Subgroups — C₆₁×#62922 #29566355

Order 15616.

7072 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3562	C₂	1	6	yes	maximal, complemented
2	C₆₁×#3552	C₂	1	3	yes	maximal, complemented
3	C₆₁×#3551	C₂	1	6	yes	maximal, complemented
4	C₆₁×#3548	C₂	1	3	yes	maximal, complemented
5	C₆₁×#3546	C₂	1	3	yes	maximal, complemented
6	C₆₁×#3546	C₂	1	3	yes	maximal, complemented
7	C₆₁×#3541	C₂	1	6	yes	maximal, complemented
8	C₆₁×#3539	C₂	1	6	yes	maximal, complemented
9	C₆₁×#3523	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#3520	C₂	1	3	yes	maximal, complemented
11	C₆₁×#3517	C₂	1	3	yes	maximal, complemented
12	C₆₁×#3517	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3516	C₂	1	2	yes	maximal, complemented
14	C₆₁×#3511	C₂	1	3	yes	maximal, complemented
15	C₆₁×#3499	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#3497	C₂	1	2	yes	maximal, complemented
17	C₆₁×#3497	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₁×#3489	C₂	1	2	yes	maximal, complemented
19	C₆₁×#3487	C₂	1	2	yes	maximal, complemented
20	C₆₁×#3482	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₁×#3480	C₂	1	1	yes	maximal, characteristic, complemented
22	D₄×#41×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#3460	C₂	1	3	yes	maximal, complemented
24	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	2	yes	complemented
25	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	2	yes	complemented
26	C₂²×#41×C₆₁	C₂²	1	2	yes	—
27	C₆₁×#563	C₂²	1	12	yes	complemented
28	C₆₁×#562	C₂²	1	12	yes	complemented
29	C₆₁×#560	C₂²	1	12	yes	complemented
30	C₆₁×#560	C₂²	1	12	yes	complemented
31	C₆₁×#559	C₂²	1	3	yes	complemented
32	C₆₁×#557	C₂²	1	3	yes	complemented
33	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
34	C₆₁×#557	C₂²	1	1	yes	characteristic, complemented
35	C₆₁×#556	C₂²	1	3	yes	—
36	C₆₁×#556	C₂²	1	3	yes	complemented
37	C₆₁×#556	C₂²	1	6	yes	complemented
38	C₆₁×#556	C₂²	1	3	yes	complemented
39	C₆₁×#555	C₂²	1	6	yes	complemented
40	C₆₁×#554	C₂²	1	6	yes	complemented
41	C₆₁×#554	C₂²	1	6	yes	complemented
42	C₆₁×#554	C₂²	1	6	yes	complemented
43	C₆₁×#553	C₂²	1	6	yes	complemented
44	C₆₁×#553	C₂²	1	6	yes	complemented
45	C₆₁×#553	C₂²	1	3	yes	complemented
46	C₆₁×#553	C₂²	1	6	yes	complemented
47	C₆₁×#553	C₂²	1	6	yes	complemented
48	C₆₁×#553	C₂²	1	3	yes	complemented
49	C₆₁×#553	C₂²	1	6	yes	complemented
50	C₆₁×#553	C₂²	1	12	yes	complemented
51	C₆₁×#552	C₂²	1	6	yes	complemented
52	C₆₁×#552	C₂²	1	6	yes	complemented
53	C₆₁×#552	C₂²	1	6	yes	complemented
54	C₆₁×#551	C₂²	1	12	yes	complemented
55	C₆₁×#550	C₂²	1	1	yes	characteristic
56	C₆₁×#550	C₂²	1	1	yes	characteristic
57	C₆₁×#550	C₂²	1	6	yes	complemented
58	C₆₁×#550	C₂²	1	3	yes	complemented
59	C₆₁×#550	C₂²	1	6	yes	complemented
60	C₆₁×#550	C₂²	1	3	yes	complemented
61	C₆₁×#550	C₂²	1	6	yes	complemented
62	C₆₁×#550	C₂²	1	2	yes	complemented
63	C₆₁×#550	C₂²	1	6	yes	complemented
64	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
65	D₄×Q₈×C₆₁	C₂²	1	3	yes	complemented
66	D₄×Q₈×C₆₁	C₂²	1	6	yes	complemented
67	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
68	D₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
69	D₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
70	C₆₁×#548	C₂²	1	2	yes	—
71	C₆₁×#548	C₂²	1	1	yes	characteristic
72	C₆₁×#548	C₂²	1	2	yes	—
73	C₆₁×#548	C₂²	1	6	yes	complemented
74	C₆₁×#548	C₂²	1	6	yes	complemented
75	C₆₁×#548	C₂²	1	6	yes	complemented
76	C₆₁×#548	C₂²	1	6	yes	complemented
77	C₆₁×#548	C₂²	1	1	yes	characteristic, complemented
78	C₆₁×#548	C₂²	1	2	yes	complemented
79	C₆₁×#548	C₂²	1	6	yes	complemented
80	C₆₁×#547	C₂²	1	3	yes	—
81	C₆₁×#547	C₂²	1	3	yes	—
82	C₆₁×#547	C₂²	1	3	yes	complemented
83	C₆₁×#547	C₂²	1	3	yes	complemented
84	C₆₁×#547	C₂²	1	3	yes	complemented
85	C₆₁×#547	C₂²	1	6	yes	complemented
86	C₆₁×#547	C₂²	1	6	yes	complemented
87	C₆₁×#547	C₂²	1	6	yes	complemented
88	C₆₁×#546	C₂²	1	6	yes	—
89	C₆₁×#546	C₂²	1	6	yes	—
90	C₆₁×#546	C₂²	1	6	yes	complemented
91	C₆₁×#546	C₂²	1	6	yes	complemented
92	D₄²×C₆₁	C₂²	1	3	yes	—
93	C₆₁×#544	C₂²	1	3	yes	complemented
94	C₆₁×#542	C₂²	1	3	yes	—
95	C₆₁×#542	C₂²	1	6	yes	complemented
96	C₆₁×#542	C₂²	1	6	yes	complemented
97	C₆₁×#542	C₂²	1	3	yes	complemented
98	C₆₁×#542	C₂²	1	6	yes	complemented
99	C₆₁×#541	C₂²	1	6	yes	complemented
100	C₆₁×#541	C₂²	1	6	yes	complemented
101	C₆₁×#540	C₂²	1	1	yes	characteristic
102	C₆₁×#540	C₂²	1	12	yes	complemented
103	C₆₁×#540	C₂²	1	12	yes	complemented
104	C₆₁×#540	C₂²	1	6	yes	complemented
105	C₆₁×#540	C₂²	1	3	yes	complemented
106	C₆₁×#540	C₂²	1	6	yes	complemented
107	C₆₁×#539	C₂²	1	12	yes	complemented
108	C₆₁×#539	C₂²	1	12	yes	complemented
109	C₆₁×#538	C₂²	1	12	yes	complemented
110	C₆₁×#538	C₂²	1	12	yes	complemented
111	C₆₁×#538	C₂²	1	6	yes	complemented
112	C₆₁×#538	C₂²	1	6	yes	complemented
113	C₆₁×#537	C₂²	1	6	yes	complemented
114	C₆₁×#537	C₂²	1	6	yes	complemented
115	C₆₁×#537	C₂²	1	3	yes	complemented
116	C₆₁×#537	C₂²	1	6	yes	complemented
117	C₆₁×#537	C₂²	1	6	yes	complemented
118	C₆₁×#537	C₂²	1	6	yes	complemented
119	C₆₁×#536	C₂²	1	6	yes	complemented
120	C₆₁×#536	C₂²	1	6	yes	complemented
121	C₆₁×#535	C₂²	1	3	yes	—
122	C₆₁×#535	C₂²	1	3	yes	—
123	C₆₁×#535	C₂²	1	6	yes	complemented
124	C₆₁×#535	C₂²	1	6	yes	complemented
125	C₆₁×#533	C₂²	1	3	yes	complemented
126	C₆₁×#533	C₂²	1	3	yes	complemented
127	C₆₁×#532	C₂²	1	3	yes	—
128	C₆₁×#532	C₂²	1	3	yes	—
129	C₆₁×#532	C₂²	1	3	yes	complemented
130	C₆₁×#532	C₂²	1	3	yes	complemented
131	C₆₁×#532	C₂²	1	3	yes	complemented
132	C₆₁×#532	C₂²	1	3	yes	complemented
133	C₆₁×#532	C₂²	1	6	yes	complemented
134	C₆₁×#532	C₂²	1	6	yes	complemented
135	C₂×C₄⋊Q₈×C₆₁	C₂²	1	3	yes	complemented
136	C₆₁×#529	C₂²	1	3	yes	—
137	C₆₁×#529	C₂²	1	3	yes	complemented
138	C₆₁×#529	C₂²	1	6	yes	complemented
139	C₆₁×#529	C₂²	1	6	yes	complemented
140	C₆₁×#529	C₂²	1	3	yes	complemented
141	C₆₁×#529	C₂²	1	6	yes	complemented
142	C₆₁×#529	C₂²	1	3	yes	complemented
143	C₆₁×#525	C₂²	1	6	yes	—
144	C₆₁×#525	C₂²	1	6	yes	complemented
145	C₆₁×#525	C₂²	1	6	yes	complemented
146	C₆₁×#525	C₂²	1	6	yes	complemented
147	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	6	yes	complemented
148	C₆₁×#520	C₂²	1	2	yes	complemented
149	C₆₁×#520	C₂²	1	6	yes	complemented
150	C₆₁×#519	C₂²	1	2	yes	complemented
151	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
152	C₄×#41×C₆₁	C₂²	1	3	yes	complemented
153	C₄×#41×C₆₁	C₂²	1	3	yes	complemented
154	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic, complemented
155	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
156	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
157	C₂×C₄×D₄×C₆₁	C₂²	1	3	yes	—
158	2₋¹⁺⁴×C₆₁	—	4	8	no	—
159	2₋¹⁺⁴×C₆₁	—	4	8	no	—
160	C₂×#41×C₆₁	—	4	8	no	—
161	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
162	C₂×#41×C₆₁	C₂³	1	2	yes	—
163	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
164	C₂×#41×C₆₁	C₂³	1	6	yes	—
165	C₂×#41×C₆₁	C₂³	1	6	yes	—
166	C₂×#41×C₆₁	C₂³	1	3	yes	—
167	C₂×#41×C₆₁	C₂³	1	6	yes	—
168	C₂×#41×C₆₁	C₂³	1	6	yes	—
169	C₂×#41×C₆₁	C₂³	1	6	yes	—
170	C₂×#41×C₆₁	C₂³	1	6	yes	—
171	C₂×#41×C₆₁	C₂³	1	6	yes	—
172	C₂×#41×C₆₁	C₂³	1	3	yes	—
173	C₂×#41×C₆₁	C₂³	1	6	yes	—
174	C₂×#41×C₆₁	C₂³	1	6	yes	—
175	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
176	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
177	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
178	C₂²×Q₈×C₆₁	C₂³	1	6	yes	—
179	C₂²×Q₈×C₆₁	C₂³	1	6	yes	—
180	C₂²×D₄×C₆₁	C₂³	1	3	yes	—
181	C₂²×D₄×C₆₁	C₂³	1	6	yes	—
182	C₂³×C₄×C₆₁	C₂³	1	6	yes	—
183	C₄⋊Q₈×C₆₁	C₂³	1	3	yes	—
184	C₄⋊Q₈×C₆₁	C₂³	1	3	yes	—
185	C₄⋊Q₈×C₆₁	C₂³	1	3	yes	—
186	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
187	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
188	C₄⋊Q₈×C₆₁	C₂³	1	3	yes	—
189	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
190	C₄⋊Q₈×C₆₁	C₂³	1	3	yes	—
191	C₄⋊Q₈×C₆₁	C₂³	1	3	yes	—
192	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
193	#127×C₆₁	C₂³	1	1	yes	characteristic
194	#127×C₆₁	C₂³	1	3	yes	—
195	#127×C₆₁	C₂³	1	3	yes	—
196	#127×C₆₁	C₂³	1	6	yes	—
197	#127×C₆₁	C₂³	1	3	yes	—
198	#127×C₆₁	C₂³	1	6	yes	—
199	#127×C₆₁	C₂³	1	12	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	#126×C₆₁	C₂³	1	6	yes	—
205	#126×C₆₁	C₂³	1	6	yes	—
206	#126×C₆₁	C₂³	1	6	yes	—
207	#126×C₆₁	C₂³	1	6	yes	—
208	#126×C₆₁	C₂³	1	12	yes	—
209	#126×C₆₁	C₂³	1	12	yes	—
210	#125×C₆₁	C₂³	1	6	yes	—
211	#125×C₆₁	C₂³	1	6	yes	—
212	#125×C₆₁	C₂³	1	6	yes	—
213	#125×C₆₁	C₂³	1	12	yes	—
214	#125×C₆₁	C₂³	1	12	yes	—
215	#125×C₆₁	C₂³	1	1	yes	characteristic
216	#125×C₆₁	C₂³	1	6	yes	—
217	#125×C₆₁	C₂³	1	3	yes	—
218	#125×C₆₁	C₂³	1	3	yes	—
219	#125×C₆₁	C₂³	1	3	yes	—
220	#124×C₆₁	C₂³	1	6	yes	—
221	#124×C₆₁	C₂³	1	6	yes	—
222	#124×C₆₁	C₂³	1	3	yes	—
223	#124×C₆₁	C₂³	1	3	yes	—
224	#124×C₆₁	C₂³	1	6	yes	—
225	#124×C₆₁	C₂³	1	6	yes	—
226	#124×C₆₁	C₂³	1	6	yes	—
227	#124×C₆₁	C₂³	1	6	yes	—
228	#124×C₆₁	C₂³	1	6	yes	—
229	#124×C₆₁	C₂³	1	6	yes	—
230	#124×C₆₁	C₂³	1	3	yes	—
231	#124×C₆₁	C₂³	1	6	yes	—
232	#124×C₆₁	C₂³	1	12	yes	—
233	#124×C₆₁	C₂³	1	3	yes	—
234	#123×C₆₁	C₂³	1	12	yes	—
235	#123×C₆₁	C₂³	1	12	yes	—
236	#123×C₆₁	C₂³	1	12	yes	—
237	#123×C₆₁	C₂³	1	12	yes	—
238	#123×C₆₁	C₂³	1	2	yes	—
239	#123×C₆₁	C₂³	1	6	yes	—
240	#123×C₆₁	C₂³	1	12	yes	—
241	#123×C₆₁	C₂³	1	6	yes	—
242	#123×C₆₁	C₂³	1	12	yes	—
243	#123×C₆₁	C₂³	1	6	yes	—
244	#123×C₆₁	C₂³	1	6	yes	—
245	#123×C₆₁	C₂³	1	6	yes	—
246	#123×C₆₁	C₂³	1	12	yes	—
247	#123×C₆₁	C₂³	1	12	yes	—
248	#123×C₆₁	C₂³	1	2	yes	—
249	#123×C₆₁	C₂³	1	6	yes	—
250	#123×C₆₁	C₂³	1	6	yes	—
251	#123×C₆₁	C₂³	1	6	yes	—
252	C₂²⋊Q₈×C₆₁	C₂³	1	3	yes	—
253	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
254	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
255	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
256	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
257	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
258	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
259	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
260	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
261	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
262	C₂²⋊Q₈×C₆₁	C₂³	1	3	yes	—
263	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
264	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
265	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
266	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
267	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
268	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
269	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
270	C₂²⋊Q₈×C₆₁	C₂³	1	3	yes	—
271	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
272	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
273	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
274	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
275	C₂²⋊Q₈×C₆₁	C₂³	1	3	yes	—
276	#121×C₆₁	C₂³	1	3	yes	—
277	#121×C₆₁	C₂³	1	3	yes	—
278	#121×C₆₁	C₂³	1	6	yes	—
279	#121×C₆₁	C₂³	1	6	yes	—
280	#121×C₆₁	C₂³	1	6	yes	—
281	#121×C₆₁	C₂³	1	3	yes	—
282	#121×C₆₁	C₂³	1	1	yes	characteristic
283	#121×C₆₁	C₂³	1	2	yes	—
284	#121×C₆₁	C₂³	1	6	yes	—
285	#121×C₆₁	C₂³	1	6	yes	—
286	#121×C₆₁	C₂³	1	6	yes	—
287	#121×C₆₁	C₂³	1	6	yes	—
288	#121×C₆₁	C₂³	1	6	yes	—
289	#121×C₆₁	C₂³	1	3	yes	—
290	#121×C₆₁	C₂³	1	3	yes	—
291	#121×C₆₁	C₂³	1	12	yes	—
292	#121×C₆₁	C₂³	1	6	yes	—
293	#121×C₆₁	C₂³	1	6	yes	—
294	#121×C₆₁	C₂³	1	6	yes	—
295	#121×C₆₁	C₂³	1	1	yes	characteristic
296	#121×C₆₁	C₂³	1	3	yes	—
297	#121×C₆₁	C₂³	1	6	yes	—
298	#121×C₆₁	C₂³	1	3	yes	—
299	#121×C₆₁	C₂³	1	12	yes	—
300	#121×C₆₁	C₂³	1	6	yes	—
301	#121×C₆₁	C₂³	1	6	yes	—
302	#121×C₆₁	C₂³	1	12	yes	—
303	#121×C₆₁	C₂³	1	6	yes	—
304	#121×C₆₁	C₂³	1	12	yes	—
305	#121×C₆₁	C₂³	1	12	yes	—
306	#121×C₆₁	C₂³	1	12	yes	—
307	#121×C₆₁	C₂³	1	12	yes	—
308	#121×C₆₁	C₂³	1	12	yes	—
309	#121×C₆₁	C₂³	1	6	yes	—
310	#121×C₆₁	C₂³	1	6	yes	—
311	#121×C₆₁	C₂³	1	6	yes	—
312	#121×C₆₁	C₂³	1	6	yes	—
313	#121×C₆₁	C₂³	1	12	yes	—
314	#121×C₆₁	C₂³	1	2	yes	—
315	#121×C₆₁	C₂³	1	6	yes	—
316	#121×C₆₁	C₂³	1	3	yes	—
317	#120×C₆₁	C₂³	1	6	yes	—
318	#120×C₆₁	C₂³	1	6	yes	—
319	#120×C₆₁	C₂³	1	6	yes	—
320	#120×C₆₁	C₂³	1	6	yes	—
321	#120×C₆₁	C₂³	1	12	yes	—
322	#120×C₆₁	C₂³	1	12	yes	—
323	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
324	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
325	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
326	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
327	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
328	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
329	C₄×Q₈×C₆₁	C₂³	1	6	yes	—
330	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
331	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
332	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
333	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
334	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
335	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
336	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
337	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
338	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
339	C₄×D₄×C₆₁	C₂³	1	3	yes	—
340	C₄×D₄×C₆₁	C₂³	1	3	yes	—
341	C₄×D₄×C₆₁	C₂³	1	3	yes	—
342	C₄×D₄×C₆₁	C₂³	1	6	yes	—
343	C₄×D₄×C₆₁	C₂³	1	6	yes	—
344	C₄×D₄×C₆₁	C₂³	1	3	yes	—
345	C₄×D₄×C₆₁	C₂³	1	6	yes	—
346	C₄×D₄×C₆₁	C₂³	1	6	yes	—
347	C₄×D₄×C₆₁	C₂³	1	12	yes	—
348	C₄×D₄×C₆₁	C₂³	1	6	yes	—
349	C₄×D₄×C₆₁	C₂³	1	12	yes	—
350	C₄×D₄×C₆₁	C₂³	1	6	yes	—
351	C₄×D₄×C₆₁	C₂³	1	3	yes	—
352	C₄×D₄×C₆₁	C₂³	1	6	yes	—
353	C₄×D₄×C₆₁	C₂³	1	6	yes	—
354	C₄×D₄×C₆₁	C₂³	1	6	yes	—
355	C₄×D₄×C₆₁	C₂³	1	3	yes	—
356	C₄×D₄×C₆₁	C₂³	1	3	yes	—
357	C₄×D₄×C₆₁	C₂³	1	6	yes	—
358	C₄×D₄×C₆₁	C₂³	1	6	yes	—
359	C₄×D₄×C₆₁	C₂³	1	6	yes	—
360	C₄×D₄×C₆₁	C₂³	1	3	yes	—
361	C₄×D₄×C₆₁	C₂³	1	3	yes	—
362	C₄×D₄×C₆₁	C₂³	1	12	yes	—
363	C₄×D₄×C₆₁	C₂³	1	6	yes	—
364	C₄×D₄×C₆₁	C₂³	1	12	yes	—
365	C₄×D₄×C₆₁	C₂³	1	12	yes	—
366	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
367	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
368	C₄×D₄×C₆₁	C₂³	1	3	yes	—
369	C₄×D₄×C₆₁	C₂³	1	3	yes	—
370	C₄×D₄×C₆₁	C₂³	1	6	yes	—
371	C₄×D₄×C₆₁	C₂³	1	3	yes	—
372	C₄×D₄×C₆₁	C₂³	1	3	yes	—
373	C₄×D₄×C₆₁	C₂³	1	6	yes	—
374	C₄×D₄×C₆₁	C₂³	1	3	yes	—
375	#117×C₆₁	C₂³	1	6	yes	—
376	#117×C₆₁	C₂³	1	6	yes	—
377	#117×C₆₁	C₂³	1	3	yes	—
378	#117×C₆₁	C₂³	1	3	yes	—
379	#117×C₆₁	C₂³	1	6	yes	—
380	#117×C₆₁	C₂³	1	6	yes	—
381	#117×C₆₁	C₂³	1	3	yes	—
382	#117×C₆₁	C₂³	1	6	yes	—
383	#117×C₆₁	C₂³	1	1	yes	characteristic
384	#117×C₆₁	C₂³	1	3	yes	—
385	#117×C₆₁	C₂³	1	6	yes	—
386	#117×C₆₁	C₂³	1	12	yes	—
387	#117×C₆₁	C₂³	1	3	yes	—
388	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
389	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
390	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
391	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
392	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
393	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
394	C₂×C₄⋊C₄×C₆₁	C₂³	1	12	yes	—
395	C₂×C₂²⋊C₄×C₆₁	C₂³	1	6	yes	—
396	C₂×C₂²⋊C₄×C₆₁	C₂³	1	12	yes	—
397	C₂×C₄²×C₆₁	C₂³	1	3	yes	—
398	C₂×C₄²×C₆₁	C₂³	1	3	yes	—
399	C₂×C₄²×C₆₁	C₂³	1	3	yes	—
400	C₂×C₄²×C₆₁	C₂³	1	6	yes	—
401	C₂⁴×C₆₁	C₂⁴	1	6	yes	—
402	#41×C₆₁	—	2	4	no	—
403	#41×C₆₁	—	2	8	no	—
404	#41×C₆₁	—	2	4	no	—
405	#41×C₆₁	—	4	6	no	—
406	#41×C₆₁	—	4	12	no	—
407	#41×C₆₁	—	4	12	no	—
408	#41×C₆₁	—	4	12	no	—
409	#41×C₆₁	—	4	12	no	—
410	#41×C₆₁	—	4	6	no	—
411	#41×C₆₁	—	4	12	no	—
412	#41×C₆₁	—	4	12	no	—
413	#41×C₆₁	—	4	12	no	—
414	#41×C₆₁	—	4	12	no	—
415	#41×C₆₁	—	4	12	no	—
416	C₂×Q₈×C₆₁	—	2	8	no	—
417	C₂×Q₈×C₆₁	—	2	4	no	—
418	C₂×Q₈×C₆₁	—	2	8	no	—
419	C₂×Q₈×C₆₁	—	4	12	no	—
420	C₂×Q₈×C₆₁	—	4	12	no	—
421	C₂×Q₈×C₆₁	C₂⁴	1	3	yes	—
422	C₂×Q₈×C₆₁	C₂⁴	1	6	yes	—
423	C₂×Q₈×C₆₁	C₂⁴	1	3	yes	—
424	C₂×Q₈×C₆₁	C₂⁴	1	6	yes	—
425	C₂×Q₈×C₆₁	C₂⁴	1	3	yes	—
426	C₂×Q₈×C₆₁	C₂⁴	1	6	yes	—
427	C₂×Q₈×C₆₁	C₂⁴	1	6	yes	—
428	C₂×Q₈×C₆₁	C₂⁴	1	1	yes	characteristic
429	C₂×D₄×C₆₁	—	4	6	no	—
430	C₂×D₄×C₆₁	—	4	12	no	—
431	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
432	C₂×D₄×C₆₁	C₂⁴	1	3	yes	—
433	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
434	C₂×D₄×C₆₁	C₂⁴	1	3	yes	—
435	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
436	C₂×D₄×C₆₁	C₂⁴	1	3	yes	—
437	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
438	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
439	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
440	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
441	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
442	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
443	C₂×D₄×C₆₁	C₂⁴	1	3	yes	—
444	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
445	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
446	C₂×D₄×C₆₁	C₂⁴	1	3	yes	—
447	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
448	C₂×D₄×C₆₁	C₂⁴	1	3	yes	—
449	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
450	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
451	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
452	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
453	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
454	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
455	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
456	C₂²×C₄×C₆₁	—	4	12	no	—
457	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
458	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
459	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
460	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
461	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
462	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
463	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
464	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
465	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
466	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
467	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
468	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
469	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
470	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
471	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
472	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
473	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
474	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
475	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
476	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
477	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
478	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
479	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
480	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
481	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
482	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
483	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
484	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
485	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
486	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
487	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
488	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
489	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
490	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
491	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
492	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
493	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
494	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
495	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
496	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
497	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
498	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
499	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
500	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
501	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
502	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
503	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
504	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
505	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
506	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
507	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
508	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
509	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
510	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
511	C₂²⋊C₄×C₆₁	C₂⁴	1	2	yes	—
512	C₂²⋊C₄×C₆₁	C₂⁴	1	6	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	12	yes	—
517	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
518	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
519	C₂²⋊C₄×C₆₁	C₂⁴	1	2	yes	—
520	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
521	C₂²⋊C₄×C₆₁	C₂⁴	1	2	yes	—
522	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
523	C₂²⋊C₄×C₆₁	C₂⁴	1	3	yes	—
524	C₂²⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
525	C₂²⋊C₄×C₆₁	C₂⁴	1	3	yes	—
526	C₂²⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
527	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
528	C₂²⋊C₄×C₆₁	C₂⁴	1	3	yes	—
529	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
530	C₂²⋊C₄×C₆₁	C₂⁴	1	3	yes	—
531	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
532	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
533	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
534	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
535	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
536	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
537	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
538	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
539	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
540	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
541	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
542	C₂²⋊C₄×C₆₁	C₂⁴	1	2	yes	—
543	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
544	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
545	C₄²×C₆₁	C₂⁴	1	3	yes	—
546	C₄²×C₆₁	C₂⁴	1	3	yes	—
547	C₄²×C₆₁	C₂⁴	1	3	yes	—
548	C₄²×C₆₁	C₂⁴	1	6	yes	—
549	C₄²×C₆₁	C₂⁴	1	3	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	3	yes	—
554	C₄²×C₆₁	C₂⁴	1	6	yes	—
555	C₄²×C₆₁	C₂⁴	1	3	yes	—
556	C₄²×C₆₁	C₂⁴	1	12	yes	—
557	C₂³×C₆₁	—	4	6	no	—
558	C₂³×C₆₁	—	4	6	no	—
559	C₂³×C₆₁	—	4	6	no	—
560	C₂³×C₆₁	C₂⁵	1	2	yes	—
561	C₂³×C₆₁	C₂⁵	1	3	yes	—
562	C₂³×C₆₁	C₂⁵	1	6	yes	—
563	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
564	C₂³×C₆₁	C₂⁵	1	2	yes	—
565	C₂³×C₆₁	C₂⁵	1	3	yes	—
566	Q₈×C₆₁	—	2	6	no	—
567	Q₈×C₆₁	—	2	12	no	—
568	Q₈×C₆₁	—	2	12	no	—
569	Q₈×C₆₁	—	2	6	no	—
570	Q₈×C₆₁	—	4	6	no	—
571	Q₈×C₆₁	—	4	6	no	—
572	Q₈×C₆₁	—	4	3	no	—
573	Q₈×C₆₁	H(5,𝔽₂)	1	4	yes	—
574	D₄×C₆₁	—	2	6	no	—
575	D₄×C₆₁	—	2	12	no	—
576	D₄×C₆₁	—	2	6	no	—
577	D₄×C₆₁	—	2	2	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	2	no	—
583	D₄×C₆₁	—	4	6	no	—
584	D₄×C₆₁	—	4	2	no	—
585	D₄×C₆₁	—	4	6	no	—
586	D₄×C₆₁	—	4	6	no	—
587	D₄×C₆₁	—	4	6	no	—
588	D₄×C₆₁	—	4	3	no	—
589	D₄×C₆₁	—	4	3	no	—
590	D₄×C₆₁	—	4	3	no	—
591	D₄×C₆₁	—	4	12	no	—
592	D₄×C₆₁	—	4	6	no	—
593	D₄×C₆₁	—	4	2	no	—
594	D₄×C₆₁	—	4	2	no	—
595	D₄×C₆₁	—	4	6	no	—
596	D₄×C₆₁	—	4	6	no	—
597	D₄×C₆₁	—	4	6	no	—
598	D₄×C₆₁	—	4	6	no	—
599	C₂×C₄×C₆₁	—	2	6	no	—
600	C₂×C₄×C₆₁	—	2	12	no	—
601	C₂×C₄×C₆₁	—	2	12	no	—
602	C₂×C₄×C₆₁	—	2	6	no	—
603	C₂×C₄×C₆₁	—	2	12	no	—
604	C₂×C₄×C₆₁	—	2	6	no	—
605	C₂×C₄×C₆₁	—	2	6	no	—
606	C₂×C₄×C₆₁	—	2	6	no	—
607	C₂×C₄×C₆₁	—	2	2	no	—
608	C₂×C₄×C₆₁	—	4	2	no	—
609	C₂×C₄×C₆₁	—	4	6	no	—
610	C₂×C₄×C₆₁	—	4	6	no	—
611	C₂×C₄×C₆₁	—	4	3	no	—
612	C₂×C₄×C₆₁	—	4	2	no	—
613	C₂×C₄×C₆₁	—	4	3	no	—
614	C₂×C₄×C₆₁	—	4	3	no	—
615	C₂×C₄×C₆₁	—	4	12	no	—
616	C₂×C₄×C₆₁	—	4	12	no	—
617	C₂×C₄×C₆₁	—	4	12	no	—
618	C₂×C₄×C₆₁	—	4	6	no	—
619	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
620	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
621	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
622	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
623	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
624	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
625	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
626	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
627	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
628	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
629	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
630	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
631	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
632	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
633	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
634	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
635	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
636	#62922	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
637	C₂²×C₆₁	—	2	2	no	—
638	C₂²×C₆₁	—	2	1	no	—
639	C₂²×C₆₁	—	2	2	no	—
640	C₂²×C₆₁	—	2	3	no	—
641	C₂²×C₆₁	—	2	6	no	—
642	C₂²×C₆₁	—	2	3	no	—
643	C₂²×C₆₁	—	2	1	no	—
644	C₂²×C₆₁	—	2	3	no	—
645	C₂²×C₆₁	—	2	3	no	—
646	C₂²×C₆₁	—	2	2	no	—
647	C₂²×C₆₁	—	2	6	no	—
648	C₂²×C₆₁	—	2	2	no	—
649	C₂²×C₆₁	—	2	1	no	—
650	C₂²×C₆₁	—	2	2	no	—
651	C₂²×C₆₁	—	2	3	no	—
652	C₂²×C₆₁	—	2	3	no	—
653	C₂²×C₆₁	—	2	6	no	—
654	C₂²×C₆₁	—	2	2	no	—
655	C₂²×C₆₁	—	8	12	no	—
656	C₂²×C₆₁	C₂⁶	1	1	yes	characteristic
657	C₄×C₆₁	—	2	1	no	—
658	C₄×C₆₁	—	2	2	no	—
659	C₄×C₆₁	—	2	1	no	—
660	C₄×C₆₁	—	2	6	no	—
661	C₄×C₆₁	—	2	6	no	—
662	C₄×C₆₁	—	2	3	no	—
663	C₄×C₆₁	—	2	3	no	—
664	C₄×C₆₁	—	2	3	no	—
665	C₄×C₆₁	—	2	1	no	—
666	C₄×C₆₁	—	2	6	no	—
667	C₄×C₆₁	—	2	1	no	—
668	C₄×C₆₁	—	2	3	no	—
669	C₄×C₆₁	—	2	1	no	—
670	C₄×C₆₁	—	2	2	no	—
671	C₄×C₆₁	—	2	3	no	—
672	C₄×C₆₁	C₂×H(5,𝔽₂)	1	6	yes	—
673	C₄×C₆₁	#585	1	2	yes	—
674	#3562	C₂×C₆₁	1	6	yes	complemented
675	#3552	C₂×C₆₁	1	3	yes	complemented
676	#3551	C₂×C₆₁	1	6	yes	complemented
677	#3548	C₂×C₆₁	1	3	yes	complemented
678	#3546	C₂×C₆₁	1	3	yes	complemented
679	#3546	C₂×C₆₁	1	3	yes	complemented
680	#3541	C₂×C₆₁	1	6	yes	complemented
681	#3539	C₂×C₆₁	1	6	yes	complemented
682	#3523	C₂×C₆₁	1	1	yes	characteristic, complemented
683	#3520	C₂×C₆₁	1	3	yes	complemented
684	#3517	C₂×C₆₁	1	3	yes	complemented
685	#3517	C₂×C₆₁	1	1	yes	characteristic, complemented
686	#3516	C₂×C₆₁	1	2	yes	complemented
687	#3511	C₂×C₆₁	1	3	yes	complemented
688	#3499	C₂×C₆₁	1	1	yes	characteristic, complemented
689	#3497	C₂×C₆₁	1	2	yes	complemented
690	#3497	C₂×C₆₁	1	1	yes	characteristic, complemented
691	#3489	C₂×C₆₁	1	2	yes	complemented
692	#3487	C₂×C₆₁	1	2	yes	complemented
693	#3482	C₂×C₆₁	1	1	yes	characteristic, complemented
694	#3480	C₂×C₆₁	1	1	yes	characteristic, complemented
695	D₄×#41	C₂×C₆₁	1	1	yes	characteristic, complemented
696	#3460	C₂×C₆₁	1	3	yes	complemented
697	C₂×C₆₁	—	4	1	no	—
698	C₂×C₆₁	—	4	2	no	—
699	C₂×C₆₁	—	4	3	no	—
700	C₂×C₆₁	—	4	6	no	—
701	C₂×C₆₁	—	4	3	no	—
702	C₂×C₆₁	—	4	2	no	—
703	C₂×C₆₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
704	C₂×C₆₁	C₂×#585	1	1	yes	characteristic
705	C₂×C₆₁	2₋¹⁺⁶	1	1	yes	characteristic
706	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	2	yes	complemented
707	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	2	yes	complemented
708	C₂²×#41	C₂²×C₆₁	1	2	yes	—
709	#563	C₂²×C₆₁	1	12	yes	complemented
710	#562	C₂²×C₆₁	1	12	yes	complemented
711	#560	C₂²×C₆₁	1	12	yes	complemented
712	#560	C₂²×C₆₁	1	12	yes	complemented
713	#559	C₂²×C₆₁	1	3	yes	complemented
714	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
715	#557	C₂²×C₆₁	1	1	yes	characteristic, complemented
716	#557	C₂²×C₆₁	1	3	yes	complemented
717	#556	C₂²×C₆₁	1	3	yes	—
718	#556	C₂²×C₆₁	1	3	yes	complemented
719	#556	C₂²×C₆₁	1	3	yes	complemented
720	#556	C₂²×C₆₁	1	6	yes	complemented
721	#555	C₂²×C₆₁	1	6	yes	complemented
722	#554	C₂²×C₆₁	1	6	yes	complemented
723	#554	C₂²×C₆₁	1	6	yes	complemented
724	#554	C₂²×C₆₁	1	6	yes	complemented
725	#553	C₂²×C₆₁	1	3	yes	complemented
726	#553	C₂²×C₆₁	1	3	yes	complemented
727	#553	C₂²×C₆₁	1	6	yes	complemented
728	#553	C₂²×C₆₁	1	6	yes	complemented
729	#553	C₂²×C₆₁	1	6	yes	complemented
730	#553	C₂²×C₆₁	1	12	yes	complemented
731	#553	C₂²×C₆₁	1	6	yes	complemented
732	#553	C₂²×C₆₁	1	6	yes	complemented
733	#552	C₂²×C₆₁	1	6	yes	complemented
734	#552	C₂²×C₆₁	1	6	yes	complemented
735	#552	C₂²×C₆₁	1	6	yes	complemented
736	#551	C₂²×C₆₁	1	12	yes	complemented
737	#550	C₂²×C₆₁	1	1	yes	characteristic
738	#550	C₂²×C₆₁	1	1	yes	characteristic
739	#550	C₂²×C₆₁	1	2	yes	complemented
740	#550	C₂²×C₆₁	1	6	yes	complemented
741	#550	C₂²×C₆₁	1	6	yes	complemented
742	#550	C₂²×C₆₁	1	3	yes	complemented
743	#550	C₂²×C₆₁	1	6	yes	complemented
744	#550	C₂²×C₆₁	1	3	yes	complemented
745	#550	C₂²×C₆₁	1	6	yes	complemented
746	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
747	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
748	D₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
749	D₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
750	D₄×Q₈	C₂²×C₆₁	1	3	yes	complemented
751	D₄×Q₈	C₂²×C₆₁	1	6	yes	complemented
752	#548	C₂²×C₆₁	1	2	yes	—
753	#548	C₂²×C₆₁	1	1	yes	characteristic
754	#548	C₂²×C₆₁	1	2	yes	—
755	#548	C₂²×C₆₁	1	1	yes	characteristic, complemented
756	#548	C₂²×C₆₁	1	2	yes	complemented
757	#548	C₂²×C₆₁	1	6	yes	complemented
758	#548	C₂²×C₆₁	1	6	yes	complemented
759	#548	C₂²×C₆₁	1	6	yes	complemented
760	#548	C₂²×C₆₁	1	6	yes	complemented
761	#548	C₂²×C₆₁	1	6	yes	complemented
762	#547	C₂²×C₆₁	1	3	yes	—
763	#547	C₂²×C₆₁	1	3	yes	—
764	#547	C₂²×C₆₁	1	3	yes	complemented
765	#547	C₂²×C₆₁	1	6	yes	complemented
766	#547	C₂²×C₆₁	1	6	yes	complemented
767	#547	C₂²×C₆₁	1	3	yes	complemented
768	#547	C₂²×C₆₁	1	6	yes	complemented
769	#547	C₂²×C₆₁	1	3	yes	complemented
770	#546	C₂²×C₆₁	1	6	yes	—
771	#546	C₂²×C₆₁	1	6	yes	—
772	#546	C₂²×C₆₁	1	6	yes	complemented
773	#546	C₂²×C₆₁	1	6	yes	complemented
774	D₄²	C₂²×C₆₁	1	3	yes	—
775	#544	C₂²×C₆₁	1	3	yes	complemented
776	#542	C₂²×C₆₁	1	3	yes	—
777	#542	C₂²×C₆₁	1	3	yes	complemented
778	#542	C₂²×C₆₁	1	6	yes	complemented
779	#542	C₂²×C₆₁	1	6	yes	complemented
780	#542	C₂²×C₆₁	1	6	yes	complemented
781	#541	C₂²×C₆₁	1	6	yes	complemented
782	#541	C₂²×C₆₁	1	6	yes	complemented
783	#540	C₂²×C₆₁	1	1	yes	characteristic
784	#540	C₂²×C₆₁	1	3	yes	complemented
785	#540	C₂²×C₆₁	1	6	yes	complemented
786	#540	C₂²×C₆₁	1	6	yes	complemented
787	#540	C₂²×C₆₁	1	12	yes	complemented
788	#540	C₂²×C₆₁	1	12	yes	complemented
789	#539	C₂²×C₆₁	1	12	yes	complemented
790	#539	C₂²×C₆₁	1	12	yes	complemented
791	#538	C₂²×C₆₁	1	6	yes	complemented
792	#538	C₂²×C₆₁	1	6	yes	complemented
793	#538	C₂²×C₆₁	1	12	yes	complemented
794	#538	C₂²×C₆₁	1	12	yes	complemented
795	#537	C₂²×C₆₁	1	3	yes	complemented
796	#537	C₂²×C₆₁	1	6	yes	complemented
797	#537	C₂²×C₆₁	1	6	yes	complemented
798	#537	C₂²×C₆₁	1	6	yes	complemented
799	#537	C₂²×C₆₁	1	6	yes	complemented
800	#537	C₂²×C₆₁	1	6	yes	complemented
801	#536	C₂²×C₆₁	1	6	yes	complemented
802	#536	C₂²×C₆₁	1	6	yes	complemented
803	#535	C₂²×C₆₁	1	3	yes	—
804	#535	C₂²×C₆₁	1	3	yes	—
805	#535	C₂²×C₆₁	1	6	yes	complemented
806	#535	C₂²×C₆₁	1	6	yes	complemented
807	#533	C₂²×C₆₁	1	3	yes	complemented
808	#533	C₂²×C₆₁	1	3	yes	complemented
809	#532	C₂²×C₆₁	1	3	yes	—
810	#532	C₂²×C₆₁	1	3	yes	—
811	#532	C₂²×C₆₁	1	3	yes	complemented
812	#532	C₂²×C₆₁	1	6	yes	complemented
813	#532	C₂²×C₆₁	1	3	yes	complemented
814	#532	C₂²×C₆₁	1	3	yes	complemented
815	#532	C₂²×C₆₁	1	6	yes	complemented
816	#532	C₂²×C₆₁	1	3	yes	complemented
817	C₂×C₄⋊Q₈	C₂²×C₆₁	1	3	yes	complemented
818	#529	C₂²×C₆₁	1	3	yes	—
819	#529	C₂²×C₆₁	1	6	yes	complemented
820	#529	C₂²×C₆₁	1	3	yes	complemented
821	#529	C₂²×C₆₁	1	3	yes	complemented
822	#529	C₂²×C₆₁	1	3	yes	complemented
823	#529	C₂²×C₆₁	1	6	yes	complemented
824	#529	C₂²×C₆₁	1	6	yes	complemented
825	#525	C₂²×C₆₁	1	6	yes	—
826	#525	C₂²×C₆₁	1	6	yes	complemented
827	#525	C₂²×C₆₁	1	6	yes	complemented
828	#525	C₂²×C₆₁	1	6	yes	complemented
829	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	6	yes	complemented
830	#520	C₂²×C₆₁	1	2	yes	complemented
831	#520	C₂²×C₆₁	1	6	yes	complemented
832	#519	C₂²×C₆₁	1	2	yes	complemented
833	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
834	C₄×#41	C₂²×C₆₁	1	3	yes	complemented
835	C₄×#41	C₂²×C₆₁	1	3	yes	complemented
836	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic, complemented
837	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
838	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
839	C₂×C₄×D₄	C₂²×C₆₁	1	3	yes	—
840	C₆₁	#62922	1	1	yes	characteristic, direct product factor, Sylow
841	2₋¹⁺⁴	—	4	8	no	—
842	2₋¹⁺⁴	—	4	8	no	—
843	C₂×#41	—	4	8	no	—
844	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
845	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
846	C₂×#41	C₂³×C₆₁	1	2	yes	—
847	C₂×#41	C₂³×C₆₁	1	3	yes	—
848	C₂×#41	C₂³×C₆₁	1	3	yes	—
849	C₂×#41	C₂³×C₆₁	1	6	yes	—
850	C₂×#41	C₂³×C₆₁	1	6	yes	—
851	C₂×#41	C₂³×C₆₁	1	6	yes	—
852	C₂×#41	C₂³×C₆₁	1	6	yes	—
853	C₂×#41	C₂³×C₆₁	1	6	yes	—
854	C₂×#41	C₂³×C₆₁	1	6	yes	—
855	C₂×#41	C₂³×C₆₁	1	6	yes	—
856	C₂×#41	C₂³×C₆₁	1	6	yes	—
857	C₂×#41	C₂³×C₆₁	1	6	yes	—
858	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
859	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
860	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
861	C₂²×Q₈	C₂³×C₆₁	1	6	yes	—
862	C₂²×Q₈	C₂³×C₆₁	1	6	yes	—
863	C₂²×D₄	C₂³×C₆₁	1	3	yes	—
864	C₂²×D₄	C₂³×C₆₁	1	6	yes	—
865	C₂³×C₄	C₂³×C₆₁	1	6	yes	—
866	C₄⋊Q₈	C₂³×C₆₁	1	3	yes	—
867	C₄⋊Q₈	C₂³×C₆₁	1	3	yes	—
868	C₄⋊Q₈	C₂³×C₆₁	1	3	yes	—
869	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
870	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
871	C₄⋊Q₈	C₂³×C₆₁	1	3	yes	—
872	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
873	C₄⋊Q₈	C₂³×C₆₁	1	3	yes	—
874	C₄⋊Q₈	C₂³×C₆₁	1	3	yes	—
875	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
876	#127	C₂³×C₆₁	1	1	yes	characteristic
877	#127	C₂³×C₆₁	1	3	yes	—
878	#127	C₂³×C₆₁	1	3	yes	—
879	#127	C₂³×C₆₁	1	6	yes	—
880	#127	C₂³×C₆₁	1	3	yes	—
881	#127	C₂³×C₆₁	1	6	yes	—
882	#127	C₂³×C₆₁	1	12	yes	—
883	#126	C₂³×C₆₁	1	6	yes	—
884	#126	C₂³×C₆₁	1	6	yes	—
885	#126	C₂³×C₆₁	1	12	yes	—
886	#126	C₂³×C₆₁	1	6	yes	—
887	#126	C₂³×C₆₁	1	6	yes	—
888	#126	C₂³×C₆₁	1	6	yes	—
889	#126	C₂³×C₆₁	1	6	yes	—
890	#126	C₂³×C₆₁	1	12	yes	—
891	#126	C₂³×C₆₁	1	12	yes	—
892	#126	C₂³×C₆₁	1	12	yes	—
893	#125	C₂³×C₆₁	1	3	yes	—
894	#125	C₂³×C₆₁	1	1	yes	characteristic
895	#125	C₂³×C₆₁	1	3	yes	—
896	#125	C₂³×C₆₁	1	6	yes	—
897	#125	C₂³×C₆₁	1	6	yes	—
898	#125	C₂³×C₆₁	1	3	yes	—
899	#125	C₂³×C₆₁	1	6	yes	—
900	#125	C₂³×C₆₁	1	6	yes	—
901	#125	C₂³×C₆₁	1	12	yes	—
902	#125	C₂³×C₆₁	1	12	yes	—
903	#124	C₂³×C₆₁	1	3	yes	—
904	#124	C₂³×C₆₁	1	6	yes	—
905	#124	C₂³×C₆₁	1	3	yes	—
906	#124	C₂³×C₆₁	1	3	yes	—
907	#124	C₂³×C₆₁	1	6	yes	—
908	#124	C₂³×C₆₁	1	6	yes	—
909	#124	C₂³×C₆₁	1	3	yes	—
910	#124	C₂³×C₆₁	1	6	yes	—
911	#124	C₂³×C₆₁	1	6	yes	—
912	#124	C₂³×C₆₁	1	6	yes	—
913	#124	C₂³×C₆₁	1	6	yes	—
914	#124	C₂³×C₆₁	1	6	yes	—
915	#124	C₂³×C₆₁	1	6	yes	—
916	#124	C₂³×C₆₁	1	12	yes	—
917	#123	C₂³×C₆₁	1	12	yes	—
918	#123	C₂³×C₆₁	1	6	yes	—
919	#123	C₂³×C₆₁	1	2	yes	—
920	#123	C₂³×C₆₁	1	6	yes	—
921	#123	C₂³×C₆₁	1	6	yes	—
922	#123	C₂³×C₆₁	1	6	yes	—
923	#123	C₂³×C₆₁	1	2	yes	—
924	#123	C₂³×C₆₁	1	6	yes	—
925	#123	C₂³×C₆₁	1	6	yes	—
926	#123	C₂³×C₆₁	1	12	yes	—
927	#123	C₂³×C₆₁	1	6	yes	—
928	#123	C₂³×C₆₁	1	6	yes	—
929	#123	C₂³×C₆₁	1	12	yes	—
930	#123	C₂³×C₆₁	1	12	yes	—
931	#123	C₂³×C₆₁	1	12	yes	—
932	#123	C₂³×C₆₁	1	12	yes	—
933	#123	C₂³×C₆₁	1	12	yes	—
934	#123	C₂³×C₆₁	1	12	yes	—
935	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
936	C₂²⋊Q₈	C₂³×C₆₁	1	3	yes	—
937	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
938	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
939	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
940	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
941	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
942	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
943	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
944	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
945	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
946	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
947	C₂²⋊Q₈	C₂³×C₆₁	1	3	yes	—
948	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
949	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
950	C₂²⋊Q₈	C₂³×C₆₁	1	3	yes	—
951	C₂²⋊Q₈	C₂³×C₆₁	1	3	yes	—
952	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
953	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
954	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
955	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
956	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
957	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
958	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
959	#121	C₂³×C₆₁	1	6	yes	—
960	#121	C₂³×C₆₁	1	6	yes	—
961	#121	C₂³×C₆₁	1	2	yes	—
962	#121	C₂³×C₆₁	1	3	yes	—
963	#121	C₂³×C₆₁	1	6	yes	—
964	#121	C₂³×C₆₁	1	6	yes	—
965	#121	C₂³×C₆₁	1	6	yes	—
966	#121	C₂³×C₆₁	1	6	yes	—
967	#121	C₂³×C₆₁	1	1	yes	characteristic
968	#121	C₂³×C₆₁	1	3	yes	—
969	#121	C₂³×C₆₁	1	6	yes	—
970	#121	C₂³×C₆₁	1	3	yes	—
971	#121	C₂³×C₆₁	1	6	yes	—
972	#121	C₂³×C₆₁	1	6	yes	—
973	#121	C₂³×C₆₁	1	3	yes	—
974	#121	C₂³×C₆₁	1	3	yes	—
975	#121	C₂³×C₆₁	1	6	yes	—
976	#121	C₂³×C₆₁	1	6	yes	—
977	#121	C₂³×C₆₁	1	6	yes	—
978	#121	C₂³×C₆₁	1	3	yes	—
979	#121	C₂³×C₆₁	1	1	yes	characteristic
980	#121	C₂³×C₆₁	1	2	yes	—
981	#121	C₂³×C₆₁	1	6	yes	—
982	#121	C₂³×C₆₁	1	6	yes	—
983	#121	C₂³×C₆₁	1	6	yes	—
984	#121	C₂³×C₆₁	1	6	yes	—
985	#121	C₂³×C₆₁	1	6	yes	—
986	#121	C₂³×C₆₁	1	3	yes	—
987	#121	C₂³×C₆₁	1	3	yes	—
988	#121	C₂³×C₆₁	1	12	yes	—
989	#121	C₂³×C₆₁	1	6	yes	—
990	#121	C₂³×C₆₁	1	6	yes	—
991	#121	C₂³×C₆₁	1	6	yes	—
992	#121	C₂³×C₆₁	1	12	yes	—
993	#121	C₂³×C₆₁	1	12	yes	—
994	#121	C₂³×C₆₁	1	12	yes	—
995	#121	C₂³×C₆₁	1	12	yes	—
996	#121	C₂³×C₆₁	1	12	yes	—
997	#121	C₂³×C₆₁	1	12	yes	—
998	#121	C₂³×C₆₁	1	12	yes	—
999	#121	C₂³×C₆₁	1	12	yes	—
1000	#120	C₂³×C₆₁	1	12	yes	—
1001	#120	C₂³×C₆₁	1	6	yes	—
1002	#120	C₂³×C₆₁	1	6	yes	—
1003	#120	C₂³×C₆₁	1	6	yes	—
1004	#120	C₂³×C₆₁	1	6	yes	—
1005	#120	C₂³×C₆₁	1	12	yes	—
1006	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
1007	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
1008	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
1009	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
1010	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
1011	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
1012	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
1013	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
1014	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
1015	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
1016	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
1017	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
1018	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
1019	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
1020	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
1021	C₄×Q₈	C₂³×C₆₁	1	6	yes	—
1022	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
1023	C₄×D₄	C₂³×C₆₁	1	3	yes	—
1024	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1025	C₄×D₄	C₂³×C₆₁	1	3	yes	—
1026	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1027	C₄×D₄	C₂³×C₆₁	1	3	yes	—
1028	C₄×D₄	C₂³×C₆₁	1	3	yes	—
1029	C₄×D₄	C₂³×C₆₁	1	3	yes	—
1030	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
1031	C₄×D₄	C₂³×C₆₁	1	3	yes	—
1032	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1033	C₄×D₄	C₂³×C₆₁	1	3	yes	—
1034	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1035	C₄×D₄	C₂³×C₆₁	1	3	yes	—
1036	C₄×D₄	C₂³×C₆₁	1	3	yes	—
1037	C₄×D₄	C₂³×C₆₁	1	3	yes	—
1038	C₄×D₄	C₂³×C₆₁	1	3	yes	—
1039	C₄×D₄	C₂³×C₆₁	1	3	yes	—
1040	C₄×D₄	C₂³×C₆₁	1	3	yes	—
1041	C₄×D₄	C₂³×C₆₁	1	3	yes	—
1042	C₄×D₄	C₂³×C₆₁	1	12	yes	—
1043	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1044	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1045	C₄×D₄	C₂³×C₆₁	1	12	yes	—
1046	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1047	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1048	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1049	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1050	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1051	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1052	C₄×D₄	C₂³×C₆₁	1	12	yes	—
1053	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1054	C₄×D₄	C₂³×C₆₁	1	12	yes	—
1055	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1056	C₄×D₄	C₂³×C₆₁	1	6	yes	—
1057	C₄×D₄	C₂³×C₆₁	1	12	yes	—
1058	#117	C₂³×C₆₁	1	3	yes	—
1059	#117	C₂³×C₆₁	1	1	yes	characteristic
1060	#117	C₂³×C₆₁	1	3	yes	—
1061	#117	C₂³×C₆₁	1	3	yes	—
1062	#117	C₂³×C₆₁	1	3	yes	—
1063	#117	C₂³×C₆₁	1	3	yes	—
1064	#117	C₂³×C₆₁	1	6	yes	—
1065	#117	C₂³×C₆₁	1	6	yes	—
1066	#117	C₂³×C₆₁	1	6	yes	—
1067	#117	C₂³×C₆₁	1	6	yes	—
1068	#117	C₂³×C₆₁	1	12	yes	—
1069	#117	C₂³×C₆₁	1	6	yes	—
1070	#117	C₂³×C₆₁	1	6	yes	—
1071	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
1072	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
1073	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
1074	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
1075	C₂×C₄⋊C₄	C₂³×C₆₁	1	12	yes	—
1076	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
1077	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
1078	C₂×C₂²⋊C₄	C₂³×C₆₁	1	6	yes	—
1079	C₂×C₂²⋊C₄	C₂³×C₆₁	1	12	yes	—
1080	C₂×C₄²	C₂³×C₆₁	1	3	yes	—
1081	C₂×C₄²	C₂³×C₆₁	1	3	yes	—
1082	C₂×C₄²	C₂³×C₆₁	1	6	yes	—
1083	C₂×C₄²	C₂³×C₆₁	1	3	yes	—
1084	C₂⁴	C₂⁴×C₆₁	1	6	yes	—
1085	#41	—	2	4	no	—
1086	#41	—	2	8	no	—
1087	#41	—	2	4	no	—
1088	#41	—	4	12	no	—
1089	#41	—	4	12	no	—
1090	#41	—	4	6	no	—
1091	#41	—	4	12	no	—
1092	#41	—	4	12	no	—
1093	#41	—	4	12	no	—
1094	#41	—	4	12	no	—
1095	#41	—	4	12	no	—
1096	#41	—	4	12	no	—
1097	#41	—	4	6	no	—
1098	#41	—	4	12	no	—
1099	C₂×Q₈	—	2	8	no	—
1100	C₂×Q₈	—	2	4	no	—
1101	C₂×Q₈	—	2	8	no	—
1102	C₂×Q₈	—	4	12	no	—
1103	C₂×Q₈	—	4	12	no	—
1104	C₂×Q₈	C₂⁴×C₆₁	1	3	yes	—
1105	C₂×Q₈	C₂⁴×C₆₁	1	3	yes	—
1106	C₂×Q₈	C₂⁴×C₆₁	1	6	yes	—
1107	C₂×Q₈	C₂⁴×C₆₁	1	6	yes	—
1108	C₂×Q₈	C₂⁴×C₆₁	1	3	yes	—
1109	C₂×Q₈	C₂⁴×C₆₁	1	6	yes	—
1110	C₂×Q₈	C₂⁴×C₆₁	1	6	yes	—
1111	C₂×Q₈	C₂⁴×C₆₁	1	1	yes	characteristic
1112	C₂×D₄	—	4	12	no	—
1113	C₂×D₄	—	4	6	no	—
1114	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
1115	C₂×D₄	C₂⁴×C₆₁	1	3	yes	—
1116	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
1117	C₂×D₄	C₂⁴×C₆₁	1	3	yes	—
1118	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
1119	C₂×D₄	C₂⁴×C₆₁	1	3	yes	—
1120	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
1121	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
1122	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
1123	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
1124	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
1125	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
1126	C₂×D₄	C₂⁴×C₆₁	1	3	yes	—
1127	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
1128	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
1129	C₂×D₄	C₂⁴×C₆₁	1	3	yes	—
1130	C₂×D₄	C₂⁴×C₆₁	1	12	yes	—
1131	C₂×D₄	C₂⁴×C₆₁	1	3	yes	—
1132	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
1133	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
1134	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
1135	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
1136	C₂×D₄	C₂⁴×C₆₁	1	12	yes	—
1137	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
1138	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
1139	C₂²×C₄	—	4	12	no	—
1140	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1141	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
1142	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
1143	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
1144	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
1145	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
1146	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
1147	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
1148	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
1149	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
1150	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
1151	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
1152	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
1153	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
1154	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
1155	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
1156	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
1157	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
1158	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
1159	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
1160	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1161	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1162	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1163	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1164	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1165	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1166	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1167	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1168	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1169	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
1170	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1171	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1172	C₄⋊C₄	C₂⁴×C₆₁	1	3	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	12	yes	—
1177	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
1178	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1179	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1180	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1181	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1182	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1183	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1184	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1185	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1186	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1187	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1188	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1189	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1190	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1191	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1192	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1193	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1194	C₂²⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1195	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1196	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1197	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1198	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1199	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
1200	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1201	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1202	C₂²⋊C₄	C₂⁴×C₆₁	1	2	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	3	yes	—
1207	C₂²⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1208	C₂²⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1209	C₂²⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
1210	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1211	C₂²⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1212	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1213	C₂²⋊C₄	C₂⁴×C₆₁	1	3	yes	—
1214	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
1215	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1216	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1217	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1218	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1219	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
1220	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1221	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1222	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1223	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1224	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
1225	C₂²⋊C₄	C₂⁴×C₆₁	1	2	yes	—
1226	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1227	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
1228	C₄²	C₂⁴×C₆₁	1	3	yes	—
1229	C₄²	C₂⁴×C₆₁	1	3	yes	—
1230	C₄²	C₂⁴×C₆₁	1	3	yes	—
1231	C₄²	C₂⁴×C₆₁	1	6	yes	—
1232	C₄²	C₂⁴×C₆₁	1	3	yes	—
1233	C₄²	C₂⁴×C₆₁	1	6	yes	—
1234	C₄²	C₂⁴×C₆₁	1	3	yes	—
1235	C₄²	C₂⁴×C₆₁	1	3	yes	—
1236	C₄²	C₂⁴×C₆₁	1	3	yes	—
1237	C₄²	C₂⁴×C₆₁	1	6	yes	—
1238	C₄²	C₂⁴×C₆₁	1	3	yes	—
1239	C₄²	C₂⁴×C₆₁	1	12	yes	—
1240	C₂³	—	4	6	no	—
1241	C₂³	—	4	6	no	—
1242	C₂³	—	4	6	no	—
1243	C₂³	C₂⁵×C₆₁	1	2	yes	—
1244	C₂³	C₂⁵×C₆₁	1	3	yes	—
1245	C₂³	C₂⁵×C₆₁	1	6	yes	—
1246	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
1247	C₂³	C₂⁵×C₆₁	1	2	yes	—
1248	C₂³	C₂⁵×C₆₁	1	3	yes	—
1249	Q₈	—	2	6	no	—
1250	Q₈	—	2	12	no	—
1251	Q₈	—	2	12	no	—
1252	Q₈	—	2	6	no	—
1253	Q₈	—	4	6	no	—
1254	Q₈	—	4	6	no	—
1255	Q₈	—	4	3	no	—
1256	Q₈	H(5,𝔽₂)×C₆₁	1	4	yes	—
1257	D₄	—	2	6	no	—
1258	D₄	—	2	12	no	—
1259	D₄	—	2	6	no	—
1260	D₄	—	2	2	no	—
1261	D₄	—	2	6	no	—
1262	D₄	—	2	2	no	—
1263	D₄	—	4	6	no	—
1264	D₄	—	4	12	no	—
1265	D₄	—	4	2	no	—
1266	D₄	—	4	6	no	—
1267	D₄	—	4	2	no	—
1268	D₄	—	4	6	no	—
1269	D₄	—	4	6	no	—
1270	D₄	—	4	6	no	—
1271	D₄	—	4	3	no	—
1272	D₄	—	4	3	no	—
1273	D₄	—	4	3	no	—
1274	D₄	—	4	12	no	—
1275	D₄	—	4	6	no	—
1276	D₄	—	4	2	no	—
1277	D₄	—	4	2	no	—
1278	D₄	—	4	6	no	—
1279	D₄	—	4	6	no	—
1280	D₄	—	4	6	no	—
1281	D₄	—	4	6	no	—
1282	C₂×C₄	—	2	6	no	—
1283	C₂×C₄	—	2	12	no	—
1284	C₂×C₄	—	2	12	no	—
1285	C₂×C₄	—	2	6	no	—
1286	C₂×C₄	—	2	12	no	—
1287	C₂×C₄	—	2	6	no	—
1288	C₂×C₄	—	2	6	no	—
1289	C₂×C₄	—	2	6	no	—
1290	C₂×C₄	—	2	2	no	—
1291	C₂×C₄	—	4	2	no	—
1292	C₂×C₄	—	4	6	no	—
1293	C₂×C₄	—	4	6	no	—
1294	C₂×C₄	—	4	3	no	—
1295	C₂×C₄	—	4	2	no	—
1296	C₂×C₄	—	4	3	no	—
1297	C₂×C₄	—	4	3	no	—
1298	C₂×C₄	—	4	12	no	—
1299	C₂×C₄	—	4	12	no	—
1300	C₂×C₄	—	4	12	no	—
1301	C₂×C₄	—	4	6	no	—
1302	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1303	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1304	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
1305	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
1306	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1307	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
1308	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1309	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
1310	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
1311	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1312	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
1313	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
1314	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
1315	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
1316	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
1317	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
1318	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
1319	C₂²	—	2	2	no	—
1320	C₂²	—	2	1	no	—
1321	C₂²	—	2	2	no	—
1322	C₂²	—	2	3	no	—
1323	C₂²	—	2	6	no	—
1324	C₂²	—	2	3	no	—
1325	C₂²	—	2	1	no	—
1326	C₂²	—	2	3	no	—
1327	C₂²	—	2	3	no	—
1328	C₂²	—	2	2	no	—
1329	C₂²	—	2	6	no	—
1330	C₂²	—	2	2	no	—
1331	C₂²	—	2	1	no	—
1332	C₂²	—	2	2	no	—
1333	C₂²	—	2	3	no	—
1334	C₂²	—	2	3	no	—
1335	C₂²	—	2	6	no	—
1336	C₂²	—	2	2	no	—
1337	C₂²	—	8	12	no	—
1338	C₂²	C₂⁶×C₆₁	1	1	yes	characteristic
1339	C₄	—	2	1	no	—
1340	C₄	—	2	2	no	—
1341	C₄	—	2	1	no	—
1342	C₄	—	2	6	no	—
1343	C₄	—	2	6	no	—
1344	C₄	—	2	3	no	—
1345	C₄	—	2	3	no	—
1346	C₄	—	2	3	no	—
1347	C₄	—	2	1	no	—
1348	C₄	—	2	6	no	—
1349	C₄	—	2	1	no	—
1350	C₄	—	2	3	no	—
1351	C₄	—	2	1	no	—
1352	C₄	—	2	2	no	—
1353	C₄	—	2	3	no	—
1354	C₄	C₂×H(5,𝔽₂)×C₆₁	1	6	yes	—
1355	C₄	C₆₁×#585	1	2	yes	—
1356	C₂	—	4	2	no	—
1357	C₂	—	4	3	no	—
1358	C₂	—	4	6	no	—
1359	C₂	—	4	1	no	—
1360	C₂	—	4	2	no	—
1361	C₂	—	4	3	no	—
1362	C₂	C₂²×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
1363	C₂	C₂×C₆₁×#585	1	1	yes	characteristic
1364	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×#3562	C₂	semidirect
2. C₆₁×#3552	C₂	semidirect
3. C₆₁×#3551	C₂	semidirect
4. C₆₁×#3548	C₂	semidirect
5. C₆₁×#3546	C₂	semidirect
6. C₆₁×#3546	C₂	semidirect
7. C₆₁×#3541	C₂	semidirect
8. C₆₁×#3539	C₂	semidirect
9. C₆₁×#3523	C₂	semidirect
10. C₆₁×#3520	C₂	semidirect
11. C₆₁×#3517	C₂	semidirect
12. C₆₁×#3517	C₂	semidirect
13. C₆₁×#3516	C₂	semidirect
14. C₆₁×#3511	C₂	semidirect
15. C₆₁×#3499	C₂	semidirect
16. C₆₁×#3497	C₂	semidirect
17. C₆₁×#3497	C₂	semidirect
18. C₆₁×#3489	C₂	semidirect
19. C₆₁×#3487	C₂	semidirect
20. C₆₁×#3482	C₂	semidirect
21. C₆₁×#3480	C₂	semidirect
22. D₄×#41×C₆₁	C₂	semidirect
23. C₆₁×#3460	C₂	semidirect
24. C₂×2₋¹⁺⁴×C₆₁	C₂²	semidirect
25. C₂×2₋¹⁺⁴×C₆₁	C₂²	semidirect
27. C₆₁×#563	C₂²	semidirect
28. C₆₁×#562	C₂²	semidirect
29. C₆₁×#560	C₂²	semidirect
30. C₆₁×#560	C₂²	semidirect
31. C₆₁×#559	C₂²	semidirect
32. C₆₁×#557	C₂²	semidirect
33. C₆₁×#557	C₂²	semidirect
34. C₆₁×#557	C₂²	semidirect
36. C₆₁×#556	C₂²	semidirect
37. C₆₁×#556	C₂²	semidirect
38. C₆₁×#556	C₂²	semidirect
39. C₆₁×#555	C₂²	semidirect
40. C₆₁×#554	C₂²	semidirect
41. C₆₁×#554	C₂²	semidirect
42. C₆₁×#554	C₂²	semidirect
43. C₆₁×#553	C₂²	semidirect
44. C₆₁×#553	C₂²	semidirect
45. C₆₁×#553	C₂²	semidirect
46. C₆₁×#553	C₂²	semidirect
47. C₆₁×#553	C₂²	semidirect
48. C₆₁×#553	C₂²	semidirect
49. C₆₁×#553	C₂²	semidirect
50. C₆₁×#553	C₂²	semidirect
51. C₆₁×#552	C₂²	semidirect
52. C₆₁×#552	C₂²	semidirect
53. C₆₁×#552	C₂²	semidirect
54. C₆₁×#551	C₂²	semidirect
57. C₆₁×#550	C₂²	semidirect
58. C₆₁×#550	C₂²	semidirect
59. C₆₁×#550	C₂²	semidirect
60. C₆₁×#550	C₂²	semidirect
61. C₆₁×#550	C₂²	semidirect
62. C₆₁×#550	C₂²	semidirect
63. C₆₁×#550	C₂²	semidirect
65. D₄×Q₈×C₆₁	C₂²	semidirect
66. D₄×Q₈×C₆₁	C₂²	semidirect
67. D₄×Q₈×C₆₁	C₂²	semidirect
68. D₄×Q₈×C₆₁	C₂²	semidirect
69. D₄×Q₈×C₆₁	C₂²	semidirect
73. C₆₁×#548	C₂²	semidirect
74. C₆₁×#548	C₂²	semidirect
75. C₆₁×#548	C₂²	semidirect
76. C₆₁×#548	C₂²	semidirect
77. C₆₁×#548	C₂²	semidirect
78. C₆₁×#548	C₂²	semidirect
79. C₆₁×#548	C₂²	semidirect
82. C₆₁×#547	C₂²	semidirect
83. C₆₁×#547	C₂²	semidirect
84. C₆₁×#547	C₂²	semidirect
85. C₆₁×#547	C₂²	semidirect
86. C₆₁×#547	C₂²	semidirect
87. C₆₁×#547	C₂²	semidirect
90. C₆₁×#546	C₂²	semidirect
91. C₆₁×#546	C₂²	semidirect
93. C₆₁×#544	C₂²	semidirect
95. C₆₁×#542	C₂²	semidirect
96. C₆₁×#542	C₂²	semidirect
97. C₆₁×#542	C₂²	semidirect
98. C₆₁×#542	C₂²	semidirect
99. C₆₁×#541	C₂²	semidirect
100. C₆₁×#541	C₂²	semidirect
102. C₆₁×#540	C₂²	semidirect
103. C₆₁×#540	C₂²	semidirect
104. C₆₁×#540	C₂²	semidirect
105. C₆₁×#540	C₂²	semidirect
106. C₆₁×#540	C₂²	semidirect
107. C₆₁×#539	C₂²	semidirect
108. C₆₁×#539	C₂²	semidirect
109. C₆₁×#538	C₂²	semidirect
110. C₆₁×#538	C₂²	semidirect
111. C₆₁×#538	C₂²	semidirect
112. C₆₁×#538	C₂²	semidirect
113. C₆₁×#537	C₂²	semidirect
114. C₆₁×#537	C₂²	semidirect
115. C₆₁×#537	C₂²	semidirect
116. C₆₁×#537	C₂²	semidirect
117. C₆₁×#537	C₂²	semidirect
118. C₆₁×#537	C₂²	semidirect
119. C₆₁×#536	C₂²	semidirect
120. C₆₁×#536	C₂²	semidirect
123. C₆₁×#535	C₂²	semidirect
124. C₆₁×#535	C₂²	semidirect
125. C₆₁×#533	C₂²	semidirect
126. C₆₁×#533	C₂²	semidirect
129. C₆₁×#532	C₂²	semidirect
130. C₆₁×#532	C₂²	semidirect
131. C₆₁×#532	C₂²	semidirect
132. C₆₁×#532	C₂²	semidirect
133. C₆₁×#532	C₂²	semidirect
134. C₆₁×#532	C₂²	semidirect
135. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
137. C₆₁×#529	C₂²	semidirect
138. C₆₁×#529	C₂²	semidirect
139. C₆₁×#529	C₂²	semidirect
140. C₆₁×#529	C₂²	semidirect
141. C₆₁×#529	C₂²	semidirect
142. C₆₁×#529	C₂²	semidirect
144. C₆₁×#525	C₂²	semidirect
145. C₆₁×#525	C₂²	semidirect
146. C₆₁×#525	C₂²	semidirect
147. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
148. C₆₁×#520	C₂²	semidirect
149. C₆₁×#520	C₂²	semidirect
150. C₆₁×#519	C₂²	semidirect
152. C₄×#41×C₆₁	C₂²	semidirect
153. C₄×#41×C₆₁	C₂²	semidirect
154. C₄×#41×C₆₁	C₂²	semidirect
155. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
156. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
636. #62922	C₆₁	direct (N × H)
674. #3562	C₂×C₆₁	semidirect
675. #3552	C₂×C₆₁	semidirect
676. #3551	C₂×C₆₁	semidirect
677. #3548	C₂×C₆₁	semidirect
678. #3546	C₂×C₆₁	semidirect
679. #3546	C₂×C₆₁	semidirect
680. #3541	C₂×C₆₁	semidirect
681. #3539	C₂×C₆₁	semidirect
682. #3523	C₂×C₆₁	semidirect
683. #3520	C₂×C₆₁	semidirect
684. #3517	C₂×C₆₁	semidirect
685. #3517	C₂×C₆₁	semidirect
686. #3516	C₂×C₆₁	semidirect
687. #3511	C₂×C₆₁	semidirect
688. #3499	C₂×C₆₁	semidirect
689. #3497	C₂×C₆₁	semidirect
690. #3497	C₂×C₆₁	semidirect
691. #3489	C₂×C₆₁	semidirect
692. #3487	C₂×C₆₁	semidirect
693. #3482	C₂×C₆₁	semidirect
694. #3480	C₂×C₆₁	semidirect
695. D₄×#41	C₂×C₆₁	semidirect
696. #3460	C₂×C₆₁	semidirect
706. C₂×2₋¹⁺⁴	C₂²×C₆₁	semidirect
707. C₂×2₋¹⁺⁴	C₂²×C₆₁	semidirect
709. #563	C₂²×C₆₁	semidirect
710. #562	C₂²×C₆₁	semidirect
711. #560	C₂²×C₆₁	semidirect
712. #560	C₂²×C₆₁	semidirect
713. #559	C₂²×C₆₁	semidirect
714. #557	C₂²×C₆₁	semidirect
715. #557	C₂²×C₆₁	semidirect
716. #557	C₂²×C₆₁	semidirect
718. #556	C₂²×C₆₁	semidirect
719. #556	C₂²×C₆₁	semidirect
720. #556	C₂²×C₆₁	semidirect
721. #555	C₂²×C₆₁	semidirect
722. #554	C₂²×C₆₁	semidirect
723. #554	C₂²×C₆₁	semidirect
724. #554	C₂²×C₆₁	semidirect
725. #553	C₂²×C₆₁	semidirect
726. #553	C₂²×C₆₁	semidirect
727. #553	C₂²×C₆₁	semidirect
728. #553	C₂²×C₆₁	semidirect
729. #553	C₂²×C₆₁	semidirect
730. #553	C₂²×C₆₁	semidirect
731. #553	C₂²×C₆₁	semidirect
732. #553	C₂²×C₆₁	semidirect
733. #552	C₂²×C₆₁	semidirect
734. #552	C₂²×C₆₁	semidirect
735. #552	C₂²×C₆₁	semidirect
736. #551	C₂²×C₆₁	semidirect
739. #550	C₂²×C₆₁	semidirect
740. #550	C₂²×C₆₁	semidirect
741. #550	C₂²×C₆₁	semidirect
742. #550	C₂²×C₆₁	semidirect
743. #550	C₂²×C₆₁	semidirect
744. #550	C₂²×C₆₁	semidirect
745. #550	C₂²×C₆₁	semidirect
747. D₄×Q₈	C₂²×C₆₁	semidirect
748. D₄×Q₈	C₂²×C₆₁	semidirect
749. D₄×Q₈	C₂²×C₆₁	semidirect
750. D₄×Q₈	C₂²×C₆₁	semidirect
751. D₄×Q₈	C₂²×C₆₁	semidirect
755. #548	C₂²×C₆₁	semidirect
756. #548	C₂²×C₆₁	semidirect
757. #548	C₂²×C₆₁	semidirect
758. #548	C₂²×C₆₁	semidirect
759. #548	C₂²×C₆₁	semidirect
760. #548	C₂²×C₆₁	semidirect
761. #548	C₂²×C₆₁	semidirect
764. #547	C₂²×C₆₁	semidirect
765. #547	C₂²×C₆₁	semidirect
766. #547	C₂²×C₆₁	semidirect
767. #547	C₂²×C₆₁	semidirect
768. #547	C₂²×C₆₁	semidirect
769. #547	C₂²×C₆₁	semidirect
772. #546	C₂²×C₆₁	semidirect
773. #546	C₂²×C₆₁	semidirect
775. #544	C₂²×C₆₁	semidirect
777. #542	C₂²×C₆₁	semidirect
778. #542	C₂²×C₆₁	semidirect
779. #542	C₂²×C₆₁	semidirect
780. #542	C₂²×C₆₁	semidirect
781. #541	C₂²×C₆₁	semidirect
782. #541	C₂²×C₆₁	semidirect
784. #540	C₂²×C₆₁	semidirect
785. #540	C₂²×C₆₁	semidirect
786. #540	C₂²×C₆₁	semidirect
787. #540	C₂²×C₆₁	semidirect
788. #540	C₂²×C₆₁	semidirect
789. #539	C₂²×C₆₁	semidirect
790. #539	C₂²×C₆₁	semidirect
791. #538	C₂²×C₆₁	semidirect
792. #538	C₂²×C₆₁	semidirect
793. #538	C₂²×C₆₁	semidirect
794. #538	C₂²×C₆₁	semidirect
795. #537	C₂²×C₆₁	semidirect
796. #537	C₂²×C₆₁	semidirect
797. #537	C₂²×C₆₁	semidirect
798. #537	C₂²×C₆₁	semidirect
799. #537	C₂²×C₆₁	semidirect
800. #537	C₂²×C₆₁	semidirect
801. #536	C₂²×C₆₁	semidirect
802. #536	C₂²×C₆₁	semidirect
805. #535	C₂²×C₆₁	semidirect
806. #535	C₂²×C₆₁	semidirect
807. #533	C₂²×C₆₁	semidirect
808. #533	C₂²×C₆₁	semidirect
811. #532	C₂²×C₆₁	semidirect
812. #532	C₂²×C₆₁	semidirect
813. #532	C₂²×C₆₁	semidirect
814. #532	C₂²×C₆₁	semidirect
815. #532	C₂²×C₆₁	semidirect
816. #532	C₂²×C₆₁	semidirect
817. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
819. #529	C₂²×C₆₁	semidirect
820. #529	C₂²×C₆₁	semidirect
821. #529	C₂²×C₆₁	semidirect
822. #529	C₂²×C₆₁	semidirect
823. #529	C₂²×C₆₁	semidirect
824. #529	C₂²×C₆₁	semidirect
826. #525	C₂²×C₆₁	semidirect
827. #525	C₂²×C₆₁	semidirect
828. #525	C₂²×C₆₁	semidirect
829. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
830. #520	C₂²×C₆₁	semidirect
831. #520	C₂²×C₆₁	semidirect
832. #519	C₂²×C₆₁	semidirect
834. C₄×#41	C₂²×C₆₁	semidirect
835. C₄×#41	C₂²×C₆₁	semidirect
836. C₄×#41	C₂²×C₆₁	semidirect
837. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
838. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
840. C₆₁	#62922	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×#3562	2
C₆₁×#3552	2
C₆₁×#3551	2
C₆₁×#3548	2
C₆₁×#3546	2
C₆₁×#3541	2
C₆₁×#3539	2
C₆₁×#3523	2
C₆₁×#3520	2
C₆₁×#3517	2
C₆₁×#3516	2
C₆₁×#3511	2
C₆₁×#3499	2
C₆₁×#3497	2
C₆₁×#3489	2
C₆₁×#3487	2
C₆₁×#3482	2
C₆₁×#3480	2
D₄×#41×C₆₁	2
C₆₁×#3460	2
#62922	61

Subgroups — C61×#62922 #29566355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62922 #29566355