Subgroups — C₆₁×#62857 #29566290

Order 15616.

7082 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3524	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3522	C₂	1	2	yes	maximal, complemented
3	C₆₁×#3521	C₂	1	6	yes	maximal, complemented
4	C₆₁×#3520	C₂	1	6	yes	maximal, complemented
5	C₆₁×#3518	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3516	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3514	C₂	1	6	yes	maximal, complemented
8	C₆₁×#3513	C₂	1	6	yes	maximal, complemented
9	C₆₁×#3511	C₂	1	3	yes	maximal, complemented
10	C₆₁×#3510	C₂	1	3	yes	maximal, complemented
11	C₆₁×#3503	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3500	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3495	C₂	1	3	yes	maximal, complemented
14	C₆₁×#3494	C₂	1	3	yes	maximal, complemented
15	C₆₁×#3489	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3488	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3461	C₂	1	3	yes	maximal, complemented
18	C₆₁×#3460	C₂	1	3	yes	maximal, complemented
19	C₆₁×#3455	C₂	1	3	yes	maximal, complemented
20	C₂×C₆₁×#542	C₂	1	3	yes	maximal, complemented
21	C₄×2₋¹⁺⁴×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×H(5,𝔽₂)×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#3428	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×H(5,𝔽₂)×C₆₁	C₂²	1	1	yes	characteristic
26	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
27	C₆₁×#559	C₂²	1	6	yes	complemented
28	C₆₁×#559	C₂²	1	6	yes	complemented
29	Q₈²×C₆₁	C₂²	1	2	yes	complemented
30	C₆₁×#557	C₂²	1	2	yes	complemented
31	C₆₁×#556	C₂²	1	6	yes	complemented
32	C₆₁×#556	C₂²	1	6	yes	complemented
33	C₆₁×#556	C₂²	1	6	yes	complemented
34	C₆₁×#556	C₂²	1	6	yes	complemented
35	C₆₁×#555	C₂²	1	6	yes	complemented
36	C₆₁×#555	C₂²	1	6	yes	complemented
37	C₆₁×#554	C₂²	1	6	yes	complemented
38	C₆₁×#554	C₂²	1	6	yes	complemented
39	C₆₁×#554	C₂²	1	6	yes	complemented
40	C₆₁×#553	C₂²	1	6	yes	complemented
41	C₆₁×#553	C₂²	1	6	yes	complemented
42	C₆₁×#553	C₂²	1	12	yes	complemented
43	C₆₁×#552	C₂²	1	6	yes	complemented
44	C₆₁×#552	C₂²	1	12	yes	complemented
45	C₆₁×#552	C₂²	1	6	yes	complemented
46	C₆₁×#551	C₂²	1	12	yes	complemented
47	C₆₁×#551	C₂²	1	12	yes	complemented
48	C₆₁×#551	C₂²	1	12	yes	complemented
49	C₆₁×#551	C₂²	1	12	yes	complemented
50	C₆₁×#550	C₂²	1	2	yes	—
51	D₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
52	D₄×Q₈×C₆₁	C₂²	1	6	yes	complemented
53	C₆₁×#548	C₂²	1	2	yes	—
54	C₆₁×#548	C₂²	1	2	yes	complemented
55	C₆₁×#548	C₂²	1	2	yes	complemented
56	C₆₁×#548	C₂²	1	2	yes	complemented
57	C₆₁×#548	C₂²	1	12	yes	complemented
58	C₆₁×#547	C₂²	1	6	yes	complemented
59	C₆₁×#547	C₂²	1	6	yes	complemented
60	C₆₁×#547	C₂²	1	6	yes	complemented
61	C₆₁×#546	C₂²	1	6	yes	—
62	C₆₁×#546	C₂²	1	6	yes	complemented
63	C₆₁×#546	C₂²	1	12	yes	complemented
64	C₆₁×#546	C₂²	1	6	yes	complemented
65	C₆₁×#546	C₂²	1	6	yes	complemented
66	D₄²×C₆₁	C₂²	1	6	yes	—
67	C₆₁×#544	C₂²	1	3	yes	complemented
68	C₆₁×#544	C₂²	1	3	yes	complemented
69	C₆₁×#542	C₂²	1	3	yes	complemented
70	C₆₁×#542	C₂²	1	6	yes	complemented
71	C₆₁×#542	C₂²	1	6	yes	complemented
72	C₆₁×#542	C₂²	1	6	yes	complemented
73	C₆₁×#542	C₂²	1	6	yes	complemented
74	C₆₁×#542	C₂²	1	6	yes	complemented
75	C₆₁×#542	C₂²	1	6	yes	complemented
76	C₆₁×#542	C₂²	1	6	yes	complemented
77	C₆₁×#542	C₂²	1	1	yes	characteristic, complemented
78	C₆₁×#542	C₂²	1	3	yes	complemented
79	C₆₁×#542	C₂²	1	3	yes	complemented
80	C₆₁×#542	C₂²	1	6	yes	complemented
81	C₆₁×#542	C₂²	1	6	yes	complemented
82	C₆₁×#541	C₂²	1	3	yes	complemented
83	C₆₁×#541	C₂²	1	3	yes	complemented
84	C₆₁×#541	C₂²	1	6	yes	complemented
85	C₆₁×#540	C₂²	1	3	yes	complemented
86	C₆₁×#540	C₂²	1	3	yes	complemented
87	C₆₁×#540	C₂²	1	6	yes	complemented
88	C₆₁×#539	C₂²	1	6	yes	complemented
89	C₆₁×#539	C₂²	1	6	yes	complemented
90	C₆₁×#539	C₂²	1	12	yes	complemented
91	C₆₁×#538	C₂²	1	6	yes	complemented
92	C₆₁×#538	C₂²	1	6	yes	complemented
93	C₆₁×#538	C₂²	1	12	yes	complemented
94	C₆₁×#537	C₂²	1	3	yes	—
95	C₆₁×#537	C₂²	1	3	yes	complemented
96	C₆₁×#536	C₂²	1	3	yes	complemented
97	C₆₁×#536	C₂²	1	3	yes	complemented
98	C₆₁×#535	C₂²	1	3	yes	—
99	C₆₁×#535	C₂²	1	3	yes	complemented
100	C₆₁×#533	C₂²	1	3	yes	complemented
101	C₆₁×#533	C₂²	1	6	yes	complemented
102	C₆₁×#533	C₂²	1	6	yes	complemented
103	C₆₁×#532	C₂²	1	3	yes	complemented
104	C₆₁×#532	C₂²	1	6	yes	complemented
105	C₆₁×#532	C₂²	1	6	yes	complemented
106	C₂×C₄⋊Q₈×C₆₁	C₂²	1	3	yes	complemented
107	C₆₁×#529	C₂²	1	6	yes	complemented
108	C₆₁×#529	C₂²	1	6	yes	complemented
109	C₆₁×#529	C₂²	1	6	yes	complemented
110	C₆₁×#529	C₂²	1	6	yes	complemented
111	C₆₁×#529	C₂²	1	6	yes	complemented
112	C₆₁×#529	C₂²	1	6	yes	complemented
113	C₆₁×#529	C₂²	1	6	yes	complemented
114	C₆₁×#529	C₂²	1	6	yes	complemented
115	C₆₁×#529	C₂²	1	12	yes	complemented
116	C₂×#126×C₆₁	C₂²	1	6	yes	complemented
117	C₂×#124×C₆₁	C₂²	1	3	yes	complemented
118	C₂×#124×C₆₁	C₂²	1	6	yes	complemented
119	C₆₁×#525	C₂²	1	3	yes	—
120	C₆₁×#525	C₂²	1	3	yes	complemented
121	C₆₁×#525	C₂²	1	12	yes	complemented
122	C₂×#123×C₆₁	C₂²	1	6	yes	complemented
123	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	3	yes	complemented
124	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	6	yes	complemented
125	C₂×#121×C₆₁	C₂²	1	3	yes	—
126	C₆₁×#520	C₂²	1	1	yes	characteristic
127	C₆₁×#520	C₂²	1	1	yes	characteristic
128	C₆₁×#520	C₂²	1	3	yes	complemented
129	C₆₁×#520	C₂²	1	3	yes	complemented
130	C₆₁×#520	C₂²	1	1	yes	characteristic, complemented
131	C₆₁×#520	C₂²	1	1	yes	characteristic, complemented
132	C₆₁×#520	C₂²	1	3	yes	complemented
133	C₆₁×#520	C₂²	1	2	yes	complemented
134	C₆₁×#520	C₂²	1	3	yes	complemented
135	C₆₁×#520	C₂²	1	6	yes	complemented
136	C₆₁×#519	C₂²	1	1	yes	characteristic, complemented
137	C₆₁×#519	C₂²	1	1	yes	characteristic, complemented
138	C₆₁×#519	C₂²	1	3	yes	complemented
139	C₆₁×#519	C₂²	1	2	yes	complemented
140	C₆₁×#518	C₂²	1	3	yes	complemented
141	C₆₁×#518	C₂²	1	3	yes	complemented
142	C₆₁×#518	C₂²	1	3	yes	complemented
143	C₆₁×#518	C₂²	1	6	yes	complemented
144	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
145	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
146	C₄×#41×C₆₁	C₂²	1	3	yes	complemented
147	C₄×#41×C₆₁	C₂²	1	3	yes	complemented
148	C₄×#41×C₆₁	C₂²	1	3	yes	complemented
149	C₄×#41×C₆₁	C₂²	1	2	yes	complemented
150	C₄×#41×C₆₁	C₂²	1	3	yes	complemented
151	C₄×#41×C₆₁	C₂²	1	6	yes	complemented
152	C₂×C₄×Q₈×C₆₁	C₂²	1	3	yes	complemented
153	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
154	C₂×C₄×D₄×C₆₁	C₂²	1	3	yes	complemented
155	C₂×C₄×D₄×C₆₁	C₂²	1	6	yes	complemented
156	C₂×#117×C₆₁	C₂²	1	3	yes	complemented
157	C₂×#117×C₆₁	C₂²	1	3	yes	complemented
158	2₋¹⁺⁴×C₆₁	—	2	8	no	—
159	H(5,𝔽₂)×C₆₁	—	2	8	no	—
160	C₂×#41×C₆₁	—	2	8	no	—
161	C₂×#41×C₆₁	C₂³	1	3	yes	—
162	C₂×#41×C₆₁	C₂³	1	3	yes	—
163	C₂×#41×C₆₁	C₂³	1	3	yes	—
164	C₂×#41×C₆₁	C₂³	1	3	yes	—
165	C₂×#41×C₆₁	C₂³	1	6	yes	—
166	C₂×#41×C₆₁	C₂³	1	2	yes	—
167	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
168	C₂×#41×C₆₁	C₂³	1	12	yes	—
169	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
170	C₂²×Q₈×C₆₁	C₂³	1	3	yes	—
171	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
172	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
173	C₂²×Q₈×C₆₁	C₂³	1	6	yes	—
174	C₂²×D₄×C₆₁	C₂³	1	3	yes	—
175	C₂²×D₄×C₆₁	C₂³	1	3	yes	—
176	C₂²×D₄×C₆₁	C₂³	1	6	yes	—
177	C₂²×D₄×C₆₁	C₂³	1	6	yes	—
178	C₂³×C₄×C₆₁	C₂³	1	3	yes	—
179	C₂³×C₄×C₆₁	C₂³	1	6	yes	—
180	C₄⋊Q₈×C₆₁	C₂³	1	3	yes	—
181	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
182	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
183	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
184	C₄⋊Q₈×C₆₁	C₂³	1	3	yes	—
185	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
186	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
187	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
188	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
189	#127×C₆₁	C₂³	1	3	yes	—
190	#127×C₆₁	C₂³	1	6	yes	—
191	#126×C₆₁	C₂³	1	6	yes	—
192	#126×C₆₁	C₂³	1	12	yes	—
193	#126×C₆₁	C₂³	1	6	yes	—
194	#126×C₆₁	C₂³	1	6	yes	—
195	#126×C₆₁	C₂³	1	6	yes	—
196	#126×C₆₁	C₂³	1	12	yes	—
197	#126×C₆₁	C₂³	1	2	yes	—
198	#126×C₆₁	C₂³	1	12	yes	—
199	#126×C₆₁	C₂³	1	6	yes	—
200	#126×C₆₁	C₂³	1	6	yes	—
201	#126×C₆₁	C₂³	1	6	yes	—
202	#126×C₆₁	C₂³	1	12	yes	—
203	#126×C₆₁	C₂³	1	12	yes	—
204	#125×C₆₁	C₂³	1	6	yes	—
205	#125×C₆₁	C₂³	1	12	yes	—
206	#125×C₆₁	C₂³	1	3	yes	—
207	#125×C₆₁	C₂³	1	3	yes	—
208	#125×C₆₁	C₂³	1	6	yes	—
209	#125×C₆₁	C₂³	1	6	yes	—
210	#125×C₆₁	C₂³	1	6	yes	—
211	#125×C₆₁	C₂³	1	6	yes	—
212	#125×C₆₁	C₂³	1	6	yes	—
213	#124×C₆₁	C₂³	1	1	yes	characteristic
214	#124×C₆₁	C₂³	1	12	yes	—
215	#124×C₆₁	C₂³	1	12	yes	—
216	#124×C₆₁	C₂³	1	3	yes	—
217	#124×C₆₁	C₂³	1	6	yes	—
218	#124×C₆₁	C₂³	1	6	yes	—
219	#124×C₆₁	C₂³	1	6	yes	—
220	#124×C₆₁	C₂³	1	2	yes	—
221	#124×C₆₁	C₂³	1	6	yes	—
222	#124×C₆₁	C₂³	1	6	yes	—
223	#124×C₆₁	C₂³	1	6	yes	—
224	#124×C₆₁	C₂³	1	6	yes	—
225	#124×C₆₁	C₂³	1	6	yes	—
226	#124×C₆₁	C₂³	1	12	yes	—
227	#124×C₆₁	C₂³	1	12	yes	—
228	#123×C₆₁	C₂³	1	12	yes	—
229	#123×C₆₁	C₂³	1	12	yes	—
230	#123×C₆₁	C₂³	1	2	yes	—
231	#123×C₆₁	C₂³	1	6	yes	—
232	#123×C₆₁	C₂³	1	12	yes	—
233	#123×C₆₁	C₂³	1	6	yes	—
234	#123×C₆₁	C₂³	1	6	yes	—
235	#123×C₆₁	C₂³	1	6	yes	—
236	#123×C₆₁	C₂³	1	6	yes	—
237	#123×C₆₁	C₂³	1	6	yes	—
238	#123×C₆₁	C₂³	1	12	yes	—
239	#123×C₆₁	C₂³	1	6	yes	—
240	#123×C₆₁	C₂³	1	6	yes	—
241	#123×C₆₁	C₂³	1	6	yes	—
242	#123×C₆₁	C₂³	1	12	yes	—
243	#123×C₆₁	C₂³	1	12	yes	—
244	#123×C₆₁	C₂³	1	12	yes	—
245	C₂²⋊Q₈×C₆₁	C₂³	1	3	yes	—
246	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
247	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
248	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
249	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
250	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
251	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
252	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
253	C₂²⋊Q₈×C₆₁	C₂³	1	3	yes	—
254	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
255	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
256	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
257	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
258	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
259	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
260	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
261	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
262	C₂²⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
263	C₂²⋊Q₈×C₆₁	C₂³	1	3	yes	—
264	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
265	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
266	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
267	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
268	#121×C₆₁	C₂³	1	3	yes	—
269	#121×C₆₁	C₂³	1	6	yes	—
270	#121×C₆₁	C₂³	1	6	yes	—
271	#121×C₆₁	C₂³	1	6	yes	—
272	#121×C₆₁	C₂³	1	6	yes	—
273	#121×C₆₁	C₂³	1	6	yes	—
274	#121×C₆₁	C₂³	1	6	yes	—
275	#121×C₆₁	C₂³	1	12	yes	—
276	#121×C₆₁	C₂³	1	3	yes	—
277	#121×C₆₁	C₂³	1	6	yes	—
278	#121×C₆₁	C₂³	1	12	yes	—
279	#121×C₆₁	C₂³	1	6	yes	—
280	#121×C₆₁	C₂³	1	12	yes	—
281	#121×C₆₁	C₂³	1	6	yes	—
282	#121×C₆₁	C₂³	1	6	yes	—
283	#121×C₆₁	C₂³	1	6	yes	—
284	#121×C₆₁	C₂³	1	1	yes	characteristic
285	#121×C₆₁	C₂³	1	3	yes	—
286	#121×C₆₁	C₂³	1	6	yes	—
287	#121×C₆₁	C₂³	1	6	yes	—
288	#120×C₆₁	C₂³	1	12	yes	—
289	#120×C₆₁	C₂³	1	12	yes	—
290	#120×C₆₁	C₂³	1	6	yes	—
291	#120×C₆₁	C₂³	1	6	yes	—
292	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
293	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
294	C₄×Q₈×C₆₁	C₂³	1	12	yes	—
295	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
296	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
297	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
298	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
299	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
300	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
301	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
302	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
303	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
304	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
305	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
306	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
307	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
308	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
309	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
310	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
311	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
312	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
313	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
314	C₄×D₄×C₆₁	C₂³	1	3	yes	—
315	C₄×D₄×C₆₁	C₂³	1	3	yes	—
316	C₄×D₄×C₆₁	C₂³	1	6	yes	—
317	C₄×D₄×C₆₁	C₂³	1	6	yes	—
318	C₄×D₄×C₆₁	C₂³	1	6	yes	—
319	C₄×D₄×C₆₁	C₂³	1	6	yes	—
320	C₄×D₄×C₆₁	C₂³	1	12	yes	—
321	C₄×D₄×C₆₁	C₂³	1	12	yes	—
322	C₄×D₄×C₆₁	C₂³	1	6	yes	—
323	C₄×D₄×C₆₁	C₂³	1	6	yes	—
324	C₄×D₄×C₆₁	C₂³	1	6	yes	—
325	C₄×D₄×C₆₁	C₂³	1	6	yes	—
326	C₄×D₄×C₆₁	C₂³	1	6	yes	—
327	C₄×D₄×C₆₁	C₂³	1	6	yes	—
328	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
329	C₄×D₄×C₆₁	C₂³	1	3	yes	—
330	C₄×D₄×C₆₁	C₂³	1	3	yes	—
331	C₄×D₄×C₆₁	C₂³	1	6	yes	—
332	C₄×D₄×C₆₁	C₂³	1	3	yes	—
333	C₄×D₄×C₆₁	C₂³	1	6	yes	—
334	C₄×D₄×C₆₁	C₂³	1	6	yes	—
335	C₄×D₄×C₆₁	C₂³	1	6	yes	—
336	C₄×D₄×C₆₁	C₂³	1	3	yes	—
337	C₄×D₄×C₆₁	C₂³	1	3	yes	—
338	C₄×D₄×C₆₁	C₂³	1	6	yes	—
339	C₄×D₄×C₆₁	C₂³	1	12	yes	—
340	C₄×D₄×C₆₁	C₂³	1	6	yes	—
341	C₄×D₄×C₆₁	C₂³	1	12	yes	—
342	C₄×D₄×C₆₁	C₂³	1	6	yes	—
343	C₄×D₄×C₆₁	C₂³	1	3	yes	—
344	C₄×D₄×C₆₁	C₂³	1	6	yes	—
345	C₄×D₄×C₆₁	C₂³	1	6	yes	—
346	C₄×D₄×C₆₁	C₂³	1	12	yes	—
347	C₄×D₄×C₆₁	C₂³	1	6	yes	—
348	C₄×D₄×C₆₁	C₂³	1	6	yes	—
349	C₄×D₄×C₆₁	C₂³	1	3	yes	—
350	C₄×D₄×C₆₁	C₂³	1	3	yes	—
351	C₄×D₄×C₆₁	C₂³	1	3	yes	—
352	#117×C₆₁	C₂³	1	3	yes	—
353	#117×C₆₁	C₂³	1	3	yes	—
354	#117×C₆₁	C₂³	1	12	yes	—
355	#117×C₆₁	C₂³	1	12	yes	—
356	#117×C₆₁	C₂³	1	3	yes	—
357	#117×C₆₁	C₂³	1	3	yes	—
358	#117×C₆₁	C₂³	1	3	yes	—
359	#117×C₆₁	C₂³	1	6	yes	—
360	#117×C₆₁	C₂³	1	6	yes	—
361	#117×C₆₁	C₂³	1	1	yes	characteristic
362	#117×C₆₁	C₂³	1	3	yes	—
363	#117×C₆₁	C₂³	1	3	yes	—
364	#117×C₆₁	C₂³	1	3	yes	—
365	#117×C₆₁	C₂³	1	3	yes	—
366	#117×C₆₁	C₂³	1	3	yes	—
367	#117×C₆₁	C₂³	1	12	yes	—
368	#117×C₆₁	C₂³	1	6	yes	—
369	#117×C₆₁	C₂³	1	12	yes	—
370	#117×C₆₁	C₂³	1	3	yes	—
371	#117×C₆₁	C₂³	1	6	yes	—
372	#117×C₆₁	C₂³	1	6	yes	—
373	#117×C₆₁	C₂³	1	3	yes	—
374	#117×C₆₁	C₂³	1	3	yes	—
375	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
376	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
377	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
378	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
379	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
380	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
381	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
382	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
383	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
384	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
385	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
386	C₂×C₂²⋊C₄×C₆₁	C₂³	1	3	yes	—
387	C₂×C₂²⋊C₄×C₆₁	C₂³	1	3	yes	—
388	C₂×C₂²⋊C₄×C₆₁	C₂³	1	6	yes	—
389	C₂×C₂²⋊C₄×C₆₁	C₂³	1	6	yes	—
390	C₂×C₂²⋊C₄×C₆₁	C₂³	1	6	yes	—
391	C₂×C₂²⋊C₄×C₆₁	C₂³	1	6	yes	—
392	C₂×C₂²⋊C₄×C₆₁	C₂³	1	6	yes	—
393	C₂×C₂²⋊C₄×C₆₁	C₂³	1	6	yes	—
394	C₂×C₂²⋊C₄×C₆₁	C₂³	1	12	yes	—
395	C₂×C₄²×C₆₁	C₂³	1	3	yes	—
396	C₂×C₄²×C₆₁	C₂³	1	6	yes	—
397	C₂×C₄²×C₆₁	C₂³	1	6	yes	—
398	C₂×C₄²×C₆₁	C₂³	1	6	yes	—
399	C₂×C₄²×C₆₁	C₂³	1	3	yes	—
400	C₂×C₄²×C₆₁	C₂³	1	6	yes	—
401	C₂⁴×C₆₁	C₂⁴	1	3	yes	—
402	C₂⁴×C₆₁	C₂⁴	1	6	yes	—
403	#41×C₆₁	—	2	4	no	—
404	#41×C₆₁	—	2	8	no	—
405	#41×C₆₁	—	2	12	no	—
406	#41×C₆₁	—	2	24	no	—
407	#41×C₆₁	—	2	12	no	—
408	#41×C₆₁	—	2	12	no	—
409	#41×C₆₁	—	2	12	no	—
410	#41×C₆₁	—	8	12	no	—
411	#41×C₆₁	#41	1	8	yes	complemented
412	C₂×Q₈×C₆₁	—	2	4	no	—
413	C₂×Q₈×C₆₁	—	2	8	no	—
414	C₂×Q₈×C₆₁	—	2	12	no	—
415	C₂×Q₈×C₆₁	—	8	6	no	—
416	C₂×Q₈×C₆₁	C₂⁴	1	3	yes	—
417	C₂×Q₈×C₆₁	C₂⁴	1	6	yes	—
418	C₂×Q₈×C₆₁	C₂⁴	1	3	yes	—
419	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
420	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
421	C₂×Q₈×C₆₁	C₂⁴	1	6	yes	—
422	C₂×Q₈×C₆₁	C₂⁴	1	12	yes	—
423	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
424	C₂×D₄×C₆₁	—	2	12	no	—
425	C₂×D₄×C₆₁	—	2	24	no	—
426	C₂×D₄×C₆₁	—	2	12	no	—
427	C₂×D₄×C₆₁	—	8	6	no	—
428	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
429	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
430	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
431	C₂×D₄×C₆₁	C₂⁴	1	3	yes	—
432	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
433	C₂×D₄×C₆₁	C₂⁴	1	3	yes	—
434	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
435	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
436	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
437	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
438	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
439	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
440	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
441	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
442	C₂×D₄×C₆₁	C₂⁴	1	3	yes	—
443	C₂²×C₄×C₆₁	—	2	12	no	—
444	C₂²×C₄×C₆₁	—	8	6	no	—
445	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
446	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
447	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
448	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
449	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
450	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
451	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
452	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
453	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
454	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
455	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
456	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
457	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
458	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
459	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
460	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
461	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
462	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
463	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
464	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
465	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
466	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
467	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
468	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
469	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
470	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
471	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
472	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
473	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
474	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
475	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
476	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
477	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
478	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
479	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
480	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
481	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
482	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
483	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
484	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
485	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
486	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
487	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
488	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
489	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
490	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
491	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
492	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
493	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
494	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
495	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
496	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
497	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
498	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
499	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
500	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
501	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
502	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
503	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
504	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
505	C₂²⋊C₄×C₆₁	C₂⁴	1	3	yes	—
506	C₂²⋊C₄×C₆₁	C₂⁴	1	3	yes	—
507	C₂²⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
508	C₂²⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
509	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
510	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
511	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
512	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
513	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
514	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
515	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
516	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
517	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
518	C₂²⋊C₄×C₆₁	C₂⁴	1	3	yes	—
519	C₂²⋊C₄×C₆₁	C₂⁴	1	3	yes	—
520	C₂²⋊C₄×C₆₁	C₂⁴	1	3	yes	—
521	C₂²⋊C₄×C₆₁	C₂⁴	1	3	yes	—
522	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
523	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
524	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
525	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
526	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
527	C₂²⋊C₄×C₆₁	C₂⁴	1	2	yes	—
528	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
529	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
530	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
531	C₂²⋊C₄×C₆₁	C₂⁴	1	2	yes	—
532	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
533	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
534	C₂²⋊C₄×C₆₁	C₂⁴	1	2	yes	—
535	C₂²⋊C₄×C₆₁	C₂⁴	1	2	yes	—
536	C₂²⋊C₄×C₆₁	C₂⁴	1	2	yes	—
537	C₄²×C₆₁	C₂⁴	1	3	yes	—
538	C₄²×C₆₁	C₂⁴	1	3	yes	—
539	C₄²×C₆₁	C₂⁴	1	3	yes	—
540	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
541	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
542	C₄²×C₆₁	C₂⁴	1	3	yes	—
543	C₄²×C₆₁	C₂⁴	1	2	yes	—
544	C₄²×C₆₁	C₂⁴	1	6	yes	—
545	C₄²×C₆₁	C₂⁴	1	6	yes	—
546	C₄²×C₆₁	C₂⁴	1	6	yes	—
547	C₄²×C₆₁	C₂⁴	1	6	yes	—
548	C₄²×C₆₁	C₂⁴	1	12	yes	—
549	C₄²×C₆₁	C₂⁴	1	6	yes	—
550	C₄²×C₆₁	C₂⁴	1	6	yes	—
551	C₄²×C₆₁	C₂⁴	1	3	yes	—
552	C₄²×C₆₁	C₂⁴	1	3	yes	—
553	C₄²×C₆₁	C₂⁴	1	6	yes	—
554	C₂³×C₆₁	—	2	6	no	—
555	C₂³×C₆₁	—	2	12	no	—
556	C₂³×C₆₁	—	4	6	no	—
557	C₂³×C₆₁	—	4	3	no	—
558	C₂³×C₆₁	—	4	3	no	—
559	C₂³×C₆₁	—	4	6	no	—
560	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
561	C₂³×C₆₁	C₂⁵	1	6	yes	—
562	C₂³×C₆₁	C₂⁵	1	3	yes	—
563	C₂³×C₆₁	C₂⁵	1	2	yes	—
564	C₂³×C₆₁	C₂⁵	1	3	yes	—
565	Q₈×C₆₁	—	2	12	no	—
566	Q₈×C₆₁	—	2	6	no	—
567	Q₈×C₆₁	—	2	6	no	—
568	Q₈×C₆₁	—	2	2	no	—
569	Q₈×C₆₁	—	4	6	no	—
570	Q₈×C₆₁	—	4	12	no	—
571	Q₈×C₆₁	—	4	2	no	—
572	Q₈×C₆₁	C₂×#41	1	4	yes	—
573	D₄×C₆₁	—	2	12	no	—
574	D₄×C₆₁	—	2	12	no	—
575	D₄×C₆₁	—	2	12	no	—
576	D₄×C₆₁	—	2	12	no	—
577	D₄×C₆₁	—	2	6	no	—
578	D₄×C₆₁	—	2	6	no	—
579	D₄×C₆₁	—	2	2	no	—
580	D₄×C₆₁	—	4	6	no	—
581	D₄×C₆₁	—	4	12	no	—
582	D₄×C₆₁	—	4	6	no	—
583	D₄×C₆₁	—	4	2	no	—
584	D₄×C₆₁	—	4	6	no	—
585	D₄×C₆₁	—	4	6	no	—
586	D₄×C₆₁	—	4	6	no	—
587	D₄×C₆₁	C₂×#41	1	12	yes	—
588	C₂×C₄×C₆₁	—	2	6	no	—
589	C₂×C₄×C₆₁	—	2	12	no	—
590	C₂×C₄×C₆₁	—	2	2	no	—
591	C₂×C₄×C₆₁	—	2	6	no	—
592	C₂×C₄×C₆₁	—	2	6	no	—
593	C₂×C₄×C₆₁	—	2	6	no	—
594	C₂×C₄×C₆₁	—	2	12	no	—
595	C₂×C₄×C₆₁	—	2	12	no	—
596	C₂×C₄×C₆₁	—	4	3	no	—
597	C₂×C₄×C₆₁	—	4	6	no	—
598	C₂×C₄×C₆₁	—	4	6	no	—
599	C₂×C₄×C₆₁	—	4	12	no	—
600	C₂×C₄×C₆₁	—	4	3	no	—
601	C₂×C₄×C₆₁	—	4	6	no	—
602	C₂×C₄×C₆₁	—	4	6	no	—
603	C₂×C₄×C₆₁	—	4	2	no	—
604	C₂×C₄×C₆₁	—	4	3	no	—
605	C₂×C₄×C₆₁	—	4	6	no	—
606	C₂×C₄×C₆₁	—	4	3	no	—
607	C₂×C₄×C₆₁	—	4	6	no	—
608	C₂×C₄×C₆₁	—	4	6	no	—
609	C₂×C₄×C₆₁	C₂×#41	1	12	yes	—
610	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
611	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
612	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
613	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
614	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
615	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
616	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
617	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
618	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
619	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
620	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
621	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
622	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
623	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
624	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
625	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
626	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
627	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
628	#62857	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
629	C₂²×C₆₁	—	2	3	no	—
630	C₂²×C₆₁	—	2	3	no	—
631	C₂²×C₆₁	—	2	1	no	—
632	C₂²×C₆₁	—	2	2	no	—
633	C₂²×C₆₁	—	2	3	no	—
634	C₂²×C₆₁	—	2	6	no	—
635	C₂²×C₆₁	—	2	2	no	—
636	C₂²×C₆₁	—	2	6	no	—
637	C₂²×C₆₁	—	2	3	no	—
638	C₂²×C₆₁	—	2	1	no	—
639	C₂²×C₆₁	—	2	3	no	—
640	C₂²×C₆₁	—	2	2	no	—
641	C₂²×C₆₁	—	2	6	no	—
642	C₂²×C₆₁	—	2	1	no	—
643	C₂²×C₆₁	—	8	6	no	—
644	C₂²×C₆₁	—	8	12	no	—
645	C₂²×C₆₁	C₂²×#41	1	6	yes	—
646	C₂²×C₆₁	C₂⁶	1	1	yes	characteristic
647	C₄×C₆₁	—	2	1	no	—
648	C₄×C₆₁	—	2	2	no	—
649	C₄×C₆₁	—	2	3	no	—
650	C₄×C₆₁	—	2	6	no	—
651	C₄×C₆₁	—	2	1	no	—
652	C₄×C₆₁	—	2	3	no	—
653	C₄×C₆₁	—	2	6	no	—
654	C₄×C₆₁	—	2	6	no	—
655	C₄×C₆₁	—	2	3	no	—
656	C₄×C₆₁	—	2	1	no	—
657	C₄×C₆₁	—	2	1	no	—
658	C₄×C₆₁	—	2	3	no	—
659	C₄×C₆₁	—	2	3	no	—
660	C₄×C₆₁	—	2	2	no	—
661	C₄×C₆₁	—	2	1	no	—
662	C₄×C₆₁	—	2	2	no	—
663	C₄×C₆₁	C₂²×#41	1	6	yes	—
664	C₄×C₆₁	C₂²×#41	1	2	yes	—
665	#3524	C₂×C₆₁	1	2	yes	complemented
666	#3522	C₂×C₆₁	1	2	yes	complemented
667	#3521	C₂×C₆₁	1	6	yes	complemented
668	#3520	C₂×C₆₁	1	6	yes	complemented
669	#3518	C₂×C₆₁	1	2	yes	complemented
670	#3516	C₂×C₆₁	1	2	yes	complemented
671	#3514	C₂×C₆₁	1	6	yes	complemented
672	#3513	C₂×C₆₁	1	6	yes	complemented
673	#3511	C₂×C₆₁	1	3	yes	complemented
674	#3510	C₂×C₆₁	1	3	yes	complemented
675	#3503	C₂×C₆₁	1	1	yes	characteristic, complemented
676	#3500	C₂×C₆₁	1	1	yes	characteristic, complemented
677	#3495	C₂×C₆₁	1	3	yes	complemented
678	#3494	C₂×C₆₁	1	3	yes	complemented
679	#3489	C₂×C₆₁	1	1	yes	characteristic, complemented
680	#3488	C₂×C₆₁	1	1	yes	characteristic, complemented
681	#3461	C₂×C₆₁	1	3	yes	complemented
682	#3460	C₂×C₆₁	1	3	yes	complemented
683	#3455	C₂×C₆₁	1	3	yes	complemented
684	C₂×#542	C₂×C₆₁	1	3	yes	complemented
685	C₄×2₋¹⁺⁴	C₂×C₆₁	1	1	yes	characteristic, complemented
686	C₄×H(5,𝔽₂)	C₂×C₆₁	1	1	yes	characteristic, complemented
687	#3428	C₂×C₆₁	1	1	yes	characteristic, complemented
688	C₂×C₆₁	—	2	6	no	—
689	C₂×C₆₁	—	4	2	no	—
690	C₂×C₆₁	—	4	3	no	—
691	C₂×C₆₁	—	4	6	no	—
692	C₂×C₆₁	—	4	1	no	—
693	C₂×C₆₁	C₂³×#41	1	1	yes	characteristic
694	C₂×C₆₁	H(7,𝔽₂)	1	1	yes	characteristic
695	C₂×C₆₁	2₋¹⁺⁶	1	1	yes	characteristic
696	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	1	yes	characteristic
697	C₂×H(5,𝔽₂)	C₂²×C₆₁	1	1	yes	characteristic
698	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
699	#559	C₂²×C₆₁	1	6	yes	complemented
700	#559	C₂²×C₆₁	1	6	yes	complemented
701	Q₈²	C₂²×C₆₁	1	2	yes	complemented
702	#557	C₂²×C₆₁	1	2	yes	complemented
703	#556	C₂²×C₆₁	1	6	yes	complemented
704	#556	C₂²×C₆₁	1	6	yes	complemented
705	#556	C₂²×C₆₁	1	6	yes	complemented
706	#556	C₂²×C₆₁	1	6	yes	complemented
707	#555	C₂²×C₆₁	1	6	yes	complemented
708	#555	C₂²×C₆₁	1	6	yes	complemented
709	#554	C₂²×C₆₁	1	6	yes	complemented
710	#554	C₂²×C₆₁	1	6	yes	complemented
711	#554	C₂²×C₆₁	1	6	yes	complemented
712	#553	C₂²×C₆₁	1	6	yes	complemented
713	#553	C₂²×C₆₁	1	6	yes	complemented
714	#553	C₂²×C₆₁	1	12	yes	complemented
715	#552	C₂²×C₆₁	1	6	yes	complemented
716	#552	C₂²×C₆₁	1	12	yes	complemented
717	#552	C₂²×C₆₁	1	6	yes	complemented
718	#551	C₂²×C₆₁	1	12	yes	complemented
719	#551	C₂²×C₆₁	1	12	yes	complemented
720	#551	C₂²×C₆₁	1	12	yes	complemented
721	#551	C₂²×C₆₁	1	12	yes	complemented
722	#550	C₂²×C₆₁	1	2	yes	—
723	D₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
724	D₄×Q₈	C₂²×C₆₁	1	6	yes	complemented
725	#548	C₂²×C₆₁	1	2	yes	—
726	#548	C₂²×C₆₁	1	2	yes	complemented
727	#548	C₂²×C₆₁	1	2	yes	complemented
728	#548	C₂²×C₆₁	1	2	yes	complemented
729	#548	C₂²×C₆₁	1	12	yes	complemented
730	#547	C₂²×C₆₁	1	6	yes	complemented
731	#547	C₂²×C₆₁	1	6	yes	complemented
732	#547	C₂²×C₆₁	1	6	yes	complemented
733	#546	C₂²×C₆₁	1	6	yes	—
734	#546	C₂²×C₆₁	1	6	yes	complemented
735	#546	C₂²×C₆₁	1	12	yes	complemented
736	#546	C₂²×C₆₁	1	6	yes	complemented
737	#546	C₂²×C₆₁	1	6	yes	complemented
738	D₄²	C₂²×C₆₁	1	6	yes	—
739	#544	C₂²×C₆₁	1	3	yes	complemented
740	#544	C₂²×C₆₁	1	3	yes	complemented
741	#542	C₂²×C₆₁	1	3	yes	complemented
742	#542	C₂²×C₆₁	1	6	yes	complemented
743	#542	C₂²×C₆₁	1	6	yes	complemented
744	#542	C₂²×C₆₁	1	6	yes	complemented
745	#542	C₂²×C₆₁	1	6	yes	complemented
746	#542	C₂²×C₆₁	1	6	yes	complemented
747	#542	C₂²×C₆₁	1	6	yes	complemented
748	#542	C₂²×C₆₁	1	6	yes	complemented
749	#542	C₂²×C₆₁	1	1	yes	characteristic, complemented
750	#542	C₂²×C₆₁	1	3	yes	complemented
751	#542	C₂²×C₆₁	1	3	yes	complemented
752	#542	C₂²×C₆₁	1	6	yes	complemented
753	#542	C₂²×C₆₁	1	6	yes	complemented
754	#541	C₂²×C₆₁	1	3	yes	complemented
755	#541	C₂²×C₆₁	1	3	yes	complemented
756	#541	C₂²×C₆₁	1	6	yes	complemented
757	#540	C₂²×C₆₁	1	3	yes	complemented
758	#540	C₂²×C₆₁	1	3	yes	complemented
759	#540	C₂²×C₆₁	1	6	yes	complemented
760	#539	C₂²×C₆₁	1	6	yes	complemented
761	#539	C₂²×C₆₁	1	6	yes	complemented
762	#539	C₂²×C₆₁	1	12	yes	complemented
763	#538	C₂²×C₆₁	1	6	yes	complemented
764	#538	C₂²×C₆₁	1	6	yes	complemented
765	#538	C₂²×C₆₁	1	12	yes	complemented
766	#537	C₂²×C₆₁	1	3	yes	—
767	#537	C₂²×C₆₁	1	3	yes	complemented
768	#536	C₂²×C₆₁	1	3	yes	complemented
769	#536	C₂²×C₆₁	1	3	yes	complemented
770	#535	C₂²×C₆₁	1	3	yes	—
771	#535	C₂²×C₆₁	1	3	yes	complemented
772	#533	C₂²×C₆₁	1	3	yes	complemented
773	#533	C₂²×C₆₁	1	6	yes	complemented
774	#533	C₂²×C₆₁	1	6	yes	complemented
775	#532	C₂²×C₆₁	1	3	yes	complemented
776	#532	C₂²×C₆₁	1	6	yes	complemented
777	#532	C₂²×C₆₁	1	6	yes	complemented
778	C₂×C₄⋊Q₈	C₂²×C₆₁	1	3	yes	complemented
779	#529	C₂²×C₆₁	1	6	yes	complemented
780	#529	C₂²×C₆₁	1	6	yes	complemented
781	#529	C₂²×C₆₁	1	6	yes	complemented
782	#529	C₂²×C₆₁	1	6	yes	complemented
783	#529	C₂²×C₆₁	1	6	yes	complemented
784	#529	C₂²×C₆₁	1	6	yes	complemented
785	#529	C₂²×C₆₁	1	6	yes	complemented
786	#529	C₂²×C₆₁	1	6	yes	complemented
787	#529	C₂²×C₆₁	1	12	yes	complemented
788	C₂×#126	C₂²×C₆₁	1	6	yes	complemented
789	C₂×#124	C₂²×C₆₁	1	3	yes	complemented
790	C₂×#124	C₂²×C₆₁	1	6	yes	complemented
791	#525	C₂²×C₆₁	1	3	yes	—
792	#525	C₂²×C₆₁	1	3	yes	complemented
793	#525	C₂²×C₆₁	1	12	yes	complemented
794	C₂×#123	C₂²×C₆₁	1	6	yes	complemented
795	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	3	yes	complemented
796	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	6	yes	complemented
797	C₂×#121	C₂²×C₆₁	1	3	yes	—
798	#520	C₂²×C₆₁	1	1	yes	characteristic
799	#520	C₂²×C₆₁	1	1	yes	characteristic
800	#520	C₂²×C₆₁	1	3	yes	complemented
801	#520	C₂²×C₆₁	1	3	yes	complemented
802	#520	C₂²×C₆₁	1	1	yes	characteristic, complemented
803	#520	C₂²×C₆₁	1	1	yes	characteristic, complemented
804	#520	C₂²×C₆₁	1	3	yes	complemented
805	#520	C₂²×C₆₁	1	2	yes	complemented
806	#520	C₂²×C₆₁	1	3	yes	complemented
807	#520	C₂²×C₆₁	1	6	yes	complemented
808	#519	C₂²×C₆₁	1	1	yes	characteristic, complemented
809	#519	C₂²×C₆₁	1	1	yes	characteristic, complemented
810	#519	C₂²×C₆₁	1	3	yes	complemented
811	#519	C₂²×C₆₁	1	2	yes	complemented
812	#518	C₂²×C₆₁	1	3	yes	complemented
813	#518	C₂²×C₆₁	1	3	yes	complemented
814	#518	C₂²×C₆₁	1	3	yes	complemented
815	#518	C₂²×C₆₁	1	6	yes	complemented
816	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
817	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
818	C₄×#41	C₂²×C₆₁	1	3	yes	complemented
819	C₄×#41	C₂²×C₆₁	1	3	yes	complemented
820	C₄×#41	C₂²×C₆₁	1	3	yes	complemented
821	C₄×#41	C₂²×C₆₁	1	2	yes	complemented
822	C₄×#41	C₂²×C₆₁	1	3	yes	complemented
823	C₄×#41	C₂²×C₆₁	1	6	yes	complemented
824	C₂×C₄×Q₈	C₂²×C₆₁	1	3	yes	complemented
825	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
826	C₂×C₄×D₄	C₂²×C₆₁	1	3	yes	complemented
827	C₂×C₄×D₄	C₂²×C₆₁	1	6	yes	complemented
828	C₂×#117	C₂²×C₆₁	1	3	yes	complemented
829	C₂×#117	C₂²×C₆₁	1	3	yes	complemented
830	C₆₁	#62857	1	1	yes	characteristic, direct product factor, Sylow
831	2₋¹⁺⁴	—	2	8	no	—
832	H(5,𝔽₂)	—	2	8	no	—
833	C₂×#41	—	2	8	no	—
834	C₂×#41	C₂³×C₆₁	1	3	yes	—
835	C₂×#41	C₂³×C₆₁	1	3	yes	—
836	C₂×#41	C₂³×C₆₁	1	3	yes	—
837	C₂×#41	C₂³×C₆₁	1	6	yes	—
838	C₂×#41	C₂³×C₆₁	1	2	yes	—
839	C₂×#41	C₂³×C₆₁	1	3	yes	—
840	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
841	C₂×#41	C₂³×C₆₁	1	12	yes	—
842	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
843	C₂²×Q₈	C₂³×C₆₁	1	3	yes	—
844	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
845	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
846	C₂²×Q₈	C₂³×C₆₁	1	6	yes	—
847	C₂²×D₄	C₂³×C₆₁	1	3	yes	—
848	C₂²×D₄	C₂³×C₆₁	1	6	yes	—
849	C₂²×D₄	C₂³×C₆₁	1	3	yes	—
850	C₂²×D₄	C₂³×C₆₁	1	6	yes	—
851	C₂³×C₄	C₂³×C₆₁	1	3	yes	—
852	C₂³×C₄	C₂³×C₆₁	1	6	yes	—
853	C₄⋊Q₈	C₂³×C₆₁	1	3	yes	—
854	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
855	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
856	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
857	C₄⋊Q₈	C₂³×C₆₁	1	3	yes	—
858	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
859	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
860	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
861	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
862	#127	C₂³×C₆₁	1	3	yes	—
863	#127	C₂³×C₆₁	1	6	yes	—
864	#126	C₂³×C₆₁	1	6	yes	—
865	#126	C₂³×C₆₁	1	12	yes	—
866	#126	C₂³×C₆₁	1	12	yes	—
867	#126	C₂³×C₆₁	1	12	yes	—
868	#126	C₂³×C₆₁	1	6	yes	—
869	#126	C₂³×C₆₁	1	6	yes	—
870	#126	C₂³×C₆₁	1	2	yes	—
871	#126	C₂³×C₆₁	1	6	yes	—
872	#126	C₂³×C₆₁	1	6	yes	—
873	#126	C₂³×C₆₁	1	12	yes	—
874	#126	C₂³×C₆₁	1	12	yes	—
875	#126	C₂³×C₆₁	1	6	yes	—
876	#126	C₂³×C₆₁	1	6	yes	—
877	#125	C₂³×C₆₁	1	6	yes	—
878	#125	C₂³×C₆₁	1	3	yes	—
879	#125	C₂³×C₆₁	1	3	yes	—
880	#125	C₂³×C₆₁	1	6	yes	—
881	#125	C₂³×C₆₁	1	6	yes	—
882	#125	C₂³×C₆₁	1	6	yes	—
883	#125	C₂³×C₆₁	1	6	yes	—
884	#125	C₂³×C₆₁	1	6	yes	—
885	#125	C₂³×C₆₁	1	12	yes	—
886	#124	C₂³×C₆₁	1	6	yes	—
887	#124	C₂³×C₆₁	1	3	yes	—
888	#124	C₂³×C₆₁	1	6	yes	—
889	#124	C₂³×C₆₁	1	12	yes	—
890	#124	C₂³×C₆₁	1	6	yes	—
891	#124	C₂³×C₆₁	1	6	yes	—
892	#124	C₂³×C₆₁	1	12	yes	—
893	#124	C₂³×C₆₁	1	12	yes	—
894	#124	C₂³×C₆₁	1	2	yes	—
895	#124	C₂³×C₆₁	1	6	yes	—
896	#124	C₂³×C₆₁	1	6	yes	—
897	#124	C₂³×C₆₁	1	6	yes	—
898	#124	C₂³×C₆₁	1	6	yes	—
899	#124	C₂³×C₆₁	1	1	yes	characteristic
900	#124	C₂³×C₆₁	1	12	yes	—
901	#123	C₂³×C₆₁	1	6	yes	—
902	#123	C₂³×C₆₁	1	12	yes	—
903	#123	C₂³×C₆₁	1	12	yes	—
904	#123	C₂³×C₆₁	1	12	yes	—
905	#123	C₂³×C₆₁	1	6	yes	—
906	#123	C₂³×C₆₁	1	6	yes	—
907	#123	C₂³×C₆₁	1	6	yes	—
908	#123	C₂³×C₆₁	1	2	yes	—
909	#123	C₂³×C₆₁	1	6	yes	—
910	#123	C₂³×C₆₁	1	12	yes	—
911	#123	C₂³×C₆₁	1	12	yes	—
912	#123	C₂³×C₆₁	1	12	yes	—
913	#123	C₂³×C₆₁	1	6	yes	—
914	#123	C₂³×C₆₁	1	6	yes	—
915	#123	C₂³×C₆₁	1	6	yes	—
916	#123	C₂³×C₆₁	1	6	yes	—
917	#123	C₂³×C₆₁	1	12	yes	—
918	C₂²⋊Q₈	C₂³×C₆₁	1	3	yes	—
919	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
920	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
921	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
922	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
923	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
924	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
925	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
926	C₂²⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
927	C₂²⋊Q₈	C₂³×C₆₁	1	3	yes	—
928	C₂²⋊Q₈	C₂³×C₆₁	1	3	yes	—
929	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
930	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
931	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
932	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
933	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
934	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
935	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
936	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
937	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
938	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
939	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
940	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
941	#121	C₂³×C₆₁	1	3	yes	—
942	#121	C₂³×C₆₁	1	6	yes	—
943	#121	C₂³×C₆₁	1	6	yes	—
944	#121	C₂³×C₆₁	1	6	yes	—
945	#121	C₂³×C₆₁	1	3	yes	—
946	#121	C₂³×C₆₁	1	1	yes	characteristic
947	#121	C₂³×C₆₁	1	6	yes	—
948	#121	C₂³×C₆₁	1	3	yes	—
949	#121	C₂³×C₆₁	1	12	yes	—
950	#121	C₂³×C₆₁	1	6	yes	—
951	#121	C₂³×C₆₁	1	6	yes	—
952	#121	C₂³×C₆₁	1	12	yes	—
953	#121	C₂³×C₆₁	1	6	yes	—
954	#121	C₂³×C₆₁	1	6	yes	—
955	#121	C₂³×C₆₁	1	6	yes	—
956	#121	C₂³×C₆₁	1	6	yes	—
957	#121	C₂³×C₆₁	1	6	yes	—
958	#121	C₂³×C₆₁	1	6	yes	—
959	#121	C₂³×C₆₁	1	6	yes	—
960	#121	C₂³×C₆₁	1	12	yes	—
961	#120	C₂³×C₆₁	1	6	yes	—
962	#120	C₂³×C₆₁	1	12	yes	—
963	#120	C₂³×C₆₁	1	12	yes	—
964	#120	C₂³×C₆₁	1	6	yes	—
965	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
966	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
967	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
968	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
969	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
970	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
971	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
972	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
973	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
974	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
975	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
976	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
977	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
978	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
979	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
980	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
981	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
982	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
983	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
984	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
985	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
986	C₄×Q₈	C₂³×C₆₁	1	12	yes	—
987	C₄×D₄	C₂³×C₆₁	1	3	yes	—
988	C₄×D₄	C₂³×C₆₁	1	6	yes	—
989	C₄×D₄	C₂³×C₆₁	1	3	yes	—
990	C₄×D₄	C₂³×C₆₁	1	6	yes	—
991	C₄×D₄	C₂³×C₆₁	1	6	yes	—
992	C₄×D₄	C₂³×C₆₁	1	6	yes	—
993	C₄×D₄	C₂³×C₆₁	1	6	yes	—
994	C₄×D₄	C₂³×C₆₁	1	6	yes	—
995	C₄×D₄	C₂³×C₆₁	1	12	yes	—
996	C₄×D₄	C₂³×C₆₁	1	3	yes	—
997	C₄×D₄	C₂³×C₆₁	1	3	yes	—
998	C₄×D₄	C₂³×C₆₁	1	3	yes	—
999	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1000	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
1001	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1002	C₄×D₄	C₂³×C₆₁	1	3	yes	—
1003	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1004	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1005	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1006	C₄×D₄	C₂³×C₆₁	1	3	yes	—
1007	C₄×D₄	C₂³×C₆₁	1	3	yes	—
1008	C₄×D₄	C₂³×C₆₁	1	3	yes	—
1009	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1010	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1011	C₄×D₄	C₂³×C₆₁	1	3	yes	—
1012	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1013	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1014	C₄×D₄	C₂³×C₆₁	1	3	yes	—
1015	C₄×D₄	C₂³×C₆₁	1	12	yes	—
1016	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1017	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1018	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1019	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1020	C₄×D₄	C₂³×C₆₁	1	12	yes	—
1021	C₄×D₄	C₂³×C₆₁	1	12	yes	—
1022	C₄×D₄	C₂³×C₆₁	1	12	yes	—
1023	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1024	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1025	#117	C₂³×C₆₁	1	3	yes	—
1026	#117	C₂³×C₆₁	1	1	yes	characteristic
1027	#117	C₂³×C₆₁	1	3	yes	—
1028	#117	C₂³×C₆₁	1	3	yes	—
1029	#117	C₂³×C₆₁	1	3	yes	—
1030	#117	C₂³×C₆₁	1	3	yes	—
1031	#117	C₂³×C₆₁	1	3	yes	—
1032	#117	C₂³×C₆₁	1	3	yes	—
1033	#117	C₂³×C₆₁	1	3	yes	—
1034	#117	C₂³×C₆₁	1	3	yes	—
1035	#117	C₂³×C₆₁	1	3	yes	—
1036	#117	C₂³×C₆₁	1	3	yes	—
1037	#117	C₂³×C₆₁	1	6	yes	—
1038	#117	C₂³×C₆₁	1	3	yes	—
1039	#117	C₂³×C₆₁	1	6	yes	—
1040	#117	C₂³×C₆₁	1	6	yes	—
1041	#117	C₂³×C₆₁	1	3	yes	—
1042	#117	C₂³×C₆₁	1	6	yes	—
1043	#117	C₂³×C₆₁	1	12	yes	—
1044	#117	C₂³×C₆₁	1	6	yes	—
1045	#117	C₂³×C₆₁	1	12	yes	—
1046	#117	C₂³×C₆₁	1	12	yes	—
1047	#117	C₂³×C₆₁	1	12	yes	—
1048	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
1049	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
1050	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
1051	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
1052	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
1053	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
1054	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
1055	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
1056	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
1057	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
1058	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
1059	C₂×C₂²⋊C₄	C₂³×C₆₁	1	3	yes	—
1060	C₂×C₂²⋊C₄	C₂³×C₆₁	1	3	yes	—
1061	C₂×C₂²⋊C₄	C₂³×C₆₁	1	6	yes	—
1062	C₂×C₂²⋊C₄	C₂³×C₆₁	1	6	yes	—
1063	C₂×C₂²⋊C₄	C₂³×C₆₁	1	12	yes	—
1064	C₂×C₂²⋊C₄	C₂³×C₆₁	1	6	yes	—
1065	C₂×C₂²⋊C₄	C₂³×C₆₁	1	6	yes	—
1066	C₂×C₂²⋊C₄	C₂³×C₆₁	1	6	yes	—
1067	C₂×C₂²⋊C₄	C₂³×C₆₁	1	6	yes	—
1068	C₂×C₄²	C₂³×C₆₁	1	3	yes	—
1069	C₂×C₄²	C₂³×C₆₁	1	3	yes	—
1070	C₂×C₄²	C₂³×C₆₁	1	6	yes	—
1071	C₂×C₄²	C₂³×C₆₁	1	6	yes	—
1072	C₂×C₄²	C₂³×C₆₁	1	6	yes	—
1073	C₂×C₄²	C₂³×C₆₁	1	6	yes	—
1074	C₂⁴	C₂⁴×C₆₁	1	3	yes	—
1075	C₂⁴	C₂⁴×C₆₁	1	6	yes	—
1076	#41	—	2	4	no	—
1077	#41	—	2	8	no	—
1078	#41	—	2	12	no	—
1079	#41	—	2	24	no	—
1080	#41	—	2	12	no	—
1081	#41	—	2	12	no	—
1082	#41	—	2	12	no	—
1083	#41	—	8	12	no	—
1084	#41	#41×C₆₁	1	8	yes	complemented
1085	C₂×Q₈	—	2	4	no	—
1086	C₂×Q₈	—	2	8	no	—
1087	C₂×Q₈	—	2	12	no	—
1088	C₂×Q₈	—	8	6	no	—
1089	C₂×Q₈	C₂⁴×C₆₁	1	3	yes	—
1090	C₂×Q₈	C₂⁴×C₆₁	1	6	yes	—
1091	C₂×Q₈	C₂⁴×C₆₁	1	3	yes	—
1092	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
1093	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
1094	C₂×Q₈	C₂⁴×C₆₁	1	6	yes	—
1095	C₂×Q₈	C₂⁴×C₆₁	1	12	yes	—
1096	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
1097	C₂×D₄	—	2	12	no	—
1098	C₂×D₄	—	2	24	no	—
1099	C₂×D₄	—	2	12	no	—
1100	C₂×D₄	—	8	6	no	—
1101	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
1102	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
1103	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
1104	C₂×D₄	C₂⁴×C₆₁	1	3	yes	—
1105	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
1106	C₂×D₄	C₂⁴×C₆₁	1	3	yes	—
1107	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
1108	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
1109	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
1110	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
1111	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
1112	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
1113	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
1114	C₂×D₄	C₂⁴×C₆₁	1	12	yes	—
1115	C₂×D₄	C₂⁴×C₆₁	1	3	yes	—
1116	C₂²×C₄	—	2	12	no	—
1117	C₂²×C₄	—	8	6	no	—
1118	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
1119	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
1120	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
1121	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
1122	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
1123	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
1124	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
1125	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1126	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
1127	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
1128	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
1129	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
1130	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
1131	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
1132	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
1133	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
1134	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
1135	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
1136	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
1137	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
1138	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
1139	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
1140	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1141	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1142	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1143	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1144	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1145	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1146	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1147	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1148	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1149	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1150	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1151	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
1152	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1153	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1154	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1155	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1156	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1157	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1158	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1159	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1160	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1161	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
1162	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
1163	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1164	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1165	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1166	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1167	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1168	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1169	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1170	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1171	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1172	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1173	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1174	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1175	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1176	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1177	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1178	C₂²⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1179	C₂²⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1180	C₂²⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1181	C₂²⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1182	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1183	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1184	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1185	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
1186	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1187	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1188	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1189	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1190	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1191	C₂²⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1192	C₂²⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1193	C₂²⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1194	C₂²⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1195	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
1196	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
1197	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
1198	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
1199	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1200	C₂²⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1201	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1202	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1203	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1204	C₂²⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1205	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1206	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1207	C₂²⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1208	C₂²⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1209	C₂²⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1210	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1211	C₄²	C₂⁴×C₆₁	1	3	yes	—
1212	C₄²	C₂⁴×C₆₁	1	3	yes	—
1213	C₄²	C₂⁴×C₆₁	1	3	yes	—
1214	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1215	C₄²	C₂⁴×C₆₁	1	3	yes	—
1216	C₄²	C₂⁴×C₆₁	1	2	yes	—
1217	C₄²	C₂⁴×C₆₁	1	6	yes	—
1218	C₄²	C₂⁴×C₆₁	1	6	yes	—
1219	C₄²	C₂⁴×C₆₁	1	6	yes	—
1220	C₄²	C₂⁴×C₆₁	1	6	yes	—
1221	C₄²	C₂⁴×C₆₁	1	12	yes	—
1222	C₄²	C₂⁴×C₆₁	1	6	yes	—
1223	C₄²	C₂⁴×C₆₁	1	6	yes	—
1224	C₄²	C₂⁴×C₆₁	1	3	yes	—
1225	C₄²	C₂⁴×C₆₁	1	3	yes	—
1226	C₄²	C₂⁴×C₆₁	1	6	yes	—
1227	C₂³	—	2	6	no	—
1228	C₂³	—	2	12	no	—
1229	C₂³	—	4	6	no	—
1230	C₂³	—	4	3	no	—
1231	C₂³	—	4	3	no	—
1232	C₂³	—	4	6	no	—
1233	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
1234	C₂³	C₂⁵×C₆₁	1	6	yes	—
1235	C₂³	C₂⁵×C₆₁	1	3	yes	—
1236	C₂³	C₂⁵×C₆₁	1	2	yes	—
1237	C₂³	C₂⁵×C₆₁	1	3	yes	—
1238	Q₈	—	2	12	no	—
1239	Q₈	—	2	6	no	—
1240	Q₈	—	2	6	no	—
1241	Q₈	—	2	2	no	—
1242	Q₈	—	4	6	no	—
1243	Q₈	—	4	12	no	—
1244	Q₈	—	4	2	no	—
1245	Q₈	C₂×#41×C₆₁	1	4	yes	—
1246	D₄	—	2	12	no	—
1247	D₄	—	2	12	no	—
1248	D₄	—	2	12	no	—
1249	D₄	—	2	12	no	—
1250	D₄	—	2	6	no	—
1251	D₄	—	2	6	no	—
1252	D₄	—	2	2	no	—
1253	D₄	—	4	6	no	—
1254	D₄	—	4	12	no	—
1255	D₄	—	4	6	no	—
1256	D₄	—	4	2	no	—
1257	D₄	—	4	6	no	—
1258	D₄	—	4	6	no	—
1259	D₄	—	4	6	no	—
1260	D₄	C₂×#41×C₆₁	1	12	yes	—
1261	C₂×C₄	—	2	6	no	—
1262	C₂×C₄	—	2	12	no	—
1263	C₂×C₄	—	2	2	no	—
1264	C₂×C₄	—	2	6	no	—
1265	C₂×C₄	—	2	6	no	—
1266	C₂×C₄	—	2	6	no	—
1267	C₂×C₄	—	2	12	no	—
1268	C₂×C₄	—	2	12	no	—
1269	C₂×C₄	—	4	3	no	—
1270	C₂×C₄	—	4	6	no	—
1271	C₂×C₄	—	4	6	no	—
1272	C₂×C₄	—	4	12	no	—
1273	C₂×C₄	—	4	3	no	—
1274	C₂×C₄	—	4	6	no	—
1275	C₂×C₄	—	4	6	no	—
1276	C₂×C₄	—	4	2	no	—
1277	C₂×C₄	—	4	3	no	—
1278	C₂×C₄	—	4	6	no	—
1279	C₂×C₄	—	4	3	no	—
1280	C₂×C₄	—	4	6	no	—
1281	C₂×C₄	—	4	6	no	—
1282	C₂×C₄	C₂×#41×C₆₁	1	12	yes	—
1283	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1284	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
1285	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
1286	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1287	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
1288	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1289	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1290	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
1291	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
1292	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
1293	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
1294	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
1295	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
1296	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
1297	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
1298	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1299	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
1300	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1301	C₂²	—	2	3	no	—
1302	C₂²	—	2	3	no	—
1303	C₂²	—	2	1	no	—
1304	C₂²	—	2	2	no	—
1305	C₂²	—	2	3	no	—
1306	C₂²	—	2	6	no	—
1307	C₂²	—	2	2	no	—
1308	C₂²	—	2	6	no	—
1309	C₂²	—	2	3	no	—
1310	C₂²	—	2	1	no	—
1311	C₂²	—	2	3	no	—
1312	C₂²	—	2	2	no	—
1313	C₂²	—	2	6	no	—
1314	C₂²	—	2	1	no	—
1315	C₂²	—	8	6	no	—
1316	C₂²	—	8	12	no	—
1317	C₂²	C₂²×#41×C₆₁	1	6	yes	—
1318	C₂²	C₂⁶×C₆₁	1	1	yes	characteristic
1319	C₄	—	2	1	no	—
1320	C₄	—	2	2	no	—
1321	C₄	—	2	3	no	—
1322	C₄	—	2	6	no	—
1323	C₄	—	2	1	no	—
1324	C₄	—	2	3	no	—
1325	C₄	—	2	6	no	—
1326	C₄	—	2	6	no	—
1327	C₄	—	2	3	no	—
1328	C₄	—	2	1	no	—
1329	C₄	—	2	1	no	—
1330	C₄	—	2	3	no	—
1331	C₄	—	2	3	no	—
1332	C₄	—	2	2	no	—
1333	C₄	—	2	1	no	—
1334	C₄	—	2	2	no	—
1335	C₄	C₂²×#41×C₆₁	1	6	yes	—
1336	C₄	C₂²×#41×C₆₁	1	2	yes	—
1337	C₂	—	2	6	no	—
1338	C₂	—	4	1	no	—
1339	C₂	—	4	6	no	—
1340	C₂	—	4	3	no	—
1341	C₂	—	4	2	no	—
1342	C₂	C₂³×#41×C₆₁	1	1	yes	characteristic
1343	C₂	C₆₁×H(7,𝔽₂)	1	1	yes	characteristic
1344	C₂	C₆₁×2₋¹⁺⁶	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3524	C₂	semidirect
2. C₆₁×#3522	C₂	semidirect
3. C₆₁×#3521	C₂	semidirect
4. C₆₁×#3520	C₂	semidirect
5. C₆₁×#3518	C₂	semidirect
6. C₆₁×#3516	C₂	semidirect
7. C₆₁×#3514	C₂	semidirect
8. C₆₁×#3513	C₂	semidirect
9. C₆₁×#3511	C₂	semidirect
10. C₆₁×#3510	C₂	semidirect
11. C₆₁×#3503	C₂	semidirect
12. C₆₁×#3500	C₂	semidirect
13. C₆₁×#3495	C₂	semidirect
14. C₆₁×#3494	C₂	semidirect
15. C₆₁×#3489	C₂	semidirect
16. C₆₁×#3488	C₂	semidirect
17. C₆₁×#3461	C₂	semidirect
18. C₆₁×#3460	C₂	semidirect
19. C₆₁×#3455	C₂	semidirect
20. C₂×C₆₁×#542	C₂	semidirect
21. C₄×2₋¹⁺⁴×C₆₁	C₂	semidirect
22. C₄×H(5,𝔽₂)×C₆₁	C₂	semidirect
23. C₆₁×#3428	C₂	semidirect
27. C₆₁×#559	C₂²	semidirect
28. C₆₁×#559	C₂²	semidirect
29. Q₈²×C₆₁	C₂²	semidirect
30. C₆₁×#557	C₂²	semidirect
31. C₆₁×#556	C₂²	semidirect
32. C₆₁×#556	C₂²	semidirect
33. C₆₁×#556	C₂²	semidirect
34. C₆₁×#556	C₂²	semidirect
35. C₆₁×#555	C₂²	semidirect
36. C₆₁×#555	C₂²	semidirect
37. C₆₁×#554	C₂²	semidirect
38. C₆₁×#554	C₂²	semidirect
39. C₆₁×#554	C₂²	semidirect
40. C₆₁×#553	C₂²	semidirect
41. C₆₁×#553	C₂²	semidirect
42. C₆₁×#553	C₂²	semidirect
43. C₆₁×#552	C₂²	semidirect
44. C₆₁×#552	C₂²	semidirect
45. C₆₁×#552	C₂²	semidirect
46. C₆₁×#551	C₂²	semidirect
47. C₆₁×#551	C₂²	semidirect
48. C₆₁×#551	C₂²	semidirect
49. C₆₁×#551	C₂²	semidirect
51. D₄×Q₈×C₆₁	C₂²	semidirect
52. D₄×Q₈×C₆₁	C₂²	semidirect
54. C₆₁×#548	C₂²	semidirect
55. C₆₁×#548	C₂²	semidirect
56. C₆₁×#548	C₂²	semidirect
57. C₆₁×#548	C₂²	semidirect
58. C₆₁×#547	C₂²	semidirect
59. C₆₁×#547	C₂²	semidirect
60. C₆₁×#547	C₂²	semidirect
62. C₆₁×#546	C₂²	semidirect
63. C₆₁×#546	C₂²	semidirect
64. C₆₁×#546	C₂²	semidirect
65. C₆₁×#546	C₂²	semidirect
67. C₆₁×#544	C₂²	semidirect
68. C₆₁×#544	C₂²	semidirect
69. C₆₁×#542	C₂²	semidirect
70. C₆₁×#542	C₂²	semidirect
71. C₆₁×#542	C₂²	semidirect
72. C₆₁×#542	C₂²	semidirect
73. C₆₁×#542	C₂²	semidirect
74. C₆₁×#542	C₂²	semidirect
75. C₆₁×#542	C₂²	semidirect
76. C₆₁×#542	C₂²	semidirect
77. C₆₁×#542	C₂²	semidirect
78. C₆₁×#542	C₂²	semidirect
79. C₆₁×#542	C₂²	semidirect
80. C₆₁×#542	C₂²	semidirect
81. C₆₁×#542	C₂²	semidirect
82. C₆₁×#541	C₂²	semidirect
83. C₆₁×#541	C₂²	semidirect
84. C₆₁×#541	C₂²	semidirect
85. C₆₁×#540	C₂²	semidirect
86. C₆₁×#540	C₂²	semidirect
87. C₆₁×#540	C₂²	semidirect
88. C₆₁×#539	C₂²	semidirect
89. C₆₁×#539	C₂²	semidirect
90. C₆₁×#539	C₂²	semidirect
91. C₆₁×#538	C₂²	semidirect
92. C₆₁×#538	C₂²	semidirect
93. C₆₁×#538	C₂²	semidirect
95. C₆₁×#537	C₂²	semidirect
96. C₆₁×#536	C₂²	semidirect
97. C₆₁×#536	C₂²	semidirect
99. C₆₁×#535	C₂²	semidirect
100. C₆₁×#533	C₂²	semidirect
101. C₆₁×#533	C₂²	semidirect
102. C₆₁×#533	C₂²	semidirect
103. C₆₁×#532	C₂²	semidirect
104. C₆₁×#532	C₂²	semidirect
105. C₆₁×#532	C₂²	semidirect
106. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
107. C₆₁×#529	C₂²	semidirect
108. C₆₁×#529	C₂²	semidirect
109. C₆₁×#529	C₂²	semidirect
110. C₆₁×#529	C₂²	semidirect
111. C₆₁×#529	C₂²	semidirect
112. C₆₁×#529	C₂²	semidirect
113. C₆₁×#529	C₂²	semidirect
114. C₆₁×#529	C₂²	semidirect
115. C₆₁×#529	C₂²	semidirect
116. C₂×#126×C₆₁	C₂²	semidirect
117. C₂×#124×C₆₁	C₂²	semidirect
118. C₂×#124×C₆₁	C₂²	semidirect
120. C₆₁×#525	C₂²	semidirect
121. C₆₁×#525	C₂²	semidirect
122. C₂×#123×C₆₁	C₂²	semidirect
123. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
124. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
128. C₆₁×#520	C₂²	semidirect
129. C₆₁×#520	C₂²	semidirect
130. C₆₁×#520	C₂²	semidirect
131. C₆₁×#520	C₂²	semidirect
132. C₆₁×#520	C₂²	semidirect
133. C₆₁×#520	C₂²	semidirect
134. C₆₁×#520	C₂²	semidirect
135. C₆₁×#520	C₂²	semidirect
136. C₆₁×#519	C₂²	semidirect
137. C₆₁×#519	C₂²	semidirect
138. C₆₁×#519	C₂²	semidirect
139. C₆₁×#519	C₂²	semidirect
140. C₆₁×#518	C₂²	semidirect
141. C₆₁×#518	C₂²	semidirect
142. C₆₁×#518	C₂²	semidirect
143. C₆₁×#518	C₂²	semidirect
146. C₄×#41×C₆₁	C₂²	semidirect
147. C₄×#41×C₆₁	C₂²	semidirect
148. C₄×#41×C₆₁	C₂²	semidirect
149. C₄×#41×C₆₁	C₂²	semidirect
150. C₄×#41×C₆₁	C₂²	semidirect
151. C₄×#41×C₆₁	C₂²	semidirect
152. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
153. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
154. C₂×C₄×D₄×C₆₁	C₂²	semidirect
155. C₂×C₄×D₄×C₆₁	C₂²	semidirect
156. C₂×#117×C₆₁	C₂²	semidirect
157. C₂×#117×C₆₁	C₂²	semidirect
411. #41×C₆₁	#41	semidirect
628. #62857	C₆₁	direct (N × H)
665. #3524	C₂×C₆₁	semidirect
666. #3522	C₂×C₆₁	semidirect
667. #3521	C₂×C₆₁	semidirect
668. #3520	C₂×C₆₁	semidirect
669. #3518	C₂×C₆₁	semidirect
670. #3516	C₂×C₆₁	semidirect
671. #3514	C₂×C₆₁	semidirect
672. #3513	C₂×C₆₁	semidirect
673. #3511	C₂×C₆₁	semidirect
674. #3510	C₂×C₆₁	semidirect
675. #3503	C₂×C₆₁	semidirect
676. #3500	C₂×C₆₁	semidirect
677. #3495	C₂×C₆₁	semidirect
678. #3494	C₂×C₆₁	semidirect
679. #3489	C₂×C₆₁	semidirect
680. #3488	C₂×C₆₁	semidirect
681. #3461	C₂×C₆₁	semidirect
682. #3460	C₂×C₆₁	semidirect
683. #3455	C₂×C₆₁	semidirect
684. C₂×#542	C₂×C₆₁	semidirect
685. C₄×2₋¹⁺⁴	C₂×C₆₁	semidirect
686. C₄×H(5,𝔽₂)	C₂×C₆₁	semidirect
687. #3428	C₂×C₆₁	semidirect
699. #559	C₂²×C₆₁	semidirect
700. #559	C₂²×C₆₁	semidirect
701. Q₈²	C₂²×C₆₁	semidirect
702. #557	C₂²×C₆₁	semidirect
703. #556	C₂²×C₆₁	semidirect
704. #556	C₂²×C₆₁	semidirect
705. #556	C₂²×C₆₁	semidirect
706. #556	C₂²×C₆₁	semidirect
707. #555	C₂²×C₆₁	semidirect
708. #555	C₂²×C₆₁	semidirect
709. #554	C₂²×C₆₁	semidirect
710. #554	C₂²×C₆₁	semidirect
711. #554	C₂²×C₆₁	semidirect
712. #553	C₂²×C₆₁	semidirect
713. #553	C₂²×C₆₁	semidirect
714. #553	C₂²×C₆₁	semidirect
715. #552	C₂²×C₆₁	semidirect
716. #552	C₂²×C₆₁	semidirect
717. #552	C₂²×C₆₁	semidirect
718. #551	C₂²×C₆₁	semidirect
719. #551	C₂²×C₆₁	semidirect
720. #551	C₂²×C₆₁	semidirect
721. #551	C₂²×C₆₁	semidirect
723. D₄×Q₈	C₂²×C₆₁	semidirect
724. D₄×Q₈	C₂²×C₆₁	semidirect
726. #548	C₂²×C₆₁	semidirect
727. #548	C₂²×C₆₁	semidirect
728. #548	C₂²×C₆₁	semidirect
729. #548	C₂²×C₆₁	semidirect
730. #547	C₂²×C₆₁	semidirect
731. #547	C₂²×C₆₁	semidirect
732. #547	C₂²×C₆₁	semidirect
734. #546	C₂²×C₆₁	semidirect
735. #546	C₂²×C₆₁	semidirect
736. #546	C₂²×C₆₁	semidirect
737. #546	C₂²×C₆₁	semidirect
739. #544	C₂²×C₆₁	semidirect
740. #544	C₂²×C₆₁	semidirect
741. #542	C₂²×C₆₁	semidirect
742. #542	C₂²×C₆₁	semidirect
743. #542	C₂²×C₆₁	semidirect
744. #542	C₂²×C₆₁	semidirect
745. #542	C₂²×C₆₁	semidirect
746. #542	C₂²×C₆₁	semidirect
747. #542	C₂²×C₆₁	semidirect
748. #542	C₂²×C₆₁	semidirect
749. #542	C₂²×C₆₁	semidirect
750. #542	C₂²×C₆₁	semidirect
751. #542	C₂²×C₆₁	semidirect
752. #542	C₂²×C₆₁	semidirect
753. #542	C₂²×C₆₁	semidirect
754. #541	C₂²×C₆₁	semidirect
755. #541	C₂²×C₆₁	semidirect
756. #541	C₂²×C₆₁	semidirect
757. #540	C₂²×C₆₁	semidirect
758. #540	C₂²×C₆₁	semidirect
759. #540	C₂²×C₆₁	semidirect
760. #539	C₂²×C₆₁	semidirect
761. #539	C₂²×C₆₁	semidirect
762. #539	C₂²×C₆₁	semidirect
763. #538	C₂²×C₆₁	semidirect
764. #538	C₂²×C₆₁	semidirect
765. #538	C₂²×C₆₁	semidirect
767. #537	C₂²×C₆₁	semidirect
768. #536	C₂²×C₆₁	semidirect
769. #536	C₂²×C₆₁	semidirect
771. #535	C₂²×C₆₁	semidirect
772. #533	C₂²×C₆₁	semidirect
773. #533	C₂²×C₆₁	semidirect
774. #533	C₂²×C₆₁	semidirect
775. #532	C₂²×C₆₁	semidirect
776. #532	C₂²×C₆₁	semidirect
777. #532	C₂²×C₆₁	semidirect
778. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
779. #529	C₂²×C₆₁	semidirect
780. #529	C₂²×C₆₁	semidirect
781. #529	C₂²×C₆₁	semidirect
782. #529	C₂²×C₆₁	semidirect
783. #529	C₂²×C₆₁	semidirect
784. #529	C₂²×C₆₁	semidirect
785. #529	C₂²×C₆₁	semidirect
786. #529	C₂²×C₆₁	semidirect
787. #529	C₂²×C₆₁	semidirect
788. C₂×#126	C₂²×C₆₁	semidirect
789. C₂×#124	C₂²×C₆₁	semidirect
790. C₂×#124	C₂²×C₆₁	semidirect
792. #525	C₂²×C₆₁	semidirect
793. #525	C₂²×C₆₁	semidirect
794. C₂×#123	C₂²×C₆₁	semidirect
795. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
796. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
800. #520	C₂²×C₆₁	semidirect
801. #520	C₂²×C₆₁	semidirect
802. #520	C₂²×C₆₁	semidirect
803. #520	C₂²×C₆₁	semidirect
804. #520	C₂²×C₆₁	semidirect
805. #520	C₂²×C₆₁	semidirect
806. #520	C₂²×C₆₁	semidirect
807. #520	C₂²×C₆₁	semidirect
808. #519	C₂²×C₆₁	semidirect
809. #519	C₂²×C₆₁	semidirect
810. #519	C₂²×C₆₁	semidirect
811. #519	C₂²×C₆₁	semidirect
812. #518	C₂²×C₆₁	semidirect
813. #518	C₂²×C₆₁	semidirect
814. #518	C₂²×C₆₁	semidirect
815. #518	C₂²×C₆₁	semidirect
818. C₄×#41	C₂²×C₆₁	semidirect
819. C₄×#41	C₂²×C₆₁	semidirect
820. C₄×#41	C₂²×C₆₁	semidirect
821. C₄×#41	C₂²×C₆₁	semidirect
822. C₄×#41	C₂²×C₆₁	semidirect
823. C₄×#41	C₂²×C₆₁	semidirect
824. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
825. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
826. C₂×C₄×D₄	C₂²×C₆₁	semidirect
827. C₂×C₄×D₄	C₂²×C₆₁	semidirect
828. C₂×#117	C₂²×C₆₁	semidirect
829. C₂×#117	C₂²×C₆₁	semidirect
830. C₆₁	#62857	direct (N × H)
1084. #41	#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×#3524	2
C₆₁×#3522	2
C₆₁×#3521	2
C₆₁×#3520	2
C₆₁×#3518	2
C₆₁×#3516	2
C₆₁×#3514	2
C₆₁×#3513	2
C₆₁×#3511	2
C₆₁×#3510	2
C₆₁×#3503	2
C₆₁×#3500	2
C₆₁×#3495	2
C₆₁×#3494	2
C₆₁×#3489	2
C₆₁×#3488	2
C₆₁×#3461	2
C₆₁×#3460	2
C₆₁×#3455	2
C₂×C₆₁×#542	2
C₄×2₋¹⁺⁴×C₆₁	2
C₄×H(5,𝔽₂)×C₆₁	2
C₆₁×#3428	2
#62857	61

Subgroups — C61×#62857 #29566290

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62857 #29566290