Subgroups — C₆₁×#62057 #29565490

Order 15616.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3522	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3396	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3306	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3295	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3294	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3287	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3282	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3265	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3257	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3224	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3119	C₂	1	2	yes	maximal, complemented
20	C₆₁×#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3045	C₂	1	2	yes	maximal, complemented
22	C₂×C₆₁×#460	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	complemented
25	C₂×#135×C₆₁	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
27	C₆₁×#560	—	2	2	no	—
28	C₆₁×#559	—	2	1	no	—
29	C₆₁×#559	C₂²	1	1	yes	characteristic
30	C₆₁×#559	C₂²	1	1	yes	characteristic, complemented
31	Q₈²×C₆₁	C₂²	1	1	yes	characteristic, complemented
32	C₆₁×#554	—	2	1	no	—
33	C₆₁×#554	C₂²	1	1	yes	characteristic, complemented
34	C₆₁×#550	C₂²	1	1	yes	characteristic
35	C₆₁×#550	C₂²	1	1	yes	characteristic
36	C₆₁×#550	C₂²	1	1	yes	characteristic, complemented
37	C₆₁×#548	C₂²	1	2	yes	complemented
38	C₆₁×#547	—	2	2	no	—
39	C₆₁×#547	C₂²	1	2	yes	complemented
40	C₆₁×#546	—	2	1	no	—
41	C₆₁×#546	C₂²	1	2	yes	—
42	D₄²×C₆₁	—	2	1	no	—
43	D₄²×C₆₁	C₂²	1	2	yes	—
44	D₄²×C₆₁	C₂²	1	1	yes	characteristic
45	C₆₁×#542	—	2	2	no	—
46	C₆₁×#542	C₂²	1	2	yes	complemented
47	C₆₁×#540	—	2	1	no	—
48	C₆₁×#540	C₂²	1	2	yes	—
49	C₆₁×#535	—	2	1	no	—
50	C₆₁×#535	C₂²	1	2	yes	—
51	C₆₁×#534	—	2	2	no	—
52	C₆₁×#532	—	2	1	no	—
53	C₆₁×#532	C₂²	1	1	yes	characteristic, complemented
54	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
55	C₆₁×#529	—	2	1	no	—
56	C₆₁×#529	C₂²	1	1	yes	characteristic
57	C₆₁×#529	C₂²	1	1	yes	characteristic
58	C₆₁×#520	C₂²	1	2	yes	complemented
59	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
60	C₆₁×#496	C₂²	1	2	yes	complemented
61	C₆₁×#495	C₂²	1	2	yes	complemented
62	C₆₁×#493	C₂²	1	1	yes	characteristic
63	C₆₁×#493	C₂²	1	1	yes	characteristic, complemented
64	C₆₁×#489	C₂²	1	2	yes	complemented
65	C₆₁×#486	C₂²	1	1	yes	characteristic
66	C₆₁×#486	C₂²	1	2	yes	complemented
67	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
68	C₆₁×#483	C₂²	1	1	yes	characteristic, complemented
69	C₆₁×#481	C₂²	1	2	yes	complemented
70	C₆₁×#480	C₂²	1	1	yes	characteristic
71	C₆₁×#480	C₂²	1	2	yes	complemented
72	C₆₁×#479	C₂²	1	1	yes	characteristic, complemented
73	C₆₁×#479	C₂²	1	1	yes	characteristic, complemented
74	C₆₁×#478	C₂²	1	2	yes	complemented
75	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
76	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
77	C₆₁×#476	C₂²	1	2	yes	complemented
78	C₆₁×#474	C₂²	1	2	yes	complemented
79	C₆₁×#469	C₂²	1	2	yes	complemented
80	C₆₁×#468	C₂²	1	2	yes	complemented
81	C₆₁×#466	C₂²	1	2	yes	—
82	C₆₁×#466	C₂²	1	2	yes	complemented
83	C₆₁×#465	C₂²	1	2	yes	complemented
84	C₆₁×#465	C₂²	1	2	yes	complemented
85	C₆₁×#464	C₂²	1	1	yes	characteristic, complemented
86	C₆₁×#464	C₂²	1	2	yes	complemented
87	C₆₁×#464	C₂²	1	1	yes	characteristic, complemented
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×#463	C₂²	1	2	yes	complemented
92	C₆₁×#460	C₂²	1	1	yes	characteristic
93	C₆₁×#460	C₂²	1	1	yes	characteristic
94	C₆₁×#460	C₂²	1	1	yes	characteristic, complemented
95	C₆₁×#460	C₂²	1	1	yes	characteristic, complemented
96	C₆₁×#460	C₂²	1	2	yes	complemented
97	C₆₁×#460	C₂²	1	1	yes	characteristic, complemented
98	C₆₁×#460	C₂²	1	2	yes	complemented
99	C₆₁×#460	C₂²	1	2	yes	complemented
100	C₆₁×#459	C₂²	1	2	yes	complemented
101	C₆₁×#459	C₂²	1	2	yes	complemented
102	C₆₁×#459	C₂²	1	2	yes	complemented
103	C₆₁×#459	C₂²	1	1	yes	characteristic, complemented
104	C₆₁×#452	C₂²	1	2	yes	complemented
105	C₆₁×#451	C₂²	1	1	yes	characteristic, complemented
106	C₆₁×#450	C₂²	1	2	yes	complemented
107	C₆₁×#449	C₂²	1	2	yes	complemented
108	C₆₁×#449	C₂²	1	2	yes	complemented
109	C₆₁×#449	C₂²	1	2	yes	complemented
110	C₆₁×#448	C₂²	1	1	yes	characteristic
111	C₆₁×#447	C₂²	1	2	yes	complemented
112	C₆₁×#447	C₂²	1	2	yes	complemented
113	C₆₁×#447	C₂²	1	2	yes	complemented
114	C₆₁×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
116	C₆₁×#442	C₂²	1	2	yes	complemented
117	C₆₁×#440	C₂²	1	2	yes	complemented
118	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
120	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
121	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
122	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
123	C₄×D₈×C₆₁	C₂²	1	2	yes	complemented
124	C₆₁×#436	C₂²	1	1	yes	characteristic, complemented
125	C₆₁×#435	C₂²	1	2	yes	complemented
126	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
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	C₂×#102×C₆₁	C₂²	1	2	yes	complemented
134	C₂×#102×C₆₁	C₂²	1	2	yes	complemented
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	—	2	2	no	—
137	C₂×#41×C₆₁	—	2	1	no	—
138	C₂×#41×C₆₁	C₂³	1	2	yes	—
139	C₂×#41×C₆₁	C₂³	1	2	yes	—
140	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₆₁	—	2	2	no	—
142	C₂²×D₄×C₆₁	—	2	1	no	—
143	C₂²×D₄×C₆₁	—	2	1	no	—
144	C₂²×D₄×C₆₁	—	2	1	no	—
145	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
146	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
147	AGL(1,ℤ/8)×C₆₁	—	4	4	no	—
148	#135×C₆₁	—	4	4	no	—
149	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
150	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₆₁	—	4	4	no	—
152	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
155	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
159	C₂×D₈×C₆₁	C₂³	1	2	yes	—
160	C₂×D₈×C₆₁	C₂³	1	2	yes	—
161	C₂×D₈×C₆₁	C₂³	1	2	yes	—
162	C₂×D₈×C₆₁	C₂³	1	2	yes	—
163	C₂×D₈×C₆₁	C₂³	1	2	yes	—
164	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
165	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
166	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
167	C₄⋊Q₈×C₆₁	—	2	1	no	—
168	C₄⋊Q₈×C₆₁	—	2	2	no	—
169	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
171	#127×C₆₁	—	2	1	no	—
172	#127×C₆₁	—	2	1	no	—
173	#127×C₆₁	—	2	1	no	—
174	#127×C₆₁	—	2	1	no	—
175	#127×C₆₁	C₂³	1	2	yes	—
176	#127×C₆₁	C₂³	1	1	yes	characteristic
177	#127×C₆₁	C₂³	1	1	yes	characteristic
178	#127×C₆₁	C₂³	1	1	yes	characteristic
179	#127×C₆₁	C₂³	1	2	yes	—
180	#126×C₆₁	—	2	2	no	—
181	#126×C₆₁	—	2	1	no	—
182	#126×C₆₁	D₄	1	2	yes	—
183	#125×C₆₁	—	2	1	no	—
184	#125×C₆₁	D₄	1	1	yes	characteristic
185	#125×C₆₁	C₂³	1	1	yes	characteristic
186	#124×C₆₁	—	2	1	no	—
187	#124×C₆₁	—	2	1	no	—
188	#124×C₆₁	—	2	2	no	—
189	#124×C₆₁	—	2	2	no	—
190	#124×C₆₁	—	2	1	no	—
191	#124×C₆₁	D₄	1	1	yes	characteristic
192	#124×C₆₁	C₂³	1	1	yes	characteristic
193	#124×C₆₁	C₂³	1	2	yes	—
194	#124×C₆₁	C₂³	1	2	yes	—
195	#123×C₆₁	—	2	1	no	—
196	#123×C₆₁	—	2	2	no	—
197	#123×C₆₁	—	2	2	no	—
198	#123×C₆₁	—	2	2	no	—
199	#123×C₆₁	—	2	2	no	—
200	#123×C₆₁	—	2	2	no	—
201	#123×C₆₁	—	2	2	no	—
202	#123×C₆₁	—	2	2	no	—
203	#123×C₆₁	—	2	2	no	—
204	#123×C₆₁	D₄	1	2	yes	—
205	C₂²⋊Q₈×C₆₁	—	2	2	no	—
206	C₂²⋊Q₈×C₆₁	—	2	2	no	—
207	C₂²⋊Q₈×C₆₁	—	2	2	no	—
208	C₂²⋊Q₈×C₆₁	—	2	2	no	—
209	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
210	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
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	2	no	—
217	#121×C₆₁	—	2	1	no	—
218	#121×C₆₁	—	2	1	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	2	yes	—
227	#121×C₆₁	C₂³	1	2	yes	—
228	#121×C₆₁	C₂³	1	2	yes	—
229	#121×C₆₁	C₂³	1	2	yes	—
230	#121×C₆₁	C₂³	1	1	yes	characteristic
231	#120×C₆₁	—	2	2	no	—
232	#120×C₆₁	—	2	2	no	—
233	#120×C₆₁	—	2	2	no	—
234	#120×C₆₁	—	2	2	no	—
235	#120×C₆₁	—	2	2	no	—
236	#120×C₆₁	—	2	2	no	—
237	C₄×Q₈×C₆₁	—	2	1	no	—
238	C₄×Q₈×C₆₁	—	2	1	no	—
239	C₄×Q₈×C₆₁	—	2	1	no	—
240	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
242	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
243	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
245	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
246	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₆₁	—	2	1	no	—
248	C₄×D₄×C₆₁	—	2	1	no	—
249	C₄×D₄×C₆₁	—	2	1	no	—
250	C₄×D₄×C₆₁	—	2	1	no	—
251	C₄×D₄×C₆₁	—	2	1	no	—
252	C₄×D₄×C₆₁	—	2	1	no	—
253	C₄×D₄×C₆₁	—	2	2	no	—
254	C₄×D₄×C₆₁	—	2	2	no	—
255	C₄×D₄×C₆₁	—	2	2	no	—
256	C₄×D₄×C₆₁	—	2	1	no	—
257	C₄×D₄×C₆₁	C₂³	1	2	yes	—
258	C₄×D₄×C₆₁	C₂³	1	2	yes	—
259	C₄×D₄×C₆₁	C₂³	1	2	yes	—
260	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₆₁	C₂³	1	2	yes	—
262	C₄×D₄×C₆₁	C₂³	1	2	yes	—
263	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
264	#117×C₆₁	—	2	2	no	—
265	#117×C₆₁	—	2	1	no	—
266	#117×C₆₁	C₂³	1	2	yes	—
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	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	#106×C₆₁	C₂³	1	1	yes	characteristic
278	#106×C₆₁	C₂³	1	2	yes	—
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	1	yes	characteristic
288	#103×C₆₁	C₂³	1	2	yes	—
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	#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	2	yes	—
298	#102×C₆₁	C₂³	1	2	yes	—
299	#102×C₆₁	C₂³	1	2	yes	—
300	#102×C₆₁	C₂³	1	2	yes	—
301	#102×C₆₁	C₂³	1	2	yes	—
302	#102×C₆₁	C₂³	1	2	yes	—
303	#102×C₆₁	C₂³	1	1	yes	characteristic
304	#102×C₆₁	C₂³	1	2	yes	—
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	C₂⁴×C₆₁	—	2	2	no	—
317	#41×C₆₁	—	2	4	no	—
318	#41×C₆₁	—	4	2	no	—
319	#41×C₆₁	—	4	2	no	—
320	#41×C₆₁	—	4	2	no	—
321	#41×C₆₁	—	8	2	no	—
322	#41×C₆₁	—	8	4	no	—
323	#41×C₆₁	—	8	2	no	—
324	C₂×Q₈×C₆₁	—	2	1	no	—
325	C₂×Q₈×C₆₁	—	2	2	no	—
326	C₂×Q₈×C₆₁	—	2	1	no	—
327	C₂×Q₈×C₆₁	—	2	2	no	—
328	C₂×Q₈×C₆₁	—	4	1	no	—
329	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₆₁	—	2	2	no	—
334	C₂×D₄×C₆₁	—	2	1	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	2	no	—
340	C₂×D₄×C₆₁	—	2	1	no	—
341	C₂×D₄×C₆₁	—	2	1	no	—
342	C₂×D₄×C₆₁	—	2	1	no	—
343	C₂×D₄×C₆₁	—	2	2	no	—
344	C₂×D₄×C₆₁	—	2	2	no	—
345	C₂×D₄×C₆₁	—	2	1	no	—
346	C₂×D₄×C₆₁	—	2	2	no	—
347	C₂×D₄×C₆₁	—	2	2	no	—
348	C₂×D₄×C₆₁	—	2	2	no	—
349	C₂×D₄×C₆₁	—	2	2	no	—
350	C₂×D₄×C₆₁	—	2	1	no	—
351	C₂×D₄×C₆₁	—	2	1	no	—
352	C₂×D₄×C₆₁	—	4	2	no	—
353	C₂×D₄×C₆₁	—	4	2	no	—
354	C₂×D₄×C₆₁	—	4	2	no	—
355	C₂×D₄×C₆₁	—	4	2	no	—
356	C₂×D₄×C₆₁	—	8	2	no	—
357	C₂×D₄×C₆₁	—	8	2	no	—
358	C₂×D₄×C₆₁	—	8	2	no	—
359	C₂×D₄×C₆₁	—	8	4	no	—
360	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
361	C₂×D₄×C₆₁	C₂×D₄	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	2	yes	—
365	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
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	2	no	—
370	C₂²×C₄×C₆₁	—	2	1	no	—
371	C₂²×C₄×C₆₁	—	2	2	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	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
378	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
380	Q₁₆×C₆₁	—	2	2	no	—
381	Q₁₆×C₆₁	—	4	1	no	—
382	SD₁₆×C₆₁	—	2	4	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	1	no	—
388	SD₁₆×C₆₁	—	4	2	no	—
389	D₈×C₆₁	—	4	2	no	—
390	D₈×C₆₁	—	4	2	no	—
391	D₈×C₆₁	—	4	2	no	—
392	D₈×C₆₁	—	4	2	no	—
393	D₈×C₆₁	—	4	2	no	—
394	M₁₆×C₆₁	—	4	2	no	—
395	C₂×C₈×C₆₁	—	4	2	no	—
396	C₂×C₈×C₆₁	—	4	2	no	—
397	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
398	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
399	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
400	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
401	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
402	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₆₁	—	2	1	no	—
404	C₄⋊C₄×C₆₁	—	2	2	no	—
405	C₄⋊C₄×C₆₁	—	2	2	no	—
406	C₄⋊C₄×C₆₁	—	2	1	no	—
407	C₄⋊C₄×C₆₁	—	2	1	no	—
408	C₄⋊C₄×C₆₁	—	2	1	no	—
409	C₄⋊C₄×C₆₁	—	2	1	no	—
410	C₄⋊C₄×C₆₁	—	2	1	no	—
411	C₄⋊C₄×C₆₁	—	2	1	no	—
412	C₄⋊C₄×C₆₁	—	2	1	no	—
413	C₄⋊C₄×C₆₁	—	2	1	no	—
414	C₄⋊C₄×C₆₁	—	2	2	no	—
415	C₄⋊C₄×C₆₁	—	2	2	no	—
416	C₄⋊C₄×C₆₁	—	2	1	no	—
417	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
421	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
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	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
428	C₂²⋊C₄×C₆₁	—	2	1	no	—
429	C₂²⋊C₄×C₆₁	—	2	2	no	—
430	C₂²⋊C₄×C₆₁	—	2	2	no	—
431	C₂²⋊C₄×C₆₁	—	2	2	no	—
432	C₂²⋊C₄×C₆₁	—	2	2	no	—
433	C₂²⋊C₄×C₆₁	—	2	2	no	—
434	C₂²⋊C₄×C₆₁	—	2	1	no	—
435	C₂²⋊C₄×C₆₁	—	2	1	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	2	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	1	no	—
455	C₄²×C₆₁	—	2	1	no	—
456	C₄²×C₆₁	—	2	2	no	—
457	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
460	C₄²×C₆₁	C₂⁴	1	2	yes	—
461	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
462	C₂³×C₆₁	—	2	2	no	—
463	C₂³×C₆₁	—	2	2	no	—
464	C₂³×C₆₁	—	2	1	no	—
465	C₂³×C₆₁	—	2	2	no	—
466	C₂³×C₆₁	—	4	4	no	—
467	C₂³×C₆₁	—	8	2	no	—
468	C₂³×C₆₁	—	8	2	no	—
469	C₂³×C₆₁	—	8	2	no	—
470	C₂³×C₆₁	—	8	2	no	—
471	C₂³×C₆₁	—	8	2	no	—
472	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
473	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
474	Q₈×C₆₁	—	2	2	no	—
475	Q₈×C₆₁	—	2	1	no	—
476	Q₈×C₆₁	—	2	1	no	—
477	Q₈×C₆₁	—	2	1	no	—
478	Q₈×C₆₁	—	2	1	no	—
479	Q₈×C₆₁	—	2	1	no	—
480	Q₈×C₆₁	—	4	2	no	—
481	Q₈×C₆₁	—	8	1	no	—
482	Q₈×C₆₁	—	8	2	no	—
483	Q₈×C₆₁	H(5,𝔽₂)	1	2	yes	—
484	D₄×C₆₁	—	2	4	no	—
485	D₄×C₆₁	—	2	2	no	—
486	D₄×C₆₁	—	2	2	no	—
487	D₄×C₆₁	—	2	1	no	—
488	D₄×C₆₁	—	2	2	no	—
489	D₄×C₆₁	—	2	2	no	—
490	D₄×C₆₁	—	2	2	no	—
491	D₄×C₆₁	—	2	2	no	—
492	D₄×C₆₁	—	2	2	no	—
493	D₄×C₆₁	—	2	1	no	—
494	D₄×C₆₁	—	4	4	no	—
495	D₄×C₆₁	—	4	2	no	—
496	D₄×C₆₁	—	4	4	no	—
497	D₄×C₆₁	—	4	2	no	—
498	D₄×C₆₁	—	4	2	no	—
499	D₄×C₆₁	—	4	2	no	—
500	D₄×C₆₁	—	8	2	no	—
501	D₄×C₆₁	—	8	2	no	—
502	D₄×C₆₁	—	8	2	no	—
503	D₄×C₆₁	—	8	1	no	—
504	D₄×C₆₁	—	8	1	no	—
505	D₄×C₆₁	—	8	2	no	—
506	D₄×C₆₁	—	8	2	no	—
507	D₄×C₆₁	—	8	1	no	—
508	D₄×C₆₁	—	8	2	no	—
509	D₄×C₆₁	—	8	2	no	—
510	D₄×C₆₁	—	8	2	no	—
511	D₄×C₆₁	—	8	2	no	—
512	D₄×C₆₁	—	8	2	no	—
513	C₂×C₄×C₆₁	—	2	2	no	—
514	C₂×C₄×C₆₁	—	2	1	no	—
515	C₂×C₄×C₆₁	—	2	2	no	—
516	C₂×C₄×C₆₁	—	2	1	no	—
517	C₂×C₄×C₆₁	—	2	2	no	—
518	C₂×C₄×C₆₁	—	2	1	no	—
519	C₂×C₄×C₆₁	—	2	2	no	—
520	C₂×C₄×C₆₁	—	2	1	no	—
521	C₂×C₄×C₆₁	—	2	1	no	—
522	C₂×C₄×C₆₁	—	2	1	no	—
523	C₂×C₄×C₆₁	—	2	1	no	—
524	C₂×C₄×C₆₁	—	2	1	no	—
525	C₂×C₄×C₆₁	—	2	2	no	—
526	C₂×C₄×C₆₁	—	2	1	no	—
527	C₂×C₄×C₆₁	—	4	4	no	—
528	C₂×C₄×C₆₁	—	4	2	no	—
529	C₂×C₄×C₆₁	—	4	2	no	—
530	C₂×C₄×C₆₁	—	4	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	—	8	2	no	—
537	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
542	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
543	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
544	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
546	C₈×C₆₁	—	2	1	no	—
547	C₈×C₆₁	—	2	2	no	—
548	C₈×C₆₁	—	2	2	no	—
549	C₈×C₆₁	—	2	1	no	—
550	C₈×C₆₁	—	2	1	no	—
551	C₈×C₆₁	—	2	1	no	—
552	#62057	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
553	C₂²×C₆₁	—	2	1	no	—
554	C₂²×C₆₁	—	2	1	no	—
555	C₂²×C₆₁	—	2	2	no	—
556	C₂²×C₆₁	—	2	2	no	—
557	C₂²×C₆₁	—	2	2	no	—
558	C₂²×C₆₁	—	4	2	no	—
559	C₂²×C₆₁	—	4	2	no	—
560	C₂²×C₆₁	—	4	1	no	—
561	C₂²×C₆₁	—	4	2	no	—
562	C₂²×C₆₁	—	4	2	no	—
563	C₂²×C₆₁	—	4	2	no	—
564	C₂²×C₆₁	—	4	1	no	—
565	C₂²×C₆₁	—	4	2	no	—
566	C₂²×C₆₁	—	4	1	no	—
567	C₂²×C₆₁	—	4	2	no	—
568	C₂²×C₆₁	—	4	2	no	—
569	C₂²×C₆₁	—	4	2	no	—
570	C₂²×C₆₁	—	16	4	no	—
571	C₂²×C₆₁	—	16	4	no	—
572	C₂²×C₆₁	#576	1	2	yes	—
573	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
574	C₄×C₆₁	—	2	2	no	—
575	C₄×C₆₁	—	2	1	no	—
576	C₄×C₆₁	—	2	2	no	—
577	C₄×C₆₁	—	2	1	no	—
578	C₄×C₆₁	—	2	1	no	—
579	C₄×C₆₁	—	2	2	no	—
580	C₄×C₆₁	—	2	1	no	—
581	C₄×C₆₁	—	2	2	no	—
582	C₄×C₆₁	—	4	1	no	—
583	C₄×C₆₁	—	4	1	no	—
584	C₄×C₆₁	—	4	1	no	—
585	C₄×C₆₁	—	4	1	no	—
586	C₄×C₆₁	—	4	1	no	—
587	C₄×C₆₁	—	4	2	no	—
588	C₄×C₆₁	—	4	1	no	—
589	C₄×C₆₁	#577	1	2	yes	—
590	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
591	C₄×C₆₁	#585	1	1	yes	characteristic
592	#3543	C₂×C₆₁	1	1	yes	characteristic, complemented
593	#3522	C₂×C₆₁	1	1	yes	characteristic, complemented
594	#3399	C₂×C₆₁	1	1	yes	characteristic, complemented
595	#3396	C₂×C₆₁	1	1	yes	characteristic, complemented
596	#3375	C₂×C₆₁	1	1	yes	characteristic, complemented
597	#3362	C₂×C₆₁	1	1	yes	characteristic, complemented
598	#3333	C₂×C₆₁	1	1	yes	characteristic, complemented
599	#3306	C₂×C₆₁	1	2	yes	complemented
600	#3295	C₂×C₆₁	1	1	yes	characteristic, complemented
601	#3294	C₂×C₆₁	1	2	yes	complemented
602	#3287	C₂×C₆₁	1	1	yes	characteristic, complemented
603	#3282	C₂×C₆₁	1	2	yes	complemented
604	#3274	C₂×C₆₁	1	1	yes	characteristic, complemented
605	#3265	C₂×C₆₁	1	2	yes	complemented
606	#3257	C₂×C₆₁	1	2	yes	complemented
607	#3247	C₂×C₆₁	1	1	yes	characteristic, complemented
608	#3224	C₂×C₆₁	1	2	yes	complemented
609	#3205	C₂×C₆₁	1	1	yes	characteristic, complemented
610	#3119	C₂×C₆₁	1	2	yes	complemented
611	#3108	C₂×C₆₁	1	1	yes	characteristic, complemented
612	#3045	C₂×C₆₁	1	2	yes	complemented
613	C₂×#460	C₂×C₆₁	1	1	yes	characteristic, complemented
614	#2994	C₂×C₆₁	1	1	yes	characteristic, complemented
615	C₂×C₆₁	—	2	2	no	—
616	C₂×C₆₁	—	4	2	no	—
617	C₂×C₆₁	—	8	2	no	—
618	C₂×C₆₁	—	8	2	no	—
619	C₂×C₆₁	—	8	2	no	—
620	C₂×C₆₁	—	8	1	no	—
621	C₂×C₆₁	#3488	1	1	yes	characteristic
622	C₂×C₆₁	C₂×#576	1	1	yes	characteristic
623	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
624	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	complemented
625	C₂×#135	C₂²×C₆₁	1	2	yes	complemented
626	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
627	#560	—	2	2	no	—
628	#559	—	2	1	no	—
629	#559	C₂²×C₆₁	1	1	yes	characteristic
630	#559	C₂²×C₆₁	1	1	yes	characteristic, complemented
631	Q₈²	C₂²×C₆₁	1	1	yes	characteristic, complemented
632	#554	—	2	1	no	—
633	#554	C₂²×C₆₁	1	1	yes	characteristic, complemented
634	#550	C₂²×C₆₁	1	1	yes	characteristic
635	#550	C₂²×C₆₁	1	1	yes	characteristic
636	#550	C₂²×C₆₁	1	1	yes	characteristic, complemented
637	#548	C₂²×C₆₁	1	2	yes	complemented
638	#547	—	2	2	no	—
639	#547	C₂²×C₆₁	1	2	yes	complemented
640	#546	—	2	1	no	—
641	#546	C₂²×C₆₁	1	2	yes	—
642	D₄²	—	2	1	no	—
643	D₄²	C₂²×C₆₁	1	2	yes	—
644	D₄²	C₂²×C₆₁	1	1	yes	characteristic
645	#542	—	2	2	no	—
646	#542	C₂²×C₆₁	1	2	yes	complemented
647	#540	—	2	1	no	—
648	#540	C₂²×C₆₁	1	2	yes	—
649	#535	—	2	1	no	—
650	#535	C₂²×C₆₁	1	2	yes	—
651	#534	—	2	2	no	—
652	#532	—	2	1	no	—
653	#532	C₂²×C₆₁	1	1	yes	characteristic, complemented
654	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
655	#529	—	2	1	no	—
656	#529	C₂²×C₆₁	1	1	yes	characteristic
657	#529	C₂²×C₆₁	1	1	yes	characteristic
658	#520	C₂²×C₆₁	1	2	yes	complemented
659	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
660	#496	C₂²×C₆₁	1	2	yes	complemented
661	#495	C₂²×C₆₁	1	2	yes	complemented
662	#493	C₂²×C₆₁	1	1	yes	characteristic
663	#493	C₂²×C₆₁	1	1	yes	characteristic, complemented
664	#489	C₂²×C₆₁	1	2	yes	complemented
665	#486	C₂²×C₆₁	1	1	yes	characteristic
666	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
667	#486	C₂²×C₆₁	1	2	yes	complemented
668	#483	C₂²×C₆₁	1	1	yes	characteristic, complemented
669	#481	C₂²×C₆₁	1	2	yes	complemented
670	#480	C₂²×C₆₁	1	1	yes	characteristic
671	#480	C₂²×C₆₁	1	2	yes	complemented
672	#479	C₂²×C₆₁	1	1	yes	characteristic, complemented
673	#479	C₂²×C₆₁	1	1	yes	characteristic, 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	#476	C₂²×C₆₁	1	2	yes	complemented
678	#474	C₂²×C₆₁	1	2	yes	complemented
679	#469	C₂²×C₆₁	1	2	yes	complemented
680	#468	C₂²×C₆₁	1	2	yes	complemented
681	#466	C₂²×C₆₁	1	2	yes	—
682	#466	C₂²×C₆₁	1	2	yes	complemented
683	#465	C₂²×C₆₁	1	2	yes	complemented
684	#465	C₂²×C₆₁	1	2	yes	complemented
685	#464	C₂²×C₆₁	1	1	yes	characteristic, complemented
686	#464	C₂²×C₆₁	1	1	yes	characteristic, complemented
687	#464	C₂²×C₆₁	1	2	yes	complemented
688	#463	C₂²×C₆₁	1	2	yes	complemented
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	#460	C₂²×C₆₁	1	1	yes	characteristic
693	#460	C₂²×C₆₁	1	1	yes	characteristic
694	#460	C₂²×C₆₁	1	1	yes	characteristic, complemented
695	#460	C₂²×C₆₁	1	2	yes	complemented
696	#460	C₂²×C₆₁	1	1	yes	characteristic, complemented
697	#460	C₂²×C₆₁	1	2	yes	complemented
698	#460	C₂²×C₆₁	1	1	yes	characteristic, complemented
699	#460	C₂²×C₆₁	1	2	yes	complemented
700	#459	C₂²×C₆₁	1	2	yes	complemented
701	#459	C₂²×C₆₁	1	1	yes	characteristic, complemented
702	#459	C₂²×C₆₁	1	2	yes	complemented
703	#459	C₂²×C₆₁	1	2	yes	complemented
704	#452	C₂²×C₆₁	1	2	yes	complemented
705	#451	C₂²×C₆₁	1	1	yes	characteristic, complemented
706	#450	C₂²×C₆₁	1	2	yes	complemented
707	#449	C₂²×C₆₁	1	2	yes	complemented
708	#449	C₂²×C₆₁	1	2	yes	complemented
709	#449	C₂²×C₆₁	1	2	yes	complemented
710	#448	C₂²×C₆₁	1	1	yes	characteristic
711	#447	C₂²×C₆₁	1	2	yes	complemented
712	#447	C₂²×C₆₁	1	2	yes	complemented
713	#447	C₂²×C₆₁	1	2	yes	complemented
714	#446	C₂²×C₆₁	1	1	yes	characteristic, complemented
715	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
716	#442	C₂²×C₆₁	1	2	yes	complemented
717	#440	C₂²×C₆₁	1	2	yes	complemented
718	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
719	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
720	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
721	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
722	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
723	C₄×D₈	C₂²×C₆₁	1	2	yes	complemented
724	#436	C₂²×C₆₁	1	1	yes	characteristic, complemented
725	#435	C₂²×C₆₁	1	2	yes	complemented
726	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
727	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
728	#433	C₂²×C₆₁	1	2	yes	complemented
729	#431	C₂²×C₆₁	1	1	yes	characteristic, complemented
730	#424	C₂²×C₆₁	1	2	yes	complemented
731	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
732	#417	C₂²×C₆₁	1	2	yes	complemented
733	C₂×#102	C₂²×C₆₁	1	2	yes	complemented
734	C₂×#102	C₂²×C₆₁	1	2	yes	complemented
735	C₆₁	#62057	1	1	yes	characteristic, direct product factor, Sylow
736	C₂×#41	—	2	1	no	—
737	C₂×#41	—	2	2	no	—
738	C₂×#41	—	2	1	no	—
739	C₂×#41	C₂³×C₆₁	1	2	yes	—
740	C₂×#41	C₂³×C₆₁	1	2	yes	—
741	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
742	C₂²×D₄	—	2	2	no	—
743	C₂²×D₄	—	2	1	no	—
744	C₂²×D₄	—	2	1	no	—
745	C₂²×D₄	—	2	1	no	—
746	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
747	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
748	AGL(1,ℤ/8)	—	4	4	no	—
749	#135	—	4	4	no	—
750	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
751	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
752	C₂×SD₁₆	—	4	4	no	—
753	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
754	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
755	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
756	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
757	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
758	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
759	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
760	C₂×D₈	C₂³×C₆₁	1	2	yes	—
761	C₂×D₈	C₂³×C₆₁	1	2	yes	—
762	C₂×D₈	C₂³×C₆₁	1	2	yes	—
763	C₂×D₈	C₂³×C₆₁	1	2	yes	—
764	C₂×D₈	C₂³×C₆₁	1	2	yes	—
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	—	2	2	no	—
770	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
771	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
772	#127	—	2	1	no	—
773	#127	—	2	1	no	—
774	#127	—	2	1	no	—
775	#127	—	2	1	no	—
776	#127	C₂³×C₆₁	1	2	yes	—
777	#127	C₂³×C₆₁	1	1	yes	characteristic
778	#127	C₂³×C₆₁	1	1	yes	characteristic
779	#127	C₂³×C₆₁	1	1	yes	characteristic
780	#127	C₂³×C₆₁	1	2	yes	—
781	#126	—	2	2	no	—
782	#126	—	2	1	no	—
783	#126	D₄×C₆₁	1	2	yes	—
784	#125	—	2	1	no	—
785	#125	D₄×C₆₁	1	1	yes	characteristic
786	#125	C₂³×C₆₁	1	1	yes	characteristic
787	#124	—	2	1	no	—
788	#124	—	2	1	no	—
789	#124	—	2	2	no	—
790	#124	—	2	2	no	—
791	#124	—	2	1	no	—
792	#124	D₄×C₆₁	1	1	yes	characteristic
793	#124	C₂³×C₆₁	1	1	yes	characteristic
794	#124	C₂³×C₆₁	1	2	yes	—
795	#124	C₂³×C₆₁	1	2	yes	—
796	#123	—	2	1	no	—
797	#123	—	2	2	no	—
798	#123	—	2	2	no	—
799	#123	—	2	2	no	—
800	#123	—	2	2	no	—
801	#123	—	2	2	no	—
802	#123	—	2	2	no	—
803	#123	—	2	2	no	—
804	#123	—	2	2	no	—
805	#123	D₄×C₆₁	1	2	yes	—
806	C₂²⋊Q₈	—	2	2	no	—
807	C₂²⋊Q₈	—	2	2	no	—
808	C₂²⋊Q₈	—	2	2	no	—
809	C₂²⋊Q₈	—	2	2	no	—
810	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
811	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
812	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
813	#121	—	2	2	no	—
814	#121	—	2	1	no	—
815	#121	—	2	2	no	—
816	#121	—	2	2	no	—
817	#121	—	2	2	no	—
818	#121	—	2	1	no	—
819	#121	—	2	1	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	D₄×C₆₁	1	1	yes	characteristic
827	#121	C₂³×C₆₁	1	1	yes	characteristic
828	#121	C₂³×C₆₁	1	2	yes	—
829	#121	C₂³×C₆₁	1	2	yes	—
830	#121	C₂³×C₆₁	1	2	yes	—
831	#121	C₂³×C₆₁	1	2	yes	—
832	#120	—	2	2	no	—
833	#120	—	2	2	no	—
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	—	2	1	no	—
840	C₄×Q₈	—	2	1	no	—
841	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
842	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
843	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
844	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
845	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
846	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
847	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
848	C₄×D₄	—	2	1	no	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	1	no	—
851	C₄×D₄	—	2	1	no	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	2	1	no	—
854	C₄×D₄	—	2	2	no	—
855	C₄×D₄	—	2	2	no	—
856	C₄×D₄	—	2	2	no	—
857	C₄×D₄	—	2	1	no	—
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	2	yes	—
862	C₄×D₄	C₂³×C₆₁	1	2	yes	—
863	C₄×D₄	C₂³×C₆₁	1	2	yes	—
864	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
865	#117	—	2	2	no	—
866	#117	—	2	1	no	—
867	#117	C₂³×C₆₁	1	2	yes	—
868	C₂×C₄⋊C₄	—	2	1	no	—
869	C₂×C₄⋊C₄	—	2	2	no	—
870	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
871	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
872	C₂×C₂²⋊C₄	—	2	2	no	—
873	C₂×C₄²	—	2	1	no	—
874	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
875	#107	C₂³×C₆₁	1	1	yes	characteristic
876	#107	C₂³×C₆₁	1	1	yes	characteristic
877	#107	C₂³×C₆₁	1	2	yes	—
878	#106	C₂³×C₆₁	1	1	yes	characteristic
879	#106	C₂³×C₆₁	1	2	yes	—
880	#106	C₂³×C₆₁	1	1	yes	characteristic
881	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
882	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
883	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
884	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
885	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
886	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
887	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
888	#103	C₂³×C₆₁	1	1	yes	characteristic
889	#103	C₂³×C₆₁	1	2	yes	—
890	#103	C₂³×C₆₁	1	1	yes	characteristic
891	#103	C₂³×C₆₁	1	1	yes	characteristic
892	#103	C₂³×C₆₁	1	1	yes	characteristic
893	#103	C₂³×C₆₁	1	1	yes	characteristic
894	#103	C₂³×C₆₁	1	1	yes	characteristic
895	#102	C₂³×C₆₁	1	2	yes	—
896	#102	C₂³×C₆₁	1	1	yes	characteristic
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	2	yes	—
901	#102	C₂³×C₆₁	1	2	yes	—
902	#102	C₂³×C₆₁	1	2	yes	—
903	#102	C₂³×C₆₁	1	2	yes	—
904	#102	C₂³×C₆₁	1	1	yes	characteristic
905	#102	C₂³×C₆₁	1	2	yes	—
906	#102	C₂³×C₆₁	1	2	yes	—
907	#102	C₂³×C₆₁	1	2	yes	—
908	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
909	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
910	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
911	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
912	#97	C₂³×C₆₁	1	2	yes	—
913	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
914	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
915	C₄×C₈	C₂³×C₆₁	1	2	yes	—
916	C₂⁴	—	2	2	no	—
917	C₂⁴	—	2	2	no	—
918	#41	—	2	4	no	—
919	#41	—	4	2	no	—
920	#41	—	4	2	no	—
921	#41	—	4	2	no	—
922	#41	—	8	2	no	—
923	#41	—	8	4	no	—
924	#41	—	8	2	no	—
925	C₂×Q₈	—	2	1	no	—
926	C₂×Q₈	—	2	2	no	—
927	C₂×Q₈	—	2	1	no	—
928	C₂×Q₈	—	2	2	no	—
929	C₂×Q₈	—	4	1	no	—
930	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
931	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
932	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
933	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	1	no	—
942	C₂×D₄	—	2	1	no	—
943	C₂×D₄	—	2	1	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	1	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	2	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	1	no	—
952	C₂×D₄	—	2	1	no	—
953	C₂×D₄	—	4	2	no	—
954	C₂×D₄	—	4	2	no	—
955	C₂×D₄	—	4	2	no	—
956	C₂×D₄	—	4	2	no	—
957	C₂×D₄	—	8	2	no	—
958	C₂×D₄	—	8	2	no	—
959	C₂×D₄	—	8	2	no	—
960	C₂×D₄	—	8	4	no	—
961	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
962	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
963	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
964	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
965	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
966	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
967	C₂²×C₄	—	2	1	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	2	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	2	no	—
973	C₂²×C₄	—	2	2	no	—
974	C₂²×C₄	—	2	2	no	—
975	C₂²×C₄	—	2	2	no	—
976	C₂²×C₄	—	2	2	no	—
977	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
978	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
979	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
980	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
981	Q₁₆	—	2	2	no	—
982	Q₁₆	—	4	1	no	—
983	SD₁₆	—	2	4	no	—
984	SD₁₆	—	2	4	no	—
985	SD₁₆	—	2	2	no	—
986	SD₁₆	—	4	2	no	—
987	SD₁₆	—	4	2	no	—
988	SD₁₆	—	4	1	no	—
989	SD₁₆	—	4	2	no	—
990	D₈	—	4	2	no	—
991	D₈	—	4	2	no	—
992	D₈	—	4	2	no	—
993	D₈	—	4	2	no	—
994	D₈	—	4	2	no	—
995	M₁₆	—	4	2	no	—
996	C₂×C₈	—	4	2	no	—
997	C₂×C₈	—	4	2	no	—
998	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
999	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
1000	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
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	C₄⋊C₄	—	2	1	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	1	no	—
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	—	2	1	no	—
1018	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1019	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1020	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
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	2	yes	—
1026	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1027	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1028	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	1	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	2	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	1	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
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	C₄²	—	2	1	no	—
1053	C₄²	—	2	1	no	—
1054	C₄²	—	2	1	no	—
1055	C₄²	—	2	1	no	—
1056	C₄²	—	2	1	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	2	no	—
1064	C₂³	—	2	2	no	—
1065	C₂³	—	2	1	no	—
1066	C₂³	—	2	2	no	—
1067	C₂³	—	4	4	no	—
1068	C₂³	—	8	2	no	—
1069	C₂³	—	8	2	no	—
1070	C₂³	—	8	2	no	—
1071	C₂³	—	8	2	no	—
1072	C₂³	—	8	2	no	—
1073	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1074	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1075	Q₈	—	2	2	no	—
1076	Q₈	—	2	1	no	—
1077	Q₈	—	2	1	no	—
1078	Q₈	—	2	1	no	—
1079	Q₈	—	2	1	no	—
1080	Q₈	—	2	1	no	—
1081	Q₈	—	4	2	no	—
1082	Q₈	—	8	1	no	—
1083	Q₈	—	8	2	no	—
1084	Q₈	H(5,𝔽₂)×C₆₁	1	2	yes	—
1085	D₄	—	2	4	no	—
1086	D₄	—	2	2	no	—
1087	D₄	—	2	2	no	—
1088	D₄	—	2	1	no	—
1089	D₄	—	2	2	no	—
1090	D₄	—	2	2	no	—
1091	D₄	—	2	2	no	—
1092	D₄	—	2	2	no	—
1093	D₄	—	2	2	no	—
1094	D₄	—	2	1	no	—
1095	D₄	—	4	4	no	—
1096	D₄	—	4	2	no	—
1097	D₄	—	4	4	no	—
1098	D₄	—	4	2	no	—
1099	D₄	—	4	2	no	—
1100	D₄	—	4	2	no	—
1101	D₄	—	8	2	no	—
1102	D₄	—	8	2	no	—
1103	D₄	—	8	2	no	—
1104	D₄	—	8	1	no	—
1105	D₄	—	8	1	no	—
1106	D₄	—	8	2	no	—
1107	D₄	—	8	2	no	—
1108	D₄	—	8	1	no	—
1109	D₄	—	8	2	no	—
1110	D₄	—	8	2	no	—
1111	D₄	—	8	2	no	—
1112	D₄	—	8	2	no	—
1113	D₄	—	8	2	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	1	no	—
1118	C₂×C₄	—	2	2	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	2	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	4	4	no	—
1129	C₂×C₄	—	4	2	no	—
1130	C₂×C₄	—	4	2	no	—
1131	C₂×C₄	—	4	2	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	1	yes	characteristic
1139	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
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	1	no	—
1148	C₈	—	2	2	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	1	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	2	2	no	—
1158	C₂²	—	4	2	no	—
1159	C₂²	—	4	2	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	2	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	—	4	2	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	2	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	4	2	no	—
1170	C₂²	—	16	4	no	—
1171	C₂²	—	16	4	no	—
1172	C₂²	C₆₁×#576	1	2	yes	—
1173	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1174	C₄	—	2	1	no	—
1175	C₄	—	2	1	no	—
1176	C₄	—	2	2	no	—
1177	C₄	—	2	1	no	—
1178	C₄	—	2	2	no	—
1179	C₄	—	2	2	no	—
1180	C₄	—	2	1	no	—
1181	C₄	—	2	2	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	1	no	—
1184	C₄	—	4	1	no	—
1185	C₄	—	4	2	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	1	no	—
1188	C₄	—	4	1	no	—
1189	C₄	C₆₁×#577	1	2	yes	—
1190	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1191	C₄	C₆₁×#585	1	1	yes	characteristic
1192	C₂	—	2	2	no	—
1193	C₂	—	4	2	no	—
1194	C₂	—	8	2	no	—
1195	C₂	—	8	1	no	—
1196	C₂	—	8	2	no	—
1197	C₂	—	8	2	no	—
1198	C₂	C₆₁×#3488	1	1	yes	characteristic
1199	C₂	C₂×C₆₁×#576	1	1	yes	characteristic
1200	C₂	C₂×C₆₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3543	C₂	semidirect
2. C₆₁×#3522	C₂	semidirect
3. C₆₁×#3399	C₂	semidirect
4. C₆₁×#3396	C₂	semidirect
5. C₆₁×#3375	C₂	semidirect
6. C₆₁×#3362	C₂	semidirect
7. C₆₁×#3333	C₂	semidirect
8. C₆₁×#3306	C₂	semidirect
9. C₆₁×#3295	C₂	semidirect
10. C₆₁×#3294	C₂	semidirect
11. C₆₁×#3287	C₂	semidirect
12. C₆₁×#3282	C₂	semidirect
13. C₆₁×#3274	C₂	semidirect
14. C₆₁×#3265	C₂	semidirect
15. C₆₁×#3257	C₂	semidirect
16. C₆₁×#3247	C₂	semidirect
17. C₆₁×#3224	C₂	semidirect
18. C₆₁×#3205	C₂	semidirect
19. C₆₁×#3119	C₂	semidirect
20. C₆₁×#3108	C₂	semidirect
21. C₆₁×#3045	C₂	semidirect
22. C₂×C₆₁×#460	C₂	semidirect
23. C₆₁×#2994	C₂	semidirect
24. C₂×AGL(1,ℤ/8)×C₆₁	C₂²	semidirect
25. C₂×#135×C₆₁	C₂²	semidirect
26. C₂²×SD₁₆×C₆₁	C₂²	semidirect
30. C₆₁×#559	C₂²	semidirect
31. Q₈²×C₆₁	C₂²	semidirect
33. C₆₁×#554	C₂²	semidirect
36. C₆₁×#550	C₂²	semidirect
37. C₆₁×#548	C₂²	semidirect
39. C₆₁×#547	C₂²	semidirect
46. C₆₁×#542	C₂²	semidirect
53. C₆₁×#532	C₂²	semidirect
58. C₆₁×#520	C₂²	semidirect
59. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
60. C₆₁×#496	C₂²	semidirect
61. C₆₁×#495	C₂²	semidirect
63. C₆₁×#493	C₂²	semidirect
64. C₆₁×#489	C₂²	semidirect
66. C₆₁×#486	C₂²	semidirect
67. C₆₁×#486	C₂²	semidirect
68. C₆₁×#483	C₂²	semidirect
69. C₆₁×#481	C₂²	semidirect
71. C₆₁×#480	C₂²	semidirect
72. C₆₁×#479	C₂²	semidirect
73. C₆₁×#479	C₂²	semidirect
74. C₆₁×#478	C₂²	semidirect
75. C₆₁×#477	C₂²	semidirect
76. C₆₁×#476	C₂²	semidirect
77. C₆₁×#476	C₂²	semidirect
78. C₆₁×#474	C₂²	semidirect
79. C₆₁×#469	C₂²	semidirect
80. C₆₁×#468	C₂²	semidirect
82. C₆₁×#466	C₂²	semidirect
83. C₆₁×#465	C₂²	semidirect
84. C₆₁×#465	C₂²	semidirect
85. C₆₁×#464	C₂²	semidirect
86. C₆₁×#464	C₂²	semidirect
87. C₆₁×#464	C₂²	semidirect
88. C₆₁×#463	C₂²	semidirect
89. C₆₁×#463	C₂²	semidirect
90. C₆₁×#463	C₂²	semidirect
91. C₆₁×#463	C₂²	semidirect
94. C₆₁×#460	C₂²	semidirect
95. C₆₁×#460	C₂²	semidirect
96. C₆₁×#460	C₂²	semidirect
97. C₆₁×#460	C₂²	semidirect
98. C₆₁×#460	C₂²	semidirect
99. C₆₁×#460	C₂²	semidirect
100. C₆₁×#459	C₂²	semidirect
101. C₆₁×#459	C₂²	semidirect
102. C₆₁×#459	C₂²	semidirect
103. C₆₁×#459	C₂²	semidirect
104. C₆₁×#452	C₂²	semidirect
105. C₆₁×#451	C₂²	semidirect
106. C₆₁×#450	C₂²	semidirect
107. C₆₁×#449	C₂²	semidirect
108. C₆₁×#449	C₂²	semidirect
109. C₆₁×#449	C₂²	semidirect
111. C₆₁×#447	C₂²	semidirect
112. C₆₁×#447	C₂²	semidirect
113. C₆₁×#447	C₂²	semidirect
114. C₆₁×#446	C₂²	semidirect
115. C₈×Q₈×C₆₁	C₂²	semidirect
116. C₆₁×#442	C₂²	semidirect
117. C₆₁×#440	C₂²	semidirect
118. C₄×Q₁₆×C₆₁	C₂²	semidirect
119. C₄×Q₁₆×C₆₁	C₂²	semidirect
120. C₄×SD₁₆×C₆₁	C₂²	semidirect
121. C₄×SD₁₆×C₆₁	C₂²	semidirect
122. C₄×SD₁₆×C₆₁	C₂²	semidirect
123. C₄×D₈×C₆₁	C₂²	semidirect
124. C₆₁×#436	C₂²	semidirect
125. C₆₁×#435	C₂²	semidirect
126. C₈×D₄×C₆₁	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. C₂×#102×C₆₁	C₂²	semidirect
134. C₂×#102×C₆₁	C₂²	semidirect
552. #62057	C₆₁	direct (N × H)
592. #3543	C₂×C₆₁	semidirect
593. #3522	C₂×C₆₁	semidirect
594. #3399	C₂×C₆₁	semidirect
595. #3396	C₂×C₆₁	semidirect
596. #3375	C₂×C₆₁	semidirect
597. #3362	C₂×C₆₁	semidirect
598. #3333	C₂×C₆₁	semidirect
599. #3306	C₂×C₆₁	semidirect
600. #3295	C₂×C₆₁	semidirect
601. #3294	C₂×C₆₁	semidirect
602. #3287	C₂×C₆₁	semidirect
603. #3282	C₂×C₆₁	semidirect
604. #3274	C₂×C₆₁	semidirect
605. #3265	C₂×C₆₁	semidirect
606. #3257	C₂×C₆₁	semidirect
607. #3247	C₂×C₆₁	semidirect
608. #3224	C₂×C₆₁	semidirect
609. #3205	C₂×C₆₁	semidirect
610. #3119	C₂×C₆₁	semidirect
611. #3108	C₂×C₆₁	semidirect
612. #3045	C₂×C₆₁	semidirect
613. C₂×#460	C₂×C₆₁	semidirect
614. #2994	C₂×C₆₁	semidirect
624. C₂×AGL(1,ℤ/8)	C₂²×C₆₁	semidirect
625. C₂×#135	C₂²×C₆₁	semidirect
626. C₂²×SD₁₆	C₂²×C₆₁	semidirect
630. #559	C₂²×C₆₁	semidirect
631. Q₈²	C₂²×C₆₁	semidirect
633. #554	C₂²×C₆₁	semidirect
636. #550	C₂²×C₆₁	semidirect
637. #548	C₂²×C₆₁	semidirect
639. #547	C₂²×C₆₁	semidirect
646. #542	C₂²×C₆₁	semidirect
653. #532	C₂²×C₆₁	semidirect
658. #520	C₂²×C₆₁	semidirect
659. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
660. #496	C₂²×C₆₁	semidirect
661. #495	C₂²×C₆₁	semidirect
663. #493	C₂²×C₆₁	semidirect
664. #489	C₂²×C₆₁	semidirect
666. #486	C₂²×C₆₁	semidirect
667. #486	C₂²×C₆₁	semidirect
668. #483	C₂²×C₆₁	semidirect
669. #481	C₂²×C₆₁	semidirect
671. #480	C₂²×C₆₁	semidirect
672. #479	C₂²×C₆₁	semidirect
673. #479	C₂²×C₆₁	semidirect
674. #478	C₂²×C₆₁	semidirect
675. #477	C₂²×C₆₁	semidirect
676. #476	C₂²×C₆₁	semidirect
677. #476	C₂²×C₆₁	semidirect
678. #474	C₂²×C₆₁	semidirect
679. #469	C₂²×C₆₁	semidirect
680. #468	C₂²×C₆₁	semidirect
682. #466	C₂²×C₆₁	semidirect
683. #465	C₂²×C₆₁	semidirect
684. #465	C₂²×C₆₁	semidirect
685. #464	C₂²×C₆₁	semidirect
686. #464	C₂²×C₆₁	semidirect
687. #464	C₂²×C₆₁	semidirect
688. #463	C₂²×C₆₁	semidirect
689. #463	C₂²×C₆₁	semidirect
690. #463	C₂²×C₆₁	semidirect
691. #463	C₂²×C₆₁	semidirect
694. #460	C₂²×C₆₁	semidirect
695. #460	C₂²×C₆₁	semidirect
696. #460	C₂²×C₆₁	semidirect
697. #460	C₂²×C₆₁	semidirect
698. #460	C₂²×C₆₁	semidirect
699. #460	C₂²×C₆₁	semidirect
700. #459	C₂²×C₆₁	semidirect
701. #459	C₂²×C₆₁	semidirect
702. #459	C₂²×C₆₁	semidirect
703. #459	C₂²×C₆₁	semidirect
704. #452	C₂²×C₆₁	semidirect
705. #451	C₂²×C₆₁	semidirect
706. #450	C₂²×C₆₁	semidirect
707. #449	C₂²×C₆₁	semidirect
708. #449	C₂²×C₆₁	semidirect
709. #449	C₂²×C₆₁	semidirect
711. #447	C₂²×C₆₁	semidirect
712. #447	C₂²×C₆₁	semidirect
713. #447	C₂²×C₆₁	semidirect
714. #446	C₂²×C₆₁	semidirect
715. C₈×Q₈	C₂²×C₆₁	semidirect
716. #442	C₂²×C₆₁	semidirect
717. #440	C₂²×C₆₁	semidirect
718. C₄×Q₁₆	C₂²×C₆₁	semidirect
719. C₄×Q₁₆	C₂²×C₆₁	semidirect
720. C₄×SD₁₆	C₂²×C₆₁	semidirect
721. C₄×SD₁₆	C₂²×C₆₁	semidirect
722. C₄×SD₁₆	C₂²×C₆₁	semidirect
723. C₄×D₈	C₂²×C₆₁	semidirect
724. #436	C₂²×C₆₁	semidirect
725. #435	C₂²×C₆₁	semidirect
726. C₈×D₄	C₂²×C₆₁	semidirect
727. C₈×D₄	C₂²×C₆₁	semidirect
728. #433	C₂²×C₆₁	semidirect
729. #431	C₂²×C₆₁	semidirect
730. #424	C₂²×C₆₁	semidirect
731. C₂×C₄⋊C₈	C₂²×C₆₁	semidirect
732. #417	C₂²×C₆₁	semidirect
733. C₂×#102	C₂²×C₆₁	semidirect
734. C₂×#102	C₂²×C₆₁	semidirect
735. C₆₁	#62057	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₁×#3543	2
C₆₁×#3522	2
C₆₁×#3399	2
C₆₁×#3396	2
C₆₁×#3375	2
C₆₁×#3362	2
C₆₁×#3333	2
C₆₁×#3306	2
C₆₁×#3295	2
C₆₁×#3294	2
C₆₁×#3287	2
C₆₁×#3282	2
C₆₁×#3274	2
C₆₁×#3265	2
C₆₁×#3257	2
C₆₁×#3247	2
C₆₁×#3224	2
C₆₁×#3205	2
C₆₁×#3119	2
C₆₁×#3108	2
C₆₁×#3045	2
C₂×C₆₁×#460	2
C₆₁×#2994	2
#62057	61

Subgroups — C61×#62057 #29565490

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62057 #29565490