Subgroups — C₆₁×#62074 #29565507

Order 15616.

1900 conjugacy classes of subgroups.

The subgroup lattice has 1204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3517	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3330	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3309	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3297	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3287	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3284	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3268	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3257	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3245	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3220	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3124	C₂	1	2	yes	maximal, complemented
20	C₆₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3045	C₂	1	2	yes	maximal, complemented
22	C₆₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
25	C₂×#135×C₆₁	C₂²	1	2	yes	complemented
26	C₂×#135×C₆₁	C₂²	1	2	yes	complemented
27	C₆₁×#560	—	2	2	no	—
28	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
29	C₆₁×#556	C₂²	1	1	yes	characteristic
30	C₆₁×#553	—	2	2	no	—
31	C₆₁×#553	—	2	1	no	—
32	C₆₁×#553	C₂²	1	2	yes	complemented
33	C₆₁×#550	—	2	1	no	—
34	C₆₁×#550	C₂²	1	2	yes	—
35	C₆₁×#550	C₂²	1	1	yes	characteristic
36	C₆₁×#550	C₂²	1	1	yes	characteristic
37	C₆₁×#550	C₂²	1	2	yes	complemented
38	C₆₁×#550	C₂²	1	1	yes	characteristic, complemented
39	C₆₁×#547	—	2	1	no	—
40	C₆₁×#547	C₂²	1	1	yes	characteristic
41	C₆₁×#547	C₂²	1	1	yes	characteristic
42	C₆₁×#546	—	2	1	no	—
43	C₆₁×#546	C₂²	1	2	yes	—
44	D₄²×C₆₁	C₂²	1	1	yes	characteristic
45	C₆₁×#542	C₂²	1	2	yes	—
46	C₆₁×#540	—	2	2	no	—
47	C₆₁×#540	C₂²	1	2	yes	complemented
48	C₆₁×#538	—	2	2	no	—
49	C₆₁×#537	—	2	1	no	—
50	C₆₁×#535	—	2	1	no	—
51	C₆₁×#535	C₂²	1	2	yes	—
52	C₆₁×#532	—	2	1	no	—
53	C₆₁×#532	C₂²	1	1	yes	characteristic
54	C₆₁×#532	C₂²	1	1	yes	characteristic
55	C₆₁×#532	C₂²	1	1	yes	characteristic, complemented
56	C₆₁×#529	—	2	1	no	—
57	C₆₁×#529	C₂²	1	1	yes	characteristic
58	C₆₁×#520	C₂²	1	2	yes	complemented
59	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic, complemented
60	C₆₁×#496	C₂²	1	2	yes	—
61	C₆₁×#493	C₂²	1	1	yes	characteristic
62	C₆₁×#493	C₂²	1	2	yes	complemented
63	C₆₁×#492	C₂²	1	1	yes	characteristic, complemented
64	C₆₁×#490	C₂²	1	2	yes	complemented
65	C₆₁×#488	C₂²	1	2	yes	—
66	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
67	C₆₁×#486	C₂²	1	1	yes	characteristic
68	C₆₁×#484	C₂²	1	2	yes	complemented
69	C₆₁×#482	C₂²	1	1	yes	characteristic
70	C₆₁×#482	C₂²	1	1	yes	characteristic, complemented
71	C₆₁×#480	C₂²	1	2	yes	—
72	C₆₁×#479	C₂²	1	2	yes	complemented
73	C₆₁×#478	C₂²	1	2	yes	complemented
74	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
75	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
76	C₆₁×#474	C₂²	1	1	yes	characteristic
77	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
78	C₆₁×#474	C₂²	1	2	yes	complemented
79	C₆₁×#469	C₂²	1	2	yes	—
80	C₆₁×#468	C₂²	1	2	yes	complemented
81	C₆₁×#466	C₂²	1	2	yes	—
82	C₆₁×#466	C₂²	1	2	yes	—
83	C₆₁×#466	C₂²	1	2	yes	complemented
84	C₆₁×#465	C₂²	1	2	yes	complemented
85	C₆₁×#464	C₂²	1	2	yes	—
86	C₆₁×#464	C₂²	1	2	yes	complemented
87	C₆₁×#463	C₂²	1	2	yes	—
88	C₆₁×#463	C₂²	1	2	yes	complemented
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×#460	C₂²	1	1	yes	characteristic
94	C₆₁×#460	C₂²	1	1	yes	characteristic
95	C₆₁×#460	C₂²	1	2	yes	complemented
96	C₆₁×#460	C₂²	1	2	yes	complemented
97	C₆₁×#459	C₂²	1	1	yes	characteristic
98	C₆₁×#459	C₂²	1	2	yes	—
99	C₆₁×#459	C₂²	1	1	yes	characteristic
100	C₆₁×#459	C₂²	1	1	yes	characteristic
101	C₆₁×#459	C₂²	1	2	yes	complemented
102	C₆₁×#459	C₂²	1	1	yes	characteristic, complemented
103	C₆₁×#459	C₂²	1	2	yes	complemented
104	C₆₁×#452	C₂²	1	2	yes	complemented
105	C₆₁×#449	C₂²	1	2	yes	—
106	C₆₁×#449	C₂²	1	1	yes	characteristic
107	C₆₁×#449	C₂²	1	1	yes	characteristic, complemented
108	C₆₁×#449	C₂²	1	2	yes	complemented
109	C₆₁×#449	C₂²	1	2	yes	complemented
110	C₆₁×#449	C₂²	1	2	yes	complemented
111	C₆₁×#449	C₂²	1	2	yes	complemented
112	C₆₁×#447	C₂²	1	2	yes	—
113	C₆₁×#447	C₂²	1	2	yes	—
114	C₆₁×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
116	C₆₁×#440	C₂²	1	2	yes	complemented
117	C₆₁×#440	C₂²	1	2	yes	complemented
118	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
119	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
122	C₄×D₈×C₆₁	C₂²	1	2	yes	complemented
123	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
124	C₆₁×#436	C₂²	1	1	yes	characteristic
125	C₆₁×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
127	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
128	C₆₁×#433	C₂²	1	2	yes	complemented
129	C₆₁×#431	C₂²	1	1	yes	characteristic, complemented
130	C₆₁×#424	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
132	C₆₁×#417	C₂²	1	2	yes	complemented
133	C₆₁×#416	C₂²	1	2	yes	complemented
134	C₂×#102×C₆₁	C₂²	1	2	yes	—
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	—	2	1	no	—
137	C₂×#41×C₆₁	—	2	1	no	—
138	C₂×#41×C₆₁	—	2	1	no	—
139	C₂×#41×C₆₁	—	2	1	no	—
140	C₂×#41×C₆₁	C₂³	1	2	yes	—
141	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
142	C₂×#41×C₆₁	C₂³	1	2	yes	—
143	C₂×#41×C₆₁	C₂³	1	2	yes	—
144	C₂²×D₄×C₆₁	—	2	1	no	—
145	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
146	AGL(1,ℤ/8)×C₆₁	—	4	4	no	—
147	#135×C₆₁	—	4	4	no	—
148	#135×C₆₁	—	4	4	no	—
149	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
153	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
156	C₂×D₈×C₆₁	C₂³	1	2	yes	—
157	C₂×D₈×C₆₁	C₂³	1	2	yes	—
158	C₂×D₈×C₆₁	C₂³	1	2	yes	—
159	C₂×D₈×C₆₁	C₂³	1	2	yes	—
160	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
161	C₂×D₈×C₆₁	C₂³	1	2	yes	—
162	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
163	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
164	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
165	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
166	C₄⋊Q₈×C₆₁	—	2	1	no	—
167	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
170	#127×C₆₁	—	2	1	no	—
171	#127×C₆₁	—	2	2	no	—
172	#127×C₆₁	—	2	2	no	—
173	#127×C₆₁	C₂³	1	1	yes	characteristic
174	#127×C₆₁	C₂³	1	1	yes	characteristic
175	#127×C₆₁	C₂³	1	1	yes	characteristic
176	#127×C₆₁	C₂³	1	2	yes	—
177	#127×C₆₁	C₂³	1	2	yes	—
178	#126×C₆₁	—	2	2	no	—
179	#126×C₆₁	—	2	2	no	—
180	#126×C₆₁	—	2	2	no	—
181	#126×C₆₁	D₄	1	2	yes	—
182	#125×C₆₁	—	2	2	no	—
183	#125×C₆₁	D₄	1	1	yes	characteristic
184	#125×C₆₁	C₂³	1	2	yes	—
185	#124×C₆₁	—	2	2	no	—
186	#124×C₆₁	—	2	1	no	—
187	#124×C₆₁	—	2	1	no	—
188	#124×C₆₁	D₄	1	1	yes	characteristic
189	#124×C₆₁	C₂³	1	2	yes	—
190	#124×C₆₁	C₂³	1	2	yes	—
191	#123×C₆₁	—	2	2	no	—
192	#123×C₆₁	—	2	2	no	—
193	#123×C₆₁	—	2	2	no	—
194	#123×C₆₁	—	2	2	no	—
195	#123×C₆₁	—	2	2	no	—
196	#123×C₆₁	—	2	2	no	—
197	#123×C₆₁	—	2	2	no	—
198	#123×C₆₁	D₄	1	2	yes	—
199	C₂²⋊Q₈×C₆₁	—	2	1	no	—
200	C₂²⋊Q₈×C₆₁	—	2	2	no	—
201	C₂²⋊Q₈×C₆₁	—	2	1	no	—
202	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
203	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
204	#121×C₆₁	—	2	1	no	—
205	#121×C₆₁	—	2	2	no	—
206	#121×C₆₁	—	2	1	no	—
207	#121×C₆₁	—	2	1	no	—
208	#121×C₆₁	—	2	1	no	—
209	#121×C₆₁	—	2	1	no	—
210	#121×C₆₁	—	2	1	no	—
211	#121×C₆₁	—	2	2	no	—
212	#121×C₆₁	—	2	2	no	—
213	#121×C₆₁	—	2	1	no	—
214	#121×C₆₁	—	2	2	no	—
215	#121×C₆₁	—	2	2	no	—
216	#121×C₆₁	—	2	1	no	—
217	#121×C₆₁	—	2	2	no	—
218	#121×C₆₁	—	2	2	no	—
219	#121×C₆₁	—	2	2	no	—
220	#121×C₆₁	—	2	2	no	—
221	#121×C₆₁	—	2	2	no	—
222	#121×C₆₁	—	2	2	no	—
223	#121×C₆₁	—	2	2	no	—
224	#121×C₆₁	—	2	2	no	—
225	#121×C₆₁	D₄	1	1	yes	characteristic
226	#121×C₆₁	C₂³	1	1	yes	characteristic
227	#121×C₆₁	C₂³	1	1	yes	characteristic
228	#121×C₆₁	C₂³	1	2	yes	—
229	#121×C₆₁	C₂³	1	2	yes	—
230	#121×C₆₁	C₂³	1	2	yes	—
231	#121×C₆₁	C₂³	1	2	yes	—
232	#120×C₆₁	—	2	2	no	—
233	#120×C₆₁	—	2	2	no	—
234	#120×C₆₁	—	2	2	no	—
235	#120×C₆₁	—	2	2	no	—
236	C₄×Q₈×C₆₁	—	2	1	no	—
237	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
238	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
240	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₆₁	—	2	1	no	—
243	C₄×D₄×C₆₁	—	2	1	no	—
244	C₄×D₄×C₆₁	—	2	2	no	—
245	C₄×D₄×C₆₁	—	2	1	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	—	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	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₆₁	C₂³	1	2	yes	—
257	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₆₁	C₂³	1	2	yes	—
259	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₆₁	C₂³	1	2	yes	—
261	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
262	C₄×D₄×C₆₁	C₂³	1	2	yes	—
263	#117×C₆₁	—	2	1	no	—
264	#117×C₆₁	—	2	2	no	—
265	#117×C₆₁	—	2	1	no	—
266	#117×C₆₁	C₂³	1	1	yes	characteristic
267	#117×C₆₁	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
269	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
270	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
271	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
272	C₂×C₄²×C₆₁	—	2	1	no	—
273	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
274	#107×C₆₁	C₂³	1	1	yes	characteristic
275	#107×C₆₁	C₂³	1	1	yes	characteristic
276	#107×C₆₁	C₂³	1	2	yes	—
277	#107×C₆₁	C₂³	1	2	yes	—
278	#106×C₆₁	C₂³	1	1	yes	characteristic
279	#106×C₆₁	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
281	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
285	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
286	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
287	#103×C₆₁	C₂³	1	2	yes	—
288	#103×C₆₁	C₂³	1	2	yes	—
289	#103×C₆₁	C₂³	1	2	yes	—
290	#103×C₆₁	C₂³	1	1	yes	characteristic
291	#103×C₆₁	C₂³	1	1	yes	characteristic
292	#103×C₆₁	C₂³	1	2	yes	—
293	#102×C₆₁	C₂³	1	1	yes	characteristic
294	#102×C₆₁	C₂³	1	2	yes	—
295	#102×C₆₁	C₂³	1	2	yes	—
296	#102×C₆₁	C₂³	1	2	yes	—
297	#102×C₆₁	C₂³	1	2	yes	—
298	#102×C₆₁	C₂³	1	1	yes	characteristic
299	#102×C₆₁	C₂³	1	2	yes	—
300	#102×C₆₁	C₂³	1	1	yes	characteristic
301	#102×C₆₁	C₂³	1	1	yes	characteristic
302	#102×C₆₁	C₂³	1	2	yes	—
303	#102×C₆₁	C₂³	1	1	yes	characteristic
304	#102×C₆₁	C₂³	1	1	yes	characteristic
305	#102×C₆₁	C₂³	1	2	yes	—
306	#102×C₆₁	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
311	#97×C₆₁	C₂³	1	2	yes	—
312	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₆₁	C₂³	1	2	yes	—
315	C₂⁴×C₆₁	—	2	2	no	—
316	#41×C₆₁	—	2	2	no	—
317	#41×C₆₁	—	2	4	no	—
318	#41×C₆₁	—	4	2	no	—
319	#41×C₆₁	—	4	1	no	—
320	#41×C₆₁	—	4	2	no	—
321	#41×C₆₁	—	4	2	no	—
322	#41×C₆₁	—	4	2	no	—
323	#41×C₆₁	—	4	2	no	—
324	#41×C₆₁	—	8	2	no	—
325	#41×C₆₁	—	8	2	no	—
326	#41×C₆₁	—	8	2	no	—
327	#41×C₆₁	—	8	2	no	—
328	#41×C₆₁	—	8	2	no	—
329	C₂×Q₈×C₆₁	—	2	1	no	—
330	C₂×Q₈×C₆₁	—	2	1	no	—
331	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
332	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₆₁	—	2	2	no	—
335	C₂×D₄×C₆₁	—	2	1	no	—
336	C₂×D₄×C₆₁	—	2	2	no	—
337	C₂×D₄×C₆₁	—	2	1	no	—
338	C₂×D₄×C₆₁	—	2	2	no	—
339	C₂×D₄×C₆₁	—	2	2	no	—
340	C₂×D₄×C₆₁	—	2	2	no	—
341	C₂×D₄×C₆₁	—	2	2	no	—
342	C₂×D₄×C₆₁	—	2	2	no	—
343	C₂×D₄×C₆₁	—	2	1	no	—
344	C₂×D₄×C₆₁	—	2	1	no	—
345	C₂×D₄×C₆₁	—	2	1	no	—
346	C₂×D₄×C₆₁	—	2	1	no	—
347	C₂×D₄×C₆₁	—	2	1	no	—
348	C₂×D₄×C₆₁	—	2	2	no	—
349	C₂×D₄×C₆₁	—	2	1	no	—
350	C₂×D₄×C₆₁	—	2	2	no	—
351	C₂×D₄×C₆₁	—	2	1	no	—
352	C₂×D₄×C₆₁	—	2	2	no	—
353	C₂×D₄×C₆₁	—	2	2	no	—
354	C₂×D₄×C₆₁	—	2	2	no	—
355	C₂×D₄×C₆₁	—	4	2	no	—
356	C₂×D₄×C₆₁	—	4	2	no	—
357	C₂×D₄×C₆₁	—	8	2	no	—
358	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
359	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
360	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
361	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
362	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
363	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
364	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₆₁	—	2	2	no	—
366	C₂²×C₄×C₆₁	—	2	1	no	—
367	C₂²×C₄×C₆₁	—	2	1	no	—
368	C₂²×C₄×C₆₁	—	2	2	no	—
369	C₂²×C₄×C₆₁	—	2	1	no	—
370	C₂²×C₄×C₆₁	—	2	1	no	—
371	C₂²×C₄×C₆₁	—	2	1	no	—
372	C₂²×C₄×C₆₁	—	2	2	no	—
373	C₂²×C₄×C₆₁	—	2	2	no	—
374	C₂²×C₄×C₆₁	—	2	2	no	—
375	C₂²×C₄×C₆₁	—	2	2	no	—
376	C₂²×C₄×C₆₁	—	2	2	no	—
377	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
378	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
379	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
381	Q₁₆×C₆₁	—	2	4	no	—
382	SD₁₆×C₆₁	—	2	2	no	—
383	SD₁₆×C₆₁	—	2	4	no	—
384	SD₁₆×C₆₁	—	2	2	no	—
385	SD₁₆×C₆₁	—	4	2	no	—
386	SD₁₆×C₆₁	—	4	2	no	—
387	SD₁₆×C₆₁	—	4	2	no	—
388	D₈×C₆₁	—	4	1	no	—
389	D₈×C₆₁	—	4	2	no	—
390	D₈×C₆₁	—	4	1	no	—
391	D₈×C₆₁	—	4	2	no	—
392	D₈×C₆₁	—	4	2	no	—
393	D₈×C₆₁	—	4	2	no	—
394	D₈×C₆₁	—	4	2	no	—
395	M₁₆×C₆₁	—	4	2	no	—
396	C₂×C₈×C₆₁	—	4	2	no	—
397	C₂×C₈×C₆₁	—	4	2	no	—
398	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
399	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
400	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
401	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
402	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
403	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₆₁	—	2	1	no	—
405	C₄⋊C₄×C₆₁	—	2	2	no	—
406	C₄⋊C₄×C₆₁	—	2	1	no	—
407	C₄⋊C₄×C₆₁	—	2	2	no	—
408	C₄⋊C₄×C₆₁	—	2	2	no	—
409	C₄⋊C₄×C₆₁	—	2	1	no	—
410	C₄⋊C₄×C₆₁	—	2	1	no	—
411	C₄⋊C₄×C₆₁	—	2	2	no	—
412	C₄⋊C₄×C₆₁	—	2	1	no	—
413	C₄⋊C₄×C₆₁	—	2	1	no	—
414	C₄⋊C₄×C₆₁	—	2	2	no	—
415	C₄⋊C₄×C₆₁	—	2	2	no	—
416	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
420	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
427	C₂²⋊C₄×C₆₁	—	2	2	no	—
428	C₂²⋊C₄×C₆₁	—	2	1	no	—
429	C₂²⋊C₄×C₆₁	—	2	1	no	—
430	C₂²⋊C₄×C₆₁	—	2	2	no	—
431	C₂²⋊C₄×C₆₁	—	2	2	no	—
432	C₂²⋊C₄×C₆₁	—	2	1	no	—
433	C₂²⋊C₄×C₆₁	—	2	1	no	—
434	C₂²⋊C₄×C₆₁	—	2	2	no	—
435	C₂²⋊C₄×C₆₁	—	2	2	no	—
436	C₂²⋊C₄×C₆₁	—	2	1	no	—
437	C₂²⋊C₄×C₆₁	—	2	2	no	—
438	C₂²⋊C₄×C₆₁	—	2	2	no	—
439	C₂²⋊C₄×C₆₁	—	2	2	no	—
440	C₂²⋊C₄×C₆₁	—	2	2	no	—
441	C₂²⋊C₄×C₆₁	—	2	2	no	—
442	C₂²⋊C₄×C₆₁	—	2	2	no	—
443	C₂²⋊C₄×C₆₁	—	2	1	no	—
444	C₂²⋊C₄×C₆₁	—	2	2	no	—
445	C₂²⋊C₄×C₆₁	—	2	1	no	—
446	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
448	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
451	C₄²×C₆₁	—	2	1	no	—
452	C₄²×C₆₁	—	2	1	no	—
453	C₄²×C₆₁	—	2	1	no	—
454	C₄²×C₆₁	—	2	2	no	—
455	C₄²×C₆₁	—	2	2	no	—
456	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
459	C₄²×C₆₁	C₂⁴	1	2	yes	—
460	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
461	C₂³×C₆₁	—	2	1	no	—
462	C₂³×C₆₁	—	2	1	no	—
463	C₂³×C₆₁	—	2	2	no	—
464	C₂³×C₆₁	—	2	2	no	—
465	C₂³×C₆₁	—	2	1	no	—
466	C₂³×C₆₁	—	8	2	no	—
467	C₂³×C₆₁	—	8	2	no	—
468	C₂³×C₆₁	—	8	2	no	—
469	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
470	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
471	Q₈×C₆₁	—	2	2	no	—
472	Q₈×C₆₁	—	2	1	no	—
473	Q₈×C₆₁	—	2	2	no	—
474	Q₈×C₆₁	—	2	2	no	—
475	Q₈×C₆₁	—	4	2	no	—
476	Q₈×C₆₁	—	8	1	no	—
477	Q₈×C₆₁	H(5,𝔽₂)	1	2	yes	—
478	D₄×C₆₁	—	2	2	no	—
479	D₄×C₆₁	—	2	2	no	—
480	D₄×C₆₁	—	2	1	no	—
481	D₄×C₆₁	—	2	2	no	—
482	D₄×C₆₁	—	2	1	no	—
483	D₄×C₆₁	—	2	1	no	—
484	D₄×C₆₁	—	2	1	no	—
485	D₄×C₆₁	—	2	2	no	—
486	D₄×C₆₁	—	2	1	no	—
487	D₄×C₆₁	—	2	2	no	—
488	D₄×C₆₁	—	2	1	no	—
489	D₄×C₆₁	—	4	2	no	—
490	D₄×C₆₁	—	4	2	no	—
491	D₄×C₆₁	—	4	4	no	—
492	D₄×C₆₁	—	4	2	no	—
493	D₄×C₆₁	—	4	2	no	—
494	D₄×C₆₁	—	8	1	no	—
495	D₄×C₆₁	—	8	1	no	—
496	D₄×C₆₁	—	8	1	no	—
497	D₄×C₆₁	—	8	2	no	—
498	D₄×C₆₁	—	8	2	no	—
499	D₄×C₆₁	—	8	2	no	—
500	D₄×C₆₁	—	8	1	no	—
501	D₄×C₆₁	—	8	2	no	—
502	D₄×C₆₁	—	8	2	no	—
503	D₄×C₆₁	—	8	2	no	—
504	D₄×C₆₁	—	8	2	no	—
505	D₄×C₆₁	—	8	2	no	—
506	D₄×C₆₁	—	8	2	no	—
507	D₄×C₆₁	—	8	1	no	—
508	D₄×C₆₁	—	8	1	no	—
509	D₄×C₆₁	—	8	2	no	—
510	D₄×C₆₁	—	8	2	no	—
511	C₂×C₄×C₆₁	—	2	1	no	—
512	C₂×C₄×C₆₁	—	2	2	no	—
513	C₂×C₄×C₆₁	—	2	1	no	—
514	C₂×C₄×C₆₁	—	2	2	no	—
515	C₂×C₄×C₆₁	—	2	2	no	—
516	C₂×C₄×C₆₁	—	2	1	no	—
517	C₂×C₄×C₆₁	—	2	1	no	—
518	C₂×C₄×C₆₁	—	2	1	no	—
519	C₂×C₄×C₆₁	—	2	1	no	—
520	C₂×C₄×C₆₁	—	2	2	no	—
521	C₂×C₄×C₆₁	—	2	2	no	—
522	C₂×C₄×C₆₁	—	2	1	no	—
523	C₂×C₄×C₆₁	—	4	1	no	—
524	C₂×C₄×C₆₁	—	4	2	no	—
525	C₂×C₄×C₆₁	—	4	4	no	—
526	C₂×C₄×C₆₁	—	4	2	no	—
527	C₂×C₄×C₆₁	—	4	2	no	—
528	C₂×C₄×C₆₁	—	4	2	no	—
529	C₂×C₄×C₆₁	—	8	1	no	—
530	C₂×C₄×C₆₁	—	8	2	no	—
531	C₂×C₄×C₆₁	—	8	2	no	—
532	C₂×C₄×C₆₁	—	8	2	no	—
533	C₂×C₄×C₆₁	—	8	2	no	—
534	C₂×C₄×C₆₁	—	8	2	no	—
535	C₂×C₄×C₆₁	—	8	2	no	—
536	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
537	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
542	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
543	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
545	C₈×C₆₁	—	2	2	no	—
546	C₈×C₆₁	—	2	1	no	—
547	C₈×C₆₁	—	2	2	no	—
548	C₈×C₆₁	—	2	1	no	—
549	C₈×C₆₁	—	2	1	no	—
550	C₈×C₆₁	—	2	1	no	—
551	#62074	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
552	C₂²×C₆₁	—	2	1	no	—
553	C₂²×C₆₁	—	2	2	no	—
554	C₂²×C₆₁	—	2	1	no	—
555	C₂²×C₆₁	—	2	2	no	—
556	C₂²×C₆₁	—	2	1	no	—
557	C₂²×C₆₁	—	2	2	no	—
558	C₂²×C₆₁	—	4	1	no	—
559	C₂²×C₆₁	—	4	1	no	—
560	C₂²×C₆₁	—	4	2	no	—
561	C₂²×C₆₁	—	4	2	no	—
562	C₂²×C₆₁	—	4	1	no	—
563	C₂²×C₆₁	—	4	2	no	—
564	C₂²×C₆₁	—	4	1	no	—
565	C₂²×C₆₁	—	4	1	no	—
566	C₂²×C₆₁	—	4	2	no	—
567	C₂²×C₆₁	—	4	1	no	—
568	C₂²×C₆₁	—	4	1	no	—
569	C₂²×C₆₁	—	4	1	no	—
570	C₂²×C₆₁	—	4	1	no	—
571	C₂²×C₆₁	—	4	2	no	—
572	C₂²×C₆₁	—	4	2	no	—
573	C₂²×C₆₁	—	16	4	no	—
574	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
575	C₄×C₆₁	—	2	1	no	—
576	C₄×C₆₁	—	2	1	no	—
577	C₄×C₆₁	—	2	2	no	—
578	C₄×C₆₁	—	2	1	no	—
579	C₄×C₆₁	—	2	2	no	—
580	C₄×C₆₁	—	2	2	no	—
581	C₄×C₆₁	—	2	1	no	—
582	C₄×C₆₁	—	2	2	no	—
583	C₄×C₆₁	—	4	1	no	—
584	C₄×C₆₁	—	4	2	no	—
585	C₄×C₆₁	—	4	1	no	—
586	C₄×C₆₁	—	4	1	no	—
587	C₄×C₆₁	—	4	1	no	—
588	C₄×C₆₁	—	4	2	no	—
589	C₄×C₆₁	#576	1	2	yes	—
590	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
591	C₄×C₆₁	#585	1	1	yes	characteristic
592	#3546	C₂×C₆₁	1	1	yes	characteristic, complemented
593	#3517	C₂×C₆₁	1	1	yes	characteristic, complemented
594	#3397	C₂×C₆₁	1	1	yes	characteristic, complemented
595	#3391	C₂×C₆₁	1	1	yes	characteristic, complemented
596	#3368	C₂×C₆₁	1	1	yes	characteristic, complemented
597	#3364	C₂×C₆₁	1	1	yes	characteristic, complemented
598	#3330	C₂×C₆₁	1	1	yes	characteristic, complemented
599	#3309	C₂×C₆₁	1	2	yes	complemented
600	#3297	C₂×C₆₁	1	2	yes	complemented
601	#3294	C₂×C₆₁	1	1	yes	characteristic, complemented
602	#3287	C₂×C₆₁	1	2	yes	complemented
603	#3284	C₂×C₆₁	1	1	yes	characteristic, complemented
604	#3274	C₂×C₆₁	1	1	yes	characteristic, complemented
605	#3268	C₂×C₆₁	1	2	yes	complemented
606	#3257	C₂×C₆₁	1	2	yes	complemented
607	#3245	C₂×C₆₁	1	1	yes	characteristic, complemented
608	#3220	C₂×C₆₁	1	2	yes	complemented
609	#3207	C₂×C₆₁	1	1	yes	characteristic, complemented
610	#3124	C₂×C₆₁	1	2	yes	complemented
611	#3106	C₂×C₆₁	1	1	yes	characteristic, complemented
612	#3045	C₂×C₆₁	1	2	yes	complemented
613	#3035	C₂×C₆₁	1	1	yes	characteristic, complemented
614	#2994	C₂×C₆₁	1	1	yes	characteristic, complemented
615	C₂×C₆₁	—	4	1	no	—
616	C₂×C₆₁	—	4	2	no	—
617	C₂×C₆₁	—	8	1	no	—
618	C₂×C₆₁	—	8	2	no	—
619	C₂×C₆₁	—	8	1	no	—
620	C₂×C₆₁	—	8	2	no	—
621	C₂×C₆₁	—	8	1	no	—
622	C₂×C₆₁	#3488	1	1	yes	characteristic
623	C₂×C₆₁	C₂×#576	1	1	yes	characteristic
624	C₂×C₆₁	#3584	1	1	yes	characteristic
625	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
626	C₂×#135	C₂²×C₆₁	1	2	yes	complemented
627	C₂×#135	C₂²×C₆₁	1	2	yes	complemented
628	#560	—	2	2	no	—
629	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
630	#556	C₂²×C₆₁	1	1	yes	characteristic
631	#553	—	2	2	no	—
632	#553	—	2	1	no	—
633	#553	C₂²×C₆₁	1	2	yes	complemented
634	#550	—	2	1	no	—
635	#550	C₂²×C₆₁	1	1	yes	characteristic
636	#550	C₂²×C₆₁	1	2	yes	—
637	#550	C₂²×C₆₁	1	1	yes	characteristic
638	#550	C₂²×C₆₁	1	2	yes	complemented
639	#550	C₂²×C₆₁	1	1	yes	characteristic, complemented
640	#547	—	2	1	no	—
641	#547	C₂²×C₆₁	1	1	yes	characteristic
642	#547	C₂²×C₆₁	1	1	yes	characteristic
643	#546	—	2	1	no	—
644	#546	C₂²×C₆₁	1	2	yes	—
645	D₄²	C₂²×C₆₁	1	1	yes	characteristic
646	#542	C₂²×C₆₁	1	2	yes	—
647	#540	—	2	2	no	—
648	#540	C₂²×C₆₁	1	2	yes	complemented
649	#538	—	2	2	no	—
650	#537	—	2	1	no	—
651	#535	—	2	1	no	—
652	#535	C₂²×C₆₁	1	2	yes	—
653	#532	—	2	1	no	—
654	#532	C₂²×C₆₁	1	1	yes	characteristic
655	#532	C₂²×C₆₁	1	1	yes	characteristic
656	#532	C₂²×C₆₁	1	1	yes	characteristic, complemented
657	#529	—	2	1	no	—
658	#529	C₂²×C₆₁	1	1	yes	characteristic
659	#520	C₂²×C₆₁	1	2	yes	complemented
660	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic, complemented
661	#496	C₂²×C₆₁	1	2	yes	—
662	#493	C₂²×C₆₁	1	1	yes	characteristic
663	#493	C₂²×C₆₁	1	2	yes	complemented
664	#492	C₂²×C₆₁	1	1	yes	characteristic, complemented
665	#490	C₂²×C₆₁	1	2	yes	complemented
666	#488	C₂²×C₆₁	1	2	yes	—
667	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
668	#486	C₂²×C₆₁	1	1	yes	characteristic
669	#484	C₂²×C₆₁	1	2	yes	complemented
670	#482	C₂²×C₆₁	1	1	yes	characteristic
671	#482	C₂²×C₆₁	1	1	yes	characteristic, complemented
672	#480	C₂²×C₆₁	1	2	yes	—
673	#479	C₂²×C₆₁	1	2	yes	complemented
674	#478	C₂²×C₆₁	1	2	yes	complemented
675	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
676	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
677	#474	C₂²×C₆₁	1	1	yes	characteristic
678	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
679	#474	C₂²×C₆₁	1	2	yes	complemented
680	#469	C₂²×C₆₁	1	2	yes	—
681	#468	C₂²×C₆₁	1	2	yes	complemented
682	#466	C₂²×C₆₁	1	2	yes	—
683	#466	C₂²×C₆₁	1	2	yes	—
684	#466	C₂²×C₆₁	1	2	yes	complemented
685	#465	C₂²×C₆₁	1	2	yes	complemented
686	#464	C₂²×C₆₁	1	2	yes	—
687	#464	C₂²×C₆₁	1	2	yes	complemented
688	#463	C₂²×C₆₁	1	2	yes	—
689	#463	C₂²×C₆₁	1	2	yes	complemented
690	#463	C₂²×C₆₁	1	2	yes	complemented
691	#463	C₂²×C₆₁	1	2	yes	complemented
692	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
693	#461	C₂²×C₆₁	1	1	yes	characteristic, complemented
694	#460	C₂²×C₆₁	1	1	yes	characteristic
695	#460	C₂²×C₆₁	1	1	yes	characteristic
696	#460	C₂²×C₆₁	1	2	yes	complemented
697	#460	C₂²×C₆₁	1	2	yes	complemented
698	#459	C₂²×C₆₁	1	1	yes	characteristic
699	#459	C₂²×C₆₁	1	1	yes	characteristic
700	#459	C₂²×C₆₁	1	1	yes	characteristic
701	#459	C₂²×C₆₁	1	2	yes	—
702	#459	C₂²×C₆₁	1	1	yes	characteristic, complemented
703	#459	C₂²×C₆₁	1	2	yes	complemented
704	#459	C₂²×C₆₁	1	2	yes	complemented
705	#452	C₂²×C₆₁	1	2	yes	complemented
706	#449	C₂²×C₆₁	1	1	yes	characteristic
707	#449	C₂²×C₆₁	1	2	yes	—
708	#449	C₂²×C₆₁	1	2	yes	complemented
709	#449	C₂²×C₆₁	1	1	yes	characteristic, complemented
710	#449	C₂²×C₆₁	1	2	yes	complemented
711	#449	C₂²×C₆₁	1	2	yes	complemented
712	#449	C₂²×C₆₁	1	2	yes	complemented
713	#447	C₂²×C₆₁	1	2	yes	—
714	#447	C₂²×C₆₁	1	2	yes	—
715	#446	C₂²×C₆₁	1	1	yes	characteristic, complemented
716	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
717	#440	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	1	yes	characteristic
721	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
722	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
723	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
724	C₄×D₈	C₂²×C₆₁	1	2	yes	complemented
725	#436	C₂²×C₆₁	1	1	yes	characteristic
726	#435	C₂²×C₆₁	1	2	yes	complemented
727	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
728	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
729	#433	C₂²×C₆₁	1	2	yes	complemented
730	#431	C₂²×C₆₁	1	1	yes	characteristic, complemented
731	#424	C₂²×C₆₁	1	2	yes	complemented
732	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
733	#417	C₂²×C₆₁	1	2	yes	complemented
734	#416	C₂²×C₆₁	1	2	yes	complemented
735	C₂×#102	C₂²×C₆₁	1	2	yes	—
736	C₆₁	#62074	1	1	yes	characteristic, direct product factor, Sylow
737	C₂×#41	—	2	1	no	—
738	C₂×#41	—	2	1	no	—
739	C₂×#41	—	2	1	no	—
740	C₂×#41	—	2	1	no	—
741	C₂×#41	—	2	1	no	—
742	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
743	C₂×#41	C₂³×C₆₁	1	2	yes	—
744	C₂×#41	C₂³×C₆₁	1	2	yes	—
745	C₂×#41	C₂³×C₆₁	1	2	yes	—
746	C₂²×D₄	—	2	1	no	—
747	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
748	AGL(1,ℤ/8)	—	4	4	no	—
749	#135	—	4	4	no	—
750	#135	—	4	4	no	—
751	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
752	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
753	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
754	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
755	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
756	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
757	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
758	C₂×D₈	C₂³×C₆₁	1	2	yes	—
759	C₂×D₈	C₂³×C₆₁	1	2	yes	—
760	C₂×D₈	C₂³×C₆₁	1	2	yes	—
761	C₂×D₈	C₂³×C₆₁	1	2	yes	—
762	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
763	C₂×D₈	C₂³×C₆₁	1	2	yes	—
764	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
765	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
766	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
767	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
768	C₄⋊Q₈	—	2	1	no	—
769	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
770	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
771	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
772	#127	—	2	1	no	—
773	#127	—	2	2	no	—
774	#127	—	2	2	no	—
775	#127	C₂³×C₆₁	1	1	yes	characteristic
776	#127	C₂³×C₆₁	1	1	yes	characteristic
777	#127	C₂³×C₆₁	1	1	yes	characteristic
778	#127	C₂³×C₆₁	1	2	yes	—
779	#127	C₂³×C₆₁	1	2	yes	—
780	#126	—	2	2	no	—
781	#126	—	2	2	no	—
782	#126	—	2	2	no	—
783	#126	D₄×C₆₁	1	2	yes	—
784	#125	—	2	2	no	—
785	#125	D₄×C₆₁	1	1	yes	characteristic
786	#125	C₂³×C₆₁	1	2	yes	—
787	#124	—	2	2	no	—
788	#124	—	2	1	no	—
789	#124	—	2	1	no	—
790	#124	D₄×C₆₁	1	1	yes	characteristic
791	#124	C₂³×C₆₁	1	2	yes	—
792	#124	C₂³×C₆₁	1	2	yes	—
793	#123	—	2	2	no	—
794	#123	—	2	2	no	—
795	#123	—	2	2	no	—
796	#123	—	2	2	no	—
797	#123	—	2	2	no	—
798	#123	—	2	2	no	—
799	#123	—	2	2	no	—
800	#123	D₄×C₆₁	1	2	yes	—
801	C₂²⋊Q₈	—	2	1	no	—
802	C₂²⋊Q₈	—	2	1	no	—
803	C₂²⋊Q₈	—	2	2	no	—
804	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
805	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
806	#121	—	2	1	no	—
807	#121	—	2	2	no	—
808	#121	—	2	1	no	—
809	#121	—	2	1	no	—
810	#121	—	2	1	no	—
811	#121	—	2	1	no	—
812	#121	—	2	1	no	—
813	#121	—	2	1	no	—
814	#121	—	2	2	no	—
815	#121	—	2	2	no	—
816	#121	—	2	1	no	—
817	#121	—	2	2	no	—
818	#121	—	2	2	no	—
819	#121	—	2	2	no	—
820	#121	—	2	2	no	—
821	#121	—	2	2	no	—
822	#121	—	2	2	no	—
823	#121	—	2	2	no	—
824	#121	—	2	2	no	—
825	#121	—	2	2	no	—
826	#121	—	2	2	no	—
827	#121	D₄×C₆₁	1	1	yes	characteristic
828	#121	C₂³×C₆₁	1	1	yes	characteristic
829	#121	C₂³×C₆₁	1	1	yes	characteristic
830	#121	C₂³×C₆₁	1	2	yes	—
831	#121	C₂³×C₆₁	1	2	yes	—
832	#121	C₂³×C₆₁	1	2	yes	—
833	#121	C₂³×C₆₁	1	2	yes	—
834	#120	—	2	2	no	—
835	#120	—	2	2	no	—
836	#120	—	2	2	no	—
837	#120	—	2	2	no	—
838	C₄×Q₈	—	2	1	no	—
839	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
840	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
841	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
842	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
843	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
844	C₄×D₄	—	2	1	no	—
845	C₄×D₄	—	2	1	no	—
846	C₄×D₄	—	2	1	no	—
847	C₄×D₄	—	2	2	no	—
848	C₄×D₄	—	2	2	no	—
849	C₄×D₄	—	2	2	no	—
850	C₄×D₄	—	2	2	no	—
851	C₄×D₄	—	2	2	no	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	2	1	no	—
854	C₄×D₄	—	2	1	no	—
855	C₄×D₄	—	2	1	no	—
856	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
857	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
858	C₄×D₄	C₂³×C₆₁	1	2	yes	—
859	C₄×D₄	C₂³×C₆₁	1	2	yes	—
860	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
861	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
862	C₄×D₄	C₂³×C₆₁	1	2	yes	—
863	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
864	C₄×D₄	C₂³×C₆₁	1	2	yes	—
865	#117	—	2	2	no	—
866	#117	—	2	1	no	—
867	#117	—	2	1	no	—
868	#117	C₂³×C₆₁	1	1	yes	characteristic
869	#117	C₂³×C₆₁	1	2	yes	—
870	C₂×C₄⋊C₄	—	2	2	no	—
871	C₂×C₄⋊C₄	—	2	1	no	—
872	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
873	C₂×C₂²⋊C₄	—	2	2	no	—
874	C₂×C₄²	—	2	1	no	—
875	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
876	#107	C₂³×C₆₁	1	1	yes	characteristic
877	#107	C₂³×C₆₁	1	1	yes	characteristic
878	#107	C₂³×C₆₁	1	2	yes	—
879	#107	C₂³×C₆₁	1	2	yes	—
880	#106	C₂³×C₆₁	1	1	yes	characteristic
881	#106	C₂³×C₆₁	1	1	yes	characteristic
882	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
883	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
884	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
885	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
886	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
887	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
888	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
889	#103	C₂³×C₆₁	1	2	yes	—
890	#103	C₂³×C₆₁	1	2	yes	—
891	#103	C₂³×C₆₁	1	2	yes	—
892	#103	C₂³×C₆₁	1	1	yes	characteristic
893	#103	C₂³×C₆₁	1	1	yes	characteristic
894	#103	C₂³×C₆₁	1	2	yes	—
895	#102	C₂³×C₆₁	1	1	yes	characteristic
896	#102	C₂³×C₆₁	1	2	yes	—
897	#102	C₂³×C₆₁	1	2	yes	—
898	#102	C₂³×C₆₁	1	2	yes	—
899	#102	C₂³×C₆₁	1	2	yes	—
900	#102	C₂³×C₆₁	1	1	yes	characteristic
901	#102	C₂³×C₆₁	1	2	yes	—
902	#102	C₂³×C₆₁	1	1	yes	characteristic
903	#102	C₂³×C₆₁	1	1	yes	characteristic
904	#102	C₂³×C₆₁	1	2	yes	—
905	#102	C₂³×C₆₁	1	1	yes	characteristic
906	#102	C₂³×C₆₁	1	1	yes	characteristic
907	#102	C₂³×C₆₁	1	2	yes	—
908	#102	C₂³×C₆₁	1	2	yes	—
909	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
910	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
911	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
912	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
913	#97	C₂³×C₆₁	1	2	yes	—
914	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
915	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
916	C₄×C₈	C₂³×C₆₁	1	2	yes	—
917	C₂⁴	—	2	2	no	—
918	#41	—	2	2	no	—
919	#41	—	2	4	no	—
920	#41	—	4	2	no	—
921	#41	—	4	1	no	—
922	#41	—	4	2	no	—
923	#41	—	4	2	no	—
924	#41	—	4	2	no	—
925	#41	—	4	2	no	—
926	#41	—	8	2	no	—
927	#41	—	8	2	no	—
928	#41	—	8	2	no	—
929	#41	—	8	2	no	—
930	#41	—	8	2	no	—
931	C₂×Q₈	—	2	1	no	—
932	C₂×Q₈	—	2	1	no	—
933	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
934	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
935	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	1	no	—
946	C₂×D₄	—	2	1	no	—
947	C₂×D₄	—	2	1	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	1	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	1	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	1	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	4	2	no	—
958	C₂×D₄	—	4	2	no	—
959	C₂×D₄	—	8	2	no	—
960	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
961	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
962	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
963	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
964	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
965	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
966	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	1	no	—
970	C₂²×C₄	—	2	2	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	2	1	no	—
974	C₂²×C₄	—	2	2	no	—
975	C₂²×C₄	—	2	2	no	—
976	C₂²×C₄	—	2	2	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	2	no	—
979	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
980	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
981	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
982	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
983	Q₁₆	—	2	4	no	—
984	SD₁₆	—	2	2	no	—
985	SD₁₆	—	2	4	no	—
986	SD₁₆	—	2	2	no	—
987	SD₁₆	—	4	2	no	—
988	SD₁₆	—	4	2	no	—
989	SD₁₆	—	4	2	no	—
990	D₈	—	4	1	no	—
991	D₈	—	4	2	no	—
992	D₈	—	4	1	no	—
993	D₈	—	4	2	no	—
994	D₈	—	4	2	no	—
995	D₈	—	4	2	no	—
996	D₈	—	4	2	no	—
997	M₁₆	—	4	2	no	—
998	C₂×C₈	—	4	2	no	—
999	C₂×C₈	—	4	2	no	—
1000	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
1001	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
1002	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
1003	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
1004	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
1005	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1019	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1020	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1021	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
1022	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1023	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1024	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1025	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1026	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1027	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1028	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	1	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	1	no	—
1048	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1049	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1050	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1051	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1052	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1053	C₄²	—	2	1	no	—
1054	C₄²	—	2	1	no	—
1055	C₄²	—	2	1	no	—
1056	C₄²	—	2	2	no	—
1057	C₄²	—	2	2	no	—
1058	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1059	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1060	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1061	C₄²	C₂⁴×C₆₁	1	2	yes	—
1062	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1063	C₂³	—	2	1	no	—
1064	C₂³	—	2	1	no	—
1065	C₂³	—	2	2	no	—
1066	C₂³	—	2	2	no	—
1067	C₂³	—	2	1	no	—
1068	C₂³	—	8	2	no	—
1069	C₂³	—	8	2	no	—
1070	C₂³	—	8	2	no	—
1071	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1072	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1073	Q₈	—	2	2	no	—
1074	Q₈	—	2	1	no	—
1075	Q₈	—	2	2	no	—
1076	Q₈	—	2	2	no	—
1077	Q₈	—	4	2	no	—
1078	Q₈	—	8	1	no	—
1079	Q₈	H(5,𝔽₂)×C₆₁	1	2	yes	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	2	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	2	no	—
1084	D₄	—	2	1	no	—
1085	D₄	—	2	1	no	—
1086	D₄	—	2	1	no	—
1087	D₄	—	2	2	no	—
1088	D₄	—	2	1	no	—
1089	D₄	—	2	2	no	—
1090	D₄	—	2	1	no	—
1091	D₄	—	4	2	no	—
1092	D₄	—	4	2	no	—
1093	D₄	—	4	4	no	—
1094	D₄	—	4	2	no	—
1095	D₄	—	4	2	no	—
1096	D₄	—	8	1	no	—
1097	D₄	—	8	1	no	—
1098	D₄	—	8	1	no	—
1099	D₄	—	8	2	no	—
1100	D₄	—	8	2	no	—
1101	D₄	—	8	2	no	—
1102	D₄	—	8	1	no	—
1103	D₄	—	8	2	no	—
1104	D₄	—	8	2	no	—
1105	D₄	—	8	2	no	—
1106	D₄	—	8	2	no	—
1107	D₄	—	8	2	no	—
1108	D₄	—	8	2	no	—
1109	D₄	—	8	1	no	—
1110	D₄	—	8	1	no	—
1111	D₄	—	8	2	no	—
1112	D₄	—	8	2	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	2	no	—
1123	C₂×C₄	—	2	2	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	4	1	no	—
1126	C₂×C₄	—	4	2	no	—
1127	C₂×C₄	—	4	4	no	—
1128	C₂×C₄	—	4	2	no	—
1129	C₂×C₄	—	4	2	no	—
1130	C₂×C₄	—	4	2	no	—
1131	C₂×C₄	—	8	1	no	—
1132	C₂×C₄	—	8	2	no	—
1133	C₂×C₄	—	8	2	no	—
1134	C₂×C₄	—	8	2	no	—
1135	C₂×C₄	—	8	2	no	—
1136	C₂×C₄	—	8	2	no	—
1137	C₂×C₄	—	8	2	no	—
1138	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1139	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1140	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1141	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1142	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1143	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1144	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1145	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1146	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1147	C₈	—	2	2	no	—
1148	C₈	—	2	1	no	—
1149	C₈	—	2	2	no	—
1150	C₈	—	2	1	no	—
1151	C₈	—	2	1	no	—
1152	C₈	—	2	1	no	—
1153	C₂²	—	2	1	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	1	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	2	1	no	—
1158	C₂²	—	2	2	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	2	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	2	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	2	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	16	4	no	—
1175	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1176	C₄	—	2	1	no	—
1177	C₄	—	2	2	no	—
1178	C₄	—	2	1	no	—
1179	C₄	—	2	1	no	—
1180	C₄	—	2	2	no	—
1181	C₄	—	2	1	no	—
1182	C₄	—	2	2	no	—
1183	C₄	—	2	2	no	—
1184	C₄	—	4	1	no	—
1185	C₄	—	4	1	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	2	no	—
1188	C₄	—	4	1	no	—
1189	C₄	—	4	2	no	—
1190	C₄	C₆₁×#576	1	2	yes	—
1191	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1192	C₄	C₆₁×#585	1	1	yes	characteristic
1193	C₂	—	4	2	no	—
1194	C₂	—	4	1	no	—
1195	C₂	—	8	1	no	—
1196	C₂	—	8	2	no	—
1197	C₂	—	8	1	no	—
1198	C₂	—	8	1	no	—
1199	C₂	—	8	2	no	—
1200	C₂	C₆₁×#3488	1	1	yes	characteristic
1201	C₂	C₂×C₆₁×#576	1	1	yes	characteristic
1202	C₂	C₆₁×#3584	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×#3546	C₂	semidirect
2. C₆₁×#3517	C₂	semidirect
3. C₆₁×#3397	C₂	semidirect
4. C₆₁×#3391	C₂	semidirect
5. C₆₁×#3368	C₂	semidirect
6. C₆₁×#3364	C₂	semidirect
7. C₆₁×#3330	C₂	semidirect
8. C₆₁×#3309	C₂	semidirect
9. C₆₁×#3297	C₂	semidirect
10. C₆₁×#3294	C₂	semidirect
11. C₆₁×#3287	C₂	semidirect
12. C₆₁×#3284	C₂	semidirect
13. C₆₁×#3274	C₂	semidirect
14. C₆₁×#3268	C₂	semidirect
15. C₆₁×#3257	C₂	semidirect
16. C₆₁×#3245	C₂	semidirect
17. C₆₁×#3220	C₂	semidirect
18. C₆₁×#3207	C₂	semidirect
19. C₆₁×#3124	C₂	semidirect
20. C₆₁×#3106	C₂	semidirect
21. C₆₁×#3045	C₂	semidirect
22. C₆₁×#3035	C₂	semidirect
23. C₆₁×#2994	C₂	semidirect
25. C₂×#135×C₆₁	C₂²	semidirect
26. C₂×#135×C₆₁	C₂²	semidirect
28. C₆₁×#557	C₂²	semidirect
32. C₆₁×#553	C₂²	semidirect
37. C₆₁×#550	C₂²	semidirect
38. C₆₁×#550	C₂²	semidirect
47. C₆₁×#540	C₂²	semidirect
55. C₆₁×#532	C₂²	semidirect
58. C₆₁×#520	C₂²	semidirect
59. C₄×#41×C₆₁	C₂²	semidirect
62. C₆₁×#493	C₂²	semidirect
63. C₆₁×#492	C₂²	semidirect
64. C₆₁×#490	C₂²	semidirect
66. C₆₁×#487	C₂²	semidirect
68. C₆₁×#484	C₂²	semidirect
70. C₆₁×#482	C₂²	semidirect
72. C₆₁×#479	C₂²	semidirect
73. C₆₁×#478	C₂²	semidirect
74. C₆₁×#477	C₂²	semidirect
75. C₆₁×#476	C₂²	semidirect
77. C₆₁×#474	C₂²	semidirect
78. C₆₁×#474	C₂²	semidirect
80. C₆₁×#468	C₂²	semidirect
83. C₆₁×#466	C₂²	semidirect
84. C₆₁×#465	C₂²	semidirect
86. C₆₁×#464	C₂²	semidirect
88. C₆₁×#463	C₂²	semidirect
89. C₆₁×#463	C₂²	semidirect
90. C₆₁×#463	C₂²	semidirect
91. C₆₁×#462	C₂²	semidirect
92. C₆₁×#461	C₂²	semidirect
95. C₆₁×#460	C₂²	semidirect
96. C₆₁×#460	C₂²	semidirect
101. C₆₁×#459	C₂²	semidirect
102. C₆₁×#459	C₂²	semidirect
103. C₆₁×#459	C₂²	semidirect
104. C₆₁×#452	C₂²	semidirect
107. C₆₁×#449	C₂²	semidirect
108. C₆₁×#449	C₂²	semidirect
109. C₆₁×#449	C₂²	semidirect
110. C₆₁×#449	C₂²	semidirect
111. C₆₁×#449	C₂²	semidirect
114. C₆₁×#446	C₂²	semidirect
115. C₈×Q₈×C₆₁	C₂²	semidirect
116. C₆₁×#440	C₂²	semidirect
117. C₆₁×#440	C₂²	semidirect
118. C₄×Q₁₆×C₆₁	C₂²	semidirect
120. C₄×SD₁₆×C₆₁	C₂²	semidirect
122. C₄×D₈×C₆₁	C₂²	semidirect
123. C₄×D₈×C₆₁	C₂²	semidirect
125. C₆₁×#435	C₂²	semidirect
127. C₈×D₄×C₆₁	C₂²	semidirect
128. C₆₁×#433	C₂²	semidirect
129. C₆₁×#431	C₂²	semidirect
130. C₆₁×#424	C₂²	semidirect
131. C₂×C₄⋊C₈×C₆₁	C₂²	semidirect
132. C₆₁×#417	C₂²	semidirect
133. C₆₁×#416	C₂²	semidirect
551. #62074	C₆₁	direct (N × H)
592. #3546	C₂×C₆₁	semidirect
593. #3517	C₂×C₆₁	semidirect
594. #3397	C₂×C₆₁	semidirect
595. #3391	C₂×C₆₁	semidirect
596. #3368	C₂×C₆₁	semidirect
597. #3364	C₂×C₆₁	semidirect
598. #3330	C₂×C₆₁	semidirect
599. #3309	C₂×C₆₁	semidirect
600. #3297	C₂×C₆₁	semidirect
601. #3294	C₂×C₆₁	semidirect
602. #3287	C₂×C₆₁	semidirect
603. #3284	C₂×C₆₁	semidirect
604. #3274	C₂×C₆₁	semidirect
605. #3268	C₂×C₆₁	semidirect
606. #3257	C₂×C₆₁	semidirect
607. #3245	C₂×C₆₁	semidirect
608. #3220	C₂×C₆₁	semidirect
609. #3207	C₂×C₆₁	semidirect
610. #3124	C₂×C₆₁	semidirect
611. #3106	C₂×C₆₁	semidirect
612. #3045	C₂×C₆₁	semidirect
613. #3035	C₂×C₆₁	semidirect
614. #2994	C₂×C₆₁	semidirect
626. C₂×#135	C₂²×C₆₁	semidirect
627. C₂×#135	C₂²×C₆₁	semidirect
629. #557	C₂²×C₆₁	semidirect
633. #553	C₂²×C₆₁	semidirect
638. #550	C₂²×C₆₁	semidirect
639. #550	C₂²×C₆₁	semidirect
648. #540	C₂²×C₆₁	semidirect
656. #532	C₂²×C₆₁	semidirect
659. #520	C₂²×C₆₁	semidirect
660. C₄×#41	C₂²×C₆₁	semidirect
663. #493	C₂²×C₆₁	semidirect
664. #492	C₂²×C₆₁	semidirect
665. #490	C₂²×C₆₁	semidirect
667. #487	C₂²×C₆₁	semidirect
669. #484	C₂²×C₆₁	semidirect
671. #482	C₂²×C₆₁	semidirect
673. #479	C₂²×C₆₁	semidirect
674. #478	C₂²×C₆₁	semidirect
675. #477	C₂²×C₆₁	semidirect
676. #476	C₂²×C₆₁	semidirect
678. #474	C₂²×C₆₁	semidirect
679. #474	C₂²×C₆₁	semidirect
681. #468	C₂²×C₆₁	semidirect
684. #466	C₂²×C₆₁	semidirect
685. #465	C₂²×C₆₁	semidirect
687. #464	C₂²×C₆₁	semidirect
689. #463	C₂²×C₆₁	semidirect
690. #463	C₂²×C₆₁	semidirect
691. #463	C₂²×C₆₁	semidirect
692. #462	C₂²×C₆₁	semidirect
693. #461	C₂²×C₆₁	semidirect
696. #460	C₂²×C₆₁	semidirect
697. #460	C₂²×C₆₁	semidirect
702. #459	C₂²×C₆₁	semidirect
703. #459	C₂²×C₆₁	semidirect
704. #459	C₂²×C₆₁	semidirect
705. #452	C₂²×C₆₁	semidirect
708. #449	C₂²×C₆₁	semidirect
709. #449	C₂²×C₆₁	semidirect
710. #449	C₂²×C₆₁	semidirect
711. #449	C₂²×C₆₁	semidirect
712. #449	C₂²×C₆₁	semidirect
715. #446	C₂²×C₆₁	semidirect
716. C₈×Q₈	C₂²×C₆₁	semidirect
717. #440	C₂²×C₆₁	semidirect
718. #440	C₂²×C₆₁	semidirect
719. C₄×Q₁₆	C₂²×C₆₁	semidirect
721. C₄×SD₁₆	C₂²×C₆₁	semidirect
723. C₄×D₈	C₂²×C₆₁	semidirect
724. C₄×D₈	C₂²×C₆₁	semidirect
726. #435	C₂²×C₆₁	semidirect
728. C₈×D₄	C₂²×C₆₁	semidirect
729. #433	C₂²×C₆₁	semidirect
730. #431	C₂²×C₆₁	semidirect
731. #424	C₂²×C₆₁	semidirect
732. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
733. #417	C₂²×C₆₁	semidirect
734. #416	C₂²×C₆₁	semidirect
736. C₆₁	#62074	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×#3546	2
C₆₁×#3517	2
C₆₁×#3397	2
C₆₁×#3391	2
C₆₁×#3368	2
C₆₁×#3364	2
C₆₁×#3330	2
C₆₁×#3309	2
C₆₁×#3297	2
C₆₁×#3294	2
C₆₁×#3287	2
C₆₁×#3284	2
C₆₁×#3274	2
C₆₁×#3268	2
C₆₁×#3257	2
C₆₁×#3245	2
C₆₁×#3220	2
C₆₁×#3207	2
C₆₁×#3124	2
C₆₁×#3106	2
C₆₁×#3045	2
C₆₁×#3035	2
C₆₁×#2994	2
#62074	61

Subgroups — C61×#62074 #29565507

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62074 #29565507