes	—
761	#440	C₂²×C₆₁	1	2	yes	—
762	#440	C₂²×C₆₁	1	2	yes	complemented
763	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
764	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
765	#435	C₂²×C₆₁	1	2	yes	—
766	#435	C₂²×C₆₁	1	2	yes	complemented
767	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
768	#432	C₂²×C₆₁	1	1	yes	characteristic, complemented
769	#432	C₂²×C₆₁	1	1	yes	characteristic, complemented
770	#431	C₂²×C₆₁	1	1	yes	characteristic, complemented
771	#428	C₂²×C₆₁	1	2	yes	complemented
772	#427	C₂²×C₆₁	1	2	yes	complemented
773	C₂×#106	C₂²×C₆₁	1	2	yes	complemented
774	#423	C₂²×C₆₁	1	1	yes	characteristic, complemented
775	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
776	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
777	#418	C₂²×C₆₁	1	2	yes	—
778	#416	C₂²×C₆₁	1	2	yes	—
779	C₂×#102	C₂²×C₆₁	1	2	yes	—
780	C₆₁	#62126	1	1	yes	characteristic, direct product factor, Sylow
781	C₂×#41	—	2	1	no	—
782	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
783	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
784	C₂²×Q₈	—	2	1	no	—
785	C₂²×D₄	—	2	1	no	—
786	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
787	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
788	C₂³×C₄	—	2	1	no	—
789	C₂³×C₄	—	2	1	no	—
790	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
791	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
792	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
793	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
794	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
795	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
796	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
797	C₄⋊Q₈	—	2	2	no	—
798	C₄⋊Q₈	—	2	1	no	—
799	C₄⋊Q₈	—	2	1	no	—
800	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
801	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
802	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
803	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
804	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
805	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
806	#127	C₂³×C₆₁	1	1	yes	characteristic
807	#126	—	2	1	no	—
808	#126	—	2	1	no	—
809	#126	—	2	2	no	—
810	#126	—	2	2	no	—
811	#126	—	2	2	no	—
812	#126	—	2	2	no	—
813	#126	—	2	1	no	—
814	#126	—	2	1	no	—
815	#125	—	2	1	no	—
816	#125	—	2	2	no	—
817	#125	—	2	2	no	—
818	#125	—	2	2	no	—
819	#125	—	2	2	no	—
820	#125	—	2	1	no	—
821	#125	—	2	1	no	—
822	#125	—	2	1	no	—
823	#125	C₂³×C₆₁	1	1	yes	characteristic
824	#125	C₂³×C₆₁	1	1	yes	characteristic
825	#125	C₂³×C₆₁	1	2	yes	—
826	#125	C₂³×C₆₁	1	2	yes	—
827	#124	—	2	1	no	—
828	#124	—	2	2	no	—
829	#124	—	2	1	no	—
830	#124	C₂³×C₆₁	1	1	yes	characteristic
831	#124	C₂³×C₆₁	1	1	yes	characteristic
832	#123	—	2	2	no	—
833	#123	—	2	2	no	—
834	#123	—	2	1	no	—
835	#123	—	2	1	no	—
836	#123	—	2	1	no	—
837	#123	—	2	1	no	—
838	#123	—	2	1	no	—
839	#123	—	2	1	no	—
840	#123	—	2	1	no	—
841	#123	—	2	1	no	—
842	C₂²⋊Q₈	—	2	1	no	—
843	C₂²⋊Q₈	—	2	1	no	—
844	C₂²⋊Q₈	—	2	1	no	—
845	C₂²⋊Q₈	—	2	1	no	—
846	C₂²⋊Q₈	—	2	1	no	—
847	C₂²⋊Q₈	—	2	1	no	—
848	C₂²⋊Q₈	—	2	1	no	—
849	C₂²⋊Q₈	—	2	1	no	—
850	C₂²⋊Q₈	—	2	1	no	—
851	C₂²⋊Q₈	—	2	1	no	—
852	C₂²⋊Q₈	—	2	1	no	—
853	C₂²⋊Q₈	—	2	1	no	—
854	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
855	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
856	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
857	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
858	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
859	#121	—	2	1	no	—
860	#121	—	2	1	no	—
861	#121	—	2	1	no	—
862	#121	—	2	1	no	—
863	#121	—	2	1	no	—
864	#121	—	2	1	no	—
865	#121	C₂³×C₆₁	1	1	yes	characteristic
866	#121	C₂³×C₆₁	1	1	yes	characteristic
867	#121	C₂³×C₆₁	1	1	yes	characteristic
868	#121	C₂³×C₆₁	1	1	yes	characteristic
869	#120	—	2	1	no	—
870	#120	—	2	1	no	—
871	#120	—	2	1	no	—
872	#120	—	2	1	no	—
873	C₄×Q₈	—	2	2	no	—
874	C₄×Q₈	—	2	2	no	—
875	C₄×Q₈	—	2	1	no	—
876	C₄×Q₈	—	2	1	no	—
877	C₄×Q₈	—	2	1	no	—
878	C₄×Q₈	—	2	1	no	—
879	C₄×Q₈	—	2	1	no	—
880	C₄×Q₈	—	2	1	no	—
881	C₄×Q₈	—	2	1	no	—
882	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
883	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
884	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
885	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
886	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
887	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
888	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
889	C₄×D₄	—	2	1	no	—
890	C₄×D₄	—	2	1	no	—
891	C₄×D₄	—	2	1	no	—
892	C₄×D₄	—	2	1	no	—
893	C₄×D₄	—	2	1	no	—
894	C₄×D₄	—	2	1	no	—
895	C₄×D₄	—	2	1	no	—
896	C₄×D₄	—	2	1	no	—
897	C₄×D₄	—	2	1	no	—
898	C₄×D₄	—	2	1	no	—
899	C₄×D₄	—	2	1	no	—
900	C₄×D₄	—	2	1	no	—
901	C₄×D₄	—	2	1	no	—
902	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
903	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
904	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
905	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
906	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
907	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
908	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
909	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
910	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
911	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
912	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
913	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
914	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
915	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
916	#117	—	2	1	no	—
917	#117	—	2	1	no	—
918	#117	—	2	1	no	—
919	#117	—	2	2	no	—
920	#117	—	2	2	no	—
921	#117	—	2	1	no	—
922	#117	—	2	1	no	—
923	#117	—	2	1	no	—
924	#117	D₄×C₆₁	1	1	yes	characteristic
925	#117	D₄×C₆₁	1	1	yes	characteristic
926	#117	D₄×C₆₁	1	1	yes	characteristic
927	#117	C₂³×C₆₁	1	1	yes	characteristic
928	#117	C₂³×C₆₁	1	2	yes	—
929	#117	C₂³×C₆₁	1	2	yes	—
930	C₂×C₄⋊C₄	—	2	1	no	—
931	C₂×C₄⋊C₄	—	2	1	no	—
932	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
933	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
934	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
935	C₂×C₂²⋊C₄	—	2	1	no	—
936	C₂×C₂²⋊C₄	—	2	1	no	—
937	C₂×C₂²⋊C₄	—	2	1	no	—
938	C₂×C₂²⋊C₄	—	2	1	no	—
939	C₂×C₄²	—	2	1	no	—
940	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
941	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
942	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
943	#107	C₂³×C₆₁	1	2	yes	—
944	#107	C₂³×C₆₁	1	2	yes	—
945	#107	C₂³×C₆₁	1	2	yes	—
946	#107	C₂³×C₆₁	1	2	yes	—
947	#107	C₂³×C₆₁	1	2	yes	—
948	#106	C₂³×C₆₁	1	2	yes	—
949	#106	C₂³×C₆₁	1	2	yes	—
950	#106	C₂³×C₆₁	1	2	yes	—
951	#106	C₂³×C₆₁	1	2	yes	—
952	#106	C₂³×C₆₁	1	2	yes	—
953	#106	C₂³×C₆₁	1	2	yes	—
954	#106	C₂³×C₆₁	1	2	yes	—
955	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
956	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
957	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
958	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
959	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
960	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
961	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
962	#103	C₂³×C₆₁	1	2	yes	—
963	#103	C₂³×C₆₁	1	2	yes	—
964	#103	C₂³×C₆₁	1	2	yes	—
965	#103	C₂³×C₆₁	1	2	yes	—
966	#103	C₂³×C₆₁	1	2	yes	—
967	#103	C₂³×C₆₁	1	2	yes	—
968	#103	C₂³×C₆₁	1	2	yes	—
969	#102	C₂³×C₆₁	1	2	yes	—
970	#102	C₂³×C₆₁	1	2	yes	—
971	#102	C₂³×C₆₁	1	2	yes	—
972	#102	C₂³×C₆₁	1	2	yes	—
973	#102	C₂³×C₆₁	1	2	yes	—
974	#102	C₂³×C₆₁	1	2	yes	—
975	#102	C₂³×C₆₁	1	2	yes	—
976	#102	C₂³×C₆₁	1	2	yes	—
977	#102	C₂³×C₆₁	1	2	yes	—
978	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
979	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
980	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
981	#97	C₂³×C₆₁	1	2	yes	—
982	#97	C₂³×C₆₁	1	2	yes	—
983	C₄×C₈	C₂³×C₆₁	1	2	yes	—
984	C₂⁴	—	2	1	no	—
985	C₂⁴	—	2	1	no	—
986	#41	—	2	2	no	—
987	#41	—	4	2	no	—
988	#41	—	4	1	no	—
989	#41	—	8	2	no	—
990	C₂×Q₈	—	2	1	no	—
991	C₂×Q₈	—	2	1	no	—
992	C₂×Q₈	—	2	1	no	—
993	C₂×Q₈	—	2	2	no	—
994	C₂×Q₈	—	2	1	no	—
995	C₂×Q₈	—	4	4	no	—
996	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
997	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
998	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	2	1	no	—
1002	C₂×D₄	—	2	1	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	2	1	no	—
1005	C₂×D₄	—	2	1	no	—
1006	C₂×D₄	—	2	1	no	—
1007	C₂×D₄	—	2	1	no	—
1008	C₂×D₄	—	2	1	no	—
1009	C₂×D₄	—	2	1	no	—
1010	C₂×D₄	—	4	1	no	—
1011	C₂×D₄	—	4	1	no	—
1012	C₂×D₄	—	4	4	no	—
1013	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1014	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1015	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1016	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
1017	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
1018	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
1019	C₂²×C₄	—	2	2	no	—
1020	C₂²×C₄	—	2	1	no	—
1021	C₂²×C₄	—	2	1	no	—
1022	C₂²×C₄	—	2	1	no	—
1023	C₂²×C₄	—	2	1	no	—
1024	C₂²×C₄	—	2	1	no	—
1025	C₂²×C₄	—	2	1	no	—
1026	C₂²×C₄	—	2	1	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	—	8	2	no	—
1032	C₂²×C₄	—	8	2	no	—
1033	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1034	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1035	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1036	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1037	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1038	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1039	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1040	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1041	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1042	Q₁₆	—	4	2	no	—
1043	SD₁₆	—	2	4	no	—
1044	SD₁₆	—	4	2	no	—
1045	SD₁₆	—	4	2	no	—
1046	M₁₆	—	4	2	no	—
1047	C₂×C₈	—	4	2	no	—
1048	C₂×C₈	—	4	2	no	—
1049	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
1050	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
1051	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
1052	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	1	no	—
1060	C₄⋊C₄	—	2	1	no	—
1061	C₄⋊C₄	—	2	2	no	—
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	—	2	1	no	—
1064	C₄⋊C₄	—	2	1	no	—
1065	C₄⋊C₄	—	2	1	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	2	no	—
1068	C₄⋊C₄	—	2	2	no	—
1069	C₄⋊C₄	—	2	2	no	—
1070	C₄⋊C₄	—	2	2	no	—
1071	C₄⋊C₄	—	2	1	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	—	2	1	no	—
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	2	no	—
1076	C₄⋊C₄	—	2	2	no	—
1077	C₄⋊C₄	—	2	2	no	—
1078	C₄⋊C₄	—	2	2	no	—
1079	C₄⋊C₄	—	2	2	no	—
1080	C₄⋊C₄	—	2	2	no	—
1081	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1082	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1083	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1084	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1085	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1086	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1087	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1088	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1089	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1090	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1091	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1092	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1093	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	2	no	—
1097	C₂²⋊C₄	—	2	2	no	—
1098	C₂²⋊C₄	—	2	2	no	—
1099	C₂²⋊C₄	—	2	1	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	—	2	1	no	—
1103	C₂²⋊C₄	—	2	1	no	—
1104	C₂²⋊C₄	—	2	1	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	1	no	—
1108	C₂²⋊C₄	—	2	1	no	—
1109	C₂²⋊C₄	—	2	1	no	—
1110	C₂²⋊C₄	—	2	1	no	—
1111	C₂²⋊C₄	—	2	1	no	—
1112	C₂²⋊C₄	—	2	1	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	—	2	1	no	—
1115	C₂²⋊C₄	—	2	1	no	—
1116	C₂²⋊C₄	—	2	1	no	—
1117	C₂²⋊C₄	—	2	1	no	—
1118	C₂²⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1119	C₂²⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1120	C₂²⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1121	C₂²⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1122	C₂²⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1123	C₂²⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1124	C₄²	—	2	1	no	—
1125	C₄²	—	2	1	no	—
1126	C₄²	—	2	1	no	—
1127	C₄²	—	2	2	no	—
1128	C₄²	—	2	2	no	—
1129	C₄²	—	2	2	no	—
1130	C₄²	—	2	2	no	—
1131	C₄²	—	2	2	no	—
1132	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1133	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1134	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1135	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1136	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1137	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1138	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1139	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1140	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1141	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1142	C₂³	—	2	1	no	—
1143	C₂³	—	2	1	no	—
1144	C₂³	—	2	1	no	—
1145	C₂³	—	4	2	no	—
1146	C₂³	—	4	2	no	—
1147	C₂³	—	4	2	no	—
1148	C₂³	—	4	2	no	—
1149	C₂³	—	8	1	no	—
1150	C₂³	—	8	1	no	—
1151	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1152	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1153	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1154	Q₈	—	2	2	no	—
1155	Q₈	—	2	1	no	—
1156	Q₈	—	2	2	no	—
1157	Q₈	—	2	1	no	—
1158	Q₈	—	4	1	no	—
1159	Q₈	—	4	2	no	—
1160	Q₈	—	4	2	no	—
1161	Q₈	—	4	4	no	—
1162	Q₈	—	4	2	no	—
1163	Q₈	—	8	1	no	—
1164	D₄	—	2	2	no	—
1165	D₄	—	2	2	no	—
1166	D₄	—	2	1	no	—
1167	D₄	—	2	1	no	—
1168	D₄	—	2	1	no	—
1169	D₄	—	2	1	no	—
1170	D₄	—	2	1	no	—
1171	D₄	—	4	1	no	—
1172	D₄	—	4	2	no	—
1173	D₄	—	4	2	no	—
1174	D₄	—	4	2	no	—
1175	D₄	—	4	2	no	—
1176	D₄	—	4	2	no	—
1177	D₄	—	4	2	no	—
1178	D₄	—	8	1	no	—
1179	D₄	—	8	1	no	—
1180	D₄	—	8	1	no	—
1181	D₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
1182	C₂×C₄	—	2	2	no	—
1183	C₂×C₄	—	2	2	no	—
1184	C₂×C₄	—	2	2	no	—
1185	C₂×C₄	—	2	2	no	—
1186	C₂×C₄	—	2	1	no	—
1187	C₂×C₄	—	2	1	no	—
1188	C₂×C₄	—	2	1	no	—
1189	C₂×C₄	—	2	1	no	—
1190	C₂×C₄	—	2	1	no	—
1191	C₂×C₄	—	2	1	no	—
1192	C₂×C₄	—	2	2	no	—
1193	C₂×C₄	—	2	2	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	4	1	no	—
1202	C₂×C₄	—	4	1	no	—
1203	C₂×C₄	—	4	2	no	—
1204	C₂×C₄	—	4	2	no	—
1205	C₂×C₄	—	4	4	no	—
1206	C₂×C₄	—	4	2	no	—
1207	C₂×C₄	—	4	2	no	—
1208	C₂×C₄	—	4	2	no	—
1209	C₂×C₄	—	8	1	no	—
1210	C₂×C₄	—	8	1	no	—
1211	C₂×C₄	—	8	1	no	—
1212	C₂×C₄	—	8	1	no	—
1213	C₂×C₄	—	8	1	no	—
1214	C₂×C₄	—	8	1	no	—
1215	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1216	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1217	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1218	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1219	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1220	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1221	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1222	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1223	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1224	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1225	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1226	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1227	C₈	—	2	2	no	—
1228	C₈	—	2	2	no	—
1229	C₈	—	2	2	no	—
1230	C₈	—	2	2	no	—
1231	C₂²	—	2	1	no	—
1232	C₂²	—	2	1	no	—
1233	C₂²	—	2	1	no	—
1234	C₂²	—	2	1	no	—
1235	C₂²	—	2	1	no	—
1236	C₂²	—	2	1	no	—
1237	C₂²	—	2	1	no	—
1238	C₂²	—	2	1	no	—
1239	C₂²	—	2	2	no	—
1240	C₂²	—	4	1	no	—
1241	C₂²	—	4	1	no	—
1242	C₂²	—	4	1	no	—
1243	C₂²	—	4	1	no	—
1244	C₂²	—	4	1	no	—
1245	C₂²	—	4	1	no	—
1246	C₂²	—	4	1	no	—
1247	C₂²	—	4	1	no	—
1248	C₂²	—	8	4	no	—
1249	C₂²	—	8	4	no	—
1250	C₂²	C₆₁×#575	1	2	yes	—
1251	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1252	C₄	—	2	1	no	—
1253	C₄	—	2	1	no	—
1254	C₄	—	2	1	no	—
1255	C₄	—	2	1	no	—
1256	C₄	—	2	1	no	—
1257	C₄	—	2	1	no	—
1258	C₄	—	2	1	no	—
1259	C₄	—	2	1	no	—
1260	C₄	—	2	1	no	—
1261	C₄	—	2	1	no	—
1262	C₄	—	4	1	no	—
1263	C₄	—	4	2	no	—
1264	C₄	—	4	2	no	—
1265	C₄	—	4	1	no	—
1266	C₄	—	4	1	no	—
1267	C₄	—	4	1	no	—
1268	C₄	—	4	2	no	—
1269	C₄	—	4	1	no	—
1270	C₄	—	4	2	no	—
1271	C₄	C₆₁×#577	1	2	yes	—
1272	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1273	C₄	C₆₁×#585	1	1	yes	characteristic
1274	C₂	—	2	2	no	—
1275	C₂	—	4	1	no	—
1276	C₂	—	4	1	no	—
1277	C₂	—	4	2	no	—
1278	C₂	—	8	1	no	—
1279	C₂	—	8	1	no	—
1280	C₂	C₆₁×#3489	1	1	yes	characteristic
1281	C₂	C₂×C₆₁×#575	1	1	yes	characteristic
1282	C₂	C₂×C₆₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3481	C₂
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×#3509	C₂	semidirect
3. C₆₁×#3388	C₂	semidirect
4. C₆₁×#3371	C₂	semidirect
5. C₆₁×#3350	C₂	semidirect
6. C₆₁×#3344	C₂	semidirect
7. C₆₁×#3337	C₂	semidirect
8. C₆₁×#3311	C₂	semidirect
9. C₆₁×#3310	C₂	semidirect
10. C₆₁×#3296	C₂	semidirect
11. C₆₁×#3252	C₂	semidirect
12. C₆₁×#3248	C₂	semidirect
13. C₆₁×#3246	C₂	semidirect
14. C₆₁×#3238	C₂	semidirect
15. C₆₁×#3235	C₂	semidirect
16. C₆₁×#3233	C₂	semidirect
17. C₆₁×#3116	C₂	semidirect
18. C₆₁×#3110	C₂	semidirect
19. C₆₁×#3101	C₂	semidirect
20. C₆₁×#3077	C₂	semidirect
21. C₆₁×#3076	C₂	semidirect
22. C₂×C₆₁×#476	C₂	semidirect
23. C₆₁×#2990	C₂	semidirect
26. C₆₁×#557	C₂²	semidirect
28. C₆₁×#556	C₂²	semidirect
37. C₆₁×#552	C₂²	semidirect
47. C₆₁×#533	C₂²	semidirect
48. C₆₁×#533	C₂²	semidirect
49. C₆₁×#533	C₂²	semidirect
50. C₆₁×#533	C₂²	semidirect
51. C₆₁×#533	C₂²	semidirect
53. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
65. C₆₁×#501	C₂²	semidirect
66. C₆₁×#501	C₂²	semidirect
67. C₆₁×#499	C₂²	semidirect
69. C₆₁×#489	C₂²	semidirect
70. C₆₁×#488	C₂²	semidirect
71. C₆₁×#485	C₂²	semidirect
72. C₆₁×#485	C₂²	semidirect
73. C₆₁×#484	C₂²	semidirect
74. C₆₁×#483	C₂²	semidirect
75. C₆₁×#483	C₂²	semidirect
77. C₆₁×#482	C₂²	semidirect
78. C₆₁×#482	C₂²	semidirect
80. C₆₁×#479	C₂²	semidirect
81. C₆₁×#479	C₂²	semidirect
82. C₆₁×#479	C₂²	semidirect
85. C₆₁×#478	C₂²	semidirect
86. C₆₁×#477	C₂²	semidirect
87. C₆₁×#477	C₂²	semidirect
91. C₆₁×#476	C₂²	semidirect
92. C₆₁×#476	C₂²	semidirect
93. C₆₁×#476	C₂²	semidirect
94. C₆₁×#476	C₂²	semidirect
95. C₆₁×#476	C₂²	semidirect
96. C₆₁×#475	C₂²	semidirect
97. C₆₁×#475	C₂²	semidirect
99. C₆₁×#474	C₂²	semidirect
100. C₆₁×#474	C₂²	semidirect
101. C₆₁×#470	C₂²	semidirect
103. C₆₁×#467	C₂²	semidirect
105. C₆₁×#465	C₂²	semidirect
106. C₆₁×#465	C₂²	semidirect
107. C₆₁×#464	C₂²	semidirect
108. C₆₁×#464	C₂²	semidirect
109. C₆₁×#462	C₂²	semidirect
111. C₆₁×#461	C₂²	semidirect
112. C₆₁×#461	C₂²	semidirect
117. C₆₁×#446	C₂²	semidirect
118. C₆₁×#441	C₂²	semidirect
121. C₆₁×#440	C₂²	semidirect
123. C₄×SD₁₆×C₆₁	C₂²	semidirect
125. C₆₁×#435	C₂²	semidirect
126. C₈×D₄×C₆₁	C₂²	semidirect
127. C₆₁×#432	C₂²	semidirect
128. C₆₁×#432	C₂²	semidirect
129. C₆₁×#431	C₂²	semidirect
130. C₆₁×#428	C₂²	semidirect
131. C₆₁×#427	C₂²	semidirect
132. C₂×#106×C₆₁	C₂²	semidirect
133. C₆₁×#423	C₂²	semidirect
134. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
135. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
589. #62126	C₆₁	direct (N × H)
633. #3509	C₂×C₆₁	semidirect
635. #3388	C₂×C₆₁	semidirect
636. #3371	C₂×C₆₁	semidirect
637. #3350	C₂×C₆₁	semidirect
638. #3344	C₂×C₆₁	semidirect
639. #3337	C₂×C₆₁	semidirect
640. #3311	C₂×C₆₁	semidirect
641. #3310	C₂×C₆₁	semidirect
642. #3296	C₂×C₆₁	semidirect
643. #3252	C₂×C₆₁	semidirect
644. #3248	C₂×C₆₁	semidirect
645. #3246	C₂×C₆₁	semidirect
646. #3238	C₂×C₆₁	semidirect
647. #3235	C₂×C₆₁	semidirect
648. #3233	C₂×C₆₁	semidirect
649. #3116	C₂×C₆₁	semidirect
650. #3110	C₂×C₆₁	semidirect
651. #3101	C₂×C₆₁	semidirect
652. #3077	C₂×C₆₁	semidirect
653. #3076	C₂×C₆₁	semidirect
654. C₂×#476	C₂×C₆₁	semidirect
655. #2990	C₂×C₆₁	semidirect
667. #557	C₂²×C₆₁	semidirect
669. #556	C₂²×C₆₁	semidirect
678. #552	C₂²×C₆₁	semidirect
688. #533	C₂²×C₆₁	semidirect
689. #533	C₂²×C₆₁	semidirect
690. #533	C₂²×C₆₁	semidirect
691. #533	C₂²×C₆₁	semidirect
692. #533	C₂²×C₆₁	semidirect
694. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
706. #501	C₂²×C₆₁	semidirect
707. #501	C₂²×C₆₁	semidirect
708. #499	C₂²×C₆₁	semidirect
710. #489	C₂²×C₆₁	semidirect
711. #488	C₂²×C₆₁	semidirect
712. #485	C₂²×C₆₁	semidirect
713. #485	C₂²×C₆₁	semidirect
714. #484	C₂²×C₆₁	semidirect
715. #483	C₂²×C₆₁	semidirect
716. #483	C₂²×C₆₁	semidirect
718. #482	C₂²×C₆₁	semidirect
719. #482	C₂²×C₆₁	semidirect
721. #479	C₂²×C₆₁	semidirect
722. #479	C₂²×C₆₁	semidirect
723. #479	C₂²×C₆₁	semidirect
726. #478	C₂²×C₆₁	semidirect
727. #477	C₂²×C₆₁	semidirect
728. #477	C₂²×C₆₁	semidirect
732. #476	C₂²×C₆₁	semidirect
733. #476	C₂²×C₆₁	semidirect
734. #476	C₂²×C₆₁	semidirect
735. #476	C₂²×C₆₁	semidirect
736. #476	C₂²×C₆₁	semidirect
737. #475	C₂²×C₆₁	semidirect
738. #475	C₂²×C₆₁	semidirect
740. #474	C₂²×C₆₁	semidirect
741. #474	C₂²×C₆₁	semidirect
742. #470	C₂²×C₆₁	semidirect
744. #467	C₂²×C₆₁	semidirect
746. #465	C₂²×C₆₁	semidirect
747. #465	C₂²×C₆₁	semidirect
748. #464	C₂²×C₆₁	semidirect
749. #464	C₂²×C₆₁	semidirect
750. #462	C₂²×C₆₁	semidirect
752. #461	C₂²×C₆₁	semidirect
753. #461	C₂²×C₆₁	semidirect
758. #446	C₂²×C₆₁	semidirect
759. #441	C₂²×C₆₁	semidirect
762. #440	C₂²×C₆₁	semidirect
764. C₄×SD₁₆	C₂²×C₆₁	semidirect
766. #435	C₂²×C₆₁	semidirect
767. C₈×D₄	C₂²×C₆₁	semidirect
768. #432	C₂²×C₆₁	semidirect
769. #432	C₂²×C₆₁	semidirect
770. #431	C₂²×C₆₁	semidirect
771. #428	C₂²×C₆₁	semidirect
772. #427	C₂²×C₆₁	semidirect
773. C₂×#106	C₂²×C₆₁	semidirect
774. #423	C₂²×C₆₁	semidirect
775. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
776. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
780. C₆₁	#62126	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×#3509	2
C₆₁×#3481	2
C₆₁×#3388	2
C₆₁×#3371	2
C₆₁×#3350	2
C₆₁×#3344	2
C₆₁×#3337	2
C₆₁×#3311	2
C₆₁×#3310	2
C₆₁×#3296	2
C₆₁×#3252	2
C₆₁×#3248	2
C₆₁×#3246	2
C₆₁×#3238	2
C₆₁×#3235	2
C₆₁×#3233	2
C₆₁×#3116	2
C₆₁×#3110	2
C₆₁×#3101	2
C₆₁×#3077	2
C₆₁×#3076	2
C₂×C₆₁×#476	2
C₆₁×#2990	2
#62126	61

Subgroups — C61×#62126 #29565559

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62126 #29565559