Subgroups — C₆₁×#61173 #29564606

Order 15616.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3489	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#3315	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3314	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3313	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3312	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3302	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3300	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3299	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3296	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3137	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3095	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3083	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₆₁×#467	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3044	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#3011	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3007	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#2947	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#2929	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₁×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₆₁×#416	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#137×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#137×C₆₁	C₂²	1	1	yes	characteristic
28	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
29	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic, complemented
30	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₆₁×#556	C₂²	1	2	yes	complemented
32	C₆₁×#554	C₂²	1	2	yes	—
33	C₆₁×#552	—	2	2	no	—
34	C₆₁×#552	C₂²	1	2	yes	—
35	C₆₁×#552	C₂²	1	2	yes	complemented
36	C₆₁×#551	—	2	2	no	—
37	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
38	C₆₁×#548	C₂²	1	2	yes	—
39	C₆₁×#547	—	2	2	no	—
40	C₆₁×#547	C₂²	1	2	yes	—
41	C₆₁×#546	—	2	2	no	—
42	C₆₁×#546	C₂²	1	2	yes	—
43	C₆₁×#544	C₂²	1	1	yes	characteristic, complemented
44	C₆₁×#542	—	2	1	no	—
45	C₆₁×#541	—	2	1	no	—
46	C₆₁×#537	—	2	1	no	—
47	C₆₁×#537	C₂²	1	1	yes	characteristic
48	C₆₁×#536	—	2	1	no	—
49	C₆₁×#536	C₂²	1	1	yes	characteristic
50	C₆₁×#536	C₂²	1	1	yes	characteristic, complemented
51	C₆₁×#533	—	2	1	no	—
52	C₆₁×#529	—	2	1	no	—
53	C₆₁×#525	—	2	1	no	—
54	C₆₁×#525	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
56	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
58	C₆₁×#520	C₂²	1	1	yes	characteristic
59	C₆₁×#520	C₂²	1	1	yes	characteristic, complemented
60	C₆₁×#519	C₂²	1	1	yes	characteristic, complemented
61	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
62	C₆₁×#491	C₂²	1	2	yes	complemented
63	C₆₁×#489	C₂²	1	2	yes	complemented
64	C₆₁×#488	C₂²	1	2	yes	complemented
65	C₆₁×#487	C₂²	1	2	yes	complemented
66	C₆₁×#485	C₂²	1	2	yes	complemented
67	C₆₁×#485	C₂²	1	2	yes	complemented
68	C₆₁×#485	C₂²	1	2	yes	complemented
69	C₆₁×#484	C₂²	1	2	yes	—
70	C₆₁×#484	C₂²	1	2	yes	complemented
71	C₆₁×#483	C₂²	1	2	yes	—
72	C₆₁×#482	C₂²	1	2	yes	complemented
73	C₆₁×#480	C₂²	1	2	yes	complemented
74	C₆₁×#479	C₂²	1	2	yes	complemented
75	C₆₁×#478	C₂²	1	2	yes	complemented
76	C₆₁×#477	C₂²	1	2	yes	complemented
77	C₆₁×#474	C₂²	1	2	yes	complemented
78	C₆₁×#470	C₂²	1	2	yes	complemented
79	C₆₁×#468	C₂²	1	2	yes	complemented
80	C₆₁×#467	C₂²	1	2	yes	—
81	C₆₁×#467	C₂²	1	2	yes	—
82	C₆₁×#467	C₂²	1	2	yes	complemented
83	C₆₁×#467	C₂²	1	2	yes	complemented
84	C₆₁×#467	C₂²	1	2	yes	complemented
85	C₆₁×#465	C₂²	1	2	yes	complemented
86	C₆₁×#464	C₂²	1	2	yes	complemented
87	C₆₁×#464	C₂²	1	2	yes	complemented
88	C₆₁×#462	C₂²	1	2	yes	complemented
89	C₆₁×#462	C₂²	1	2	yes	complemented
90	C₆₁×#452	C₂²	1	2	yes	—
91	C₆₁×#452	C₂²	1	2	yes	—
92	C₆₁×#452	C₂²	1	2	yes	complemented
93	C₆₁×#452	C₂²	1	2	yes	complemented
94	C₆₁×#451	C₂²	1	2	yes	—
95	C₆₁×#451	C₂²	1	2	yes	complemented
96	C₆₁×#451	C₂²	1	2	yes	complemented
97	C₆₁×#450	C₂²	1	2	yes	—
98	C₆₁×#441	C₂²	1	2	yes	complemented
99	C₆₁×#440	C₂²	1	2	yes	complemented
100	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
101	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
102	C₆₁×#435	C₂²	1	2	yes	—
103	C₆₁×#435	C₂²	1	2	yes	complemented
104	C₈×D₄×C₆₁	C₂²	1	2	yes	—
105	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
106	C₆₁×#428	C₂²	1	1	yes	characteristic, complemented
107	C₆₁×#428	C₂²	1	1	yes	characteristic, complemented
108	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic, complemented
109	C₆₁×#424	C₂²	1	1	yes	characteristic, complemented
110	C₆₁×#419	C₂²	1	1	yes	characteristic, complemented
111	C₆₁×#419	C₂²	1	2	yes	complemented
112	C₆₁×#419	C₂²	1	1	yes	characteristic, complemented
113	C₆₁×#417	C₂²	1	1	yes	characteristic
114	C₆₁×#417	C₂²	1	1	yes	characteristic
115	C₆₁×#417	C₂²	1	2	yes	complemented
116	C₆₁×#416	C₂²	1	1	yes	characteristic
117	C₆₁×#416	C₂²	1	1	yes	characteristic
118	C₆₁×#416	C₂²	1	1	yes	characteristic
119	C₆₁×#416	C₂²	1	1	yes	characteristic
120	C₆₁×#416	C₂²	1	1	yes	characteristic
121	C₆₁×#416	C₂²	1	1	yes	characteristic
122	C₆₁×#416	C₂²	1	1	yes	characteristic
123	C₆₁×#416	C₂²	1	1	yes	characteristic
124	C₆₁×#416	C₂²	1	2	yes	complemented
125	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
126	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
127	C₂×#103×C₆₁	C₂²	1	2	yes	complemented
128	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic, complemented
129	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic, complemented
130	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
131	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
132	C₆₁×#408	C₂²	1	1	yes	characteristic, complemented
133	C₆₁×#407	C₂²	1	1	yes	characteristic
134	C₆₁×#405	C₂²	1	1	yes	characteristic, complemented
135	2₋¹⁺⁴×C₆₁	—	2	4	no	—
136	2₋¹⁺⁴×C₆₁	—	4	2	no	—
137	C₂×#41×C₆₁	—	2	1	no	—
138	C₂×#41×C₆₁	—	2	2	no	—
139	C₂×#41×C₆₁	—	2	1	no	—
140	C₂×#41×C₆₁	—	2	1	no	—
141	C₂×#41×C₆₁	—	2	4	no	—
142	C₂×#41×C₆₁	—	4	2	no	—
143	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
144	C₂×#41×C₆₁	C₂³	1	2	yes	—
145	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
146	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
147	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
148	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₆₁	—	2	1	no	—
150	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
151	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
152	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
153	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
154	C₂²×D₄×C₆₁	—	2	1	no	—
155	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
156	C₂³×C₄×C₆₁	—	2	1	no	—
157	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
158	#137×C₆₁	—	2	4	no	—
159	#137×C₆₁	—	4	2	no	—
160	C₂×Q₁₆×C₆₁	—	4	2	no	—
161	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
162	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
163	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
164	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
167	#131×C₆₁	—	4	2	no	—
168	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
169	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
170	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
171	C₂²×C₈×C₆₁	—	4	2	no	—
172	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
173	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
174	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
179	C₄⋊Q₈×C₆₁	—	2	1	no	—
180	C₄⋊Q₈×C₆₁	—	2	1	no	—
181	C₄⋊Q₈×C₆₁	—	2	2	no	—
182	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
183	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
184	#126×C₆₁	—	2	2	no	—
185	#126×C₆₁	—	2	2	no	—
186	#126×C₆₁	—	2	2	no	—
187	#126×C₆₁	—	2	2	no	—
188	#125×C₆₁	—	2	2	no	—
189	#125×C₆₁	—	2	1	no	—
190	#125×C₆₁	—	2	2	no	—
191	#125×C₆₁	—	2	2	no	—
192	#125×C₆₁	C₂³	1	2	yes	—
193	#124×C₆₁	—	2	1	no	—
194	#124×C₆₁	—	2	2	no	—
195	#124×C₆₁	—	2	2	no	—
196	#124×C₆₁	C₂³	1	2	yes	—
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	—	2	2	no	—
204	#123×C₆₁	D₄	1	2	yes	—
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	—	2	2	no	—
213	C₂²⋊Q₈×C₆₁	—	2	2	no	—
214	C₂²⋊Q₈×C₆₁	—	2	2	no	—
215	C₂²⋊Q₈×C₆₁	—	2	2	no	—
216	C₂²⋊Q₈×C₆₁	—	2	2	no	—
217	C₂²⋊Q₈×C₆₁	—	2	2	no	—
218	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
219	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
220	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
221	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
222	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
223	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
224	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
225	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
226	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
227	#121×C₆₁	—	2	1	no	—
228	#121×C₆₁	—	2	2	no	—
229	#121×C₆₁	—	2	2	no	—
230	#121×C₆₁	—	2	2	no	—
231	#121×C₆₁	—	2	2	no	—
232	#121×C₆₁	D₄	1	1	yes	characteristic
233	#121×C₆₁	D₄	1	1	yes	characteristic
234	#121×C₆₁	C₂³	1	2	yes	—
235	#120×C₆₁	—	2	2	no	—
236	#120×C₆₁	D₄	1	2	yes	—
237	C₄×Q₈×C₆₁	—	2	1	no	—
238	C₄×Q₈×C₆₁	—	2	1	no	—
239	C₄×Q₈×C₆₁	—	2	2	no	—
240	C₄×Q₈×C₆₁	—	2	1	no	—
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×D₄×C₆₁	—	2	1	no	—
245	C₄×D₄×C₆₁	—	2	2	no	—
246	C₄×D₄×C₆₁	—	2	2	no	—
247	C₄×D₄×C₆₁	—	2	2	no	—
248	C₄×D₄×C₆₁	—	2	2	no	—
249	C₄×D₄×C₆₁	—	2	2	no	—
250	C₄×D₄×C₆₁	C₂³	1	2	yes	—
251	C₄×D₄×C₆₁	C₂³	1	2	yes	—
252	C₄×D₄×C₆₁	C₂³	1	2	yes	—
253	#117×C₆₁	—	2	1	no	—
254	#117×C₆₁	—	2	1	no	—
255	#117×C₆₁	—	2	1	no	—
256	#117×C₆₁	—	2	2	no	—
257	#117×C₆₁	—	2	2	no	—
258	#117×C₆₁	—	2	2	no	—
259	#117×C₆₁	C₂³	1	1	yes	characteristic
260	#117×C₆₁	C₂³	1	2	yes	—
261	#117×C₆₁	C₂³	1	1	yes	characteristic
262	#117×C₆₁	C₂³	1	1	yes	characteristic
263	#117×C₆₁	C₂³	1	1	yes	characteristic
264	#117×C₆₁	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
266	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
267	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
268	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
269	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
273	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
275	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
276	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
277	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
278	C₂×C₄²×C₆₁	—	2	1	no	—
279	#107×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	#106×C₆₁	C₂³	1	2	yes	—
284	#106×C₆₁	C₂³	1	2	yes	—
285	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
286	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
287	#103×C₆₁	C₂³	1	1	yes	characteristic
288	#103×C₆₁	C₂³	1	1	yes	characteristic
289	#103×C₆₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
294	#103×C₆₁	C₂³	1	1	yes	characteristic
295	#103×C₆₁	C₂³	1	2	yes	—
296	#103×C₆₁	C₂³	1	2	yes	—
297	#103×C₆₁	C₂³	1	2	yes	—
298	#103×C₆₁	C₂³	1	2	yes	—
299	#103×C₆₁	C₂³	1	2	yes	—
300	#103×C₆₁	C₂³	1	2	yes	—
301	#103×C₆₁	C₂³	1	2	yes	—
302	#103×C₆₁	C₂³	1	2	yes	—
303	#103×C₆₁	C₂³	1	2	yes	—
304	#103×C₆₁	C₂³	1	2	yes	—
305	#102×C₆₁	C₂³	1	1	yes	characteristic
306	#102×C₆₁	C₂³	1	1	yes	characteristic
307	#102×C₆₁	C₂³	1	1	yes	characteristic
308	#102×C₆₁	C₂³	1	1	yes	characteristic
309	#102×C₆₁	C₂³	1	1	yes	characteristic
310	#102×C₆₁	C₂³	1	1	yes	characteristic
311	#102×C₆₁	C₂³	1	1	yes	characteristic
312	#102×C₆₁	C₂³	1	1	yes	characteristic
313	#102×C₆₁	C₂³	1	2	yes	—
314	#102×C₆₁	C₂³	1	2	yes	—
315	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
316	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
317	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
318	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
319	#97×C₆₁	C₂³	1	2	yes	—
320	C₄×C₈×C₆₁	C₂³	1	2	yes	—
321	C₂⁴×C₆₁	—	2	1	no	—
322	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
323	#41×C₆₁	—	2	2	no	—
324	#41×C₆₁	—	2	2	no	—
325	#41×C₆₁	—	2	2	no	—
326	#41×C₆₁	—	2	2	no	—
327	#41×C₆₁	—	2	2	no	—
328	#41×C₆₁	—	2	4	no	—
329	#41×C₆₁	—	2	2	no	—
330	#41×C₆₁	—	2	2	no	—
331	#41×C₆₁	—	4	4	no	—
332	#41×C₆₁	—	4	1	no	—
333	#41×C₆₁	—	4	1	no	—
334	#41×C₆₁	—	4	2	no	—
335	#41×C₆₁	—	4	4	no	—
336	#41×C₆₁	—	4	4	no	—
337	#41×C₆₁	—	4	8	no	—
338	#41×C₆₁	#41	1	4	yes	—
339	C₂×Q₈×C₆₁	—	2	1	no	—
340	C₂×Q₈×C₆₁	—	2	1	no	—
341	C₂×Q₈×C₆₁	—	2	2	no	—
342	C₂×Q₈×C₆₁	—	2	1	no	—
343	C₂×Q₈×C₆₁	—	2	2	no	—
344	C₂×Q₈×C₆₁	—	2	2	no	—
345	C₂×Q₈×C₆₁	—	2	4	no	—
346	C₂×Q₈×C₆₁	—	2	2	no	—
347	C₂×Q₈×C₆₁	—	2	2	no	—
348	C₂×Q₈×C₆₁	—	2	2	no	—
349	C₂×Q₈×C₆₁	—	2	2	no	—
350	C₂×Q₈×C₆₁	—	4	1	no	—
351	C₂×Q₈×C₆₁	—	4	2	no	—
352	C₂×Q₈×C₆₁	—	4	4	no	—
353	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
354	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
355	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
356	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
357	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₆₁	—	2	1	no	—
359	C₂×D₄×C₆₁	—	2	2	no	—
360	C₂×D₄×C₆₁	—	2	2	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	2	no	—
365	C₂×D₄×C₆₁	—	2	1	no	—
366	C₂×D₄×C₆₁	—	4	1	no	—
367	C₂×D₄×C₆₁	—	4	4	no	—
368	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
369	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
370	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
371	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
372	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
373	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₆₁	—	2	1	no	—
375	C₂²×C₄×C₆₁	—	2	2	no	—
376	C₂²×C₄×C₆₁	—	2	2	no	—
377	C₂²×C₄×C₆₁	—	2	1	no	—
378	C₂²×C₄×C₆₁	—	2	1	no	—
379	C₂²×C₄×C₆₁	—	2	1	no	—
380	C₂²×C₄×C₆₁	—	2	2	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	2	no	—
386	C₂²×C₄×C₆₁	—	2	2	no	—
387	C₂²×C₄×C₆₁	—	2	1	no	—
388	C₂²×C₄×C₆₁	—	2	1	no	—
389	C₂²×C₄×C₆₁	—	2	1	no	—
390	C₂²×C₄×C₆₁	—	2	2	no	—
391	C₂²×C₄×C₆₁	—	4	4	no	—
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	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
397	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
399	Q₁₆×C₆₁	—	2	4	no	—
400	Q₁₆×C₆₁	—	4	2	no	—
401	Q₁₆×C₆₁	—	4	2	no	—
402	Q₁₆×C₆₁	—	4	2	no	—
403	SD₁₆×C₆₁	—	2	4	no	—
404	SD₁₆×C₆₁	—	4	2	no	—
405	M₁₆×C₆₁	—	2	2	no	—
406	M₁₆×C₆₁	—	2	2	no	—
407	M₁₆×C₆₁	—	4	2	no	—
408	C₂×C₈×C₆₁	—	2	2	no	—
409	C₂×C₈×C₆₁	—	2	2	no	—
410	C₂×C₈×C₆₁	—	4	1	no	—
411	C₂×C₈×C₆₁	—	4	1	no	—
412	C₂×C₈×C₆₁	—	4	1	no	—
413	C₂×C₈×C₆₁	—	4	1	no	—
414	C₂×C₈×C₆₁	—	4	2	no	—
415	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
416	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
417	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
418	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
419	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
420	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
421	C₄⋊C₄×C₆₁	—	2	2	no	—
422	C₄⋊C₄×C₆₁	—	2	1	no	—
423	C₄⋊C₄×C₆₁	—	2	2	no	—
424	C₄⋊C₄×C₆₁	—	2	2	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	2	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	—	2	2	no	—
440	C₄⋊C₄×C₆₁	—	2	2	no	—
441	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
442	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
443	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
445	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
446	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
447	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
448	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
449	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
451	C₂²⋊C₄×C₆₁	—	2	2	no	—
452	C₂²⋊C₄×C₆₁	—	2	1	no	—
453	C₂²⋊C₄×C₆₁	—	2	1	no	—
454	C₂²⋊C₄×C₆₁	—	2	1	no	—
455	C₂²⋊C₄×C₆₁	—	2	1	no	—
456	C₂²⋊C₄×C₆₁	—	2	2	no	—
457	C₂²⋊C₄×C₆₁	—	2	2	no	—
458	C₂²⋊C₄×C₆₁	—	2	2	no	—
459	C₂²⋊C₄×C₆₁	—	2	2	no	—
460	C₂²⋊C₄×C₆₁	—	2	2	no	—
461	C₂²⋊C₄×C₆₁	—	2	2	no	—
462	C₂²⋊C₄×C₆₁	—	2	2	no	—
463	C₂²⋊C₄×C₆₁	—	2	2	no	—
464	C₂²⋊C₄×C₆₁	—	2	2	no	—
465	C₂²⋊C₄×C₆₁	—	2	2	no	—
466	C₂²⋊C₄×C₆₁	—	2	2	no	—
467	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
468	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
469	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
470	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
471	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
472	C₄²×C₆₁	—	2	1	no	—
473	C₄²×C₆₁	—	2	1	no	—
474	C₄²×C₆₁	—	2	1	no	—
475	C₄²×C₆₁	—	2	1	no	—
476	C₄²×C₆₁	—	2	2	no	—
477	C₄²×C₆₁	—	2	2	no	—
478	C₄²×C₆₁	—	2	2	no	—
479	C₄²×C₆₁	—	2	2	no	—
480	C₄²×C₆₁	C₂⁴	1	2	yes	—
481	C₂³×C₆₁	—	2	2	no	—
482	C₂³×C₆₁	—	2	2	no	—
483	C₂³×C₆₁	—	2	1	no	—
484	C₂³×C₆₁	—	2	1	no	—
485	C₂³×C₆₁	—	4	1	no	—
486	C₂³×C₆₁	—	4	2	no	—
487	C₂³×C₆₁	—	4	2	no	—
488	C₂³×C₆₁	—	8	1	no	—
489	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
490	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
491	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
492	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
493	Q₈×C₆₁	—	2	2	no	—
494	Q₈×C₆₁	—	2	1	no	—
495	Q₈×C₆₁	—	2	2	no	—
496	Q₈×C₆₁	—	2	2	no	—
497	Q₈×C₆₁	—	2	1	no	—
498	Q₈×C₆₁	—	2	2	no	—
499	Q₈×C₆₁	—	2	2	no	—
500	Q₈×C₆₁	—	2	1	no	—
501	Q₈×C₆₁	—	4	4	no	—
502	Q₈×C₆₁	—	4	2	no	—
503	Q₈×C₆₁	—	4	2	no	—
504	Q₈×C₆₁	—	4	2	no	—
505	Q₈×C₆₁	—	8	2	no	—
506	Q₈×C₆₁	C₂×#41	1	2	yes	—
507	D₄×C₆₁	—	2	4	no	—
508	D₄×C₆₁	—	2	4	no	—
509	D₄×C₆₁	—	2	4	no	—
510	D₄×C₆₁	—	2	2	no	—
511	D₄×C₆₁	—	2	1	no	—
512	D₄×C₆₁	—	2	1	no	—
513	D₄×C₆₁	—	2	1	no	—
514	D₄×C₆₁	—	4	2	no	—
515	D₄×C₆₁	—	4	2	no	—
516	D₄×C₆₁	—	4	2	no	—
517	D₄×C₆₁	—	4	2	no	—
518	D₄×C₆₁	—	4	4	no	—
519	D₄×C₆₁	—	4	2	no	—
520	D₄×C₆₁	—	8	2	no	—
521	D₄×C₆₁	C₂×#41	1	2	yes	—
522	C₂×C₄×C₆₁	—	2	2	no	—
523	C₂×C₄×C₆₁	—	2	1	no	—
524	C₂×C₄×C₆₁	—	2	2	no	—
525	C₂×C₄×C₆₁	—	2	2	no	—
526	C₂×C₄×C₆₁	—	2	4	no	—
527	C₂×C₄×C₆₁	—	2	1	no	—
528	C₂×C₄×C₆₁	—	2	1	no	—
529	C₂×C₄×C₆₁	—	2	2	no	—
530	C₂×C₄×C₆₁	—	2	1	no	—
531	C₂×C₄×C₆₁	—	2	1	no	—
532	C₂×C₄×C₆₁	—	2	2	no	—
533	C₂×C₄×C₆₁	—	2	1	no	—
534	C₂×C₄×C₆₁	—	2	1	no	—
535	C₂×C₄×C₆₁	—	2	1	no	—
536	C₂×C₄×C₆₁	—	2	2	no	—
537	C₂×C₄×C₆₁	—	2	1	no	—
538	C₂×C₄×C₆₁	—	2	2	no	—
539	C₂×C₄×C₆₁	—	2	2	no	—
540	C₂×C₄×C₆₁	—	2	2	no	—
541	C₂×C₄×C₆₁	—	2	1	no	—
542	C₂×C₄×C₆₁	—	4	2	no	—
543	C₂×C₄×C₆₁	—	4	2	no	—
544	C₂×C₄×C₆₁	—	4	2	no	—
545	C₂×C₄×C₆₁	—	4	4	no	—
546	C₂×C₄×C₆₁	—	4	4	no	—
547	C₂×C₄×C₆₁	—	4	2	no	—
548	C₂×C₄×C₆₁	—	4	2	no	—
549	C₂×C₄×C₆₁	—	4	2	no	—
550	C₂×C₄×C₆₁	—	4	2	no	—
551	C₂×C₄×C₆₁	—	8	2	no	—
552	C₂×C₄×C₆₁	—	8	2	no	—
553	C₂×C₄×C₆₁	—	8	1	no	—
554	C₂×C₄×C₆₁	—	8	1	no	—
555	C₂×C₄×C₆₁	—	8	1	no	—
556	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
557	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
559	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
560	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
561	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
562	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
563	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
564	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
565	C₈×C₆₁	—	2	2	no	—
566	C₈×C₆₁	—	2	1	no	—
567	C₈×C₆₁	—	2	1	no	—
568	C₈×C₆₁	—	2	1	no	—
569	C₈×C₆₁	—	2	1	no	—
570	C₈×C₆₁	—	2	2	no	—
571	#61173	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
572	C₂²×C₆₁	—	2	1	no	—
573	C₂²×C₆₁	—	2	1	no	—
574	C₂²×C₆₁	—	2	1	no	—
575	C₂²×C₆₁	—	2	1	no	—
576	C₂²×C₆₁	—	2	2	no	—
577	C₂²×C₆₁	—	2	1	no	—
578	C₂²×C₆₁	—	2	1	no	—
579	C₂²×C₆₁	—	2	2	no	—
580	C₂²×C₆₁	—	2	2	no	—
581	C₂²×C₆₁	—	2	2	no	—
582	C₂²×C₆₁	—	2	1	no	—
583	C₂²×C₆₁	—	4	4	no	—
584	C₂²×C₆₁	—	4	1	no	—
585	C₂²×C₆₁	—	4	1	no	—
586	C₂²×C₆₁	—	4	1	no	—
587	C₂²×C₆₁	—	4	1	no	—
588	C₂²×C₆₁	—	4	1	no	—
589	C₂²×C₆₁	—	8	4	no	—
590	C₂²×C₆₁	#546	1	2	yes	—
591	C₂²×C₆₁	#578	1	2	yes	—
592	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
593	C₄×C₆₁	—	2	2	no	—
594	C₄×C₆₁	—	2	1	no	—
595	C₄×C₆₁	—	2	1	no	—
596	C₄×C₆₁	—	2	2	no	—
597	C₄×C₆₁	—	2	2	no	—
598	C₄×C₆₁	—	2	2	no	—
599	C₄×C₆₁	—	4	1	no	—
600	C₄×C₆₁	—	4	2	no	—
601	C₄×C₆₁	—	4	2	no	—
602	C₄×C₆₁	—	4	1	no	—
603	C₄×C₆₁	—	4	1	no	—
604	C₄×C₆₁	—	4	2	no	—
605	C₄×C₆₁	—	4	2	no	—
606	C₄×C₆₁	—	4	1	no	—
607	C₄×C₆₁	—	4	1	no	—
608	C₄×C₆₁	#546	1	2	yes	—
609	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
610	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
611	#3495	C₂×C₆₁	1	1	yes	characteristic, complemented
612	#3489	C₂×C₆₁	1	1	yes	characteristic
613	#3315	C₂×C₆₁	1	2	yes	complemented
614	#3314	C₂×C₆₁	1	2	yes	complemented
615	#3313	C₂×C₆₁	1	2	yes	complemented
616	#3312	C₂×C₆₁	1	2	yes	complemented
617	#3302	C₂×C₆₁	1	2	yes	complemented
618	#3300	C₂×C₆₁	1	2	yes	complemented
619	#3299	C₂×C₆₁	1	2	yes	complemented
620	#3296	C₂×C₆₁	1	2	yes	complemented
621	#3137	C₂×C₆₁	1	1	yes	characteristic, complemented
622	#3098	C₂×C₆₁	1	1	yes	characteristic, complemented
623	#3095	C₂×C₆₁	1	1	yes	characteristic, complemented
624	#3083	C₂×C₆₁	1	1	yes	characteristic, complemented
625	#3063	C₂×C₆₁	1	1	yes	characteristic, complemented
626	C₂×#467	C₂×C₆₁	1	1	yes	characteristic, complemented
627	#3044	C₂×C₆₁	1	1	yes	characteristic, complemented
628	#3011	C₂×C₆₁	1	1	yes	characteristic, complemented
629	#3007	C₂×C₆₁	1	1	yes	characteristic, complemented
630	#2947	C₂×C₆₁	1	1	yes	characteristic, complemented
631	#2929	C₂×C₆₁	1	1	yes	characteristic, complemented
632	#2898	C₂×C₆₁	1	1	yes	characteristic, complemented
633	C₂×#416	C₂×C₆₁	1	1	yes	characteristic, complemented
634	C₂×C₆₁	—	2	2	no	—
635	C₂×C₆₁	—	2	2	no	—
636	C₂×C₆₁	—	4	2	no	—
637	C₂×C₆₁	—	4	1	no	—
638	C₂×C₆₁	—	4	2	no	—
639	C₂×C₆₁	—	8	1	no	—
640	C₂×C₆₁	C₂×#546	1	1	yes	characteristic
641	C₂×C₆₁	C₂×#578	1	1	yes	characteristic
642	C₂×C₆₁	#3584	1	1	yes	characteristic
643	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	1	yes	characteristic
644	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
645	C₂×#137	C₂²×C₆₁	1	1	yes	characteristic
646	C₂×#137	C₂²×C₆₁	1	1	yes	characteristic
647	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
648	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic, complemented
649	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
650	#556	C₂²×C₆₁	1	2	yes	complemented
651	#554	C₂²×C₆₁	1	2	yes	—
652	#552	—	2	2	no	—
653	#552	C₂²×C₆₁	1	2	yes	—
654	#552	C₂²×C₆₁	1	2	yes	complemented
655	#551	—	2	2	no	—
656	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
657	#548	C₂²×C₆₁	1	2	yes	—
658	#547	—	2	2	no	—
659	#547	C₂²×C₆₁	1	2	yes	—
660	#546	—	2	2	no	—
661	#546	C₂²×C₆₁	1	2	yes	—
662	#544	C₂²×C₆₁	1	1	yes	characteristic, complemented
663	#542	—	2	1	no	—
664	#541	—	2	1	no	—
665	#537	—	2	1	no	—
666	#537	C₂²×C₆₁	1	1	yes	characteristic
667	#536	—	2	1	no	—
668	#536	C₂²×C₆₁	1	1	yes	characteristic
669	#536	C₂²×C₆₁	1	1	yes	characteristic, complemented
670	#533	—	2	1	no	—
671	#529	—	2	1	no	—
672	#525	—	2	1	no	—
673	#525	C₂²×C₆₁	1	1	yes	characteristic
674	C₂×C₂²⋊Q₈	—	2	1	no	—
675	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
676	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
677	#520	C₂²×C₆₁	1	1	yes	characteristic
678	#520	C₂²×C₆₁	1	1	yes	characteristic, complemented
679	#519	C₂²×C₆₁	1	1	yes	characteristic, complemented
680	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
681	#491	C₂²×C₆₁	1	2	yes	complemented
682	#489	C₂²×C₆₁	1	2	yes	complemented
683	#488	C₂²×C₆₁	1	2	yes	complemented
684	#487	C₂²×C₆₁	1	2	yes	complemented
685	#485	C₂²×C₆₁	1	2	yes	complemented
686	#485	C₂²×C₆₁	1	2	yes	complemented
687	#485	C₂²×C₆₁	1	2	yes	complemented
688	#484	C₂²×C₆₁	1	2	yes	—
689	#484	C₂²×C₆₁	1	2	yes	complemented
690	#483	C₂²×C₆₁	1	2	yes	—
691	#482	C₂²×C₆₁	1	2	yes	complemented
692	#480	C₂²×C₆₁	1	2	yes	complemented
693	#479	C₂²×C₆₁	1	2	yes	complemented
694	#478	C₂²×C₆₁	1	2	yes	complemented
695	#477	C₂²×C₆₁	1	2	yes	complemented
696	#474	C₂²×C₆₁	1	2	yes	complemented
697	#470	C₂²×C₆₁	1	2	yes	complemented
698	#468	C₂²×C₆₁	1	2	yes	complemented
699	#467	C₂²×C₆₁	1	2	yes	—
700	#467	C₂²×C₆₁	1	2	yes	—
701	#467	C₂²×C₆₁	1	2	yes	complemented
702	#467	C₂²×C₆₁	1	2	yes	complemented
703	#467	C₂²×C₆₁	1	2	yes	complemented
704	#465	C₂²×C₆₁	1	2	yes	complemented
705	#464	C₂²×C₆₁	1	2	yes	complemented
706	#464	C₂²×C₆₁	1	2	yes	complemented
707	#462	C₂²×C₆₁	1	2	yes	complemented
708	#462	C₂²×C₆₁	1	2	yes	complemented
709	#452	C₂²×C₆₁	1	2	yes	—
710	#452	C₂²×C₆₁	1	2	yes	—
711	#452	C₂²×C₆₁	1	2	yes	complemented
712	#452	C₂²×C₆₁	1	2	yes	complemented
713	#451	C₂²×C₆₁	1	2	yes	—
714	#451	C₂²×C₆₁	1	2	yes	complemented
715	#451	C₂²×C₆₁	1	2	yes	complemented
716	#450	C₂²×C₆₁	1	2	yes	—
717	#441	C₂²×C₆₁	1	2	yes	complemented
718	#440	C₂²×C₆₁	1	2	yes	complemented
719	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
720	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
721	#435	C₂²×C₆₁	1	2	yes	—
722	#435	C₂²×C₆₁	1	2	yes	complemented
723	C₈×D₄	C₂²×C₆₁	1	2	yes	—
724	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
725	#428	C₂²×C₆₁	1	1	yes	characteristic, complemented
726	#428	C₂²×C₆₁	1	1	yes	characteristic, complemented
727	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic, complemented
728	#424	C₂²×C₆₁	1	1	yes	characteristic, complemented
729	#419	C₂²×C₆₁	1	1	yes	characteristic, complemented
730	#419	C₂²×C₆₁	1	1	yes	characteristic, complemented
731	#419	C₂²×C₆₁	1	2	yes	complemented
732	#417	C₂²×C₆₁	1	1	yes	characteristic
733	#417	C₂²×C₆₁	1	1	yes	characteristic
734	#417	C₂²×C₆₁	1	2	yes	complemented
735	#416	C₂²×C₆₁	1	1	yes	characteristic
736	#416	C₂²×C₆₁	1	1	yes	characteristic
737	#416	C₂²×C₆₁	1	1	yes	characteristic
738	#416	C₂²×C₆₁	1	1	yes	characteristic
739	#416	C₂²×C₆₁	1	1	yes	characteristic
740	#416	C₂²×C₆₁	1	1	yes	characteristic
741	#416	C₂²×C₆₁	1	1	yes	characteristic
742	#416	C₂²×C₆₁	1	1	yes	characteristic
743	#416	C₂²×C₆₁	1	2	yes	complemented
744	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
745	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
746	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic, complemented
747	C₂×#103	C₂²×C₆₁	1	2	yes	complemented
748	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic, complemented
749	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
750	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
751	#408	C₂²×C₆₁	1	1	yes	characteristic, complemented
752	#407	C₂²×C₆₁	1	1	yes	characteristic
753	#405	C₂²×C₆₁	1	1	yes	characteristic, complemented
754	C₆₁	#61173	1	1	yes	characteristic, direct product factor, Sylow
755	2₋¹⁺⁴	—	2	4	no	—
756	2₋¹⁺⁴	—	4	2	no	—
757	C₂×#41	—	2	1	no	—
758	C₂×#41	—	2	2	no	—
759	C₂×#41	—	2	1	no	—
760	C₂×#41	—	2	1	no	—
761	C₂×#41	—	2	4	no	—
762	C₂×#41	—	4	2	no	—
763	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
764	C₂×#41	C₂³×C₆₁	1	2	yes	—
765	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
766	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
767	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
768	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
769	C₂²×Q₈	—	2	1	no	—
770	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
771	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
772	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
773	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
774	C₂²×D₄	—	2	1	no	—
775	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
776	C₂³×C₄	—	2	1	no	—
777	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
778	#137	—	2	4	no	—
779	#137	—	4	2	no	—
780	C₂×Q₁₆	—	4	2	no	—
781	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
782	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
783	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
784	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
785	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
786	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
787	#131	—	4	2	no	—
788	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
789	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
790	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
791	C₂²×C₈	—	4	2	no	—
792	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
793	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
794	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
795	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
796	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
797	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
798	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
799	C₄⋊Q₈	—	2	1	no	—
800	C₄⋊Q₈	—	2	1	no	—
801	C₄⋊Q₈	—	2	2	no	—
802	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
803	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
804	#126	—	2	2	no	—
805	#126	—	2	2	no	—
806	#126	—	2	2	no	—
807	#126	—	2	2	no	—
808	#125	—	2	1	no	—
809	#125	—	2	2	no	—
810	#125	—	2	2	no	—
811	#125	—	2	2	no	—
812	#125	C₂³×C₆₁	1	2	yes	—
813	#124	—	2	1	no	—
814	#124	—	2	2	no	—
815	#124	—	2	2	no	—
816	#124	C₂³×C₆₁	1	2	yes	—
817	#123	—	2	2	no	—
818	#123	—	2	2	no	—
819	#123	—	2	2	no	—
820	#123	—	2	2	no	—
821	#123	—	2	2	no	—
822	#123	—	2	2	no	—
823	#123	—	2	2	no	—
824	#123	D₄×C₆₁	1	2	yes	—
825	C₂²⋊Q₈	—	2	1	no	—
826	C₂²⋊Q₈	—	2	1	no	—
827	C₂²⋊Q₈	—	2	1	no	—
828	C₂²⋊Q₈	—	2	1	no	—
829	C₂²⋊Q₈	—	2	1	no	—
830	C₂²⋊Q₈	—	2	1	no	—
831	C₂²⋊Q₈	—	2	2	no	—
832	C₂²⋊Q₈	—	2	1	no	—
833	C₂²⋊Q₈	—	2	2	no	—
834	C₂²⋊Q₈	—	2	2	no	—
835	C₂²⋊Q₈	—	2	2	no	—
836	C₂²⋊Q₈	—	2	2	no	—
837	C₂²⋊Q₈	—	2	2	no	—
838	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
839	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
840	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
841	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
842	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
843	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
844	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
845	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
846	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
847	#121	—	2	1	no	—
848	#121	—	2	2	no	—
849	#121	—	2	2	no	—
850	#121	—	2	2	no	—
851	#121	—	2	2	no	—
852	#121	D₄×C₆₁	1	1	yes	characteristic
853	#121	D₄×C₆₁	1	1	yes	characteristic
854	#121	C₂³×C₆₁	1	2	yes	—
855	#120	—	2	2	no	—
856	#120	D₄×C₆₁	1	2	yes	—
857	C₄×Q₈	—	2	1	no	—
858	C₄×Q₈	—	2	1	no	—
859	C₄×Q₈	—	2	1	no	—
860	C₄×Q₈	—	2	2	no	—
861	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
862	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
863	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	2	2	no	—
866	C₄×D₄	—	2	2	no	—
867	C₄×D₄	—	2	2	no	—
868	C₄×D₄	—	2	2	no	—
869	C₄×D₄	—	2	2	no	—
870	C₄×D₄	C₂³×C₆₁	1	2	yes	—
871	C₄×D₄	C₂³×C₆₁	1	2	yes	—
872	C₄×D₄	C₂³×C₆₁	1	2	yes	—
873	#117	—	2	1	no	—
874	#117	—	2	1	no	—
875	#117	—	2	1	no	—
876	#117	—	2	2	no	—
877	#117	—	2	2	no	—
878	#117	—	2	2	no	—
879	#117	C₂³×C₆₁	1	1	yes	characteristic
880	#117	C₂³×C₆₁	1	1	yes	characteristic
881	#117	C₂³×C₆₁	1	1	yes	characteristic
882	#117	C₂³×C₆₁	1	1	yes	characteristic
883	#117	C₂³×C₆₁	1	2	yes	—
884	#117	C₂³×C₆₁	1	1	yes	characteristic
885	C₂×C₄⋊C₄	—	2	1	no	—
886	C₂×C₄⋊C₄	—	2	1	no	—
887	C₂×C₄⋊C₄	—	2	1	no	—
888	C₂×C₄⋊C₄	—	2	2	no	—
889	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
890	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
891	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
892	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
893	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
894	C₂×C₂²⋊C₄	—	2	1	no	—
895	C₂×C₂²⋊C₄	—	2	1	no	—
896	C₂×C₂²⋊C₄	—	2	1	no	—
897	C₂×C₂²⋊C₄	—	2	2	no	—
898	C₂×C₄²	—	2	1	no	—
899	#107	C₂³×C₆₁	1	2	yes	—
900	#107	C₂³×C₆₁	1	2	yes	—
901	#107	C₂³×C₆₁	1	2	yes	—
902	#107	C₂³×C₆₁	1	2	yes	—
903	#106	C₂³×C₆₁	1	2	yes	—
904	#106	C₂³×C₆₁	1	2	yes	—
905	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
906	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
907	#103	C₂³×C₆₁	1	1	yes	characteristic
908	#103	C₂³×C₆₁	1	1	yes	characteristic
909	#103	C₂³×C₆₁	1	1	yes	characteristic
910	#103	C₂³×C₆₁	1	1	yes	characteristic
911	#103	C₂³×C₆₁	1	1	yes	characteristic
912	#103	C₂³×C₆₁	1	1	yes	characteristic
913	#103	C₂³×C₆₁	1	1	yes	characteristic
914	#103	C₂³×C₆₁	1	1	yes	characteristic
915	#103	C₂³×C₆₁	1	2	yes	—
916	#103	C₂³×C₆₁	1	2	yes	—
917	#103	C₂³×C₆₁	1	2	yes	—
918	#103	C₂³×C₆₁	1	2	yes	—
919	#103	C₂³×C₆₁	1	2	yes	—
920	#103	C₂³×C₆₁	1	2	yes	—
921	#103	C₂³×C₆₁	1	2	yes	—
922	#103	C₂³×C₆₁	1	2	yes	—
923	#103	C₂³×C₆₁	1	2	yes	—
924	#103	C₂³×C₆₁	1	2	yes	—
925	#102	C₂³×C₆₁	1	1	yes	characteristic
926	#102	C₂³×C₆₁	1	1	yes	characteristic
927	#102	C₂³×C₆₁	1	1	yes	characteristic
928	#102	C₂³×C₆₁	1	1	yes	characteristic
929	#102	C₂³×C₆₁	1	1	yes	characteristic
930	#102	C₂³×C₆₁	1	1	yes	characteristic
931	#102	C₂³×C₆₁	1	1	yes	characteristic
932	#102	C₂³×C₆₁	1	1	yes	characteristic
933	#102	C₂³×C₆₁	1	2	yes	—
934	#102	C₂³×C₆₁	1	2	yes	—
935	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
936	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
937	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
938	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
939	#97	C₂³×C₆₁	1	2	yes	—
940	C₄×C₈	C₂³×C₆₁	1	2	yes	—
941	C₂⁴	—	2	1	no	—
942	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
943	#41	—	2	2	no	—
944	#41	—	2	2	no	—
945	#41	—	2	2	no	—
946	#41	—	2	2	no	—
947	#41	—	2	2	no	—
948	#41	—	2	4	no	—
949	#41	—	2	2	no	—
950	#41	—	2	2	no	—
951	#41	—	4	4	no	—
952	#41	—	4	1	no	—
953	#41	—	4	1	no	—
954	#41	—	4	2	no	—
955	#41	—	4	4	no	—
956	#41	—	4	4	no	—
957	#41	—	4	8	no	—
958	#41	#41×C₆₁	1	4	yes	—
959	C₂×Q₈	—	2	1	no	—
960	C₂×Q₈	—	2	1	no	—
961	C₂×Q₈	—	2	2	no	—
962	C₂×Q₈	—	2	1	no	—
963	C₂×Q₈	—	2	2	no	—
964	C₂×Q₈	—	2	2	no	—
965	C₂×Q₈	—	2	4	no	—
966	C₂×Q₈	—	2	2	no	—
967	C₂×Q₈	—	2	2	no	—
968	C₂×Q₈	—	2	2	no	—
969	C₂×Q₈	—	2	2	no	—
970	C₂×Q₈	—	4	1	no	—
971	C₂×Q₈	—	4	2	no	—
972	C₂×Q₈	—	4	4	no	—
973	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
974	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
975	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
976	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
977	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
978	C₂×D₄	—	2	1	no	—
979	C₂×D₄	—	2	2	no	—
980	C₂×D₄	—	2	2	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	1	no	—
983	C₂×D₄	—	2	1	no	—
984	C₂×D₄	—	2	2	no	—
985	C₂×D₄	—	2	1	no	—
986	C₂×D₄	—	4	1	no	—
987	C₂×D₄	—	4	4	no	—
988	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
989	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
990	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
991	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
992	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
993	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	2	no	—
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	1	no	—
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	2	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	1	no	—
1003	C₂²×C₄	—	2	1	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	2	no	—
1006	C₂²×C₄	—	2	2	no	—
1007	C₂²×C₄	—	2	1	no	—
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	2	no	—
1011	C₂²×C₄	—	4	4	no	—
1012	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1013	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1014	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1015	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1016	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
1017	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1018	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1019	Q₁₆	—	2	4	no	—
1020	Q₁₆	—	4	2	no	—
1021	Q₁₆	—	4	2	no	—
1022	Q₁₆	—	4	2	no	—
1023	SD₁₆	—	2	4	no	—
1024	SD₁₆	—	4	2	no	—
1025	M₁₆	—	2	2	no	—
1026	M₁₆	—	2	2	no	—
1027	M₁₆	—	4	2	no	—
1028	C₂×C₈	—	2	2	no	—
1029	C₂×C₈	—	2	2	no	—
1030	C₂×C₈	—	4	1	no	—
1031	C₂×C₈	—	4	1	no	—
1032	C₂×C₈	—	4	1	no	—
1033	C₂×C₈	—	4	1	no	—
1034	C₂×C₈	—	4	2	no	—
1035	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
1036	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
1037	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
1038	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
1039	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
1040	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
1041	C₄⋊C₄	—	2	2	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	2	no	—
1044	C₄⋊C₄	—	2	2	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	2	1	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	2	no	—
1061	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1062	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1063	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1064	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1065	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1066	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1067	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1068	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1069	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1070	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	1	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	2	no	—
1077	C₂²⋊C₄	—	2	2	no	—
1078	C₂²⋊C₄	—	2	2	no	—
1079	C₂²⋊C₄	—	2	2	no	—
1080	C₂²⋊C₄	—	2	2	no	—
1081	C₂²⋊C₄	—	2	2	no	—
1082	C₂²⋊C₄	—	2	2	no	—
1083	C₂²⋊C₄	—	2	2	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1088	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1089	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1090	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1091	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1092	C₄²	—	2	1	no	—
1093	C₄²	—	2	1	no	—
1094	C₄²	—	2	1	no	—
1095	C₄²	—	2	1	no	—
1096	C₄²	—	2	2	no	—
1097	C₄²	—	2	2	no	—
1098	C₄²	—	2	2	no	—
1099	C₄²	—	2	2	no	—
1100	C₄²	C₂⁴×C₆₁	1	2	yes	—
1101	C₂³	—	2	2	no	—
1102	C₂³	—	2	2	no	—
1103	C₂³	—	2	1	no	—
1104	C₂³	—	2	1	no	—
1105	C₂³	—	4	1	no	—
1106	C₂³	—	4	2	no	—
1107	C₂³	—	4	2	no	—
1108	C₂³	—	8	1	no	—
1109	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1110	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1111	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1112	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1113	Q₈	—	2	2	no	—
1114	Q₈	—	2	1	no	—
1115	Q₈	—	2	2	no	—
1116	Q₈	—	2	2	no	—
1117	Q₈	—	2	1	no	—
1118	Q₈	—	2	2	no	—
1119	Q₈	—	2	2	no	—
1120	Q₈	—	2	1	no	—
1121	Q₈	—	4	4	no	—
1122	Q₈	—	4	2	no	—
1123	Q₈	—	4	2	no	—
1124	Q₈	—	4	2	no	—
1125	Q₈	—	8	2	no	—
1126	Q₈	C₂×#41×C₆₁	1	2	yes	—
1127	D₄	—	2	4	no	—
1128	D₄	—	2	4	no	—
1129	D₄	—	2	4	no	—
1130	D₄	—	2	2	no	—
1131	D₄	—	2	1	no	—
1132	D₄	—	2	1	no	—
1133	D₄	—	2	1	no	—
1134	D₄	—	4	2	no	—
1135	D₄	—	4	2	no	—
1136	D₄	—	4	2	no	—
1137	D₄	—	4	2	no	—
1138	D₄	—	4	4	no	—
1139	D₄	—	4	2	no	—
1140	D₄	—	8	2	no	—
1141	D₄	C₂×#41×C₆₁	1	2	yes	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	4	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	2	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	2	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	2	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	2	no	—
1159	C₂×C₄	—	2	2	no	—
1160	C₂×C₄	—	2	2	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	4	2	no	—
1163	C₂×C₄	—	4	2	no	—
1164	C₂×C₄	—	4	2	no	—
1165	C₂×C₄	—	4	4	no	—
1166	C₂×C₄	—	4	4	no	—
1167	C₂×C₄	—	4	2	no	—
1168	C₂×C₄	—	4	2	no	—
1169	C₂×C₄	—	4	2	no	—
1170	C₂×C₄	—	4	2	no	—
1171	C₂×C₄	—	8	2	no	—
1172	C₂×C₄	—	8	2	no	—
1173	C₂×C₄	—	8	1	no	—
1174	C₂×C₄	—	8	1	no	—
1175	C₂×C₄	—	8	1	no	—
1176	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1177	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1178	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1179	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1180	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1181	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1182	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1183	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
1184	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1185	C₈	—	2	2	no	—
1186	C₈	—	2	1	no	—
1187	C₈	—	2	1	no	—
1188	C₈	—	2	1	no	—
1189	C₈	—	2	1	no	—
1190	C₈	—	2	2	no	—
1191	C₂²	—	2	1	no	—
1192	C₂²	—	2	1	no	—
1193	C₂²	—	2	1	no	—
1194	C₂²	—	2	1	no	—
1195	C₂²	—	2	2	no	—
1196	C₂²	—	2	1	no	—
1197	C₂²	—	2	2	no	—
1198	C₂²	—	2	1	no	—
1199	C₂²	—	2	1	no	—
1200	C₂²	—	2	2	no	—
1201	C₂²	—	2	2	no	—
1202	C₂²	—	4	4	no	—
1203	C₂²	—	4	1	no	—
1204	C₂²	—	4	1	no	—
1205	C₂²	—	4	1	no	—
1206	C₂²	—	4	1	no	—
1207	C₂²	—	4	1	no	—
1208	C₂²	—	8	4	no	—
1209	C₂²	C₆₁×#546	1	2	yes	—
1210	C₂²	C₆₁×#578	1	2	yes	—
1211	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1212	C₄	—	2	2	no	—
1213	C₄	—	2	2	no	—
1214	C₄	—	2	1	no	—
1215	C₄	—	2	1	no	—
1216	C₄	—	2	2	no	—
1217	C₄	—	2	2	no	—
1218	C₄	—	4	1	no	—
1219	C₄	—	4	1	no	—
1220	C₄	—	4	1	no	—
1221	C₄	—	4	2	no	—
1222	C₄	—	4	2	no	—
1223	C₄	—	4	1	no	—
1224	C₄	—	4	1	no	—
1225	C₄	—	4	2	no	—
1226	C₄	—	4	2	no	—
1227	C₄	C₆₁×#546	1	2	yes	—
1228	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
1229	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1230	C₂	—	2	2	no	—
1231	C₂	—	2	2	no	—
1232	C₂	—	4	1	no	—
1233	C₂	—	4	2	no	—
1234	C₂	—	4	2	no	—
1235	C₂	—	8	1	no	—
1236	C₂	C₂×C₆₁×#546	1	1	yes	characteristic
1237	C₂	C₂×C₆₁×#578	1	1	yes	characteristic
1238	C₂	C₆₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3489	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3495	C₂	semidirect
3. C₆₁×#3315	C₂	semidirect
4. C₆₁×#3314	C₂	semidirect
5. C₆₁×#3313	C₂	semidirect
6. C₆₁×#3312	C₂	semidirect
7. C₆₁×#3302	C₂	semidirect
8. C₆₁×#3300	C₂	semidirect
9. C₆₁×#3299	C₂	semidirect
10. C₆₁×#3296	C₂	semidirect
11. C₆₁×#3137	C₂	semidirect
12. C₆₁×#3098	C₂	semidirect
13. C₆₁×#3095	C₂	semidirect
14. C₆₁×#3083	C₂	semidirect
15. C₆₁×#3063	C₂	semidirect
16. C₂×C₆₁×#467	C₂	semidirect
17. C₆₁×#3044	C₂	semidirect
18. C₆₁×#3011	C₂	semidirect
19. C₆₁×#3007	C₂	semidirect
20. C₆₁×#2947	C₂	semidirect
21. C₆₁×#2929	C₂	semidirect
22. C₆₁×#2898	C₂	semidirect
23. C₂×C₆₁×#416	C₂	semidirect
28. C₂²×Q₁₆×C₆₁	C₂²	semidirect
29. C₂×#131×C₆₁	C₂²	semidirect
31. C₆₁×#556	C₂²	semidirect
35. C₆₁×#552	C₂²	semidirect
43. C₆₁×#544	C₂²	semidirect
50. C₆₁×#536	C₂²	semidirect
59. C₆₁×#520	C₂²	semidirect
60. C₆₁×#519	C₂²	semidirect
62. C₆₁×#491	C₂²	semidirect
63. C₆₁×#489	C₂²	semidirect
64. C₆₁×#488	C₂²	semidirect
65. C₆₁×#487	C₂²	semidirect
66. C₆₁×#485	C₂²	semidirect
67. C₆₁×#485	C₂²	semidirect
68. C₆₁×#485	C₂²	semidirect
70. C₆₁×#484	C₂²	semidirect
72. C₆₁×#482	C₂²	semidirect
73. C₆₁×#480	C₂²	semidirect
74. C₆₁×#479	C₂²	semidirect
75. C₆₁×#478	C₂²	semidirect
76. C₆₁×#477	C₂²	semidirect
77. C₆₁×#474	C₂²	semidirect
78. C₆₁×#470	C₂²	semidirect
79. C₆₁×#468	C₂²	semidirect
82. C₆₁×#467	C₂²	semidirect
83. C₆₁×#467	C₂²	semidirect
84. C₆₁×#467	C₂²	semidirect
85. C₆₁×#465	C₂²	semidirect
86. C₆₁×#464	C₂²	semidirect
87. C₆₁×#464	C₂²	semidirect
88. C₆₁×#462	C₂²	semidirect
89. C₆₁×#462	C₂²	semidirect
92. C₆₁×#452	C₂²	semidirect
93. C₆₁×#452	C₂²	semidirect
95. C₆₁×#451	C₂²	semidirect
96. C₆₁×#451	C₂²	semidirect
98. C₆₁×#441	C₂²	semidirect
99. C₆₁×#440	C₂²	semidirect
100. C₄×Q₁₆×C₆₁	C₂²	semidirect
101. C₄×SD₁₆×C₆₁	C₂²	semidirect
103. C₆₁×#435	C₂²	semidirect
105. C₈×D₄×C₆₁	C₂²	semidirect
106. C₆₁×#428	C₂²	semidirect
107. C₆₁×#428	C₂²	semidirect
108. C₂×#107×C₆₁	C₂²	semidirect
109. C₆₁×#424	C₂²	semidirect
110. C₆₁×#419	C₂²	semidirect
111. C₆₁×#419	C₂²	semidirect
112. C₆₁×#419	C₂²	semidirect
115. C₆₁×#417	C₂²	semidirect
124. C₆₁×#416	C₂²	semidirect
127. C₂×#103×C₆₁	C₂²	semidirect
128. C₂×#103×C₆₁	C₂²	semidirect
129. C₂×#103×C₆₁	C₂²	semidirect
132. C₆₁×#408	C₂²	semidirect
134. C₆₁×#405	C₂²	semidirect
571. #61173	C₆₁	direct (N × H)
611. #3495	C₂×C₆₁	semidirect
613. #3315	C₂×C₆₁	semidirect
614. #3314	C₂×C₆₁	semidirect
615. #3313	C₂×C₆₁	semidirect
616. #3312	C₂×C₆₁	semidirect
617. #3302	C₂×C₆₁	semidirect
618. #3300	C₂×C₆₁	semidirect
619. #3299	C₂×C₆₁	semidirect
620. #3296	C₂×C₆₁	semidirect
621. #3137	C₂×C₆₁	semidirect
622. #3098	C₂×C₆₁	semidirect
623. #3095	C₂×C₆₁	semidirect
624. #3083	C₂×C₆₁	semidirect
625. #3063	C₂×C₆₁	semidirect
626. C₂×#467	C₂×C₆₁	semidirect
627. #3044	C₂×C₆₁	semidirect
628. #3011	C₂×C₆₁	semidirect
629. #3007	C₂×C₆₁	semidirect
630. #2947	C₂×C₆₁	semidirect
631. #2929	C₂×C₆₁	semidirect
632. #2898	C₂×C₆₁	semidirect
633. C₂×#416	C₂×C₆₁	semidirect
647. C₂²×Q₁₆	C₂²×C₆₁	semidirect
648. C₂×#131	C₂²×C₆₁	semidirect
650. #556	C₂²×C₆₁	semidirect
654. #552	C₂²×C₆₁	semidirect
662. #544	C₂²×C₆₁	semidirect
669. #536	C₂²×C₆₁	semidirect
678. #520	C₂²×C₆₁	semidirect
679. #519	C₂²×C₆₁	semidirect
681. #491	C₂²×C₆₁	semidirect
682. #489	C₂²×C₆₁	semidirect
683. #488	C₂²×C₆₁	semidirect
684. #487	C₂²×C₆₁	semidirect
685. #485	C₂²×C₆₁	semidirect
686. #485	C₂²×C₆₁	semidirect
687. #485	C₂²×C₆₁	semidirect
689. #484	C₂²×C₆₁	semidirect
691. #482	C₂²×C₆₁	semidirect
692. #480	C₂²×C₆₁	semidirect
693. #479	C₂²×C₆₁	semidirect
694. #478	C₂²×C₆₁	semidirect
695. #477	C₂²×C₆₁	semidirect
696. #474	C₂²×C₆₁	semidirect
697. #470	C₂²×C₆₁	semidirect
698. #468	C₂²×C₆₁	semidirect
701. #467	C₂²×C₆₁	semidirect
702. #467	C₂²×C₆₁	semidirect
703. #467	C₂²×C₆₁	semidirect
704. #465	C₂²×C₆₁	semidirect
705. #464	C₂²×C₆₁	semidirect
706. #464	C₂²×C₆₁	semidirect
707. #462	C₂²×C₆₁	semidirect
708. #462	C₂²×C₆₁	semidirect
711. #452	C₂²×C₆₁	semidirect
712. #452	C₂²×C₆₁	semidirect
714. #451	C₂²×C₆₁	semidirect
715. #451	C₂²×C₆₁	semidirect
717. #441	C₂²×C₆₁	semidirect
718. #440	C₂²×C₆₁	semidirect
719. C₄×Q₁₆	C₂²×C₆₁	semidirect
720. C₄×SD₁₆	C₂²×C₆₁	semidirect
722. #435	C₂²×C₆₁	semidirect
724. C₈×D₄	C₂²×C₆₁	semidirect
725. #428	C₂²×C₆₁	semidirect
726. #428	C₂²×C₆₁	semidirect
727. C₂×#107	C₂²×C₆₁	semidirect
728. #424	C₂²×C₆₁	semidirect
729. #419	C₂²×C₆₁	semidirect
730. #419	C₂²×C₆₁	semidirect
731. #419	C₂²×C₆₁	semidirect
734. #417	C₂²×C₆₁	semidirect
743. #416	C₂²×C₆₁	semidirect
746. C₂×#103	C₂²×C₆₁	semidirect
747. C₂×#103	C₂²×C₆₁	semidirect
748. C₂×#103	C₂²×C₆₁	semidirect
751. #408	C₂²×C₆₁	semidirect
753. #405	C₂²×C₆₁	semidirect
754. C₆₁	#61173	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×#3495	2
C₆₁×#3489	2
C₆₁×#3315	2
C₆₁×#3314	2
C₆₁×#3313	2
C₆₁×#3312	2
C₆₁×#3302	2
C₆₁×#3300	2
C₆₁×#3299	2
C₆₁×#3296	2
C₆₁×#3137	2
C₆₁×#3098	2
C₆₁×#3095	2
C₆₁×#3083	2
C₆₁×#3063	2
C₂×C₆₁×#467	2
C₆₁×#3044	2
C₆₁×#3011	2
C₆₁×#3007	2
C₆₁×#2947	2
C₆₁×#2929	2
C₆₁×#2898	2
C₂×C₆₁×#416	2
#61173	61

Subgroups — C61×#61173 #29564606

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61173 #29564606