Subgroups — C₆₁×#62044 #29565477

Order 15616.

1830 conjugacy classes of subgroups.

The subgroup lattice has 1164 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
2	C₆₁×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3392	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×#3324	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3323	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3317	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3278	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3266	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3258	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3222	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₁×#3121	C₂	1	2	yes	maximal, complemented
20	C₆₁×#3103	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3043	C₂	1	2	yes	maximal, complemented
22	C₆₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#2993	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	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
27	C₆₁×#560	—	2	2	no	—
28	C₆₁×#557	—	2	1	no	—
29	C₆₁×#557	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×#553	—	2	1	no	—
35	C₆₁×#552	—	2	2	no	—
36	C₆₁×#552	C₂²	1	2	yes	complemented
37	C₆₁×#550	C₂²	1	2	yes	—
38	C₆₁×#550	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
40	D₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
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×#541	—	2	2	no	—
47	C₆₁×#541	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×#533	—	2	1	no	—
53	C₆₁×#533	C₂²	1	1	yes	characteristic, complemented
54	C₆₁×#532	C₂²	1	1	yes	characteristic
55	C₆₁×#532	C₂²	1	1	yes	characteristic
56	C₆₁×#529	—	2	1	no	—
57	C₆₁×#529	C₂²	1	1	yes	characteristic
58	C₆₁×#519	C₂²	1	2	yes	complemented
59	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
60	C₆₁×#497	C₂²	1	2	yes	—
61	C₆₁×#494	C₂²	1	1	yes	characteristic, complemented
62	C₆₁×#492	C₂²	1	1	yes	characteristic
63	C₆₁×#492	C₂²	1	2	yes	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×#485	C₂²	1	2	yes	complemented
69	C₆₁×#482	C₂²	1	2	yes	—
70	C₆₁×#481	C₂²	1	1	yes	characteristic
71	C₆₁×#481	C₂²	1	1	yes	characteristic, complemented
72	C₆₁×#479	C₂²	1	2	yes	complemented
73	C₆₁×#478	C₂²	1	2	yes	complemented
74	C₆₁×#477	C₂²	1	2	yes	complemented
75	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
76	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
77	C₆₁×#474	C₂²	1	1	yes	characteristic
78	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
79	C₆₁×#470	C₂²	1	2	yes	complemented
80	C₆₁×#468	C₂²	1	2	yes	—
81	C₆₁×#468	C₂²	1	2	yes	—
82	C₆₁×#468	C₂²	1	2	yes	complemented
83	C₆₁×#467	C₂²	1	2	yes	complemented
84	C₆₁×#465	C₂²	1	2	yes	—
85	C₆₁×#464	C₂²	1	2	yes	—
86	C₆₁×#464	C₂²	1	2	yes	—
87	C₆₁×#464	C₂²	1	2	yes	complemented
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×#462	C₂²	1	1	yes	characteristic, complemented
92	C₆₁×#462	C₂²	1	1	yes	characteristic, complemented
93	C₆₁×#462	C₂²	1	2	yes	complemented
94	C₆₁×#461	C₂²	1	1	yes	characteristic
95	C₆₁×#461	C₂²	1	1	yes	characteristic, complemented
96	C₆₁×#461	C₂²	1	2	yes	complemented
97	C₆₁×#460	C₂²	1	1	yes	characteristic
98	C₆₁×#460	C₂²	1	1	yes	characteristic
99	C₆₁×#460	C₂²	1	1	yes	characteristic
100	C₆₁×#460	C₂²	1	2	yes	—
101	C₆₁×#460	C₂²	1	1	yes	characteristic
102	C₆₁×#460	C₂²	1	2	yes	complemented
103	C₆₁×#460	C₂²	1	2	yes	complemented
104	C₆₁×#452	C₂²	1	2	yes	complemented
105	C₆₁×#452	C₂²	1	2	yes	complemented
106	C₆₁×#452	C₂²	1	2	yes	complemented
107	C₆₁×#452	C₂²	1	2	yes	complemented
108	C₆₁×#451	C₂²	1	2	yes	complemented
109	C₆₁×#450	C₂²	1	2	yes	—
110	C₆₁×#450	C₂²	1	2	yes	—
111	C₆₁×#448	C₂²	1	1	yes	characteristic
112	C₆₁×#448	C₂²	1	2	yes	—
113	C₆₁×#448	C₂²	1	1	yes	characteristic, complemented
114	C₆₁×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
116	C₆₁×#441	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
121	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
122	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
123	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
124	C₆₁×#436	C₂²	1	1	yes	characteristic
125	C₆₁×#436	C₂²	1	2	yes	complemented
126	C₆₁×#435	C₂²	1	2	yes	complemented
127	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
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	C₆₁×#423	C₂²	1	1	yes	characteristic, complemented
132	C₆₁×#418	C₂²	1	2	yes	—
133	C₆₁×#417	C₂²	1	2	yes	complemented
134	C₆₁×#416	C₂²	1	2	yes	complemented
135	C₂×#41×C₆₁	—	2	1	no	—
136	C₂×#41×C₆₁	—	2	1	no	—
137	C₂×#41×C₆₁	C₂³	1	2	yes	—
138	C₂×#41×C₆₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
140	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
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	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₆₁	—	4	4	no	—
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×SD₁₆×C₆₁	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
158	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
160	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
161	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
162	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₆₁	—	2	1	no	—
164	C₄⋊Q₈×C₆₁	—	2	1	no	—
165	C₄⋊Q₈×C₆₁	—	2	2	no	—
166	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
169	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
171	#127×C₆₁	—	2	2	no	—
172	#127×C₆₁	C₂³	1	1	yes	characteristic
173	#127×C₆₁	C₂³	1	1	yes	characteristic
174	#127×C₆₁	C₂³	1	2	yes	—
175	#126×C₆₁	—	2	2	no	—
176	#126×C₆₁	—	2	2	no	—
177	#126×C₆₁	—	2	2	no	—
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	—	2	2	no	—
184	#125×C₆₁	—	2	2	no	—
185	#125×C₆₁	—	2	2	no	—
186	#125×C₆₁	—	2	2	no	—
187	#125×C₆₁	—	2	1	no	—
188	#125×C₆₁	—	2	1	no	—
189	#125×C₆₁	D₄	1	1	yes	characteristic
190	#125×C₆₁	C₂³	1	2	yes	—
191	#124×C₆₁	—	2	1	no	—
192	#124×C₆₁	—	2	2	no	—
193	#124×C₆₁	—	2	1	no	—
194	#124×C₆₁	D₄	1	1	yes	characteristic
195	#124×C₆₁	C₂³	1	2	yes	—
196	#124×C₆₁	C₂³	1	2	yes	—
197	#123×C₆₁	—	2	2	no	—
198	#123×C₆₁	—	2	2	no	—
199	#123×C₆₁	—	2	2	no	—
200	#123×C₆₁	—	2	2	no	—
201	#123×C₆₁	D₄	1	2	yes	—
202	C₂²⋊Q₈×C₆₁	—	2	1	no	—
203	C₂²⋊Q₈×C₆₁	—	2	1	no	—
204	C₂²⋊Q₈×C₆₁	—	2	2	no	—
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	D₄	1	1	yes	characteristic
209	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
210	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
211	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
212	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
213	#121×C₆₁	—	2	1	no	—
214	#121×C₆₁	—	2	1	no	—
215	#121×C₆₁	—	2	1	no	—
216	#121×C₆₁	—	2	1	no	—
217	#121×C₆₁	—	2	1	no	—
218	#121×C₆₁	—	2	2	no	—
219	#121×C₆₁	—	2	2	no	—
220	#121×C₆₁	—	2	1	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	#120×C₆₁	—	2	2	no	—
230	#120×C₆₁	—	2	2	no	—
231	#120×C₆₁	—	2	2	no	—
232	#120×C₆₁	—	2	2	no	—
233	C₄×Q₈×C₆₁	—	2	1	no	—
234	C₄×Q₈×C₆₁	—	2	2	no	—
235	C₄×Q₈×C₆₁	—	2	1	no	—
236	C₄×Q₈×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	—	2	1	no	—
241	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
242	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
243	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
244	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
245	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
246	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
247	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
249	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₆₁	—	2	1	no	—
251	C₄×D₄×C₆₁	—	2	2	no	—
252	C₄×D₄×C₆₁	—	2	2	no	—
253	C₄×D₄×C₆₁	—	2	1	no	—
254	C₄×D₄×C₆₁	—	2	1	no	—
255	C₄×D₄×C₆₁	—	2	1	no	—
256	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
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	#117×C₆₁	—	2	1	no	—
262	#117×C₆₁	—	2	1	no	—
263	#117×C₆₁	—	2	2	no	—
264	#117×C₆₁	—	2	2	no	—
265	#117×C₆₁	—	2	2	no	—
266	#117×C₆₁	C₂³	1	2	yes	—
267	#117×C₆₁	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
269	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
270	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
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	2	yes	—
275	#107×C₆₁	C₂³	1	2	yes	—
276	#106×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	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	1	yes	characteristic
293	#103×C₆₁	C₂³	1	1	yes	characteristic
294	#103×C₆₁	C₂³	1	2	yes	—
295	#103×C₆₁	C₂³	1	2	yes	—
296	#103×C₆₁	C₂³	1	2	yes	—
297	#102×C₆₁	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
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	—	4	2	no	—
317	#41×C₆₁	—	4	2	no	—
318	#41×C₆₁	—	4	2	no	—
319	#41×C₆₁	—	4	2	no	—
320	#41×C₆₁	—	8	2	no	—
321	#41×C₆₁	—	8	2	no	—
322	C₂×Q₈×C₆₁	—	2	1	no	—
323	C₂×Q₈×C₆₁	—	2	2	no	—
324	C₂×Q₈×C₆₁	—	2	1	no	—
325	C₂×Q₈×C₆₁	—	2	1	no	—
326	C₂×Q₈×C₆₁	—	2	4	no	—
327	C₂×Q₈×C₆₁	—	2	2	no	—
328	C₂×Q₈×C₆₁	—	4	2	no	—
329	C₂×Q₈×C₆₁	—	4	1	no	—
330	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₆₁	—	2	1	no	—
336	C₂×D₄×C₆₁	—	2	2	no	—
337	C₂×D₄×C₆₁	—	2	2	no	—
338	C₂×D₄×C₆₁	—	2	2	no	—
339	C₂×D₄×C₆₁	—	2	1	no	—
340	C₂×D₄×C₆₁	—	2	1	no	—
341	C₂×D₄×C₆₁	—	2	1	no	—
342	C₂×D₄×C₆₁	—	2	1	no	—
343	C₂×D₄×C₆₁	—	2	2	no	—
344	C₂×D₄×C₆₁	—	2	1	no	—
345	C₂×D₄×C₆₁	—	2	2	no	—
346	C₂×D₄×C₆₁	—	2	2	no	—
347	C₂×D₄×C₆₁	—	4	2	no	—
348	C₂×D₄×C₆₁	—	4	2	no	—
349	C₂×D₄×C₆₁	—	8	2	no	—
350	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
351	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
354	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₆₁	—	2	1	no	—
356	C₂²×C₄×C₆₁	—	2	1	no	—
357	C₂²×C₄×C₆₁	—	2	2	no	—
358	C₂²×C₄×C₆₁	—	2	1	no	—
359	C₂²×C₄×C₆₁	—	2	1	no	—
360	C₂²×C₄×C₆₁	—	2	2	no	—
361	C₂²×C₄×C₆₁	—	2	2	no	—
362	C₂²×C₄×C₆₁	—	2	2	no	—
363	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
367	Q₁₆×C₆₁	—	2	4	no	—
368	Q₁₆×C₆₁	—	4	2	no	—
369	Q₁₆×C₆₁	—	4	2	no	—
370	Q₁₆×C₆₁	—	4	2	no	—
371	SD₁₆×C₆₁	—	2	2	no	—
372	SD₁₆×C₆₁	—	2	4	no	—
373	SD₁₆×C₆₁	—	2	2	no	—
374	SD₁₆×C₆₁	—	4	2	no	—
375	SD₁₆×C₆₁	—	4	2	no	—
376	SD₁₆×C₆₁	—	4	2	no	—
377	SD₁₆×C₆₁	—	4	1	no	—
378	SD₁₆×C₆₁	—	4	1	no	—
379	SD₁₆×C₆₁	—	4	2	no	—
380	SD₁₆×C₆₁	—	4	2	no	—
381	M₁₆×C₆₁	—	4	2	no	—
382	M₁₆×C₆₁	—	4	2	no	—
383	C₂×C₈×C₆₁	—	4	2	no	—
384	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
388	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
390	C₄⋊C₄×C₆₁	—	2	1	no	—
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	2	no	—
396	C₄⋊C₄×C₆₁	—	2	1	no	—
397	C₄⋊C₄×C₆₁	—	2	2	no	—
398	C₄⋊C₄×C₆₁	—	2	2	no	—
399	C₄⋊C₄×C₆₁	—	2	2	no	—
400	C₄⋊C₄×C₆₁	—	2	1	no	—
401	C₄⋊C₄×C₆₁	—	2	2	no	—
402	C₄⋊C₄×C₆₁	—	2	1	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	1	no	—
407	C₄⋊C₄×C₆₁	—	2	2	no	—
408	C₄⋊C₄×C₆₁	—	2	2	no	—
409	C₄⋊C₄×C₆₁	—	2	2	no	—
410	C₄⋊C₄×C₆₁	—	2	2	no	—
411	C₄⋊C₄×C₆₁	—	2	2	no	—
412	C₄⋊C₄×C₆₁	—	2	2	no	—
413	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
415	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
418	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
422	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
424	C₂²⋊C₄×C₆₁	—	2	2	no	—
425	C₂²⋊C₄×C₆₁	—	2	2	no	—
426	C₂²⋊C₄×C₆₁	—	2	2	no	—
427	C₂²⋊C₄×C₆₁	—	2	2	no	—
428	C₂²⋊C₄×C₆₁	—	2	2	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	2	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	1	no	—
439	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
444	C₄²×C₆₁	—	2	1	no	—
445	C₄²×C₆₁	—	2	1	no	—
446	C₄²×C₆₁	—	2	1	no	—
447	C₄²×C₆₁	—	2	1	no	—
448	C₄²×C₆₁	—	2	2	no	—
449	C₄²×C₆₁	—	2	2	no	—
450	C₄²×C₆₁	—	2	2	no	—
451	C₄²×C₆₁	—	2	2	no	—
452	C₄²×C₆₁	—	2	2	no	—
453	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
456	C₄²×C₆₁	C₂⁴	1	2	yes	—
457	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
458	C₂³×C₆₁	—	2	1	no	—
459	C₂³×C₆₁	—	2	2	no	—
460	C₂³×C₆₁	—	2	1	no	—
461	C₂³×C₆₁	—	8	2	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	2	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	2	no	—
474	Q₈×C₆₁	—	4	2	no	—
475	Q₈×C₆₁	—	4	4	no	—
476	Q₈×C₆₁	—	4	2	no	—
477	Q₈×C₆₁	—	8	1	no	—
478	Q₈×C₆₁	H(5,𝔽₂)	1	2	yes	—
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	2	no	—
485	D₄×C₆₁	—	2	1	no	—
486	D₄×C₆₁	—	4	2	no	—
487	D₄×C₆₁	—	4	2	no	—
488	D₄×C₆₁	—	8	1	no	—
489	D₄×C₆₁	—	8	1	no	—
490	D₄×C₆₁	—	8	2	no	—
491	D₄×C₆₁	—	8	2	no	—
492	D₄×C₆₁	—	8	1	no	—
493	D₄×C₆₁	—	8	2	no	—
494	D₄×C₆₁	—	8	2	no	—
495	D₄×C₆₁	—	8	2	no	—
496	D₄×C₆₁	—	8	2	no	—
497	D₄×C₆₁	—	8	1	no	—
498	D₄×C₆₁	—	8	1	no	—
499	C₂×C₄×C₆₁	—	2	1	no	—
500	C₂×C₄×C₆₁	—	2	2	no	—
501	C₂×C₄×C₆₁	—	2	2	no	—
502	C₂×C₄×C₆₁	—	2	1	no	—
503	C₂×C₄×C₆₁	—	2	2	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	—	2	2	no	—
512	C₂×C₄×C₆₁	—	2	1	no	—
513	C₂×C₄×C₆₁	—	4	1	no	—
514	C₂×C₄×C₆₁	—	4	2	no	—
515	C₂×C₄×C₆₁	—	4	4	no	—
516	C₂×C₄×C₆₁	—	4	2	no	—
517	C₂×C₄×C₆₁	—	4	2	no	—
518	C₂×C₄×C₆₁	—	4	2	no	—
519	C₂×C₄×C₆₁	—	8	2	no	—
520	C₂×C₄×C₆₁	—	8	2	no	—
521	C₂×C₄×C₆₁	—	8	2	no	—
522	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
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	2	yes	—
527	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
531	C₈×C₆₁	—	2	1	no	—
532	C₈×C₆₁	—	2	2	no	—
533	C₈×C₆₁	—	2	1	no	—
534	C₈×C₆₁	—	2	2	no	—
535	C₈×C₆₁	—	2	1	no	—
536	C₈×C₆₁	—	2	1	no	—
537	#62044	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
538	C₂²×C₆₁	—	2	1	no	—
539	C₂²×C₆₁	—	2	2	no	—
540	C₂²×C₆₁	—	2	1	no	—
541	C₂²×C₆₁	—	2	2	no	—
542	C₂²×C₆₁	—	2	1	no	—
543	C₂²×C₆₁	—	2	2	no	—
544	C₂²×C₆₁	—	4	1	no	—
545	C₂²×C₆₁	—	4	2	no	—
546	C₂²×C₆₁	—	4	1	no	—
547	C₂²×C₆₁	—	4	1	no	—
548	C₂²×C₆₁	—	4	2	no	—
549	C₂²×C₆₁	—	4	1	no	—
550	C₂²×C₆₁	—	4	1	no	—
551	C₂²×C₆₁	—	4	1	no	—
552	C₂²×C₆₁	—	4	2	no	—
553	C₂²×C₆₁	—	16	4	no	—
554	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
555	C₄×C₆₁	—	2	1	no	—
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	2	no	—
561	C₄×C₆₁	—	2	1	no	—
562	C₄×C₆₁	—	2	2	no	—
563	C₄×C₆₁	—	4	1	no	—
564	C₄×C₆₁	—	4	1	no	—
565	C₄×C₆₁	—	4	2	no	—
566	C₄×C₆₁	—	4	1	no	—
567	C₄×C₆₁	—	4	2	no	—
568	C₄×C₆₁	—	4	1	no	—
569	C₄×C₆₁	—	4	1	no	—
570	C₄×C₆₁	—	4	2	no	—
571	C₄×C₆₁	#577	1	2	yes	—
572	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
573	C₄×C₆₁	#585	1	1	yes	characteristic
574	#3546	C₂×C₆₁	1	1	yes	characteristic
575	#3523	C₂×C₆₁	1	1	yes	characteristic, complemented
576	#3398	C₂×C₆₁	1	1	yes	characteristic, complemented
577	#3392	C₂×C₆₁	1	1	yes	characteristic, complemented
578	#3368	C₂×C₆₁	1	1	yes	characteristic, complemented
579	#3364	C₂×C₆₁	1	1	yes	characteristic, complemented
580	#3324	C₂×C₆₁	1	1	yes	characteristic, complemented
581	#3323	C₂×C₆₁	1	2	yes	complemented
582	#3317	C₂×C₆₁	1	2	yes	complemented
583	#3302	C₂×C₆₁	1	1	yes	characteristic, complemented
584	D₄×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
585	#3278	C₂×C₆₁	1	2	yes	complemented
586	#3276	C₂×C₆₁	1	1	yes	characteristic, complemented
587	#3266	C₂×C₆₁	1	2	yes	complemented
588	#3258	C₂×C₆₁	1	2	yes	complemented
589	#3254	C₂×C₆₁	1	1	yes	characteristic, complemented
590	#3222	C₂×C₆₁	1	2	yes	complemented
591	#3210	C₂×C₆₁	1	1	yes	characteristic, complemented
592	#3121	C₂×C₆₁	1	2	yes	complemented
593	#3103	C₂×C₆₁	1	1	yes	characteristic, complemented
594	#3043	C₂×C₆₁	1	2	yes	complemented
595	#3037	C₂×C₆₁	1	1	yes	characteristic, complemented
596	#2993	C₂×C₆₁	1	1	yes	characteristic, complemented
597	C₂×C₆₁	—	4	1	no	—
598	C₂×C₆₁	—	4	2	no	—
599	C₂×C₆₁	—	8	1	no	—
600	C₂×C₆₁	—	8	2	no	—
601	C₂×C₆₁	—	8	1	no	—
602	C₂×C₆₁	#3488	1	1	yes	characteristic
603	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
604	C₂×C₆₁	#3586	1	1	yes	characteristic
605	C₂×#137	C₂²×C₆₁	1	2	yes	complemented
606	C₂×#137	C₂²×C₆₁	1	2	yes	complemented
607	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
608	#560	—	2	2	no	—
609	#557	—	2	1	no	—
610	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
611	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
612	#556	—	2	1	no	—
613	#556	C₂²×C₆₁	1	1	yes	characteristic
614	#556	C₂²×C₆₁	1	1	yes	characteristic
615	#553	—	2	1	no	—
616	#552	—	2	2	no	—
617	#552	C₂²×C₆₁	1	2	yes	complemented
618	#550	C₂²×C₆₁	1	2	yes	—
619	#550	C₂²×C₆₁	1	1	yes	characteristic
620	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
621	D₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
622	#547	C₂²×C₆₁	1	1	yes	characteristic
623	#546	—	2	1	no	—
624	#546	C₂²×C₆₁	1	2	yes	—
625	D₄²	C₂²×C₆₁	1	1	yes	characteristic
626	#542	C₂²×C₆₁	1	2	yes	—
627	#541	—	2	2	no	—
628	#541	C₂²×C₆₁	1	2	yes	complemented
629	#538	—	2	2	no	—
630	#537	—	2	1	no	—
631	#535	—	2	1	no	—
632	#535	C₂²×C₆₁	1	2	yes	—
633	#533	—	2	1	no	—
634	#533	C₂²×C₆₁	1	1	yes	characteristic, complemented
635	#532	C₂²×C₆₁	1	1	yes	characteristic
636	#532	C₂²×C₆₁	1	1	yes	characteristic
637	#529	—	2	1	no	—
638	#529	C₂²×C₆₁	1	1	yes	characteristic
639	#519	C₂²×C₆₁	1	2	yes	complemented
640	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
641	#497	C₂²×C₆₁	1	2	yes	—
642	#494	C₂²×C₆₁	1	1	yes	characteristic, complemented
643	#492	C₂²×C₆₁	1	1	yes	characteristic
644	#492	C₂²×C₆₁	1	2	yes	complemented
645	#490	C₂²×C₆₁	1	2	yes	complemented
646	#488	C₂²×C₆₁	1	2	yes	—
647	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
648	#486	C₂²×C₆₁	1	1	yes	characteristic
649	#485	C₂²×C₆₁	1	2	yes	complemented
650	#482	C₂²×C₆₁	1	2	yes	—
651	#481	C₂²×C₆₁	1	1	yes	characteristic
652	#481	C₂²×C₆₁	1	1	yes	characteristic, complemented
653	#479	C₂²×C₆₁	1	2	yes	complemented
654	#478	C₂²×C₆₁	1	2	yes	complemented
655	#477	C₂²×C₆₁	1	2	yes	complemented
656	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
657	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
658	#474	C₂²×C₆₁	1	1	yes	characteristic
659	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
660	#470	C₂²×C₆₁	1	2	yes	complemented
661	#468	C₂²×C₆₁	1	2	yes	—
662	#468	C₂²×C₆₁	1	2	yes	—
663	#468	C₂²×C₆₁	1	2	yes	complemented
664	#467	C₂²×C₆₁	1	2	yes	complemented
665	#465	C₂²×C₆₁	1	2	yes	—
666	#464	C₂²×C₆₁	1	2	yes	—
667	#464	C₂²×C₆₁	1	2	yes	—
668	#464	C₂²×C₆₁	1	2	yes	complemented
669	#464	C₂²×C₆₁	1	2	yes	complemented
670	#464	C₂²×C₆₁	1	2	yes	complemented
671	#464	C₂²×C₆₁	1	2	yes	complemented
672	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
673	#462	C₂²×C₆₁	1	2	yes	complemented
674	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
675	#461	C₂²×C₆₁	1	1	yes	characteristic
676	#461	C₂²×C₆₁	1	1	yes	characteristic, complemented
677	#461	C₂²×C₆₁	1	2	yes	complemented
678	#460	C₂²×C₆₁	1	1	yes	characteristic
679	#460	C₂²×C₆₁	1	1	yes	characteristic
680	#460	C₂²×C₆₁	1	1	yes	characteristic
681	#460	C₂²×C₆₁	1	1	yes	characteristic
682	#460	C₂²×C₆₁	1	2	yes	—
683	#460	C₂²×C₆₁	1	2	yes	complemented
684	#460	C₂²×C₆₁	1	2	yes	complemented
685	#452	C₂²×C₆₁	1	2	yes	complemented
686	#452	C₂²×C₆₁	1	2	yes	complemented
687	#452	C₂²×C₆₁	1	2	yes	complemented
688	#452	C₂²×C₆₁	1	2	yes	complemented
689	#451	C₂²×C₆₁	1	2	yes	complemented
690	#450	C₂²×C₆₁	1	2	yes	—
691	#450	C₂²×C₆₁	1	2	yes	—
692	#448	C₂²×C₆₁	1	1	yes	characteristic
693	#448	C₂²×C₆₁	1	2	yes	—
694	#448	C₂²×C₆₁	1	1	yes	characteristic, complemented
695	#446	C₂²×C₆₁	1	1	yes	characteristic, complemented
696	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
697	#441	C₂²×C₆₁	1	2	yes	complemented
698	#440	C₂²×C₆₁	1	2	yes	complemented
699	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
700	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
701	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
702	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
703	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
704	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
705	#436	C₂²×C₆₁	1	1	yes	characteristic
706	#436	C₂²×C₆₁	1	2	yes	complemented
707	#435	C₂²×C₆₁	1	2	yes	complemented
708	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
709	#433	C₂²×C₆₁	1	2	yes	complemented
710	#431	C₂²×C₆₁	1	1	yes	characteristic, complemented
711	#424	C₂²×C₆₁	1	2	yes	complemented
712	#423	C₂²×C₆₁	1	1	yes	characteristic, complemented
713	#418	C₂²×C₆₁	1	2	yes	—
714	#417	C₂²×C₆₁	1	2	yes	complemented
715	#416	C₂²×C₆₁	1	2	yes	complemented
716	C₆₁	#62044	1	1	yes	characteristic, direct product factor, Sylow
717	C₂×#41	—	2	1	no	—
718	C₂×#41	—	2	1	no	—
719	C₂×#41	C₂³×C₆₁	1	2	yes	—
720	C₂×#41	C₂³×C₆₁	1	2	yes	—
721	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
722	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
723	C₂²×D₄	—	2	1	no	—
724	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
725	#137	—	4	4	no	—
726	#137	—	4	4	no	—
727	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
728	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
729	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
730	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
731	C₂×SD₁₆	—	4	4	no	—
732	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
733	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
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	2	yes	—
739	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
740	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
742	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
743	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
744	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
745	C₄⋊Q₈	—	2	1	no	—
746	C₄⋊Q₈	—	2	1	no	—
747	C₄⋊Q₈	—	2	2	no	—
748	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
749	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
750	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
751	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
752	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
753	#127	—	2	2	no	—
754	#127	C₂³×C₆₁	1	1	yes	characteristic
755	#127	C₂³×C₆₁	1	1	yes	characteristic
756	#127	C₂³×C₆₁	1	2	yes	—
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#126	—	2	2	no	—
760	#126	—	2	2	no	—
761	#126	—	2	2	no	—
762	#126	—	2	2	no	—
763	#126	D₄×C₆₁	1	2	yes	—
764	#125	—	2	1	no	—
765	#125	—	2	2	no	—
766	#125	—	2	2	no	—
767	#125	—	2	2	no	—
768	#125	—	2	2	no	—
769	#125	—	2	2	no	—
770	#125	—	2	1	no	—
771	#125	D₄×C₆₁	1	1	yes	characteristic
772	#125	C₂³×C₆₁	1	2	yes	—
773	#124	—	2	1	no	—
774	#124	—	2	2	no	—
775	#124	—	2	1	no	—
776	#124	D₄×C₆₁	1	1	yes	characteristic
777	#124	C₂³×C₆₁	1	2	yes	—
778	#124	C₂³×C₆₁	1	2	yes	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	D₄×C₆₁	1	2	yes	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	—	2	1	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
791	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
792	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
793	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
794	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
795	#121	—	2	1	no	—
796	#121	—	2	1	no	—
797	#121	—	2	1	no	—
798	#121	—	2	1	no	—
799	#121	—	2	1	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	1	no	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	D₄×C₆₁	1	1	yes	characteristic
808	#121	C₂³×C₆₁	1	1	yes	characteristic
809	#121	C₂³×C₆₁	1	1	yes	characteristic
810	#121	C₂³×C₆₁	1	2	yes	—
811	#120	—	2	2	no	—
812	#120	—	2	2	no	—
813	#120	—	2	2	no	—
814	#120	—	2	2	no	—
815	C₄×Q₈	—	2	1	no	—
816	C₄×Q₈	—	2	2	no	—
817	C₄×Q₈	—	2	2	no	—
818	C₄×Q₈	—	2	1	no	—
819	C₄×Q₈	—	2	1	no	—
820	C₄×Q₈	—	2	1	no	—
821	C₄×Q₈	—	2	1	no	—
822	C₄×Q₈	—	2	1	no	—
823	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
824	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
825	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
826	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
827	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
828	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
829	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
830	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
831	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
840	C₄×D₄	C₂³×C₆₁	1	2	yes	—
841	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
842	C₄×D₄	C₂³×C₆₁	1	2	yes	—
843	#117	—	2	1	no	—
844	#117	—	2	1	no	—
845	#117	—	2	2	no	—
846	#117	—	2	2	no	—
847	#117	—	2	2	no	—
848	#117	C₂³×C₆₁	1	2	yes	—
849	#117	C₂³×C₆₁	1	2	yes	—
850	C₂×C₄⋊C₄	—	2	1	no	—
851	C₂×C₄⋊C₄	—	2	1	no	—
852	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
853	C₂×C₂²⋊C₄	—	2	2	no	—
854	C₂×C₄²	—	2	1	no	—
855	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
856	#107	C₂³×C₆₁	1	2	yes	—
857	#107	C₂³×C₆₁	1	2	yes	—
858	#106	C₂³×C₆₁	1	1	yes	characteristic
859	#106	C₂³×C₆₁	1	1	yes	characteristic
860	#106	C₂³×C₆₁	1	1	yes	characteristic
861	#106	C₂³×C₆₁	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
863	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
864	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
865	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
866	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
867	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
868	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
869	#103	C₂³×C₆₁	1	2	yes	—
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	1	yes	characteristic
874	#103	C₂³×C₆₁	1	1	yes	characteristic
875	#103	C₂³×C₆₁	1	1	yes	characteristic
876	#103	C₂³×C₆₁	1	2	yes	—
877	#103	C₂³×C₆₁	1	2	yes	—
878	#103	C₂³×C₆₁	1	2	yes	—
879	#102	C₂³×C₆₁	1	1	yes	characteristic
880	#102	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	1	yes	characteristic
887	#102	C₂³×C₆₁	1	1	yes	characteristic
888	#102	C₂³×C₆₁	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
890	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
891	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
892	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
893	#97	C₂³×C₆₁	1	2	yes	—
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	C₂⁴	—	2	2	no	—
898	#41	—	4	2	no	—
899	#41	—	4	2	no	—
900	#41	—	4	2	no	—
901	#41	—	4	2	no	—
902	#41	—	8	2	no	—
903	#41	—	8	2	no	—
904	C₂×Q₈	—	2	1	no	—
905	C₂×Q₈	—	2	2	no	—
906	C₂×Q₈	—	2	1	no	—
907	C₂×Q₈	—	2	1	no	—
908	C₂×Q₈	—	2	4	no	—
909	C₂×Q₈	—	2	2	no	—
910	C₂×Q₈	—	4	2	no	—
911	C₂×Q₈	—	4	1	no	—
912	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
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	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	1	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	4	2	no	—
930	C₂×D₄	—	4	2	no	—
931	C₂×D₄	—	8	2	no	—
932	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
933	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
934	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
935	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
936	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	1	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	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	1	yes	characteristic
947	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
948	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
949	Q₁₆	—	2	4	no	—
950	Q₁₆	—	4	2	no	—
951	Q₁₆	—	4	2	no	—
952	Q₁₆	—	4	2	no	—
953	SD₁₆	—	2	2	no	—
954	SD₁₆	—	2	4	no	—
955	SD₁₆	—	2	2	no	—
956	SD₁₆	—	4	2	no	—
957	SD₁₆	—	4	2	no	—
958	SD₁₆	—	4	2	no	—
959	SD₁₆	—	4	1	no	—
960	SD₁₆	—	4	1	no	—
961	SD₁₆	—	4	2	no	—
962	SD₁₆	—	4	2	no	—
963	M₁₆	—	4	2	no	—
964	M₁₆	—	4	2	no	—
965	C₂×C₈	—	4	2	no	—
966	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
967	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
968	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
970	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
971	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
996	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
997	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
998	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
999	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1000	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1001	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1002	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1003	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1004	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1005	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1022	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
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	1	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	2	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	—	2	2	no	—
1034	C₄²	—	2	2	no	—
1035	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1036	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1037	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1038	C₄²	C₂⁴×C₆₁	1	2	yes	—
1039	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	2	no	—
1042	C₂³	—	2	1	no	—
1043	C₂³	—	8	2	no	—
1044	C₂³	—	8	2	no	—
1045	C₂³	—	8	2	no	—
1046	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1047	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	1	no	—
1050	Q₈	—	2	2	no	—
1051	Q₈	—	2	1	no	—
1052	Q₈	—	2	2	no	—
1053	Q₈	—	2	1	no	—
1054	Q₈	—	2	2	no	—
1055	Q₈	—	2	2	no	—
1056	Q₈	—	4	2	no	—
1057	Q₈	—	4	4	no	—
1058	Q₈	—	4	2	no	—
1059	Q₈	—	8	1	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	1	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	8	1	no	—
1071	D₄	—	8	1	no	—
1072	D₄	—	8	2	no	—
1073	D₄	—	8	2	no	—
1074	D₄	—	8	1	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	2	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	1	no	—
1080	D₄	—	8	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	4	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	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	C₂²×D₄×C₆₁	1	1	yes	characteristic
1105	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1106	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
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	1	yes	characteristic
1112	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1113	C₈	—	2	1	no	—
1114	C₈	—	2	2	no	—
1115	C₈	—	2	1	no	—
1116	C₈	—	2	2	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₂²	—	2	1	no	—
1120	C₂²	—	2	2	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	2	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	2	2	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	4	2	no	—
1130	C₂²	—	4	1	no	—
1131	C₂²	—	4	1	no	—
1132	C₂²	—	4	2	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	16	4	no	—
1135	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1136	C₄	—	2	1	no	—
1137	C₄	—	2	2	no	—
1138	C₄	—	2	1	no	—
1139	C₄	—	2	1	no	—
1140	C₄	—	2	2	no	—
1141	C₄	—	2	1	no	—
1142	C₄	—	2	2	no	—
1143	C₄	—	2	2	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	2	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	4	2	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	2	no	—
1152	C₄	C₆₁×#577	1	2	yes	—
1153	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1154	C₄	C₆₁×#585	1	1	yes	characteristic
1155	C₂	—	4	2	no	—
1156	C₂	—	4	1	no	—
1157	C₂	—	8	1	no	—
1158	C₂	—	8	2	no	—
1159	C₂	—	8	1	no	—
1160	C₂	C₆₁×#3488	1	1	yes	characteristic
1161	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
1162	C₂	C₆₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3546	C₂
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
2. C₆₁×#3523	C₂	semidirect
3. C₆₁×#3398	C₂	semidirect
4. C₆₁×#3392	C₂	semidirect
5. C₆₁×#3368	C₂	semidirect
6. C₆₁×#3364	C₂	semidirect
7. C₆₁×#3324	C₂	semidirect
8. C₆₁×#3323	C₂	semidirect
9. C₆₁×#3317	C₂	semidirect
10. C₆₁×#3302	C₂	semidirect
11. D₄×SD₁₆×C₆₁	C₂	semidirect
12. C₆₁×#3278	C₂	semidirect
13. C₆₁×#3276	C₂	semidirect
14. C₆₁×#3266	C₂	semidirect
15. C₆₁×#3258	C₂	semidirect
16. C₆₁×#3254	C₂	semidirect
17. C₆₁×#3222	C₂	semidirect
18. C₆₁×#3210	C₂	semidirect
19. C₆₁×#3121	C₂	semidirect
20. C₆₁×#3103	C₂	semidirect
21. C₆₁×#3043	C₂	semidirect
22. C₆₁×#3037	C₂	semidirect
23. C₆₁×#2993	C₂	semidirect
24. C₂×#137×C₆₁	C₂²	semidirect
25. C₂×#137×C₆₁	C₂²	semidirect
29. C₆₁×#557	C₂²	semidirect
30. C₆₁×#557	C₂²	semidirect
36. C₆₁×#552	C₂²	semidirect
40. D₄×Q₈×C₆₁	C₂²	semidirect
47. C₆₁×#541	C₂²	semidirect
53. C₆₁×#533	C₂²	semidirect
58. C₆₁×#519	C₂²	semidirect
59. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
61. C₆₁×#494	C₂²	semidirect
63. C₆₁×#492	C₂²	semidirect
64. C₆₁×#490	C₂²	semidirect
66. C₆₁×#487	C₂²	semidirect
68. C₆₁×#485	C₂²	semidirect
71. C₆₁×#481	C₂²	semidirect
72. C₆₁×#479	C₂²	semidirect
73. C₆₁×#478	C₂²	semidirect
74. C₆₁×#477	C₂²	semidirect
75. C₆₁×#475	C₂²	semidirect
76. C₆₁×#475	C₂²	semidirect
78. C₆₁×#474	C₂²	semidirect
79. C₆₁×#470	C₂²	semidirect
82. C₆₁×#468	C₂²	semidirect
83. C₆₁×#467	C₂²	semidirect
87. C₆₁×#464	C₂²	semidirect
88. C₆₁×#464	C₂²	semidirect
89. C₆₁×#464	C₂²	semidirect
90. C₆₁×#464	C₂²	semidirect
91. C₆₁×#462	C₂²	semidirect
92. C₆₁×#462	C₂²	semidirect
93. C₆₁×#462	C₂²	semidirect
95. C₆₁×#461	C₂²	semidirect
96. C₆₁×#461	C₂²	semidirect
102. C₆₁×#460	C₂²	semidirect
103. C₆₁×#460	C₂²	semidirect
104. C₆₁×#452	C₂²	semidirect
105. C₆₁×#452	C₂²	semidirect
106. C₆₁×#452	C₂²	semidirect
107. C₆₁×#452	C₂²	semidirect
108. C₆₁×#451	C₂²	semidirect
113. C₆₁×#448	C₂²	semidirect
114. C₆₁×#446	C₂²	semidirect
115. C₈×Q₈×C₆₁	C₂²	semidirect
116. C₆₁×#441	C₂²	semidirect
117. C₆₁×#440	C₂²	semidirect
118. C₄×Q₁₆×C₆₁	C₂²	semidirect
121. C₄×SD₁₆×C₆₁	C₂²	semidirect
122. C₄×SD₁₆×C₆₁	C₂²	semidirect
123. C₄×SD₁₆×C₆₁	C₂²	semidirect
125. C₆₁×#436	C₂²	semidirect
126. C₆₁×#435	C₂²	semidirect
128. C₆₁×#433	C₂²	semidirect
129. C₆₁×#431	C₂²	semidirect
130. C₆₁×#424	C₂²	semidirect
131. C₆₁×#423	C₂²	semidirect
133. C₆₁×#417	C₂²	semidirect
134. C₆₁×#416	C₂²	semidirect
537. #62044	C₆₁	direct (N × H)
575. #3523	C₂×C₆₁	semidirect
576. #3398	C₂×C₆₁	semidirect
577. #3392	C₂×C₆₁	semidirect
578. #3368	C₂×C₆₁	semidirect
579. #3364	C₂×C₆₁	semidirect
580. #3324	C₂×C₆₁	semidirect
581. #3323	C₂×C₆₁	semidirect
582. #3317	C₂×C₆₁	semidirect
583. #3302	C₂×C₆₁	semidirect
584. D₄×SD₁₆	C₂×C₆₁	semidirect
585. #3278	C₂×C₆₁	semidirect
586. #3276	C₂×C₆₁	semidirect
587. #3266	C₂×C₆₁	semidirect
588. #3258	C₂×C₆₁	semidirect
589. #3254	C₂×C₆₁	semidirect
590. #3222	C₂×C₆₁	semidirect
591. #3210	C₂×C₆₁	semidirect
592. #3121	C₂×C₆₁	semidirect
593. #3103	C₂×C₆₁	semidirect
594. #3043	C₂×C₆₁	semidirect
595. #3037	C₂×C₆₁	semidirect
596. #2993	C₂×C₆₁	semidirect
605. C₂×#137	C₂²×C₆₁	semidirect
606. C₂×#137	C₂²×C₆₁	semidirect
610. #557	C₂²×C₆₁	semidirect
611. #557	C₂²×C₆₁	semidirect
617. #552	C₂²×C₆₁	semidirect
621. D₄×Q₈	C₂²×C₆₁	semidirect
628. #541	C₂²×C₆₁	semidirect
634. #533	C₂²×C₆₁	semidirect
639. #519	C₂²×C₆₁	semidirect
640. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
642. #494	C₂²×C₆₁	semidirect
644. #492	C₂²×C₆₁	semidirect
645. #490	C₂²×C₆₁	semidirect
647. #487	C₂²×C₆₁	semidirect
649. #485	C₂²×C₆₁	semidirect
652. #481	C₂²×C₆₁	semidirect
653. #479	C₂²×C₆₁	semidirect
654. #478	C₂²×C₆₁	semidirect
655. #477	C₂²×C₆₁	semidirect
656. #475	C₂²×C₆₁	semidirect
657. #475	C₂²×C₆₁	semidirect
659. #474	C₂²×C₆₁	semidirect
660. #470	C₂²×C₆₁	semidirect
663. #468	C₂²×C₆₁	semidirect
664. #467	C₂²×C₆₁	semidirect
668. #464	C₂²×C₆₁	semidirect
669. #464	C₂²×C₆₁	semidirect
670. #464	C₂²×C₆₁	semidirect
671. #464	C₂²×C₆₁	semidirect
672. #462	C₂²×C₆₁	semidirect
673. #462	C₂²×C₆₁	semidirect
674. #462	C₂²×C₆₁	semidirect
676. #461	C₂²×C₆₁	semidirect
677. #461	C₂²×C₆₁	semidirect
683. #460	C₂²×C₆₁	semidirect
684. #460	C₂²×C₆₁	semidirect
685. #452	C₂²×C₆₁	semidirect
686. #452	C₂²×C₆₁	semidirect
687. #452	C₂²×C₆₁	semidirect
688. #452	C₂²×C₆₁	semidirect
689. #451	C₂²×C₆₁	semidirect
694. #448	C₂²×C₆₁	semidirect
695. #446	C₂²×C₆₁	semidirect
696. C₈×Q₈	C₂²×C₆₁	semidirect
697. #441	C₂²×C₆₁	semidirect
698. #440	C₂²×C₆₁	semidirect
699. C₄×Q₁₆	C₂²×C₆₁	semidirect
702. C₄×SD₁₆	C₂²×C₆₁	semidirect
703. C₄×SD₁₆	C₂²×C₆₁	semidirect
704. C₄×SD₁₆	C₂²×C₆₁	semidirect
706. #436	C₂²×C₆₁	semidirect
707. #435	C₂²×C₆₁	semidirect
709. #433	C₂²×C₆₁	semidirect
710. #431	C₂²×C₆₁	semidirect
711. #424	C₂²×C₆₁	semidirect
712. #423	C₂²×C₆₁	semidirect
714. #417	C₂²×C₆₁	semidirect
715. #416	C₂²×C₆₁	semidirect
716. C₆₁	#62044	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×#3523	2
C₆₁×#3398	2
C₆₁×#3392	2
C₆₁×#3368	2
C₆₁×#3364	2
C₆₁×#3324	2
C₆₁×#3323	2
C₆₁×#3317	2
C₆₁×#3302	2
D₄×SD₁₆×C₆₁	2
C₆₁×#3278	2
C₆₁×#3276	2
C₆₁×#3266	2
C₆₁×#3258	2
C₆₁×#3254	2
C₆₁×#3222	2
C₆₁×#3210	2
C₆₁×#3121	2
C₆₁×#3103	2
C₆₁×#3043	2
C₆₁×#3037	2
C₆₁×#2993	2
#62044	61

Subgroups — C61×#62044 #29565477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62044 #29565477