Subgroups — C₆₁×#62072 #29565505

Order 15616.

1780 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#3329	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#3313	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3305	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3302	C₂	1	2	yes	maximal, complemented
11	D₄×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3285	C₂	1	2	yes	maximal, complemented
13	C₆₁×#3278	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3269	C₂	1	2	yes	maximal, complemented
15	C₆₁×#3262	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3249	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3225	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×#3107	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3044	C₂	1	2	yes	maximal, complemented
22	C₆₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₆₁	C₂²	1	2	yes	—
25	C₂×#135×C₆₁	C₂²	1	2	yes	—
26	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
27	C₆₁×#562	—	2	2	no	—
28	C₆₁×#559	—	2	1	no	—
29	C₆₁×#559	C₂²	1	1	yes	characteristic
30	Q₈²×C₆₁	C₂²	1	1	yes	characteristic
31	C₆₁×#557	C₂²	1	1	yes	characteristic
32	C₆₁×#556	—	2	2	no	—
33	C₆₁×#556	—	2	1	no	—
34	C₆₁×#556	C₂²	1	1	yes	characteristic
35	C₆₁×#556	C₂²	1	2	yes	—
36	C₆₁×#555	—	2	1	no	—
37	C₆₁×#555	C₂²	1	1	yes	characteristic
38	C₆₁×#554	—	2	1	no	—
39	C₆₁×#550	C₂²	1	1	yes	characteristic
40	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
41	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
42	C₆₁×#548	C₂²	1	2	yes	—
43	C₆₁×#548	C₂²	1	2	yes	—
44	C₆₁×#547	C₂²	1	2	yes	—
45	C₆₁×#542	—	2	2	no	—
46	C₆₁×#542	—	2	1	no	—
47	C₆₁×#542	C₂²	1	2	yes	—
48	C₆₁×#542	C₂²	1	2	yes	—
49	C₆₁×#540	—	2	1	no	—
50	C₆₁×#539	—	2	2	no	—
51	C₆₁×#536	C₂²	1	2	yes	—
52	C₆₁×#533	—	2	1	no	—
53	C₆₁×#533	C₂²	1	1	yes	characteristic
54	C₆₁×#533	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	—
59	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
60	C₆₁×#497	C₂²	1	2	yes	—
61	C₆₁×#495	C₂²	1	2	yes	—
62	C₆₁×#494	C₂²	1	1	yes	characteristic
63	C₆₁×#492	C₂²	1	1	yes	characteristic
64	C₆₁×#489	C₂²	1	2	yes	—
65	C₆₁×#487	C₂²	1	2	yes	—
66	C₆₁×#487	C₂²	1	1	yes	characteristic
67	C₆₁×#486	C₂²	1	1	yes	characteristic
68	C₆₁×#485	C₂²	1	1	yes	characteristic
69	C₆₁×#485	C₂²	1	2	yes	—
70	C₆₁×#485	C₂²	1	1	yes	characteristic
71	C₆₁×#482	C₂²	1	2	yes	—
72	C₆₁×#477	C₂²	1	1	yes	characteristic
73	C₆₁×#477	C₂²	1	2	yes	—
74	C₆₁×#477	C₂²	1	1	yes	characteristic
75	C₆₁×#477	C₂²	1	2	yes	—
76	C₆₁×#475	C₂²	1	1	yes	characteristic
77	C₆₁×#474	C₂²	1	2	yes	—
78	C₆₁×#474	C₂²	1	1	yes	characteristic
79	C₆₁×#468	C₂²	1	2	yes	—
80	C₆₁×#468	C₂²	1	2	yes	—
81	C₆₁×#467	C₂²	1	2	yes	—
82	C₆₁×#467	C₂²	1	2	yes	—
83	C₆₁×#467	C₂²	1	2	yes	—
84	C₆₁×#466	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	—
88	C₆₁×#464	C₂²	1	2	yes	—
89	C₆₁×#464	C₂²	1	2	yes	—
90	C₆₁×#464	C₂²	1	2	yes	—
91	C₆₁×#463	C₂²	1	2	yes	—
92	C₆₁×#463	C₂²	1	2	yes	—
93	C₆₁×#462	C₂²	1	1	yes	characteristic
94	C₆₁×#462	C₂²	1	1	yes	characteristic
95	C₆₁×#462	C₂²	1	2	yes	—
96	C₆₁×#462	C₂²	1	2	yes	—
97	C₆₁×#462	C₂²	1	2	yes	—
98	C₆₁×#462	C₂²	1	1	yes	characteristic
99	C₆₁×#462	C₂²	1	1	yes	characteristic
100	C₆₁×#461	C₂²	1	1	yes	characteristic
101	C₆₁×#461	C₂²	1	1	yes	characteristic
102	C₆₁×#460	C₂²	1	1	yes	characteristic
103	C₆₁×#459	C₂²	1	1	yes	characteristic
104	C₆₁×#452	C₂²	1	2	yes	—
105	C₆₁×#452	C₂²	1	2	yes	—
106	C₆₁×#452	C₂²	1	2	yes	—
107	C₆₁×#452	C₂²	1	1	yes	characteristic
108	C₆₁×#452	C₂²	1	1	yes	characteristic
109	C₆₁×#451	C₂²	1	2	yes	—
110	C₆₁×#451	C₂²	1	2	yes	—
111	C₆₁×#449	C₂²	1	2	yes	—
112	C₆₁×#448	C₂²	1	2	yes	—
113	C₆₁×#448	C₂²	1	2	yes	—
114	C₆₁×#446	C₂²	1	1	yes	characteristic
115	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
116	C₆₁×#441	C₂²	1	2	yes	—
117	C₆₁×#440	C₂²	1	2	yes	—
118	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
119	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
120	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
121	C₄×SD₁₆×C₆₁	C₂²	1	2	yes	—
122	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
123	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
124	C₆₁×#436	C₂²	1	1	yes	characteristic
125	C₆₁×#435	C₂²	1	2	yes	—
126	C₈×D₄×C₆₁	C₂²	1	2	yes	—
127	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
128	C₆₁×#433	C₂²	1	2	yes	—
129	C₆₁×#431	C₂²	1	1	yes	characteristic
130	C₆₁×#424	C₂²	1	2	yes	—
131	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
132	C₆₁×#419	C₂²	1	2	yes	—
133	C₆₁×#416	C₂²	1	2	yes	—
134	C₆₁×#416	C₂²	1	2	yes	—
135	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
136	C₂×#41×C₆₁	C₂³	1	2	yes	—
137	C₂×#41×C₆₁	C₂³	1	2	yes	—
138	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
140	#137×C₆₁	—	4	4	no	—
141	#135×C₆₁	—	4	4	no	—
142	C₂×Q₁₆×C₆₁	—	4	4	no	—
143	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
144	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
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×Q₁₆×C₆₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
154	C₂×SD₁₆×C₆₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₆₁	C₂³	1	1	yes	characteristic
156	C₂×D₈×C₆₁	C₂³	1	2	yes	—
157	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
158	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
159	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
160	C₄⋊Q₈×C₆₁	—	2	1	no	—
161	C₄⋊Q₈×C₆₁	—	2	1	no	—
162	C₄⋊Q₈×C₆₁	—	2	1	no	—
163	C₄⋊Q₈×C₆₁	—	2	2	no	—
164	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
168	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
171	#127×C₆₁	—	2	1	no	—
172	#127×C₆₁	C₂³	1	1	yes	characteristic
173	#126×C₆₁	—	2	2	no	—
174	#126×C₆₁	—	2	2	no	—
175	#126×C₆₁	—	2	2	no	—
176	#126×C₆₁	—	2	2	no	—
177	#126×C₆₁	—	2	2	no	—
178	#126×C₆₁	D₄	1	2	yes	—
179	#125×C₆₁	—	2	2	no	—
180	#125×C₆₁	—	2	1	no	—
181	#125×C₆₁	—	2	1	no	—
182	#125×C₆₁	—	2	1	no	—
183	#125×C₆₁	D₄	1	1	yes	characteristic
184	#124×C₆₁	—	2	1	no	—
185	#124×C₆₁	—	2	2	no	—
186	#124×C₆₁	—	2	2	no	—
187	#124×C₆₁	—	2	2	no	—
188	#124×C₆₁	—	2	2	no	—
189	#124×C₆₁	—	2	2	no	—
190	#124×C₆₁	—	2	2	no	—
191	#124×C₆₁	D₄	1	1	yes	characteristic
192	#124×C₆₁	C₂³	1	2	yes	—
193	#124×C₆₁	C₂³	1	2	yes	—
194	#124×C₆₁	C₂³	1	2	yes	—
195	#123×C₆₁	—	2	2	no	—
196	#123×C₆₁	—	2	2	no	—
197	#123×C₆₁	—	2	2	no	—
198	#123×C₆₁	—	2	2	no	—
199	#123×C₆₁	—	2	2	no	—
200	#123×C₆₁	—	2	2	no	—
201	#123×C₆₁	—	2	2	no	—
202	#123×C₆₁	D₄	1	2	yes	—
203	C₂²⋊Q₈×C₆₁	—	2	1	no	—
204	C₂²⋊Q₈×C₆₁	—	2	1	no	—
205	C₂²⋊Q₈×C₆₁	—	2	1	no	—
206	C₂²⋊Q₈×C₆₁	—	2	2	no	—
207	C₂²⋊Q₈×C₆₁	—	2	2	no	—
208	C₂²⋊Q₈×C₆₁	—	2	2	no	—
209	C₂²⋊Q₈×C₆₁	—	2	2	no	—
210	C₂²⋊Q₈×C₆₁	—	2	2	no	—
211	C₂²⋊Q₈×C₆₁	—	2	2	no	—
212	C₂²⋊Q₈×C₆₁	—	2	2	no	—
213	C₂²⋊Q₈×C₆₁	—	2	2	no	—
214	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
215	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
216	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
217	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
218	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
219	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
220	#121×C₆₁	—	2	2	no	—
221	#121×C₆₁	—	2	2	no	—
222	#121×C₆₁	—	2	2	no	—
223	#121×C₆₁	—	2	1	no	—
224	#121×C₆₁	—	2	1	no	—
225	#121×C₆₁	—	2	1	no	—
226	#121×C₆₁	—	2	2	no	—
227	#121×C₆₁	D₄	1	1	yes	characteristic
228	#121×C₆₁	C₂³	1	2	yes	—
229	#121×C₆₁	C₂³	1	2	yes	—
230	C₄×Q₈×C₆₁	—	2	1	no	—
231	C₄×Q₈×C₆₁	—	2	1	no	—
232	C₄×Q₈×C₆₁	—	2	2	no	—
233	C₄×Q₈×C₆₁	—	2	2	no	—
234	C₄×Q₈×C₆₁	—	2	2	no	—
235	C₄×Q₈×C₆₁	—	2	1	no	—
236	C₄×Q₈×C₆₁	—	2	1	no	—
237	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
238	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
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	1	yes	characteristic
246	C₄×D₄×C₆₁	—	2	1	no	—
247	C₄×D₄×C₆₁	—	2	1	no	—
248	C₄×D₄×C₆₁	—	2	1	no	—
249	C₄×D₄×C₆₁	—	2	1	no	—
250	C₄×D₄×C₆₁	—	2	1	no	—
251	C₄×D₄×C₆₁	—	2	1	no	—
252	C₄×D₄×C₆₁	—	2	2	no	—
253	C₄×D₄×C₆₁	—	2	2	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	2	yes	—
258	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₆₁	C₂³	1	2	yes	—
260	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
261	#117×C₆₁	—	2	1	no	—
262	#117×C₆₁	—	2	1	no	—
263	#117×C₆₁	—	2	1	no	—
264	#117×C₆₁	—	2	1	no	—
265	#117×C₆₁	—	2	2	no	—
266	#117×C₆₁	—	2	2	no	—
267	#117×C₆₁	—	2	1	no	—
268	#117×C₆₁	C₂³	1	2	yes	—
269	#117×C₆₁	C₂³	1	1	yes	characteristic
270	#117×C₆₁	C₂³	1	2	yes	—
271	C₂×C₄⋊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	1	yes	characteristic
276	#107×C₆₁	C₂³	1	1	yes	characteristic
277	#107×C₆₁	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
292	#103×C₆₁	C₂³	1	2	yes	—
293	#103×C₆₁	C₂³	1	2	yes	—
294	#103×C₆₁	C₂³	1	2	yes	—
295	#103×C₆₁	C₂³	1	1	yes	characteristic
296	#103×C₆₁	C₂³	1	1	yes	characteristic
297	#103×C₆₁	C₂³	1	2	yes	—
298	#103×C₆₁	C₂³	1	1	yes	characteristic
299	#103×C₆₁	C₂³	1	1	yes	characteristic
300	#103×C₆₁	C₂³	1	2	yes	—
301	#102×C₆₁	C₂³	1	2	yes	—
302	#102×C₆₁	C₂³	1	2	yes	—
303	#102×C₆₁	C₂³	1	2	yes	—
304	#102×C₆₁	C₂³	1	1	yes	characteristic
305	#102×C₆₁	C₂³	1	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	#41×C₆₁	—	2	2	no	—
316	#41×C₆₁	—	4	1	no	—
317	#41×C₆₁	—	4	2	no	—
318	#41×C₆₁	—	4	2	no	—
319	#41×C₆₁	—	4	2	no	—
320	#41×C₆₁	—	4	2	no	—
321	C₂×Q₈×C₆₁	—	2	2	no	—
322	C₂×Q₈×C₆₁	—	2	1	no	—
323	C₂×Q₈×C₆₁	—	2	1	no	—
324	C₂×Q₈×C₆₁	—	2	2	no	—
325	C₂×Q₈×C₆₁	—	2	2	no	—
326	C₂×Q₈×C₆₁	—	2	4	no	—
327	C₂×Q₈×C₆₁	—	4	2	no	—
328	C₂×Q₈×C₆₁	—	4	2	no	—
329	C₂×Q₈×C₆₁	—	4	2	no	—
330	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
335	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₆₁	—	2	1	no	—
337	C₂×D₄×C₆₁	—	2	2	no	—
338	C₂×D₄×C₆₁	—	2	2	no	—
339	C₂×D₄×C₆₁	—	2	2	no	—
340	C₂×D₄×C₆₁	—	2	2	no	—
341	C₂×D₄×C₆₁	—	2	1	no	—
342	C₂×D₄×C₆₁	—	2	1	no	—
343	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
344	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
345	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
346	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₆₁	—	2	2	no	—
348	C₂²×C₄×C₆₁	—	2	2	no	—
349	C₂²×C₄×C₆₁	—	2	1	no	—
350	C₂²×C₄×C₆₁	—	2	1	no	—
351	C₂²×C₄×C₆₁	—	2	1	no	—
352	C₂²×C₄×C₆₁	—	2	2	no	—
353	C₂²×C₄×C₆₁	—	2	2	no	—
354	C₂²×C₄×C₆₁	—	2	2	no	—
355	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
357	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
359	Q₁₆×C₆₁	—	2	2	no	—
360	Q₁₆×C₆₁	—	2	4	no	—
361	Q₁₆×C₆₁	—	2	2	no	—
362	Q₁₆×C₆₁	—	4	2	no	—
363	Q₁₆×C₆₁	—	4	2	no	—
364	Q₁₆×C₆₁	—	4	2	no	—
365	Q₁₆×C₆₁	—	4	2	no	—
366	SD₁₆×C₆₁	—	2	4	no	—
367	SD₁₆×C₆₁	—	4	1	no	—
368	SD₁₆×C₆₁	—	4	2	no	—
369	SD₁₆×C₆₁	—	4	1	no	—
370	SD₁₆×C₆₁	—	4	2	no	—
371	SD₁₆×C₆₁	—	4	2	no	—
372	D₈×C₆₁	—	4	2	no	—
373	M₁₆×C₆₁	—	4	2	no	—
374	C₂×C₈×C₆₁	—	4	2	no	—
375	C₂×C₈×C₆₁	—	4	2	no	—
376	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
380	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
382	C₄⋊C₄×C₆₁	—	2	1	no	—
383	C₄⋊C₄×C₆₁	—	2	2	no	—
384	C₄⋊C₄×C₆₁	—	2	2	no	—
385	C₄⋊C₄×C₆₁	—	2	1	no	—
386	C₄⋊C₄×C₆₁	—	2	1	no	—
387	C₄⋊C₄×C₆₁	—	2	1	no	—
388	C₄⋊C₄×C₆₁	—	2	1	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	1	no	—
393	C₄⋊C₄×C₆₁	—	2	1	no	—
394	C₄⋊C₄×C₆₁	—	2	1	no	—
395	C₄⋊C₄×C₆₁	—	2	1	no	—
396	C₄⋊C₄×C₆₁	—	2	2	no	—
397	C₄⋊C₄×C₆₁	—	2	1	no	—
398	C₄⋊C₄×C₆₁	—	2	1	no	—
399	C₄⋊C₄×C₆₁	—	2	1	no	—
400	C₄⋊C₄×C₆₁	—	2	2	no	—
401	C₄⋊C₄×C₆₁	—	2	2	no	—
402	C₄⋊C₄×C₆₁	—	2	2	no	—
403	C₄⋊C₄×C₆₁	—	2	1	no	—
404	C₄⋊C₄×C₆₁	—	2	2	no	—
405	C₄⋊C₄×C₆₁	—	2	1	no	—
406	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
417	C₂²⋊C₄×C₆₁	—	2	2	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	1	no	—
422	C₂²⋊C₄×C₆₁	—	2	2	no	—
423	C₂²⋊C₄×C₆₁	—	2	2	no	—
424	C₂²⋊C₄×C₆₁	—	2	1	no	—
425	C₂²⋊C₄×C₆₁	—	2	1	no	—
426	C₂²⋊C₄×C₆₁	—	2	2	no	—
427	C₂²⋊C₄×C₆₁	—	2	2	no	—
428	C₂²⋊C₄×C₆₁	—	2	2	no	—
429	C₂²⋊C₄×C₆₁	—	2	2	no	—
430	C₂²⋊C₄×C₆₁	—	2	2	no	—
431	C₂²⋊C₄×C₆₁	—	2	2	no	—
432	C₂²⋊C₄×C₆₁	—	2	2	no	—
433	C₂²⋊C₄×C₆₁	—	2	2	no	—
434	C₂²⋊C₄×C₆₁	—	2	2	no	—
435	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
440	C₄²×C₆₁	—	2	1	no	—
441	C₄²×C₆₁	—	2	1	no	—
442	C₄²×C₆₁	—	2	1	no	—
443	C₄²×C₆₁	—	2	2	no	—
444	C₄²×C₆₁	—	2	2	no	—
445	C₄²×C₆₁	—	2	2	no	—
446	C₄²×C₆₁	—	2	1	no	—
447	C₄²×C₆₁	—	2	2	no	—
448	C₄²×C₆₁	—	2	1	no	—
449	C₄²×C₆₁	—	2	2	no	—
450	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
453	C₄²×C₆₁	C₂⁴	1	2	yes	—
454	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
455	C₂³×C₆₁	—	2	1	no	—
456	C₂³×C₆₁	—	2	2	no	—
457	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
458	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
459	Q₈×C₆₁	—	2	2	no	—
460	Q₈×C₆₁	—	2	1	no	—
461	Q₈×C₆₁	—	2	2	no	—
462	Q₈×C₆₁	—	2	2	no	—
463	Q₈×C₆₁	—	2	1	no	—
464	Q₈×C₆₁	—	2	1	no	—
465	Q₈×C₆₁	—	2	2	no	—
466	Q₈×C₆₁	—	2	1	no	—
467	Q₈×C₆₁	—	2	1	no	—
468	Q₈×C₆₁	—	2	2	no	—
469	Q₈×C₆₁	—	4	4	no	—
470	Q₈×C₆₁	—	8	1	no	—
471	Q₈×C₆₁	—	8	1	no	—
472	Q₈×C₆₁	—	8	2	no	—
473	Q₈×C₆₁	—	8	2	no	—
474	Q₈×C₆₁	H(5,𝔽₂)	1	2	yes	—
475	D₄×C₆₁	—	2	2	no	—
476	D₄×C₆₁	—	2	1	no	—
477	D₄×C₆₁	—	2	2	no	—
478	D₄×C₆₁	—	2	1	no	—
479	D₄×C₆₁	—	2	2	no	—
480	D₄×C₆₁	—	4	2	no	—
481	D₄×C₆₁	—	4	2	no	—
482	D₄×C₆₁	—	4	2	no	—
483	D₄×C₆₁	—	8	1	no	—
484	D₄×C₆₁	—	8	2	no	—
485	D₄×C₆₁	—	8	2	no	—
486	D₄×C₆₁	—	8	2	no	—
487	D₄×C₆₁	—	8	2	no	—
488	C₂×C₄×C₆₁	—	2	1	no	—
489	C₂×C₄×C₆₁	—	2	2	no	—
490	C₂×C₄×C₆₁	—	2	1	no	—
491	C₂×C₄×C₆₁	—	2	2	no	—
492	C₂×C₄×C₆₁	—	2	2	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	—	2	1	no	—
499	C₂×C₄×C₆₁	—	2	1	no	—
500	C₂×C₄×C₆₁	—	2	1	no	—
501	C₂×C₄×C₆₁	—	2	2	no	—
502	C₂×C₄×C₆₁	—	2	1	no	—
503	C₂×C₄×C₆₁	—	4	1	no	—
504	C₂×C₄×C₆₁	—	4	2	no	—
505	C₂×C₄×C₆₁	—	4	4	no	—
506	C₂×C₄×C₆₁	—	4	2	no	—
507	C₂×C₄×C₆₁	—	8	1	no	—
508	C₂×C₄×C₆₁	—	8	2	no	—
509	C₂×C₄×C₆₁	—	8	2	no	—
510	C₂×C₄×C₆₁	—	8	2	no	—
511	C₂×C₄×C₆₁	—	8	2	no	—
512	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
521	C₈×C₆₁	—	2	2	no	—
522	C₈×C₆₁	—	2	1	no	—
523	C₈×C₆₁	—	2	2	no	—
524	C₈×C₆₁	—	2	1	no	—
525	C₈×C₆₁	—	2	1	no	—
526	C₈×C₆₁	—	2	1	no	—
527	#62072	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
528	C₂²×C₆₁	—	2	1	no	—
529	C₂²×C₆₁	—	2	2	no	—
530	C₂²×C₆₁	—	2	2	no	—
531	C₂²×C₆₁	—	2	1	no	—
532	C₂²×C₆₁	—	2	1	no	—
533	C₂²×C₆₁	—	2	2	no	—
534	C₂²×C₆₁	—	4	2	no	—
535	C₂²×C₆₁	—	4	1	no	—
536	C₂²×C₆₁	—	4	1	no	—
537	C₂²×C₆₁	—	4	2	no	—
538	C₂²×C₆₁	—	4	1	no	—
539	C₂²×C₆₁	—	4	2	no	—
540	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
541	C₄×C₆₁	—	2	1	no	—
542	C₄×C₆₁	—	2	1	no	—
543	C₄×C₆₁	—	2	2	no	—
544	C₄×C₆₁	—	2	1	no	—
545	C₄×C₆₁	—	2	2	no	—
546	C₄×C₆₁	—	2	2	no	—
547	C₄×C₆₁	—	2	1	no	—
548	C₄×C₆₁	—	2	2	no	—
549	C₄×C₆₁	—	4	1	no	—
550	C₄×C₆₁	—	4	1	no	—
551	C₄×C₆₁	—	4	1	no	—
552	C₄×C₆₁	—	4	2	no	—
553	C₄×C₆₁	—	4	2	no	—
554	C₄×C₆₁	—	4	1	no	—
555	C₄×C₆₁	—	4	2	no	—
556	C₄×C₆₁	—	4	1	no	—
557	C₄×C₆₁	—	4	1	no	—
558	C₄×C₆₁	#578	1	2	yes	—
559	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
560	C₄×C₆₁	#585	1	1	yes	characteristic
561	#3554	C₂×C₆₁	1	1	yes	characteristic, complemented
562	#3518	C₂×C₆₁	1	1	yes	characteristic, complemented
563	#3398	C₂×C₆₁	1	1	yes	characteristic, complemented
564	#3394	C₂×C₆₁	1	1	yes	characteristic, complemented
565	#3375	C₂×C₆₁	1	1	yes	characteristic, complemented
566	#3363	C₂×C₆₁	1	1	yes	characteristic, complemented
567	#3329	C₂×C₆₁	1	1	yes	characteristic, complemented
568	#3313	C₂×C₆₁	1	2	yes	complemented
569	#3305	C₂×C₆₁	1	1	yes	characteristic, complemented
570	#3302	C₂×C₆₁	1	2	yes	complemented
571	D₄×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
572	#3285	C₂×C₆₁	1	2	yes	complemented
573	#3278	C₂×C₆₁	1	1	yes	characteristic, complemented
574	#3269	C₂×C₆₁	1	2	yes	complemented
575	#3262	C₂×C₆₁	1	2	yes	complemented
576	#3249	C₂×C₆₁	1	1	yes	characteristic, complemented
577	#3225	C₂×C₆₁	1	2	yes	complemented
578	#3210	C₂×C₆₁	1	1	yes	characteristic, complemented
579	#3121	C₂×C₆₁	1	2	yes	complemented
580	#3107	C₂×C₆₁	1	1	yes	characteristic, complemented
581	#3044	C₂×C₆₁	1	2	yes	complemented
582	#3035	C₂×C₆₁	1	1	yes	characteristic, complemented
583	#2994	C₂×C₆₁	1	1	yes	characteristic, complemented
584	C₂×C₆₁	—	4	1	no	—
585	C₂×C₆₁	—	4	2	no	—
586	C₂×C₆₁	—	8	1	no	—
587	C₂×C₆₁	—	8	2	no	—
588	C₂×C₆₁	#3488	1	1	yes	characteristic
589	C₂×C₆₁	C₂×#578	1	1	yes	characteristic
590	C₂×C₆₁	#3584	1	1	yes	characteristic
591	C₂×#137	C₂²×C₆₁	1	2	yes	—
592	C₂×#135	C₂²×C₆₁	1	2	yes	—
593	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
594	#562	—	2	2	no	—
595	#559	—	2	1	no	—
596	#559	C₂²×C₆₁	1	1	yes	characteristic
597	Q₈²	C₂²×C₆₁	1	1	yes	characteristic
598	#557	C₂²×C₆₁	1	1	yes	characteristic
599	#556	—	2	2	no	—
600	#556	—	2	1	no	—
601	#556	C₂²×C₆₁	1	1	yes	characteristic
602	#556	C₂²×C₆₁	1	2	yes	—
603	#555	—	2	1	no	—
604	#555	C₂²×C₆₁	1	1	yes	characteristic
605	#554	—	2	1	no	—
606	#550	C₂²×C₆₁	1	1	yes	characteristic
607	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
608	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
609	#548	C₂²×C₆₁	1	2	yes	—
610	#548	C₂²×C₆₁	1	2	yes	—
611	#547	C₂²×C₆₁	1	2	yes	—
612	#542	—	2	2	no	—
613	#542	—	2	1	no	—
614	#542	C₂²×C₆₁	1	2	yes	—
615	#542	C₂²×C₆₁	1	2	yes	—
616	#540	—	2	1	no	—
617	#539	—	2	2	no	—
618	#536	C₂²×C₆₁	1	2	yes	—
619	#533	—	2	1	no	—
620	#533	C₂²×C₆₁	1	1	yes	characteristic
621	#533	C₂²×C₆₁	1	1	yes	characteristic
622	#532	C₂²×C₆₁	1	1	yes	characteristic
623	#529	—	2	1	no	—
624	#529	C₂²×C₆₁	1	1	yes	characteristic
625	#519	C₂²×C₆₁	1	2	yes	—
626	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
627	#497	C₂²×C₆₁	1	2	yes	—
628	#495	C₂²×C₆₁	1	2	yes	—
629	#494	C₂²×C₆₁	1	1	yes	characteristic
630	#492	C₂²×C₆₁	1	1	yes	characteristic
631	#489	C₂²×C₆₁	1	2	yes	—
632	#487	C₂²×C₆₁	1	1	yes	characteristic
633	#487	C₂²×C₆₁	1	2	yes	—
634	#486	C₂²×C₆₁	1	1	yes	characteristic
635	#485	C₂²×C₆₁	1	2	yes	—
636	#485	C₂²×C₆₁	1	1	yes	characteristic
637	#485	C₂²×C₆₁	1	1	yes	characteristic
638	#482	C₂²×C₆₁	1	2	yes	—
639	#477	C₂²×C₆₁	1	1	yes	characteristic
640	#477	C₂²×C₆₁	1	1	yes	characteristic
641	#477	C₂²×C₆₁	1	2	yes	—
642	#477	C₂²×C₆₁	1	2	yes	—
643	#475	C₂²×C₆₁	1	1	yes	characteristic
644	#474	C₂²×C₆₁	1	1	yes	characteristic
645	#474	C₂²×C₆₁	1	2	yes	—
646	#468	C₂²×C₆₁	1	2	yes	—
647	#468	C₂²×C₆₁	1	2	yes	—
648	#467	C₂²×C₆₁	1	2	yes	—
649	#467	C₂²×C₆₁	1	2	yes	—
650	#467	C₂²×C₆₁	1	2	yes	—
651	#466	C₂²×C₆₁	1	2	yes	—
652	#464	C₂²×C₆₁	1	2	yes	—
653	#464	C₂²×C₆₁	1	2	yes	—
654	#464	C₂²×C₆₁	1	2	yes	—
655	#464	C₂²×C₆₁	1	2	yes	—
656	#464	C₂²×C₆₁	1	2	yes	—
657	#464	C₂²×C₆₁	1	2	yes	—
658	#463	C₂²×C₆₁	1	2	yes	—
659	#463	C₂²×C₆₁	1	2	yes	—
660	#462	C₂²×C₆₁	1	1	yes	characteristic
661	#462	C₂²×C₆₁	1	2	yes	—
662	#462	C₂²×C₆₁	1	1	yes	characteristic
663	#462	C₂²×C₆₁	1	1	yes	characteristic
664	#462	C₂²×C₆₁	1	1	yes	characteristic
665	#462	C₂²×C₆₁	1	2	yes	—
666	#462	C₂²×C₆₁	1	2	yes	—
667	#461	C₂²×C₆₁	1	1	yes	characteristic
668	#461	C₂²×C₆₁	1	1	yes	characteristic
669	#460	C₂²×C₆₁	1	1	yes	characteristic
670	#459	C₂²×C₆₁	1	1	yes	characteristic
671	#452	C₂²×C₆₁	1	1	yes	characteristic
672	#452	C₂²×C₆₁	1	1	yes	characteristic
673	#452	C₂²×C₆₁	1	2	yes	—
674	#452	C₂²×C₆₁	1	2	yes	—
675	#452	C₂²×C₆₁	1	2	yes	—
676	#451	C₂²×C₆₁	1	2	yes	—
677	#451	C₂²×C₆₁	1	2	yes	—
678	#449	C₂²×C₆₁	1	2	yes	—
679	#448	C₂²×C₆₁	1	2	yes	—
680	#448	C₂²×C₆₁	1	2	yes	—
681	#446	C₂²×C₆₁	1	1	yes	characteristic
682	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
683	#441	C₂²×C₆₁	1	2	yes	—
684	#440	C₂²×C₆₁	1	2	yes	—
685	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
686	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
687	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
688	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
689	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
690	C₄×SD₁₆	C₂²×C₆₁	1	2	yes	—
691	#436	C₂²×C₆₁	1	1	yes	characteristic
692	#435	C₂²×C₆₁	1	2	yes	—
693	C₈×D₄	C₂²×C₆₁	1	2	yes	—
694	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
695	#433	C₂²×C₆₁	1	2	yes	—
696	#431	C₂²×C₆₁	1	1	yes	characteristic
697	#424	C₂²×C₆₁	1	2	yes	—
698	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
699	#419	C₂²×C₆₁	1	2	yes	—
700	#416	C₂²×C₆₁	1	2	yes	—
701	#416	C₂²×C₆₁	1	2	yes	—
702	C₆₁	#62072	1	1	yes	characteristic, direct product factor, Sylow
703	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
704	C₂×#41	C₂³×C₆₁	1	2	yes	—
705	C₂×#41	C₂³×C₆₁	1	2	yes	—
706	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
707	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
708	#137	—	4	4	no	—
709	#135	—	4	4	no	—
710	C₂×Q₁₆	—	4	4	no	—
711	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
712	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
713	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
714	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
715	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
716	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
717	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
719	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
720	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
722	C₂×SD₁₆	C₂³×C₆₁	1	2	yes	—
723	C₂×SD₁₆	C₂³×C₆₁	1	1	yes	characteristic
724	C₂×D₈	C₂³×C₆₁	1	2	yes	—
725	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
726	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
727	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
728	C₄⋊Q₈	—	2	1	no	—
729	C₄⋊Q₈	—	2	1	no	—
730	C₄⋊Q₈	—	2	1	no	—
731	C₄⋊Q₈	—	2	2	no	—
732	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
733	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
734	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
735	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
736	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
737	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
738	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
739	#127	—	2	1	no	—
740	#127	C₂³×C₆₁	1	1	yes	characteristic
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	D₄×C₆₁	1	2	yes	—
747	#125	—	2	2	no	—
748	#125	—	2	1	no	—
749	#125	—	2	1	no	—
750	#125	—	2	1	no	—
751	#125	D₄×C₆₁	1	1	yes	characteristic
752	#124	—	2	1	no	—
753	#124	—	2	2	no	—
754	#124	—	2	2	no	—
755	#124	—	2	2	no	—
756	#124	—	2	2	no	—
757	#124	—	2	2	no	—
758	#124	—	2	2	no	—
759	#124	D₄×C₆₁	1	1	yes	characteristic
760	#124	C₂³×C₆₁	1	2	yes	—
761	#124	C₂³×C₆₁	1	2	yes	—
762	#124	C₂³×C₆₁	1	2	yes	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	#123	—	2	2	no	—
770	#123	D₄×C₆₁	1	2	yes	—
771	C₂²⋊Q₈	—	2	1	no	—
772	C₂²⋊Q₈	—	2	1	no	—
773	C₂²⋊Q₈	—	2	1	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
783	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
784	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
785	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
786	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
787	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
788	#121	—	2	1	no	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	—	2	2	no	—
792	#121	—	2	1	no	—
793	#121	—	2	1	no	—
794	#121	—	2	2	no	—
795	#121	D₄×C₆₁	1	1	yes	characteristic
796	#121	C₂³×C₆₁	1	2	yes	—
797	#121	C₂³×C₆₁	1	2	yes	—
798	C₄×Q₈	—	2	1	no	—
799	C₄×Q₈	—	2	1	no	—
800	C₄×Q₈	—	2	2	no	—
801	C₄×Q₈	—	2	2	no	—
802	C₄×Q₈	—	2	2	no	—
803	C₄×Q₈	—	2	1	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
806	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
807	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
808	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
809	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
810	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
812	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
813	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
826	C₄×D₄	C₂³×C₆₁	1	2	yes	—
827	C₄×D₄	C₂³×C₆₁	1	2	yes	—
828	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
829	#117	—	2	1	no	—
830	#117	—	2	1	no	—
831	#117	—	2	1	no	—
832	#117	—	2	1	no	—
833	#117	—	2	2	no	—
834	#117	—	2	2	no	—
835	#117	—	2	1	no	—
836	#117	C₂³×C₆₁	1	1	yes	characteristic
837	#117	C₂³×C₆₁	1	2	yes	—
838	#117	C₂³×C₆₁	1	2	yes	—
839	C₂×C₄⋊C₄	—	2	2	no	—
840	C₂×C₄²	—	2	1	no	—
841	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
842	#107	C₂³×C₆₁	1	2	yes	—
843	#107	C₂³×C₆₁	1	1	yes	characteristic
844	#107	C₂³×C₆₁	1	1	yes	characteristic
845	#107	C₂³×C₆₁	1	2	yes	—
846	#106	C₂³×C₆₁	1	1	yes	characteristic
847	#106	C₂³×C₆₁	1	1	yes	characteristic
848	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
849	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
850	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
851	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
852	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
853	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
854	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
855	#103	C₂³×C₆₁	1	1	yes	characteristic
856	#103	C₂³×C₆₁	1	2	yes	—
857	#103	C₂³×C₆₁	1	2	yes	—
858	#103	C₂³×C₆₁	1	2	yes	—
859	#103	C₂³×C₆₁	1	1	yes	characteristic
860	#103	C₂³×C₆₁	1	2	yes	—
861	#103	C₂³×C₆₁	1	2	yes	—
862	#103	C₂³×C₆₁	1	2	yes	—
863	#103	C₂³×C₆₁	1	1	yes	characteristic
864	#103	C₂³×C₆₁	1	1	yes	characteristic
865	#103	C₂³×C₆₁	1	2	yes	—
866	#103	C₂³×C₆₁	1	1	yes	characteristic
867	#103	C₂³×C₆₁	1	1	yes	characteristic
868	#103	C₂³×C₆₁	1	2	yes	—
869	#102	C₂³×C₆₁	1	2	yes	—
870	#102	C₂³×C₆₁	1	2	yes	—
871	#102	C₂³×C₆₁	1	2	yes	—
872	#102	C₂³×C₆₁	1	1	yes	characteristic
873	#102	C₂³×C₆₁	1	1	yes	characteristic
874	#102	C₂³×C₆₁	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
876	C₂²⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
877	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
879	#97	C₂³×C₆₁	1	2	yes	—
880	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
881	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
882	C₄×C₈	C₂³×C₆₁	1	2	yes	—
883	#41	—	2	2	no	—
884	#41	—	4	1	no	—
885	#41	—	4	2	no	—
886	#41	—	4	2	no	—
887	#41	—	4	2	no	—
888	#41	—	4	2	no	—
889	C₂×Q₈	—	2	2	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	1	no	—
892	C₂×Q₈	—	2	2	no	—
893	C₂×Q₈	—	2	2	no	—
894	C₂×Q₈	—	2	4	no	—
895	C₂×Q₈	—	4	2	no	—
896	C₂×Q₈	—	4	2	no	—
897	C₂×Q₈	—	4	2	no	—
898	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
899	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
900	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
901	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
902	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
903	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
912	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
913	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
914	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	1	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	C₂⁴×C₆₁	1	1	yes	characteristic
926	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
927	Q₁₆	—	2	2	no	—
928	Q₁₆	—	2	4	no	—
929	Q₁₆	—	2	2	no	—
930	Q₁₆	—	4	2	no	—
931	Q₁₆	—	4	2	no	—
932	Q₁₆	—	4	2	no	—
933	Q₁₆	—	4	2	no	—
934	SD₁₆	—	2	4	no	—
935	SD₁₆	—	4	1	no	—
936	SD₁₆	—	4	2	no	—
937	SD₁₆	—	4	1	no	—
938	SD₁₆	—	4	2	no	—
939	SD₁₆	—	4	2	no	—
940	D₈	—	4	2	no	—
941	M₁₆	—	4	2	no	—
942	C₂×C₈	—	4	2	no	—
943	C₂×C₈	—	4	2	no	—
944	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
945	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
946	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
947	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
948	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
949	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
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	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
975	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
976	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
977	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
978	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
979	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
981	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
982	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
983	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	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	—	2	2	no	—
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	C₂²⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	2	no	—
1012	C₄²	—	2	2	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1019	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
1020	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1021	C₄²	C₂⁴×C₆₁	1	2	yes	—
1022	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1023	C₂³	—	2	1	no	—
1024	C₂³	—	2	2	no	—
1025	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
1026	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
1027	Q₈	—	2	2	no	—
1028	Q₈	—	2	1	no	—
1029	Q₈	—	2	2	no	—
1030	Q₈	—	2	2	no	—
1031	Q₈	—	2	1	no	—
1032	Q₈	—	2	1	no	—
1033	Q₈	—	2	2	no	—
1034	Q₈	—	2	1	no	—
1035	Q₈	—	2	1	no	—
1036	Q₈	—	2	2	no	—
1037	Q₈	—	4	4	no	—
1038	Q₈	—	8	1	no	—
1039	Q₈	—	8	1	no	—
1040	Q₈	—	8	2	no	—
1041	Q₈	—	8	2	no	—
1042	Q₈	H(5,𝔽₂)×C₆₁	1	2	yes	—
1043	D₄	—	2	2	no	—
1044	D₄	—	2	1	no	—
1045	D₄	—	2	2	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	2	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	4	2	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	8	1	no	—
1052	D₄	—	8	2	no	—
1053	D₄	—	8	2	no	—
1054	D₄	—	8	2	no	—
1055	D₄	—	8	2	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	4	1	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	4	4	no	—
1074	C₂×C₄	—	4	2	no	—
1075	C₂×C₄	—	8	1	no	—
1076	C₂×C₄	—	8	2	no	—
1077	C₂×C₄	—	8	2	no	—
1078	C₂×C₄	—	8	2	no	—
1079	C₂×C₄	—	8	2	no	—
1080	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1081	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1082	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1083	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1084	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1085	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
1086	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1087	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
1088	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1089	C₈	—	2	2	no	—
1090	C₈	—	2	1	no	—
1091	C₈	—	2	2	no	—
1092	C₈	—	2	1	no	—
1093	C₈	—	2	1	no	—
1094	C₈	—	2	1	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	2	2	no	—
1097	C₂²	—	2	1	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	2	2	no	—
1100	C₂²	—	2	1	no	—
1101	C₂²	—	4	1	no	—
1102	C₂²	—	4	2	no	—
1103	C₂²	—	4	2	no	—
1104	C₂²	—	4	1	no	—
1105	C₂²	—	4	1	no	—
1106	C₂²	—	4	2	no	—
1107	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
1108	C₄	—	2	1	no	—
1109	C₄	—	2	2	no	—
1110	C₄	—	2	1	no	—
1111	C₄	—	2	1	no	—
1112	C₄	—	2	2	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	2	2	no	—
1115	C₄	—	2	2	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	1	no	—
1119	C₄	—	4	1	no	—
1120	C₄	—	4	2	no	—
1121	C₄	—	4	2	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	2	no	—
1124	C₄	—	4	1	no	—
1125	C₄	C₆₁×#578	1	2	yes	—
1126	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1127	C₄	C₆₁×#585	1	1	yes	characteristic
1128	C₂	—	4	1	no	—
1129	C₂	—	4	2	no	—
1130	C₂	—	8	1	no	—
1131	C₂	—	8	2	no	—
1132	C₂	C₆₁×#3488	1	1	yes	characteristic
1133	C₂	C₂×C₆₁×#578	1	1	yes	characteristic
1134	C₂	C₆₁×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3554	C₂	semidirect
2. C₆₁×#3518	C₂	semidirect
3. C₆₁×#3398	C₂	semidirect
4. C₆₁×#3394	C₂	semidirect
5. C₆₁×#3375	C₂	semidirect
6. C₆₁×#3363	C₂	semidirect
7. C₆₁×#3329	C₂	semidirect
8. C₆₁×#3313	C₂	semidirect
9. C₆₁×#3305	C₂	semidirect
10. C₆₁×#3302	C₂	semidirect
11. D₄×Q₁₆×C₆₁	C₂	semidirect
12. C₆₁×#3285	C₂	semidirect
13. C₆₁×#3278	C₂	semidirect
14. C₆₁×#3269	C₂	semidirect
15. C₆₁×#3262	C₂	semidirect
16. C₆₁×#3249	C₂	semidirect
17. C₆₁×#3225	C₂	semidirect
18. C₆₁×#3210	C₂	semidirect
19. C₆₁×#3121	C₂	semidirect
20. C₆₁×#3107	C₂	semidirect
21. C₆₁×#3044	C₂	semidirect
22. C₆₁×#3035	C₂	semidirect
23. C₆₁×#2994	C₂	semidirect
527. #62072	C₆₁	direct (N × H)
561. #3554	C₂×C₆₁	semidirect
562. #3518	C₂×C₆₁	semidirect
563. #3398	C₂×C₆₁	semidirect
564. #3394	C₂×C₆₁	semidirect
565. #3375	C₂×C₆₁	semidirect
566. #3363	C₂×C₆₁	semidirect
567. #3329	C₂×C₆₁	semidirect
568. #3313	C₂×C₆₁	semidirect
569. #3305	C₂×C₆₁	semidirect
570. #3302	C₂×C₆₁	semidirect
571. D₄×Q₁₆	C₂×C₆₁	semidirect
572. #3285	C₂×C₆₁	semidirect
573. #3278	C₂×C₆₁	semidirect
574. #3269	C₂×C₆₁	semidirect
575. #3262	C₂×C₆₁	semidirect
576. #3249	C₂×C₆₁	semidirect
577. #3225	C₂×C₆₁	semidirect
578. #3210	C₂×C₆₁	semidirect
579. #3121	C₂×C₆₁	semidirect
580. #3107	C₂×C₆₁	semidirect
581. #3044	C₂×C₆₁	semidirect
582. #3035	C₂×C₆₁	semidirect
583. #2994	C₂×C₆₁	semidirect
702. C₆₁	#62072	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×#3554	2
C₆₁×#3518	2
C₆₁×#3398	2
C₆₁×#3394	2
C₆₁×#3375	2
C₆₁×#3363	2
C₆₁×#3329	2
C₆₁×#3313	2
C₆₁×#3305	2
C₆₁×#3302	2
D₄×Q₁₆×C₆₁	2
C₆₁×#3285	2
C₆₁×#3278	2
C₆₁×#3269	2
C₆₁×#3262	2
C₆₁×#3249	2
C₆₁×#3225	2
C₆₁×#3210	2
C₆₁×#3121	2
C₆₁×#3107	2
C₆₁×#3044	2
C₆₁×#3035	2
C₆₁×#2994	2
#62072	61

Subgroups — C61×#62072 #29565505

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62072 #29565505