Subgroups — C₆₁×#61553 #29564986

Order 15616.

1886 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3394	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×D₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3357	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3353	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3319	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3314	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3273	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3272	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3175	C₂	1	2	yes	maximal, complemented
17	C₆₁×#3124	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3118	C₂	1	2	yes	maximal, complemented
19	C₆₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#2969	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₁×#2946	C₂	1	2	yes	maximal, complemented
23	C₄×AGL(1,ℤ/8)×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
26	C₆₁×#559	C₂²	1	1	yes	characteristic, complemented
27	C₆₁×#556	C₂²	1	1	yes	characteristic, complemented
28	C₆₁×#556	C₂²	1	1	yes	characteristic, complemented
29	C₆₁×#555	C₂²	1	2	yes	—
30	C₆₁×#554	C₂²	1	2	yes	complemented
31	C₆₁×#552	—	2	1	no	—
32	C₆₁×#551	—	2	2	no	—
33	C₆₁×#551	—	2	2	no	—
34	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
35	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
36	C₆₁×#548	—	2	1	no	—
37	C₆₁×#548	—	2	1	no	—
38	C₆₁×#547	C₂²	1	1	yes	characteristic
39	C₆₁×#547	C₂²	1	1	yes	characteristic
40	C₆₁×#546	—	2	1	no	—
41	C₆₁×#546	C₂²	1	2	yes	—
42	C₆₁×#546	C₂²	1	2	yes	complemented
43	D₄²×C₆₁	C₂²	1	1	yes	characteristic, complemented
44	C₆₁×#542	C₂²	1	2	yes	complemented
45	C₆₁×#542	C₂²	1	2	yes	complemented
46	C₆₁×#539	—	2	2	no	—
47	C₆₁×#538	—	2	2	no	—
48	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
49	C₆₁×#532	C₂²	1	1	yes	characteristic
50	C₆₁×#529	—	2	1	no	—
51	C₆₁×#529	C₂²	1	1	yes	characteristic
52	C₂×#124×C₆₁	—	2	1	no	—
53	C₆₁×#525	—	2	1	no	—
54	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
55	C₆₁×#520	C₂²	1	2	yes	complemented
56	C₆₁×#518	C₂²	1	2	yes	complemented
57	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
59	C₆₁×#500	C₂²	1	1	yes	characteristic, complemented
60	C₆₁×#500	C₂²	1	2	yes	complemented
61	C₆₁×#495	C₂²	1	2	yes	complemented
62	C₆₁×#492	C₂²	1	1	yes	characteristic, complemented
63	C₆₁×#489	C₂²	1	2	yes	complemented
64	C₆₁×#489	C₂²	1	2	yes	complemented
65	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
66	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
67	C₆₁×#485	C₂²	1	2	yes	complemented
68	C₆₁×#485	C₂²	1	2	yes	complemented
69	C₆₁×#484	C₂²	1	2	yes	complemented
70	C₆₁×#482	C₂²	1	2	yes	complemented
71	C₆₁×#480	C₂²	1	2	yes	complemented
72	C₆₁×#480	C₂²	1	2	yes	complemented
73	C₆₁×#477	C₂²	1	2	yes	complemented
74	C₆₁×#476	C₂²	1	2	yes	complemented
75	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
76	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
77	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
78	C₆₁×#474	C₂²	1	2	yes	complemented
79	C₆₁×#474	C₂²	1	2	yes	complemented
80	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
81	C₆₁×#468	C₂²	1	2	yes	complemented
82	C₆₁×#468	C₂²	1	2	yes	complemented
83	C₆₁×#468	C₂²	1	2	yes	complemented
84	C₆₁×#468	C₂²	1	2	yes	complemented
85	C₆₁×#467	C₂²	1	2	yes	complemented
86	C₆₁×#466	C₂²	1	2	yes	—
87	C₆₁×#464	C₂²	1	2	yes	complemented
88	C₆₁×#463	C₂²	1	2	yes	—
89	C₆₁×#463	C₂²	1	2	yes	complemented
90	C₆₁×#463	C₂²	1	2	yes	complemented
91	C₆₁×#462	C₂²	1	1	yes	characteristic, complemented
92	C₆₁×#461	C₂²	1	1	yes	characteristic, complemented
93	C₆₁×#459	C₂²	1	1	yes	characteristic
94	C₆₁×#459	C₂²	1	1	yes	characteristic
95	C₆₁×#452	C₂²	1	2	yes	—
96	C₆₁×#452	C₂²	1	2	yes	complemented
97	C₆₁×#450	C₂²	1	2	yes	complemented
98	C₆₁×#449	C₂²	1	2	yes	—
99	C₆₁×#447	C₂²	1	2	yes	—
100	C₆₁×#447	C₂²	1	2	yes	complemented
101	C₆₁×#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
103	C₆₁×#442	C₂²	1	1	yes	characteristic
104	C₆₁×#442	C₂²	1	1	yes	characteristic
105	C₆₁×#442	C₂²	1	2	yes	complemented
106	C₆₁×#440	C₂²	1	2	yes	complemented
107	C₆₁×#440	C₂²	1	2	yes	complemented
108	C₆₁×#440	C₂²	1	1	yes	characteristic, complemented
109	C₆₁×#440	C₂²	1	1	yes	characteristic, complemented
110	C₆₁×#440	C₂²	1	2	yes	complemented
111	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
112	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
113	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
116	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
117	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
118	C₄×D₈×C₆₁	C₂²	1	2	yes	—
119	C₄×D₈×C₆₁	C₂²	1	2	yes	complemented
120	C₄×D₈×C₆₁	C₂²	1	2	yes	complemented
121	C₆₁×#436	C₂²	1	1	yes	characteristic, complemented
122	C₆₁×#436	C₂²	1	2	yes	complemented
123	C₆₁×#435	C₂²	1	2	yes	complemented
124	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
125	C₆₁×#433	C₂²	1	2	yes	complemented
126	C₆₁×#431	C₂²	1	1	yes	characteristic, complemented
127	C₆₁×#428	C₂²	1	2	yes	complemented
128	C₆₁×#428	C₂²	1	1	yes	characteristic, complemented
129	C₆₁×#418	C₂²	1	1	yes	characteristic, complemented
130	C₆₁×#417	C₂²	1	1	yes	characteristic
131	C₆₁×#416	C₂²	1	2	yes	complemented
132	C₂×#102×C₆₁	C₂²	1	2	yes	complemented
133	C₆₁×#405	C₂²	1	2	yes	complemented
134	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	—	2	1	no	—
137	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
138	C₂×#41×C₆₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₆₁	—	2	1	no	—
140	C₂²×Q₈×C₆₁	—	2	1	no	—
141	C₂²×D₄×C₆₁	—	2	1	no	—
142	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
143	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₆₁	—	2	1	no	—
145	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
146	AGL(1,ℤ/8)×C₆₁	—	2	8	no	—
147	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
153	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₆₁	C₂³	1	2	yes	—
155	C₂×D₈×C₆₁	C₂³	1	2	yes	—
156	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
157	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
158	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
159	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
160	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
161	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
166	#127×C₆₁	C₂³	1	1	yes	characteristic
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	D₄	1	2	yes	—
172	#125×C₆₁	—	2	2	no	—
173	#125×C₆₁	—	2	1	no	—
174	#125×C₆₁	D₄	1	1	yes	characteristic
175	#124×C₆₁	—	2	1	no	—
176	#124×C₆₁	—	2	1	no	—
177	#124×C₆₁	—	2	2	no	—
178	#124×C₆₁	—	2	2	no	—
179	#124×C₆₁	—	2	2	no	—
180	#124×C₆₁	—	2	2	no	—
181	#124×C₆₁	—	2	1	no	—
182	#124×C₆₁	D₄	1	1	yes	characteristic
183	#124×C₆₁	C₂³	1	2	yes	—
184	#124×C₆₁	C₂³	1	2	yes	—
185	#123×C₆₁	—	2	2	no	—
186	#123×C₆₁	—	2	2	no	—
187	#123×C₆₁	—	2	2	no	—
188	#123×C₆₁	—	2	2	no	—
189	#123×C₆₁	—	2	2	no	—
190	#123×C₆₁	—	2	2	no	—
191	#123×C₆₁	—	2	2	no	—
192	#123×C₆₁	D₄	1	2	yes	—
193	C₂²⋊Q₈×C₆₁	—	2	1	no	—
194	C₂²⋊Q₈×C₆₁	—	2	1	no	—
195	C₂²⋊Q₈×C₆₁	—	2	2	no	—
196	C₂²⋊Q₈×C₆₁	—	2	2	no	—
197	C₂²⋊Q₈×C₆₁	—	2	2	no	—
198	C₂²⋊Q₈×C₆₁	—	2	2	no	—
199	C₂²⋊Q₈×C₆₁	—	2	1	no	—
200	C₂²⋊Q₈×C₆₁	—	2	1	no	—
201	C₂²⋊Q₈×C₆₁	—	2	1	no	—
202	C₂²⋊Q₈×C₆₁	—	2	2	no	—
203	C₂²⋊Q₈×C₆₁	—	2	2	no	—
204	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
205	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
206	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
207	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
208	#121×C₆₁	—	2	2	no	—
209	#121×C₆₁	—	2	1	no	—
210	#121×C₆₁	—	2	1	no	—
211	#121×C₆₁	—	2	1	no	—
212	#121×C₆₁	—	2	2	no	—
213	#121×C₆₁	—	2	2	no	—
214	#121×C₆₁	D₄	1	1	yes	characteristic
215	#121×C₆₁	C₂³	1	2	yes	—
216	#121×C₆₁	C₂³	1	2	yes	—
217	#121×C₆₁	C₂³	1	2	yes	—
218	#120×C₆₁	—	2	2	no	—
219	#120×C₆₁	—	2	2	no	—
220	#120×C₆₁	—	2	2	no	—
221	C₄×Q₈×C₆₁	—	2	1	no	—
222	C₄×Q₈×C₆₁	—	2	1	no	—
223	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
224	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
226	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₆₁	—	2	2	no	—
229	C₄×D₄×C₆₁	—	2	1	no	—
230	C₄×D₄×C₆₁	—	2	1	no	—
231	C₄×D₄×C₆₁	—	2	2	no	—
232	C₄×D₄×C₆₁	—	2	1	no	—
233	C₄×D₄×C₆₁	—	2	2	no	—
234	C₄×D₄×C₆₁	—	2	2	no	—
235	C₄×D₄×C₆₁	—	2	2	no	—
236	C₄×D₄×C₆₁	—	2	1	no	—
237	C₄×D₄×C₆₁	—	2	1	no	—
238	C₄×D₄×C₆₁	—	2	1	no	—
239	C₄×D₄×C₆₁	C₂³	1	2	yes	—
240	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₆₁	C₂³	1	2	yes	—
243	C₄×D₄×C₆₁	C₂³	1	2	yes	—
244	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₆₁	C₂³	1	2	yes	—
247	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₆₁	C₂³	1	2	yes	—
251	#117×C₆₁	—	2	1	no	—
252	#117×C₆₁	—	2	2	no	—
253	#117×C₆₁	—	2	2	no	—
254	#117×C₆₁	—	2	1	no	—
255	#117×C₆₁	—	2	1	no	—
256	#117×C₆₁	C₂³	1	1	yes	characteristic
257	#117×C₆₁	C₂³	1	2	yes	—
258	#117×C₆₁	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
260	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
261	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
266	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
268	C₂×C₄²×C₆₁	—	2	1	no	—
269	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
270	#107×C₆₁	C₂³	1	1	yes	characteristic
271	#107×C₆₁	C₂³	1	2	yes	—
272	#107×C₆₁	C₂³	1	1	yes	characteristic
273	#107×C₆₁	C₂³	1	2	yes	—
274	#107×C₆₁	C₂³	1	2	yes	—
275	#107×C₆₁	C₂³	1	2	yes	—
276	#107×C₆₁	C₂³	1	2	yes	—
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	1	yes	characteristic
281	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
283	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
284	#103×C₆₁	C₂³	1	2	yes	—
285	#103×C₆₁	C₂³	1	2	yes	—
286	#103×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	2	yes	—
291	#102×C₆₁	C₂³	1	1	yes	characteristic
292	#102×C₆₁	C₂³	1	2	yes	—
293	#102×C₆₁	C₂³	1	2	yes	—
294	#102×C₆₁	C₂³	1	2	yes	—
295	#102×C₆₁	C₂³	1	1	yes	characteristic
296	#102×C₆₁	C₂³	1	2	yes	—
297	#102×C₆₁	C₂³	1	1	yes	characteristic
298	#102×C₆₁	C₂³	1	1	yes	characteristic
299	#102×C₆₁	C₂³	1	1	yes	characteristic
300	#102×C₆₁	C₂³	1	1	yes	characteristic
301	#102×C₆₁	C₂³	1	2	yes	—
302	#102×C₆₁	C₂³	1	2	yes	—
303	#102×C₆₁	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
307	#97×C₆₁	C₂³	1	1	yes	characteristic
308	#97×C₆₁	C₂³	1	1	yes	characteristic
309	#97×C₆₁	C₂³	1	2	yes	—
310	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₆₁	C₂³	1	2	yes	—
313	C₄×C₈×C₆₁	C₂³	1	2	yes	—
314	C₂⁴×C₆₁	—	2	1	no	—
315	C₂⁴×C₆₁	—	2	2	no	—
316	#41×C₆₁	—	2	4	no	—
317	#41×C₆₁	—	2	2	no	—
318	#41×C₆₁	—	4	2	no	—
319	#41×C₆₁	—	4	1	no	—
320	#41×C₆₁	—	8	2	no	—
321	#41×C₆₁	—	8	2	no	—
322	C₂×Q₈×C₆₁	—	2	1	no	—
323	C₂×Q₈×C₆₁	—	2	1	no	—
324	C₂×Q₈×C₆₁	—	2	2	no	—
325	C₂×Q₈×C₆₁	—	2	2	no	—
326	C₂×Q₈×C₆₁	—	8	2	no	—
327	C₂×Q₈×C₆₁	—	8	2	no	—
328	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
331	C₂×D₄×C₆₁	—	2	2	no	—
332	C₂×D₄×C₆₁	—	2	4	no	—
333	C₂×D₄×C₆₁	—	2	1	no	—
334	C₂×D₄×C₆₁	—	2	2	no	—
335	C₂×D₄×C₆₁	—	2	2	no	—
336	C₂×D₄×C₆₁	—	2	2	no	—
337	C₂×D₄×C₆₁	—	2	2	no	—
338	C₂×D₄×C₆₁	—	2	2	no	—
339	C₂×D₄×C₆₁	—	2	1	no	—
340	C₂×D₄×C₆₁	—	2	1	no	—
341	C₂×D₄×C₆₁	—	2	1	no	—
342	C₂×D₄×C₆₁	—	4	2	no	—
343	C₂×D₄×C₆₁	—	4	1	no	—
344	C₂×D₄×C₆₁	—	8	2	no	—
345	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
346	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
347	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
349	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₆₁	—	2	1	no	—
352	C₂²×C₄×C₆₁	—	2	2	no	—
353	C₂²×C₄×C₆₁	—	2	1	no	—
354	C₂²×C₄×C₆₁	—	2	1	no	—
355	C₂²×C₄×C₆₁	—	2	2	no	—
356	C₂²×C₄×C₆₁	—	2	1	no	—
357	C₂²×C₄×C₆₁	—	2	1	no	—
358	C₂²×C₄×C₆₁	—	2	1	no	—
359	C₂²×C₄×C₆₁	—	2	2	no	—
360	C₂²×C₄×C₆₁	—	2	2	no	—
361	C₂²×C₄×C₆₁	—	2	2	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	—	8	2	no	—
366	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
370	Q₁₆×C₆₁	—	4	2	no	—
371	SD₁₆×C₆₁	—	2	2	no	—
372	SD₁₆×C₆₁	—	2	4	no	—
373	SD₁₆×C₆₁	—	2	4	no	—
374	SD₁₆×C₆₁	—	2	2	no	—
375	SD₁₆×C₆₁	—	4	2	no	—
376	D₈×C₆₁	—	2	4	no	—
377	D₈×C₆₁	—	2	2	no	—
378	D₈×C₆₁	—	4	2	no	—
379	D₈×C₆₁	#41	1	4	yes	complemented
380	M₁₆×C₆₁	—	2	2	no	—
381	M₁₆×C₆₁	—	2	4	no	—
382	M₁₆×C₆₁	—	4	1	no	—
383	C₂×C₈×C₆₁	—	4	2	no	—
384	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
385	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
389	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
390	C₄⋊C₄×C₆₁	—	2	2	no	—
391	C₄⋊C₄×C₆₁	—	2	1	no	—
392	C₄⋊C₄×C₆₁	—	2	2	no	—
393	C₄⋊C₄×C₆₁	—	2	2	no	—
394	C₄⋊C₄×C₆₁	—	2	2	no	—
395	C₄⋊C₄×C₆₁	—	2	1	no	—
396	C₄⋊C₄×C₆₁	—	2	1	no	—
397	C₄⋊C₄×C₆₁	—	2	1	no	—
398	C₄⋊C₄×C₆₁	—	2	2	no	—
399	C₄⋊C₄×C₆₁	—	2	1	no	—
400	C₄⋊C₄×C₆₁	—	2	1	no	—
401	C₄⋊C₄×C₆₁	—	2	1	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	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
417	C₂²⋊C₄×C₆₁	—	2	2	no	—
418	C₂²⋊C₄×C₆₁	—	2	2	no	—
419	C₂²⋊C₄×C₆₁	—	2	2	no	—
420	C₂²⋊C₄×C₆₁	—	2	1	no	—
421	C₂²⋊C₄×C₆₁	—	2	2	no	—
422	C₂²⋊C₄×C₆₁	—	2	1	no	—
423	C₂²⋊C₄×C₆₁	—	2	1	no	—
424	C₂²⋊C₄×C₆₁	—	2	2	no	—
425	C₂²⋊C₄×C₆₁	—	2	2	no	—
426	C₂²⋊C₄×C₆₁	—	2	2	no	—
427	C₂²⋊C₄×C₆₁	—	2	1	no	—
428	C₂²⋊C₄×C₆₁	—	2	1	no	—
429	C₂²⋊C₄×C₆₁	—	2	2	no	—
430	C₂²⋊C₄×C₆₁	—	2	1	no	—
431	C₂²⋊C₄×C₆₁	—	2	2	no	—
432	C₂²⋊C₄×C₆₁	—	2	2	no	—
433	C₂²⋊C₄×C₆₁	—	2	2	no	—
434	C₂²⋊C₄×C₆₁	—	2	1	no	—
435	C₂²⋊C₄×C₆₁	—	2	2	no	—
436	C₂²⋊C₄×C₆₁	—	2	2	no	—
437	C₂²⋊C₄×C₆₁	—	2	2	no	—
438	C₂²⋊C₄×C₆₁	—	2	2	no	—
439	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
444	C₄²×C₆₁	—	2	1	no	—
445	C₄²×C₆₁	—	2	1	no	—
446	C₄²×C₆₁	—	2	1	no	—
447	C₄²×C₆₁	—	2	2	no	—
448	C₄²×C₆₁	—	2	2	no	—
449	C₄²×C₆₁	—	2	2	no	—
450	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
453	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
454	C₄²×C₆₁	C₂⁴	1	2	yes	—
455	C₂³×C₆₁	—	2	1	no	—
456	C₂³×C₆₁	—	2	1	no	—
457	C₂³×C₆₁	—	2	1	no	—
458	C₂³×C₆₁	—	2	2	no	—
459	C₂³×C₆₁	—	4	2	no	—
460	C₂³×C₆₁	—	4	4	no	—
461	C₂³×C₆₁	—	4	2	no	—
462	C₂³×C₆₁	—	8	1	no	—
463	C₂³×C₆₁	—	8	2	no	—
464	C₂³×C₆₁	—	8	2	no	—
465	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
466	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
467	Q₈×C₆₁	—	2	2	no	—
468	Q₈×C₆₁	—	2	1	no	—
469	Q₈×C₆₁	—	2	2	no	—
470	Q₈×C₆₁	—	2	2	no	—
471	Q₈×C₆₁	—	2	1	no	—
472	Q₈×C₆₁	—	4	2	no	—
473	Q₈×C₆₁	—	4	2	no	—
474	Q₈×C₆₁	—	8	2	no	—
475	Q₈×C₆₁	—	8	2	no	—
476	D₄×C₆₁	—	2	2	no	—
477	D₄×C₆₁	—	2	1	no	—
478	D₄×C₆₁	—	2	2	no	—
479	D₄×C₆₁	—	2	1	no	—
480	D₄×C₆₁	—	2	1	no	—
481	D₄×C₆₁	—	2	1	no	—
482	D₄×C₆₁	—	2	2	no	—
483	D₄×C₆₁	—	4	2	no	—
484	D₄×C₆₁	—	4	2	no	—
485	D₄×C₆₁	—	4	4	no	—
486	D₄×C₆₁	—	4	4	no	—
487	D₄×C₆₁	—	4	2	no	—
488	D₄×C₆₁	—	4	2	no	—
489	D₄×C₆₁	—	8	1	no	—
490	D₄×C₆₁	—	8	2	no	—
491	D₄×C₆₁	—	8	2	no	—
492	D₄×C₆₁	—	8	2	no	—
493	D₄×C₆₁	C₂×#41	1	2	yes	—
494	D₄×C₆₁	C₂×#41	1	2	yes	—
495	C₂×C₄×C₆₁	—	2	2	no	—
496	C₂×C₄×C₆₁	—	2	1	no	—
497	C₂×C₄×C₆₁	—	2	2	no	—
498	C₂×C₄×C₆₁	—	2	2	no	—
499	C₂×C₄×C₆₁	—	2	1	no	—
500	C₂×C₄×C₆₁	—	2	1	no	—
501	C₂×C₄×C₆₁	—	2	1	no	—
502	C₂×C₄×C₆₁	—	2	2	no	—
503	C₂×C₄×C₆₁	—	2	1	no	—
504	C₂×C₄×C₆₁	—	2	1	no	—
505	C₂×C₄×C₆₁	—	2	2	no	—
506	C₂×C₄×C₆₁	—	2	2	no	—
507	C₂×C₄×C₆₁	—	2	1	no	—
508	C₂×C₄×C₆₁	—	4	1	no	—
509	C₂×C₄×C₆₁	—	4	4	no	—
510	C₂×C₄×C₆₁	—	4	2	no	—
511	C₂×C₄×C₆₁	—	4	2	no	—
512	C₂×C₄×C₆₁	—	4	2	no	—
513	C₂×C₄×C₆₁	—	4	2	no	—
514	C₂×C₄×C₆₁	—	8	1	no	—
515	C₂×C₄×C₆₁	—	8	2	no	—
516	C₂×C₄×C₆₁	—	8	1	no	—
517	C₂×C₄×C₆₁	—	8	1	no	—
518	C₂×C₄×C₆₁	—	8	2	no	—
519	C₂×C₄×C₆₁	—	8	2	no	—
520	C₂×C₄×C₆₁	—	8	2	no	—
521	C₂×C₄×C₆₁	—	8	1	no	—
522	C₂×C₄×C₆₁	—	8	2	no	—
523	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
532	C₈×C₆₁	—	2	1	no	—
533	C₈×C₆₁	—	2	2	no	—
534	C₈×C₆₁	—	2	1	no	—
535	C₈×C₆₁	—	2	2	no	—
536	C₈×C₆₁	—	2	1	no	—
537	C₈×C₆₁	C₂×#41	1	2	yes	—
538	#61553	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
539	C₂²×C₆₁	—	2	1	no	—
540	C₂²×C₆₁	—	2	2	no	—
541	C₂²×C₆₁	—	2	1	no	—
542	C₂²×C₆₁	—	2	2	no	—
543	C₂²×C₆₁	—	2	2	no	—
544	C₂²×C₆₁	—	2	2	no	—
545	C₂²×C₆₁	—	2	1	no	—
546	C₂²×C₆₁	—	2	2	no	—
547	C₂²×C₆₁	—	4	1	no	—
548	C₂²×C₆₁	—	4	1	no	—
549	C₂²×C₆₁	—	4	1	no	—
550	C₂²×C₆₁	—	4	1	no	—
551	C₂²×C₆₁	—	4	2	no	—
552	C₂²×C₆₁	—	4	1	no	—
553	C₂²×C₆₁	—	4	1	no	—
554	C₂²×C₆₁	—	4	2	no	—
555	C₂²×C₆₁	—	4	1	no	—
556	C₂²×C₆₁	—	4	2	no	—
557	C₂²×C₆₁	—	8	4	no	—
558	C₂²×C₆₁	—	16	4	no	—
559	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
560	C₄×C₆₁	—	2	1	no	—
561	C₄×C₆₁	—	2	1	no	—
562	C₄×C₆₁	—	2	2	no	—
563	C₄×C₆₁	—	2	2	no	—
564	C₄×C₆₁	—	2	1	no	—
565	C₄×C₆₁	—	2	1	no	—
566	C₄×C₆₁	—	2	2	no	—
567	C₄×C₆₁	—	4	1	no	—
568	C₄×C₆₁	—	4	1	no	—
569	C₄×C₆₁	—	4	2	no	—
570	C₄×C₆₁	—	4	1	no	—
571	C₄×C₆₁	—	4	1	no	—
572	C₄×C₆₁	—	4	1	no	—
573	C₄×C₆₁	—	4	2	no	—
574	C₄×C₆₁	—	4	2	no	—
575	C₄×C₆₁	#576	1	2	yes	—
576	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
577	C₄×C₆₁	#585	1	1	yes	characteristic
578	#3520	C₂×C₆₁	1	1	yes	characteristic, complemented
579	#3514	C₂×C₆₁	1	1	yes	characteristic, complemented
580	#3394	C₂×C₆₁	1	1	yes	characteristic, complemented
581	Q₈×D₈	C₂×C₆₁	1	1	yes	characteristic, complemented
582	#3373	C₂×C₆₁	1	1	yes	characteristic, complemented
583	#3367	C₂×C₆₁	1	1	yes	characteristic, complemented
584	#3357	C₂×C₆₁	1	2	yes	complemented
585	#3353	C₂×C₆₁	1	1	yes	characteristic, complemented
586	#3319	C₂×C₆₁	1	2	yes	complemented
587	#3314	C₂×C₆₁	1	2	yes	complemented
588	#3302	C₂×C₆₁	1	1	yes	characteristic, complemented
589	#3294	C₂×C₆₁	1	1	yes	characteristic, complemented
590	#3273	C₂×C₆₁	1	2	yes	complemented
591	#3272	C₂×C₆₁	1	1	yes	characteristic, complemented
592	#3182	C₂×C₆₁	1	1	yes	characteristic, complemented
593	#3175	C₂×C₆₁	1	2	yes	complemented
594	#3124	C₂×C₆₁	1	2	yes	complemented
595	#3118	C₂×C₆₁	1	2	yes	complemented
596	#3107	C₂×C₆₁	1	1	yes	characteristic, complemented
597	#3100	C₂×C₆₁	1	1	yes	characteristic, complemented
598	#2969	C₂×C₆₁	1	1	yes	characteristic, complemented
599	#2946	C₂×C₆₁	1	2	yes	complemented
600	C₄×AGL(1,ℤ/8)	C₂×C₆₁	1	1	yes	characteristic, complemented
601	C₂×C₆₁	—	4	1	no	—
602	C₂×C₆₁	—	4	2	no	—
603	C₂×C₆₁	—	4	2	no	—
604	C₂×C₆₁	—	4	2	no	—
605	C₂×C₆₁	—	8	1	no	—
606	C₂×C₆₁	—	8	2	no	—
607	C₂×C₆₁	D₄×#41	1	1	yes	characteristic
608	C₂×C₆₁	C₂×#576	1	1	yes	characteristic
609	C₂×C₆₁	#3586	1	1	yes	characteristic
610	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	1	yes	characteristic
611	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
612	#559	C₂²×C₆₁	1	1	yes	characteristic, complemented
613	#556	C₂²×C₆₁	1	1	yes	characteristic, complemented
614	#556	C₂²×C₆₁	1	1	yes	characteristic, complemented
615	#555	C₂²×C₆₁	1	2	yes	—
616	#554	C₂²×C₆₁	1	2	yes	complemented
617	#552	—	2	1	no	—
618	#551	—	2	2	no	—
619	#551	—	2	2	no	—
620	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
621	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
622	#548	—	2	1	no	—
623	#548	—	2	1	no	—
624	#547	C₂²×C₆₁	1	1	yes	characteristic
625	#547	C₂²×C₆₁	1	1	yes	characteristic
626	#546	—	2	1	no	—
627	#546	C₂²×C₆₁	1	2	yes	—
628	#546	C₂²×C₆₁	1	2	yes	complemented
629	D₄²	C₂²×C₆₁	1	1	yes	characteristic, complemented
630	#542	C₂²×C₆₁	1	2	yes	complemented
631	#542	C₂²×C₆₁	1	2	yes	complemented
632	#539	—	2	2	no	—
633	#538	—	2	2	no	—
634	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
635	#532	C₂²×C₆₁	1	1	yes	characteristic
636	#529	—	2	1	no	—
637	#529	C₂²×C₆₁	1	1	yes	characteristic
638	C₂×#124	—	2	1	no	—
639	#525	—	2	1	no	—
640	C₂×C₂²⋊Q₈	—	2	1	no	—
641	#520	C₂²×C₆₁	1	2	yes	complemented
642	#518	C₂²×C₆₁	1	2	yes	complemented
643	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
644	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
645	#500	C₂²×C₆₁	1	1	yes	characteristic, complemented
646	#500	C₂²×C₆₁	1	2	yes	complemented
647	#495	C₂²×C₆₁	1	2	yes	complemented
648	#492	C₂²×C₆₁	1	1	yes	characteristic, complemented
649	#489	C₂²×C₆₁	1	2	yes	complemented
650	#489	C₂²×C₆₁	1	2	yes	complemented
651	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
652	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
653	#485	C₂²×C₆₁	1	2	yes	complemented
654	#485	C₂²×C₆₁	1	2	yes	complemented
655	#484	C₂²×C₆₁	1	2	yes	complemented
656	#482	C₂²×C₆₁	1	2	yes	complemented
657	#480	C₂²×C₆₁	1	2	yes	complemented
658	#480	C₂²×C₆₁	1	2	yes	complemented
659	#477	C₂²×C₆₁	1	2	yes	complemented
660	#476	C₂²×C₆₁	1	2	yes	complemented
661	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
662	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
663	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
664	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
665	#474	C₂²×C₆₁	1	2	yes	complemented
666	#474	C₂²×C₆₁	1	2	yes	complemented
667	#468	C₂²×C₆₁	1	2	yes	complemented
668	#468	C₂²×C₆₁	1	2	yes	complemented
669	#468	C₂²×C₆₁	1	2	yes	complemented
670	#468	C₂²×C₆₁	1	2	yes	complemented
671	#467	C₂²×C₆₁	1	2	yes	complemented
672	#466	C₂²×C₆₁	1	2	yes	—
673	#464	C₂²×C₆₁	1	2	yes	complemented
674	#463	C₂²×C₆₁	1	2	yes	—
675	#463	C₂²×C₆₁	1	2	yes	complemented
676	#463	C₂²×C₆₁	1	2	yes	complemented
677	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
678	#461	C₂²×C₆₁	1	1	yes	characteristic, complemented
679	#459	C₂²×C₆₁	1	1	yes	characteristic
680	#459	C₂²×C₆₁	1	1	yes	characteristic
681	#452	C₂²×C₆₁	1	2	yes	—
682	#452	C₂²×C₆₁	1	2	yes	complemented
683	#450	C₂²×C₆₁	1	2	yes	complemented
684	#449	C₂²×C₆₁	1	2	yes	—
685	#447	C₂²×C₆₁	1	2	yes	—
686	#447	C₂²×C₆₁	1	2	yes	complemented
687	#446	C₂²×C₆₁	1	1	yes	characteristic, complemented
688	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
689	#442	C₂²×C₆₁	1	1	yes	characteristic
690	#442	C₂²×C₆₁	1	1	yes	characteristic
691	#442	C₂²×C₆₁	1	2	yes	complemented
692	#440	C₂²×C₆₁	1	2	yes	complemented
693	#440	C₂²×C₆₁	1	2	yes	complemented
694	#440	C₂²×C₆₁	1	1	yes	characteristic, complemented
695	#440	C₂²×C₆₁	1	1	yes	characteristic, complemented
696	#440	C₂²×C₆₁	1	2	yes	complemented
697	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
698	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
699	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
700	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
701	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
702	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
703	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
704	C₄×D₈	C₂²×C₆₁	1	2	yes	—
705	C₄×D₈	C₂²×C₆₁	1	2	yes	complemented
706	C₄×D₈	C₂²×C₆₁	1	2	yes	complemented
707	#436	C₂²×C₆₁	1	1	yes	characteristic, complemented
708	#436	C₂²×C₆₁	1	2	yes	complemented
709	#435	C₂²×C₆₁	1	2	yes	complemented
710	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
711	#433	C₂²×C₆₁	1	2	yes	complemented
712	#431	C₂²×C₆₁	1	1	yes	characteristic, complemented
713	#428	C₂²×C₆₁	1	2	yes	complemented
714	#428	C₂²×C₆₁	1	1	yes	characteristic, complemented
715	#418	C₂²×C₆₁	1	1	yes	characteristic, complemented
716	#417	C₂²×C₆₁	1	1	yes	characteristic
717	#416	C₂²×C₆₁	1	2	yes	complemented
718	C₂×#102	C₂²×C₆₁	1	2	yes	complemented
719	#405	C₂²×C₆₁	1	2	yes	complemented
720	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
721	C₆₁	#61553	1	1	yes	characteristic, direct product factor, Sylow
722	C₂×#41	—	2	1	no	—
723	C₂×#41	—	2	1	no	—
724	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
725	C₂×#41	C₂³×C₆₁	1	2	yes	—
726	C₂²×Q₈	—	2	1	no	—
727	C₂²×Q₈	—	2	1	no	—
728	C₂²×D₄	—	2	1	no	—
729	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
730	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
731	C₂³×C₄	—	2	1	no	—
732	AGL(1,ℤ/8)	—	2	4	no	—
733	AGL(1,ℤ/8)	—	2	8	no	—
734	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
737	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
738	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
739	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
740	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
741	C₂×D₈	C₂³×C₆₁	1	2	yes	—
742	C₂×D₈	C₂³×C₆₁	1	2	yes	—
743	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
744	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
745	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
746	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
747	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
748	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
749	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
750	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
751	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
752	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
753	#127	C₂³×C₆₁	1	1	yes	characteristic
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	D₄×C₆₁	1	2	yes	—
759	#125	—	2	2	no	—
760	#125	—	2	1	no	—
761	#125	D₄×C₆₁	1	1	yes	characteristic
762	#124	—	2	1	no	—
763	#124	—	2	1	no	—
764	#124	—	2	2	no	—
765	#124	—	2	2	no	—
766	#124	—	2	2	no	—
767	#124	—	2	2	no	—
768	#124	—	2	1	no	—
769	#124	D₄×C₆₁	1	1	yes	characteristic
770	#124	C₂³×C₆₁	1	2	yes	—
771	#124	C₂³×C₆₁	1	2	yes	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	D₄×C₆₁	1	2	yes	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	1	no	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	—	2	1	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
792	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
793	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
794	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
795	#121	—	2	1	no	—
796	#121	—	2	2	no	—
797	#121	—	2	1	no	—
798	#121	—	2	1	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	D₄×C₆₁	1	1	yes	characteristic
802	#121	C₂³×C₆₁	1	2	yes	—
803	#121	C₂³×C₆₁	1	2	yes	—
804	#121	C₂³×C₆₁	1	2	yes	—
805	#120	—	2	2	no	—
806	#120	—	2	2	no	—
807	#120	—	2	2	no	—
808	C₄×Q₈	—	2	1	no	—
809	C₄×Q₈	—	2	1	no	—
810	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
812	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
813	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
814	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
827	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
830	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₆₁	1	2	yes	—
833	C₄×D₄	C₂³×C₆₁	1	2	yes	—
834	C₄×D₄	C₂³×C₆₁	1	2	yes	—
835	C₄×D₄	C₂³×C₆₁	1	2	yes	—
836	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
837	C₄×D₄	C₂³×C₆₁	1	2	yes	—
838	#117	—	2	1	no	—
839	#117	—	2	2	no	—
840	#117	—	2	1	no	—
841	#117	—	2	2	no	—
842	#117	—	2	1	no	—
843	#117	C₂³×C₆₁	1	1	yes	characteristic
844	#117	C₂³×C₆₁	1	2	yes	—
845	#117	C₂³×C₆₁	1	2	yes	—
846	C₂×C₄⋊C₄	—	2	2	no	—
847	C₂×C₄⋊C₄	—	2	1	no	—
848	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
849	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
850	C₂×C₂²⋊C₄	—	2	1	no	—
851	C₂×C₂²⋊C₄	—	2	2	no	—
852	C₂×C₂²⋊C₄	—	2	2	no	—
853	C₂×C₂²⋊C₄	—	2	2	no	—
854	C₂×C₂²⋊C₄	—	2	2	no	—
855	C₂×C₄²	—	2	1	no	—
856	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
857	#107	C₂³×C₆₁	1	1	yes	characteristic
858	#107	C₂³×C₆₁	1	2	yes	—
859	#107	C₂³×C₆₁	1	1	yes	characteristic
860	#107	C₂³×C₆₁	1	2	yes	—
861	#107	C₂³×C₆₁	1	2	yes	—
862	#107	C₂³×C₆₁	1	2	yes	—
863	#107	C₂³×C₆₁	1	2	yes	—
864	#106	C₂³×C₆₁	1	1	yes	characteristic
865	#106	C₂³×C₆₁	1	1	yes	characteristic
866	#106	C₂³×C₆₁	1	2	yes	—
867	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
868	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
869	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
870	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
871	#103	C₂³×C₆₁	1	2	yes	—
872	#103	C₂³×C₆₁	1	2	yes	—
873	#103	C₂³×C₆₁	1	1	yes	characteristic
874	#103	C₂³×C₆₁	1	1	yes	characteristic
875	#103	C₂³×C₆₁	1	2	yes	—
876	#103	C₂³×C₆₁	1	2	yes	—
877	#103	C₂³×C₆₁	1	2	yes	—
878	#102	C₂³×C₆₁	1	1	yes	characteristic
879	#102	C₂³×C₆₁	1	2	yes	—
880	#102	C₂³×C₆₁	1	2	yes	—
881	#102	C₂³×C₆₁	1	2	yes	—
882	#102	C₂³×C₆₁	1	1	yes	characteristic
883	#102	C₂³×C₆₁	1	2	yes	—
884	#102	C₂³×C₆₁	1	1	yes	characteristic
885	#102	C₂³×C₆₁	1	1	yes	characteristic
886	#102	C₂³×C₆₁	1	1	yes	characteristic
887	#102	C₂³×C₆₁	1	1	yes	characteristic
888	#102	C₂³×C₆₁	1	2	yes	—
889	#102	C₂³×C₆₁	1	2	yes	—
890	#102	C₂³×C₆₁	1	2	yes	—
891	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
892	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
893	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
894	#97	C₂³×C₆₁	1	1	yes	characteristic
895	#97	C₂³×C₆₁	1	1	yes	characteristic
896	#97	C₂³×C₆₁	1	2	yes	—
897	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
898	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
899	C₄×C₈	C₂³×C₆₁	1	2	yes	—
900	C₄×C₈	C₂³×C₆₁	1	2	yes	—
901	C₂⁴	—	2	1	no	—
902	C₂⁴	—	2	2	no	—
903	#41	—	2	4	no	—
904	#41	—	2	2	no	—
905	#41	—	4	2	no	—
906	#41	—	4	1	no	—
907	#41	—	8	2	no	—
908	#41	—	8	2	no	—
909	C₂×Q₈	—	2	1	no	—
910	C₂×Q₈	—	2	1	no	—
911	C₂×Q₈	—	2	2	no	—
912	C₂×Q₈	—	2	2	no	—
913	C₂×Q₈	—	8	2	no	—
914	C₂×Q₈	—	8	2	no	—
915	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
916	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
917	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	4	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	4	2	no	—
930	C₂×D₄	—	4	1	no	—
931	C₂×D₄	—	8	2	no	—
932	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
933	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
934	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
935	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
936	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
937	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	8	2	no	—
953	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
954	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
955	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
956	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
957	Q₁₆	—	4	2	no	—
958	SD₁₆	—	2	2	no	—
959	SD₁₆	—	2	4	no	—
960	SD₁₆	—	2	4	no	—
961	SD₁₆	—	2	2	no	—
962	SD₁₆	—	4	2	no	—
963	D₈	—	2	4	no	—
964	D₈	—	2	2	no	—
965	D₈	—	4	2	no	—
966	D₈	#41×C₆₁	1	4	yes	complemented
967	M₁₆	—	2	2	no	—
968	M₁₆	—	2	4	no	—
969	M₁₆	—	4	1	no	—
970	C₂×C₈	—	4	2	no	—
971	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
972	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
974	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
975	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
976	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
993	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
994	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
995	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
996	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
997	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
998	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
999	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1001	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1002	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1003	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1027	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1028	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1029	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1030	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	—	2	2	no	—
1035	C₄²	—	2	2	no	—
1036	C₄²	—	2	2	no	—
1037	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1038	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1039	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1040	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1041	C₄²	C₂⁴×C₆₁	1	2	yes	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	2	1	no	—
1044	C₂³	—	2	1	no	—
1045	C₂³	—	2	2	no	—
1046	C₂³	—	4	2	no	—
1047	C₂³	—	4	4	no	—
1048	C₂³	—	4	2	no	—
1049	C₂³	—	8	1	no	—
1050	C₂³	—	8	2	no	—
1051	C₂³	—	8	2	no	—
1052	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1053	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1054	Q₈	—	2	2	no	—
1055	Q₈	—	2	1	no	—
1056	Q₈	—	2	2	no	—
1057	Q₈	—	2	2	no	—
1058	Q₈	—	2	1	no	—
1059	Q₈	—	4	2	no	—
1060	Q₈	—	4	2	no	—
1061	Q₈	—	8	2	no	—
1062	Q₈	—	8	2	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	1	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	2	1	no	—
1069	D₄	—	2	2	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	4	no	—
1073	D₄	—	4	4	no	—
1074	D₄	—	4	2	no	—
1075	D₄	—	4	2	no	—
1076	D₄	—	8	1	no	—
1077	D₄	—	8	2	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	D₄	C₂×#41×C₆₁	1	2	yes	—
1081	D₄	C₂×#41×C₆₁	1	2	yes	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	4	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	8	1	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	1	no	—
1104	C₂×C₄	—	8	1	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	—	8	2	no	—
1107	C₂×C₄	—	8	2	no	—
1108	C₂×C₄	—	8	1	no	—
1109	C₂×C₄	—	8	2	no	—
1110	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1112	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1113	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1114	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1115	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1116	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1117	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1118	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1119	C₈	—	2	1	no	—
1120	C₈	—	2	2	no	—
1121	C₈	—	2	1	no	—
1122	C₈	—	2	2	no	—
1123	C₈	—	2	1	no	—
1124	C₈	C₂×#41×C₆₁	1	2	yes	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	4	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	2	no	—
1139	C₂²	—	4	2	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	4	2	no	—
1143	C₂²	—	8	4	no	—
1144	C₂²	—	16	4	no	—
1145	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1146	C₄	—	2	1	no	—
1147	C₄	—	2	2	no	—
1148	C₄	—	2	1	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	2	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	4	1	no	—
1156	C₄	—	4	2	no	—
1157	C₄	—	4	2	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	2	no	—
1161	C₄	C₆₁×#576	1	2	yes	—
1162	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
1163	C₄	C₆₁×#585	1	1	yes	characteristic
1164	C₂	—	4	1	no	—
1165	C₂	—	4	2	no	—
1166	C₂	—	4	2	no	—
1167	C₂	—	4	2	no	—
1168	C₂	—	8	1	no	—
1169	C₂	—	8	2	no	—
1170	C₂	D₄×#41×C₆₁	1	1	yes	characteristic
1171	C₂	C₂×C₆₁×#576	1	1	yes	characteristic
1172	C₂	C₆₁×#3586	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×#3520	C₂	semidirect
2. C₆₁×#3514	C₂	semidirect
3. C₆₁×#3394	C₂	semidirect
4. Q₈×D₈×C₆₁	C₂	semidirect
5. C₆₁×#3373	C₂	semidirect
6. C₆₁×#3367	C₂	semidirect
7. C₆₁×#3357	C₂	semidirect
8. C₆₁×#3353	C₂	semidirect
9. C₆₁×#3319	C₂	semidirect
10. C₆₁×#3314	C₂	semidirect
11. C₆₁×#3302	C₂	semidirect
12. C₆₁×#3294	C₂	semidirect
13. C₆₁×#3273	C₂	semidirect
14. C₆₁×#3272	C₂	semidirect
15. C₆₁×#3182	C₂	semidirect
16. C₆₁×#3175	C₂	semidirect
17. C₆₁×#3124	C₂	semidirect
18. C₆₁×#3118	C₂	semidirect
19. C₆₁×#3107	C₂	semidirect
20. C₆₁×#3100	C₂	semidirect
21. C₆₁×#2969	C₂	semidirect
22. C₆₁×#2946	C₂	semidirect
23. C₄×AGL(1,ℤ/8)×C₆₁	C₂	semidirect
26. C₆₁×#559	C₂²	semidirect
27. C₆₁×#556	C₂²	semidirect
28. C₆₁×#556	C₂²	semidirect
30. C₆₁×#554	C₂²	semidirect
34. D₄×Q₈×C₆₁	C₂²	semidirect
35. D₄×Q₈×C₆₁	C₂²	semidirect
42. C₆₁×#546	C₂²	semidirect
43. D₄²×C₆₁	C₂²	semidirect
44. C₆₁×#542	C₂²	semidirect
45. C₆₁×#542	C₂²	semidirect
48. C₆₁×#533	C₂²	semidirect
55. C₆₁×#520	C₂²	semidirect
56. C₆₁×#518	C₂²	semidirect
58. C₂×C₄×D₄×C₆₁	C₂²	semidirect
59. C₆₁×#500	C₂²	semidirect
60. C₆₁×#500	C₂²	semidirect
61. C₆₁×#495	C₂²	semidirect
62. C₆₁×#492	C₂²	semidirect
63. C₆₁×#489	C₂²	semidirect
64. C₆₁×#489	C₂²	semidirect
65. C₆₁×#487	C₂²	semidirect
66. C₆₁×#486	C₂²	semidirect
67. C₆₁×#485	C₂²	semidirect
68. C₆₁×#485	C₂²	semidirect
69. C₆₁×#484	C₂²	semidirect
70. C₆₁×#482	C₂²	semidirect
71. C₆₁×#480	C₂²	semidirect
72. C₆₁×#480	C₂²	semidirect
73. C₆₁×#477	C₂²	semidirect
74. C₆₁×#476	C₂²	semidirect
75. C₆₁×#475	C₂²	semidirect
76. C₆₁×#474	C₂²	semidirect
77. C₆₁×#474	C₂²	semidirect
78. C₆₁×#474	C₂²	semidirect
79. C₆₁×#474	C₂²	semidirect
80. C₆₁×#474	C₂²	semidirect
81. C₆₁×#468	C₂²	semidirect
82. C₆₁×#468	C₂²	semidirect
83. C₆₁×#468	C₂²	semidirect
84. C₆₁×#468	C₂²	semidirect
85. C₆₁×#467	C₂²	semidirect
87. C₆₁×#464	C₂²	semidirect
89. C₆₁×#463	C₂²	semidirect
90. C₆₁×#463	C₂²	semidirect
91. C₆₁×#462	C₂²	semidirect
92. C₆₁×#461	C₂²	semidirect
96. C₆₁×#452	C₂²	semidirect
97. C₆₁×#450	C₂²	semidirect
100. C₆₁×#447	C₂²	semidirect
101. C₆₁×#446	C₂²	semidirect
102. C₈×Q₈×C₆₁	C₂²	semidirect
105. C₆₁×#442	C₂²	semidirect
106. C₆₁×#440	C₂²	semidirect
107. C₆₁×#440	C₂²	semidirect
108. C₆₁×#440	C₂²	semidirect
109. C₆₁×#440	C₂²	semidirect
110. C₆₁×#440	C₂²	semidirect
111. C₄×Q₁₆×C₆₁	C₂²	semidirect
112. C₄×SD₁₆×C₆₁	C₂²	semidirect
113. C₄×SD₁₆×C₆₁	C₂²	semidirect
114. C₄×SD₁₆×C₆₁	C₂²	semidirect
115. C₄×SD₁₆×C₆₁	C₂²	semidirect
119. C₄×D₈×C₆₁	C₂²	semidirect
120. C₄×D₈×C₆₁	C₂²	semidirect
121. C₆₁×#436	C₂²	semidirect
122. C₆₁×#436	C₂²	semidirect
123. C₆₁×#435	C₂²	semidirect
124. C₈×D₄×C₆₁	C₂²	semidirect
125. C₆₁×#433	C₂²	semidirect
126. C₆₁×#431	C₂²	semidirect
127. C₆₁×#428	C₂²	semidirect
128. C₆₁×#428	C₂²	semidirect
129. C₆₁×#418	C₂²	semidirect
131. C₆₁×#416	C₂²	semidirect
132. C₂×#102×C₆₁	C₂²	semidirect
133. C₆₁×#405	C₂²	semidirect
134. C₄×M₁₆×C₆₁	C₂²	semidirect
379. D₈×C₆₁	#41	semidirect
538. #61553	C₆₁	direct (N × H)
578. #3520	C₂×C₆₁	semidirect
579. #3514	C₂×C₆₁	semidirect
580. #3394	C₂×C₆₁	semidirect
581. Q₈×D₈	C₂×C₆₁	semidirect
582. #3373	C₂×C₆₁	semidirect
583. #3367	C₂×C₆₁	semidirect
584. #3357	C₂×C₆₁	semidirect
585. #3353	C₂×C₆₁	semidirect
586. #3319	C₂×C₆₁	semidirect
587. #3314	C₂×C₆₁	semidirect
588. #3302	C₂×C₆₁	semidirect
589. #3294	C₂×C₆₁	semidirect
590. #3273	C₂×C₆₁	semidirect
591. #3272	C₂×C₆₁	semidirect
592. #3182	C₂×C₆₁	semidirect
593. #3175	C₂×C₆₁	semidirect
594. #3124	C₂×C₆₁	semidirect
595. #3118	C₂×C₆₁	semidirect
596. #3107	C₂×C₆₁	semidirect
597. #3100	C₂×C₆₁	semidirect
598. #2969	C₂×C₆₁	semidirect
599. #2946	C₂×C₆₁	semidirect
600. C₄×AGL(1,ℤ/8)	C₂×C₆₁	semidirect
612. #559	C₂²×C₆₁	semidirect
613. #556	C₂²×C₆₁	semidirect
614. #556	C₂²×C₆₁	semidirect
616. #554	C₂²×C₆₁	semidirect
620. D₄×Q₈	C₂²×C₆₁	semidirect
621. D₄×Q₈	C₂²×C₆₁	semidirect
628. #546	C₂²×C₆₁	semidirect
629. D₄²	C₂²×C₆₁	semidirect
630. #542	C₂²×C₆₁	semidirect
631. #542	C₂²×C₆₁	semidirect
634. #533	C₂²×C₆₁	semidirect
641. #520	C₂²×C₆₁	semidirect
642. #518	C₂²×C₆₁	semidirect
644. C₂×C₄×D₄	C₂²×C₆₁	semidirect
645. #500	C₂²×C₆₁	semidirect
646. #500	C₂²×C₆₁	semidirect
647. #495	C₂²×C₆₁	semidirect
648. #492	C₂²×C₆₁	semidirect
649. #489	C₂²×C₆₁	semidirect
650. #489	C₂²×C₆₁	semidirect
651. #487	C₂²×C₆₁	semidirect
652. #486	C₂²×C₆₁	semidirect
653. #485	C₂²×C₆₁	semidirect
654. #485	C₂²×C₆₁	semidirect
655. #484	C₂²×C₆₁	semidirect
656. #482	C₂²×C₆₁	semidirect
657. #480	C₂²×C₆₁	semidirect
658. #480	C₂²×C₆₁	semidirect
659. #477	C₂²×C₆₁	semidirect
660. #476	C₂²×C₆₁	semidirect
661. #475	C₂²×C₆₁	semidirect
662. #474	C₂²×C₆₁	semidirect
663. #474	C₂²×C₆₁	semidirect
664. #474	C₂²×C₆₁	semidirect
665. #474	C₂²×C₆₁	semidirect
666. #474	C₂²×C₆₁	semidirect
667. #468	C₂²×C₆₁	semidirect
668. #468	C₂²×C₆₁	semidirect
669. #468	C₂²×C₆₁	semidirect
670. #468	C₂²×C₆₁	semidirect
671. #467	C₂²×C₆₁	semidirect
673. #464	C₂²×C₆₁	semidirect
675. #463	C₂²×C₆₁	semidirect
676. #463	C₂²×C₆₁	semidirect
677. #462	C₂²×C₆₁	semidirect
678. #461	C₂²×C₆₁	semidirect
682. #452	C₂²×C₆₁	semidirect
683. #450	C₂²×C₆₁	semidirect
686. #447	C₂²×C₆₁	semidirect
687. #446	C₂²×C₆₁	semidirect
688. C₈×Q₈	C₂²×C₆₁	semidirect
691. #442	C₂²×C₆₁	semidirect
692. #440	C₂²×C₆₁	semidirect
693. #440	C₂²×C₆₁	semidirect
694. #440	C₂²×C₆₁	semidirect
695. #440	C₂²×C₆₁	semidirect
696. #440	C₂²×C₆₁	semidirect
697. C₄×Q₁₆	C₂²×C₆₁	semidirect
698. C₄×SD₁₆	C₂²×C₆₁	semidirect
699. C₄×SD₁₆	C₂²×C₆₁	semidirect
700. C₄×SD₁₆	C₂²×C₆₁	semidirect
701. C₄×SD₁₆	C₂²×C₆₁	semidirect
705. C₄×D₈	C₂²×C₆₁	semidirect
706. C₄×D₈	C₂²×C₆₁	semidirect
707. #436	C₂²×C₆₁	semidirect
708. #436	C₂²×C₆₁	semidirect
709. #435	C₂²×C₆₁	semidirect
710. C₈×D₄	C₂²×C₆₁	semidirect
711. #433	C₂²×C₆₁	semidirect
712. #431	C₂²×C₆₁	semidirect
713. #428	C₂²×C₆₁	semidirect
714. #428	C₂²×C₆₁	semidirect
715. #418	C₂²×C₆₁	semidirect
717. #416	C₂²×C₆₁	semidirect
718. C₂×#102	C₂²×C₆₁	semidirect
719. #405	C₂²×C₆₁	semidirect
720. C₄×M₁₆	C₂²×C₆₁	semidirect
721. C₆₁	#61553	direct (N × H)
966. D₈	#41×C₆₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₆₁×#3520	2
C₆₁×#3514	2
C₆₁×#3394	2
Q₈×D₈×C₆₁	2
C₆₁×#3373	2
C₆₁×#3367	2
C₆₁×#3357	2
C₆₁×#3353	2
C₆₁×#3319	2
C₆₁×#3314	2
C₆₁×#3302	2
C₆₁×#3294	2
C₆₁×#3273	2
C₆₁×#3272	2
C₆₁×#3182	2
C₆₁×#3175	2
C₆₁×#3124	2
C₆₁×#3118	2
C₆₁×#3107	2
C₆₁×#3100	2
C₆₁×#2969	2
C₆₁×#2946	2
C₄×AGL(1,ℤ/8)×C₆₁	2
#61553	61

Subgroups — C61×#61553 #29564986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61553 #29564986