Subgroups — C₆₁×#62962 #29566395

Order 15616.

6566 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3561	C₂	1	4	yes	maximal, complemented
2	C₆₁×#3557	C₂	1	8	yes	maximal, complemented
3	C₆₁×#3554	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3554	C₂	1	8	yes	maximal, complemented
5	C₆₁×#3550	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3535	C₂	1	8	yes	maximal, complemented
7	C₆₁×#3522	C₂	1	4	yes	maximal, complemented
8	C₆₁×#3520	C₂	1	4	yes	maximal, complemented
9	C₆₁×#3510	C₂	1	4	yes	maximal, complemented
10	C₆₁×#3508	C₂	1	2	yes	maximal, complemented
11	C₆₁×#3507	C₂	1	4	yes	maximal, complemented
12	C₆₁×#3502	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#3501	C₂	1	2	yes	maximal, complemented
14	C₂×C₆₁×#559	C₂	1	1	yes	maximal, characteristic, complemented
15	Q₈×#41×C₆₁	C₂	1	2	yes	maximal, complemented
16	C₆₁×#3461	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₁×#3460	C₂	1	2	yes	maximal, complemented
18	C₆₁×#563	C₂²	1	16	yes	complemented
19	C₆₁×#563	C₂²	1	8	yes	complemented
20	C₆₁×#562	C₂²	1	8	yes	complemented
21	C₆₁×#562	C₂²	1	16	yes	complemented
22	C₆₁×#559	C₂²	1	4	yes	—
23	C₆₁×#559	C₂²	1	4	yes	—
24	C₆₁×#559	C₂²	1	8	yes	—
25	C₆₁×#559	C₂²	1	4	yes	—
26	C₆₁×#559	C₂²	1	4	yes	—
27	C₆₁×#559	C₂²	1	8	yes	complemented
28	C₆₁×#559	C₂²	1	8	yes	complemented
29	Q₈²×C₆₁	C₂²	1	2	yes	complemented
30	Q₈²×C₆₁	C₂²	1	4	yes	complemented
31	C₆₁×#557	C₂²	1	8	yes	complemented
32	C₆₁×#557	C₂²	1	4	yes	complemented
33	C₆₁×#557	C₂²	1	4	yes	complemented
34	C₆₁×#557	C₂²	1	2	yes	complemented
35	C₆₁×#556	C₂²	1	8	yes	complemented
36	C₆₁×#556	C₂²	1	8	yes	complemented
37	C₆₁×#556	C₂²	1	8	yes	complemented
38	C₆₁×#556	C₂²	1	4	yes	complemented
39	C₆₁×#554	C₂²	1	4	yes	—
40	C₆₁×#554	C₂²	1	8	yes	—
41	C₆₁×#554	C₂²	1	4	yes	complemented
42	C₆₁×#554	C₂²	1	8	yes	complemented
43	C₆₁×#554	C₂²	1	8	yes	complemented
44	C₆₁×#554	C₂²	1	8	yes	complemented
45	C₆₁×#554	C₂²	1	2	yes	complemented
46	C₆₁×#552	C₂²	1	8	yes	complemented
47	C₆₁×#552	C₂²	1	16	yes	complemented
48	C₆₁×#551	C₂²	1	16	yes	—
49	C₆₁×#551	C₂²	1	16	yes	—
50	C₆₁×#550	C₂²	1	4	yes	—
51	C₆₁×#550	C₂²	1	4	yes	—
52	D₄×Q₈×C₆₁	C₂²	1	4	yes	—
53	D₄×Q₈×C₆₁	C₂²	1	4	yes	complemented
54	D₄×Q₈×C₆₁	C₂²	1	8	yes	complemented
55	D₄×Q₈×C₆₁	C₂²	1	2	yes	complemented
56	C₆₁×#548	C₂²	1	8	yes	complemented
57	C₆₁×#548	C₂²	1	8	yes	complemented
58	C₆₁×#547	C₂²	1	4	yes	complemented
59	C₆₁×#547	C₂²	1	16	yes	complemented
60	C₆₁×#547	C₂²	1	4	yes	complemented
61	C₆₁×#546	C₂²	1	8	yes	—
62	C₆₁×#546	C₂²	1	8	yes	—
63	C₆₁×#544	C₂²	1	2	yes	—
64	C₆₁×#544	C₂²	1	1	yes	characteristic
65	C₆₁×#544	C₂²	1	4	yes	—
66	C₆₁×#543	C₂²	1	8	yes	—
67	C₆₁×#542	C₂²	1	8	yes	complemented
68	C₆₁×#542	C₂²	1	8	yes	complemented
69	C₆₁×#542	C₂²	1	8	yes	complemented
70	C₆₁×#542	C₂²	1	8	yes	complemented
71	C₆₁×#542	C₂²	1	4	yes	complemented
72	C₆₁×#542	C₂²	1	16	yes	complemented
73	C₆₁×#542	C₂²	1	8	yes	complemented
74	C₆₁×#542	C₂²	1	16	yes	complemented
75	C₆₁×#541	C₂²	1	4	yes	complemented
76	C₆₁×#540	C₂²	1	8	yes	—
77	C₆₁×#540	C₂²	1	8	yes	complemented
78	C₆₁×#539	C₂²	1	4	yes	—
79	C₆₁×#539	C₂²	1	16	yes	complemented
80	C₆₁×#539	C₂²	1	16	yes	complemented
81	C₆₁×#539	C₂²	1	16	yes	complemented
82	C₆₁×#538	C₂²	1	8	yes	—
83	C₆₁×#537	C₂²	1	1	yes	characteristic
84	C₆₁×#536	C₂²	1	2	yes	—
85	C₆₁×#536	C₂²	1	16	yes	complemented
86	C₆₁×#536	C₂²	1	8	yes	complemented
87	C₆₁×#535	C₂²	1	4	yes	—
88	C₆₁×#533	C₂²	1	4	yes	—
89	C₆₁×#533	C₂²	1	4	yes	—
90	C₆₁×#533	C₂²	1	2	yes	—
91	C₆₁×#533	C₂²	1	4	yes	complemented
92	C₆₁×#533	C₂²	1	4	yes	complemented
93	C₆₁×#533	C₂²	1	8	yes	complemented
94	C₆₁×#532	C₂²	1	4	yes	—
95	C₆₁×#532	C₂²	1	4	yes	—
96	C₆₁×#532	C₂²	1	8	yes	complemented
97	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
98	C₆₁×#529	C₂²	1	4	yes	—
99	C₆₁×#529	C₂²	1	4	yes	complemented
100	C₆₁×#529	C₂²	1	8	yes	complemented
101	C₆₁×#529	C₂²	1	8	yes	complemented
102	C₆₁×#529	C₂²	1	8	yes	complemented
103	C₂×#124×C₆₁	C₂²	1	2	yes	—
104	C₂×#124×C₆₁	C₂²	1	2	yes	—
105	C₆₁×#525	C₂²	1	8	yes	—
106	C₂×#123×C₆₁	C₂²	1	4	yes	—
107	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	8	yes	—
108	C₆₁×#520	C₂²	1	8	yes	complemented
109	C₆₁×#519	C₂²	1	2	yes	—
110	C₆₁×#518	C₂²	1	4	yes	—
111	C₄×#41×C₆₁	C₂²	1	4	yes	—
112	C₄×#41×C₆₁	C₂²	1	2	yes	—
113	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
114	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
115	C₂×C₄×Q₈×C₆₁	C₂²	1	4	yes	complemented
116	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
117	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
118	C₂×#41×C₆₁	C₂³	1	2	yes	—
119	C₂×#41×C₆₁	C₂³	1	8	yes	—
120	C₂×#41×C₆₁	C₂³	1	8	yes	—
121	C₂×#41×C₆₁	C₂³	1	8	yes	—
122	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
124	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₆₁	C₂³	1	8	yes	—
126	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
127	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
128	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
129	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
130	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
131	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
132	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
133	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
134	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
135	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
136	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
137	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
138	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
139	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
140	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
141	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
142	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
143	C₄⋊Q₈×C₆₁	C₂³	1	16	yes	—
144	#127×C₆₁	C₂³	1	4	yes	—
145	#127×C₆₁	C₂³	1	4	yes	—
146	#127×C₆₁	C₂³	1	8	yes	—
147	#126×C₆₁	C₂³	1	16	yes	—
148	#126×C₆₁	C₂³	1	8	yes	—
149	#126×C₆₁	C₂³	1	8	yes	—
150	#126×C₆₁	C₂³	1	16	yes	—
151	#126×C₆₁	C₂³	1	16	yes	—
152	#126×C₆₁	C₂³	1	16	yes	—
153	#126×C₆₁	C₂³	1	16	yes	—
154	#125×C₆₁	C₂³	1	8	yes	—
155	#125×C₆₁	C₂³	1	4	yes	—
156	#125×C₆₁	C₂³	1	4	yes	—
157	#125×C₆₁	C₂³	1	4	yes	—
158	#125×C₆₁	C₂³	1	8	yes	—
159	#125×C₆₁	C₂³	1	8	yes	—
160	#125×C₆₁	C₂³	1	8	yes	—
161	#125×C₆₁	C₂³	1	8	yes	—
162	#125×C₆₁	C₂³	1	16	yes	—
163	#125×C₆₁	C₂³	1	8	yes	—
164	#125×C₆₁	C₂³	1	4	yes	—
165	#125×C₆₁	C₂³	1	4	yes	—
166	#124×C₆₁	C₂³	1	8	yes	—
167	#124×C₆₁	C₂³	1	8	yes	—
168	#124×C₆₁	C₂³	1	16	yes	—
169	#124×C₆₁	C₂³	1	8	yes	—
170	#124×C₆₁	C₂³	1	4	yes	—
171	#124×C₆₁	C₂³	1	16	yes	—
172	#124×C₆₁	C₂³	1	8	yes	—
173	#124×C₆₁	C₂³	1	16	yes	—
174	#124×C₆₁	C₂³	1	4	yes	—
175	#124×C₆₁	C₂³	1	8	yes	—
176	#124×C₆₁	C₂³	1	8	yes	—
177	#124×C₆₁	C₂³	1	8	yes	—
178	#123×C₆₁	C₂³	1	8	yes	—
179	#123×C₆₁	C₂³	1	16	yes	—
180	#123×C₆₁	C₂³	1	16	yes	—
181	#123×C₆₁	C₂³	1	16	yes	—
182	#123×C₆₁	C₂³	1	16	yes	—
183	#123×C₆₁	C₂³	1	16	yes	—
184	#123×C₆₁	C₂³	1	16	yes	—
185	#123×C₆₁	C₂³	1	8	yes	—
186	#123×C₆₁	C₂³	1	16	yes	—
187	#123×C₆₁	C₂³	1	16	yes	—
188	#123×C₆₁	C₂³	1	16	yes	—
189	#123×C₆₁	C₂³	1	16	yes	—
190	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
191	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
192	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
193	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
194	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
195	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
196	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
197	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
198	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
199	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
200	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
201	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
202	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
203	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
204	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
205	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
206	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
207	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
208	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
209	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
210	C₂²⋊Q₈×C₆₁	C₂³	1	4	yes	—
211	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
212	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
213	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
214	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
215	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
216	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
217	#121×C₆₁	C₂³	1	8	yes	—
218	#121×C₆₁	C₂³	1	8	yes	—
219	#121×C₆₁	C₂³	1	8	yes	—
220	#121×C₆₁	C₂³	1	8	yes	—
221	#121×C₆₁	C₂³	1	4	yes	—
222	#121×C₆₁	C₂³	1	16	yes	—
223	#121×C₆₁	C₂³	1	4	yes	—
224	#121×C₆₁	C₂³	1	16	yes	—
225	#121×C₆₁	C₂³	1	16	yes	—
226	#121×C₆₁	C₂³	1	8	yes	—
227	#120×C₆₁	C₂³	1	16	yes	—
228	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
229	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
230	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
231	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
232	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
233	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
234	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
235	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
236	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
237	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
238	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
239	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
240	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
241	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
242	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
243	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
244	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
245	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
246	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
247	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
248	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
249	C₄×D₄×C₆₁	C₂³	1	8	yes	—
250	C₄×D₄×C₆₁	C₂³	1	8	yes	—
251	C₄×D₄×C₆₁	C₂³	1	8	yes	—
252	C₄×D₄×C₆₁	C₂³	1	8	yes	—
253	C₄×D₄×C₆₁	C₂³	1	4	yes	—
254	C₄×D₄×C₆₁	C₂³	1	16	yes	—
255	C₄×D₄×C₆₁	C₂³	1	8	yes	—
256	C₄×D₄×C₆₁	C₂³	1	8	yes	—
257	C₄×D₄×C₆₁	C₂³	1	4	yes	—
258	C₄×D₄×C₆₁	C₂³	1	8	yes	—
259	C₄×D₄×C₆₁	C₂³	1	16	yes	—
260	C₄×D₄×C₆₁	C₂³	1	16	yes	—
261	C₄×D₄×C₆₁	C₂³	1	4	yes	—
262	C₄×D₄×C₆₁	C₂³	1	8	yes	—
263	C₄×D₄×C₆₁	C₂³	1	4	yes	—
264	C₄×D₄×C₆₁	C₂³	1	2	yes	—
265	C₄×D₄×C₆₁	C₂³	1	8	yes	—
266	C₄×D₄×C₆₁	C₂³	1	8	yes	—
267	C₄×D₄×C₆₁	C₂³	1	4	yes	—
268	C₄×D₄×C₆₁	C₂³	1	4	yes	—
269	C₄×D₄×C₆₁	C₂³	1	4	yes	—
270	C₄×D₄×C₆₁	C₂³	1	2	yes	—
271	C₄×D₄×C₆₁	C₂³	1	8	yes	—
272	#117×C₆₁	C₂³	1	4	yes	—
273	#117×C₆₁	C₂³	1	2	yes	—
274	#117×C₆₁	C₂³	1	8	yes	—
275	#117×C₆₁	C₂³	1	4	yes	—
276	#117×C₆₁	C₂³	1	8	yes	—
277	#117×C₆₁	C₂³	1	8	yes	—
278	#117×C₆₁	C₂³	1	16	yes	—
279	#117×C₆₁	C₂³	1	16	yes	—
280	#117×C₆₁	C₂³	1	8	yes	—
281	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
282	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
283	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
284	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
285	C₂×C₄⋊C₄×C₆₁	C₂³	1	16	yes	—
286	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
287	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
288	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
289	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
290	C₂×C₂²⋊C₄×C₆₁	C₂³	1	16	yes	—
291	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
292	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
293	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
294	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
295	C₂×C₄²×C₆₁	C₂³	1	8	yes	—
296	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
297	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
298	C₂⁴×C₆₁	C₂⁴	1	4	yes	—
299	#41×C₆₁	—	2	8	no	—
300	#41×C₆₁	—	4	16	no	—
301	#41×C₆₁	—	8	8	no	—
302	#41×C₆₁	—	8	8	no	—
303	C₂×Q₈×C₆₁	—	2	4	no	—
304	C₂×Q₈×C₆₁	—	4	2	no	—
305	C₂×Q₈×C₆₁	—	4	8	no	—
306	C₂×Q₈×C₆₁	—	8	8	no	—
307	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
308	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
309	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
310	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
311	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
312	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
313	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
314	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
315	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
316	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
317	C₂×D₄×C₆₁	—	2	8	no	—
318	C₂×D₄×C₆₁	—	4	4	no	—
319	C₂×D₄×C₆₁	—	8	2	no	—
320	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
321	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
322	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
323	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
324	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
325	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
326	C₂×D₄×C₆₁	C₂⁴	1	16	yes	—
327	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
328	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
329	C₂²×C₄×C₆₁	—	8	4	no	—
330	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
332	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
334	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
339	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
340	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
341	C₂²×C₄×C₆₁	C₂⁴	1	16	yes	—
342	C₂²×C₄×C₆₁	C₂⁴	1	16	yes	—
343	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
344	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
345	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
346	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
347	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
348	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
349	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
350	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
351	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
352	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
353	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
354	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
355	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
356	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
357	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
358	C₄⋊C₄×C₆₁	C₂⁴	1	16	yes	—
359	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
360	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
361	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
362	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
363	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
364	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
365	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
366	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
367	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
368	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
369	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
370	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
371	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
372	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
373	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
374	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
375	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
376	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
377	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
378	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
379	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
380	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
381	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
382	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
383	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
384	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
385	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
386	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
387	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
388	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
389	C₂²⋊C₄×C₆₁	C₂⁴	1	16	yes	—
390	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
391	C₂²⋊C₄×C₆₁	C₂⁴	1	4	yes	—
392	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
393	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
394	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
395	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
396	C₂²⋊C₄×C₆₁	C₂⁴	1	8	yes	—
397	C₄²×C₆₁	C₂⁴	1	4	yes	—
398	C₄²×C₆₁	C₂⁴	1	2	yes	—
399	C₄²×C₆₁	C₂⁴	1	8	yes	—
400	C₄²×C₆₁	C₂⁴	1	4	yes	—
401	C₄²×C₆₁	C₂⁴	1	4	yes	—
402	C₄²×C₆₁	C₂⁴	1	4	yes	—
403	C₄²×C₆₁	C₂⁴	1	4	yes	—
404	C₄²×C₆₁	C₂⁴	1	8	yes	—
405	C₄²×C₆₁	C₂⁴	1	2	yes	—
406	C₄²×C₆₁	C₂⁴	1	8	yes	—
407	C₄²×C₆₁	C₂⁴	1	4	yes	—
408	C₄²×C₆₁	C₂⁴	1	4	yes	—
409	C₄²×C₆₁	C₂⁴	1	16	yes	—
410	C₂³×C₆₁	—	2	8	no	—
411	C₂³×C₆₁	—	4	4	no	—
412	C₂³×C₆₁	—	4	4	no	—
413	C₂³×C₆₁	C₂⁵	1	8	yes	—
414	C₂³×C₆₁	C₂⁵	1	4	yes	—
415	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
416	Q₈×C₆₁	—	2	8	no	—
417	Q₈×C₆₁	—	2	4	no	—
418	Q₈×C₆₁	—	2	4	no	—
419	Q₈×C₆₁	—	2	8	no	—
420	Q₈×C₆₁	—	4	8	no	—
421	Q₈×C₆₁	—	4	2	no	—
422	Q₈×C₆₁	—	4	4	no	—
423	Q₈×C₆₁	—	4	8	no	—
424	Q₈×C₆₁	—	4	8	no	—
425	Q₈×C₆₁	—	4	4	no	—
426	D₄×C₆₁	—	2	8	no	—
427	D₄×C₆₁	—	2	16	no	—
428	D₄×C₆₁	—	2	4	no	—
429	D₄×C₆₁	—	2	8	no	—
430	D₄×C₆₁	—	4	4	no	—
431	D₄×C₆₁	—	4	8	no	—
432	D₄×C₆₁	—	4	16	no	—
433	D₄×C₆₁	—	4	4	no	—
434	D₄×C₆₁	—	4	16	no	—
435	C₂×C₄×C₆₁	—	2	4	no	—
436	C₂×C₄×C₆₁	—	2	8	no	—
437	C₂×C₄×C₆₁	—	2	2	no	—
438	C₂×C₄×C₆₁	—	2	8	no	—
439	C₂×C₄×C₆₁	—	4	2	no	—
440	C₂×C₄×C₆₁	—	4	2	no	—
441	C₂×C₄×C₆₁	—	4	8	no	—
442	C₂×C₄×C₆₁	—	4	8	no	—
443	C₂×C₄×C₆₁	—	4	1	no	—
444	C₂×C₄×C₆₁	—	4	8	no	—
445	C₂×C₄×C₆₁	—	4	2	no	—
446	C₂×C₄×C₆₁	—	4	16	no	—
447	C₂×C₄×C₆₁	—	4	16	no	—
448	C₂×C₄×C₆₁	—	4	8	no	—
449	C₂×C₄×C₆₁	—	4	4	no	—
450	C₂×C₄×C₆₁	2₋¹⁺⁴	1	4	yes	—
451	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
452	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
453	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
454	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
455	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
456	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
457	C₂×C₄×C₆₁	C₂⁵	1	8	yes	—
458	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
459	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
460	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
461	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
462	C₂×C₄×C₆₁	C₂⁵	1	4	yes	—
463	C₂×C₄×C₆₁	C₂⁵	1	2	yes	—
464	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
465	#62962	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
466	C₂²×C₆₁	—	2	1	no	—
467	C₂²×C₆₁	—	2	1	no	—
468	C₂²×C₆₁	—	2	4	no	—
469	C₂²×C₆₁	—	2	8	no	—
470	C₂²×C₆₁	—	2	4	no	—
471	C₂²×C₆₁	—	2	8	no	—
472	C₂²×C₆₁	—	2	8	no	—
473	C₂²×C₆₁	—	2	4	no	—
474	C₂²×C₆₁	—	8	8	no	—
475	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
476	C₂²×C₆₁	C₂⁶	1	1	yes	characteristic
477	C₄×C₆₁	—	2	4	no	—
478	C₄×C₆₁	—	2	4	no	—
479	C₄×C₆₁	—	2	4	no	—
480	C₄×C₆₁	—	2	1	no	—
481	C₄×C₆₁	—	2	8	no	—
482	C₄×C₆₁	—	2	4	no	—
483	C₄×C₆₁	—	2	2	no	—
484	C₄×C₆₁	—	2	4	no	—
485	C₄×C₆₁	—	2	2	no	—
486	C₄×C₆₁	—	2	4	no	—
487	C₄×C₆₁	—	2	2	no	—
488	C₄×C₆₁	—	2	8	no	—
489	C₄×C₆₁	C₂×2₋¹⁺⁴	1	4	yes	—
490	C₄×C₆₁	#585	1	2	yes	—
491	#3561	C₂×C₆₁	1	4	yes	complemented
492	#3557	C₂×C₆₁	1	8	yes	complemented
493	#3554	C₂×C₆₁	1	4	yes	complemented
494	#3554	C₂×C₆₁	1	8	yes	complemented
495	#3550	C₂×C₆₁	1	4	yes	complemented
496	#3535	C₂×C₆₁	1	8	yes	complemented
497	#3522	C₂×C₆₁	1	4	yes	complemented
498	#3520	C₂×C₆₁	1	4	yes	complemented
499	#3510	C₂×C₆₁	1	4	yes	complemented
500	#3508	C₂×C₆₁	1	2	yes	complemented
501	#3507	C₂×C₆₁	1	4	yes	complemented
502	#3502	C₂×C₆₁	1	1	yes	characteristic, complemented
503	#3501	C₂×C₆₁	1	2	yes	complemented
504	C₂×#559	C₂×C₆₁	1	1	yes	characteristic, complemented
505	Q₈×#41	C₂×C₆₁	1	2	yes	complemented
506	#3461	C₂×C₆₁	1	1	yes	characteristic, complemented
507	#3460	C₂×C₆₁	1	2	yes	complemented
508	C₂×C₆₁	—	2	2	no	—
509	C₂×C₆₁	—	4	4	no	—
510	C₂×C₆₁	—	4	8	no	—
511	C₂×C₆₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
512	C₂×C₆₁	C₂×#585	1	1	yes	characteristic
513	C₂×C₆₁	H(7,𝔽₂)	1	1	yes	characteristic
514	#563	C₂²×C₆₁	1	16	yes	complemented
515	#563	C₂²×C₆₁	1	8	yes	complemented
516	#562	C₂²×C₆₁	1	16	yes	complemented
517	#562	C₂²×C₆₁	1	8	yes	complemented
518	#559	C₂²×C₆₁	1	4	yes	—
519	#559	C₂²×C₆₁	1	4	yes	—
520	#559	C₂²×C₆₁	1	8	yes	—
521	#559	C₂²×C₆₁	1	4	yes	—
522	#559	C₂²×C₆₁	1	4	yes	—
523	#559	C₂²×C₆₁	1	8	yes	complemented
524	#559	C₂²×C₆₁	1	8	yes	complemented
525	Q₈²	C₂²×C₆₁	1	2	yes	complemented
526	Q₈²	C₂²×C₆₁	1	4	yes	complemented
527	#557	C₂²×C₆₁	1	2	yes	complemented
528	#557	C₂²×C₆₁	1	4	yes	complemented
529	#557	C₂²×C₆₁	1	4	yes	complemented
530	#557	C₂²×C₆₁	1	8	yes	complemented
531	#556	C₂²×C₆₁	1	4	yes	complemented
532	#556	C₂²×C₆₁	1	8	yes	complemented
533	#556	C₂²×C₆₁	1	8	yes	complemented
534	#556	C₂²×C₆₁	1	8	yes	complemented
535	#554	C₂²×C₆₁	1	4	yes	—
536	#554	C₂²×C₆₁	1	8	yes	—
537	#554	C₂²×C₆₁	1	2	yes	complemented
538	#554	C₂²×C₆₁	1	4	yes	complemented
539	#554	C₂²×C₆₁	1	8	yes	complemented
540	#554	C₂²×C₆₁	1	8	yes	complemented
541	#554	C₂²×C₆₁	1	8	yes	complemented
542	#552	C₂²×C₆₁	1	16	yes	complemented
543	#552	C₂²×C₆₁	1	8	yes	complemented
544	#551	C₂²×C₆₁	1	16	yes	—
545	#551	C₂²×C₆₁	1	16	yes	—
546	#550	C₂²×C₆₁	1	4	yes	—
547	#550	C₂²×C₆₁	1	4	yes	—
548	D₄×Q₈	C₂²×C₆₁	1	4	yes	—
549	D₄×Q₈	C₂²×C₆₁	1	2	yes	complemented
550	D₄×Q₈	C₂²×C₆₁	1	8	yes	complemented
551	D₄×Q₈	C₂²×C₆₁	1	4	yes	complemented
552	#548	C₂²×C₆₁	1	8	yes	complemented
553	#548	C₂²×C₆₁	1	8	yes	complemented
554	#547	C₂²×C₆₁	1	4	yes	complemented
555	#547	C₂²×C₆₁	1	4	yes	complemented
556	#547	C₂²×C₆₁	1	16	yes	complemented
557	#546	C₂²×C₆₁	1	8	yes	—
558	#546	C₂²×C₆₁	1	8	yes	—
559	#544	C₂²×C₆₁	1	2	yes	—
560	#544	C₂²×C₆₁	1	1	yes	characteristic
561	#544	C₂²×C₆₁	1	4	yes	—
562	#543	C₂²×C₆₁	1	8	yes	—
563	#542	C₂²×C₆₁	1	8	yes	complemented
564	#542	C₂²×C₆₁	1	4	yes	complemented
565	#542	C₂²×C₆₁	1	8	yes	complemented
566	#542	C₂²×C₆₁	1	8	yes	complemented
567	#542	C₂²×C₆₁	1	8	yes	complemented
568	#542	C₂²×C₆₁	1	16	yes	complemented
569	#542	C₂²×C₆₁	1	8	yes	complemented
570	#542	C₂²×C₆₁	1	16	yes	complemented
571	#541	C₂²×C₆₁	1	4	yes	complemented
572	#540	C₂²×C₆₁	1	8	yes	—
573	#540	C₂²×C₆₁	1	8	yes	complemented
574	#539	C₂²×C₆₁	1	4	yes	—
575	#539	C₂²×C₆₁	1	16	yes	complemented
576	#539	C₂²×C₆₁	1	16	yes	complemented
577	#539	C₂²×C₆₁	1	16	yes	complemented
578	#538	C₂²×C₆₁	1	8	yes	—
579	#537	C₂²×C₆₁	1	1	yes	characteristic
580	#536	C₂²×C₆₁	1	2	yes	—
581	#536	C₂²×C₆₁	1	8	yes	complemented
582	#536	C₂²×C₆₁	1	16	yes	complemented
583	#535	C₂²×C₆₁	1	4	yes	—
584	#533	C₂²×C₆₁	1	4	yes	—
585	#533	C₂²×C₆₁	1	2	yes	—
586	#533	C₂²×C₆₁	1	4	yes	—
587	#533	C₂²×C₆₁	1	4	yes	complemented
588	#533	C₂²×C₆₁	1	4	yes	complemented
589	#533	C₂²×C₆₁	1	8	yes	complemented
590	#532	C₂²×C₆₁	1	4	yes	—
591	#532	C₂²×C₆₁	1	4	yes	—
592	#532	C₂²×C₆₁	1	8	yes	complemented
593	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
594	#529	C₂²×C₆₁	1	4	yes	—
595	#529	C₂²×C₆₁	1	8	yes	complemented
596	#529	C₂²×C₆₁	1	4	yes	complemented
597	#529	C₂²×C₆₁	1	8	yes	complemented
598	#529	C₂²×C₆₁	1	8	yes	complemented
599	C₂×#124	C₂²×C₆₁	1	2	yes	—
600	C₂×#124	C₂²×C₆₁	1	2	yes	—
601	#525	C₂²×C₆₁	1	8	yes	—
602	C₂×#123	C₂²×C₆₁	1	4	yes	—
603	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	8	yes	—
604	#520	C₂²×C₆₁	1	8	yes	complemented
605	#519	C₂²×C₆₁	1	2	yes	—
606	#518	C₂²×C₆₁	1	4	yes	—
607	C₄×#41	C₂²×C₆₁	1	4	yes	—
608	C₄×#41	C₂²×C₆₁	1	2	yes	—
609	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
610	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
611	C₂×C₄×Q₈	C₂²×C₆₁	1	4	yes	complemented
612	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
613	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
614	C₆₁	#62962	1	1	yes	characteristic, direct product factor, Sylow
615	C₂×#41	C₂³×C₆₁	1	2	yes	—
616	C₂×#41	C₂³×C₆₁	1	8	yes	—
617	C₂×#41	C₂³×C₆₁	1	8	yes	—
618	C₂×#41	C₂³×C₆₁	1	8	yes	—
619	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
620	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
621	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
622	C₂²×Q₈	C₂³×C₆₁	1	8	yes	—
623	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
624	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
625	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
626	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
627	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
628	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
629	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
630	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
631	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
632	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
633	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
634	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
635	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
636	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
637	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
638	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
639	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
640	C₄⋊Q₈	C₂³×C₆₁	1	16	yes	—
641	#127	C₂³×C₆₁	1	4	yes	—
642	#127	C₂³×C₆₁	1	4	yes	—
643	#127	C₂³×C₆₁	1	8	yes	—
644	#126	C₂³×C₆₁	1	8	yes	—
645	#126	C₂³×C₆₁	1	16	yes	—
646	#126	C₂³×C₆₁	1	8	yes	—
647	#126	C₂³×C₆₁	1	16	yes	—
648	#126	C₂³×C₆₁	1	16	yes	—
649	#126	C₂³×C₆₁	1	16	yes	—
650	#126	C₂³×C₆₁	1	16	yes	—
651	#125	C₂³×C₆₁	1	4	yes	—
652	#125	C₂³×C₆₁	1	4	yes	—
653	#125	C₂³×C₆₁	1	4	yes	—
654	#125	C₂³×C₆₁	1	8	yes	—
655	#125	C₂³×C₆₁	1	4	yes	—
656	#125	C₂³×C₆₁	1	8	yes	—
657	#125	C₂³×C₆₁	1	4	yes	—
658	#125	C₂³×C₆₁	1	8	yes	—
659	#125	C₂³×C₆₁	1	8	yes	—
660	#125	C₂³×C₆₁	1	8	yes	—
661	#125	C₂³×C₆₁	1	8	yes	—
662	#125	C₂³×C₆₁	1	16	yes	—
663	#124	C₂³×C₆₁	1	8	yes	—
664	#124	C₂³×C₆₁	1	8	yes	—
665	#124	C₂³×C₆₁	1	8	yes	—
666	#124	C₂³×C₆₁	1	8	yes	—
667	#124	C₂³×C₆₁	1	4	yes	—
668	#124	C₂³×C₆₁	1	8	yes	—
669	#124	C₂³×C₆₁	1	4	yes	—
670	#124	C₂³×C₆₁	1	8	yes	—
671	#124	C₂³×C₆₁	1	8	yes	—
672	#124	C₂³×C₆₁	1	16	yes	—
673	#124	C₂³×C₆₁	1	16	yes	—
674	#124	C₂³×C₆₁	1	16	yes	—
675	#123	C₂³×C₆₁	1	16	yes	—
676	#123	C₂³×C₆₁	1	16	yes	—
677	#123	C₂³×C₆₁	1	16	yes	—
678	#123	C₂³×C₆₁	1	8	yes	—
679	#123	C₂³×C₆₁	1	16	yes	—
680	#123	C₂³×C₆₁	1	16	yes	—
681	#123	C₂³×C₆₁	1	8	yes	—
682	#123	C₂³×C₆₁	1	16	yes	—
683	#123	C₂³×C₆₁	1	16	yes	—
684	#123	C₂³×C₆₁	1	16	yes	—
685	#123	C₂³×C₆₁	1	16	yes	—
686	#123	C₂³×C₆₁	1	16	yes	—
687	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
688	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
689	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
690	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
691	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
692	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
693	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
694	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
695	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
696	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
697	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
698	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
699	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
700	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
701	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
702	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
703	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
704	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
705	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
706	C₂²⋊Q₈	C₂³×C₆₁	1	4	yes	—
707	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
708	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
709	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
710	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
711	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
712	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
713	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
714	#121	C₂³×C₆₁	1	4	yes	—
715	#121	C₂³×C₆₁	1	8	yes	—
716	#121	C₂³×C₆₁	1	8	yes	—
717	#121	C₂³×C₆₁	1	8	yes	—
718	#121	C₂³×C₆₁	1	4	yes	—
719	#121	C₂³×C₆₁	1	8	yes	—
720	#121	C₂³×C₆₁	1	8	yes	—
721	#121	C₂³×C₆₁	1	16	yes	—
722	#121	C₂³×C₆₁	1	16	yes	—
723	#121	C₂³×C₆₁	1	16	yes	—
724	#120	C₂³×C₆₁	1	16	yes	—
725	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
726	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
727	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
728	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
729	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
730	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
731	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
732	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
733	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
734	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
735	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
736	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
737	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
738	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
739	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
740	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
741	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
742	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
743	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
744	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
745	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
746	C₄×D₄	C₂³×C₆₁	1	4	yes	—
747	C₄×D₄	C₂³×C₆₁	1	8	yes	—
748	C₄×D₄	C₂³×C₆₁	1	8	yes	—
749	C₄×D₄	C₂³×C₆₁	1	8	yes	—
750	C₄×D₄	C₂³×C₆₁	1	4	yes	—
751	C₄×D₄	C₂³×C₆₁	1	8	yes	—
752	C₄×D₄	C₂³×C₆₁	1	4	yes	—
753	C₄×D₄	C₂³×C₆₁	1	2	yes	—
754	C₄×D₄	C₂³×C₆₁	1	4	yes	—
755	C₄×D₄	C₂³×C₆₁	1	8	yes	—
756	C₄×D₄	C₂³×C₆₁	1	4	yes	—
757	C₄×D₄	C₂³×C₆₁	1	4	yes	—
758	C₄×D₄	C₂³×C₆₁	1	2	yes	—
759	C₄×D₄	C₂³×C₆₁	1	8	yes	—
760	C₄×D₄	C₂³×C₆₁	1	8	yes	—
761	C₄×D₄	C₂³×C₆₁	1	8	yes	—
762	C₄×D₄	C₂³×C₆₁	1	8	yes	—
763	C₄×D₄	C₂³×C₆₁	1	16	yes	—
764	C₄×D₄	C₂³×C₆₁	1	16	yes	—
765	C₄×D₄	C₂³×C₆₁	1	8	yes	—
766	C₄×D₄	C₂³×C₆₁	1	4	yes	—
767	C₄×D₄	C₂³×C₆₁	1	16	yes	—
768	C₄×D₄	C₂³×C₆₁	1	8	yes	—
769	#117	C₂³×C₆₁	1	2	yes	—
770	#117	C₂³×C₆₁	1	4	yes	—
771	#117	C₂³×C₆₁	1	4	yes	—
772	#117	C₂³×C₆₁	1	8	yes	—
773	#117	C₂³×C₆₁	1	8	yes	—
774	#117	C₂³×C₆₁	1	8	yes	—
775	#117	C₂³×C₆₁	1	16	yes	—
776	#117	C₂³×C₆₁	1	8	yes	—
777	#117	C₂³×C₆₁	1	16	yes	—
778	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
779	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
780	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
781	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
782	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
783	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
784	C₂×C₄⋊C₄	C₂³×C₆₁	1	16	yes	—
785	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
786	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₆₁	1	16	yes	—
789	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
790	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
791	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
792	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
793	C₂×C₄²	C₂³×C₆₁	1	8	yes	—
794	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
795	C₂⁴	C₂⁴×C₆₁	1	4	yes	—
796	#41	—	2	8	no	—
797	#41	—	4	16	no	—
798	#41	—	8	8	no	—
799	#41	—	8	8	no	—
800	C₂×Q₈	—	2	4	no	—
801	C₂×Q₈	—	4	2	no	—
802	C₂×Q₈	—	4	8	no	—
803	C₂×Q₈	—	8	8	no	—
804	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
805	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
806	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
807	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
808	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
809	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
810	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
811	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
812	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
813	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
814	C₂×D₄	—	2	8	no	—
815	C₂×D₄	—	4	4	no	—
816	C₂×D₄	—	8	2	no	—
817	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
818	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
819	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
820	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
821	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
822	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
823	C₂×D₄	C₂⁴×C₆₁	1	16	yes	—
824	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
825	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
826	C₂²×C₄	—	8	4	no	—
827	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
829	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
830	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
831	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
832	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
833	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
836	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
837	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
838	C₂²×C₄	C₂⁴×C₆₁	1	16	yes	—
839	C₂²×C₄	C₂⁴×C₆₁	1	16	yes	—
840	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
841	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
842	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
843	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
844	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
845	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
846	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
847	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
848	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
849	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
850	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
851	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
852	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
853	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
854	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
855	C₄⋊C₄	C₂⁴×C₆₁	1	16	yes	—
856	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
857	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
858	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
859	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
860	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
861	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
862	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
863	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
864	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
865	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
866	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
867	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
868	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
869	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
870	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
871	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
872	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
873	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
874	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
875	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
876	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
877	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
878	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
879	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
880	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
881	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
882	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
883	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
884	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
885	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
886	C₂²⋊C₄	C₂⁴×C₆₁	1	16	yes	—
887	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
888	C₂²⋊C₄	C₂⁴×C₆₁	1	4	yes	—
889	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
890	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
891	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
892	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
893	C₂²⋊C₄	C₂⁴×C₆₁	1	8	yes	—
894	C₄²	C₂⁴×C₆₁	1	4	yes	—
895	C₄²	C₂⁴×C₆₁	1	2	yes	—
896	C₄²	C₂⁴×C₆₁	1	8	yes	—
897	C₄²	C₂⁴×C₆₁	1	4	yes	—
898	C₄²	C₂⁴×C₆₁	1	4	yes	—
899	C₄²	C₂⁴×C₆₁	1	4	yes	—
900	C₄²	C₂⁴×C₆₁	1	4	yes	—
901	C₄²	C₂⁴×C₆₁	1	8	yes	—
902	C₄²	C₂⁴×C₆₁	1	2	yes	—
903	C₄²	C₂⁴×C₆₁	1	8	yes	—
904	C₄²	C₂⁴×C₆₁	1	4	yes	—
905	C₄²	C₂⁴×C₆₁	1	4	yes	—
906	C₄²	C₂⁴×C₆₁	1	16	yes	—
907	C₂³	—	2	8	no	—
908	C₂³	—	4	4	no	—
909	C₂³	—	4	4	no	—
910	C₂³	C₂⁵×C₆₁	1	8	yes	—
911	C₂³	C₂⁵×C₆₁	1	4	yes	—
912	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
913	Q₈	—	2	8	no	—
914	Q₈	—	2	4	no	—
915	Q₈	—	2	4	no	—
916	Q₈	—	2	8	no	—
917	Q₈	—	4	8	no	—
918	Q₈	—	4	2	no	—
919	Q₈	—	4	4	no	—
920	Q₈	—	4	8	no	—
921	Q₈	—	4	8	no	—
922	Q₈	—	4	4	no	—
923	D₄	—	2	8	no	—
924	D₄	—	2	16	no	—
925	D₄	—	2	4	no	—
926	D₄	—	2	8	no	—
927	D₄	—	4	4	no	—
928	D₄	—	4	8	no	—
929	D₄	—	4	16	no	—
930	D₄	—	4	4	no	—
931	D₄	—	4	16	no	—
932	C₂×C₄	—	2	4	no	—
933	C₂×C₄	—	2	8	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	8	no	—
936	C₂×C₄	—	4	2	no	—
937	C₂×C₄	—	4	2	no	—
938	C₂×C₄	—	4	8	no	—
939	C₂×C₄	—	4	8	no	—
940	C₂×C₄	—	4	1	no	—
941	C₂×C₄	—	4	8	no	—
942	C₂×C₄	—	4	2	no	—
943	C₂×C₄	—	4	16	no	—
944	C₂×C₄	—	4	16	no	—
945	C₂×C₄	—	4	8	no	—
946	C₂×C₄	—	4	4	no	—
947	C₂×C₄	2₋¹⁺⁴×C₆₁	1	4	yes	—
948	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
949	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
950	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
951	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
952	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
953	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
954	C₂×C₄	C₂⁵×C₆₁	1	8	yes	—
955	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
956	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
957	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
958	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
959	C₂×C₄	C₂⁵×C₆₁	1	4	yes	—
960	C₂×C₄	C₂⁵×C₆₁	1	2	yes	—
961	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
962	C₂²	—	2	1	no	—
963	C₂²	—	2	1	no	—
964	C₂²	—	2	4	no	—
965	C₂²	—	2	8	no	—
966	C₂²	—	2	4	no	—
967	C₂²	—	2	8	no	—
968	C₂²	—	2	8	no	—
969	C₂²	—	2	4	no	—
970	C₂²	—	8	8	no	—
971	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
972	C₂²	C₂⁶×C₆₁	1	1	yes	characteristic
973	C₄	—	2	4	no	—
974	C₄	—	2	4	no	—
975	C₄	—	2	4	no	—
976	C₄	—	2	1	no	—
977	C₄	—	2	8	no	—
978	C₄	—	2	4	no	—
979	C₄	—	2	2	no	—
980	C₄	—	2	4	no	—
981	C₄	—	2	2	no	—
982	C₄	—	2	4	no	—
983	C₄	—	2	2	no	—
984	C₄	—	2	8	no	—
985	C₄	C₂×2₋¹⁺⁴×C₆₁	1	4	yes	—
986	C₄	C₆₁×#585	1	2	yes	—
987	C₂	—	2	2	no	—
988	C₂	—	4	8	no	—
989	C₂	—	4	4	no	—
990	C₂	C₂²×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
991	C₂	C₂×C₆₁×#585	1	1	yes	characteristic
992	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×#3561	C₂	semidirect
2. C₆₁×#3557	C₂	semidirect
3. C₆₁×#3554	C₂	semidirect
4. C₆₁×#3554	C₂	semidirect
5. C₆₁×#3550	C₂	semidirect
6. C₆₁×#3535	C₂	semidirect
7. C₆₁×#3522	C₂	semidirect
8. C₆₁×#3520	C₂	semidirect
9. C₆₁×#3510	C₂	semidirect
10. C₆₁×#3508	C₂	semidirect
11. C₆₁×#3507	C₂	semidirect
12. C₆₁×#3502	C₂	semidirect
13. C₆₁×#3501	C₂	semidirect
14. C₂×C₆₁×#559	C₂	semidirect
15. Q₈×#41×C₆₁	C₂	semidirect
16. C₆₁×#3461	C₂	semidirect
17. C₆₁×#3460	C₂	semidirect
18. C₆₁×#563	C₂²	semidirect
19. C₆₁×#563	C₂²	semidirect
20. C₆₁×#562	C₂²	semidirect
21. C₆₁×#562	C₂²	semidirect
27. C₆₁×#559	C₂²	semidirect
28. C₆₁×#559	C₂²	semidirect
29. Q₈²×C₆₁	C₂²	semidirect
30. Q₈²×C₆₁	C₂²	semidirect
31. C₆₁×#557	C₂²	semidirect
32. C₆₁×#557	C₂²	semidirect
33. C₆₁×#557	C₂²	semidirect
34. C₆₁×#557	C₂²	semidirect
35. C₆₁×#556	C₂²	semidirect
36. C₆₁×#556	C₂²	semidirect
37. C₆₁×#556	C₂²	semidirect
38. C₆₁×#556	C₂²	semidirect
41. C₆₁×#554	C₂²	semidirect
42. C₆₁×#554	C₂²	semidirect
43. C₆₁×#554	C₂²	semidirect
44. C₆₁×#554	C₂²	semidirect
45. C₆₁×#554	C₂²	semidirect
46. C₆₁×#552	C₂²	semidirect
47. C₆₁×#552	C₂²	semidirect
53. D₄×Q₈×C₆₁	C₂²	semidirect
54. D₄×Q₈×C₆₁	C₂²	semidirect
55. D₄×Q₈×C₆₁	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
67. C₆₁×#542	C₂²	semidirect
68. C₆₁×#542	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×#541	C₂²	semidirect
77. C₆₁×#540	C₂²	semidirect
79. C₆₁×#539	C₂²	semidirect
80. C₆₁×#539	C₂²	semidirect
81. C₆₁×#539	C₂²	semidirect
85. C₆₁×#536	C₂²	semidirect
86. C₆₁×#536	C₂²	semidirect
91. C₆₁×#533	C₂²	semidirect
92. C₆₁×#533	C₂²	semidirect
93. C₆₁×#533	C₂²	semidirect
96. C₆₁×#532	C₂²	semidirect
99. C₆₁×#529	C₂²	semidirect
100. C₆₁×#529	C₂²	semidirect
101. C₆₁×#529	C₂²	semidirect
102. C₆₁×#529	C₂²	semidirect
108. C₆₁×#520	C₂²	semidirect
115. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
465. #62962	C₆₁	direct (N × H)
491. #3561	C₂×C₆₁	semidirect
492. #3557	C₂×C₆₁	semidirect
493. #3554	C₂×C₆₁	semidirect
494. #3554	C₂×C₆₁	semidirect
495. #3550	C₂×C₆₁	semidirect
496. #3535	C₂×C₆₁	semidirect
497. #3522	C₂×C₆₁	semidirect
498. #3520	C₂×C₆₁	semidirect
499. #3510	C₂×C₆₁	semidirect
500. #3508	C₂×C₆₁	semidirect
501. #3507	C₂×C₆₁	semidirect
502. #3502	C₂×C₆₁	semidirect
503. #3501	C₂×C₆₁	semidirect
504. C₂×#559	C₂×C₆₁	semidirect
505. Q₈×#41	C₂×C₆₁	semidirect
506. #3461	C₂×C₆₁	semidirect
507. #3460	C₂×C₆₁	semidirect
514. #563	C₂²×C₆₁	semidirect
515. #563	C₂²×C₆₁	semidirect
516. #562	C₂²×C₆₁	semidirect
517. #562	C₂²×C₆₁	semidirect
523. #559	C₂²×C₆₁	semidirect
524. #559	C₂²×C₆₁	semidirect
525. Q₈²	C₂²×C₆₁	semidirect
526. Q₈²	C₂²×C₆₁	semidirect
527. #557	C₂²×C₆₁	semidirect
528. #557	C₂²×C₆₁	semidirect
529. #557	C₂²×C₆₁	semidirect
530. #557	C₂²×C₆₁	semidirect
531. #556	C₂²×C₆₁	semidirect
532. #556	C₂²×C₆₁	semidirect
533. #556	C₂²×C₆₁	semidirect
534. #556	C₂²×C₆₁	semidirect
537. #554	C₂²×C₆₁	semidirect
538. #554	C₂²×C₆₁	semidirect
539. #554	C₂²×C₆₁	semidirect
540. #554	C₂²×C₆₁	semidirect
541. #554	C₂²×C₆₁	semidirect
542. #552	C₂²×C₆₁	semidirect
543. #552	C₂²×C₆₁	semidirect
549. D₄×Q₈	C₂²×C₆₁	semidirect
550. D₄×Q₈	C₂²×C₆₁	semidirect
551. D₄×Q₈	C₂²×C₆₁	semidirect
552. #548	C₂²×C₆₁	semidirect
553. #548	C₂²×C₆₁	semidirect
554. #547	C₂²×C₆₁	semidirect
555. #547	C₂²×C₆₁	semidirect
556. #547	C₂²×C₆₁	semidirect
563. #542	C₂²×C₆₁	semidirect
564. #542	C₂²×C₆₁	semidirect
565. #542	C₂²×C₆₁	semidirect
566. #542	C₂²×C₆₁	semidirect
567. #542	C₂²×C₆₁	semidirect
568. #542	C₂²×C₆₁	semidirect
569. #542	C₂²×C₆₁	semidirect
570. #542	C₂²×C₆₁	semidirect
571. #541	C₂²×C₆₁	semidirect
573. #540	C₂²×C₆₁	semidirect
575. #539	C₂²×C₆₁	semidirect
576. #539	C₂²×C₆₁	semidirect
577. #539	C₂²×C₆₁	semidirect
581. #536	C₂²×C₆₁	semidirect
582. #536	C₂²×C₆₁	semidirect
587. #533	C₂²×C₆₁	semidirect
588. #533	C₂²×C₆₁	semidirect
589. #533	C₂²×C₆₁	semidirect
592. #532	C₂²×C₆₁	semidirect
595. #529	C₂²×C₆₁	semidirect
596. #529	C₂²×C₆₁	semidirect
597. #529	C₂²×C₆₁	semidirect
598. #529	C₂²×C₆₁	semidirect
604. #520	C₂²×C₆₁	semidirect
611. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
614. C₆₁	#62962	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×#3561	2
C₆₁×#3557	2
C₆₁×#3554	2
C₆₁×#3550	2
C₆₁×#3535	2
C₆₁×#3522	2
C₆₁×#3520	2
C₆₁×#3510	2
C₆₁×#3508	2
C₆₁×#3507	2
C₆₁×#3502	2
C₆₁×#3501	2
C₂×C₆₁×#559	2
Q₈×#41×C₆₁	2
C₆₁×#3461	2
C₆₁×#3460	2
#62962	61

Subgroups — C61×#62962 #29566395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62962 #29566395