Subgroups — C₆₁×#61263 #29564696

Order 15616.

1824 conjugacy classes of subgroups.

The subgroup lattice has 1140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3494	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#3350	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3348	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3346	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3343	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3340	C₂	1	2	yes	maximal, complemented
8	C₆₁×#3337	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3337	C₂	1	2	yes	maximal, complemented
10	C₆₁×#3335	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3163	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3096	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3095	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3094	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3082	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3081	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#3057	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₆₁×#465	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₁×#2949	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#2929	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₁×#2912	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₆₁×#427	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
26	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
27	C₆₁×#556	C₂²	1	2	yes	complemented
28	C₆₁×#555	C₂²	1	2	yes	—
29	C₆₁×#554	C₂²	1	2	yes	complemented
30	C₆₁×#553	C₂²	1	2	yes	—
31	C₆₁×#553	C₂²	1	2	yes	—
32	C₆₁×#552	—	2	2	no	—
33	C₆₁×#552	C₂²	1	2	yes	complemented
34	C₆₁×#552	C₂²	1	2	yes	complemented
35	C₆₁×#551	—	2	2	no	—
36	C₆₁×#551	—	2	2	no	—
37	C₆₁×#547	C₂²	1	2	yes	—
38	C₆₁×#546	—	2	2	no	—
39	C₆₁×#544	C₂²	1	1	yes	characteristic
40	C₆₁×#544	C₂²	1	1	yes	characteristic
41	C₆₁×#542	—	2	1	no	—
42	C₆₁×#542	—	2	1	no	—
43	C₆₁×#541	—	2	1	no	—
44	C₆₁×#540	—	2	1	no	—
45	C₆₁×#536	C₂²	1	1	yes	characteristic
46	C₆₁×#535	C₂²	1	1	yes	characteristic
47	C₆₁×#533	—	2	1	no	—
48	C₆₁×#532	—	2	1	no	—
49	C₆₁×#529	—	2	1	no	—
50	C₆₁×#529	—	2	1	no	—
51	C₆₁×#525	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
53	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
54	C₆₁×#520	C₂²	1	1	yes	characteristic
55	C₆₁×#520	C₂²	1	1	yes	characteristic
56	C₆₁×#519	C₂²	1	1	yes	characteristic
57	C₆₁×#518	C₂²	1	1	yes	characteristic
58	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
59	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
60	C₆₁×#501	C₂²	1	2	yes	complemented
61	C₆₁×#501	C₂²	1	2	yes	complemented
62	C₆₁×#499	C₂²	1	2	yes	complemented
63	C₆₁×#498	C₂²	1	2	yes	complemented
64	C₆₁×#485	C₂²	1	2	yes	complemented
65	C₆₁×#485	C₂²	1	2	yes	complemented
66	C₆₁×#485	C₂²	1	2	yes	complemented
67	C₆₁×#485	C₂²	1	2	yes	complemented
68	C₆₁×#484	C₂²	1	2	yes	complemented
69	C₆₁×#484	C₂²	1	2	yes	complemented
70	C₆₁×#483	C₂²	1	2	yes	complemented
71	C₆₁×#483	C₂²	1	2	yes	complemented
72	C₆₁×#482	C₂²	1	2	yes	—
73	C₆₁×#482	C₂²	1	2	yes	—
74	C₆₁×#482	C₂²	1	2	yes	complemented
75	C₆₁×#482	C₂²	1	2	yes	complemented
76	C₆₁×#481	C₂²	1	2	yes	—
77	C₆₁×#481	C₂²	1	2	yes	complemented
78	C₆₁×#480	C₂²	1	2	yes	—
79	C₆₁×#480	C₂²	1	2	yes	complemented
80	C₆₁×#479	C₂²	1	2	yes	complemented
81	C₆₁×#479	C₂²	1	2	yes	complemented
82	C₆₁×#478	C₂²	1	2	yes	complemented
83	C₆₁×#478	C₂²	1	2	yes	complemented
84	C₆₁×#477	C₂²	1	2	yes	complemented
85	C₆₁×#476	C₂²	1	2	yes	complemented
86	C₆₁×#475	C₂²	1	2	yes	complemented
87	C₆₁×#474	C₂²	1	2	yes	complemented
88	C₆₁×#468	C₂²	1	2	yes	complemented
89	C₆₁×#468	C₂²	1	2	yes	complemented
90	C₆₁×#465	C₂²	1	2	yes	—
91	C₆₁×#465	C₂²	1	2	yes	—
92	C₆₁×#465	C₂²	1	2	yes	—
93	C₆₁×#465	C₂²	1	2	yes	—
94	C₆₁×#465	C₂²	1	2	yes	complemented
95	C₆₁×#465	C₂²	1	2	yes	complemented
96	C₆₁×#440	C₂²	1	2	yes	complemented
97	C₆₁×#440	C₂²	1	2	yes	complemented
98	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
99	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	complemented
100	C₆₁×#435	C₂²	1	2	yes	complemented
101	C₆₁×#435	C₂²	1	2	yes	complemented
102	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
103	C₈×D₄×C₆₁	C₂²	1	2	yes	complemented
104	C₆₁×#428	C₂²	1	1	yes	characteristic
105	C₆₁×#428	C₂²	1	1	yes	characteristic
106	C₆₁×#428	C₂²	1	1	yes	characteristic
107	C₆₁×#428	C₂²	1	1	yes	characteristic
108	C₆₁×#428	C₂²	1	2	yes	complemented
109	C₆₁×#428	C₂²	1	2	yes	complemented
110	C₆₁×#427	C₂²	1	1	yes	characteristic
111	C₆₁×#427	C₂²	1	1	yes	characteristic
112	C₆₁×#427	C₂²	1	1	yes	characteristic
113	C₆₁×#427	C₂²	1	1	yes	characteristic
114	C₆₁×#427	C₂²	1	1	yes	characteristic, complemented
115	C₆₁×#427	C₂²	1	2	yes	complemented
116	C₆₁×#427	C₂²	1	1	yes	characteristic, complemented
117	C₆₁×#427	C₂²	1	1	yes	characteristic, complemented
118	C₆₁×#427	C₂²	1	1	yes	characteristic, complemented
119	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic, complemented
120	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic, complemented
121	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
122	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic, complemented
123	C₂×#106×C₆₁	C₂²	1	2	yes	complemented
124	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic, complemented
125	C₆₁×#424	C₂²	1	1	yes	characteristic
126	C₆₁×#419	C₂²	1	1	yes	characteristic
127	C₆₁×#419	C₂²	1	1	yes	characteristic
128	C₆₁×#418	C₂²	1	1	yes	characteristic
129	C₆₁×#418	C₂²	1	1	yes	characteristic
130	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
131	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
132	C₆₁×#408	C₂²	1	1	yes	characteristic
133	C₆₁×#407	C₂²	1	1	yes	characteristic
134	C₆₁×#405	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₁	—	2	2	no	—
136	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
138	C₂²×D₄×C₆₁	—	2	1	no	—
139	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
141	C₂×SD₁₆×C₆₁	—	2	4	no	—
142	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
144	#131×C₆₁	—	2	4	no	—
145	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
147	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₆₁	—	2	4	no	—
149	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
153	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
154	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
155	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
156	C₄⋊Q₈×C₆₁	—	2	1	no	—
157	C₄⋊Q₈×C₆₁	—	2	1	no	—
158	C₄⋊Q₈×C₆₁	—	2	1	no	—
159	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
161	#127×C₆₁	—	2	1	no	—
162	#126×C₆₁	—	2	2	no	—
163	#126×C₆₁	—	2	2	no	—
164	#126×C₆₁	—	2	2	no	—
165	#126×C₆₁	—	2	2	no	—
166	#126×C₆₁	—	2	2	no	—
167	#126×C₆₁	—	2	2	no	—
168	#125×C₆₁	—	2	2	no	—
169	#125×C₆₁	—	2	1	no	—
170	#125×C₆₁	—	2	1	no	—
171	#125×C₆₁	—	2	2	no	—
172	#125×C₆₁	—	2	2	no	—
173	#125×C₆₁	C₂³	1	2	yes	—
174	#125×C₆₁	C₂³	1	2	yes	—
175	#124×C₆₁	—	2	1	no	—
176	#124×C₆₁	—	2	1	no	—
177	#124×C₆₁	—	2	2	no	—
178	#124×C₆₁	—	2	2	no	—
179	#124×C₆₁	—	2	2	no	—
180	#123×C₆₁	—	2	2	no	—
181	#123×C₆₁	—	2	2	no	—
182	#123×C₆₁	—	2	2	no	—
183	#123×C₆₁	—	2	2	no	—
184	#123×C₆₁	—	2	2	no	—
185	#123×C₆₁	—	2	2	no	—
186	#123×C₆₁	—	2	2	no	—
187	#123×C₆₁	D₄	1	2	yes	—
188	C₂²⋊Q₈×C₆₁	—	2	1	no	—
189	C₂²⋊Q₈×C₆₁	—	2	1	no	—
190	C₂²⋊Q₈×C₆₁	—	2	2	no	—
191	C₂²⋊Q₈×C₆₁	—	2	2	no	—
192	C₂²⋊Q₈×C₆₁	—	2	2	no	—
193	C₂²⋊Q₈×C₆₁	—	2	2	no	—
194	C₂²⋊Q₈×C₆₁	—	2	2	no	—
195	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
196	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
197	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
198	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
200	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
201	#121×C₆₁	—	2	2	no	—
202	#121×C₆₁	—	2	2	no	—
203	#121×C₆₁	—	2	2	no	—
204	#121×C₆₁	—	2	1	no	—
205	#121×C₆₁	—	2	1	no	—
206	#121×C₆₁	D₄	1	1	yes	characteristic
207	#121×C₆₁	D₄	1	1	yes	characteristic
208	#121×C₆₁	C₂³	1	2	yes	—
209	#121×C₆₁	C₂³	1	2	yes	—
210	#121×C₆₁	C₂³	1	2	yes	—
211	#121×C₆₁	C₂³	1	2	yes	—
212	#120×C₆₁	—	2	2	no	—
213	#120×C₆₁	D₄	1	2	yes	—
214	C₄×Q₈×C₆₁	—	2	1	no	—
215	C₄×Q₈×C₆₁	—	2	1	no	—
216	C₄×Q₈×C₆₁	—	2	1	no	—
217	C₄×Q₈×C₆₁	—	2	2	no	—
218	C₄×Q₈×C₆₁	—	2	1	no	—
219	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
221	C₄×D₄×C₆₁	—	2	1	no	—
222	C₄×D₄×C₆₁	—	2	1	no	—
223	C₄×D₄×C₆₁	—	2	2	no	—
224	C₄×D₄×C₆₁	—	2	2	no	—
225	C₄×D₄×C₆₁	—	2	2	no	—
226	C₄×D₄×C₆₁	—	2	1	no	—
227	C₄×D₄×C₆₁	—	2	1	no	—
228	C₄×D₄×C₆₁	—	2	2	no	—
229	C₄×D₄×C₆₁	—	2	2	no	—
230	C₄×D₄×C₆₁	C₂³	1	2	yes	—
231	C₄×D₄×C₆₁	C₂³	1	2	yes	—
232	C₄×D₄×C₆₁	C₂³	1	2	yes	—
233	C₄×D₄×C₆₁	C₂³	1	2	yes	—
234	#117×C₆₁	—	2	1	no	—
235	#117×C₆₁	—	2	1	no	—
236	#117×C₆₁	—	2	1	no	—
237	#117×C₆₁	—	2	1	no	—
238	#117×C₆₁	—	2	2	no	—
239	#117×C₆₁	—	2	2	no	—
240	#117×C₆₁	—	2	2	no	—
241	#117×C₆₁	—	2	2	no	—
242	#117×C₆₁	C₂³	1	1	yes	characteristic
243	#117×C₆₁	C₂³	1	1	yes	characteristic
244	#117×C₆₁	C₂³	1	1	yes	characteristic
245	#117×C₆₁	C₂³	1	2	yes	—
246	#117×C₆₁	C₂³	1	1	yes	characteristic
247	#117×C₆₁	C₂³	1	2	yes	—
248	#117×C₆₁	C₂³	1	1	yes	characteristic
249	#117×C₆₁	C₂³	1	1	yes	characteristic
250	#117×C₆₁	C₂³	1	1	yes	characteristic
251	#117×C₆₁	C₂³	1	1	yes	characteristic
252	#117×C₆₁	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
254	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
260	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
263	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
265	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
266	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
267	C₂×C₄²×C₆₁	—	2	1	no	—
268	C₂×C₄²×C₆₁	—	2	1	no	—
269	#107×C₆₁	C₂³	1	1	yes	characteristic
270	#107×C₆₁	C₂³	1	1	yes	characteristic
271	#107×C₆₁	C₂³	1	1	yes	characteristic
272	#107×C₆₁	C₂³	1	1	yes	characteristic
273	#107×C₆₁	C₂³	1	1	yes	characteristic
274	#107×C₆₁	C₂³	1	1	yes	characteristic
275	#107×C₆₁	C₂³	1	1	yes	characteristic
276	#107×C₆₁	C₂³	1	1	yes	characteristic
277	#107×C₆₁	C₂³	1	2	yes	—
278	#107×C₆₁	C₂³	1	2	yes	—
279	#107×C₆₁	C₂³	1	2	yes	—
280	#107×C₆₁	C₂³	1	2	yes	—
281	#106×C₆₁	C₂³	1	2	yes	—
282	#106×C₆₁	C₂³	1	2	yes	—
283	#106×C₆₁	C₂³	1	1	yes	characteristic
284	#106×C₆₁	C₂³	1	1	yes	characteristic
285	#106×C₆₁	C₂³	1	1	yes	characteristic
286	#106×C₆₁	C₂³	1	1	yes	characteristic
287	#106×C₆₁	C₂³	1	1	yes	characteristic
288	#106×C₆₁	C₂³	1	1	yes	characteristic
289	#106×C₆₁	C₂³	1	1	yes	characteristic
290	#106×C₆₁	C₂³	1	1	yes	characteristic
291	#106×C₆₁	C₂³	1	2	yes	—
292	#106×C₆₁	C₂³	1	2	yes	—
293	#106×C₆₁	C₂³	1	2	yes	—
294	#106×C₆₁	C₂³	1	2	yes	—
295	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
296	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
297	#103×C₆₁	C₂³	1	2	yes	—
298	#103×C₆₁	C₂³	1	2	yes	—
299	#103×C₆₁	C₂³	1	2	yes	—
300	#103×C₆₁	C₂³	1	2	yes	—
301	#103×C₆₁	C₂³	1	2	yes	—
302	#103×C₆₁	C₂³	1	2	yes	—
303	#102×C₆₁	C₂³	1	2	yes	—
304	#102×C₆₁	C₂³	1	2	yes	—
305	#102×C₆₁	C₂³	1	2	yes	—
306	#102×C₆₁	C₂³	1	2	yes	—
307	#102×C₆₁	C₂³	1	2	yes	—
308	#102×C₆₁	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
312	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
313	#97×C₆₁	C₂³	1	2	yes	—
314	C₄×C₈×C₆₁	C₂³	1	2	yes	—
315	C₂⁴×C₆₁	—	2	1	no	—
316	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
317	#41×C₆₁	—	2	2	no	—
318	#41×C₆₁	—	2	2	no	—
319	#41×C₆₁	—	8	4	no	—
320	C₂×Q₈×C₆₁	—	2	1	no	—
321	C₂×Q₈×C₆₁	—	2	2	no	—
322	C₂×Q₈×C₆₁	—	2	2	no	—
323	C₂×Q₈×C₆₁	—	2	2	no	—
324	C₂×Q₈×C₆₁	—	2	2	no	—
325	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
327	C₂×D₄×C₆₁	—	2	2	no	—
328	C₂×D₄×C₆₁	—	2	2	no	—
329	C₂×D₄×C₆₁	—	2	2	no	—
330	C₂×D₄×C₆₁	—	2	2	no	—
331	C₂×D₄×C₆₁	—	2	1	no	—
332	C₂×D₄×C₆₁	—	2	2	no	—
333	C₂×D₄×C₆₁	—	2	2	no	—
334	C₂×D₄×C₆₁	—	8	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	2	yes	—
338	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₆₁	—	2	2	no	—
341	C₂²×C₄×C₆₁	—	2	2	no	—
342	C₂²×C₄×C₆₁	—	2	1	no	—
343	C₂²×C₄×C₆₁	—	2	1	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	1	no	—
349	C₂²×C₄×C₆₁	—	2	2	no	—
350	C₂²×C₄×C₆₁	—	2	2	no	—
351	C₂²×C₄×C₆₁	—	2	2	no	—
352	C₂²×C₄×C₆₁	—	2	2	no	—
353	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
358	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
360	SD₁₆×C₆₁	—	2	4	no	—
361	SD₁₆×C₆₁	—	2	4	no	—
362	M₁₆×C₆₁	—	2	2	no	—
363	M₁₆×C₆₁	—	2	2	no	—
364	M₁₆×C₆₁	—	2	4	no	—
365	C₂×C₈×C₆₁	—	2	2	no	—
366	C₂×C₈×C₆₁	—	2	2	no	—
367	C₂×C₈×C₆₁	—	2	2	no	—
368	C₂×C₈×C₆₁	—	2	2	no	—
369	C₂×C₈×C₆₁	—	2	2	no	—
370	C₂×C₈×C₆₁	—	2	4	no	—
371	C₂×C₈×C₆₁	#41	1	4	yes	complemented
372	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
373	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
375	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄×C₆₁	—	2	2	no	—
379	C₄⋊C₄×C₆₁	—	2	2	no	—
380	C₄⋊C₄×C₆₁	—	2	1	no	—
381	C₄⋊C₄×C₆₁	—	2	1	no	—
382	C₄⋊C₄×C₆₁	—	2	1	no	—
383	C₄⋊C₄×C₆₁	—	2	1	no	—
384	C₄⋊C₄×C₆₁	—	2	1	no	—
385	C₄⋊C₄×C₆₁	—	2	1	no	—
386	C₄⋊C₄×C₆₁	—	2	2	no	—
387	C₄⋊C₄×C₆₁	—	2	2	no	—
388	C₄⋊C₄×C₆₁	—	2	2	no	—
389	C₄⋊C₄×C₆₁	—	2	2	no	—
390	C₄⋊C₄×C₆₁	—	2	2	no	—
391	C₄⋊C₄×C₆₁	—	2	2	no	—
392	C₄⋊C₄×C₆₁	—	2	2	no	—
393	C₄⋊C₄×C₆₁	—	2	2	no	—
394	C₄⋊C₄×C₆₁	—	2	2	no	—
395	C₄⋊C₄×C₆₁	—	2	2	no	—
396	C₄⋊C₄×C₆₁	—	2	2	no	—
397	C₄⋊C₄×C₆₁	—	2	2	no	—
398	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
412	C₂²⋊C₄×C₆₁	—	2	1	no	—
413	C₂²⋊C₄×C₆₁	—	2	1	no	—
414	C₂²⋊C₄×C₆₁	—	2	1	no	—
415	C₂²⋊C₄×C₆₁	—	2	1	no	—
416	C₂²⋊C₄×C₆₁	—	2	1	no	—
417	C₂²⋊C₄×C₆₁	—	2	1	no	—
418	C₂²⋊C₄×C₆₁	—	2	1	no	—
419	C₂²⋊C₄×C₆₁	—	2	1	no	—
420	C₂²⋊C₄×C₆₁	—	2	2	no	—
421	C₂²⋊C₄×C₆₁	—	2	2	no	—
422	C₂²⋊C₄×C₆₁	—	2	2	no	—
423	C₂²⋊C₄×C₆₁	—	2	2	no	—
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	2	no	—
430	C₂²⋊C₄×C₆₁	—	2	2	no	—
431	C₂²⋊C₄×C₆₁	—	2	2	no	—
432	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
437	C₄²×C₆₁	—	2	1	no	—
438	C₄²×C₆₁	—	2	1	no	—
439	C₄²×C₆₁	—	2	1	no	—
440	C₄²×C₆₁	—	2	1	no	—
441	C₄²×C₆₁	—	2	1	no	—
442	C₄²×C₆₁	—	2	1	no	—
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	2	no	—
448	C₄²×C₆₁	—	2	2	no	—
449	C₄²×C₆₁	C₂⁴	1	2	yes	—
450	C₂³×C₆₁	—	2	2	no	—
451	C₂³×C₆₁	—	2	2	no	—
452	C₂³×C₆₁	—	2	2	no	—
453	C₂³×C₆₁	—	4	1	no	—
454	C₂³×C₆₁	—	4	2	no	—
455	C₂³×C₆₁	—	8	1	no	—
456	C₂³×C₆₁	—	8	1	no	—
457	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
458	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
459	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
460	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
461	Q₈×C₆₁	—	2	2	no	—
462	Q₈×C₆₁	—	2	2	no	—
463	Q₈×C₆₁	—	2	2	no	—
464	Q₈×C₆₁	—	4	2	no	—
465	Q₈×C₆₁	—	8	2	no	—
466	Q₈×C₆₁	—	8	2	no	—
467	D₄×C₆₁	—	2	4	no	—
468	D₄×C₆₁	—	2	4	no	—
469	D₄×C₆₁	—	2	2	no	—
470	D₄×C₆₁	—	2	2	no	—
471	D₄×C₆₁	—	2	2	no	—
472	D₄×C₆₁	—	4	2	no	—
473	D₄×C₆₁	—	4	4	no	—
474	D₄×C₆₁	—	4	2	no	—
475	D₄×C₆₁	—	8	2	no	—
476	D₄×C₆₁	—	8	2	no	—
477	D₄×C₆₁	—	8	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	1	no	—
482	C₂×C₄×C₆₁	—	2	1	no	—
483	C₂×C₄×C₆₁	—	2	2	no	—
484	C₂×C₄×C₆₁	—	2	1	no	—
485	C₂×C₄×C₆₁	—	2	1	no	—
486	C₂×C₄×C₆₁	—	2	2	no	—
487	C₂×C₄×C₆₁	—	2	1	no	—
488	C₂×C₄×C₆₁	—	2	1	no	—
489	C₂×C₄×C₆₁	—	2	1	no	—
490	C₂×C₄×C₆₁	—	2	1	no	—
491	C₂×C₄×C₆₁	—	2	2	no	—
492	C₂×C₄×C₆₁	—	2	1	no	—
493	C₂×C₄×C₆₁	—	2	1	no	—
494	C₂×C₄×C₆₁	—	2	1	no	—
495	C₂×C₄×C₆₁	—	2	1	no	—
496	C₂×C₄×C₆₁	—	2	2	no	—
497	C₂×C₄×C₆₁	—	2	2	no	—
498	C₂×C₄×C₆₁	—	4	2	no	—
499	C₂×C₄×C₆₁	—	4	2	no	—
500	C₂×C₄×C₆₁	—	4	2	no	—
501	C₂×C₄×C₆₁	—	8	2	no	—
502	C₂×C₄×C₆₁	—	8	2	no	—
503	C₂×C₄×C₆₁	—	8	2	no	—
504	C₂×C₄×C₆₁	—	8	1	no	—
505	C₂×C₄×C₆₁	—	8	1	no	—
506	C₂×C₄×C₆₁	—	8	1	no	—
507	C₂×C₄×C₆₁	—	8	1	no	—
508	C₂×C₄×C₆₁	—	8	2	no	—
509	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
516	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
517	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
518	C₈×C₆₁	—	2	1	no	—
519	C₈×C₆₁	—	2	1	no	—
520	C₈×C₆₁	—	2	2	no	—
521	C₈×C₆₁	—	2	2	no	—
522	C₈×C₆₁	C₂×#41	1	2	yes	—
523	C₈×C₆₁	C₂×#41	1	2	yes	—
524	#61263	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
525	C₂²×C₆₁	—	2	1	no	—
526	C₂²×C₆₁	—	2	1	no	—
527	C₂²×C₆₁	—	2	1	no	—
528	C₂²×C₆₁	—	2	1	no	—
529	C₂²×C₆₁	—	2	2	no	—
530	C₂²×C₆₁	—	2	1	no	—
531	C₂²×C₆₁	—	2	1	no	—
532	C₂²×C₆₁	—	2	2	no	—
533	C₂²×C₆₁	—	2	2	no	—
534	C₂²×C₆₁	—	2	1	no	—
535	C₂²×C₆₁	—	4	4	no	—
536	C₂²×C₆₁	—	4	2	no	—
537	C₂²×C₆₁	—	4	2	no	—
538	C₂²×C₆₁	—	4	2	no	—
539	C₂²×C₆₁	—	16	2	no	—
540	C₂²×C₆₁	#547	1	2	yes	—
541	C₂²×C₆₁	#577	1	2	yes	—
542	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
543	C₄×C₆₁	—	2	2	no	—
544	C₄×C₆₁	—	2	1	no	—
545	C₄×C₆₁	—	2	1	no	—
546	C₄×C₆₁	—	2	2	no	—
547	C₄×C₆₁	—	2	2	no	—
548	C₄×C₆₁	—	4	1	no	—
549	C₄×C₆₁	—	4	1	no	—
550	C₄×C₆₁	—	4	2	no	—
551	C₄×C₆₁	—	4	1	no	—
552	C₄×C₆₁	—	4	1	no	—
553	C₄×C₆₁	—	4	2	no	—
554	C₄×C₆₁	—	4	1	no	—
555	C₄×C₆₁	—	4	1	no	—
556	C₄×C₆₁	—	4	1	no	—
557	C₄×C₆₁	—	4	1	no	—
558	C₄×C₆₁	—	4	2	no	—
559	C₄×C₆₁	#547	1	2	yes	—
560	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
561	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
562	#3495	C₂×C₆₁	1	1	yes	characteristic, complemented
563	#3494	C₂×C₆₁	1	1	yes	characteristic
564	#3350	C₂×C₆₁	1	2	yes	complemented
565	#3348	C₂×C₆₁	1	2	yes	complemented
566	#3346	C₂×C₆₁	1	2	yes	complemented
567	#3343	C₂×C₆₁	1	2	yes	complemented
568	#3340	C₂×C₆₁	1	2	yes	complemented
569	#3337	C₂×C₆₁	1	2	yes	complemented
570	#3337	C₂×C₆₁	1	2	yes	complemented
571	#3335	C₂×C₆₁	1	2	yes	complemented
572	#3163	C₂×C₆₁	1	1	yes	characteristic, complemented
573	#3097	C₂×C₆₁	1	1	yes	characteristic, complemented
574	#3096	C₂×C₆₁	1	1	yes	characteristic, complemented
575	#3095	C₂×C₆₁	1	1	yes	characteristic, complemented
576	#3094	C₂×C₆₁	1	1	yes	characteristic, complemented
577	#3082	C₂×C₆₁	1	1	yes	characteristic, complemented
578	#3081	C₂×C₆₁	1	1	yes	characteristic, complemented
579	#3057	C₂×C₆₁	1	1	yes	characteristic, complemented
580	C₂×#465	C₂×C₆₁	1	1	yes	characteristic, complemented
581	#2949	C₂×C₆₁	1	1	yes	characteristic, complemented
582	#2929	C₂×C₆₁	1	1	yes	characteristic, complemented
583	#2912	C₂×C₆₁	1	1	yes	characteristic, complemented
584	C₂×#427	C₂×C₆₁	1	1	yes	characteristic, complemented
585	C₂×C₆₁	—	2	2	no	—
586	C₂×C₆₁	—	2	2	no	—
587	C₂×C₆₁	—	4	2	no	—
588	C₂×C₆₁	—	4	1	no	—
589	C₂×C₆₁	—	8	2	no	—
590	C₂×C₆₁	C₂×#547	1	1	yes	characteristic
591	C₂×C₆₁	C₂×#577	1	1	yes	characteristic
592	C₂×C₆₁	#3584	1	1	yes	characteristic
593	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
594	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
595	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
596	#556	C₂²×C₆₁	1	2	yes	complemented
597	#555	C₂²×C₆₁	1	2	yes	—
598	#554	C₂²×C₆₁	1	2	yes	complemented
599	#553	C₂²×C₆₁	1	2	yes	—
600	#553	C₂²×C₆₁	1	2	yes	—
601	#552	—	2	2	no	—
602	#552	C₂²×C₆₁	1	2	yes	complemented
603	#552	C₂²×C₆₁	1	2	yes	complemented
604	#551	—	2	2	no	—
605	#551	—	2	2	no	—
606	#547	C₂²×C₆₁	1	2	yes	—
607	#546	—	2	2	no	—
608	#544	C₂²×C₆₁	1	1	yes	characteristic
609	#544	C₂²×C₆₁	1	1	yes	characteristic
610	#542	—	2	1	no	—
611	#542	—	2	1	no	—
612	#541	—	2	1	no	—
613	#540	—	2	1	no	—
614	#536	C₂²×C₆₁	1	1	yes	characteristic
615	#535	C₂²×C₆₁	1	1	yes	characteristic
616	#533	—	2	1	no	—
617	#532	—	2	1	no	—
618	#529	—	2	1	no	—
619	#529	—	2	1	no	—
620	#525	C₂²×C₆₁	1	1	yes	characteristic
621	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
622	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
623	#520	C₂²×C₆₁	1	1	yes	characteristic
624	#520	C₂²×C₆₁	1	1	yes	characteristic
625	#519	C₂²×C₆₁	1	1	yes	characteristic
626	#518	C₂²×C₆₁	1	1	yes	characteristic
627	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
628	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
629	#501	C₂²×C₆₁	1	2	yes	complemented
630	#501	C₂²×C₆₁	1	2	yes	complemented
631	#499	C₂²×C₆₁	1	2	yes	complemented
632	#498	C₂²×C₆₁	1	2	yes	complemented
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	#484	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	2	yes	—
642	#482	C₂²×C₆₁	1	2	yes	—
643	#482	C₂²×C₆₁	1	2	yes	complemented
644	#482	C₂²×C₆₁	1	2	yes	complemented
645	#481	C₂²×C₆₁	1	2	yes	—
646	#481	C₂²×C₆₁	1	2	yes	complemented
647	#480	C₂²×C₆₁	1	2	yes	—
648	#480	C₂²×C₆₁	1	2	yes	complemented
649	#479	C₂²×C₆₁	1	2	yes	complemented
650	#479	C₂²×C₆₁	1	2	yes	complemented
651	#478	C₂²×C₆₁	1	2	yes	complemented
652	#478	C₂²×C₆₁	1	2	yes	complemented
653	#477	C₂²×C₆₁	1	2	yes	complemented
654	#476	C₂²×C₆₁	1	2	yes	complemented
655	#475	C₂²×C₆₁	1	2	yes	complemented
656	#474	C₂²×C₆₁	1	2	yes	complemented
657	#468	C₂²×C₆₁	1	2	yes	complemented
658	#468	C₂²×C₆₁	1	2	yes	complemented
659	#465	C₂²×C₆₁	1	2	yes	—
660	#465	C₂²×C₆₁	1	2	yes	—
661	#465	C₂²×C₆₁	1	2	yes	—
662	#465	C₂²×C₆₁	1	2	yes	—
663	#465	C₂²×C₆₁	1	2	yes	complemented
664	#465	C₂²×C₆₁	1	2	yes	complemented
665	#440	C₂²×C₆₁	1	2	yes	complemented
666	#440	C₂²×C₆₁	1	2	yes	complemented
667	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
668	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	complemented
669	#435	C₂²×C₆₁	1	2	yes	complemented
670	#435	C₂²×C₆₁	1	2	yes	complemented
671	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
672	C₈×D₄	C₂²×C₆₁	1	2	yes	complemented
673	#428	C₂²×C₆₁	1	1	yes	characteristic
674	#428	C₂²×C₆₁	1	1	yes	characteristic
675	#428	C₂²×C₆₁	1	1	yes	characteristic
676	#428	C₂²×C₆₁	1	1	yes	characteristic
677	#428	C₂²×C₆₁	1	2	yes	complemented
678	#428	C₂²×C₆₁	1	2	yes	complemented
679	#427	C₂²×C₆₁	1	1	yes	characteristic
680	#427	C₂²×C₆₁	1	1	yes	characteristic
681	#427	C₂²×C₆₁	1	1	yes	characteristic
682	#427	C₂²×C₆₁	1	1	yes	characteristic
683	#427	C₂²×C₆₁	1	1	yes	characteristic, complemented
684	#427	C₂²×C₆₁	1	2	yes	complemented
685	#427	C₂²×C₆₁	1	1	yes	characteristic, complemented
686	#427	C₂²×C₆₁	1	1	yes	characteristic, complemented
687	#427	C₂²×C₆₁	1	1	yes	characteristic, complemented
688	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic, complemented
689	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic, complemented
690	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
691	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic, complemented
692	C₂×#106	C₂²×C₆₁	1	2	yes	complemented
693	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic, complemented
694	#424	C₂²×C₆₁	1	1	yes	characteristic
695	#419	C₂²×C₆₁	1	1	yes	characteristic
696	#419	C₂²×C₆₁	1	1	yes	characteristic
697	#418	C₂²×C₆₁	1	1	yes	characteristic
698	#418	C₂²×C₆₁	1	1	yes	characteristic
699	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
700	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
701	#408	C₂²×C₆₁	1	1	yes	characteristic
702	#407	C₂²×C₆₁	1	1	yes	characteristic
703	#405	C₂²×C₆₁	1	1	yes	characteristic
704	C₆₁	#61263	1	1	yes	characteristic, direct product factor, Sylow
705	C₂×#41	—	2	2	no	—
706	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
707	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
708	C₂²×D₄	—	2	1	no	—
709	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
710	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
711	C₂×SD₁₆	—	2	4	no	—
712	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
713	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
714	#131	—	2	4	no	—
715	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
716	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
717	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
718	C₂²×C₈	—	2	4	no	—
719	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
720	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
721	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
722	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
723	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
724	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
725	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
726	C₄⋊Q₈	—	2	1	no	—
727	C₄⋊Q₈	—	2	1	no	—
728	C₄⋊Q₈	—	2	1	no	—
729	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
730	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
731	#127	—	2	1	no	—
732	#126	—	2	2	no	—
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#125	—	2	1	no	—
739	#125	—	2	1	no	—
740	#125	—	2	2	no	—
741	#125	—	2	2	no	—
742	#125	—	2	2	no	—
743	#125	C₂³×C₆₁	1	2	yes	—
744	#125	C₂³×C₆₁	1	2	yes	—
745	#124	—	2	1	no	—
746	#124	—	2	1	no	—
747	#124	—	2	2	no	—
748	#124	—	2	2	no	—
749	#124	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	D₄×C₆₁	1	2	yes	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
766	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
767	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
768	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
769	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
770	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
771	#121	—	2	2	no	—
772	#121	—	2	2	no	—
773	#121	—	2	2	no	—
774	#121	—	2	1	no	—
775	#121	—	2	1	no	—
776	#121	D₄×C₆₁	1	1	yes	characteristic
777	#121	D₄×C₆₁	1	1	yes	characteristic
778	#121	C₂³×C₆₁	1	2	yes	—
779	#121	C₂³×C₆₁	1	2	yes	—
780	#121	C₂³×C₆₁	1	2	yes	—
781	#121	C₂³×C₆₁	1	2	yes	—
782	#120	—	2	2	no	—
783	#120	D₄×C₆₁	1	2	yes	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	—	2	1	no	—
786	C₄×Q₈	—	2	1	no	—
787	C₄×Q₈	—	2	1	no	—
788	C₄×Q₈	—	2	2	no	—
789	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
790	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	C₂³×C₆₁	1	2	yes	—
801	C₄×D₄	C₂³×C₆₁	1	2	yes	—
802	C₄×D₄	C₂³×C₆₁	1	2	yes	—
803	C₄×D₄	C₂³×C₆₁	1	2	yes	—
804	#117	—	2	1	no	—
805	#117	—	2	1	no	—
806	#117	—	2	1	no	—
807	#117	—	2	1	no	—
808	#117	—	2	2	no	—
809	#117	—	2	2	no	—
810	#117	—	2	2	no	—
811	#117	—	2	2	no	—
812	#117	C₂³×C₆₁	1	1	yes	characteristic
813	#117	C₂³×C₆₁	1	1	yes	characteristic
814	#117	C₂³×C₆₁	1	1	yes	characteristic
815	#117	C₂³×C₆₁	1	1	yes	characteristic
816	#117	C₂³×C₆₁	1	1	yes	characteristic
817	#117	C₂³×C₆₁	1	1	yes	characteristic
818	#117	C₂³×C₆₁	1	1	yes	characteristic
819	#117	C₂³×C₆₁	1	1	yes	characteristic
820	#117	C₂³×C₆₁	1	2	yes	—
821	#117	C₂³×C₆₁	1	2	yes	—
822	#117	C₂³×C₆₁	1	1	yes	characteristic
823	C₂×C₄⋊C₄	—	2	1	no	—
824	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
825	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
826	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
827	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
828	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
829	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
830	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
831	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
832	C₂×C₂²⋊C₄	—	2	1	no	—
833	C₂×C₂²⋊C₄	—	2	1	no	—
834	C₂×C₂²⋊C₄	—	2	1	no	—
835	C₂×C₂²⋊C₄	—	2	1	no	—
836	C₂×C₂²⋊C₄	—	2	2	no	—
837	C₂×C₄²	—	2	1	no	—
838	C₂×C₄²	—	2	1	no	—
839	#107	C₂³×C₆₁	1	1	yes	characteristic
840	#107	C₂³×C₆₁	1	1	yes	characteristic
841	#107	C₂³×C₆₁	1	1	yes	characteristic
842	#107	C₂³×C₆₁	1	1	yes	characteristic
843	#107	C₂³×C₆₁	1	1	yes	characteristic
844	#107	C₂³×C₆₁	1	1	yes	characteristic
845	#107	C₂³×C₆₁	1	1	yes	characteristic
846	#107	C₂³×C₆₁	1	1	yes	characteristic
847	#107	C₂³×C₆₁	1	2	yes	—
848	#107	C₂³×C₆₁	1	2	yes	—
849	#107	C₂³×C₆₁	1	2	yes	—
850	#107	C₂³×C₆₁	1	2	yes	—
851	#106	C₂³×C₆₁	1	2	yes	—
852	#106	C₂³×C₆₁	1	2	yes	—
853	#106	C₂³×C₆₁	1	1	yes	characteristic
854	#106	C₂³×C₆₁	1	1	yes	characteristic
855	#106	C₂³×C₆₁	1	1	yes	characteristic
856	#106	C₂³×C₆₁	1	1	yes	characteristic
857	#106	C₂³×C₆₁	1	1	yes	characteristic
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	2	yes	—
862	#106	C₂³×C₆₁	1	2	yes	—
863	#106	C₂³×C₆₁	1	2	yes	—
864	#106	C₂³×C₆₁	1	2	yes	—
865	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
866	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
867	#103	C₂³×C₆₁	1	2	yes	—
868	#103	C₂³×C₆₁	1	2	yes	—
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	2	yes	—
873	#102	C₂³×C₆₁	1	2	yes	—
874	#102	C₂³×C₆₁	1	2	yes	—
875	#102	C₂³×C₆₁	1	2	yes	—
876	#102	C₂³×C₆₁	1	2	yes	—
877	#102	C₂³×C₆₁	1	2	yes	—
878	#102	C₂³×C₆₁	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
883	#97	C₂³×C₆₁	1	2	yes	—
884	C₄×C₈	C₂³×C₆₁	1	2	yes	—
885	C₂⁴	—	2	1	no	—
886	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
887	#41	—	2	2	no	—
888	#41	—	2	2	no	—
889	#41	—	8	4	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	2	no	—
892	C₂×Q₈	—	2	2	no	—
893	C₂×Q₈	—	2	2	no	—
894	C₂×Q₈	—	2	2	no	—
895	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
896	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
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	—	2	1	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	8	2	no	—
905	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
906	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
907	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
908	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
909	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
924	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
925	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
926	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
927	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
928	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
929	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
930	SD₁₆	—	2	4	no	—
931	SD₁₆	—	2	4	no	—
932	M₁₆	—	2	2	no	—
933	M₁₆	—	2	2	no	—
934	M₁₆	—	2	4	no	—
935	C₂×C₈	—	2	2	no	—
936	C₂×C₈	—	2	2	no	—
937	C₂×C₈	—	2	2	no	—
938	C₂×C₈	—	2	2	no	—
939	C₂×C₈	—	2	2	no	—
940	C₂×C₈	—	2	4	no	—
941	C₂×C₈	#41×C₆₁	1	4	yes	complemented
942	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
943	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
944	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
945	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
946	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
947	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
969	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
970	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
971	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
972	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
975	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
977	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
978	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
979	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
980	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
981	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	2	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1003	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1004	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1005	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1006	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	C₂⁴×C₆₁	1	2	yes	—
1020	C₂³	—	2	2	no	—
1021	C₂³	—	2	2	no	—
1022	C₂³	—	2	2	no	—
1023	C₂³	—	4	1	no	—
1024	C₂³	—	4	2	no	—
1025	C₂³	—	8	1	no	—
1026	C₂³	—	8	1	no	—
1027	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1028	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1029	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1030	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1031	Q₈	—	2	2	no	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	2	2	no	—
1034	Q₈	—	4	2	no	—
1035	Q₈	—	8	2	no	—
1036	Q₈	—	8	2	no	—
1037	D₄	—	2	4	no	—
1038	D₄	—	2	4	no	—
1039	D₄	—	2	2	no	—
1040	D₄	—	2	2	no	—
1041	D₄	—	2	2	no	—
1042	D₄	—	4	2	no	—
1043	D₄	—	4	4	no	—
1044	D₄	—	4	2	no	—
1045	D₄	—	8	2	no	—
1046	D₄	—	8	2	no	—
1047	D₄	—	8	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	4	2	no	—
1071	C₂×C₄	—	8	2	no	—
1072	C₂×C₄	—	8	2	no	—
1073	C₂×C₄	—	8	2	no	—
1074	C₂×C₄	—	8	1	no	—
1075	C₂×C₄	—	8	1	no	—
1076	C₂×C₄	—	8	1	no	—
1077	C₂×C₄	—	8	1	no	—
1078	C₂×C₄	—	8	2	no	—
1079	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1080	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1081	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1082	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1083	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1084	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1085	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
1086	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
1087	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1088	C₈	—	2	1	no	—
1089	C₈	—	2	1	no	—
1090	C₈	—	2	2	no	—
1091	C₈	—	2	2	no	—
1092	C₈	C₂×#41×C₆₁	1	2	yes	—
1093	C₈	C₂×#41×C₆₁	1	2	yes	—
1094	C₂²	—	2	1	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	1	no	—
1097	C₂²	—	2	1	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	1	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	4	4	no	—
1105	C₂²	—	4	2	no	—
1106	C₂²	—	4	2	no	—
1107	C₂²	—	4	2	no	—
1108	C₂²	—	16	2	no	—
1109	C₂²	C₆₁×#547	1	2	yes	—
1110	C₂²	C₆₁×#577	1	2	yes	—
1111	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1112	C₄	—	2	2	no	—
1113	C₄	—	2	2	no	—
1114	C₄	—	2	1	no	—
1115	C₄	—	2	1	no	—
1116	C₄	—	2	2	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	1	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	1	no	—
1121	C₄	—	4	2	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	2	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	2	no	—
1128	C₄	C₆₁×#547	1	2	yes	—
1129	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
1130	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
1131	C₂	—	2	2	no	—
1132	C₂	—	2	2	no	—
1133	C₂	—	4	1	no	—
1134	C₂	—	4	2	no	—
1135	C₂	—	8	2	no	—
1136	C₂	C₂×C₆₁×#547	1	1	yes	characteristic
1137	C₂	C₂×C₆₁×#577	1	1	yes	characteristic
1138	C₂	C₆₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₆₁×#3494	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3495	C₂	semidirect
3. C₆₁×#3350	C₂	semidirect
4. C₆₁×#3348	C₂	semidirect
5. C₆₁×#3346	C₂	semidirect
6. C₆₁×#3343	C₂	semidirect
7. C₆₁×#3340	C₂	semidirect
8. C₆₁×#3337	C₂	semidirect
9. C₆₁×#3337	C₂	semidirect
10. C₆₁×#3335	C₂	semidirect
11. C₆₁×#3163	C₂	semidirect
12. C₆₁×#3097	C₂	semidirect
13. C₆₁×#3096	C₂	semidirect
14. C₆₁×#3095	C₂	semidirect
15. C₆₁×#3094	C₂	semidirect
16. C₆₁×#3082	C₂	semidirect
17. C₆₁×#3081	C₂	semidirect
18. C₆₁×#3057	C₂	semidirect
19. C₂×C₆₁×#465	C₂	semidirect
20. C₆₁×#2949	C₂	semidirect
21. C₆₁×#2929	C₂	semidirect
22. C₆₁×#2912	C₂	semidirect
23. C₂×C₆₁×#427	C₂	semidirect
27. C₆₁×#556	C₂²	semidirect
29. C₆₁×#554	C₂²	semidirect
33. C₆₁×#552	C₂²	semidirect
34. C₆₁×#552	C₂²	semidirect
60. C₆₁×#501	C₂²	semidirect
61. C₆₁×#501	C₂²	semidirect
62. C₆₁×#499	C₂²	semidirect
63. C₆₁×#498	C₂²	semidirect
64. C₆₁×#485	C₂²	semidirect
65. C₆₁×#485	C₂²	semidirect
66. C₆₁×#485	C₂²	semidirect
67. C₆₁×#485	C₂²	semidirect
68. C₆₁×#484	C₂²	semidirect
69. C₆₁×#484	C₂²	semidirect
70. C₆₁×#483	C₂²	semidirect
71. C₆₁×#483	C₂²	semidirect
74. C₆₁×#482	C₂²	semidirect
75. C₆₁×#482	C₂²	semidirect
77. C₆₁×#481	C₂²	semidirect
79. C₆₁×#480	C₂²	semidirect
80. C₆₁×#479	C₂²	semidirect
81. C₆₁×#479	C₂²	semidirect
82. C₆₁×#478	C₂²	semidirect
83. C₆₁×#478	C₂²	semidirect
84. C₆₁×#477	C₂²	semidirect
85. C₆₁×#476	C₂²	semidirect
86. C₆₁×#475	C₂²	semidirect
87. C₆₁×#474	C₂²	semidirect
88. C₆₁×#468	C₂²	semidirect
89. C₆₁×#468	C₂²	semidirect
94. C₆₁×#465	C₂²	semidirect
95. C₆₁×#465	C₂²	semidirect
96. C₆₁×#440	C₂²	semidirect
97. C₆₁×#440	C₂²	semidirect
98. C₄×SD₁₆×C₆₁	C₂²	semidirect
99. C₄×SD₁₆×C₆₁	C₂²	semidirect
100. C₆₁×#435	C₂²	semidirect
101. C₆₁×#435	C₂²	semidirect
102. C₈×D₄×C₆₁	C₂²	semidirect
103. C₈×D₄×C₆₁	C₂²	semidirect
108. C₆₁×#428	C₂²	semidirect
109. C₆₁×#428	C₂²	semidirect
114. C₆₁×#427	C₂²	semidirect
115. C₆₁×#427	C₂²	semidirect
116. C₆₁×#427	C₂²	semidirect
117. C₆₁×#427	C₂²	semidirect
118. C₆₁×#427	C₂²	semidirect
119. C₂×#107×C₆₁	C₂²	semidirect
120. C₂×#107×C₆₁	C₂²	semidirect
122. C₂×#106×C₆₁	C₂²	semidirect
123. C₂×#106×C₆₁	C₂²	semidirect
124. C₂×#106×C₆₁	C₂²	semidirect
371. C₂×C₈×C₆₁	#41	semidirect
524. #61263	C₆₁	direct (N × H)
562. #3495	C₂×C₆₁	semidirect
564. #3350	C₂×C₆₁	semidirect
565. #3348	C₂×C₆₁	semidirect
566. #3346	C₂×C₆₁	semidirect
567. #3343	C₂×C₆₁	semidirect
568. #3340	C₂×C₆₁	semidirect
569. #3337	C₂×C₆₁	semidirect
570. #3337	C₂×C₆₁	semidirect
571. #3335	C₂×C₆₁	semidirect
572. #3163	C₂×C₆₁	semidirect
573. #3097	C₂×C₆₁	semidirect
574. #3096	C₂×C₆₁	semidirect
575. #3095	C₂×C₆₁	semidirect
576. #3094	C₂×C₆₁	semidirect
577. #3082	C₂×C₆₁	semidirect
578. #3081	C₂×C₆₁	semidirect
579. #3057	C₂×C₆₁	semidirect
580. C₂×#465	C₂×C₆₁	semidirect
581. #2949	C₂×C₆₁	semidirect
582. #2929	C₂×C₆₁	semidirect
583. #2912	C₂×C₆₁	semidirect
584. C₂×#427	C₂×C₆₁	semidirect
596. #556	C₂²×C₆₁	semidirect
598. #554	C₂²×C₆₁	semidirect
602. #552	C₂²×C₆₁	semidirect
603. #552	C₂²×C₆₁	semidirect
629. #501	C₂²×C₆₁	semidirect
630. #501	C₂²×C₆₁	semidirect
631. #499	C₂²×C₆₁	semidirect
632. #498	C₂²×C₆₁	semidirect
633. #485	C₂²×C₆₁	semidirect
634. #485	C₂²×C₆₁	semidirect
635. #485	C₂²×C₆₁	semidirect
636. #485	C₂²×C₆₁	semidirect
637. #484	C₂²×C₆₁	semidirect
638. #484	C₂²×C₆₁	semidirect
639. #483	C₂²×C₆₁	semidirect
640. #483	C₂²×C₆₁	semidirect
643. #482	C₂²×C₆₁	semidirect
644. #482	C₂²×C₆₁	semidirect
646. #481	C₂²×C₆₁	semidirect
648. #480	C₂²×C₆₁	semidirect
649. #479	C₂²×C₆₁	semidirect
650. #479	C₂²×C₆₁	semidirect
651. #478	C₂²×C₆₁	semidirect
652. #478	C₂²×C₆₁	semidirect
653. #477	C₂²×C₆₁	semidirect
654. #476	C₂²×C₆₁	semidirect
655. #475	C₂²×C₆₁	semidirect
656. #474	C₂²×C₆₁	semidirect
657. #468	C₂²×C₆₁	semidirect
658. #468	C₂²×C₆₁	semidirect
663. #465	C₂²×C₆₁	semidirect
664. #465	C₂²×C₆₁	semidirect
665. #440	C₂²×C₆₁	semidirect
666. #440	C₂²×C₆₁	semidirect
667. C₄×SD₁₆	C₂²×C₆₁	semidirect
668. C₄×SD₁₆	C₂²×C₆₁	semidirect
669. #435	C₂²×C₆₁	semidirect
670. #435	C₂²×C₆₁	semidirect
671. C₈×D₄	C₂²×C₆₁	semidirect
672. C₈×D₄	C₂²×C₆₁	semidirect
677. #428	C₂²×C₆₁	semidirect
678. #428	C₂²×C₆₁	semidirect
683. #427	C₂²×C₆₁	semidirect
684. #427	C₂²×C₆₁	semidirect
685. #427	C₂²×C₆₁	semidirect
686. #427	C₂²×C₆₁	semidirect
687. #427	C₂²×C₆₁	semidirect
688. C₂×#107	C₂²×C₆₁	semidirect
689. C₂×#107	C₂²×C₆₁	semidirect
691. C₂×#106	C₂²×C₆₁	semidirect
692. C₂×#106	C₂²×C₆₁	semidirect
693. C₂×#106	C₂²×C₆₁	semidirect
704. C₆₁	#61263	direct (N × H)
941. C₂×C₈	#41×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3495	2
C₆₁×#3494	2
C₆₁×#3350	2
C₆₁×#3348	2
C₆₁×#3346	2
C₆₁×#3343	2
C₆₁×#3340	2
C₆₁×#3337	2
C₆₁×#3335	2
C₆₁×#3163	2
C₆₁×#3097	2
C₆₁×#3096	2
C₆₁×#3095	2
C₆₁×#3094	2
C₆₁×#3082	2
C₆₁×#3081	2
C₆₁×#3057	2
C₂×C₆₁×#465	2
C₆₁×#2949	2
C₆₁×#2929	2
C₆₁×#2912	2
C₂×C₆₁×#427	2
#61263	61

Subgroups — C61×#61263 #29564696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61263 #29564696