Subgroups — C₆₁×#62903 #29566336

Order 15616.

6628 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3564	C₂	1	6	yes	maximal, complemented
2	C₆₁×#3564	C₂	1	6	yes	maximal, complemented
3	C₆₁×#3561	C₂	1	6	yes	maximal, complemented
4	C₆₁×#3538	C₂	1	6	yes	maximal, complemented
5	C₆₁×#3535	C₂	1	6	yes	maximal, complemented
6	C₆₁×#3535	C₂	1	6	yes	maximal, complemented
7	C₆₁×#3520	C₂	1	6	yes	maximal, complemented
8	C₆₁×#3501	C₂	1	3	yes	maximal, complemented
9	C₆₁×#3495	C₂	1	6	yes	maximal, complemented
10	C₆₁×#3491	C₂	1	3	yes	maximal, complemented
11	C₆₁×#3490	C₂	1	3	yes	maximal, complemented
12	C₂×C₆₁×#551	C₂	1	3	yes	maximal, complemented
13	C₆₁×#3459	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3458	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₆₁×#543	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#563	C₂²	1	12	yes	complemented
17	C₆₁×#563	C₂²	1	12	yes	complemented
18	C₆₁×#563	C₂²	1	12	yes	complemented
19	C₆₁×#562	C₂²	1	12	yes	complemented
20	C₆₁×#556	C₂²	1	12	yes	complemented
21	C₆₁×#556	C₂²	1	6	yes	complemented
22	C₆₁×#554	C₂²	1	12	yes	complemented
23	C₆₁×#554	C₂²	1	12	yes	complemented
24	C₆₁×#554	C₂²	1	12	yes	complemented
25	C₆₁×#552	C₂²	1	12	yes	complemented
26	C₆₁×#552	C₂²	1	12	yes	complemented
27	C₆₁×#552	C₂²	1	6	yes	complemented
28	C₆₁×#552	C₂²	1	12	yes	complemented
29	C₆₁×#552	C₂²	1	6	yes	complemented
30	C₆₁×#552	C₂²	1	12	yes	complemented
31	C₆₁×#551	C₂²	1	12	yes	complemented
32	C₆₁×#551	C₂²	1	12	yes	complemented
33	C₆₁×#551	C₂²	1	12	yes	complemented
34	C₆₁×#551	C₂²	1	12	yes	complemented
35	C₆₁×#551	C₂²	1	12	yes	complemented
36	C₆₁×#551	C₂²	1	12	yes	complemented
37	C₆₁×#551	C₂²	1	12	yes	complemented
38	C₆₁×#551	C₂²	1	12	yes	complemented
39	D₄×Q₈×C₆₁	C₂²	1	12	yes	complemented
40	D₄×Q₈×C₆₁	C₂²	1	6	yes	complemented
41	C₆₁×#548	C₂²	1	2	yes	complemented
42	C₆₁×#548	C₂²	1	6	yes	complemented
43	C₆₁×#547	C₂²	1	6	yes	complemented
44	C₆₁×#547	C₂²	1	6	yes	complemented
45	C₆₁×#546	C₂²	1	12	yes	complemented
46	C₆₁×#546	C₂²	1	12	yes	complemented
47	C₆₁×#544	C₂²	1	6	yes	complemented
48	C₆₁×#544	C₂²	1	6	yes	complemented
49	C₆₁×#544	C₂²	1	6	yes	complemented
50	C₆₁×#544	C₂²	1	6	yes	complemented
51	C₆₁×#543	C₂²	1	1	yes	characteristic
52	C₆₁×#543	C₂²	1	3	yes	—
53	C₆₁×#543	C₂²	1	3	yes	—
54	C₆₁×#543	C₂²	1	6	yes	complemented
55	C₆₁×#543	C₂²	1	6	yes	complemented
56	C₆₁×#543	C₂²	1	6	yes	complemented
57	C₆₁×#542	C₂²	1	6	yes	complemented
58	C₆₁×#542	C₂²	1	6	yes	complemented
59	C₆₁×#542	C₂²	1	12	yes	complemented
60	C₆₁×#542	C₂²	1	12	yes	complemented
61	C₆₁×#541	C₂²	1	6	yes	complemented
62	C₆₁×#541	C₂²	1	6	yes	complemented
63	C₆₁×#541	C₂²	1	12	yes	complemented
64	C₆₁×#539	C₂²	1	6	yes	complemented
65	C₆₁×#539	C₂²	1	6	yes	complemented
66	C₆₁×#539	C₂²	1	6	yes	complemented
67	C₆₁×#539	C₂²	1	12	yes	complemented
68	C₆₁×#539	C₂²	1	12	yes	complemented
69	C₆₁×#539	C₂²	1	12	yes	complemented
70	C₆₁×#538	C₂²	1	6	yes	—
71	C₆₁×#538	C₂²	1	6	yes	—
72	C₆₁×#538	C₂²	1	6	yes	complemented
73	C₆₁×#536	C₂²	1	6	yes	complemented
74	C₆₁×#536	C₂²	1	12	yes	complemented
75	C₆₁×#534	C₂²	1	3	yes	—
76	C₆₁×#533	C₂²	1	6	yes	complemented
77	C₆₁×#533	C₂²	1	6	yes	complemented
78	C₆₁×#533	C₂²	1	6	yes	complemented
79	C₆₁×#529	C₂²	1	6	yes	complemented
80	C₆₁×#529	C₂²	1	6	yes	complemented
81	C₆₁×#529	C₂²	1	6	yes	complemented
82	C₂×#126×C₆₁	C₂²	1	3	yes	complemented
83	C₂×#126×C₆₁	C₂²	1	3	yes	complemented
84	C₂×#124×C₆₁	C₂²	1	3	yes	complemented
85	C₆₁×#525	C₂²	1	6	yes	—
86	C₆₁×#525	C₂²	1	6	yes	—
87	C₆₁×#525	C₂²	1	6	yes	complemented
88	C₂×#123×C₆₁	C₂²	1	3	yes	—
89	C₂×#123×C₆₁	C₂²	1	3	yes	complemented
90	C₂×#123×C₆₁	C₂²	1	3	yes	complemented
91	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	3	yes	—
92	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	6	yes	complemented
93	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	6	yes	complemented
94	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	3	yes	complemented
95	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	6	yes	complemented
96	C₂×#120×C₆₁	C₂²	1	3	yes	—
97	C₆₁×#520	C₂²	1	6	yes	complemented
98	C₆₁×#519	C₂²	1	2	yes	complemented
99	C₆₁×#518	C₂²	1	6	yes	—
100	C₂×C₄×D₄×C₆₁	C₂²	1	3	yes	—
101	C₂×C₄×D₄×C₆₁	C₂²	1	3	yes	complemented
102	C₂×#117×C₆₁	C₂²	1	3	yes	—
103	C₂×#117×C₆₁	C₂²	1	3	yes	complemented
104	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	3	yes	—
105	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
106	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
107	C₂×#41×C₆₁	C₂³	1	6	yes	—
108	C₂×#41×C₆₁	C₂³	1	6	yes	—
109	C₂×#41×C₆₁	C₂³	1	2	yes	complemented
110	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
111	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
112	C₂²×Q₈×C₆₁	C₂³	1	3	yes	—
113	C₂²×Q₈×C₆₁	C₂³	1	6	yes	complemented
114	C₂²×D₄×C₆₁	C₂³	1	3	yes	—
115	C₂²×D₄×C₆₁	C₂³	1	3	yes	—
116	C₂²×D₄×C₆₁	C₂³	1	3	yes	—
117	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₆₁	C₂³	1	3	yes	—
119	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₆₁	C₂³	1	3	yes	—
121	C₂³×C₄×C₆₁	C₂³	1	3	yes	—
122	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	complemented
123	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	complemented
124	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	complemented
125	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	complemented
126	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	complemented
127	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	complemented
128	C₄⋊Q₈×C₆₁	C₂³	1	12	yes	complemented
129	C₄⋊Q₈×C₆₁	C₂³	1	12	yes	complemented
130	#126×C₆₁	C₂³	1	12	yes	—
131	#126×C₆₁	C₂³	1	12	yes	—
132	#126×C₆₁	C₂³	1	12	yes	—
133	#126×C₆₁	C₂³	1	12	yes	—
134	#126×C₆₁	C₂³	1	12	yes	—
135	#126×C₆₁	C₂³	1	12	yes	—
136	#126×C₆₁	C₂³	1	12	yes	complemented
137	#126×C₆₁	C₂³	1	12	yes	complemented
138	#126×C₆₁	C₂³	1	12	yes	complemented
139	#126×C₆₁	C₂³	1	12	yes	complemented
140	#126×C₆₁	C₂³	1	12	yes	complemented
141	#125×C₆₁	C₂³	1	12	yes	complemented
142	#125×C₆₁	C₂³	1	12	yes	complemented
143	#125×C₆₁	C₂³	1	12	yes	complemented
144	#125×C₆₁	C₂³	1	6	yes	complemented
145	#125×C₆₁	C₂³	1	12	yes	complemented
146	#125×C₆₁	C₂³	1	12	yes	complemented
147	#125×C₆₁	C₂³	1	12	yes	complemented
148	#125×C₆₁	C₂³	1	12	yes	complemented
149	#125×C₆₁	C₂³	1	6	yes	complemented
150	#125×C₆₁	C₂³	1	6	yes	complemented
151	#124×C₆₁	C₂³	1	12	yes	—
152	#124×C₆₁	C₂³	1	12	yes	—
153	#124×C₆₁	C₂³	1	12	yes	—
154	#124×C₆₁	C₂³	1	12	yes	—
155	#124×C₆₁	C₂³	1	6	yes	complemented
156	#124×C₆₁	C₂³	1	6	yes	complemented
157	#124×C₆₁	C₂³	1	6	yes	complemented
158	#123×C₆₁	C₂³	1	12	yes	—
159	#123×C₆₁	C₂³	1	12	yes	—
160	#123×C₆₁	C₂³	1	12	yes	—
161	#123×C₆₁	C₂³	1	12	yes	—
162	#123×C₆₁	C₂³	1	12	yes	—
163	#123×C₆₁	C₂³	1	12	yes	—
164	#123×C₆₁	C₂³	1	12	yes	—
165	#123×C₆₁	C₂³	1	12	yes	—
166	#123×C₆₁	C₂³	1	12	yes	—
167	#123×C₆₁	C₂³	1	12	yes	—
168	#123×C₆₁	C₂³	1	12	yes	—
169	#123×C₆₁	C₂³	1	12	yes	complemented
170	#123×C₆₁	C₂³	1	12	yes	complemented
171	#123×C₆₁	C₂³	1	12	yes	complemented
172	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
173	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
174	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
175	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
176	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
177	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
178	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
179	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
180	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
181	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
182	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
183	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
184	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
185	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
186	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
187	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
188	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
189	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
190	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
191	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
192	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	—
193	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
194	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	complemented
195	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	complemented
196	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	complemented
197	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	complemented
198	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	complemented
199	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	complemented
200	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	complemented
201	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	complemented
202	C₂²⋊Q₈×C₆₁	C₂³	1	12	yes	complemented
203	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	complemented
204	#121×C₆₁	C₂³	1	6	yes	—
205	#121×C₆₁	C₂³	1	6	yes	—
206	#121×C₆₁	C₂³	1	12	yes	—
207	#121×C₆₁	C₂³	1	12	yes	—
208	#121×C₆₁	C₂³	1	6	yes	—
209	#121×C₆₁	C₂³	1	6	yes	—
210	#121×C₆₁	C₂³	1	6	yes	complemented
211	#120×C₆₁	C₂³	1	12	yes	—
212	#120×C₆₁	C₂³	1	12	yes	—
213	#120×C₆₁	C₂³	1	12	yes	—
214	C₄×Q₈×C₆₁	C₂³	1	6	yes	complemented
215	C₄×Q₈×C₆₁	C₂³	1	2	yes	complemented
216	C₄×Q₈×C₆₁	C₂³	1	2	yes	complemented
217	C₄×Q₈×C₆₁	C₂³	1	6	yes	complemented
218	C₄×Q₈×C₆₁	C₂³	1	12	yes	complemented
219	C₄×Q₈×C₆₁	C₂³	1	6	yes	complemented
220	C₄×Q₈×C₆₁	C₂³	1	6	yes	complemented
221	C₄×Q₈×C₆₁	C₂³	1	2	yes	complemented
222	C₄×Q₈×C₆₁	C₂³	1	6	yes	complemented
223	C₄×Q₈×C₆₁	C₂³	1	6	yes	complemented
224	C₄×D₄×C₆₁	C₂³	1	12	yes	—
225	C₄×D₄×C₆₁	C₂³	1	12	yes	—
226	C₄×D₄×C₆₁	C₂³	1	12	yes	—
227	C₄×D₄×C₆₁	C₂³	1	6	yes	—
228	C₄×D₄×C₆₁	C₂³	1	6	yes	—
229	C₄×D₄×C₆₁	C₂³	1	12	yes	—
230	C₄×D₄×C₆₁	C₂³	1	12	yes	—
231	C₄×D₄×C₆₁	C₂³	1	12	yes	—
232	C₄×D₄×C₆₁	C₂³	1	12	yes	—
233	C₄×D₄×C₆₁	C₂³	1	6	yes	—
234	C₄×D₄×C₆₁	C₂³	1	6	yes	—
235	C₄×D₄×C₆₁	C₂³	1	12	yes	—
236	C₄×D₄×C₆₁	C₂³	1	6	yes	complemented
237	C₄×D₄×C₆₁	C₂³	1	6	yes	complemented
238	C₄×D₄×C₆₁	C₂³	1	6	yes	complemented
239	#117×C₆₁	C₂³	1	12	yes	—
240	#117×C₆₁	C₂³	1	12	yes	—
241	#117×C₆₁	C₂³	1	6	yes	—
242	#117×C₆₁	C₂³	1	6	yes	—
243	#117×C₆₁	C₂³	1	6	yes	—
244	#117×C₆₁	C₂³	1	6	yes	—
245	#117×C₆₁	C₂³	1	12	yes	—
246	#117×C₆₁	C₂³	1	6	yes	—
247	#117×C₆₁	C₂³	1	6	yes	—
248	#117×C₆₁	C₂³	1	12	yes	complemented
249	#117×C₆₁	C₂³	1	12	yes	complemented
250	#117×C₆₁	C₂³	1	6	yes	complemented
251	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
252	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
253	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
254	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
255	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
256	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
257	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
258	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
259	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
260	C₂×C₄⋊C₄×C₆₁	C₂³	1	3	yes	—
261	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	complemented
262	C₂×C₄⋊C₄×C₆₁	C₂³	1	12	yes	complemented
263	C₂×C₂²⋊C₄×C₆₁	C₂³	1	3	yes	—
264	C₂×C₂²⋊C₄×C₆₁	C₂³	1	3	yes	—
265	C₂×C₂²⋊C₄×C₆₁	C₂³	1	3	yes	—
266	C₂×C₂²⋊C₄×C₆₁	C₂³	1	3	yes	—
267	C₂×C₂²⋊C₄×C₆₁	C₂³	1	3	yes	—
268	C₂×C₂²⋊C₄×C₆₁	C₂³	1	3	yes	—
269	C₂×C₂²⋊C₄×C₆₁	C₂³	1	12	yes	—
270	C₂×C₂²⋊C₄×C₆₁	C₂³	1	12	yes	—
271	C₂×C₂²⋊C₄×C₆₁	C₂³	1	12	yes	—
272	C₂×C₂²⋊C₄×C₆₁	C₂³	1	3	yes	—
273	C₂×C₂²⋊C₄×C₆₁	C₂³	1	3	yes	—
274	C₂×C₂²⋊C₄×C₆₁	C₂³	1	3	yes	—
275	C₂×C₂²⋊C₄×C₆₁	C₂³	1	3	yes	—
276	C₂×C₂²⋊C₄×C₆₁	C₂³	1	3	yes	—
277	C₂×C₂²⋊C₄×C₆₁	C₂³	1	3	yes	—
278	C₂×C₂²⋊C₄×C₆₁	C₂³	1	3	yes	—
279	C₂×C₂²⋊C₄×C₆₁	C₂³	1	3	yes	—
280	C₂×C₄²×C₆₁	C₂³	1	3	yes	—
281	C₂×C₄²×C₆₁	C₂³	1	3	yes	—
282	C₂×C₄²×C₆₁	C₂³	1	3	yes	—
283	C₂⁴×C₆₁	—	2	4	no	—
284	C₂⁴×C₆₁	—	4	2	no	—
285	C₂⁴×C₆₁	—	8	1	no	—
286	C₂⁴×C₆₁	C₂⁴	1	3	yes	—
287	C₂⁴×C₆₁	C₂⁴	1	3	yes	—
288	C₂⁴×C₆₁	C₂⁴	1	3	yes	—
289	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
290	#41×C₆₁	—	4	12	no	—
291	#41×C₆₁	—	8	6	no	—
292	#41×C₆₁	—	8	2	no	—
293	C₂×Q₈×C₆₁	—	4	4	no	—
294	C₂×Q₈×C₆₁	—	8	2	no	—
295	C₂×Q₈×C₆₁	—	8	3	no	—
296	C₂×Q₈×C₆₁	—	8	6	no	—
297	C₂×Q₈×C₆₁	C₂⁴	1	6	yes	—
298	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
299	C₂×Q₈×C₆₁	C₂⁴	1	6	yes	—
300	C₂×Q₈×C₆₁	C₂⁴	1	6	yes	—
301	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
302	C₂×Q₈×C₆₁	C₂⁴	1	12	yes	—
303	C₂×Q₈×C₆₁	C₂⁴	1	6	yes	—
304	C₂×D₄×C₆₁	—	2	12	no	—
305	C₂×D₄×C₆₁	—	4	6	no	—
306	C₂×D₄×C₆₁	—	8	3	no	—
307	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
308	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
309	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
310	C₂×D₄×C₆₁	C₂⁴	1	12	yes	—
311	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
312	C₂×D₄×C₆₁	C₂⁴	1	6	yes	—
313	C₂²×C₄×C₆₁	—	2	4	no	—
314	C₂²×C₄×C₆₁	—	4	6	no	—
315	C₂²×C₄×C₆₁	—	8	1	no	—
316	C₂²×C₄×C₆₁	—	8	3	no	—
317	C₂²×C₄×C₆₁	—	8	3	no	—
318	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
319	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
320	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
321	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
322	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
323	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
324	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
325	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
326	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
327	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
328	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
329	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
330	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
331	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
332	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
333	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
334	C₂²×C₄×C₆₁	C₂⁴	1	12	yes	—
335	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
336	C₂²×C₄×C₆₁	C₂⁴	1	6	yes	—
337	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
338	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
339	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
340	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
341	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
342	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
343	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
344	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
345	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
346	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
347	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
348	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
349	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
350	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
351	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
352	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
353	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
354	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
355	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
356	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
357	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
358	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
359	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
360	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
361	C₄⋊C₄×C₆₁	C₂⁴	1	12	yes	—
362	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
363	C₂²⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
364	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
365	C₂²⋊C₄×C₆₁	C₂⁴	1	3	yes	—
366	C₂²⋊C₄×C₆₁	C₂⁴	1	3	yes	—
367	C₂²⋊C₄×C₆₁	C₂⁴	1	3	yes	—
368	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
369	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
370	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
371	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
372	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
373	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
374	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
375	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
376	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
377	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
378	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
379	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
380	C₂²⋊C₄×C₆₁	C₂⁴	1	6	yes	—
381	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
382	C₂²⋊C₄×C₆₁	C₂⁴	1	12	yes	—
383	C₄²×C₆₁	C₂⁴	1	6	yes	—
384	C₄²×C₆₁	C₂⁴	1	6	yes	—
385	C₄²×C₆₁	C₂⁴	1	6	yes	—
386	C₄²×C₆₁	C₂⁴	1	6	yes	—
387	C₄²×C₆₁	C₂⁴	1	6	yes	—
388	C₄²×C₆₁	C₂⁴	1	6	yes	—
389	C₄²×C₆₁	C₂⁴	1	12	yes	—
390	C₄²×C₆₁	C₂⁴	1	12	yes	—
391	C₂³×C₆₁	—	2	6	no	—
392	C₂³×C₆₁	—	2	6	no	—
393	C₂³×C₆₁	—	2	6	no	—
394	C₂³×C₆₁	—	2	6	no	—
395	C₂³×C₆₁	—	4	3	no	—
396	C₂³×C₆₁	—	4	1	no	—
397	C₂³×C₆₁	—	4	1	no	—
398	C₂³×C₆₁	—	4	3	no	—
399	C₂³×C₆₁	—	4	3	no	—
400	C₂³×C₆₁	—	4	3	no	—
401	C₂³×C₆₁	—	4	3	no	—
402	C₂³×C₆₁	—	8	8	no	—
403	C₂³×C₆₁	2₋¹⁺⁴	1	4	yes	—
404	C₂³×C₆₁	C₂⁵	1	3	yes	—
405	C₂³×C₆₁	C₂⁵	1	6	yes	—
406	C₂³×C₆₁	C₂⁵	1	3	yes	—
407	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
408	Q₈×C₆₁	—	4	6	no	—
409	Q₈×C₆₁	—	4	2	no	—
410	Q₈×C₆₁	—	4	6	no	—
411	Q₈×C₆₁	—	4	12	no	—
412	Q₈×C₆₁	—	4	2	no	—
413	Q₈×C₆₁	—	4	6	no	—
414	Q₈×C₆₁	—	4	6	no	—
415	D₄×C₆₁	—	2	24	no	—
416	D₄×C₆₁	—	2	12	no	—
417	D₄×C₆₁	—	4	6	no	—
418	D₄×C₆₁	—	4	12	no	—
419	D₄×C₆₁	—	4	6	no	—
420	D₄×C₆₁	—	4	6	no	—
421	C₂×C₄×C₆₁	—	2	6	no	—
422	C₂×C₄×C₆₁	—	2	6	no	—
423	C₂×C₄×C₆₁	—	2	6	no	—
424	C₂×C₄×C₆₁	—	2	12	no	—
425	C₂×C₄×C₆₁	—	4	3	no	—
426	C₂×C₄×C₆₁	—	4	6	no	—
427	C₂×C₄×C₆₁	—	4	3	no	—
428	C₂×C₄×C₆₁	—	4	3	no	—
429	C₂×C₄×C₆₁	—	4	3	no	—
430	C₂×C₄×C₆₁	—	4	6	no	—
431	C₂×C₄×C₆₁	—	4	6	no	—
432	C₂×C₄×C₆₁	—	4	3	no	—
433	C₂×C₄×C₆₁	—	4	3	no	—
434	C₂×C₄×C₆₁	—	4	6	no	—
435	C₂×C₄×C₆₁	—	4	6	no	—
436	C₂×C₄×C₆₁	—	4	3	no	—
437	C₂×C₄×C₆₁	—	4	3	no	—
438	C₂×C₄×C₆₁	—	4	12	no	—
439	C₂×C₄×C₆₁	—	4	12	no	—
440	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
441	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
442	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
443	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
444	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
445	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
446	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
447	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
448	C₂×C₄×C₆₁	C₂⁵	1	3	yes	—
449	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
450	C₂×C₄×C₆₁	C₂⁵	1	6	yes	—
451	#62903	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
452	C₂²×C₆₁	—	2	1	no	—
453	C₂²×C₆₁	—	2	3	no	—
454	C₂²×C₆₁	—	2	1	no	—
455	C₂²×C₆₁	—	2	3	no	—
456	C₂²×C₆₁	—	2	6	no	—
457	C₂²×C₆₁	—	2	3	no	—
458	C₂²×C₆₁	—	2	6	no	—
459	C₂²×C₆₁	—	2	3	no	—
460	C₂²×C₆₁	—	2	6	no	—
461	C₂²×C₆₁	—	2	3	no	—
462	C₂²×C₆₁	—	4	4	no	—
463	C₂²×C₆₁	—	4	12	no	—
464	C₂²×C₆₁	—	8	6	no	—
465	C₂²×C₆₁	—	8	6	no	—
466	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	6	yes	—
467	C₂²×C₆₁	#585	1	2	yes	—
468	C₂²×C₆₁	C₂⁶	1	1	yes	characteristic
469	C₄×C₆₁	—	2	1	no	—
470	C₄×C₆₁	—	2	3	no	—
471	C₄×C₆₁	—	2	6	no	—
472	C₄×C₆₁	—	2	6	no	—
473	C₄×C₆₁	—	2	6	no	—
474	C₄×C₆₁	—	2	6	no	—
475	C₄×C₆₁	—	2	1	no	—
476	C₄×C₆₁	—	2	6	no	—
477	C₄×C₆₁	—	2	3	no	—
478	C₄×C₆₁	—	2	6	no	—
479	C₄×C₆₁	—	2	6	no	—
480	#3564	C₂×C₆₁	1	6	yes	complemented
481	#3564	C₂×C₆₁	1	6	yes	complemented
482	#3561	C₂×C₆₁	1	6	yes	complemented
483	#3538	C₂×C₆₁	1	6	yes	complemented
484	#3535	C₂×C₆₁	1	6	yes	complemented
485	#3535	C₂×C₆₁	1	6	yes	complemented
486	#3520	C₂×C₆₁	1	6	yes	complemented
487	#3501	C₂×C₆₁	1	3	yes	complemented
488	#3495	C₂×C₆₁	1	6	yes	complemented
489	#3491	C₂×C₆₁	1	3	yes	complemented
490	#3490	C₂×C₆₁	1	3	yes	complemented
491	C₂×#551	C₂×C₆₁	1	3	yes	complemented
492	#3459	C₂×C₆₁	1	1	yes	characteristic, complemented
493	#3458	C₂×C₆₁	1	1	yes	characteristic, complemented
494	C₂×#543	C₂×C₆₁	1	1	yes	characteristic, complemented
495	C₂×C₆₁	—	2	2	no	—
496	C₂×C₆₁	—	2	6	no	—
497	C₂×C₆₁	—	4	3	no	—
498	C₂×C₆₁	—	4	6	no	—
499	C₂×C₆₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
500	C₂×C₆₁	C₂×#585	1	1	yes	characteristic
501	C₂×C₆₁	H(7,𝔽₂)	1	1	yes	characteristic
502	#563	C₂²×C₆₁	1	12	yes	complemented
503	#563	C₂²×C₆₁	1	12	yes	complemented
504	#563	C₂²×C₆₁	1	12	yes	complemented
505	#562	C₂²×C₆₁	1	12	yes	complemented
506	#556	C₂²×C₆₁	1	12	yes	complemented
507	#556	C₂²×C₆₁	1	6	yes	complemented
508	#554	C₂²×C₆₁	1	12	yes	complemented
509	#554	C₂²×C₆₁	1	12	yes	complemented
510	#554	C₂²×C₆₁	1	12	yes	complemented
511	#552	C₂²×C₆₁	1	12	yes	complemented
512	#552	C₂²×C₆₁	1	12	yes	complemented
513	#552	C₂²×C₆₁	1	6	yes	complemented
514	#552	C₂²×C₆₁	1	12	yes	complemented
515	#552	C₂²×C₆₁	1	12	yes	complemented
516	#552	C₂²×C₆₁	1	6	yes	complemented
517	#551	C₂²×C₆₁	1	12	yes	complemented
518	#551	C₂²×C₆₁	1	12	yes	complemented
519	#551	C₂²×C₆₁	1	12	yes	complemented
520	#551	C₂²×C₆₁	1	12	yes	complemented
521	#551	C₂²×C₆₁	1	12	yes	complemented
522	#551	C₂²×C₆₁	1	12	yes	complemented
523	#551	C₂²×C₆₁	1	12	yes	complemented
524	#551	C₂²×C₆₁	1	12	yes	complemented
525	D₄×Q₈	C₂²×C₆₁	1	12	yes	complemented
526	D₄×Q₈	C₂²×C₆₁	1	6	yes	complemented
527	#548	C₂²×C₆₁	1	2	yes	complemented
528	#548	C₂²×C₆₁	1	6	yes	complemented
529	#547	C₂²×C₆₁	1	6	yes	complemented
530	#547	C₂²×C₆₁	1	6	yes	complemented
531	#546	C₂²×C₆₁	1	12	yes	complemented
532	#546	C₂²×C₆₁	1	12	yes	complemented
533	#544	C₂²×C₆₁	1	6	yes	complemented
534	#544	C₂²×C₆₁	1	6	yes	complemented
535	#544	C₂²×C₆₁	1	6	yes	complemented
536	#544	C₂²×C₆₁	1	6	yes	complemented
537	#543	C₂²×C₆₁	1	1	yes	characteristic
538	#543	C₂²×C₆₁	1	3	yes	—
539	#543	C₂²×C₆₁	1	3	yes	—
540	#543	C₂²×C₆₁	1	6	yes	complemented
541	#543	C₂²×C₆₁	1	6	yes	complemented
542	#543	C₂²×C₆₁	1	6	yes	complemented
543	#542	C₂²×C₆₁	1	6	yes	complemented
544	#542	C₂²×C₆₁	1	6	yes	complemented
545	#542	C₂²×C₆₁	1	12	yes	complemented
546	#542	C₂²×C₆₁	1	12	yes	complemented
547	#541	C₂²×C₆₁	1	6	yes	complemented
548	#541	C₂²×C₆₁	1	6	yes	complemented
549	#541	C₂²×C₆₁	1	12	yes	complemented
550	#539	C₂²×C₆₁	1	6	yes	complemented
551	#539	C₂²×C₆₁	1	6	yes	complemented
552	#539	C₂²×C₆₁	1	6	yes	complemented
553	#539	C₂²×C₆₁	1	12	yes	complemented
554	#539	C₂²×C₆₁	1	12	yes	complemented
555	#539	C₂²×C₆₁	1	12	yes	complemented
556	#538	C₂²×C₆₁	1	6	yes	—
557	#538	C₂²×C₆₁	1	6	yes	—
558	#538	C₂²×C₆₁	1	6	yes	complemented
559	#536	C₂²×C₆₁	1	6	yes	complemented
560	#536	C₂²×C₆₁	1	12	yes	complemented
561	#534	C₂²×C₆₁	1	3	yes	—
562	#533	C₂²×C₆₁	1	6	yes	complemented
563	#533	C₂²×C₆₁	1	6	yes	complemented
564	#533	C₂²×C₆₁	1	6	yes	complemented
565	#529	C₂²×C₆₁	1	6	yes	complemented
566	#529	C₂²×C₆₁	1	6	yes	complemented
567	#529	C₂²×C₆₁	1	6	yes	complemented
568	C₂×#126	C₂²×C₆₁	1	3	yes	complemented
569	C₂×#126	C₂²×C₆₁	1	3	yes	complemented
570	C₂×#124	C₂²×C₆₁	1	3	yes	complemented
571	#525	C₂²×C₆₁	1	6	yes	—
572	#525	C₂²×C₆₁	1	6	yes	—
573	#525	C₂²×C₆₁	1	6	yes	complemented
574	C₂×#123	C₂²×C₆₁	1	3	yes	—
575	C₂×#123	C₂²×C₆₁	1	3	yes	complemented
576	C₂×#123	C₂²×C₆₁	1	3	yes	complemented
577	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	3	yes	—
578	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	6	yes	complemented
579	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	6	yes	complemented
580	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	3	yes	complemented
581	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	6	yes	complemented
582	C₂×#120	C₂²×C₆₁	1	3	yes	—
583	#520	C₂²×C₆₁	1	6	yes	complemented
584	#519	C₂²×C₆₁	1	2	yes	complemented
585	#518	C₂²×C₆₁	1	6	yes	—
586	C₂×C₄×D₄	C₂²×C₆₁	1	3	yes	—
587	C₂×C₄×D₄	C₂²×C₆₁	1	3	yes	complemented
588	C₂×#117	C₂²×C₆₁	1	3	yes	—
589	C₂×#117	C₂²×C₆₁	1	3	yes	complemented
590	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	3	yes	—
591	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
592	C₆₁	#62903	1	1	yes	characteristic, direct product factor, Sylow
593	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
594	C₂×#41	C₂³×C₆₁	1	6	yes	—
595	C₂×#41	C₂³×C₆₁	1	6	yes	—
596	C₂×#41	C₂³×C₆₁	1	2	yes	complemented
597	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
598	C₂²×Q₈	C₂³×C₆₁	1	3	yes	—
599	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
600	C₂²×Q₈	C₂³×C₆₁	1	6	yes	complemented
601	C₂²×D₄	C₂³×C₆₁	1	3	yes	—
602	C₂²×D₄	C₂³×C₆₁	1	3	yes	—
603	C₂²×D₄	C₂³×C₆₁	1	3	yes	—
604	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
605	C₂³×C₄	C₂³×C₆₁	1	3	yes	—
606	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
607	C₂³×C₄	C₂³×C₆₁	1	3	yes	—
608	C₂³×C₄	C₂³×C₆₁	1	3	yes	—
609	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	complemented
610	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	complemented
611	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	complemented
612	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	complemented
613	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	complemented
614	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	complemented
615	C₄⋊Q₈	C₂³×C₆₁	1	12	yes	complemented
616	C₄⋊Q₈	C₂³×C₆₁	1	12	yes	complemented
617	#126	C₂³×C₆₁	1	12	yes	—
618	#126	C₂³×C₆₁	1	12	yes	—
619	#126	C₂³×C₆₁	1	12	yes	—
620	#126	C₂³×C₆₁	1	12	yes	—
621	#126	C₂³×C₆₁	1	12	yes	—
622	#126	C₂³×C₆₁	1	12	yes	—
623	#126	C₂³×C₆₁	1	12	yes	complemented
624	#126	C₂³×C₆₁	1	12	yes	complemented
625	#126	C₂³×C₆₁	1	12	yes	complemented
626	#126	C₂³×C₆₁	1	12	yes	complemented
627	#126	C₂³×C₆₁	1	12	yes	complemented
628	#125	C₂³×C₆₁	1	6	yes	complemented
629	#125	C₂³×C₆₁	1	6	yes	complemented
630	#125	C₂³×C₆₁	1	6	yes	complemented
631	#125	C₂³×C₆₁	1	12	yes	complemented
632	#125	C₂³×C₆₁	1	12	yes	complemented
633	#125	C₂³×C₆₁	1	12	yes	complemented
634	#125	C₂³×C₆₁	1	12	yes	complemented
635	#125	C₂³×C₆₁	1	12	yes	complemented
636	#125	C₂³×C₆₁	1	12	yes	complemented
637	#125	C₂³×C₆₁	1	12	yes	complemented
638	#124	C₂³×C₆₁	1	12	yes	—
639	#124	C₂³×C₆₁	1	12	yes	—
640	#124	C₂³×C₆₁	1	12	yes	—
641	#124	C₂³×C₆₁	1	12	yes	—
642	#124	C₂³×C₆₁	1	6	yes	complemented
643	#124	C₂³×C₆₁	1	6	yes	complemented
644	#124	C₂³×C₆₁	1	6	yes	complemented
645	#123	C₂³×C₆₁	1	12	yes	—
646	#123	C₂³×C₆₁	1	12	yes	—
647	#123	C₂³×C₆₁	1	12	yes	—
648	#123	C₂³×C₆₁	1	12	yes	—
649	#123	C₂³×C₆₁	1	12	yes	—
650	#123	C₂³×C₆₁	1	12	yes	—
651	#123	C₂³×C₆₁	1	12	yes	—
652	#123	C₂³×C₆₁	1	12	yes	—
653	#123	C₂³×C₆₁	1	12	yes	—
654	#123	C₂³×C₆₁	1	12	yes	—
655	#123	C₂³×C₆₁	1	12	yes	—
656	#123	C₂³×C₆₁	1	12	yes	complemented
657	#123	C₂³×C₆₁	1	12	yes	complemented
658	#123	C₂³×C₆₁	1	12	yes	complemented
659	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
660	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
661	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
662	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
663	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
664	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
665	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
666	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
667	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
668	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
669	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
670	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
671	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
672	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
673	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
674	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
675	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
676	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
677	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
678	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
679	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
680	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	—
681	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	complemented
682	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	complemented
683	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	complemented
684	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	complemented
685	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	complemented
686	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	complemented
687	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	complemented
688	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	complemented
689	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	complemented
690	C₂²⋊Q₈	C₂³×C₆₁	1	12	yes	complemented
691	#121	C₂³×C₆₁	1	6	yes	—
692	#121	C₂³×C₆₁	1	6	yes	—
693	#121	C₂³×C₆₁	1	6	yes	—
694	#121	C₂³×C₆₁	1	6	yes	—
695	#121	C₂³×C₆₁	1	12	yes	—
696	#121	C₂³×C₆₁	1	12	yes	—
697	#121	C₂³×C₆₁	1	6	yes	complemented
698	#120	C₂³×C₆₁	1	12	yes	—
699	#120	C₂³×C₆₁	1	12	yes	—
700	#120	C₂³×C₆₁	1	12	yes	—
701	C₄×Q₈	C₂³×C₆₁	1	2	yes	complemented
702	C₄×Q₈	C₂³×C₆₁	1	6	yes	complemented
703	C₄×Q₈	C₂³×C₆₁	1	2	yes	complemented
704	C₄×Q₈	C₂³×C₆₁	1	6	yes	complemented
705	C₄×Q₈	C₂³×C₆₁	1	6	yes	complemented
706	C₄×Q₈	C₂³×C₆₁	1	6	yes	complemented
707	C₄×Q₈	C₂³×C₆₁	1	6	yes	complemented
708	C₄×Q₈	C₂³×C₆₁	1	2	yes	complemented
709	C₄×Q₈	C₂³×C₆₁	1	6	yes	complemented
710	C₄×Q₈	C₂³×C₆₁	1	12	yes	complemented
711	C₄×D₄	C₂³×C₆₁	1	12	yes	—
712	C₄×D₄	C₂³×C₆₁	1	12	yes	—
713	C₄×D₄	C₂³×C₆₁	1	6	yes	—
714	C₄×D₄	C₂³×C₆₁	1	6	yes	—
715	C₄×D₄	C₂³×C₆₁	1	6	yes	—
716	C₄×D₄	C₂³×C₆₁	1	6	yes	—
717	C₄×D₄	C₂³×C₆₁	1	12	yes	—
718	C₄×D₄	C₂³×C₆₁	1	12	yes	—
719	C₄×D₄	C₂³×C₆₁	1	12	yes	—
720	C₄×D₄	C₂³×C₆₁	1	12	yes	—
721	C₄×D₄	C₂³×C₆₁	1	12	yes	—
722	C₄×D₄	C₂³×C₆₁	1	12	yes	—
723	C₄×D₄	C₂³×C₆₁	1	6	yes	complemented
724	C₄×D₄	C₂³×C₆₁	1	6	yes	complemented
725	C₄×D₄	C₂³×C₆₁	1	6	yes	complemented
726	#117	C₂³×C₆₁	1	12	yes	—
727	#117	C₂³×C₆₁	1	12	yes	—
728	#117	C₂³×C₆₁	1	6	yes	—
729	#117	C₂³×C₆₁	1	6	yes	—
730	#117	C₂³×C₆₁	1	6	yes	—
731	#117	C₂³×C₆₁	1	6	yes	—
732	#117	C₂³×C₆₁	1	12	yes	—
733	#117	C₂³×C₆₁	1	6	yes	—
734	#117	C₂³×C₆₁	1	6	yes	—
735	#117	C₂³×C₆₁	1	12	yes	complemented
736	#117	C₂³×C₆₁	1	6	yes	complemented
737	#117	C₂³×C₆₁	1	12	yes	complemented
738	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
739	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
740	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
741	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
742	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
743	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
744	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
745	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
746	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
747	C₂×C₄⋊C₄	C₂³×C₆₁	1	3	yes	—
748	C₂×C₄⋊C₄	C₂³×C₆₁	1	12	yes	complemented
749	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	complemented
750	C₂×C₂²⋊C₄	C₂³×C₆₁	1	3	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₆₁	1	3	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₆₁	1	3	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₆₁	1	12	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₆₁	1	3	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₆₁	1	3	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₆₁	1	3	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₆₁	1	3	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₆₁	1	3	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₆₁	1	12	yes	—
760	C₂×C₂²⋊C₄	C₂³×C₆₁	1	3	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₆₁	1	3	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₆₁	1	3	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₆₁	1	3	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₆₁	1	12	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₆₁	1	3	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₆₁	1	3	yes	—
767	C₂×C₄²	C₂³×C₆₁	1	3	yes	—
768	C₂×C₄²	C₂³×C₆₁	1	3	yes	—
769	C₂×C₄²	C₂³×C₆₁	1	3	yes	—
770	C₂⁴	—	2	4	no	—
771	C₂⁴	—	4	2	no	—
772	C₂⁴	—	8	1	no	—
773	C₂⁴	C₂⁴×C₆₁	1	3	yes	—
774	C₂⁴	C₂⁴×C₆₁	1	3	yes	—
775	C₂⁴	C₂⁴×C₆₁	1	3	yes	—
776	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
777	#41	—	4	12	no	—
778	#41	—	8	6	no	—
779	#41	—	8	2	no	—
780	C₂×Q₈	—	4	4	no	—
781	C₂×Q₈	—	8	2	no	—
782	C₂×Q₈	—	8	3	no	—
783	C₂×Q₈	—	8	6	no	—
784	C₂×Q₈	C₂⁴×C₆₁	1	6	yes	—
785	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
786	C₂×Q₈	C₂⁴×C₆₁	1	6	yes	—
787	C₂×Q₈	C₂⁴×C₆₁	1	6	yes	—
788	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
789	C₂×Q₈	C₂⁴×C₆₁	1	12	yes	—
790	C₂×Q₈	C₂⁴×C₆₁	1	6	yes	—
791	C₂×D₄	—	2	12	no	—
792	C₂×D₄	—	4	6	no	—
793	C₂×D₄	—	8	3	no	—
794	C₂×D₄	C₂⁴×C₆₁	1	12	yes	—
795	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
796	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
797	C₂×D₄	C₂⁴×C₆₁	1	12	yes	—
798	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
799	C₂×D₄	C₂⁴×C₆₁	1	6	yes	—
800	C₂²×C₄	—	2	4	no	—
801	C₂²×C₄	—	4	6	no	—
802	C₂²×C₄	—	8	1	no	—
803	C₂²×C₄	—	8	3	no	—
804	C₂²×C₄	—	8	3	no	—
805	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
806	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
807	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
808	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
809	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
810	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
811	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
812	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
813	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
814	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
815	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
816	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
817	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
818	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
819	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
820	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
821	C₂²×C₄	C₂⁴×C₆₁	1	12	yes	—
822	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
823	C₂²×C₄	C₂⁴×C₆₁	1	6	yes	—
824	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
825	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
826	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
827	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
828	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
829	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
830	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
831	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
832	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
833	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
834	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
835	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
836	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
837	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
838	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
839	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
840	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
841	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
842	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
843	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
844	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
845	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
846	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
847	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
848	C₄⋊C₄	C₂⁴×C₆₁	1	12	yes	—
849	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
850	C₂²⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
851	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
852	C₂²⋊C₄	C₂⁴×C₆₁	1	3	yes	—
853	C₂²⋊C₄	C₂⁴×C₆₁	1	3	yes	—
854	C₂²⋊C₄	C₂⁴×C₆₁	1	3	yes	—
855	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
856	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
857	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
858	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
859	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
860	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
861	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
862	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
863	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
864	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
865	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
866	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
867	C₂²⋊C₄	C₂⁴×C₆₁	1	6	yes	—
868	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
869	C₂²⋊C₄	C₂⁴×C₆₁	1	12	yes	—
870	C₄²	C₂⁴×C₆₁	1	6	yes	—
871	C₄²	C₂⁴×C₆₁	1	6	yes	—
872	C₄²	C₂⁴×C₆₁	1	6	yes	—
873	C₄²	C₂⁴×C₆₁	1	6	yes	—
874	C₄²	C₂⁴×C₆₁	1	6	yes	—
875	C₄²	C₂⁴×C₆₁	1	6	yes	—
876	C₄²	C₂⁴×C₆₁	1	12	yes	—
877	C₄²	C₂⁴×C₆₁	1	12	yes	—
878	C₂³	—	2	6	no	—
879	C₂³	—	2	6	no	—
880	C₂³	—	2	6	no	—
881	C₂³	—	2	6	no	—
882	C₂³	—	4	3	no	—
883	C₂³	—	4	1	no	—
884	C₂³	—	4	1	no	—
885	C₂³	—	4	3	no	—
886	C₂³	—	4	3	no	—
887	C₂³	—	4	3	no	—
888	C₂³	—	4	3	no	—
889	C₂³	—	8	8	no	—
890	C₂³	2₋¹⁺⁴×C₆₁	1	4	yes	—
891	C₂³	C₂⁵×C₆₁	1	3	yes	—
892	C₂³	C₂⁵×C₆₁	1	6	yes	—
893	C₂³	C₂⁵×C₆₁	1	3	yes	—
894	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
895	Q₈	—	4	6	no	—
896	Q₈	—	4	2	no	—
897	Q₈	—	4	6	no	—
898	Q₈	—	4	12	no	—
899	Q₈	—	4	2	no	—
900	Q₈	—	4	6	no	—
901	Q₈	—	4	6	no	—
902	D₄	—	2	24	no	—
903	D₄	—	2	12	no	—
904	D₄	—	4	6	no	—
905	D₄	—	4	12	no	—
906	D₄	—	4	6	no	—
907	D₄	—	4	6	no	—
908	C₂×C₄	—	2	6	no	—
909	C₂×C₄	—	2	6	no	—
910	C₂×C₄	—	2	6	no	—
911	C₂×C₄	—	2	12	no	—
912	C₂×C₄	—	4	3	no	—
913	C₂×C₄	—	4	6	no	—
914	C₂×C₄	—	4	3	no	—
915	C₂×C₄	—	4	3	no	—
916	C₂×C₄	—	4	3	no	—
917	C₂×C₄	—	4	6	no	—
918	C₂×C₄	—	4	6	no	—
919	C₂×C₄	—	4	3	no	—
920	C₂×C₄	—	4	3	no	—
921	C₂×C₄	—	4	6	no	—
922	C₂×C₄	—	4	6	no	—
923	C₂×C₄	—	4	3	no	—
924	C₂×C₄	—	4	3	no	—
925	C₂×C₄	—	4	12	no	—
926	C₂×C₄	—	4	12	no	—
927	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
928	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
929	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
930	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
931	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
932	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
933	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
934	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
935	C₂×C₄	C₂⁵×C₆₁	1	3	yes	—
936	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
937	C₂×C₄	C₂⁵×C₆₁	1	6	yes	—
938	C₂²	—	2	1	no	—
939	C₂²	—	2	3	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	3	no	—
942	C₂²	—	2	6	no	—
943	C₂²	—	2	3	no	—
944	C₂²	—	2	6	no	—
945	C₂²	—	2	3	no	—
946	C₂²	—	2	6	no	—
947	C₂²	—	2	3	no	—
948	C₂²	—	4	4	no	—
949	C₂²	—	4	12	no	—
950	C₂²	—	8	6	no	—
951	C₂²	—	8	6	no	—
952	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	6	yes	—
953	C₂²	C₆₁×#585	1	2	yes	—
954	C₂²	C₂⁶×C₆₁	1	1	yes	characteristic
955	C₄	—	2	1	no	—
956	C₄	—	2	3	no	—
957	C₄	—	2	6	no	—
958	C₄	—	2	6	no	—
959	C₄	—	2	6	no	—
960	C₄	—	2	6	no	—
961	C₄	—	2	1	no	—
962	C₄	—	2	6	no	—
963	C₄	—	2	3	no	—
964	C₄	—	2	6	no	—
965	C₄	—	2	6	no	—
966	C₂	—	2	2	no	—
967	C₂	—	2	6	no	—
968	C₂	—	4	3	no	—
969	C₂	—	4	6	no	—
970	C₂	C₂²×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
971	C₂	C₂×C₆₁×#585	1	1	yes	characteristic
972	C₂	C₆₁×H(7,𝔽₂)	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×#3564	C₂	semidirect
2. C₆₁×#3564	C₂	semidirect
3. C₆₁×#3561	C₂	semidirect
4. C₆₁×#3538	C₂	semidirect
5. C₆₁×#3535	C₂	semidirect
6. C₆₁×#3535	C₂	semidirect
7. C₆₁×#3520	C₂	semidirect
8. C₆₁×#3501	C₂	semidirect
9. C₆₁×#3495	C₂	semidirect
10. C₆₁×#3491	C₂	semidirect
11. C₆₁×#3490	C₂	semidirect
12. C₂×C₆₁×#551	C₂	semidirect
13. C₆₁×#3459	C₂	semidirect
14. C₆₁×#3458	C₂	semidirect
15. C₂×C₆₁×#543	C₂	semidirect
16. C₆₁×#563	C₂²	semidirect
17. C₆₁×#563	C₂²	semidirect
18. C₆₁×#563	C₂²	semidirect
19. C₆₁×#562	C₂²	semidirect
20. C₆₁×#556	C₂²	semidirect
21. C₆₁×#556	C₂²	semidirect
22. C₆₁×#554	C₂²	semidirect
23. C₆₁×#554	C₂²	semidirect
24. C₆₁×#554	C₂²	semidirect
25. C₆₁×#552	C₂²	semidirect
26. C₆₁×#552	C₂²	semidirect
27. C₆₁×#552	C₂²	semidirect
28. C₆₁×#552	C₂²	semidirect
29. C₆₁×#552	C₂²	semidirect
30. C₆₁×#552	C₂²	semidirect
31. C₆₁×#551	C₂²	semidirect
32. C₆₁×#551	C₂²	semidirect
33. C₆₁×#551	C₂²	semidirect
34. C₆₁×#551	C₂²	semidirect
35. C₆₁×#551	C₂²	semidirect
36. C₆₁×#551	C₂²	semidirect
37. C₆₁×#551	C₂²	semidirect
38. C₆₁×#551	C₂²	semidirect
39. D₄×Q₈×C₆₁	C₂²	semidirect
40. D₄×Q₈×C₆₁	C₂²	semidirect
41. C₆₁×#548	C₂²	semidirect
42. C₆₁×#548	C₂²	semidirect
43. C₆₁×#547	C₂²	semidirect
44. C₆₁×#547	C₂²	semidirect
45. C₆₁×#546	C₂²	semidirect
46. C₆₁×#546	C₂²	semidirect
47. C₆₁×#544	C₂²	semidirect
48. C₆₁×#544	C₂²	semidirect
49. C₆₁×#544	C₂²	semidirect
50. C₆₁×#544	C₂²	semidirect
54. C₆₁×#543	C₂²	semidirect
55. C₆₁×#543	C₂²	semidirect
56. C₆₁×#543	C₂²	semidirect
57. C₆₁×#542	C₂²	semidirect
58. C₆₁×#542	C₂²	semidirect
59. C₆₁×#542	C₂²	semidirect
60. C₆₁×#542	C₂²	semidirect
61. C₆₁×#541	C₂²	semidirect
62. C₆₁×#541	C₂²	semidirect
63. C₆₁×#541	C₂²	semidirect
64. C₆₁×#539	C₂²	semidirect
65. C₆₁×#539	C₂²	semidirect
66. C₆₁×#539	C₂²	semidirect
67. C₆₁×#539	C₂²	semidirect
68. C₆₁×#539	C₂²	semidirect
69. C₆₁×#539	C₂²	semidirect
72. C₆₁×#538	C₂²	semidirect
73. C₆₁×#536	C₂²	semidirect
74. C₆₁×#536	C₂²	semidirect
76. C₆₁×#533	C₂²	semidirect
77. C₆₁×#533	C₂²	semidirect
78. C₆₁×#533	C₂²	semidirect
79. C₆₁×#529	C₂²	semidirect
80. C₆₁×#529	C₂²	semidirect
81. C₆₁×#529	C₂²	semidirect
82. C₂×#126×C₆₁	C₂²	semidirect
83. C₂×#126×C₆₁	C₂²	semidirect
84. C₂×#124×C₆₁	C₂²	semidirect
87. C₆₁×#525	C₂²	semidirect
89. C₂×#123×C₆₁	C₂²	semidirect
90. C₂×#123×C₆₁	C₂²	semidirect
92. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
93. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
94. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
95. C₂×C₂²⋊Q₈×C₆₁	C₂²	semidirect
97. C₆₁×#520	C₂²	semidirect
98. C₆₁×#519	C₂²	semidirect
101. C₂×C₄×D₄×C₆₁	C₂²	semidirect
103. C₂×#117×C₆₁	C₂²	semidirect
109. C₂×#41×C₆₁	C₂³	semidirect
113. C₂²×Q₈×C₆₁	C₂³	semidirect
122. C₄⋊Q₈×C₆₁	C₂³	semidirect
123. C₄⋊Q₈×C₆₁	C₂³	semidirect
124. C₄⋊Q₈×C₆₁	C₂³	semidirect
125. C₄⋊Q₈×C₆₁	C₂³	semidirect
126. C₄⋊Q₈×C₆₁	C₂³	semidirect
127. C₄⋊Q₈×C₆₁	C₂³	semidirect
128. C₄⋊Q₈×C₆₁	C₂³	semidirect
129. C₄⋊Q₈×C₆₁	C₂³	semidirect
136. #126×C₆₁	C₂³	semidirect
137. #126×C₆₁	C₂³	semidirect
138. #126×C₆₁	C₂³	semidirect
139. #126×C₆₁	C₂³	semidirect
140. #126×C₆₁	C₂³	semidirect
141. #125×C₆₁	C₂³	semidirect
142. #125×C₆₁	C₂³	semidirect
143. #125×C₆₁	C₂³	semidirect
144. #125×C₆₁	C₂³	semidirect
145. #125×C₆₁	C₂³	semidirect
146. #125×C₆₁	C₂³	semidirect
147. #125×C₆₁	C₂³	semidirect
148. #125×C₆₁	C₂³	semidirect
149. #125×C₆₁	C₂³	semidirect
150. #125×C₆₁	C₂³	semidirect
155. #124×C₆₁	C₂³	semidirect
156. #124×C₆₁	C₂³	semidirect
157. #124×C₆₁	C₂³	semidirect
169. #123×C₆₁	C₂³	semidirect
170. #123×C₆₁	C₂³	semidirect
171. #123×C₆₁	C₂³	semidirect
194. C₂²⋊Q₈×C₆₁	C₂³	semidirect
195. C₂²⋊Q₈×C₆₁	C₂³	semidirect
196. C₂²⋊Q₈×C₆₁	C₂³	semidirect
197. C₂²⋊Q₈×C₆₁	C₂³	semidirect
198. C₂²⋊Q₈×C₆₁	C₂³	semidirect
199. C₂²⋊Q₈×C₆₁	C₂³	semidirect
200. C₂²⋊Q₈×C₆₁	C₂³	semidirect
201. C₂²⋊Q₈×C₆₁	C₂³	semidirect
202. C₂²⋊Q₈×C₆₁	C₂³	semidirect
203. C₂²⋊Q₈×C₆₁	C₂³	semidirect
210. #121×C₆₁	C₂³	semidirect
214. C₄×Q₈×C₆₁	C₂³	semidirect
215. C₄×Q₈×C₆₁	C₂³	semidirect
216. C₄×Q₈×C₆₁	C₂³	semidirect
217. C₄×Q₈×C₆₁	C₂³	semidirect
218. C₄×Q₈×C₆₁	C₂³	semidirect
219. C₄×Q₈×C₆₁	C₂³	semidirect
220. C₄×Q₈×C₆₁	C₂³	semidirect
221. C₄×Q₈×C₆₁	C₂³	semidirect
222. C₄×Q₈×C₆₁	C₂³	semidirect
223. C₄×Q₈×C₆₁	C₂³	semidirect
236. C₄×D₄×C₆₁	C₂³	semidirect
237. C₄×D₄×C₆₁	C₂³	semidirect
238. C₄×D₄×C₆₁	C₂³	semidirect
248. #117×C₆₁	C₂³	semidirect
249. #117×C₆₁	C₂³	semidirect
250. #117×C₆₁	C₂³	semidirect
261. C₂×C₄⋊C₄×C₆₁	C₂³	semidirect
262. C₂×C₄⋊C₄×C₆₁	C₂³	semidirect
451. #62903	C₆₁	direct (N × H)
480. #3564	C₂×C₆₁	semidirect
481. #3564	C₂×C₆₁	semidirect
482. #3561	C₂×C₆₁	semidirect
483. #3538	C₂×C₆₁	semidirect
484. #3535	C₂×C₆₁	semidirect
485. #3535	C₂×C₆₁	semidirect
486. #3520	C₂×C₆₁	semidirect
487. #3501	C₂×C₆₁	semidirect
488. #3495	C₂×C₆₁	semidirect
489. #3491	C₂×C₆₁	semidirect
490. #3490	C₂×C₆₁	semidirect
491. C₂×#551	C₂×C₆₁	semidirect
492. #3459	C₂×C₆₁	semidirect
493. #3458	C₂×C₆₁	semidirect
494. C₂×#543	C₂×C₆₁	semidirect
502. #563	C₂²×C₆₁	semidirect
503. #563	C₂²×C₆₁	semidirect
504. #563	C₂²×C₆₁	semidirect
505. #562	C₂²×C₆₁	semidirect
506. #556	C₂²×C₆₁	semidirect
507. #556	C₂²×C₆₁	semidirect
508. #554	C₂²×C₆₁	semidirect
509. #554	C₂²×C₆₁	semidirect
510. #554	C₂²×C₆₁	semidirect
511. #552	C₂²×C₆₁	semidirect
512. #552	C₂²×C₆₁	semidirect
513. #552	C₂²×C₆₁	semidirect
514. #552	C₂²×C₆₁	semidirect
515. #552	C₂²×C₆₁	semidirect
516. #552	C₂²×C₆₁	semidirect
517. #551	C₂²×C₆₁	semidirect
518. #551	C₂²×C₆₁	semidirect
519. #551	C₂²×C₆₁	semidirect
520. #551	C₂²×C₆₁	semidirect
521. #551	C₂²×C₆₁	semidirect
522. #551	C₂²×C₆₁	semidirect
523. #551	C₂²×C₆₁	semidirect
524. #551	C₂²×C₆₁	semidirect
525. D₄×Q₈	C₂²×C₆₁	semidirect
526. D₄×Q₈	C₂²×C₆₁	semidirect
527. #548	C₂²×C₆₁	semidirect
528. #548	C₂²×C₆₁	semidirect
529. #547	C₂²×C₆₁	semidirect
530. #547	C₂²×C₆₁	semidirect
531. #546	C₂²×C₆₁	semidirect
532. #546	C₂²×C₆₁	semidirect
533. #544	C₂²×C₆₁	semidirect
534. #544	C₂²×C₆₁	semidirect
535. #544	C₂²×C₆₁	semidirect
536. #544	C₂²×C₆₁	semidirect
540. #543	C₂²×C₆₁	semidirect
541. #543	C₂²×C₆₁	semidirect
542. #543	C₂²×C₆₁	semidirect
543. #542	C₂²×C₆₁	semidirect
544. #542	C₂²×C₆₁	semidirect
545. #542	C₂²×C₆₁	semidirect
546. #542	C₂²×C₆₁	semidirect
547. #541	C₂²×C₆₁	semidirect
548. #541	C₂²×C₆₁	semidirect
549. #541	C₂²×C₆₁	semidirect
550. #539	C₂²×C₆₁	semidirect
551. #539	C₂²×C₆₁	semidirect
552. #539	C₂²×C₆₁	semidirect
553. #539	C₂²×C₆₁	semidirect
554. #539	C₂²×C₆₁	semidirect
555. #539	C₂²×C₆₁	semidirect
558. #538	C₂²×C₆₁	semidirect
559. #536	C₂²×C₆₁	semidirect
560. #536	C₂²×C₆₁	semidirect
562. #533	C₂²×C₆₁	semidirect
563. #533	C₂²×C₆₁	semidirect
564. #533	C₂²×C₆₁	semidirect
565. #529	C₂²×C₆₁	semidirect
566. #529	C₂²×C₆₁	semidirect
567. #529	C₂²×C₆₁	semidirect
568. C₂×#126	C₂²×C₆₁	semidirect
569. C₂×#126	C₂²×C₆₁	semidirect
570. C₂×#124	C₂²×C₆₁	semidirect
573. #525	C₂²×C₆₁	semidirect
575. C₂×#123	C₂²×C₆₁	semidirect
576. C₂×#123	C₂²×C₆₁	semidirect
578. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
579. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
580. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
581. C₂×C₂²⋊Q₈	C₂²×C₆₁	semidirect
583. #520	C₂²×C₆₁	semidirect
584. #519	C₂²×C₆₁	semidirect
587. C₂×C₄×D₄	C₂²×C₆₁	semidirect
589. C₂×#117	C₂²×C₆₁	semidirect
592. C₆₁	#62903	direct (N × H)
596. C₂×#41	C₂³×C₆₁	semidirect
600. C₂²×Q₈	C₂³×C₆₁	semidirect
609. C₄⋊Q₈	C₂³×C₆₁	semidirect
610. C₄⋊Q₈	C₂³×C₆₁	semidirect
611. C₄⋊Q₈	C₂³×C₆₁	semidirect
612. C₄⋊Q₈	C₂³×C₆₁	semidirect
613. C₄⋊Q₈	C₂³×C₆₁	semidirect
614. C₄⋊Q₈	C₂³×C₆₁	semidirect
615. C₄⋊Q₈	C₂³×C₆₁	semidirect
616. C₄⋊Q₈	C₂³×C₆₁	semidirect
623. #126	C₂³×C₆₁	semidirect
624. #126	C₂³×C₆₁	semidirect
625. #126	C₂³×C₆₁	semidirect
626. #126	C₂³×C₆₁	semidirect
627. #126	C₂³×C₆₁	semidirect
628. #125	C₂³×C₆₁	semidirect
629. #125	C₂³×C₆₁	semidirect
630. #125	C₂³×C₆₁	semidirect
631. #125	C₂³×C₆₁	semidirect
632. #125	C₂³×C₆₁	semidirect
633. #125	C₂³×C₆₁	semidirect
634. #125	C₂³×C₆₁	semidirect
635. #125	C₂³×C₆₁	semidirect
636. #125	C₂³×C₆₁	semidirect
637. #125	C₂³×C₆₁	semidirect
642. #124	C₂³×C₆₁	semidirect
643. #124	C₂³×C₆₁	semidirect
644. #124	C₂³×C₆₁	semidirect
656. #123	C₂³×C₆₁	semidirect
657. #123	C₂³×C₆₁	semidirect
658. #123	C₂³×C₆₁	semidirect
681. C₂²⋊Q₈	C₂³×C₆₁	semidirect
682. C₂²⋊Q₈	C₂³×C₆₁	semidirect
683. C₂²⋊Q₈	C₂³×C₆₁	semidirect
684. C₂²⋊Q₈	C₂³×C₆₁	semidirect
685. C₂²⋊Q₈	C₂³×C₆₁	semidirect
686. C₂²⋊Q₈	C₂³×C₆₁	semidirect
687. C₂²⋊Q₈	C₂³×C₆₁	semidirect
688. C₂²⋊Q₈	C₂³×C₆₁	semidirect
689. C₂²⋊Q₈	C₂³×C₆₁	semidirect
690. C₂²⋊Q₈	C₂³×C₆₁	semidirect
697. #121	C₂³×C₆₁	semidirect
701. C₄×Q₈	C₂³×C₆₁	semidirect
702. C₄×Q₈	C₂³×C₆₁	semidirect
703. C₄×Q₈	C₂³×C₆₁	semidirect
704. C₄×Q₈	C₂³×C₆₁	semidirect
705. C₄×Q₈	C₂³×C₆₁	semidirect
706. C₄×Q₈	C₂³×C₆₁	semidirect
707. C₄×Q₈	C₂³×C₆₁	semidirect
708. C₄×Q₈	C₂³×C₆₁	semidirect
709. C₄×Q₈	C₂³×C₆₁	semidirect
710. C₄×Q₈	C₂³×C₆₁	semidirect
723. C₄×D₄	C₂³×C₆₁	semidirect
724. C₄×D₄	C₂³×C₆₁	semidirect
725. C₄×D₄	C₂³×C₆₁	semidirect
735. #117	C₂³×C₆₁	semidirect
736. #117	C₂³×C₆₁	semidirect
737. #117	C₂³×C₆₁	semidirect
748. C₂×C₄⋊C₄	C₂³×C₆₁	semidirect
749. C₂×C₄⋊C₄	C₂³×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3564	2
C₆₁×#3561	2
C₆₁×#3538	2
C₆₁×#3535	2
C₆₁×#3520	2
C₆₁×#3501	2
C₆₁×#3495	2
C₆₁×#3491	2
C₆₁×#3490	2
C₂×C₆₁×#551	2
C₆₁×#3459	2
C₆₁×#3458	2
C₂×C₆₁×#543	2
#62903	61

Subgroups — C61×#62903 #29566336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62903 #29566336