Subgroups — C₆₁×#62006 #29565439

Order 15616.

1868 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3396	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3328	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3326	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3324	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3322	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3278	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3277	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3275	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3274	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3256	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3211	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3108	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#3102	C₂	1	2	yes	maximal, complemented
21	C₆₁×#3040	C₂	1	2	yes	maximal, complemented
22	C₆₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#2991	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₆₁	C₂²	1	2	yes	complemented
25	C₂×#137×C₆₁	C₂²	1	2	yes	complemented
26	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
27	C₆₁×#559	—	2	1	no	—
28	C₆₁×#559	C₂²	1	1	yes	characteristic
29	C₆₁×#559	C₂²	1	1	yes	characteristic, complemented
30	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
31	C₆₁×#556	—	2	1	no	—
32	C₆₁×#556	C₂²	1	1	yes	characteristic
33	C₆₁×#556	C₂²	1	1	yes	characteristic
34	C₆₁×#555	—	2	1	no	—
35	C₆₁×#553	—	2	2	no	—
36	C₆₁×#553	C₂²	1	2	yes	complemented
37	C₆₁×#551	—	2	2	no	—
38	C₆₁×#550	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
40	C₆₁×#548	C₂²	1	2	yes	—
41	C₆₁×#548	C₂²	1	2	yes	complemented
42	C₆₁×#546	—	2	1	no	—
43	C₆₁×#546	C₂²	1	2	yes	—
44	D₄²×C₆₁	C₂²	1	1	yes	characteristic
45	C₆₁×#542	—	2	1	no	—
46	C₆₁×#538	—	2	2	no	—
47	C₆₁×#532	—	2	1	no	—
48	C₆₁×#532	C₂²	1	1	yes	characteristic
49	C₆₁×#532	C₂²	1	1	yes	characteristic, complemented
50	C₆₁×#529	—	2	2	no	—
51	C₆₁×#529	C₂²	1	2	yes	—
52	C₆₁×#529	C₂²	1	1	yes	characteristic
53	C₆₁×#529	C₂²	1	2	yes	complemented
54	C₂×#124×C₆₁	C₂²	1	2	yes	—
55	C₆₁×#518	—	2	1	no	—
56	C₄×#41×C₆₁	—	2	1	no	—
57	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
58	C₄×#41×C₆₁	C₂²	1	2	yes	complemented
59	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
60	C₆₁×#495	C₂²	1	2	yes	—
61	C₆₁×#495	C₂²	1	2	yes	complemented
62	C₆₁×#493	C₂²	1	1	yes	characteristic
63	C₆₁×#492	C₂²	1	1	yes	characteristic, complemented
64	C₆₁×#488	C₂²	1	2	yes	—
65	C₆₁×#488	C₂²	1	2	yes	complemented
66	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
67	C₆₁×#486	C₂²	1	1	yes	characteristic
68	C₆₁×#485	C₂²	1	2	yes	complemented
69	C₆₁×#483	C₂²	1	1	yes	characteristic, complemented
70	C₆₁×#482	C₂²	1	2	yes	—
71	C₆₁×#480	C₂²	1	1	yes	characteristic
72	C₆₁×#479	C₂²	1	2	yes	complemented
73	C₆₁×#479	C₂²	1	1	yes	characteristic, complemented
74	C₆₁×#479	C₂²	1	1	yes	characteristic, complemented
75	C₆₁×#478	C₂²	1	2	yes	complemented
76	C₆₁×#478	C₂²	1	2	yes	complemented
77	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
78	C₆₁×#474	C₂²	1	1	yes	characteristic
79	C₆₁×#470	C₂²	1	2	yes	complemented
80	C₆₁×#469	C₂²	1	2	yes	—
81	C₆₁×#469	C₂²	1	2	yes	—
82	C₆₁×#468	C₂²	1	2	yes	—
83	C₆₁×#468	C₂²	1	2	yes	complemented
84	C₆₁×#468	C₂²	1	2	yes	complemented
85	C₆₁×#464	C₂²	1	1	yes	characteristic
86	C₆₁×#464	C₂²	1	2	yes	—
87	C₆₁×#464	C₂²	1	1	yes	characteristic
88	C₆₁×#464	C₂²	1	2	yes	complemented
89	C₆₁×#464	C₂²	1	2	yes	complemented
90	C₆₁×#464	C₂²	1	2	yes	complemented
91	C₆₁×#464	C₂²	1	2	yes	complemented
92	C₆₁×#463	C₂²	1	2	yes	—
93	C₆₁×#463	C₂²	1	2	yes	—
94	C₆₁×#463	C₂²	1	2	yes	complemented
95	C₆₁×#463	C₂²	1	2	yes	complemented
96	C₆₁×#463	C₂²	1	2	yes	complemented
97	C₆₁×#463	C₂²	1	2	yes	complemented
98	C₆₁×#462	C₂²	1	1	yes	characteristic, complemented
99	C₆₁×#462	C₂²	1	1	yes	characteristic, complemented
100	C₆₁×#460	C₂²	1	1	yes	characteristic
101	C₆₁×#460	C₂²	1	1	yes	characteristic
102	C₆₁×#460	C₂²	1	1	yes	characteristic, complemented
103	C₆₁×#459	C₂²	1	1	yes	characteristic
104	C₆₁×#452	C₂²	1	2	yes	complemented
105	C₆₁×#451	C₂²	1	2	yes	complemented
106	C₆₁×#451	C₂²	1	1	yes	characteristic, complemented
107	C₆₁×#450	C₂²	1	2	yes	—
108	C₆₁×#449	C₂²	1	2	yes	—
109	C₆₁×#449	C₂²	1	2	yes	complemented
110	C₆₁×#449	C₂²	1	2	yes	complemented
111	C₆₁×#448	C₂²	1	1	yes	characteristic
112	C₆₁×#448	C₂²	1	2	yes	complemented
113	C₆₁×#447	C₂²	1	2	yes	—
114	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
117	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
118	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
121	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	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
125	C₆₁×#436	C₂²	1	1	yes	characteristic
126	C₆₁×#436	C₂²	1	2	yes	complemented
127	C₆₁×#436	C₂²	1	2	yes	complemented
128	C₆₁×#431	C₂²	1	2	yes	complemented
129	C₆₁×#431	C₂²	1	1	yes	characteristic, complemented
130	C₆₁×#423	C₂²	1	1	yes	characteristic, complemented
131	C₆₁×#423	C₂²	1	2	yes	complemented
132	C₆₁×#419	C₂²	1	2	yes	complemented
133	C₆₁×#418	C₂²	1	2	yes	—
134	C₆₁×#417	C₂²	1	2	yes	complemented
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
137	C₂×#41×C₆₁	C₂³	1	2	yes	—
138	C₂×#41×C₆₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
140	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
141	C₂²×D₄×C₆₁	—	2	1	no	—
142	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
143	#137×C₆₁	—	4	4	no	—
144	#137×C₆₁	—	4	4	no	—
145	AGL(1,ℤ/8)×C₆₁	—	4	4	no	—
146	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
156	C₂×SD₁₆×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×M₁₆×C₆₁	C₂³	1	2	yes	—
161	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
162	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₆₁	—	2	1	no	—
164	C₄⋊Q₈×C₆₁	—	2	1	no	—
165	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
167	#127×C₆₁	—	2	1	no	—
168	#127×C₆₁	C₂³	1	1	yes	characteristic
169	#127×C₆₁	C₂³	1	1	yes	characteristic
170	#126×C₆₁	—	2	2	no	—
171	#126×C₆₁	—	2	2	no	—
172	#126×C₆₁	—	2	2	no	—
173	#126×C₆₁	—	2	2	no	—
174	#126×C₆₁	—	2	1	no	—
175	#126×C₆₁	—	2	2	no	—
176	#125×C₆₁	—	2	2	no	—
177	#125×C₆₁	C₂³	1	2	yes	—
178	#125×C₆₁	C₂³	1	1	yes	characteristic
179	#124×C₆₁	—	2	1	no	—
180	#124×C₆₁	—	2	1	no	—
181	#124×C₆₁	—	2	1	no	—
182	#124×C₆₁	—	2	2	no	—
183	#124×C₆₁	—	2	2	no	—
184	#124×C₆₁	—	2	1	no	—
185	#124×C₆₁	—	2	2	no	—
186	#124×C₆₁	—	2	2	no	—
187	#124×C₆₁	C₂³	1	2	yes	—
188	#124×C₆₁	C₂³	1	2	yes	—
189	#124×C₆₁	C₂³	1	2	yes	—
190	#124×C₆₁	C₂³	1	2	yes	—
191	#124×C₆₁	C₂³	1	1	yes	characteristic
192	#123×C₆₁	—	2	1	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	—	2	2	no	—
199	C₂²⋊Q₈×C₆₁	—	2	1	no	—
200	C₂²⋊Q₈×C₆₁	—	2	2	no	—
201	C₂²⋊Q₈×C₆₁	—	2	2	no	—
202	C₂²⋊Q₈×C₆₁	—	2	2	no	—
203	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
204	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
205	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
206	#121×C₆₁	—	2	2	no	—
207	#121×C₆₁	—	2	2	no	—
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	1	no	—
213	#121×C₆₁	—	2	2	no	—
214	#121×C₆₁	—	2	2	no	—
215	#121×C₆₁	C₂³	1	2	yes	—
216	#121×C₆₁	C₂³	1	2	yes	—
217	#121×C₆₁	C₂³	1	1	yes	characteristic
218	#121×C₆₁	C₂³	1	2	yes	—
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	—	2	1	no	—
224	C₄×Q₈×C₆₁	—	2	1	no	—
225	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
226	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
228	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₆₁	—	2	1	no	—
235	C₄×D₄×C₆₁	—	2	2	no	—
236	C₄×D₄×C₆₁	—	2	2	no	—
237	C₄×D₄×C₆₁	—	2	2	no	—
238	C₄×D₄×C₆₁	—	2	1	no	—
239	C₄×D₄×C₆₁	—	2	2	no	—
240	C₄×D₄×C₆₁	—	2	1	no	—
241	C₄×D₄×C₆₁	—	2	1	no	—
242	C₄×D₄×C₆₁	—	2	1	no	—
243	C₄×D₄×C₆₁	—	2	2	no	—
244	C₄×D₄×C₆₁	—	2	2	no	—
245	C₄×D₄×C₆₁	—	2	2	no	—
246	C₄×D₄×C₆₁	—	2	1	no	—
247	C₄×D₄×C₆₁	—	2	1	no	—
248	C₄×D₄×C₆₁	—	2	1	no	—
249	C₄×D₄×C₆₁	D₄	1	2	yes	—
250	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
251	C₄×D₄×C₆₁	C₂³	1	2	yes	—
252	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₆₁	C₂³	1	2	yes	—
254	C₄×D₄×C₆₁	C₂³	1	2	yes	—
255	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₆₁	C₂³	1	2	yes	—
257	#117×C₆₁	—	2	1	no	—
258	#117×C₆₁	—	2	1	no	—
259	#117×C₆₁	—	2	2	no	—
260	#117×C₆₁	—	2	2	no	—
261	#117×C₆₁	—	2	2	no	—
262	#117×C₆₁	D₄	1	2	yes	—
263	#117×C₆₁	D₄	1	1	yes	characteristic
264	#117×C₆₁	C₂³	1	2	yes	—
265	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
266	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
268	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
269	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
270	C₂×C₄²×C₆₁	—	2	1	no	—
271	C₂×C₄²×C₆₁	—	2	2	no	—
272	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
274	#107×C₆₁	C₂³	1	1	yes	characteristic
275	#107×C₆₁	C₂³	1	2	yes	—
276	#107×C₆₁	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
290	#103×C₆₁	C₂³	1	2	yes	—
291	#103×C₆₁	C₂³	1	2	yes	—
292	#103×C₆₁	C₂³	1	1	yes	characteristic
293	#103×C₆₁	C₂³	1	1	yes	characteristic
294	#103×C₆₁	C₂³	1	1	yes	characteristic
295	#103×C₆₁	C₂³	1	1	yes	characteristic
296	#103×C₆₁	C₂³	1	1	yes	characteristic
297	#103×C₆₁	C₂³	1	2	yes	—
298	#102×C₆₁	C₂³	1	2	yes	—
299	#102×C₆₁	C₂³	1	2	yes	—
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	#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	2	yes	—
308	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
310	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₆₁	C₂³	1	2	yes	—
314	C₄×C₈×C₆₁	C₂³	1	2	yes	—
315	C₂⁴×C₆₁	—	2	2	no	—
316	#41×C₆₁	—	2	4	no	—
317	#41×C₆₁	—	4	2	no	—
318	#41×C₆₁	—	4	2	no	—
319	#41×C₆₁	—	4	4	no	—
320	#41×C₆₁	—	4	2	no	—
321	#41×C₆₁	—	4	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	—	4	1	no	—
327	C₂×Q₈×C₆₁	—	4	2	no	—
328	C₂×Q₈×C₆₁	—	4	2	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	2	yes	—
332	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
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	1	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	1	no	—
344	C₂×D₄×C₆₁	—	2	2	no	—
345	C₂×D₄×C₆₁	—	4	2	no	—
346	C₂×D₄×C₆₁	—	4	2	no	—
347	C₂×D₄×C₆₁	—	4	4	no	—
348	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
349	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
350	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
352	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
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	2	no	—
357	C₂²×C₄×C₆₁	—	2	2	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	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
364	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
365	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
368	Q₁₆×C₆₁	—	2	2	no	—
369	Q₁₆×C₆₁	—	2	4	no	—
370	Q₁₆×C₆₁	—	4	1	no	—
371	Q₁₆×C₆₁	—	4	2	no	—
372	SD₁₆×C₆₁	—	2	2	no	—
373	SD₁₆×C₆₁	—	2	4	no	—
374	SD₁₆×C₆₁	—	4	2	no	—
375	SD₁₆×C₆₁	—	4	1	no	—
376	SD₁₆×C₆₁	—	4	2	no	—
377	SD₁₆×C₆₁	—	4	2	no	—
378	SD₁₆×C₆₁	—	4	2	no	—
379	D₈×C₆₁	—	4	2	no	—
380	D₈×C₆₁	—	4	2	no	—
381	D₈×C₆₁	—	4	2	no	—
382	M₁₆×C₆₁	—	4	2	no	—
383	M₁₆×C₆₁	—	4	2	no	—
384	M₁₆×C₆₁	—	4	2	no	—
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	2	yes	—
390	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
391	C₄⋊C₄×C₆₁	—	2	1	no	—
392	C₄⋊C₄×C₆₁	—	2	1	no	—
393	C₄⋊C₄×C₆₁	—	2	1	no	—
394	C₄⋊C₄×C₆₁	—	2	1	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	1	no	—
399	C₄⋊C₄×C₆₁	—	2	1	no	—
400	C₄⋊C₄×C₆₁	—	2	2	no	—
401	C₄⋊C₄×C₆₁	—	2	2	no	—
402	C₄⋊C₄×C₆₁	—	2	2	no	—
403	C₄⋊C₄×C₆₁	—	2	2	no	—
404	C₄⋊C₄×C₆₁	—	2	1	no	—
405	C₄⋊C₄×C₆₁	—	2	1	no	—
406	C₄⋊C₄×C₆₁	—	2	2	no	—
407	C₄⋊C₄×C₆₁	—	2	2	no	—
408	C₄⋊C₄×C₆₁	—	2	1	no	—
409	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
411	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
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	2	no	—
423	C₂²⋊C₄×C₆₁	—	2	1	no	—
424	C₂²⋊C₄×C₆₁	—	2	1	no	—
425	C₂²⋊C₄×C₆₁	—	2	1	no	—
426	C₂²⋊C₄×C₆₁	—	2	2	no	—
427	C₂²⋊C₄×C₆₁	—	2	2	no	—
428	C₂²⋊C₄×C₆₁	—	2	2	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	2	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	1	no	—
439	C₂²⋊C₄×C₆₁	—	2	2	no	—
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	C₄²×C₆₁	—	2	1	no	—
444	C₄²×C₆₁	—	2	1	no	—
445	C₄²×C₆₁	—	2	2	no	—
446	C₄²×C₆₁	—	2	2	no	—
447	C₄²×C₆₁	—	2	1	no	—
448	C₄²×C₆₁	—	2	1	no	—
449	C₄²×C₆₁	—	2	2	no	—
450	C₄²×C₆₁	—	2	1	no	—
451	C₄²×C₆₁	C₂×D₄	1	2	yes	—
452	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₆₁	C₂×D₄	1	2	yes	—
454	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₆₁	C₂⁴	1	2	yes	—
456	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
457	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
458	C₂³×C₆₁	—	2	1	no	—
459	C₂³×C₆₁	—	2	2	no	—
460	C₂³×C₆₁	—	2	2	no	—
461	C₂³×C₆₁	—	4	4	no	—
462	C₂³×C₆₁	—	8	2	no	—
463	C₂³×C₆₁	—	8	2	no	—
464	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
465	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
466	Q₈×C₆₁	—	2	2	no	—
467	Q₈×C₆₁	—	2	1	no	—
468	Q₈×C₆₁	—	2	1	no	—
469	Q₈×C₆₁	—	2	1	no	—
470	Q₈×C₆₁	—	2	2	no	—
471	Q₈×C₆₁	—	2	1	no	—
472	Q₈×C₆₁	—	2	2	no	—
473	Q₈×C₆₁	—	2	1	no	—
474	Q₈×C₆₁	—	4	2	no	—
475	Q₈×C₆₁	—	4	2	no	—
476	Q₈×C₆₁	—	8	2	no	—
477	Q₈×C₆₁	H(5,𝔽₂)	1	2	yes	—
478	D₄×C₆₁	—	2	2	no	—
479	D₄×C₆₁	—	2	1	no	—
480	D₄×C₆₁	—	2	2	no	—
481	D₄×C₆₁	—	2	2	no	—
482	D₄×C₆₁	—	2	2	no	—
483	D₄×C₆₁	—	2	2	no	—
484	D₄×C₆₁	—	2	1	no	—
485	D₄×C₆₁	—	4	2	no	—
486	D₄×C₆₁	—	4	4	no	—
487	D₄×C₆₁	—	4	4	no	—
488	D₄×C₆₁	—	4	4	no	—
489	D₄×C₆₁	—	4	2	no	—
490	D₄×C₆₁	—	4	2	no	—
491	D₄×C₆₁	—	8	1	no	—
492	D₄×C₆₁	—	8	1	no	—
493	D₄×C₆₁	—	8	2	no	—
494	D₄×C₆₁	—	8	1	no	—
495	D₄×C₆₁	—	8	2	no	—
496	D₄×C₆₁	—	8	2	no	—
497	C₂×C₄×C₆₁	—	2	1	no	—
498	C₂×C₄×C₆₁	—	2	2	no	—
499	C₂×C₄×C₆₁	—	2	2	no	—
500	C₂×C₄×C₆₁	—	2	1	no	—
501	C₂×C₄×C₆₁	—	2	2	no	—
502	C₂×C₄×C₆₁	—	2	1	no	—
503	C₂×C₄×C₆₁	—	2	1	no	—
504	C₂×C₄×C₆₁	—	2	1	no	—
505	C₂×C₄×C₆₁	—	2	1	no	—
506	C₂×C₄×C₆₁	—	2	2	no	—
507	C₂×C₄×C₆₁	—	2	1	no	—
508	C₂×C₄×C₆₁	—	2	1	no	—
509	C₂×C₄×C₆₁	—	2	1	no	—
510	C₂×C₄×C₆₁	—	2	2	no	—
511	C₂×C₄×C₆₁	—	4	2	no	—
512	C₂×C₄×C₆₁	—	4	1	no	—
513	C₂×C₄×C₆₁	—	4	2	no	—
514	C₂×C₄×C₆₁	—	4	4	no	—
515	C₂×C₄×C₆₁	—	4	2	no	—
516	C₂×C₄×C₆₁	—	4	4	no	—
517	C₂×C₄×C₆₁	—	4	2	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	2	yes	—
525	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
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	—	2	1	no	—
538	#62006	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	1	no	—
544	C₂²×C₆₁	—	2	2	no	—
545	C₂²×C₆₁	—	4	2	no	—
546	C₂²×C₆₁	—	4	2	no	—
547	C₂²×C₆₁	—	4	1	no	—
548	C₂²×C₆₁	—	4	2	no	—
549	C₂²×C₆₁	—	4	2	no	—
550	C₂²×C₆₁	—	4	1	no	—
551	C₂²×C₆₁	—	4	2	no	—
552	C₂²×C₆₁	—	4	1	no	—
553	C₂²×C₆₁	—	4	2	no	—
554	C₂²×C₆₁	—	16	4	no	—
555	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
556	C₄×C₆₁	—	2	1	no	—
557	C₄×C₆₁	—	2	2	no	—
558	C₄×C₆₁	—	2	1	no	—
559	C₄×C₆₁	—	2	2	no	—
560	C₄×C₆₁	—	2	1	no	—
561	C₄×C₆₁	—	2	2	no	—
562	C₄×C₆₁	—	2	1	no	—
563	C₄×C₆₁	—	2	2	no	—
564	C₄×C₆₁	—	4	1	no	—
565	C₄×C₆₁	—	4	1	no	—
566	C₄×C₆₁	—	4	1	no	—
567	C₄×C₆₁	—	4	1	no	—
568	C₄×C₆₁	—	4	2	no	—
569	C₄×C₆₁	—	4	1	no	—
570	C₄×C₆₁	—	4	1	no	—
571	C₄×C₆₁	—	4	2	no	—
572	C₄×C₆₁	#575	1	2	yes	—
573	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
574	C₄×C₆₁	#585	1	1	yes	characteristic
575	#3514	C₂×C₆₁	1	1	yes	characteristic, complemented
576	#3480	C₂×C₆₁	1	1	yes	characteristic, complemented
577	#3396	C₂×C₆₁	1	1	yes	characteristic, complemented
578	#3394	C₂×C₆₁	1	1	yes	characteristic, complemented
579	#3365	C₂×C₆₁	1	1	yes	characteristic, complemented
580	#3364	C₂×C₆₁	1	1	yes	characteristic, complemented
581	#3328	C₂×C₆₁	1	1	yes	characteristic, complemented
582	#3326	C₂×C₆₁	1	2	yes	complemented
583	#3324	C₂×C₆₁	1	1	yes	characteristic, complemented
584	#3322	C₂×C₆₁	1	2	yes	complemented
585	#3278	C₂×C₆₁	1	1	yes	characteristic, complemented
586	#3277	C₂×C₆₁	1	2	yes	complemented
587	#3275	C₂×C₆₁	1	2	yes	complemented
588	#3274	C₂×C₆₁	1	1	yes	characteristic, complemented
589	#3256	C₂×C₆₁	1	2	yes	complemented
590	#3251	C₂×C₆₁	1	1	yes	characteristic, complemented
591	#3211	C₂×C₆₁	1	2	yes	complemented
592	#3207	C₂×C₆₁	1	1	yes	characteristic, complemented
593	#3108	C₂×C₆₁	1	1	yes	characteristic, complemented
594	#3102	C₂×C₆₁	1	2	yes	complemented
595	#3040	C₂×C₆₁	1	2	yes	complemented
596	#3037	C₂×C₆₁	1	1	yes	characteristic, complemented
597	#2991	C₂×C₆₁	1	1	yes	characteristic, complemented
598	C₂×C₆₁	—	4	1	no	—
599	C₂×C₆₁	—	4	2	no	—
600	C₂×C₆₁	—	8	2	no	—
601	C₂×C₆₁	—	8	2	no	—
602	C₂×C₆₁	—	8	1	no	—
603	C₂×C₆₁	#3488	1	1	yes	characteristic
604	C₂×C₆₁	C₂×#575	1	1	yes	characteristic
605	C₂×C₆₁	#3584	1	1	yes	characteristic
606	C₂×#137	C₂²×C₆₁	1	2	yes	complemented
607	C₂×#137	C₂²×C₆₁	1	2	yes	complemented
608	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
609	#559	—	2	1	no	—
610	#559	C₂²×C₆₁	1	1	yes	characteristic
611	#559	C₂²×C₆₁	1	1	yes	characteristic, complemented
612	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
613	#556	—	2	1	no	—
614	#556	C₂²×C₆₁	1	1	yes	characteristic
615	#556	C₂²×C₆₁	1	1	yes	characteristic
616	#555	—	2	1	no	—
617	#553	—	2	2	no	—
618	#553	C₂²×C₆₁	1	2	yes	complemented
619	#551	—	2	2	no	—
620	#550	C₂²×C₆₁	1	1	yes	characteristic
621	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
622	#548	C₂²×C₆₁	1	2	yes	—
623	#548	C₂²×C₆₁	1	2	yes	complemented
624	#546	—	2	1	no	—
625	#546	C₂²×C₆₁	1	2	yes	—
626	D₄²	C₂²×C₆₁	1	1	yes	characteristic
627	#542	—	2	1	no	—
628	#538	—	2	2	no	—
629	#532	—	2	1	no	—
630	#532	C₂²×C₆₁	1	1	yes	characteristic
631	#532	C₂²×C₆₁	1	1	yes	characteristic, complemented
632	#529	—	2	2	no	—
633	#529	C₂²×C₆₁	1	2	yes	—
634	#529	C₂²×C₆₁	1	1	yes	characteristic
635	#529	C₂²×C₆₁	1	2	yes	complemented
636	C₂×#124	C₂²×C₆₁	1	2	yes	—
637	#518	—	2	1	no	—
638	C₄×#41	—	2	1	no	—
639	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
640	C₄×#41	C₂²×C₆₁	1	2	yes	complemented
641	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
642	#495	C₂²×C₆₁	1	2	yes	—
643	#495	C₂²×C₆₁	1	2	yes	complemented
644	#493	C₂²×C₆₁	1	1	yes	characteristic
645	#492	C₂²×C₆₁	1	1	yes	characteristic, complemented
646	#488	C₂²×C₆₁	1	2	yes	—
647	#488	C₂²×C₆₁	1	2	yes	complemented
648	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
649	#486	C₂²×C₆₁	1	1	yes	characteristic
650	#485	C₂²×C₆₁	1	2	yes	complemented
651	#483	C₂²×C₆₁	1	1	yes	characteristic, complemented
652	#482	C₂²×C₆₁	1	2	yes	—
653	#480	C₂²×C₆₁	1	1	yes	characteristic
654	#479	C₂²×C₆₁	1	1	yes	characteristic, complemented
655	#479	C₂²×C₆₁	1	1	yes	characteristic, complemented
656	#479	C₂²×C₆₁	1	2	yes	complemented
657	#478	C₂²×C₆₁	1	2	yes	complemented
658	#478	C₂²×C₆₁	1	2	yes	complemented
659	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
660	#474	C₂²×C₆₁	1	1	yes	characteristic
661	#470	C₂²×C₆₁	1	2	yes	complemented
662	#469	C₂²×C₆₁	1	2	yes	—
663	#469	C₂²×C₆₁	1	2	yes	—
664	#468	C₂²×C₆₁	1	2	yes	—
665	#468	C₂²×C₆₁	1	2	yes	complemented
666	#468	C₂²×C₆₁	1	2	yes	complemented
667	#464	C₂²×C₆₁	1	1	yes	characteristic
668	#464	C₂²×C₆₁	1	1	yes	characteristic
669	#464	C₂²×C₆₁	1	2	yes	—
670	#464	C₂²×C₆₁	1	2	yes	complemented
671	#464	C₂²×C₆₁	1	2	yes	complemented
672	#464	C₂²×C₆₁	1	2	yes	complemented
673	#464	C₂²×C₆₁	1	2	yes	complemented
674	#463	C₂²×C₆₁	1	2	yes	—
675	#463	C₂²×C₆₁	1	2	yes	—
676	#463	C₂²×C₆₁	1	2	yes	complemented
677	#463	C₂²×C₆₁	1	2	yes	complemented
678	#463	C₂²×C₆₁	1	2	yes	complemented
679	#463	C₂²×C₆₁	1	2	yes	complemented
680	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
681	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
682	#460	C₂²×C₆₁	1	1	yes	characteristic
683	#460	C₂²×C₆₁	1	1	yes	characteristic
684	#460	C₂²×C₆₁	1	1	yes	characteristic, complemented
685	#459	C₂²×C₆₁	1	1	yes	characteristic
686	#452	C₂²×C₆₁	1	2	yes	complemented
687	#451	C₂²×C₆₁	1	2	yes	complemented
688	#451	C₂²×C₆₁	1	1	yes	characteristic, complemented
689	#450	C₂²×C₆₁	1	2	yes	—
690	#449	C₂²×C₆₁	1	2	yes	—
691	#449	C₂²×C₆₁	1	2	yes	complemented
692	#449	C₂²×C₆₁	1	2	yes	complemented
693	#448	C₂²×C₆₁	1	1	yes	characteristic
694	#448	C₂²×C₆₁	1	2	yes	complemented
695	#447	C₂²×C₆₁	1	2	yes	—
696	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
697	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
698	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
699	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
700	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
701	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
702	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
703	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
704	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
705	C₄×D₈	C₂²×C₆₁	1	2	yes	complemented
706	#436	C₂²×C₆₁	1	1	yes	characteristic
707	#436	C₂²×C₆₁	1	1	yes	characteristic
708	#436	C₂²×C₆₁	1	2	yes	complemented
709	#436	C₂²×C₆₁	1	2	yes	complemented
710	#431	C₂²×C₆₁	1	2	yes	complemented
711	#431	C₂²×C₆₁	1	1	yes	characteristic, complemented
712	#423	C₂²×C₆₁	1	1	yes	characteristic, complemented
713	#423	C₂²×C₆₁	1	2	yes	complemented
714	#419	C₂²×C₆₁	1	2	yes	complemented
715	#418	C₂²×C₆₁	1	2	yes	—
716	#417	C₂²×C₆₁	1	2	yes	complemented
717	C₆₁	#62006	1	1	yes	characteristic, direct product factor, Sylow
718	C₂×#41	—	2	1	no	—
719	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
720	C₂×#41	C₂³×C₆₁	1	2	yes	—
721	C₂×#41	C₂³×C₆₁	1	2	yes	—
722	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
723	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
724	C₂²×D₄	—	2	1	no	—
725	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
726	#137	—	4	4	no	—
727	#137	—	4	4	no	—
728	AGL(1,ℤ/8)	—	4	4	no	—
729	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
730	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
731	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
732	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
733	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
734	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
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	2	yes	—
741	C₂×D₈	C₂³×C₆₁	1	2	yes	—
742	C₂×D₈	C₂³×C₆₁	1	2	yes	—
743	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
744	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
745	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
746	C₄⋊Q₈	—	2	1	no	—
747	C₄⋊Q₈	—	2	1	no	—
748	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
749	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
750	#127	—	2	1	no	—
751	#127	C₂³×C₆₁	1	1	yes	characteristic
752	#127	C₂³×C₆₁	1	1	yes	characteristic
753	#126	—	2	2	no	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	1	no	—
758	#126	—	2	2	no	—
759	#125	—	2	2	no	—
760	#125	C₂³×C₆₁	1	1	yes	characteristic
761	#125	C₂³×C₆₁	1	2	yes	—
762	#124	—	2	1	no	—
763	#124	—	2	1	no	—
764	#124	—	2	1	no	—
765	#124	—	2	2	no	—
766	#124	—	2	2	no	—
767	#124	—	2	2	no	—
768	#124	—	2	2	no	—
769	#124	—	2	1	no	—
770	#124	C₂³×C₆₁	1	1	yes	characteristic
771	#124	C₂³×C₆₁	1	2	yes	—
772	#124	C₂³×C₆₁	1	2	yes	—
773	#124	C₂³×C₆₁	1	2	yes	—
774	#124	C₂³×C₆₁	1	2	yes	—
775	#123	—	2	1	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	C₂²⋊Q₈	—	2	1	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
787	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
788	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	—	2	1	no	—
793	#121	—	2	1	no	—
794	#121	—	2	1	no	—
795	#121	—	2	1	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	C₂³×C₆₁	1	2	yes	—
799	#121	C₂³×C₆₁	1	1	yes	characteristic
800	#121	C₂³×C₆₁	1	2	yes	—
801	#121	C₂³×C₆₁	1	2	yes	—
802	#120	—	2	2	no	—
803	#120	—	2	2	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	—	2	1	no	—
807	C₄×Q₈	—	2	1	no	—
808	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
812	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
813	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
814	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
815	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
816	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
833	C₄×D₄	D₄×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	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₆₁	1	2	yes	—
840	#117	—	2	1	no	—
841	#117	—	2	2	no	—
842	#117	—	2	2	no	—
843	#117	—	2	1	no	—
844	#117	—	2	2	no	—
845	#117	D₄×C₆₁	1	1	yes	characteristic
846	#117	D₄×C₆₁	1	2	yes	—
847	#117	C₂³×C₆₁	1	2	yes	—
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
850	C₂×C₂²⋊C₄	—	2	2	no	—
851	C₂×C₂²⋊C₄	—	2	2	no	—
852	C₂×C₂²⋊C₄	—	2	2	no	—
853	C₂×C₄²	—	2	1	no	—
854	C₂×C₄²	—	2	2	no	—
855	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
856	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
857	#107	C₂³×C₆₁	1	1	yes	characteristic
858	#107	C₂³×C₆₁	1	2	yes	—
859	#107	C₂³×C₆₁	1	1	yes	characteristic
860	#106	C₂³×C₆₁	1	1	yes	characteristic
861	#106	C₂³×C₆₁	1	1	yes	characteristic
862	#106	C₂³×C₆₁	1	2	yes	—
863	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
864	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
865	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
866	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
867	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
868	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
869	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
870	#103	C₂³×C₆₁	1	2	yes	—
871	#103	C₂³×C₆₁	1	2	yes	—
872	#103	C₂³×C₆₁	1	1	yes	characteristic
873	#103	C₂³×C₆₁	1	2	yes	—
874	#103	C₂³×C₆₁	1	2	yes	—
875	#103	C₂³×C₆₁	1	1	yes	characteristic
876	#103	C₂³×C₆₁	1	1	yes	characteristic
877	#103	C₂³×C₆₁	1	1	yes	characteristic
878	#103	C₂³×C₆₁	1	1	yes	characteristic
879	#103	C₂³×C₆₁	1	1	yes	characteristic
880	#103	C₂³×C₆₁	1	2	yes	—
881	#102	C₂³×C₆₁	1	2	yes	—
882	#102	C₂³×C₆₁	1	2	yes	—
883	#102	C₂³×C₆₁	1	1	yes	characteristic
884	#102	C₂³×C₆₁	1	2	yes	—
885	#102	C₂³×C₆₁	1	2	yes	—
886	#102	C₂³×C₆₁	1	2	yes	—
887	#102	C₂³×C₆₁	1	1	yes	characteristic
888	#102	C₂³×C₆₁	1	2	yes	—
889	#102	C₂³×C₆₁	1	2	yes	—
890	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
891	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
892	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
893	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
894	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
895	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
896	C₄×C₈	C₂³×C₆₁	1	2	yes	—
897	C₄×C₈	C₂³×C₆₁	1	2	yes	—
898	C₂⁴	—	2	2	no	—
899	#41	—	2	4	no	—
900	#41	—	4	2	no	—
901	#41	—	4	2	no	—
902	#41	—	4	4	no	—
903	#41	—	4	2	no	—
904	#41	—	4	2	no	—
905	C₂×Q₈	—	2	1	no	—
906	C₂×Q₈	—	2	1	no	—
907	C₂×Q₈	—	2	2	no	—
908	C₂×Q₈	—	2	2	no	—
909	C₂×Q₈	—	4	1	no	—
910	C₂×Q₈	—	4	2	no	—
911	C₂×Q₈	—	4	2	no	—
912	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
914	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
915	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
916	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	4	2	no	—
929	C₂×D₄	—	4	2	no	—
930	C₂×D₄	—	4	4	no	—
931	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
932	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
933	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
934	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
935	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
946	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
947	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
948	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
950	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
951	Q₁₆	—	2	2	no	—
952	Q₁₆	—	2	4	no	—
953	Q₁₆	—	4	1	no	—
954	Q₁₆	—	4	2	no	—
955	SD₁₆	—	2	2	no	—
956	SD₁₆	—	2	4	no	—
957	SD₁₆	—	4	2	no	—
958	SD₁₆	—	4	1	no	—
959	SD₁₆	—	4	2	no	—
960	SD₁₆	—	4	2	no	—
961	SD₁₆	—	4	2	no	—
962	D₈	—	4	2	no	—
963	D₈	—	4	2	no	—
964	D₈	—	4	2	no	—
965	M₁₆	—	4	2	no	—
966	M₁₆	—	4	2	no	—
967	M₁₆	—	4	2	no	—
968	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
972	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
973	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	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	1	no	—
992	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
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	2	yes	—
996	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
999	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1000	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	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	C₂×D₄×C₆₁	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	C₂×D₄×C₆₁	1	2	yes	—
1035	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1036	C₄²	C₂×D₄×C₆₁	1	2	yes	—
1037	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1038	C₄²	C₂⁴×C₆₁	1	2	yes	—
1039	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1040	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	—	2	2	no	—
1044	C₂³	—	4	4	no	—
1045	C₂³	—	8	2	no	—
1046	C₂³	—	8	2	no	—
1047	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1048	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	1	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	2	2	no	—
1054	Q₈	—	2	1	no	—
1055	Q₈	—	2	2	no	—
1056	Q₈	—	2	1	no	—
1057	Q₈	—	4	2	no	—
1058	Q₈	—	4	2	no	—
1059	Q₈	—	8	2	no	—
1060	Q₈	H(5,𝔽₂)×C₆₁	1	2	yes	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	4	no	—
1070	D₄	—	4	4	no	—
1071	D₄	—	4	4	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	8	1	no	—
1075	D₄	—	8	1	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	1	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	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	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	4	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	4	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	8	2	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	1	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1108	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1109	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1111	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1112	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1113	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1114	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1115	C₈	—	2	1	no	—
1116	C₈	—	2	2	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	2	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	1	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	2	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	2	1	no	—
1126	C₂²	—	2	2	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	1	no	—
1133	C₂²	—	4	2	no	—
1134	C₂²	—	4	2	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	16	4	no	—
1137	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1138	C₄	—	2	1	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	2	1	no	—
1141	C₄	—	2	2	no	—
1142	C₄	—	2	1	no	—
1143	C₄	—	2	2	no	—
1144	C₄	—	2	1	no	—
1145	C₄	—	2	2	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	2	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	4	1	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	1	no	—
1152	C₄	—	4	2	no	—
1153	C₄	—	4	1	no	—
1154	C₄	C₆₁×#575	1	2	yes	—
1155	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1156	C₄	C₆₁×#585	1	1	yes	characteristic
1157	C₂	—	4	2	no	—
1158	C₂	—	4	1	no	—
1159	C₂	—	8	1	no	—
1160	C₂	—	8	2	no	—
1161	C₂	—	8	2	no	—
1162	C₂	C₆₁×#3488	1	1	yes	characteristic
1163	C₂	C₂×C₆₁×#575	1	1	yes	characteristic
1164	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 ◁ C₄×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3514	C₂	semidirect
2. C₆₁×#3480	C₂	semidirect
3. C₆₁×#3396	C₂	semidirect
4. C₆₁×#3394	C₂	semidirect
5. C₆₁×#3365	C₂	semidirect
6. C₆₁×#3364	C₂	semidirect
7. C₆₁×#3328	C₂	semidirect
8. C₆₁×#3326	C₂	semidirect
9. C₆₁×#3324	C₂	semidirect
10. C₆₁×#3322	C₂	semidirect
11. C₆₁×#3278	C₂	semidirect
12. C₆₁×#3277	C₂	semidirect
13. C₆₁×#3275	C₂	semidirect
14. C₆₁×#3274	C₂	semidirect
15. C₆₁×#3256	C₂	semidirect
16. C₆₁×#3251	C₂	semidirect
17. C₆₁×#3211	C₂	semidirect
18. C₆₁×#3207	C₂	semidirect
19. C₆₁×#3108	C₂	semidirect
20. C₆₁×#3102	C₂	semidirect
21. C₆₁×#3040	C₂	semidirect
22. C₆₁×#3037	C₂	semidirect
23. C₆₁×#2991	C₂	semidirect
24. C₂×#137×C₆₁	C₂²	semidirect
25. C₂×#137×C₆₁	C₂²	semidirect
29. C₆₁×#559	C₂²	semidirect
30. C₆₁×#557	C₂²	semidirect
36. C₆₁×#553	C₂²	semidirect
41. C₆₁×#548	C₂²	semidirect
49. C₆₁×#532	C₂²	semidirect
53. C₆₁×#529	C₂²	semidirect
58. C₄×#41×C₆₁	C₂²	semidirect
59. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
61. C₆₁×#495	C₂²	semidirect
63. C₆₁×#492	C₂²	semidirect
65. C₆₁×#488	C₂²	semidirect
66. C₆₁×#487	C₂²	semidirect
68. C₆₁×#485	C₂²	semidirect
69. C₆₁×#483	C₂²	semidirect
72. C₆₁×#479	C₂²	semidirect
73. C₆₁×#479	C₂²	semidirect
74. C₆₁×#479	C₂²	semidirect
75. C₆₁×#478	C₂²	semidirect
76. C₆₁×#478	C₂²	semidirect
77. C₆₁×#475	C₂²	semidirect
79. C₆₁×#470	C₂²	semidirect
83. C₆₁×#468	C₂²	semidirect
84. C₆₁×#468	C₂²	semidirect
88. C₆₁×#464	C₂²	semidirect
89. C₆₁×#464	C₂²	semidirect
90. C₆₁×#464	C₂²	semidirect
91. C₆₁×#464	C₂²	semidirect
94. C₆₁×#463	C₂²	semidirect
95. C₆₁×#463	C₂²	semidirect
96. C₆₁×#463	C₂²	semidirect
97. C₆₁×#463	C₂²	semidirect
98. C₆₁×#462	C₂²	semidirect
99. C₆₁×#462	C₂²	semidirect
102. C₆₁×#460	C₂²	semidirect
104. C₆₁×#452	C₂²	semidirect
105. C₆₁×#451	C₂²	semidirect
106. C₆₁×#451	C₂²	semidirect
109. C₆₁×#449	C₂²	semidirect
110. C₆₁×#449	C₂²	semidirect
112. C₆₁×#448	C₂²	semidirect
114. C₈×Q₈×C₆₁	C₂²	semidirect
115. C₈×Q₈×C₆₁	C₂²	semidirect
116. C₄×Q₁₆×C₆₁	C₂²	semidirect
117. C₄×Q₁₆×C₆₁	C₂²	semidirect
118. C₄×Q₁₆×C₆₁	C₂²	semidirect
121. C₄×SD₁₆×C₆₁	C₂²	semidirect
122. C₄×SD₁₆×C₆₁	C₂²	semidirect
123. C₄×D₈×C₆₁	C₂²	semidirect
126. C₆₁×#436	C₂²	semidirect
127. C₆₁×#436	C₂²	semidirect
128. C₆₁×#431	C₂²	semidirect
129. C₆₁×#431	C₂²	semidirect
130. C₆₁×#423	C₂²	semidirect
131. C₆₁×#423	C₂²	semidirect
132. C₆₁×#419	C₂²	semidirect
134. C₆₁×#417	C₂²	semidirect
538. #62006	C₆₁	direct (N × H)
575. #3514	C₂×C₆₁	semidirect
576. #3480	C₂×C₆₁	semidirect
577. #3396	C₂×C₆₁	semidirect
578. #3394	C₂×C₆₁	semidirect
579. #3365	C₂×C₆₁	semidirect
580. #3364	C₂×C₆₁	semidirect
581. #3328	C₂×C₆₁	semidirect
582. #3326	C₂×C₆₁	semidirect
583. #3324	C₂×C₆₁	semidirect
584. #3322	C₂×C₆₁	semidirect
585. #3278	C₂×C₆₁	semidirect
586. #3277	C₂×C₆₁	semidirect
587. #3275	C₂×C₆₁	semidirect
588. #3274	C₂×C₆₁	semidirect
589. #3256	C₂×C₆₁	semidirect
590. #3251	C₂×C₆₁	semidirect
591. #3211	C₂×C₆₁	semidirect
592. #3207	C₂×C₆₁	semidirect
593. #3108	C₂×C₆₁	semidirect
594. #3102	C₂×C₆₁	semidirect
595. #3040	C₂×C₆₁	semidirect
596. #3037	C₂×C₆₁	semidirect
597. #2991	C₂×C₆₁	semidirect
606. C₂×#137	C₂²×C₆₁	semidirect
607. C₂×#137	C₂²×C₆₁	semidirect
611. #559	C₂²×C₆₁	semidirect
612. #557	C₂²×C₆₁	semidirect
618. #553	C₂²×C₆₁	semidirect
623. #548	C₂²×C₆₁	semidirect
631. #532	C₂²×C₆₁	semidirect
635. #529	C₂²×C₆₁	semidirect
640. C₄×#41	C₂²×C₆₁	semidirect
641. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
643. #495	C₂²×C₆₁	semidirect
645. #492	C₂²×C₆₁	semidirect
647. #488	C₂²×C₆₁	semidirect
648. #487	C₂²×C₆₁	semidirect
650. #485	C₂²×C₆₁	semidirect
651. #483	C₂²×C₆₁	semidirect
654. #479	C₂²×C₆₁	semidirect
655. #479	C₂²×C₆₁	semidirect
656. #479	C₂²×C₆₁	semidirect
657. #478	C₂²×C₆₁	semidirect
658. #478	C₂²×C₆₁	semidirect
659. #475	C₂²×C₆₁	semidirect
661. #470	C₂²×C₆₁	semidirect
665. #468	C₂²×C₆₁	semidirect
666. #468	C₂²×C₆₁	semidirect
670. #464	C₂²×C₆₁	semidirect
671. #464	C₂²×C₆₁	semidirect
672. #464	C₂²×C₆₁	semidirect
673. #464	C₂²×C₆₁	semidirect
676. #463	C₂²×C₆₁	semidirect
677. #463	C₂²×C₆₁	semidirect
678. #463	C₂²×C₆₁	semidirect
679. #463	C₂²×C₆₁	semidirect
680. #462	C₂²×C₆₁	semidirect
681. #462	C₂²×C₆₁	semidirect
684. #460	C₂²×C₆₁	semidirect
686. #452	C₂²×C₆₁	semidirect
687. #451	C₂²×C₆₁	semidirect
688. #451	C₂²×C₆₁	semidirect
691. #449	C₂²×C₆₁	semidirect
692. #449	C₂²×C₆₁	semidirect
694. #448	C₂²×C₆₁	semidirect
696. C₈×Q₈	C₂²×C₆₁	semidirect
697. C₈×Q₈	C₂²×C₆₁	semidirect
698. C₄×Q₁₆	C₂²×C₆₁	semidirect
699. C₄×Q₁₆	C₂²×C₆₁	semidirect
700. C₄×Q₁₆	C₂²×C₆₁	semidirect
703. C₄×SD₁₆	C₂²×C₆₁	semidirect
704. C₄×SD₁₆	C₂²×C₆₁	semidirect
705. C₄×D₈	C₂²×C₆₁	semidirect
708. #436	C₂²×C₆₁	semidirect
709. #436	C₂²×C₆₁	semidirect
710. #431	C₂²×C₆₁	semidirect
711. #431	C₂²×C₆₁	semidirect
712. #423	C₂²×C₆₁	semidirect
713. #423	C₂²×C₆₁	semidirect
714. #419	C₂²×C₆₁	semidirect
716. #417	C₂²×C₆₁	semidirect
717. C₆₁	#62006	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×#3514	2
C₆₁×#3480	2
C₆₁×#3396	2
C₆₁×#3394	2
C₆₁×#3365	2
C₆₁×#3364	2
C₆₁×#3328	2
C₆₁×#3326	2
C₆₁×#3324	2
C₆₁×#3322	2
C₆₁×#3278	2
C₆₁×#3277	2
C₆₁×#3275	2
C₆₁×#3274	2
C₆₁×#3256	2
C₆₁×#3251	2
C₆₁×#3211	2
C₆₁×#3207	2
C₆₁×#3108	2
C₆₁×#3102	2
C₆₁×#3040	2
C₆₁×#3037	2
C₆₁×#2991	2
#62006	61

Subgroups — C61×#62006 #29565439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62006 #29565439