Subgroups — C₆₁×#61703 #29565136

Order 15616.

1780 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3342	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3340	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3337	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3336	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3335	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3334	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3301	C₂	1	2	yes	maximal, complemented
12	C₆₁×#3300	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3299	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3298	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3233	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3191	C₂	1	2	yes	maximal, complemented
18	C₆₁×#3190	C₂	1	2	yes	maximal, complemented
19	C₆₁×#3107	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3091	C₂	1	2	yes	maximal, complemented
22	C₂×C₆₁×#485	C₂	1	2	yes	maximal, complemented
23	C₆₁×#2972	C₂	1	1	yes	maximal, characteristic, complemented
24	C₆₁×#556	C₂²	1	1	yes	characteristic
25	C₆₁×#556	C₂²	1	1	yes	characteristic
26	C₆₁×#555	C₂²	1	1	yes	characteristic
27	C₆₁×#554	—	2	1	no	—
28	C₆₁×#554	C₂²	1	1	yes	characteristic
29	C₆₁×#553	C₂²	1	2	yes	—
30	C₆₁×#552	—	2	1	no	—
31	C₆₁×#552	C₂²	1	2	yes	—
32	C₆₁×#552	C₂²	1	2	yes	—
33	C₆₁×#551	—	2	2	no	—
34	C₆₁×#551	—	2	2	no	—
35	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
36	C₆₁×#548	C₂²	1	2	yes	—
37	C₆₁×#547	C₂²	1	1	yes	characteristic
38	C₆₁×#547	C₂²	1	1	yes	characteristic
39	C₆₁×#547	C₂²	1	1	yes	characteristic
40	C₆₁×#546	—	2	1	no	—
41	C₆₁×#546	—	2	1	no	—
42	C₆₁×#542	—	2	1	no	—
43	C₆₁×#539	—	2	2	no	—
44	C₆₁×#533	C₂²	1	1	yes	characteristic
45	C₆₁×#533	C₂²	1	1	yes	characteristic
46	C₆₁×#529	—	2	2	no	—
47	C₆₁×#529	—	2	1	no	—
48	C₆₁×#529	C₂²	1	1	yes	characteristic
49	C₆₁×#525	C₂²	1	2	yes	—
50	C₆₁×#525	C₂²	1	2	yes	—
51	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
52	C₆₁×#520	—	2	1	no	—
53	C₄×#41×C₆₁	—	2	1	no	—
54	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
56	C₂×#117×C₆₁	C₂²	1	2	yes	—
57	C₆₁×#500	C₂²	1	1	yes	characteristic, complemented
58	C₆₁×#499	C₂²	1	2	yes	complemented
59	C₆₁×#498	C₂²	1	1	yes	characteristic, complemented
60	C₆₁×#488	C₂²	1	2	yes	complemented
61	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
62	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
63	C₆₁×#485	C₂²	1	1	yes	characteristic
64	C₆₁×#485	C₂²	1	2	yes	—
65	C₆₁×#485	C₂²	1	2	yes	—
66	C₆₁×#485	C₂²	1	2	yes	—
67	C₆₁×#485	C₂²	1	2	yes	—
68	C₆₁×#485	C₂²	1	2	yes	complemented
69	C₆₁×#485	C₂²	1	2	yes	complemented
70	C₆₁×#485	C₂²	1	2	yes	complemented
71	C₆₁×#485	C₂²	1	2	yes	complemented
72	C₆₁×#485	C₂²	1	2	yes	complemented
73	C₆₁×#484	C₂²	1	2	yes	complemented
74	C₆₁×#483	C₂²	1	2	yes	complemented
75	C₆₁×#483	C₂²	1	2	yes	complemented
76	C₆₁×#482	C₂²	1	1	yes	characteristic
77	C₆₁×#482	C₂²	1	2	yes	—
78	C₆₁×#482	C₂²	1	2	yes	complemented
79	C₆₁×#481	C₂²	1	2	yes	complemented
80	C₆₁×#480	C₂²	1	2	yes	complemented
81	C₆₁×#480	C₂²	1	2	yes	complemented
82	C₆₁×#479	C₂²	1	2	yes	complemented
83	C₆₁×#479	C₂²	1	2	yes	complemented
84	C₆₁×#479	C₂²	1	1	yes	characteristic, complemented
85	C₆₁×#478	C₂²	1	1	yes	characteristic, complemented
86	C₆₁×#477	C₂²	1	1	yes	characteristic, complemented
87	C₆₁×#476	C₂²	1	1	yes	characteristic, complemented
88	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
89	C₆₁×#475	C₂²	1	1	yes	characteristic, complemented
90	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
91	C₆₁×#474	C₂²	1	1	yes	characteristic, complemented
92	C₆₁×#467	C₂²	1	2	yes	complemented
93	C₆₁×#467	C₂²	1	2	yes	complemented
94	C₆₁×#467	C₂²	1	2	yes	complemented
95	C₆₁×#466	C₂²	1	2	yes	complemented
96	C₆₁×#465	C₂²	1	2	yes	complemented
97	C₆₁×#465	C₂²	1	2	yes	complemented
98	C₆₁×#465	C₂²	1	2	yes	complemented
99	C₆₁×#465	C₂²	1	2	yes	complemented
100	C₆₁×#464	C₂²	1	1	yes	characteristic, complemented
101	C₆₁×#463	C₂²	1	1	yes	characteristic, complemented
102	C₆₁×#462	C₂²	1	1	yes	characteristic, complemented
103	C₆₁×#461	C₂²	1	1	yes	characteristic, complemented
104	C₆₁×#452	C₂²	1	1	yes	characteristic
105	C₆₁×#452	C₂²	1	2	yes	—
106	C₆₁×#452	C₂²	1	2	yes	complemented
107	C₆₁×#451	C₂²	1	2	yes	complemented
108	C₆₁×#449	C₂²	1	1	yes	characteristic
109	C₆₁×#449	C₂²	1	2	yes	complemented
110	C₆₁×#448	C₂²	1	2	yes	complemented
111	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
112	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
117	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
118	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
119	C₈×D₄×C₆₁	C₂²	1	2	yes	—
120	C₈×D₄×C₆₁	C₂²	1	2	yes	—
121	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
123	C₆₁×#431	C₂²	1	1	yes	characteristic
124	C₆₁×#431	C₂²	1	1	yes	characteristic
125	C₆₁×#427	C₂²	1	2	yes	complemented
126	C₆₁×#427	C₂²	1	2	yes	complemented
127	C₂×#107×C₆₁	C₂²	1	2	yes	complemented
128	C₂×#106×C₆₁	C₂²	1	2	yes	complemented
129	C₆₁×#416	C₂²	1	2	yes	complemented
130	C₆₁×#416	C₂²	1	2	yes	complemented
131	C₂×#103×C₆₁	C₂²	1	2	yes	complemented
132	C₂×#103×C₆₁	C₂²	1	2	yes	complemented
133	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
134	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
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	1	yes	characteristic
139	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
140	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
141	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
143	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
149	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
150	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
151	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
152	C₄⋊Q₈×C₆₁	—	2	1	no	—
153	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
155	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
157	#126×C₆₁	—	2	2	no	—
158	#126×C₆₁	—	2	2	no	—
159	#126×C₆₁	—	2	2	no	—
160	#126×C₆₁	—	2	2	no	—
161	#126×C₆₁	—	2	2	no	—
162	#126×C₆₁	—	2	1	no	—
163	#125×C₆₁	—	2	2	no	—
164	#125×C₆₁	—	2	2	no	—
165	#125×C₆₁	—	2	1	no	—
166	#125×C₆₁	—	2	1	no	—
167	#125×C₆₁	C₂³	1	2	yes	—
168	#125×C₆₁	C₂³	1	1	yes	characteristic
169	#124×C₆₁	—	2	1	no	—
170	#124×C₆₁	—	2	1	no	—
171	#124×C₆₁	—	2	2	no	—
172	#124×C₆₁	—	2	2	no	—
173	#124×C₆₁	C₂³	1	1	yes	characteristic
174	#123×C₆₁	—	2	2	no	—
175	#123×C₆₁	—	2	2	no	—
176	#123×C₆₁	—	2	2	no	—
177	#123×C₆₁	—	2	1	no	—
178	#123×C₆₁	—	2	2	no	—
179	#123×C₆₁	—	2	2	no	—
180	#123×C₆₁	—	2	2	no	—
181	#123×C₆₁	—	2	2	no	—
182	#123×C₆₁	—	2	2	no	—
183	C₂²⋊Q₈×C₆₁	—	2	1	no	—
184	C₂²⋊Q₈×C₆₁	—	2	1	no	—
185	C₂²⋊Q₈×C₆₁	—	2	1	no	—
186	C₂²⋊Q₈×C₆₁	—	2	2	no	—
187	C₂²⋊Q₈×C₆₁	—	2	2	no	—
188	C₂²⋊Q₈×C₆₁	—	2	2	no	—
189	C₂²⋊Q₈×C₆₁	—	2	1	no	—
190	C₂²⋊Q₈×C₆₁	—	2	1	no	—
191	C₂²⋊Q₈×C₆₁	—	2	2	no	—
192	C₂²⋊Q₈×C₆₁	—	2	2	no	—
193	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
194	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
195	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
198	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
200	#121×C₆₁	—	2	2	no	—
201	#121×C₆₁	—	2	1	no	—
202	#121×C₆₁	—	2	2	no	—
203	#121×C₆₁	—	2	1	no	—
204	#121×C₆₁	C₂³	1	2	yes	—
205	#121×C₆₁	C₂³	1	2	yes	—
206	#121×C₆₁	C₂³	1	2	yes	—
207	#121×C₆₁	C₂³	1	1	yes	characteristic
208	#120×C₆₁	—	2	2	no	—
209	#120×C₆₁	—	2	2	no	—
210	C₄×Q₈×C₆₁	—	2	1	no	—
211	C₄×Q₈×C₆₁	—	2	1	no	—
212	C₄×Q₈×C₆₁	—	2	1	no	—
213	C₄×Q₈×C₆₁	—	2	1	no	—
214	C₄×Q₈×C₆₁	—	2	1	no	—
215	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
216	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₆₁	—	2	1	no	—
220	C₄×D₄×C₆₁	—	2	1	no	—
221	C₄×D₄×C₆₁	—	2	2	no	—
222	C₄×D₄×C₆₁	—	2	1	no	—
223	C₄×D₄×C₆₁	—	2	1	no	—
224	C₄×D₄×C₆₁	—	2	1	no	—
225	C₄×D₄×C₆₁	—	2	2	no	—
226	C₄×D₄×C₆₁	—	2	2	no	—
227	C₄×D₄×C₆₁	—	2	2	no	—
228	C₄×D₄×C₆₁	—	2	2	no	—
229	C₄×D₄×C₆₁	—	2	2	no	—
230	C₄×D₄×C₆₁	D₄	1	2	yes	—
231	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
232	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
233	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₆₁	C₂³	1	2	yes	—
239	#117×C₆₁	—	2	1	no	—
240	#117×C₆₁	—	2	2	no	—
241	#117×C₆₁	—	2	2	no	—
242	#117×C₆₁	—	2	1	no	—
243	#117×C₆₁	—	2	2	no	—
244	#117×C₆₁	—	2	2	no	—
245	#117×C₆₁	—	2	1	no	—
246	#117×C₆₁	—	2	1	no	—
247	#117×C₆₁	C₂³	1	2	yes	—
248	#117×C₆₁	C₂³	1	2	yes	—
249	#117×C₆₁	C₂³	1	2	yes	—
250	#117×C₆₁	C₂³	1	2	yes	—
251	#117×C₆₁	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
253	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
254	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
259	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
260	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
261	C₂×C₄²×C₆₁	—	2	2	no	—
262	C₂×C₄²×C₆₁	—	2	1	no	—
263	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
264	#107×C₆₁	C₂³	1	1	yes	characteristic
265	#107×C₆₁	C₂³	1	2	yes	—
266	#107×C₆₁	C₂³	1	2	yes	—
267	#107×C₆₁	C₂³	1	2	yes	—
268	#107×C₆₁	C₂³	1	1	yes	characteristic
269	#107×C₆₁	C₂³	1	2	yes	—
270	#107×C₆₁	C₂³	1	2	yes	—
271	#106×C₆₁	C₂³	1	1	yes	characteristic
272	#106×C₆₁	C₂³	1	2	yes	—
273	#106×C₆₁	C₂³	1	2	yes	—
274	#106×C₆₁	C₂³	1	2	yes	—
275	#106×C₆₁	C₂³	1	1	yes	characteristic
276	#106×C₆₁	C₂³	1	2	yes	—
277	#106×C₆₁	C₂³	1	2	yes	—
278	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
282	#103×C₆₁	C₂³	1	1	yes	characteristic
283	#103×C₆₁	C₂³	1	1	yes	characteristic
284	#103×C₆₁	C₂³	1	2	yes	—
285	#103×C₆₁	C₂³	1	2	yes	—
286	#103×C₆₁	C₂³	1	2	yes	—
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	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	2	yes	—
295	#102×C₆₁	C₂³	1	1	yes	characteristic
296	#102×C₆₁	C₂³	1	1	yes	characteristic
297	#102×C₆₁	C₂³	1	2	yes	—
298	#102×C₆₁	C₂³	1	2	yes	—
299	#102×C₆₁	C₂³	1	1	yes	characteristic
300	#102×C₆₁	C₂³	1	1	yes	characteristic
301	#102×C₆₁	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
303	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
309	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₁	C₂³	1	2	yes	—
312	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
313	#41×C₆₁	—	4	1	no	—
314	#41×C₆₁	—	4	1	no	—
315	#41×C₆₁	—	4	2	no	—
316	#41×C₆₁	—	4	2	no	—
317	#41×C₆₁	—	4	4	no	—
318	#41×C₆₁	—	4	4	no	—
319	C₂×Q₈×C₆₁	—	2	1	no	—
320	C₂×Q₈×C₆₁	—	2	1	no	—
321	C₂×Q₈×C₆₁	—	2	1	no	—
322	C₂×Q₈×C₆₁	—	2	2	no	—
323	C₂×Q₈×C₆₁	—	4	2	no	—
324	C₂×Q₈×C₆₁	—	4	2	no	—
325	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
327	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₆₁	—	2	4	no	—
329	C₂×D₄×C₆₁	—	2	1	no	—
330	C₂×D₄×C₆₁	—	2	1	no	—
331	C₂×D₄×C₆₁	—	2	2	no	—
332	C₂×D₄×C₆₁	—	2	2	no	—
333	C₂×D₄×C₆₁	—	2	2	no	—
334	C₂×D₄×C₆₁	—	2	2	no	—
335	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
338	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₆₁	—	2	2	no	—
341	C₂²×C₄×C₆₁	—	2	2	no	—
342	C₂²×C₄×C₆₁	—	2	2	no	—
343	C₂²×C₄×C₆₁	—	2	2	no	—
344	C₂²×C₄×C₆₁	—	2	1	no	—
345	C₂²×C₄×C₆₁	—	2	1	no	—
346	C₂²×C₄×C₆₁	—	2	1	no	—
347	C₂²×C₄×C₆₁	—	2	1	no	—
348	C₂²×C₄×C₆₁	—	2	2	no	—
349	C₂²×C₄×C₆₁	—	4	2	no	—
350	C₂²×C₄×C₆₁	—	4	2	no	—
351	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
353	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
355	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
356	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
358	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
359	Q₁₆×C₆₁	—	4	1	no	—
360	Q₁₆×C₆₁	—	4	2	no	—
361	SD₁₆×C₆₁	—	4	1	no	—
362	SD₁₆×C₆₁	—	4	2	no	—
363	SD₁₆×C₆₁	—	4	1	no	—
364	D₈×C₆₁	—	4	1	no	—
365	C₂×C₈×C₆₁	—	4	2	no	—
366	C₂×C₈×C₆₁	—	4	2	no	—
367	C₂×C₈×C₆₁	—	4	2	no	—
368	C₂×C₈×C₆₁	—	4	2	no	—
369	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
371	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
374	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
375	C₄⋊C₄×C₆₁	—	2	1	no	—
376	C₄⋊C₄×C₆₁	—	2	2	no	—
377	C₄⋊C₄×C₆₁	—	2	1	no	—
378	C₄⋊C₄×C₆₁	—	2	2	no	—
379	C₄⋊C₄×C₆₁	—	2	2	no	—
380	C₄⋊C₄×C₆₁	—	2	2	no	—
381	C₄⋊C₄×C₆₁	—	2	2	no	—
382	C₄⋊C₄×C₆₁	—	2	2	no	—
383	C₄⋊C₄×C₆₁	—	2	1	no	—
384	C₄⋊C₄×C₆₁	—	2	1	no	—
385	C₄⋊C₄×C₆₁	—	2	2	no	—
386	C₄⋊C₄×C₆₁	—	2	2	no	—
387	C₄⋊C₄×C₆₁	—	2	1	no	—
388	C₄⋊C₄×C₆₁	—	2	1	no	—
389	C₄⋊C₄×C₆₁	—	2	1	no	—
390	C₄⋊C₄×C₆₁	—	2	1	no	—
391	C₄⋊C₄×C₆₁	—	2	2	no	—
392	C₄⋊C₄×C₆₁	—	2	2	no	—
393	C₄⋊C₄×C₆₁	—	2	1	no	—
394	C₄⋊C₄×C₆₁	—	2	2	no	—
395	C₄⋊C₄×C₆₁	—	2	1	no	—
396	C₄⋊C₄×C₆₁	—	2	2	no	—
397	C₄⋊C₄×C₆₁	—	2	1	no	—
398	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
399	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
408	C₂²⋊C₄×C₆₁	—	2	1	no	—
409	C₂²⋊C₄×C₆₁	—	2	1	no	—
410	C₂²⋊C₄×C₆₁	—	2	2	no	—
411	C₂²⋊C₄×C₆₁	—	2	2	no	—
412	C₂²⋊C₄×C₆₁	—	2	2	no	—
413	C₂²⋊C₄×C₆₁	—	2	2	no	—
414	C₂²⋊C₄×C₆₁	—	2	2	no	—
415	C₂²⋊C₄×C₆₁	—	2	2	no	—
416	C₂²⋊C₄×C₆₁	—	2	2	no	—
417	C₂²⋊C₄×C₆₁	—	2	2	no	—
418	C₂²⋊C₄×C₆₁	—	2	2	no	—
419	C₂²⋊C₄×C₆₁	—	2	2	no	—
420	C₂²⋊C₄×C₆₁	—	2	1	no	—
421	C₂²⋊C₄×C₆₁	—	2	2	no	—
422	C₂²⋊C₄×C₆₁	—	2	1	no	—
423	C₂²⋊C₄×C₆₁	—	2	1	no	—
424	C₂²⋊C₄×C₆₁	—	2	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	1	no	—
429	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
433	C₄²×C₆₁	—	2	1	no	—
434	C₄²×C₆₁	—	2	2	no	—
435	C₄²×C₆₁	—	2	1	no	—
436	C₄²×C₆₁	—	2	2	no	—
437	C₄²×C₆₁	—	2	2	no	—
438	C₄²×C₆₁	—	2	1	no	—
439	C₄²×C₆₁	—	2	2	no	—
440	C₄²×C₆₁	—	2	2	no	—
441	C₄²×C₆₁	—	2	1	no	—
442	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
444	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
445	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
446	C₂³×C₆₁	—	2	4	no	—
447	C₂³×C₆₁	—	2	1	no	—
448	C₂³×C₆₁	—	2	1	no	—
449	C₂³×C₆₁	—	4	2	no	—
450	C₂³×C₆₁	—	4	2	no	—
451	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
452	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
453	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
454	Q₈×C₆₁	—	2	1	no	—
455	Q₈×C₆₁	—	2	1	no	—
456	Q₈×C₆₁	—	2	2	no	—
457	Q₈×C₆₁	—	2	1	no	—
458	Q₈×C₆₁	—	2	1	no	—
459	Q₈×C₆₁	—	2	2	no	—
460	Q₈×C₆₁	—	4	2	no	—
461	Q₈×C₆₁	—	4	2	no	—
462	Q₈×C₆₁	—	8	1	no	—
463	Q₈×C₆₁	—	8	2	no	—
464	D₄×C₆₁	—	2	4	no	—
465	D₄×C₆₁	—	2	2	no	—
466	D₄×C₆₁	—	2	1	no	—
467	D₄×C₆₁	—	2	1	no	—
468	D₄×C₆₁	—	2	1	no	—
469	D₄×C₆₁	—	2	1	no	—
470	D₄×C₆₁	—	4	2	no	—
471	D₄×C₆₁	—	4	2	no	—
472	D₄×C₆₁	—	4	4	no	—
473	D₄×C₆₁	—	4	4	no	—
474	D₄×C₆₁	—	8	2	no	—
475	D₄×C₆₁	—	8	2	no	—
476	D₄×C₆₁	#135	1	4	yes	—
477	C₂×C₄×C₆₁	—	2	2	no	—
478	C₂×C₄×C₆₁	—	2	2	no	—
479	C₂×C₄×C₆₁	—	2	2	no	—
480	C₂×C₄×C₆₁	—	2	2	no	—
481	C₂×C₄×C₆₁	—	2	2	no	—
482	C₂×C₄×C₆₁	—	2	1	no	—
483	C₂×C₄×C₆₁	—	2	1	no	—
484	C₂×C₄×C₆₁	—	2	1	no	—
485	C₂×C₄×C₆₁	—	2	1	no	—
486	C₂×C₄×C₆₁	—	2	1	no	—
487	C₂×C₄×C₆₁	—	2	1	no	—
488	C₂×C₄×C₆₁	—	2	2	no	—
489	C₂×C₄×C₆₁	—	2	2	no	—
490	C₂×C₄×C₆₁	—	2	2	no	—
491	C₂×C₄×C₆₁	—	2	1	no	—
492	C₂×C₄×C₆₁	—	2	2	no	—
493	C₂×C₄×C₆₁	—	2	1	no	—
494	C₂×C₄×C₆₁	—	4	2	no	—
495	C₂×C₄×C₆₁	—	4	2	no	—
496	C₂×C₄×C₆₁	—	4	2	no	—
497	C₂×C₄×C₆₁	—	4	1	no	—
498	C₂×C₄×C₆₁	—	4	2	no	—
499	C₂×C₄×C₆₁	—	4	4	no	—
500	C₂×C₄×C₆₁	—	4	4	no	—
501	C₂×C₄×C₆₁	—	4	2	no	—
502	C₂×C₄×C₆₁	—	4	2	no	—
503	C₂×C₄×C₆₁	—	8	1	no	—
504	C₂×C₄×C₆₁	—	8	2	no	—
505	C₂×C₄×C₆₁	—	8	2	no	—
506	C₂×C₄×C₆₁	—	8	2	no	—
507	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
515	C₈×C₆₁	—	2	1	no	—
516	C₈×C₆₁	—	2	1	no	—
517	C₈×C₆₁	—	2	1	no	—
518	C₈×C₆₁	—	2	2	no	—
519	C₈×C₆₁	—	2	2	no	—
520	C₈×C₆₁	—	2	1	no	—
521	#61703	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
522	C₂²×C₆₁	—	2	2	no	—
523	C₂²×C₆₁	—	2	2	no	—
524	C₂²×C₆₁	—	2	1	no	—
525	C₂²×C₆₁	—	2	2	no	—
526	C₂²×C₆₁	—	2	1	no	—
527	C₂²×C₆₁	—	2	2	no	—
528	C₂²×C₆₁	—	2	1	no	—
529	C₂²×C₆₁	—	2	2	no	—
530	C₂²×C₆₁	—	4	1	no	—
531	C₂²×C₆₁	—	4	1	no	—
532	C₂²×C₆₁	—	4	1	no	—
533	C₂²×C₆₁	—	4	1	no	—
534	C₂²×C₆₁	—	4	1	no	—
535	C₂²×C₆₁	—	4	1	no	—
536	C₂²×C₆₁	—	8	4	no	—
537	C₂²×C₆₁	C₂×#135	1	4	yes	—
538	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
539	C₄×C₆₁	—	2	1	no	—
540	C₄×C₆₁	—	2	1	no	—
541	C₄×C₆₁	—	2	1	no	—
542	C₄×C₆₁	—	2	2	no	—
543	C₄×C₆₁	—	2	2	no	—
544	C₄×C₆₁	—	2	1	no	—
545	C₄×C₆₁	—	4	1	no	—
546	C₄×C₆₁	—	4	2	no	—
547	C₄×C₆₁	—	4	1	no	—
548	C₄×C₆₁	—	4	1	no	—
549	C₄×C₆₁	—	4	2	no	—
550	C₄×C₆₁	—	4	1	no	—
551	C₄×C₆₁	—	4	1	no	—
552	C₄×C₆₁	—	4	1	no	—
553	C₄×C₆₁	—	4	2	no	—
554	C₄×C₆₁	—	4	2	no	—
555	C₄×C₆₁	C₂×#135	1	2	yes	—
556	C₄×C₆₁	#585	1	1	yes	characteristic
557	C₄×C₆₁	#585	1	1	yes	characteristic
558	#3520	C₂×C₆₁	1	1	yes	characteristic, complemented
559	#3475	C₂×C₆₁	1	1	yes	characteristic, complemented
560	#3342	C₂×C₆₁	1	1	yes	characteristic, complemented
561	#3340	C₂×C₆₁	1	1	yes	characteristic, complemented
562	#3337	C₂×C₆₁	1	2	yes	complemented
563	#3336	C₂×C₆₁	1	2	yes	complemented
564	#3335	C₂×C₆₁	1	1	yes	characteristic, complemented
565	#3334	C₂×C₆₁	1	1	yes	characteristic, complemented
566	#3303	C₂×C₆₁	1	1	yes	characteristic, complemented
567	#3302	C₂×C₆₁	1	1	yes	characteristic, complemented
568	#3301	C₂×C₆₁	1	2	yes	complemented
569	#3300	C₂×C₆₁	1	2	yes	complemented
570	#3299	C₂×C₆₁	1	1	yes	characteristic, complemented
571	#3298	C₂×C₆₁	1	1	yes	characteristic, complemented
572	#3233	C₂×C₆₁	1	1	yes	characteristic, complemented
573	#3231	C₂×C₆₁	1	1	yes	characteristic, complemented
574	#3191	C₂×C₆₁	1	2	yes	complemented
575	#3190	C₂×C₆₁	1	2	yes	complemented
576	#3107	C₂×C₆₁	1	1	yes	characteristic, complemented
577	#3102	C₂×C₆₁	1	1	yes	characteristic, complemented
578	#3091	C₂×C₆₁	1	2	yes	complemented
579	C₂×#485	C₂×C₆₁	1	2	yes	complemented
580	#2972	C₂×C₆₁	1	1	yes	characteristic, complemented
581	C₂×C₆₁	—	2	4	no	—
582	C₂×C₆₁	—	4	2	no	—
583	C₂×C₆₁	—	4	1	no	—
584	C₂×C₆₁	—	8	1	no	—
585	C₂×C₆₁	—	8	1	no	—
586	C₂×C₆₁	#3485	1	1	yes	characteristic
587	C₂×C₆₁	C₂²×#135	1	1	yes	characteristic
588	C₂×C₆₁	#3586	1	1	yes	characteristic
589	#556	C₂²×C₆₁	1	1	yes	characteristic
590	#556	C₂²×C₆₁	1	1	yes	characteristic
591	#555	C₂²×C₆₁	1	1	yes	characteristic
592	#554	—	2	1	no	—
593	#554	C₂²×C₆₁	1	1	yes	characteristic
594	#553	C₂²×C₆₁	1	2	yes	—
595	#552	—	2	1	no	—
596	#552	C₂²×C₆₁	1	2	yes	—
597	#552	C₂²×C₆₁	1	2	yes	—
598	#551	—	2	2	no	—
599	#551	—	2	2	no	—
600	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
601	#548	C₂²×C₆₁	1	2	yes	—
602	#547	C₂²×C₆₁	1	1	yes	characteristic
603	#547	C₂²×C₆₁	1	1	yes	characteristic
604	#547	C₂²×C₆₁	1	1	yes	characteristic
605	#546	—	2	1	no	—
606	#546	—	2	1	no	—
607	#542	—	2	1	no	—
608	#539	—	2	2	no	—
609	#533	C₂²×C₆₁	1	1	yes	characteristic
610	#533	C₂²×C₆₁	1	1	yes	characteristic
611	#529	—	2	2	no	—
612	#529	—	2	1	no	—
613	#529	C₂²×C₆₁	1	1	yes	characteristic
614	#525	C₂²×C₆₁	1	2	yes	—
615	#525	C₂²×C₆₁	1	2	yes	—
616	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
617	#520	—	2	1	no	—
618	C₄×#41	—	2	1	no	—
619	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
620	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
621	C₂×#117	C₂²×C₆₁	1	2	yes	—
622	#500	C₂²×C₆₁	1	1	yes	characteristic, complemented
623	#499	C₂²×C₆₁	1	2	yes	complemented
624	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
625	#488	C₂²×C₆₁	1	2	yes	complemented
626	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
627	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
628	#485	C₂²×C₆₁	1	1	yes	characteristic
629	#485	C₂²×C₆₁	1	2	yes	—
630	#485	C₂²×C₆₁	1	2	yes	—
631	#485	C₂²×C₆₁	1	2	yes	—
632	#485	C₂²×C₆₁	1	2	yes	—
633	#485	C₂²×C₆₁	1	2	yes	complemented
634	#485	C₂²×C₆₁	1	2	yes	complemented
635	#485	C₂²×C₆₁	1	2	yes	complemented
636	#485	C₂²×C₆₁	1	2	yes	complemented
637	#485	C₂²×C₆₁	1	2	yes	complemented
638	#484	C₂²×C₆₁	1	2	yes	complemented
639	#483	C₂²×C₆₁	1	2	yes	complemented
640	#483	C₂²×C₆₁	1	2	yes	complemented
641	#482	C₂²×C₆₁	1	1	yes	characteristic
642	#482	C₂²×C₆₁	1	2	yes	—
643	#482	C₂²×C₆₁	1	2	yes	complemented
644	#481	C₂²×C₆₁	1	2	yes	complemented
645	#480	C₂²×C₆₁	1	2	yes	complemented
646	#480	C₂²×C₆₁	1	2	yes	complemented
647	#479	C₂²×C₆₁	1	1	yes	characteristic, complemented
648	#479	C₂²×C₆₁	1	2	yes	complemented
649	#479	C₂²×C₆₁	1	2	yes	complemented
650	#478	C₂²×C₆₁	1	1	yes	characteristic, complemented
651	#477	C₂²×C₆₁	1	1	yes	characteristic, complemented
652	#476	C₂²×C₆₁	1	1	yes	characteristic, complemented
653	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
654	#475	C₂²×C₆₁	1	1	yes	characteristic, complemented
655	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
656	#474	C₂²×C₆₁	1	1	yes	characteristic, complemented
657	#467	C₂²×C₆₁	1	2	yes	complemented
658	#467	C₂²×C₆₁	1	2	yes	complemented
659	#467	C₂²×C₆₁	1	2	yes	complemented
660	#466	C₂²×C₆₁	1	2	yes	complemented
661	#465	C₂²×C₆₁	1	2	yes	complemented
662	#465	C₂²×C₆₁	1	2	yes	complemented
663	#465	C₂²×C₆₁	1	2	yes	complemented
664	#465	C₂²×C₆₁	1	2	yes	complemented
665	#464	C₂²×C₆₁	1	1	yes	characteristic, complemented
666	#463	C₂²×C₆₁	1	1	yes	characteristic, complemented
667	#462	C₂²×C₆₁	1	1	yes	characteristic, complemented
668	#461	C₂²×C₆₁	1	1	yes	characteristic, complemented
669	#452	C₂²×C₆₁	1	1	yes	characteristic
670	#452	C₂²×C₆₁	1	2	yes	—
671	#452	C₂²×C₆₁	1	2	yes	complemented
672	#451	C₂²×C₆₁	1	2	yes	complemented
673	#449	C₂²×C₆₁	1	1	yes	characteristic
674	#449	C₂²×C₆₁	1	2	yes	complemented
675	#448	C₂²×C₆₁	1	2	yes	complemented
676	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	complemented
677	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
678	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
679	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
680	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic, complemented
681	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
682	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
683	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
684	C₈×D₄	C₂²×C₆₁	1	2	yes	—
685	C₈×D₄	C₂²×C₆₁	1	2	yes	—
686	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
687	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
688	#431	C₂²×C₆₁	1	1	yes	characteristic
689	#431	C₂²×C₆₁	1	1	yes	characteristic
690	#427	C₂²×C₆₁	1	2	yes	complemented
691	#427	C₂²×C₆₁	1	2	yes	complemented
692	C₂×#107	C₂²×C₆₁	1	2	yes	complemented
693	C₂×#106	C₂²×C₆₁	1	2	yes	complemented
694	#416	C₂²×C₆₁	1	2	yes	complemented
695	#416	C₂²×C₆₁	1	2	yes	complemented
696	C₂×#103	C₂²×C₆₁	1	2	yes	complemented
697	C₂×#103	C₂²×C₆₁	1	2	yes	complemented
698	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
699	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
700	C₆₁	#61703	1	1	yes	characteristic, direct product factor, Sylow
701	C₂×#41	—	2	1	no	—
702	C₂×#41	—	2	1	no	—
703	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
704	C₂×#41	C₂³×C₆₁	1	2	yes	—
705	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
706	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
707	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
708	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
709	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
710	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
711	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
712	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
713	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
714	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
715	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
716	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
717	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
718	C₄⋊Q₈	—	2	1	no	—
719	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
720	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
721	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
723	#126	—	2	2	no	—
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	1	no	—
729	#125	—	2	2	no	—
730	#125	—	2	1	no	—
731	#125	—	2	2	no	—
732	#125	—	2	1	no	—
733	#125	C₂³×C₆₁	1	1	yes	characteristic
734	#125	C₂³×C₆₁	1	2	yes	—
735	#124	—	2	1	no	—
736	#124	—	2	1	no	—
737	#124	—	2	2	no	—
738	#124	—	2	2	no	—
739	#124	C₂³×C₆₁	1	1	yes	characteristic
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	1	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	1	no	—
754	C₂²⋊Q₈	—	2	1	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	1	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
760	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
762	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
763	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
764	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
765	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
766	#121	—	2	2	no	—
767	#121	—	2	1	no	—
768	#121	—	2	2	no	—
769	#121	—	2	1	no	—
770	#121	C₂³×C₆₁	1	1	yes	characteristic
771	#121	C₂³×C₆₁	1	2	yes	—
772	#121	C₂³×C₆₁	1	2	yes	—
773	#121	C₂³×C₆₁	1	2	yes	—
774	#120	—	2	2	no	—
775	#120	—	2	2	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	1	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	2	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
797	C₄×D₄	D₄×C₆₁	1	2	yes	—
798	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
799	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
801	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
802	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
803	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
804	C₄×D₄	C₂³×C₆₁	1	2	yes	—
805	#117	—	2	2	no	—
806	#117	—	2	2	no	—
807	#117	—	2	1	no	—
808	#117	—	2	1	no	—
809	#117	—	2	2	no	—
810	#117	—	2	2	no	—
811	#117	—	2	1	no	—
812	#117	—	2	1	no	—
813	#117	C₂³×C₆₁	1	1	yes	characteristic
814	#117	C₂³×C₆₁	1	2	yes	—
815	#117	C₂³×C₆₁	1	2	yes	—
816	#117	C₂³×C₆₁	1	2	yes	—
817	#117	C₂³×C₆₁	1	2	yes	—
818	C₂×C₄⋊C₄	—	2	2	no	—
819	C₂×C₄⋊C₄	—	2	1	no	—
820	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
821	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
822	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
823	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
824	C₂×C₂²⋊C₄	—	2	2	no	—
825	C₂×C₂²⋊C₄	—	2	2	no	—
826	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
827	C₂×C₄²	—	2	2	no	—
828	C₂×C₄²	—	2	1	no	—
829	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
830	#107	C₂³×C₆₁	1	1	yes	characteristic
831	#107	C₂³×C₆₁	1	2	yes	—
832	#107	C₂³×C₆₁	1	2	yes	—
833	#107	C₂³×C₆₁	1	2	yes	—
834	#107	C₂³×C₆₁	1	1	yes	characteristic
835	#107	C₂³×C₆₁	1	2	yes	—
836	#107	C₂³×C₆₁	1	2	yes	—
837	#106	C₂³×C₆₁	1	1	yes	characteristic
838	#106	C₂³×C₆₁	1	2	yes	—
839	#106	C₂³×C₆₁	1	2	yes	—
840	#106	C₂³×C₆₁	1	2	yes	—
841	#106	C₂³×C₆₁	1	1	yes	characteristic
842	#106	C₂³×C₆₁	1	2	yes	—
843	#106	C₂³×C₆₁	1	2	yes	—
844	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
845	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
846	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
848	#103	C₂³×C₆₁	1	1	yes	characteristic
849	#103	C₂³×C₆₁	1	1	yes	characteristic
850	#103	C₂³×C₆₁	1	2	yes	—
851	#103	C₂³×C₆₁	1	2	yes	—
852	#103	C₂³×C₆₁	1	2	yes	—
853	#103	C₂³×C₆₁	1	2	yes	—
854	#103	C₂³×C₆₁	1	2	yes	—
855	#103	C₂³×C₆₁	1	2	yes	—
856	#103	C₂³×C₆₁	1	2	yes	—
857	#103	C₂³×C₆₁	1	2	yes	—
858	#103	C₂³×C₆₁	1	1	yes	characteristic
859	#103	C₂³×C₆₁	1	1	yes	characteristic
860	#103	C₂³×C₆₁	1	2	yes	—
861	#102	C₂³×C₆₁	1	1	yes	characteristic
862	#102	C₂³×C₆₁	1	1	yes	characteristic
863	#102	C₂³×C₆₁	1	2	yes	—
864	#102	C₂³×C₆₁	1	2	yes	—
865	#102	C₂³×C₆₁	1	1	yes	characteristic
866	#102	C₂³×C₆₁	1	1	yes	characteristic
867	#102	C₂³×C₆₁	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
869	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
871	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
873	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
874	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
875	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
876	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
877	C₄×C₈	C₂³×C₆₁	1	2	yes	—
878	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
879	#41	—	4	1	no	—
880	#41	—	4	1	no	—
881	#41	—	4	2	no	—
882	#41	—	4	2	no	—
883	#41	—	4	4	no	—
884	#41	—	4	4	no	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	—	2	1	no	—
887	C₂×Q₈	—	2	1	no	—
888	C₂×Q₈	—	2	2	no	—
889	C₂×Q₈	—	4	2	no	—
890	C₂×Q₈	—	4	2	no	—
891	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
892	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
893	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
894	C₂×D₄	—	2	4	no	—
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	2	1	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	2	no	—
901	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
902	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
903	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
904	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
905	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	4	2	no	—
916	C₂²×C₄	—	4	2	no	—
917	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
918	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
919	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
920	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
921	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
922	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
923	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
924	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
925	Q₁₆	—	4	1	no	—
926	Q₁₆	—	4	2	no	—
927	SD₁₆	—	4	1	no	—
928	SD₁₆	—	4	2	no	—
929	SD₁₆	—	4	1	no	—
930	D₈	—	4	1	no	—
931	C₂×C₈	—	4	2	no	—
932	C₂×C₈	—	4	2	no	—
933	C₂×C₈	—	4	2	no	—
934	C₂×C₈	—	4	2	no	—
935	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
936	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
937	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
938	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
939	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
940	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
965	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
966	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
967	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
968	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
969	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
970	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
973	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
996	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
997	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
998	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	2	no	—
1006	C₄²	—	2	2	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1009	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1010	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1011	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1012	C₂³	—	2	4	no	—
1013	C₂³	—	2	1	no	—
1014	C₂³	—	2	1	no	—
1015	C₂³	—	4	2	no	—
1016	C₂³	—	4	2	no	—
1017	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1018	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1019	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1020	Q₈	—	2	1	no	—
1021	Q₈	—	2	1	no	—
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	1	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	4	2	no	—
1027	Q₈	—	4	2	no	—
1028	Q₈	—	8	1	no	—
1029	Q₈	—	8	2	no	—
1030	D₄	—	2	4	no	—
1031	D₄	—	2	2	no	—
1032	D₄	—	2	1	no	—
1033	D₄	—	2	1	no	—
1034	D₄	—	2	1	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	4	2	no	—
1037	D₄	—	4	2	no	—
1038	D₄	—	4	4	no	—
1039	D₄	—	4	4	no	—
1040	D₄	—	8	2	no	—
1041	D₄	—	8	2	no	—
1042	D₄	#135×C₆₁	1	4	yes	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	4	2	no	—
1063	C₂×C₄	—	4	1	no	—
1064	C₂×C₄	—	4	2	no	—
1065	C₂×C₄	—	4	4	no	—
1066	C₂×C₄	—	4	4	no	—
1067	C₂×C₄	—	4	2	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	8	1	no	—
1070	C₂×C₄	—	8	2	no	—
1071	C₂×C₄	—	8	2	no	—
1072	C₂×C₄	—	8	2	no	—
1073	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1074	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1075	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1076	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1077	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1078	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1079	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1080	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1081	C₈	—	2	1	no	—
1082	C₈	—	2	1	no	—
1083	C₈	—	2	1	no	—
1084	C₈	—	2	2	no	—
1085	C₈	—	2	2	no	—
1086	C₈	—	2	1	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	2	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	—	8	4	no	—
1102	C₂²	C₂×#135×C₆₁	1	4	yes	—
1103	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1104	C₄	—	2	1	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	2	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	2	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	2	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	2	no	—
1119	C₄	—	4	1	no	—
1120	C₄	C₂×#135×C₆₁	1	2	yes	—
1121	C₄	C₆₁×#585	1	1	yes	characteristic
1122	C₄	C₆₁×#585	1	1	yes	characteristic
1123	C₂	—	2	4	no	—
1124	C₂	—	4	1	no	—
1125	C₂	—	4	2	no	—
1126	C₂	—	8	1	no	—
1127	C₂	—	8	1	no	—
1128	C₂	C₆₁×#3485	1	1	yes	characteristic
1129	C₂	C₂²×#135×C₆₁	1	1	yes	characteristic
1130	C₂	C₆₁×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3520	C₂	semidirect
2. C₆₁×#3475	C₂	semidirect
3. C₆₁×#3342	C₂	semidirect
4. C₆₁×#3340	C₂	semidirect
5. C₆₁×#3337	C₂	semidirect
6. C₆₁×#3336	C₂	semidirect
7. C₆₁×#3335	C₂	semidirect
8. C₆₁×#3334	C₂	semidirect
9. C₆₁×#3303	C₂	semidirect
10. C₆₁×#3302	C₂	semidirect
11. C₆₁×#3301	C₂	semidirect
12. C₆₁×#3300	C₂	semidirect
13. C₆₁×#3299	C₂	semidirect
14. C₆₁×#3298	C₂	semidirect
15. C₆₁×#3233	C₂	semidirect
16. C₆₁×#3231	C₂	semidirect
17. C₆₁×#3191	C₂	semidirect
18. C₆₁×#3190	C₂	semidirect
19. C₆₁×#3107	C₂	semidirect
20. C₆₁×#3102	C₂	semidirect
21. C₆₁×#3091	C₂	semidirect
22. C₂×C₆₁×#485	C₂	semidirect
23. C₆₁×#2972	C₂	semidirect
57. C₆₁×#500	C₂²	semidirect
58. C₆₁×#499	C₂²	semidirect
59. C₆₁×#498	C₂²	semidirect
60. C₆₁×#488	C₂²	semidirect
61. C₆₁×#487	C₂²	semidirect
62. C₆₁×#487	C₂²	semidirect
68. C₆₁×#485	C₂²	semidirect
69. C₆₁×#485	C₂²	semidirect
70. C₆₁×#485	C₂²	semidirect
71. C₆₁×#485	C₂²	semidirect
72. C₆₁×#485	C₂²	semidirect
73. C₆₁×#484	C₂²	semidirect
74. C₆₁×#483	C₂²	semidirect
75. C₆₁×#483	C₂²	semidirect
78. C₆₁×#482	C₂²	semidirect
79. C₆₁×#481	C₂²	semidirect
80. C₆₁×#480	C₂²	semidirect
81. C₆₁×#480	C₂²	semidirect
82. C₆₁×#479	C₂²	semidirect
83. C₆₁×#479	C₂²	semidirect
84. C₆₁×#479	C₂²	semidirect
85. C₆₁×#478	C₂²	semidirect
86. C₆₁×#477	C₂²	semidirect
87. C₆₁×#476	C₂²	semidirect
88. C₆₁×#475	C₂²	semidirect
89. C₆₁×#475	C₂²	semidirect
90. C₆₁×#474	C₂²	semidirect
91. C₆₁×#474	C₂²	semidirect
92. C₆₁×#467	C₂²	semidirect
93. C₆₁×#467	C₂²	semidirect
94. C₆₁×#467	C₂²	semidirect
95. C₆₁×#466	C₂²	semidirect
96. C₆₁×#465	C₂²	semidirect
97. C₆₁×#465	C₂²	semidirect
98. C₆₁×#465	C₂²	semidirect
99. C₆₁×#465	C₂²	semidirect
100. C₆₁×#464	C₂²	semidirect
101. C₆₁×#463	C₂²	semidirect
102. C₆₁×#462	C₂²	semidirect
103. C₆₁×#461	C₂²	semidirect
106. C₆₁×#452	C₂²	semidirect
107. C₆₁×#451	C₂²	semidirect
109. C₆₁×#449	C₂²	semidirect
110. C₆₁×#448	C₂²	semidirect
111. C₄×Q₁₆×C₆₁	C₂²	semidirect
112. C₄×Q₁₆×C₆₁	C₂²	semidirect
113. C₄×SD₁₆×C₆₁	C₂²	semidirect
114. C₄×SD₁₆×C₆₁	C₂²	semidirect
115. C₄×SD₁₆×C₆₁	C₂²	semidirect
116. C₄×D₈×C₆₁	C₂²	semidirect
125. C₆₁×#427	C₂²	semidirect
126. C₆₁×#427	C₂²	semidirect
127. C₂×#107×C₆₁	C₂²	semidirect
128. C₂×#106×C₆₁	C₂²	semidirect
129. C₆₁×#416	C₂²	semidirect
130. C₆₁×#416	C₂²	semidirect
131. C₂×#103×C₆₁	C₂²	semidirect
132. C₂×#103×C₆₁	C₂²	semidirect
521. #61703	C₆₁	direct (N × H)
558. #3520	C₂×C₆₁	semidirect
559. #3475	C₂×C₆₁	semidirect
560. #3342	C₂×C₆₁	semidirect
561. #3340	C₂×C₆₁	semidirect
562. #3337	C₂×C₆₁	semidirect
563. #3336	C₂×C₆₁	semidirect
564. #3335	C₂×C₆₁	semidirect
565. #3334	C₂×C₆₁	semidirect
566. #3303	C₂×C₆₁	semidirect
567. #3302	C₂×C₆₁	semidirect
568. #3301	C₂×C₆₁	semidirect
569. #3300	C₂×C₆₁	semidirect
570. #3299	C₂×C₆₁	semidirect
571. #3298	C₂×C₆₁	semidirect
572. #3233	C₂×C₆₁	semidirect
573. #3231	C₂×C₆₁	semidirect
574. #3191	C₂×C₆₁	semidirect
575. #3190	C₂×C₆₁	semidirect
576. #3107	C₂×C₆₁	semidirect
577. #3102	C₂×C₆₁	semidirect
578. #3091	C₂×C₆₁	semidirect
579. C₂×#485	C₂×C₆₁	semidirect
580. #2972	C₂×C₆₁	semidirect
622. #500	C₂²×C₆₁	semidirect
623. #499	C₂²×C₆₁	semidirect
624. #498	C₂²×C₆₁	semidirect
625. #488	C₂²×C₆₁	semidirect
626. #487	C₂²×C₆₁	semidirect
627. #487	C₂²×C₆₁	semidirect
633. #485	C₂²×C₆₁	semidirect
634. #485	C₂²×C₆₁	semidirect
635. #485	C₂²×C₆₁	semidirect
636. #485	C₂²×C₆₁	semidirect
637. #485	C₂²×C₆₁	semidirect
638. #484	C₂²×C₆₁	semidirect
639. #483	C₂²×C₆₁	semidirect
640. #483	C₂²×C₆₁	semidirect
643. #482	C₂²×C₆₁	semidirect
644. #481	C₂²×C₆₁	semidirect
645. #480	C₂²×C₆₁	semidirect
646. #480	C₂²×C₆₁	semidirect
647. #479	C₂²×C₆₁	semidirect
648. #479	C₂²×C₆₁	semidirect
649. #479	C₂²×C₆₁	semidirect
650. #478	C₂²×C₆₁	semidirect
651. #477	C₂²×C₆₁	semidirect
652. #476	C₂²×C₆₁	semidirect
653. #475	C₂²×C₆₁	semidirect
654. #475	C₂²×C₆₁	semidirect
655. #474	C₂²×C₆₁	semidirect
656. #474	C₂²×C₆₁	semidirect
657. #467	C₂²×C₆₁	semidirect
658. #467	C₂²×C₆₁	semidirect
659. #467	C₂²×C₆₁	semidirect
660. #466	C₂²×C₆₁	semidirect
661. #465	C₂²×C₆₁	semidirect
662. #465	C₂²×C₆₁	semidirect
663. #465	C₂²×C₆₁	semidirect
664. #465	C₂²×C₆₁	semidirect
665. #464	C₂²×C₆₁	semidirect
666. #463	C₂²×C₆₁	semidirect
667. #462	C₂²×C₆₁	semidirect
668. #461	C₂²×C₆₁	semidirect
671. #452	C₂²×C₆₁	semidirect
672. #451	C₂²×C₆₁	semidirect
674. #449	C₂²×C₆₁	semidirect
675. #448	C₂²×C₆₁	semidirect
676. C₄×Q₁₆	C₂²×C₆₁	semidirect
677. C₄×Q₁₆	C₂²×C₆₁	semidirect
678. C₄×SD₁₆	C₂²×C₆₁	semidirect
679. C₄×SD₁₆	C₂²×C₆₁	semidirect
680. C₄×SD₁₆	C₂²×C₆₁	semidirect
681. C₄×D₈	C₂²×C₆₁	semidirect
690. #427	C₂²×C₆₁	semidirect
691. #427	C₂²×C₆₁	semidirect
692. C₂×#107	C₂²×C₆₁	semidirect
693. C₂×#106	C₂²×C₆₁	semidirect
694. #416	C₂²×C₆₁	semidirect
695. #416	C₂²×C₆₁	semidirect
696. C₂×#103	C₂²×C₆₁	semidirect
697. C₂×#103	C₂²×C₆₁	semidirect
700. C₆₁	#61703	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×#3520	2
C₆₁×#3475	2
C₆₁×#3342	2
C₆₁×#3340	2
C₆₁×#3337	2
C₆₁×#3336	2
C₆₁×#3335	2
C₆₁×#3334	2
C₆₁×#3303	2
C₆₁×#3302	2
C₆₁×#3301	2
C₆₁×#3300	2
C₆₁×#3299	2
C₆₁×#3298	2
C₆₁×#3233	2
C₆₁×#3231	2
C₆₁×#3191	2
C₆₁×#3190	2
C₆₁×#3107	2
C₆₁×#3102	2
C₆₁×#3091	2
C₂×C₆₁×#485	2
C₆₁×#2972	2
#61703	61

Subgroups — C61×#61703 #29565136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61703 #29565136